diff options
Diffstat (limited to 'Modules/_decimal')
53 files changed, 0 insertions, 27464 deletions
diff --git a/Modules/_decimal/README.txt b/Modules/_decimal/README.txt deleted file mode 100644 index 7eae0f8..0000000 --- a/Modules/_decimal/README.txt +++ /dev/null @@ -1,46 +0,0 @@ - - -About -===== - -_decimal.c is a wrapper for the libmpdec library. libmpdec is a fast C -library for correctly-rounded arbitrary precision decimal floating point -arithmetic. It is a complete implementation of Mike Cowlishaw/IBM's -General Decimal Arithmetic Specification. - - -Build process for the module -============================ - -As usual, the build process for _decimal.so is driven by setup.py in the top -level directory. setup.py autodetects the following build configurations: - - 1) x64 - 64-bit Python, x86_64 processor (AMD, Intel) - - 2) uint128 - 64-bit Python, compiler provides __uint128_t (gcc) - - 3) ansi64 - 64-bit Python, ANSI C - - 4) ppro - 32-bit Python, x86 CPU, PentiumPro or later - - 5) ansi32 - 32-bit Python, ANSI C - - 6) ansi-legacy - 32-bit Python, compiler without uint64_t - - 7) universal - Mac OS only (multi-arch) - - -It is possible to override autodetection by exporting: - - PYTHON_DECIMAL_WITH_MACHINE=value, where value is one of the above options. - - -NOTE -==== - -decimal.so is not built from a static libmpdec.a since doing so led to -failures on AIX (user report) and Windows (mixing static and dynamic CRTs -causes locale problems and more). - - - diff --git a/Modules/_decimal/_decimal.c b/Modules/_decimal/_decimal.c deleted file mode 100644 index e2ac198..0000000 --- a/Modules/_decimal/_decimal.c +++ /dev/null @@ -1,5784 +0,0 @@ -/* - * Copyright (c) 2008-2012 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include <Python.h> -#include "longintrepr.h" -#include "pythread.h" -#include "structmember.h" -#include "complexobject.h" -#include "mpdecimal.h" - -#include <stdlib.h> - -#include "docstrings.h" - - -#if !defined(MPD_VERSION_HEX) || MPD_VERSION_HEX < 0x02040100 - #error "libmpdec version >= 2.4.1 required" -#endif - - -/* - * Type sizes with assertions in mpdecimal.h and pyport.h: - * sizeof(size_t) == sizeof(Py_ssize_t) - * sizeof(size_t) == sizeof(mpd_uint_t) == sizeof(mpd_ssize_t) - */ - -#ifdef TEST_COVERAGE - #undef Py_LOCAL_INLINE - #define Py_LOCAL_INLINE Py_LOCAL -#endif - -#define MPD_Float_operation MPD_Not_implemented - -#define BOUNDS_CHECK(x, MIN, MAX) x = (x < MIN || MAX < x) ? MAX : x - - -/* _Py_DEC_MINALLOC >= MPD_MINALLOC */ -#define _Py_DEC_MINALLOC 4 - -typedef struct { - PyObject_HEAD - Py_hash_t hash; - mpd_t dec; - mpd_uint_t data[_Py_DEC_MINALLOC]; -} PyDecObject; - -typedef struct { - PyObject_HEAD - uint32_t *flags; -} PyDecSignalDictObject; - -typedef struct { - PyObject_HEAD - mpd_context_t ctx; - PyObject *traps; - PyObject *flags; - int capitals; - PyThreadState *tstate; -} PyDecContextObject; - -typedef struct { - PyObject_HEAD - PyObject *local; - PyObject *global; -} PyDecContextManagerObject; - - -#undef MPD -#undef CTX -static PyTypeObject PyDec_Type; -static PyTypeObject *PyDecSignalDict_Type; -static PyTypeObject PyDecContext_Type; -static PyTypeObject PyDecContextManager_Type; -#define PyDec_CheckExact(v) (Py_TYPE(v) == &PyDec_Type) -#define PyDec_Check(v) PyObject_TypeCheck(v, &PyDec_Type) -#define PyDecSignalDict_Check(v) (Py_TYPE(v) == PyDecSignalDict_Type) -#define PyDecContext_Check(v) PyObject_TypeCheck(v, &PyDecContext_Type) -#define MPD(v) (&((PyDecObject *)v)->dec) -#define SdFlagAddr(v) (((PyDecSignalDictObject *)v)->flags) -#define SdFlags(v) (*((PyDecSignalDictObject *)v)->flags) -#define CTX(v) (&((PyDecContextObject *)v)->ctx) -#define CtxCaps(v) (((PyDecContextObject *)v)->capitals) - - -Py_LOCAL_INLINE(PyObject *) -incr_true(void) -{ - Py_INCREF(Py_True); - return Py_True; -} - -Py_LOCAL_INLINE(PyObject *) -incr_false(void) -{ - Py_INCREF(Py_False); - return Py_False; -} - - -static PyObject *current_context_var; - -/* Template for creating new thread contexts, calling Context() without - * arguments and initializing the module_context on first access. */ -static PyObject *default_context_template = NULL; -/* Basic and extended context templates */ -static PyObject *basic_context_template = NULL; -static PyObject *extended_context_template = NULL; - - -/* Error codes for functions that return signals or conditions */ -#define DEC_INVALID_SIGNALS (MPD_Max_status+1U) -#define DEC_ERR_OCCURRED (DEC_INVALID_SIGNALS<<1) -#define DEC_ERRORS (DEC_INVALID_SIGNALS|DEC_ERR_OCCURRED) - -typedef struct { - const char *name; /* condition or signal name */ - const char *fqname; /* fully qualified name */ - uint32_t flag; /* libmpdec flag */ - PyObject *ex; /* corresponding exception */ -} DecCondMap; - -/* Top level Exception; inherits from ArithmeticError */ -static PyObject *DecimalException = NULL; - -/* Exceptions that correspond to IEEE signals */ -#define SUBNORMAL 5 -#define INEXACT 6 -#define ROUNDED 7 -#define SIGNAL_MAP_LEN 9 -static DecCondMap signal_map[] = { - {"InvalidOperation", "decimal.InvalidOperation", MPD_IEEE_Invalid_operation, NULL}, - {"FloatOperation", "decimal.FloatOperation", MPD_Float_operation, NULL}, - {"DivisionByZero", "decimal.DivisionByZero", MPD_Division_by_zero, NULL}, - {"Overflow", "decimal.Overflow", MPD_Overflow, NULL}, - {"Underflow", "decimal.Underflow", MPD_Underflow, NULL}, - {"Subnormal", "decimal.Subnormal", MPD_Subnormal, NULL}, - {"Inexact", "decimal.Inexact", MPD_Inexact, NULL}, - {"Rounded", "decimal.Rounded", MPD_Rounded, NULL}, - {"Clamped", "decimal.Clamped", MPD_Clamped, NULL}, - {NULL} -}; - -/* Exceptions that inherit from InvalidOperation */ -static DecCondMap cond_map[] = { - {"InvalidOperation", "decimal.InvalidOperation", MPD_Invalid_operation, NULL}, - {"ConversionSyntax", "decimal.ConversionSyntax", MPD_Conversion_syntax, NULL}, - {"DivisionImpossible", "decimal.DivisionImpossible", MPD_Division_impossible, NULL}, - {"DivisionUndefined", "decimal.DivisionUndefined", MPD_Division_undefined, NULL}, - {"InvalidContext", "decimal.InvalidContext", MPD_Invalid_context, NULL}, -#ifdef EXTRA_FUNCTIONALITY - {"MallocError", "decimal.MallocError", MPD_Malloc_error, NULL}, -#endif - {NULL} -}; - -static const char *dec_signal_string[MPD_NUM_FLAGS] = { - "Clamped", - "InvalidOperation", - "DivisionByZero", - "InvalidOperation", - "InvalidOperation", - "InvalidOperation", - "Inexact", - "InvalidOperation", - "InvalidOperation", - "InvalidOperation", - "FloatOperation", - "Overflow", - "Rounded", - "Subnormal", - "Underflow", -}; - -#ifdef EXTRA_FUNCTIONALITY - #define _PY_DEC_ROUND_GUARD MPD_ROUND_GUARD -#else - #define _PY_DEC_ROUND_GUARD (MPD_ROUND_GUARD-1) -#endif -static PyObject *round_map[_PY_DEC_ROUND_GUARD]; - -static const char *invalid_rounding_err = -"valid values for rounding are:\n\ - [ROUND_CEILING, ROUND_FLOOR, ROUND_UP, ROUND_DOWN,\n\ - ROUND_HALF_UP, ROUND_HALF_DOWN, ROUND_HALF_EVEN,\n\ - ROUND_05UP]"; - -static const char *invalid_signals_err = -"valid values for signals are:\n\ - [InvalidOperation, FloatOperation, DivisionByZero,\n\ - Overflow, Underflow, Subnormal, Inexact, Rounded,\n\ - Clamped]"; - -#ifdef EXTRA_FUNCTIONALITY -static const char *invalid_flags_err = -"valid values for _flags or _traps are:\n\ - signals:\n\ - [DecIEEEInvalidOperation, DecFloatOperation, DecDivisionByZero,\n\ - DecOverflow, DecUnderflow, DecSubnormal, DecInexact, DecRounded,\n\ - DecClamped]\n\ - conditions which trigger DecIEEEInvalidOperation:\n\ - [DecInvalidOperation, DecConversionSyntax, DecDivisionImpossible,\n\ - DecDivisionUndefined, DecFpuError, DecInvalidContext, DecMallocError]"; -#endif - -static int -value_error_int(const char *mesg) -{ - PyErr_SetString(PyExc_ValueError, mesg); - return -1; -} - -#ifdef CONFIG_32 -static PyObject * -value_error_ptr(const char *mesg) -{ - PyErr_SetString(PyExc_ValueError, mesg); - return NULL; -} -#endif - -static int -type_error_int(const char *mesg) -{ - PyErr_SetString(PyExc_TypeError, mesg); - return -1; -} - -static int -runtime_error_int(const char *mesg) -{ - PyErr_SetString(PyExc_RuntimeError, mesg); - return -1; -} -#define INTERNAL_ERROR_INT(funcname) \ - return runtime_error_int("internal error in " funcname) - -static PyObject * -runtime_error_ptr(const char *mesg) -{ - PyErr_SetString(PyExc_RuntimeError, mesg); - return NULL; -} -#define INTERNAL_ERROR_PTR(funcname) \ - return runtime_error_ptr("internal error in " funcname) - -static void -dec_traphandler(mpd_context_t *ctx UNUSED) /* GCOV_NOT_REACHED */ -{ /* GCOV_NOT_REACHED */ - return; /* GCOV_NOT_REACHED */ -} - -static PyObject * -flags_as_exception(uint32_t flags) -{ - DecCondMap *cm; - - for (cm = signal_map; cm->name != NULL; cm++) { - if (flags&cm->flag) { - return cm->ex; - } - } - - INTERNAL_ERROR_PTR("flags_as_exception"); /* GCOV_NOT_REACHED */ -} - -Py_LOCAL_INLINE(uint32_t) -exception_as_flag(PyObject *ex) -{ - DecCondMap *cm; - - for (cm = signal_map; cm->name != NULL; cm++) { - if (cm->ex == ex) { - return cm->flag; - } - } - - PyErr_SetString(PyExc_KeyError, invalid_signals_err); - return DEC_INVALID_SIGNALS; -} - -static PyObject * -flags_as_list(uint32_t flags) -{ - PyObject *list; - DecCondMap *cm; - - list = PyList_New(0); - if (list == NULL) { - return NULL; - } - - for (cm = cond_map; cm->name != NULL; cm++) { - if (flags&cm->flag) { - if (PyList_Append(list, cm->ex) < 0) { - goto error; - } - } - } - for (cm = signal_map+1; cm->name != NULL; cm++) { - if (flags&cm->flag) { - if (PyList_Append(list, cm->ex) < 0) { - goto error; - } - } - } - - return list; - -error: - Py_DECREF(list); - return NULL; -} - -static PyObject * -signals_as_list(uint32_t flags) -{ - PyObject *list; - DecCondMap *cm; - - list = PyList_New(0); - if (list == NULL) { - return NULL; - } - - for (cm = signal_map; cm->name != NULL; cm++) { - if (flags&cm->flag) { - if (PyList_Append(list, cm->ex) < 0) { - Py_DECREF(list); - return NULL; - } - } - } - - return list; -} - -static uint32_t -list_as_flags(PyObject *list) -{ - PyObject *item; - uint32_t flags, x; - Py_ssize_t n, j; - - assert(PyList_Check(list)); - - n = PyList_Size(list); - flags = 0; - for (j = 0; j < n; j++) { - item = PyList_GetItem(list, j); - x = exception_as_flag(item); - if (x & DEC_ERRORS) { - return x; - } - flags |= x; - } - - return flags; -} - -static PyObject * -flags_as_dict(uint32_t flags) -{ - DecCondMap *cm; - PyObject *dict; - - dict = PyDict_New(); - if (dict == NULL) { - return NULL; - } - - for (cm = signal_map; cm->name != NULL; cm++) { - PyObject *b = flags&cm->flag ? Py_True : Py_False; - if (PyDict_SetItem(dict, cm->ex, b) < 0) { - Py_DECREF(dict); - return NULL; - } - } - - return dict; -} - -static uint32_t -dict_as_flags(PyObject *val) -{ - PyObject *b; - DecCondMap *cm; - uint32_t flags = 0; - int x; - - if (!PyDict_Check(val)) { - PyErr_SetString(PyExc_TypeError, - "argument must be a signal dict"); - return DEC_INVALID_SIGNALS; - } - - if (PyDict_Size(val) != SIGNAL_MAP_LEN) { - PyErr_SetString(PyExc_KeyError, - "invalid signal dict"); - return DEC_INVALID_SIGNALS; - } - - for (cm = signal_map; cm->name != NULL; cm++) { - b = PyDict_GetItemWithError(val, cm->ex); - if (b == NULL) { - if (PyErr_Occurred()) { - return DEC_ERR_OCCURRED; - } - PyErr_SetString(PyExc_KeyError, - "invalid signal dict"); - return DEC_INVALID_SIGNALS; - } - - x = PyObject_IsTrue(b); - if (x < 0) { - return DEC_ERR_OCCURRED; - } - if (x == 1) { - flags |= cm->flag; - } - } - - return flags; -} - -#ifdef EXTRA_FUNCTIONALITY -static uint32_t -long_as_flags(PyObject *v) -{ - long x; - - x = PyLong_AsLong(v); - if (x == -1 && PyErr_Occurred()) { - return DEC_ERR_OCCURRED; - } - if (x < 0 || x > (long)MPD_Max_status) { - PyErr_SetString(PyExc_TypeError, invalid_flags_err); - return DEC_INVALID_SIGNALS; - } - - return x; -} -#endif - -static int -dec_addstatus(PyObject *context, uint32_t status) -{ - mpd_context_t *ctx = CTX(context); - - ctx->status |= status; - if (status & (ctx->traps|MPD_Malloc_error)) { - PyObject *ex, *siglist; - - if (status & MPD_Malloc_error) { - PyErr_NoMemory(); - return 1; - } - - ex = flags_as_exception(ctx->traps&status); - if (ex == NULL) { - return 1; /* GCOV_NOT_REACHED */ - } - siglist = flags_as_list(ctx->traps&status); - if (siglist == NULL) { - return 1; - } - - PyErr_SetObject(ex, siglist); - Py_DECREF(siglist); - return 1; - } - return 0; -} - -static int -getround(PyObject *v) -{ - int i; - - if (PyUnicode_Check(v)) { - for (i = 0; i < _PY_DEC_ROUND_GUARD; i++) { - if (v == round_map[i]) { - return i; - } - } - for (i = 0; i < _PY_DEC_ROUND_GUARD; i++) { - if (PyUnicode_Compare(v, round_map[i]) == 0) { - return i; - } - } - } - - return type_error_int(invalid_rounding_err); -} - - -/******************************************************************************/ -/* SignalDict Object */ -/******************************************************************************/ - -/* The SignalDict is a MutableMapping that provides access to the - mpd_context_t flags, which reside in the context object. When a - new context is created, context.traps and context.flags are - initialized to new SignalDicts. Once a SignalDict is tied to - a context, it cannot be deleted. */ - -static int -signaldict_init(PyObject *self, PyObject *args UNUSED, PyObject *kwds UNUSED) -{ - SdFlagAddr(self) = NULL; - return 0; -} - -static Py_ssize_t -signaldict_len(PyObject *self UNUSED) -{ - return SIGNAL_MAP_LEN; -} - -static PyObject *SignalTuple; -static PyObject * -signaldict_iter(PyObject *self UNUSED) -{ - return PyTuple_Type.tp_iter(SignalTuple); -} - -static PyObject * -signaldict_getitem(PyObject *self, PyObject *key) -{ - uint32_t flag; - - flag = exception_as_flag(key); - if (flag & DEC_ERRORS) { - return NULL; - } - - return SdFlags(self)&flag ? incr_true() : incr_false(); -} - -static int -signaldict_setitem(PyObject *self, PyObject *key, PyObject *value) -{ - uint32_t flag; - int x; - - if (value == NULL) { - return value_error_int("signal keys cannot be deleted"); - } - - flag = exception_as_flag(key); - if (flag & DEC_ERRORS) { - return -1; - } - - x = PyObject_IsTrue(value); - if (x < 0) { - return -1; - } - - if (x == 1) { - SdFlags(self) |= flag; - } - else { - SdFlags(self) &= ~flag; - } - - return 0; -} - -static PyObject * -signaldict_repr(PyObject *self) -{ - DecCondMap *cm; - const char *n[SIGNAL_MAP_LEN]; /* name */ - const char *b[SIGNAL_MAP_LEN]; /* bool */ - int i; - - assert(SIGNAL_MAP_LEN == 9); - - for (cm=signal_map, i=0; cm->name != NULL; cm++, i++) { - n[i] = cm->fqname; - b[i] = SdFlags(self)&cm->flag ? "True" : "False"; - } - return PyUnicode_FromFormat( - "{<class '%s'>:%s, <class '%s'>:%s, <class '%s'>:%s, " - "<class '%s'>:%s, <class '%s'>:%s, <class '%s'>:%s, " - "<class '%s'>:%s, <class '%s'>:%s, <class '%s'>:%s}", - n[0], b[0], n[1], b[1], n[2], b[2], - n[3], b[3], n[4], b[4], n[5], b[5], - n[6], b[6], n[7], b[7], n[8], b[8]); -} - -static PyObject * -signaldict_richcompare(PyObject *v, PyObject *w, int op) -{ - PyObject *res = Py_NotImplemented; - - assert(PyDecSignalDict_Check(v)); - - if (op == Py_EQ || op == Py_NE) { - if (PyDecSignalDict_Check(w)) { - res = (SdFlags(v)==SdFlags(w)) ^ (op==Py_NE) ? Py_True : Py_False; - } - else if (PyDict_Check(w)) { - uint32_t flags = dict_as_flags(w); - if (flags & DEC_ERRORS) { - if (flags & DEC_INVALID_SIGNALS) { - /* non-comparable: Py_NotImplemented */ - PyErr_Clear(); - } - else { - return NULL; - } - } - else { - res = (SdFlags(v)==flags) ^ (op==Py_NE) ? Py_True : Py_False; - } - } - } - - Py_INCREF(res); - return res; -} - -static PyObject * -signaldict_copy(PyObject *self, PyObject *args UNUSED) -{ - return flags_as_dict(SdFlags(self)); -} - - -static PyMappingMethods signaldict_as_mapping = { - (lenfunc)signaldict_len, /* mp_length */ - (binaryfunc)signaldict_getitem, /* mp_subscript */ - (objobjargproc)signaldict_setitem /* mp_ass_subscript */ -}; - -static PyMethodDef signaldict_methods[] = { - { "copy", (PyCFunction)signaldict_copy, METH_NOARGS, NULL}, - {NULL, NULL} -}; - - -static PyTypeObject PyDecSignalDictMixin_Type = -{ - PyVarObject_HEAD_INIT(0, 0) - "decimal.SignalDictMixin", /* tp_name */ - sizeof(PyDecSignalDictObject), /* tp_basicsize */ - 0, /* tp_itemsize */ - 0, /* tp_dealloc */ - 0, /* tp_vectorcall_offset */ - (getattrfunc) 0, /* tp_getattr */ - (setattrfunc) 0, /* tp_setattr */ - 0, /* tp_as_async */ - (reprfunc) signaldict_repr, /* tp_repr */ - 0, /* tp_as_number */ - 0, /* tp_as_sequence */ - &signaldict_as_mapping, /* tp_as_mapping */ - PyObject_HashNotImplemented, /* tp_hash */ - 0, /* tp_call */ - (reprfunc) 0, /* tp_str */ - PyObject_GenericGetAttr, /* tp_getattro */ - (setattrofunc) 0, /* tp_setattro */ - (PyBufferProcs *) 0, /* tp_as_buffer */ - Py_TPFLAGS_DEFAULT|Py_TPFLAGS_BASETYPE| - Py_TPFLAGS_HAVE_GC, /* tp_flags */ - 0, /* tp_doc */ - 0, /* tp_traverse */ - 0, /* tp_clear */ - signaldict_richcompare, /* tp_richcompare */ - 0, /* tp_weaklistoffset */ - (getiterfunc)signaldict_iter, /* tp_iter */ - 0, /* tp_iternext */ - signaldict_methods, /* tp_methods */ - 0, /* tp_members */ - 0, /* tp_getset */ - 0, /* tp_base */ - 0, /* tp_dict */ - 0, /* tp_descr_get */ - 0, /* tp_descr_set */ - 0, /* tp_dictoffset */ - (initproc)signaldict_init, /* tp_init */ - 0, /* tp_alloc */ - PyType_GenericNew, /* tp_new */ -}; - - -/******************************************************************************/ -/* Context Object, Part 1 */ -/******************************************************************************/ - -#define Dec_CONTEXT_GET_SSIZE(mem) \ -static PyObject * \ -context_get##mem(PyObject *self, void *closure UNUSED) \ -{ \ - return PyLong_FromSsize_t(mpd_get##mem(CTX(self))); \ -} - -#define Dec_CONTEXT_GET_ULONG(mem) \ -static PyObject * \ -context_get##mem(PyObject *self, void *closure UNUSED) \ -{ \ - return PyLong_FromUnsignedLong(mpd_get##mem(CTX(self))); \ -} - -Dec_CONTEXT_GET_SSIZE(prec) -Dec_CONTEXT_GET_SSIZE(emax) -Dec_CONTEXT_GET_SSIZE(emin) -Dec_CONTEXT_GET_SSIZE(clamp) - -#ifdef EXTRA_FUNCTIONALITY -Dec_CONTEXT_GET_ULONG(traps) -Dec_CONTEXT_GET_ULONG(status) -#endif - -static PyObject * -context_getround(PyObject *self, void *closure UNUSED) -{ - int i = mpd_getround(CTX(self)); - - Py_INCREF(round_map[i]); - return round_map[i]; -} - -static PyObject * -context_getcapitals(PyObject *self, void *closure UNUSED) -{ - return PyLong_FromLong(CtxCaps(self)); -} - -#ifdef EXTRA_FUNCTIONALITY -static PyObject * -context_getallcr(PyObject *self, void *closure UNUSED) -{ - return PyLong_FromLong(mpd_getcr(CTX(self))); -} -#endif - -static PyObject * -context_getetiny(PyObject *self, PyObject *dummy UNUSED) -{ - return PyLong_FromSsize_t(mpd_etiny(CTX(self))); -} - -static PyObject * -context_getetop(PyObject *self, PyObject *dummy UNUSED) -{ - return PyLong_FromSsize_t(mpd_etop(CTX(self))); -} - -static int -context_setprec(PyObject *self, PyObject *value, void *closure UNUSED) -{ - mpd_context_t *ctx; - mpd_ssize_t x; - - x = PyLong_AsSsize_t(value); - if (x == -1 && PyErr_Occurred()) { - return -1; - } - - ctx = CTX(self); - if (!mpd_qsetprec(ctx, x)) { - return value_error_int( - "valid range for prec is [1, MAX_PREC]"); - } - - return 0; -} - -static int -context_setemin(PyObject *self, PyObject *value, void *closure UNUSED) -{ - mpd_context_t *ctx; - mpd_ssize_t x; - - x = PyLong_AsSsize_t(value); - if (x == -1 && PyErr_Occurred()) { - return -1; - } - - ctx = CTX(self); - if (!mpd_qsetemin(ctx, x)) { - return value_error_int( - "valid range for Emin is [MIN_EMIN, 0]"); - } - - return 0; -} - -static int -context_setemax(PyObject *self, PyObject *value, void *closure UNUSED) -{ - mpd_context_t *ctx; - mpd_ssize_t x; - - x = PyLong_AsSsize_t(value); - if (x == -1 && PyErr_Occurred()) { - return -1; - } - - ctx = CTX(self); - if (!mpd_qsetemax(ctx, x)) { - return value_error_int( - "valid range for Emax is [0, MAX_EMAX]"); - } - - return 0; -} - -#ifdef CONFIG_32 -static PyObject * -context_unsafe_setprec(PyObject *self, PyObject *value) -{ - mpd_context_t *ctx = CTX(self); - mpd_ssize_t x; - - x = PyLong_AsSsize_t(value); - if (x == -1 && PyErr_Occurred()) { - return NULL; - } - - if (x < 1 || x > 1070000000L) { - return value_error_ptr( - "valid range for unsafe prec is [1, 1070000000]"); - } - - ctx->prec = x; - Py_RETURN_NONE; -} - -static PyObject * -context_unsafe_setemin(PyObject *self, PyObject *value) -{ - mpd_context_t *ctx = CTX(self); - mpd_ssize_t x; - - x = PyLong_AsSsize_t(value); - if (x == -1 && PyErr_Occurred()) { - return NULL; - } - - if (x < -1070000000L || x > 0) { - return value_error_ptr( - "valid range for unsafe emin is [-1070000000, 0]"); - } - - ctx->emin = x; - Py_RETURN_NONE; -} - -static PyObject * -context_unsafe_setemax(PyObject *self, PyObject *value) -{ - mpd_context_t *ctx = CTX(self); - mpd_ssize_t x; - - x = PyLong_AsSsize_t(value); - if (x == -1 && PyErr_Occurred()) { - return NULL; - } - - if (x < 0 || x > 1070000000L) { - return value_error_ptr( - "valid range for unsafe emax is [0, 1070000000]"); - } - - ctx->emax = x; - Py_RETURN_NONE; -} -#endif - -static int -context_setround(PyObject *self, PyObject *value, void *closure UNUSED) -{ - mpd_context_t *ctx; - int x; - - x = getround(value); - if (x == -1) { - return -1; - } - - ctx = CTX(self); - if (!mpd_qsetround(ctx, x)) { - INTERNAL_ERROR_INT("context_setround"); /* GCOV_NOT_REACHED */ - } - - return 0; -} - -static int -context_setcapitals(PyObject *self, PyObject *value, void *closure UNUSED) -{ - mpd_ssize_t x; - - x = PyLong_AsSsize_t(value); - if (x == -1 && PyErr_Occurred()) { - return -1; - } - - if (x != 0 && x != 1) { - return value_error_int( - "valid values for capitals are 0 or 1"); - } - CtxCaps(self) = (int)x; - - return 0; -} - -#ifdef EXTRA_FUNCTIONALITY -static int -context_settraps(PyObject *self, PyObject *value, void *closure UNUSED) -{ - mpd_context_t *ctx; - uint32_t flags; - - flags = long_as_flags(value); - if (flags & DEC_ERRORS) { - return -1; - } - - ctx = CTX(self); - if (!mpd_qsettraps(ctx, flags)) { - INTERNAL_ERROR_INT("context_settraps"); - } - - return 0; -} -#endif - -static int -context_settraps_list(PyObject *self, PyObject *value) -{ - mpd_context_t *ctx; - uint32_t flags; - - flags = list_as_flags(value); - if (flags & DEC_ERRORS) { - return -1; - } - - ctx = CTX(self); - if (!mpd_qsettraps(ctx, flags)) { - INTERNAL_ERROR_INT("context_settraps_list"); - } - - return 0; -} - -static int -context_settraps_dict(PyObject *self, PyObject *value) -{ - mpd_context_t *ctx; - uint32_t flags; - - if (PyDecSignalDict_Check(value)) { - flags = SdFlags(value); - } - else { - flags = dict_as_flags(value); - if (flags & DEC_ERRORS) { - return -1; - } - } - - ctx = CTX(self); - if (!mpd_qsettraps(ctx, flags)) { - INTERNAL_ERROR_INT("context_settraps_dict"); - } - - return 0; -} - -#ifdef EXTRA_FUNCTIONALITY -static int -context_setstatus(PyObject *self, PyObject *value, void *closure UNUSED) -{ - mpd_context_t *ctx; - uint32_t flags; - - flags = long_as_flags(value); - if (flags & DEC_ERRORS) { - return -1; - } - - ctx = CTX(self); - if (!mpd_qsetstatus(ctx, flags)) { - INTERNAL_ERROR_INT("context_setstatus"); - } - - return 0; -} -#endif - -static int -context_setstatus_list(PyObject *self, PyObject *value) -{ - mpd_context_t *ctx; - uint32_t flags; - - flags = list_as_flags(value); - if (flags & DEC_ERRORS) { - return -1; - } - - ctx = CTX(self); - if (!mpd_qsetstatus(ctx, flags)) { - INTERNAL_ERROR_INT("context_setstatus_list"); - } - - return 0; -} - -static int -context_setstatus_dict(PyObject *self, PyObject *value) -{ - mpd_context_t *ctx; - uint32_t flags; - - if (PyDecSignalDict_Check(value)) { - flags = SdFlags(value); - } - else { - flags = dict_as_flags(value); - if (flags & DEC_ERRORS) { - return -1; - } - } - - ctx = CTX(self); - if (!mpd_qsetstatus(ctx, flags)) { - INTERNAL_ERROR_INT("context_setstatus_dict"); - } - - return 0; -} - -static int -context_setclamp(PyObject *self, PyObject *value, void *closure UNUSED) -{ - mpd_context_t *ctx; - mpd_ssize_t x; - - x = PyLong_AsSsize_t(value); - if (x == -1 && PyErr_Occurred()) { - return -1; - } - BOUNDS_CHECK(x, INT_MIN, INT_MAX); - - ctx = CTX(self); - if (!mpd_qsetclamp(ctx, (int)x)) { - return value_error_int("valid values for clamp are 0 or 1"); - } - - return 0; -} - -#ifdef EXTRA_FUNCTIONALITY -static int -context_setallcr(PyObject *self, PyObject *value, void *closure UNUSED) -{ - mpd_context_t *ctx; - mpd_ssize_t x; - - x = PyLong_AsSsize_t(value); - if (x == -1 && PyErr_Occurred()) { - return -1; - } - BOUNDS_CHECK(x, INT_MIN, INT_MAX); - - ctx = CTX(self); - if (!mpd_qsetcr(ctx, (int)x)) { - return value_error_int("valid values for _allcr are 0 or 1"); - } - - return 0; -} -#endif - -static PyObject * -context_getattr(PyObject *self, PyObject *name) -{ - PyObject *retval; - - if (PyUnicode_Check(name)) { - if (PyUnicode_CompareWithASCIIString(name, "traps") == 0) { - retval = ((PyDecContextObject *)self)->traps; - Py_INCREF(retval); - return retval; - } - if (PyUnicode_CompareWithASCIIString(name, "flags") == 0) { - retval = ((PyDecContextObject *)self)->flags; - Py_INCREF(retval); - return retval; - } - } - - return PyObject_GenericGetAttr(self, name); -} - -static int -context_setattr(PyObject *self, PyObject *name, PyObject *value) -{ - if (value == NULL) { - PyErr_SetString(PyExc_AttributeError, - "context attributes cannot be deleted"); - return -1; - } - - if (PyUnicode_Check(name)) { - if (PyUnicode_CompareWithASCIIString(name, "traps") == 0) { - return context_settraps_dict(self, value); - } - if (PyUnicode_CompareWithASCIIString(name, "flags") == 0) { - return context_setstatus_dict(self, value); - } - } - - return PyObject_GenericSetAttr(self, name, value); -} - -static PyObject * -context_clear_traps(PyObject *self, PyObject *dummy UNUSED) -{ - CTX(self)->traps = 0; - Py_RETURN_NONE; -} - -static PyObject * -context_clear_flags(PyObject *self, PyObject *dummy UNUSED) -{ - CTX(self)->status = 0; - Py_RETURN_NONE; -} - -#define DEC_DFLT_EMAX 999999 -#define DEC_DFLT_EMIN -999999 - -static mpd_context_t dflt_ctx = { - 28, DEC_DFLT_EMAX, DEC_DFLT_EMIN, - MPD_IEEE_Invalid_operation|MPD_Division_by_zero|MPD_Overflow, - 0, 0, MPD_ROUND_HALF_EVEN, 0, 1 -}; - -static PyObject * -context_new(PyTypeObject *type, PyObject *args UNUSED, PyObject *kwds UNUSED) -{ - PyDecContextObject *self = NULL; - mpd_context_t *ctx; - - if (type == &PyDecContext_Type) { - self = PyObject_New(PyDecContextObject, &PyDecContext_Type); - } - else { - self = (PyDecContextObject *)type->tp_alloc(type, 0); - } - - if (self == NULL) { - return NULL; - } - - self->traps = PyObject_CallObject((PyObject *)PyDecSignalDict_Type, NULL); - if (self->traps == NULL) { - self->flags = NULL; - Py_DECREF(self); - return NULL; - } - self->flags = PyObject_CallObject((PyObject *)PyDecSignalDict_Type, NULL); - if (self->flags == NULL) { - Py_DECREF(self); - return NULL; - } - - ctx = CTX(self); - - if (default_context_template) { - *ctx = *CTX(default_context_template); - } - else { - *ctx = dflt_ctx; - } - - SdFlagAddr(self->traps) = &ctx->traps; - SdFlagAddr(self->flags) = &ctx->status; - - CtxCaps(self) = 1; - self->tstate = NULL; - - return (PyObject *)self; -} - -static void -context_dealloc(PyDecContextObject *self) -{ - Py_XDECREF(self->traps); - Py_XDECREF(self->flags); - Py_TYPE(self)->tp_free(self); -} - -static int -context_init(PyObject *self, PyObject *args, PyObject *kwds) -{ - static char *kwlist[] = { - "prec", "rounding", "Emin", "Emax", "capitals", "clamp", - "flags", "traps", NULL - }; - PyObject *prec = Py_None; - PyObject *rounding = Py_None; - PyObject *emin = Py_None; - PyObject *emax = Py_None; - PyObject *capitals = Py_None; - PyObject *clamp = Py_None; - PyObject *status = Py_None; - PyObject *traps = Py_None; - int ret; - - assert(PyTuple_Check(args)); - - if (!PyArg_ParseTupleAndKeywords( - args, kwds, - "|OOOOOOOO", kwlist, - &prec, &rounding, &emin, &emax, &capitals, &clamp, &status, &traps - )) { - return -1; - } - - if (prec != Py_None && context_setprec(self, prec, NULL) < 0) { - return -1; - } - if (rounding != Py_None && context_setround(self, rounding, NULL) < 0) { - return -1; - } - if (emin != Py_None && context_setemin(self, emin, NULL) < 0) { - return -1; - } - if (emax != Py_None && context_setemax(self, emax, NULL) < 0) { - return -1; - } - if (capitals != Py_None && context_setcapitals(self, capitals, NULL) < 0) { - return -1; - } - if (clamp != Py_None && context_setclamp(self, clamp, NULL) < 0) { - return -1; - } - - if (traps != Py_None) { - if (PyList_Check(traps)) { - ret = context_settraps_list(self, traps); - } -#ifdef EXTRA_FUNCTIONALITY - else if (PyLong_Check(traps)) { - ret = context_settraps(self, traps, NULL); - } -#endif - else { - ret = context_settraps_dict(self, traps); - } - if (ret < 0) { - return ret; - } - } - if (status != Py_None) { - if (PyList_Check(status)) { - ret = context_setstatus_list(self, status); - } -#ifdef EXTRA_FUNCTIONALITY - else if (PyLong_Check(status)) { - ret = context_setstatus(self, status, NULL); - } -#endif - else { - ret = context_setstatus_dict(self, status); - } - if (ret < 0) { - return ret; - } - } - - return 0; -} - -static PyObject * -context_repr(PyDecContextObject *self) -{ - mpd_context_t *ctx; - char flags[MPD_MAX_SIGNAL_LIST]; - char traps[MPD_MAX_SIGNAL_LIST]; - int n, mem; - - assert(PyDecContext_Check(self)); - ctx = CTX(self); - - mem = MPD_MAX_SIGNAL_LIST; - n = mpd_lsnprint_signals(flags, mem, ctx->status, dec_signal_string); - if (n < 0 || n >= mem) { - INTERNAL_ERROR_PTR("context_repr"); - } - - n = mpd_lsnprint_signals(traps, mem, ctx->traps, dec_signal_string); - if (n < 0 || n >= mem) { - INTERNAL_ERROR_PTR("context_repr"); - } - - return PyUnicode_FromFormat( - "Context(prec=%zd, rounding=%s, Emin=%zd, Emax=%zd, " - "capitals=%d, clamp=%d, flags=%s, traps=%s)", - ctx->prec, mpd_round_string[ctx->round], ctx->emin, ctx->emax, - self->capitals, ctx->clamp, flags, traps); -} - -static void -init_basic_context(PyObject *v) -{ - mpd_context_t ctx = dflt_ctx; - - ctx.prec = 9; - ctx.traps |= (MPD_Underflow|MPD_Clamped); - ctx.round = MPD_ROUND_HALF_UP; - - *CTX(v) = ctx; - CtxCaps(v) = 1; -} - -static void -init_extended_context(PyObject *v) -{ - mpd_context_t ctx = dflt_ctx; - - ctx.prec = 9; - ctx.traps = 0; - - *CTX(v) = ctx; - CtxCaps(v) = 1; -} - -#ifdef EXTRA_FUNCTIONALITY -/* Factory function for creating IEEE interchange format contexts */ -static PyObject * -ieee_context(PyObject *dummy UNUSED, PyObject *v) -{ - PyObject *context; - mpd_ssize_t bits; - mpd_context_t ctx; - - bits = PyLong_AsSsize_t(v); - if (bits == -1 && PyErr_Occurred()) { - return NULL; - } - if (bits <= 0 || bits > INT_MAX) { - goto error; - } - if (mpd_ieee_context(&ctx, (int)bits) < 0) { - goto error; - } - - context = PyObject_CallObject((PyObject *)&PyDecContext_Type, NULL); - if (context == NULL) { - return NULL; - } - *CTX(context) = ctx; - - return context; - -error: - PyErr_Format(PyExc_ValueError, - "argument must be a multiple of 32, with a maximum of %d", - MPD_IEEE_CONTEXT_MAX_BITS); - - return NULL; -} -#endif - -static PyObject * -context_copy(PyObject *self, PyObject *args UNUSED) -{ - PyObject *copy; - - copy = PyObject_CallObject((PyObject *)&PyDecContext_Type, NULL); - if (copy == NULL) { - return NULL; - } - - *CTX(copy) = *CTX(self); - CTX(copy)->newtrap = 0; - CtxCaps(copy) = CtxCaps(self); - - return copy; -} - -static PyObject * -context_reduce(PyObject *self, PyObject *args UNUSED) -{ - PyObject *flags; - PyObject *traps; - PyObject *ret; - mpd_context_t *ctx; - - ctx = CTX(self); - - flags = signals_as_list(ctx->status); - if (flags == NULL) { - return NULL; - } - traps = signals_as_list(ctx->traps); - if (traps == NULL) { - Py_DECREF(flags); - return NULL; - } - - ret = Py_BuildValue( - "O(nsnniiOO)", - Py_TYPE(self), - ctx->prec, mpd_round_string[ctx->round], ctx->emin, ctx->emax, - CtxCaps(self), ctx->clamp, flags, traps - ); - - Py_DECREF(flags); - Py_DECREF(traps); - return ret; -} - - -static PyGetSetDef context_getsets [] = -{ - { "prec", (getter)context_getprec, (setter)context_setprec, NULL, NULL}, - { "Emax", (getter)context_getemax, (setter)context_setemax, NULL, NULL}, - { "Emin", (getter)context_getemin, (setter)context_setemin, NULL, NULL}, - { "rounding", (getter)context_getround, (setter)context_setround, NULL, NULL}, - { "capitals", (getter)context_getcapitals, (setter)context_setcapitals, NULL, NULL}, - { "clamp", (getter)context_getclamp, (setter)context_setclamp, NULL, NULL}, -#ifdef EXTRA_FUNCTIONALITY - { "_allcr", (getter)context_getallcr, (setter)context_setallcr, NULL, NULL}, - { "_traps", (getter)context_gettraps, (setter)context_settraps, NULL, NULL}, - { "_flags", (getter)context_getstatus, (setter)context_setstatus, NULL, NULL}, -#endif - {NULL} -}; - - -#define CONTEXT_CHECK(obj) \ - if (!PyDecContext_Check(obj)) { \ - PyErr_SetString(PyExc_TypeError, \ - "argument must be a context"); \ - return NULL; \ - } - -#define CONTEXT_CHECK_VA(obj) \ - if (obj == Py_None) { \ - CURRENT_CONTEXT(obj); \ - } \ - else if (!PyDecContext_Check(obj)) { \ - PyErr_SetString(PyExc_TypeError, \ - "optional argument must be a context"); \ - return NULL; \ - } - - -/******************************************************************************/ -/* Global, thread local and temporary contexts */ -/******************************************************************************/ - -/* - * Thread local storage currently has a speed penalty of about 4%. - * All functions that map Python's arithmetic operators to mpdecimal - * functions have to look up the current context for each and every - * operation. - */ - -static PyObject * -init_current_context(void) -{ - PyObject *tl_context = context_copy(default_context_template, NULL); - if (tl_context == NULL) { - return NULL; - } - CTX(tl_context)->status = 0; - - PyObject *tok = PyContextVar_Set(current_context_var, tl_context); - if (tok == NULL) { - Py_DECREF(tl_context); - return NULL; - } - Py_DECREF(tok); - - return tl_context; -} - -static inline PyObject * -current_context(void) -{ - PyObject *tl_context; - if (PyContextVar_Get(current_context_var, NULL, &tl_context) < 0) { - return NULL; - } - - if (tl_context != NULL) { - return tl_context; - } - - return init_current_context(); -} - -/* ctxobj := borrowed reference to the current context */ -#define CURRENT_CONTEXT(ctxobj) \ - ctxobj = current_context(); \ - if (ctxobj == NULL) { \ - return NULL; \ - } \ - Py_DECREF(ctxobj); - -/* Return a new reference to the current context */ -static PyObject * -PyDec_GetCurrentContext(PyObject *self UNUSED, PyObject *args UNUSED) -{ - return current_context(); -} - -/* Set the thread local context to a new context, decrement old reference */ -static PyObject * -PyDec_SetCurrentContext(PyObject *self UNUSED, PyObject *v) -{ - CONTEXT_CHECK(v); - - /* If the new context is one of the templates, make a copy. - * This is the current behavior of decimal.py. */ - if (v == default_context_template || - v == basic_context_template || - v == extended_context_template) { - v = context_copy(v, NULL); - if (v == NULL) { - return NULL; - } - CTX(v)->status = 0; - } - else { - Py_INCREF(v); - } - - PyObject *tok = PyContextVar_Set(current_context_var, v); - Py_DECREF(v); - if (tok == NULL) { - return NULL; - } - Py_DECREF(tok); - - Py_RETURN_NONE; -} - -/* Context manager object for the 'with' statement. The manager - * owns one reference to the global (outer) context and one - * to the local (inner) context. */ -static PyObject * -ctxmanager_new(PyTypeObject *type UNUSED, PyObject *args, PyObject *kwds) -{ - static char *kwlist[] = {"ctx", NULL}; - PyDecContextManagerObject *self; - PyObject *local = Py_None; - PyObject *global; - - CURRENT_CONTEXT(global); - if (!PyArg_ParseTupleAndKeywords(args, kwds, "|O", kwlist, &local)) { - return NULL; - } - if (local == Py_None) { - local = global; - } - else if (!PyDecContext_Check(local)) { - PyErr_SetString(PyExc_TypeError, - "optional argument must be a context"); - return NULL; - } - - self = PyObject_New(PyDecContextManagerObject, - &PyDecContextManager_Type); - if (self == NULL) { - return NULL; - } - - self->local = context_copy(local, NULL); - if (self->local == NULL) { - self->global = NULL; - Py_DECREF(self); - return NULL; - } - self->global = global; - Py_INCREF(self->global); - - return (PyObject *)self; -} - -static void -ctxmanager_dealloc(PyDecContextManagerObject *self) -{ - Py_XDECREF(self->local); - Py_XDECREF(self->global); - PyObject_Del(self); -} - -static PyObject * -ctxmanager_set_local(PyDecContextManagerObject *self, PyObject *args UNUSED) -{ - PyObject *ret; - - ret = PyDec_SetCurrentContext(NULL, self->local); - if (ret == NULL) { - return NULL; - } - Py_DECREF(ret); - - Py_INCREF(self->local); - return self->local; -} - -static PyObject * -ctxmanager_restore_global(PyDecContextManagerObject *self, - PyObject *args UNUSED) -{ - PyObject *ret; - - ret = PyDec_SetCurrentContext(NULL, self->global); - if (ret == NULL) { - return NULL; - } - Py_DECREF(ret); - - Py_RETURN_NONE; -} - - -static PyMethodDef ctxmanager_methods[] = { - {"__enter__", (PyCFunction)ctxmanager_set_local, METH_NOARGS, NULL}, - {"__exit__", (PyCFunction)ctxmanager_restore_global, METH_VARARGS, NULL}, - {NULL, NULL} -}; - -static PyTypeObject PyDecContextManager_Type = -{ - PyVarObject_HEAD_INIT(NULL, 0) - "decimal.ContextManager", /* tp_name */ - sizeof(PyDecContextManagerObject), /* tp_basicsize */ - 0, /* tp_itemsize */ - (destructor) ctxmanager_dealloc, /* tp_dealloc */ - 0, /* tp_vectorcall_offset */ - (getattrfunc) 0, /* tp_getattr */ - (setattrfunc) 0, /* tp_setattr */ - 0, /* tp_as_async */ - (reprfunc) 0, /* tp_repr */ - 0, /* tp_as_number */ - 0, /* tp_as_sequence */ - 0, /* tp_as_mapping */ - 0, /* tp_hash */ - 0, /* tp_call */ - 0, /* tp_str */ - (getattrofunc) PyObject_GenericGetAttr, /* tp_getattro */ - (setattrofunc) 0, /* tp_setattro */ - (PyBufferProcs *) 0, /* tp_as_buffer */ - Py_TPFLAGS_DEFAULT, /* tp_flags */ - 0, /* tp_doc */ - 0, /* tp_traverse */ - 0, /* tp_clear */ - 0, /* tp_richcompare */ - 0, /* tp_weaklistoffset */ - 0, /* tp_iter */ - 0, /* tp_iternext */ - ctxmanager_methods, /* tp_methods */ -}; - - -/******************************************************************************/ -/* New Decimal Object */ -/******************************************************************************/ - -static PyObject * -PyDecType_New(PyTypeObject *type) -{ - PyDecObject *dec; - - if (type == &PyDec_Type) { - dec = PyObject_New(PyDecObject, &PyDec_Type); - } - else { - dec = (PyDecObject *)type->tp_alloc(type, 0); - } - if (dec == NULL) { - return NULL; - } - - dec->hash = -1; - - MPD(dec)->flags = MPD_STATIC|MPD_STATIC_DATA; - MPD(dec)->exp = 0; - MPD(dec)->digits = 0; - MPD(dec)->len = 0; - MPD(dec)->alloc = _Py_DEC_MINALLOC; - MPD(dec)->data = dec->data; - - return (PyObject *)dec; -} -#define dec_alloc() PyDecType_New(&PyDec_Type) - -static void -dec_dealloc(PyObject *dec) -{ - mpd_del(MPD(dec)); - Py_TYPE(dec)->tp_free(dec); -} - - -/******************************************************************************/ -/* Conversions to Decimal */ -/******************************************************************************/ - -Py_LOCAL_INLINE(int) -is_space(enum PyUnicode_Kind kind, void *data, Py_ssize_t pos) -{ - Py_UCS4 ch = PyUnicode_READ(kind, data, pos); - return Py_UNICODE_ISSPACE(ch); -} - -/* Return the ASCII representation of a numeric Unicode string. The numeric - string may contain ascii characters in the range [1, 127], any Unicode - space and any unicode digit. If strip_ws is true, leading and trailing - whitespace is stripped. If ignore_underscores is true, underscores are - ignored. - - Return NULL if malloc fails and an empty string if invalid characters - are found. */ -static char * -numeric_as_ascii(const PyObject *u, int strip_ws, int ignore_underscores) -{ - enum PyUnicode_Kind kind; - void *data; - Py_UCS4 ch; - char *res, *cp; - Py_ssize_t j, len; - int d; - - if (PyUnicode_READY(u) == -1) { - return NULL; - } - - kind = PyUnicode_KIND(u); - data = PyUnicode_DATA(u); - len = PyUnicode_GET_LENGTH(u); - - cp = res = PyMem_Malloc(len+1); - if (res == NULL) { - PyErr_NoMemory(); - return NULL; - } - - j = 0; - if (strip_ws) { - while (len > 0 && is_space(kind, data, len-1)) { - len--; - } - while (j < len && is_space(kind, data, j)) { - j++; - } - } - - for (; j < len; j++) { - ch = PyUnicode_READ(kind, data, j); - if (ignore_underscores && ch == '_') { - continue; - } - if (0 < ch && ch <= 127) { - *cp++ = ch; - continue; - } - if (Py_UNICODE_ISSPACE(ch)) { - *cp++ = ' '; - continue; - } - d = Py_UNICODE_TODECIMAL(ch); - if (d < 0) { - /* empty string triggers ConversionSyntax */ - *res = '\0'; - return res; - } - *cp++ = '0' + d; - } - *cp = '\0'; - return res; -} - -/* Return a new PyDecObject or a subtype from a C string. Use the context - during conversion. */ -static PyObject * -PyDecType_FromCString(PyTypeObject *type, const char *s, - PyObject *context) -{ - PyObject *dec; - uint32_t status = 0; - - dec = PyDecType_New(type); - if (dec == NULL) { - return NULL; - } - - mpd_qset_string(MPD(dec), s, CTX(context), &status); - if (dec_addstatus(context, status)) { - Py_DECREF(dec); - return NULL; - } - return dec; -} - -/* Return a new PyDecObject or a subtype from a C string. Attempt exact - conversion. If the operand cannot be converted exactly, set - InvalidOperation. */ -static PyObject * -PyDecType_FromCStringExact(PyTypeObject *type, const char *s, - PyObject *context) -{ - PyObject *dec; - uint32_t status = 0; - mpd_context_t maxctx; - - dec = PyDecType_New(type); - if (dec == NULL) { - return NULL; - } - - mpd_maxcontext(&maxctx); - - mpd_qset_string(MPD(dec), s, &maxctx, &status); - if (status & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { - /* we want exact results */ - mpd_seterror(MPD(dec), MPD_Invalid_operation, &status); - } - status &= MPD_Errors; - if (dec_addstatus(context, status)) { - Py_DECREF(dec); - return NULL; - } - - return dec; -} - -/* Return a new PyDecObject or a subtype from a PyUnicodeObject. */ -static PyObject * -PyDecType_FromUnicode(PyTypeObject *type, const PyObject *u, - PyObject *context) -{ - PyObject *dec; - char *s; - - s = numeric_as_ascii(u, 0, 0); - if (s == NULL) { - return NULL; - } - - dec = PyDecType_FromCString(type, s, context); - PyMem_Free(s); - return dec; -} - -/* Return a new PyDecObject or a subtype from a PyUnicodeObject. Attempt exact - * conversion. If the conversion is not exact, fail with InvalidOperation. - * Allow leading and trailing whitespace in the input operand. */ -static PyObject * -PyDecType_FromUnicodeExactWS(PyTypeObject *type, const PyObject *u, - PyObject *context) -{ - PyObject *dec; - char *s; - - s = numeric_as_ascii(u, 1, 1); - if (s == NULL) { - return NULL; - } - - dec = PyDecType_FromCStringExact(type, s, context); - PyMem_Free(s); - return dec; -} - -/* Set PyDecObject from triple without any error checking. */ -Py_LOCAL_INLINE(void) -_dec_settriple(PyObject *dec, uint8_t sign, uint32_t v, mpd_ssize_t exp) -{ - -#ifdef CONFIG_64 - MPD(dec)->data[0] = v; - MPD(dec)->len = 1; -#else - uint32_t q, r; - q = v / MPD_RADIX; - r = v - q * MPD_RADIX; - MPD(dec)->data[1] = q; - MPD(dec)->data[0] = r; - MPD(dec)->len = q ? 2 : 1; -#endif - mpd_set_flags(MPD(dec), sign); - MPD(dec)->exp = exp; - mpd_setdigits(MPD(dec)); -} - -/* Return a new PyDecObject from an mpd_ssize_t. */ -static PyObject * -PyDecType_FromSsize(PyTypeObject *type, mpd_ssize_t v, PyObject *context) -{ - PyObject *dec; - uint32_t status = 0; - - dec = PyDecType_New(type); - if (dec == NULL) { - return NULL; - } - - mpd_qset_ssize(MPD(dec), v, CTX(context), &status); - if (dec_addstatus(context, status)) { - Py_DECREF(dec); - return NULL; - } - return dec; -} - -/* Return a new PyDecObject from an mpd_ssize_t. Conversion is exact. */ -static PyObject * -PyDecType_FromSsizeExact(PyTypeObject *type, mpd_ssize_t v, PyObject *context) -{ - PyObject *dec; - uint32_t status = 0; - mpd_context_t maxctx; - - dec = PyDecType_New(type); - if (dec == NULL) { - return NULL; - } - - mpd_maxcontext(&maxctx); - - mpd_qset_ssize(MPD(dec), v, &maxctx, &status); - if (dec_addstatus(context, status)) { - Py_DECREF(dec); - return NULL; - } - return dec; -} - -/* Convert from a PyLongObject. The context is not modified; flags set - during conversion are accumulated in the status parameter. */ -static PyObject * -dec_from_long(PyTypeObject *type, const PyObject *v, - const mpd_context_t *ctx, uint32_t *status) -{ - PyObject *dec; - PyLongObject *l = (PyLongObject *)v; - Py_ssize_t ob_size; - size_t len; - uint8_t sign; - - dec = PyDecType_New(type); - if (dec == NULL) { - return NULL; - } - - ob_size = Py_SIZE(l); - if (ob_size == 0) { - _dec_settriple(dec, MPD_POS, 0, 0); - return dec; - } - - if (ob_size < 0) { - len = -ob_size; - sign = MPD_NEG; - } - else { - len = ob_size; - sign = MPD_POS; - } - - if (len == 1) { - _dec_settriple(dec, sign, *l->ob_digit, 0); - mpd_qfinalize(MPD(dec), ctx, status); - return dec; - } - -#if PYLONG_BITS_IN_DIGIT == 30 - mpd_qimport_u32(MPD(dec), l->ob_digit, len, sign, PyLong_BASE, - ctx, status); -#elif PYLONG_BITS_IN_DIGIT == 15 - mpd_qimport_u16(MPD(dec), l->ob_digit, len, sign, PyLong_BASE, - ctx, status); -#else - #error "PYLONG_BITS_IN_DIGIT should be 15 or 30" -#endif - - return dec; -} - -/* Return a new PyDecObject from a PyLongObject. Use the context for - conversion. */ -static PyObject * -PyDecType_FromLong(PyTypeObject *type, const PyObject *v, PyObject *context) -{ - PyObject *dec; - uint32_t status = 0; - - if (!PyLong_Check(v)) { - PyErr_SetString(PyExc_TypeError, "argument must be an integer"); - return NULL; - } - - dec = dec_from_long(type, v, CTX(context), &status); - if (dec == NULL) { - return NULL; - } - - if (dec_addstatus(context, status)) { - Py_DECREF(dec); - return NULL; - } - - return dec; -} - -/* Return a new PyDecObject from a PyLongObject. Use a maximum context - for conversion. If the conversion is not exact, set InvalidOperation. */ -static PyObject * -PyDecType_FromLongExact(PyTypeObject *type, const PyObject *v, - PyObject *context) -{ - PyObject *dec; - uint32_t status = 0; - mpd_context_t maxctx; - - if (!PyLong_Check(v)) { - PyErr_SetString(PyExc_TypeError, "argument must be an integer"); - return NULL; - } - - mpd_maxcontext(&maxctx); - dec = dec_from_long(type, v, &maxctx, &status); - if (dec == NULL) { - return NULL; - } - - if (status & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { - /* we want exact results */ - mpd_seterror(MPD(dec), MPD_Invalid_operation, &status); - } - status &= MPD_Errors; - if (dec_addstatus(context, status)) { - Py_DECREF(dec); - return NULL; - } - - return dec; -} - -/* External C-API functions */ -static binaryfunc _py_long_multiply; -static binaryfunc _py_long_floor_divide; -static ternaryfunc _py_long_power; -static unaryfunc _py_float_abs; -static PyCFunction _py_long_bit_length; -static PyCFunction _py_float_as_integer_ratio; - -/* Return a PyDecObject or a subtype from a PyFloatObject. - Conversion is exact. */ -static PyObject * -PyDecType_FromFloatExact(PyTypeObject *type, PyObject *v, - PyObject *context) -{ - PyObject *dec, *tmp; - PyObject *n, *d, *n_d; - mpd_ssize_t k; - double x; - int sign; - mpd_t *d1, *d2; - uint32_t status = 0; - mpd_context_t maxctx; - - - assert(PyType_IsSubtype(type, &PyDec_Type)); - - if (PyLong_Check(v)) { - return PyDecType_FromLongExact(type, v, context); - } - if (!PyFloat_Check(v)) { - PyErr_SetString(PyExc_TypeError, - "argument must be int or float"); - return NULL; - } - - x = PyFloat_AsDouble(v); - if (x == -1.0 && PyErr_Occurred()) { - return NULL; - } - sign = (copysign(1.0, x) == 1.0) ? 0 : 1; - - if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) { - dec = PyDecType_New(type); - if (dec == NULL) { - return NULL; - } - if (Py_IS_NAN(x)) { - /* decimal.py calls repr(float(+-nan)), - * which always gives a positive result. */ - mpd_setspecial(MPD(dec), MPD_POS, MPD_NAN); - } - else { - mpd_setspecial(MPD(dec), sign, MPD_INF); - } - return dec; - } - - /* absolute value of the float */ - tmp = _py_float_abs(v); - if (tmp == NULL) { - return NULL; - } - - /* float as integer ratio: numerator/denominator */ - n_d = _py_float_as_integer_ratio(tmp, NULL); - Py_DECREF(tmp); - if (n_d == NULL) { - return NULL; - } - n = PyTuple_GET_ITEM(n_d, 0); - d = PyTuple_GET_ITEM(n_d, 1); - - tmp = _py_long_bit_length(d, NULL); - if (tmp == NULL) { - Py_DECREF(n_d); - return NULL; - } - k = PyLong_AsSsize_t(tmp); - Py_DECREF(tmp); - if (k == -1 && PyErr_Occurred()) { - Py_DECREF(n_d); - return NULL; - } - k--; - - dec = PyDecType_FromLongExact(type, n, context); - Py_DECREF(n_d); - if (dec == NULL) { - return NULL; - } - - d1 = mpd_qnew(); - if (d1 == NULL) { - Py_DECREF(dec); - PyErr_NoMemory(); - return NULL; - } - d2 = mpd_qnew(); - if (d2 == NULL) { - mpd_del(d1); - Py_DECREF(dec); - PyErr_NoMemory(); - return NULL; - } - - mpd_maxcontext(&maxctx); - mpd_qset_uint(d1, 5, &maxctx, &status); - mpd_qset_ssize(d2, k, &maxctx, &status); - mpd_qpow(d1, d1, d2, &maxctx, &status); - if (dec_addstatus(context, status)) { - mpd_del(d1); - mpd_del(d2); - Py_DECREF(dec); - return NULL; - } - - /* result = n * 5**k */ - mpd_qmul(MPD(dec), MPD(dec), d1, &maxctx, &status); - mpd_del(d1); - mpd_del(d2); - if (dec_addstatus(context, status)) { - Py_DECREF(dec); - return NULL; - } - /* result = +- n * 5**k * 10**-k */ - mpd_set_sign(MPD(dec), sign); - MPD(dec)->exp = -k; - - return dec; -} - -static PyObject * -PyDecType_FromFloat(PyTypeObject *type, PyObject *v, - PyObject *context) -{ - PyObject *dec; - uint32_t status = 0; - - dec = PyDecType_FromFloatExact(type, v, context); - if (dec == NULL) { - return NULL; - } - - mpd_qfinalize(MPD(dec), CTX(context), &status); - if (dec_addstatus(context, status)) { - Py_DECREF(dec); - return NULL; - } - - return dec; -} - -/* Return a new PyDecObject or a subtype from a Decimal. */ -static PyObject * -PyDecType_FromDecimalExact(PyTypeObject *type, PyObject *v, PyObject *context) -{ - PyObject *dec; - uint32_t status = 0; - - if (type == &PyDec_Type && PyDec_CheckExact(v)) { - Py_INCREF(v); - return v; - } - - dec = PyDecType_New(type); - if (dec == NULL) { - return NULL; - } - - mpd_qcopy(MPD(dec), MPD(v), &status); - if (dec_addstatus(context, status)) { - Py_DECREF(dec); - return NULL; - } - - return dec; -} - -static PyObject * -sequence_as_tuple(PyObject *v, PyObject *ex, const char *mesg) -{ - if (PyTuple_Check(v)) { - Py_INCREF(v); - return v; - } - if (PyList_Check(v)) { - return PyList_AsTuple(v); - } - - PyErr_SetString(ex, mesg); - return NULL; -} - -/* Return a new C string representation of a DecimalTuple. */ -static char * -dectuple_as_str(PyObject *dectuple) -{ - PyObject *digits = NULL, *tmp; - char *decstring = NULL; - char sign_special[6]; - char *cp; - long sign, l; - mpd_ssize_t exp = 0; - Py_ssize_t i, mem, tsize; - int is_infinite = 0; - int n; - - assert(PyTuple_Check(dectuple)); - - if (PyTuple_Size(dectuple) != 3) { - PyErr_SetString(PyExc_ValueError, - "argument must be a sequence of length 3"); - goto error; - } - - /* sign */ - tmp = PyTuple_GET_ITEM(dectuple, 0); - if (!PyLong_Check(tmp)) { - PyErr_SetString(PyExc_ValueError, - "sign must be an integer with the value 0 or 1"); - goto error; - } - sign = PyLong_AsLong(tmp); - if (sign == -1 && PyErr_Occurred()) { - goto error; - } - if (sign != 0 && sign != 1) { - PyErr_SetString(PyExc_ValueError, - "sign must be an integer with the value 0 or 1"); - goto error; - } - sign_special[0] = sign ? '-' : '+'; - sign_special[1] = '\0'; - - /* exponent or encoding for a special number */ - tmp = PyTuple_GET_ITEM(dectuple, 2); - if (PyUnicode_Check(tmp)) { - /* special */ - if (PyUnicode_CompareWithASCIIString(tmp, "F") == 0) { - strcat(sign_special, "Inf"); - is_infinite = 1; - } - else if (PyUnicode_CompareWithASCIIString(tmp, "n") == 0) { - strcat(sign_special, "NaN"); - } - else if (PyUnicode_CompareWithASCIIString(tmp, "N") == 0) { - strcat(sign_special, "sNaN"); - } - else { - PyErr_SetString(PyExc_ValueError, - "string argument in the third position " - "must be 'F', 'n' or 'N'"); - goto error; - } - } - else { - /* exponent */ - if (!PyLong_Check(tmp)) { - PyErr_SetString(PyExc_ValueError, - "exponent must be an integer"); - goto error; - } - exp = PyLong_AsSsize_t(tmp); - if (exp == -1 && PyErr_Occurred()) { - goto error; - } - } - - /* coefficient */ - digits = sequence_as_tuple(PyTuple_GET_ITEM(dectuple, 1), PyExc_ValueError, - "coefficient must be a tuple of digits"); - if (digits == NULL) { - goto error; - } - - tsize = PyTuple_Size(digits); - /* [sign][coeffdigits+1][E][-][expdigits+1]['\0'] */ - mem = 1 + tsize + 3 + MPD_EXPDIGITS + 2; - cp = decstring = PyMem_Malloc(mem); - if (decstring == NULL) { - PyErr_NoMemory(); - goto error; - } - - n = snprintf(cp, mem, "%s", sign_special); - if (n < 0 || n >= mem) { - PyErr_SetString(PyExc_RuntimeError, - "internal error in dec_sequence_as_str"); - goto error; - } - cp += n; - - if (tsize == 0 && sign_special[1] == '\0') { - /* empty tuple: zero coefficient, except for special numbers */ - *cp++ = '0'; - } - for (i = 0; i < tsize; i++) { - tmp = PyTuple_GET_ITEM(digits, i); - if (!PyLong_Check(tmp)) { - PyErr_SetString(PyExc_ValueError, - "coefficient must be a tuple of digits"); - goto error; - } - l = PyLong_AsLong(tmp); - if (l == -1 && PyErr_Occurred()) { - goto error; - } - if (l < 0 || l > 9) { - PyErr_SetString(PyExc_ValueError, - "coefficient must be a tuple of digits"); - goto error; - } - if (is_infinite) { - /* accept but ignore any well-formed coefficient for compatibility - with decimal.py */ - continue; - } - *cp++ = (char)l + '0'; - } - *cp = '\0'; - - if (sign_special[1] == '\0') { - /* not a special number */ - *cp++ = 'E'; - n = snprintf(cp, MPD_EXPDIGITS+2, "%" PRI_mpd_ssize_t, exp); - if (n < 0 || n >= MPD_EXPDIGITS+2) { - PyErr_SetString(PyExc_RuntimeError, - "internal error in dec_sequence_as_str"); - goto error; - } - } - - Py_XDECREF(digits); - return decstring; - - -error: - Py_XDECREF(digits); - if (decstring) PyMem_Free(decstring); - return NULL; -} - -/* Currently accepts tuples and lists. */ -static PyObject * -PyDecType_FromSequence(PyTypeObject *type, PyObject *v, - PyObject *context) -{ - PyObject *dectuple; - PyObject *dec; - char *s; - - dectuple = sequence_as_tuple(v, PyExc_TypeError, - "argument must be a tuple or list"); - if (dectuple == NULL) { - return NULL; - } - - s = dectuple_as_str(dectuple); - Py_DECREF(dectuple); - if (s == NULL) { - return NULL; - } - - dec = PyDecType_FromCString(type, s, context); - - PyMem_Free(s); - return dec; -} - -/* Currently accepts tuples and lists. */ -static PyObject * -PyDecType_FromSequenceExact(PyTypeObject *type, PyObject *v, - PyObject *context) -{ - PyObject *dectuple; - PyObject *dec; - char *s; - - dectuple = sequence_as_tuple(v, PyExc_TypeError, - "argument must be a tuple or list"); - if (dectuple == NULL) { - return NULL; - } - - s = dectuple_as_str(dectuple); - Py_DECREF(dectuple); - if (s == NULL) { - return NULL; - } - - dec = PyDecType_FromCStringExact(type, s, context); - - PyMem_Free(s); - return dec; -} - -#define PyDec_FromCString(str, context) \ - PyDecType_FromCString(&PyDec_Type, str, context) -#define PyDec_FromCStringExact(str, context) \ - PyDecType_FromCStringExact(&PyDec_Type, str, context) - -#define PyDec_FromUnicode(unicode, context) \ - PyDecType_FromUnicode(&PyDec_Type, unicode, context) -#define PyDec_FromUnicodeExact(unicode, context) \ - PyDecType_FromUnicodeExact(&PyDec_Type, unicode, context) -#define PyDec_FromUnicodeExactWS(unicode, context) \ - PyDecType_FromUnicodeExactWS(&PyDec_Type, unicode, context) - -#define PyDec_FromSsize(v, context) \ - PyDecType_FromSsize(&PyDec_Type, v, context) -#define PyDec_FromSsizeExact(v, context) \ - PyDecType_FromSsizeExact(&PyDec_Type, v, context) - -#define PyDec_FromLong(pylong, context) \ - PyDecType_FromLong(&PyDec_Type, pylong, context) -#define PyDec_FromLongExact(pylong, context) \ - PyDecType_FromLongExact(&PyDec_Type, pylong, context) - -#define PyDec_FromFloat(pyfloat, context) \ - PyDecType_FromFloat(&PyDec_Type, pyfloat, context) -#define PyDec_FromFloatExact(pyfloat, context) \ - PyDecType_FromFloatExact(&PyDec_Type, pyfloat, context) - -#define PyDec_FromSequence(sequence, context) \ - PyDecType_FromSequence(&PyDec_Type, sequence, context) -#define PyDec_FromSequenceExact(sequence, context) \ - PyDecType_FromSequenceExact(&PyDec_Type, sequence, context) - -/* class method */ -static PyObject * -dec_from_float(PyObject *type, PyObject *pyfloat) -{ - PyObject *context; - PyObject *result; - - CURRENT_CONTEXT(context); - result = PyDecType_FromFloatExact(&PyDec_Type, pyfloat, context); - if (type != (PyObject *)&PyDec_Type && result != NULL) { - Py_SETREF(result, PyObject_CallFunctionObjArgs(type, result, NULL)); - } - - return result; -} - -/* create_decimal_from_float */ -static PyObject * -ctx_from_float(PyObject *context, PyObject *v) -{ - return PyDec_FromFloat(v, context); -} - -/* Apply the context to the input operand. Return a new PyDecObject. */ -static PyObject * -dec_apply(PyObject *v, PyObject *context) -{ - PyObject *result; - uint32_t status = 0; - - result = dec_alloc(); - if (result == NULL) { - return NULL; - } - - mpd_qcopy(MPD(result), MPD(v), &status); - if (dec_addstatus(context, status)) { - Py_DECREF(result); - return NULL; - } - - mpd_qfinalize(MPD(result), CTX(context), &status); - if (dec_addstatus(context, status)) { - Py_DECREF(result); - return NULL; - } - - return result; -} - -/* 'v' can have any type accepted by the Decimal constructor. Attempt - an exact conversion. If the result does not meet the restrictions - for an mpd_t, fail with InvalidOperation. */ -static PyObject * -PyDecType_FromObjectExact(PyTypeObject *type, PyObject *v, PyObject *context) -{ - if (v == NULL) { - return PyDecType_FromSsizeExact(type, 0, context); - } - else if (PyDec_Check(v)) { - return PyDecType_FromDecimalExact(type, v, context); - } - else if (PyUnicode_Check(v)) { - return PyDecType_FromUnicodeExactWS(type, v, context); - } - else if (PyLong_Check(v)) { - return PyDecType_FromLongExact(type, v, context); - } - else if (PyTuple_Check(v) || PyList_Check(v)) { - return PyDecType_FromSequenceExact(type, v, context); - } - else if (PyFloat_Check(v)) { - if (dec_addstatus(context, MPD_Float_operation)) { - return NULL; - } - return PyDecType_FromFloatExact(type, v, context); - } - else { - PyErr_Format(PyExc_TypeError, - "conversion from %s to Decimal is not supported", - v->ob_type->tp_name); - return NULL; - } -} - -/* The context is used during conversion. This function is the - equivalent of context.create_decimal(). */ -static PyObject * -PyDec_FromObject(PyObject *v, PyObject *context) -{ - if (v == NULL) { - return PyDec_FromSsize(0, context); - } - else if (PyDec_Check(v)) { - mpd_context_t *ctx = CTX(context); - if (mpd_isnan(MPD(v)) && - MPD(v)->digits > ctx->prec - ctx->clamp) { - /* Special case: too many NaN payload digits */ - PyObject *result; - if (dec_addstatus(context, MPD_Conversion_syntax)) { - return NULL; - } - result = dec_alloc(); - if (result == NULL) { - return NULL; - } - mpd_setspecial(MPD(result), MPD_POS, MPD_NAN); - return result; - } - return dec_apply(v, context); - } - else if (PyUnicode_Check(v)) { - return PyDec_FromUnicode(v, context); - } - else if (PyLong_Check(v)) { - return PyDec_FromLong(v, context); - } - else if (PyTuple_Check(v) || PyList_Check(v)) { - return PyDec_FromSequence(v, context); - } - else if (PyFloat_Check(v)) { - if (dec_addstatus(context, MPD_Float_operation)) { - return NULL; - } - return PyDec_FromFloat(v, context); - } - else { - PyErr_Format(PyExc_TypeError, - "conversion from %s to Decimal is not supported", - v->ob_type->tp_name); - return NULL; - } -} - -static PyObject * -dec_new(PyTypeObject *type, PyObject *args, PyObject *kwds) -{ - static char *kwlist[] = {"value", "context", NULL}; - PyObject *v = NULL; - PyObject *context = Py_None; - - if (!PyArg_ParseTupleAndKeywords(args, kwds, "|OO", kwlist, - &v, &context)) { - return NULL; - } - CONTEXT_CHECK_VA(context); - - return PyDecType_FromObjectExact(type, v, context); -} - -static PyObject * -ctx_create_decimal(PyObject *context, PyObject *args) -{ - PyObject *v = NULL; - - if (!PyArg_ParseTuple(args, "|O", &v)) { - return NULL; - } - - return PyDec_FromObject(v, context); -} - - -/******************************************************************************/ -/* Implicit conversions to Decimal */ -/******************************************************************************/ - -/* Try to convert PyObject v to a new PyDecObject conv. If the conversion - fails, set conv to NULL (exception is set). If the conversion is not - implemented, set conv to Py_NotImplemented. */ -#define NOT_IMPL 0 -#define TYPE_ERR 1 -Py_LOCAL_INLINE(int) -convert_op(int type_err, PyObject **conv, PyObject *v, PyObject *context) -{ - - if (PyDec_Check(v)) { - *conv = v; - Py_INCREF(v); - return 1; - } - if (PyLong_Check(v)) { - *conv = PyDec_FromLongExact(v, context); - if (*conv == NULL) { - return 0; - } - return 1; - } - - if (type_err) { - PyErr_Format(PyExc_TypeError, - "conversion from %s to Decimal is not supported", - v->ob_type->tp_name); - } - else { - Py_INCREF(Py_NotImplemented); - *conv = Py_NotImplemented; - } - return 0; -} - -/* Return NotImplemented for unsupported types. */ -#define CONVERT_OP(a, v, context) \ - if (!convert_op(NOT_IMPL, a, v, context)) { \ - return *(a); \ - } - -#define CONVERT_BINOP(a, b, v, w, context) \ - if (!convert_op(NOT_IMPL, a, v, context)) { \ - return *(a); \ - } \ - if (!convert_op(NOT_IMPL, b, w, context)) { \ - Py_DECREF(*(a)); \ - return *(b); \ - } - -#define CONVERT_TERNOP(a, b, c, v, w, x, context) \ - if (!convert_op(NOT_IMPL, a, v, context)) { \ - return *(a); \ - } \ - if (!convert_op(NOT_IMPL, b, w, context)) { \ - Py_DECREF(*(a)); \ - return *(b); \ - } \ - if (!convert_op(NOT_IMPL, c, x, context)) { \ - Py_DECREF(*(a)); \ - Py_DECREF(*(b)); \ - return *(c); \ - } - -/* Raise TypeError for unsupported types. */ -#define CONVERT_OP_RAISE(a, v, context) \ - if (!convert_op(TYPE_ERR, a, v, context)) { \ - return NULL; \ - } - -#define CONVERT_BINOP_RAISE(a, b, v, w, context) \ - if (!convert_op(TYPE_ERR, a, v, context)) { \ - return NULL; \ - } \ - if (!convert_op(TYPE_ERR, b, w, context)) { \ - Py_DECREF(*(a)); \ - return NULL; \ - } - -#define CONVERT_TERNOP_RAISE(a, b, c, v, w, x, context) \ - if (!convert_op(TYPE_ERR, a, v, context)) { \ - return NULL; \ - } \ - if (!convert_op(TYPE_ERR, b, w, context)) { \ - Py_DECREF(*(a)); \ - return NULL; \ - } \ - if (!convert_op(TYPE_ERR, c, x, context)) { \ - Py_DECREF(*(a)); \ - Py_DECREF(*(b)); \ - return NULL; \ - } - - -/******************************************************************************/ -/* Implicit conversions to Decimal for comparison */ -/******************************************************************************/ - -/* Convert rationals for comparison */ -static PyObject *Rational = NULL; -static PyObject * -multiply_by_denominator(PyObject *v, PyObject *r, PyObject *context) -{ - PyObject *result; - PyObject *tmp = NULL; - PyObject *denom = NULL; - uint32_t status = 0; - mpd_context_t maxctx; - mpd_ssize_t exp; - mpd_t *vv; - - /* v is not special, r is a rational */ - tmp = PyObject_GetAttrString(r, "denominator"); - if (tmp == NULL) { - return NULL; - } - denom = PyDec_FromLongExact(tmp, context); - Py_DECREF(tmp); - if (denom == NULL) { - return NULL; - } - - vv = mpd_qncopy(MPD(v)); - if (vv == NULL) { - Py_DECREF(denom); - PyErr_NoMemory(); - return NULL; - } - result = dec_alloc(); - if (result == NULL) { - Py_DECREF(denom); - mpd_del(vv); - return NULL; - } - - mpd_maxcontext(&maxctx); - /* Prevent Overflow in the following multiplication. The result of - the multiplication is only used in mpd_qcmp, which can handle - values that are technically out of bounds, like (for 32-bit) - 99999999999999999999...99999999e+425000000. */ - exp = vv->exp; - vv->exp = 0; - mpd_qmul(MPD(result), vv, MPD(denom), &maxctx, &status); - MPD(result)->exp = exp; - - Py_DECREF(denom); - mpd_del(vv); - /* If any status has been accumulated during the multiplication, - the result is invalid. This is very unlikely, since even the - 32-bit version supports 425000000 digits. */ - if (status) { - PyErr_SetString(PyExc_ValueError, - "exact conversion for comparison failed"); - Py_DECREF(result); - return NULL; - } - - return result; -} - -static PyObject * -numerator_as_decimal(PyObject *r, PyObject *context) -{ - PyObject *tmp, *num; - - tmp = PyObject_GetAttrString(r, "numerator"); - if (tmp == NULL) { - return NULL; - } - - num = PyDec_FromLongExact(tmp, context); - Py_DECREF(tmp); - return num; -} - -/* Convert v and w for comparison. v is a Decimal. If w is a Rational, both - v and w have to be transformed. Return 1 for success, with new references - to the converted objects in vcmp and wcmp. Return 0 for failure. In that - case wcmp is either NULL or Py_NotImplemented (new reference) and vcmp - is undefined. */ -static int -convert_op_cmp(PyObject **vcmp, PyObject **wcmp, PyObject *v, PyObject *w, - int op, PyObject *context) -{ - mpd_context_t *ctx = CTX(context); - - *vcmp = v; - - if (PyDec_Check(w)) { - Py_INCREF(w); - *wcmp = w; - } - else if (PyLong_Check(w)) { - *wcmp = PyDec_FromLongExact(w, context); - } - else if (PyFloat_Check(w)) { - if (op != Py_EQ && op != Py_NE && - dec_addstatus(context, MPD_Float_operation)) { - *wcmp = NULL; - } - else { - ctx->status |= MPD_Float_operation; - *wcmp = PyDec_FromFloatExact(w, context); - } - } - else if (PyComplex_Check(w) && (op == Py_EQ || op == Py_NE)) { - Py_complex c = PyComplex_AsCComplex(w); - if (c.real == -1.0 && PyErr_Occurred()) { - *wcmp = NULL; - } - else if (c.imag == 0.0) { - PyObject *tmp = PyFloat_FromDouble(c.real); - if (tmp == NULL) { - *wcmp = NULL; - } - else { - ctx->status |= MPD_Float_operation; - *wcmp = PyDec_FromFloatExact(tmp, context); - Py_DECREF(tmp); - } - } - else { - Py_INCREF(Py_NotImplemented); - *wcmp = Py_NotImplemented; - } - } - else { - int is_rational = PyObject_IsInstance(w, Rational); - if (is_rational < 0) { - *wcmp = NULL; - } - else if (is_rational > 0) { - *wcmp = numerator_as_decimal(w, context); - if (*wcmp && !mpd_isspecial(MPD(v))) { - *vcmp = multiply_by_denominator(v, w, context); - if (*vcmp == NULL) { - Py_CLEAR(*wcmp); - } - } - } - else { - Py_INCREF(Py_NotImplemented); - *wcmp = Py_NotImplemented; - } - } - - if (*wcmp == NULL || *wcmp == Py_NotImplemented) { - return 0; - } - if (*vcmp == v) { - Py_INCREF(v); - } - return 1; -} - -#define CONVERT_BINOP_CMP(vcmp, wcmp, v, w, op, ctx) \ - if (!convert_op_cmp(vcmp, wcmp, v, w, op, ctx)) { \ - return *(wcmp); \ - } \ - - -/******************************************************************************/ -/* Conversions from decimal */ -/******************************************************************************/ - -static PyObject * -unicode_fromascii(const char *s, Py_ssize_t size) -{ - PyObject *res; - - res = PyUnicode_New(size, 127); - if (res == NULL) { - return NULL; - } - - memcpy(PyUnicode_1BYTE_DATA(res), s, size); - return res; -} - -/* PyDecObject as a string. The default module context is only used for - the value of 'capitals'. */ -static PyObject * -dec_str(PyObject *dec) -{ - PyObject *res, *context; - mpd_ssize_t size; - char *cp; - - CURRENT_CONTEXT(context); - size = mpd_to_sci_size(&cp, MPD(dec), CtxCaps(context)); - if (size < 0) { - PyErr_NoMemory(); - return NULL; - } - - res = unicode_fromascii(cp, size); - mpd_free(cp); - return res; -} - -/* Representation of a PyDecObject. */ -static PyObject * -dec_repr(PyObject *dec) -{ - PyObject *res, *context; - char *cp; - - CURRENT_CONTEXT(context); - cp = mpd_to_sci(MPD(dec), CtxCaps(context)); - if (cp == NULL) { - PyErr_NoMemory(); - return NULL; - } - - res = PyUnicode_FromFormat("Decimal('%s')", cp); - mpd_free(cp); - return res; -} - -/* Return a duplicate of src, copy embedded null characters. */ -static char * -dec_strdup(const char *src, Py_ssize_t size) -{ - char *dest = PyMem_Malloc(size+1); - if (dest == NULL) { - PyErr_NoMemory(); - return NULL; - } - - memcpy(dest, src, size); - dest[size] = '\0'; - return dest; -} - -static void -dec_replace_fillchar(char *dest) -{ - while (*dest != '\0') { - if (*dest == '\xff') *dest = '\0'; - dest++; - } -} - -/* Convert decimal_point or thousands_sep, which may be multibyte or in - the range [128, 255], to a UTF8 string. */ -static PyObject * -dotsep_as_utf8(const char *s) -{ - PyObject *utf8; - PyObject *tmp; - wchar_t buf[2]; - size_t n; - - n = mbstowcs(buf, s, 2); - if (n != 1) { /* Issue #7442 */ - PyErr_SetString(PyExc_ValueError, - "invalid decimal point or unsupported " - "combination of LC_CTYPE and LC_NUMERIC"); - return NULL; - } - tmp = PyUnicode_FromWideChar(buf, n); - if (tmp == NULL) { - return NULL; - } - utf8 = PyUnicode_AsUTF8String(tmp); - Py_DECREF(tmp); - return utf8; -} - -/* Formatted representation of a PyDecObject. */ -static PyObject * -dec_format(PyObject *dec, PyObject *args) -{ - PyObject *result = NULL; - PyObject *override = NULL; - PyObject *dot = NULL; - PyObject *sep = NULL; - PyObject *grouping = NULL; - PyObject *fmtarg; - PyObject *context; - mpd_spec_t spec; - char *fmt; - char *decstring = NULL; - uint32_t status = 0; - int replace_fillchar = 0; - Py_ssize_t size; - - - CURRENT_CONTEXT(context); - if (!PyArg_ParseTuple(args, "O|O", &fmtarg, &override)) { - return NULL; - } - - if (PyUnicode_Check(fmtarg)) { - fmt = (char *)PyUnicode_AsUTF8AndSize(fmtarg, &size); - if (fmt == NULL) { - return NULL; - } - if (size > 0 && fmt[0] == '\0') { - /* NUL fill character: must be replaced with a valid UTF-8 char - before calling mpd_parse_fmt_str(). */ - replace_fillchar = 1; - fmt = dec_strdup(fmt, size); - if (fmt == NULL) { - return NULL; - } - fmt[0] = '_'; - } - } - else { - PyErr_SetString(PyExc_TypeError, - "format arg must be str"); - return NULL; - } - - if (!mpd_parse_fmt_str(&spec, fmt, CtxCaps(context))) { - PyErr_SetString(PyExc_ValueError, - "invalid format string"); - goto finish; - } - if (replace_fillchar) { - /* In order to avoid clobbering parts of UTF-8 thousands separators or - decimal points when the substitution is reversed later, the actual - placeholder must be an invalid UTF-8 byte. */ - spec.fill[0] = '\xff'; - spec.fill[1] = '\0'; - } - - if (override) { - /* Values for decimal_point, thousands_sep and grouping can - be explicitly specified in the override dict. These values - take precedence over the values obtained from localeconv() - in mpd_parse_fmt_str(). The feature is not documented and - is only used in test_decimal. */ - if (!PyDict_Check(override)) { - PyErr_SetString(PyExc_TypeError, - "optional argument must be a dict"); - goto finish; - } - if ((dot = PyDict_GetItemString(override, "decimal_point"))) { - if ((dot = PyUnicode_AsUTF8String(dot)) == NULL) { - goto finish; - } - spec.dot = PyBytes_AS_STRING(dot); - } - if ((sep = PyDict_GetItemString(override, "thousands_sep"))) { - if ((sep = PyUnicode_AsUTF8String(sep)) == NULL) { - goto finish; - } - spec.sep = PyBytes_AS_STRING(sep); - } - if ((grouping = PyDict_GetItemString(override, "grouping"))) { - if ((grouping = PyUnicode_AsUTF8String(grouping)) == NULL) { - goto finish; - } - spec.grouping = PyBytes_AS_STRING(grouping); - } - if (mpd_validate_lconv(&spec) < 0) { - PyErr_SetString(PyExc_ValueError, - "invalid override dict"); - goto finish; - } - } - else { - size_t n = strlen(spec.dot); - if (n > 1 || (n == 1 && !isascii((uchar)spec.dot[0]))) { - /* fix locale dependent non-ascii characters */ - dot = dotsep_as_utf8(spec.dot); - if (dot == NULL) { - goto finish; - } - spec.dot = PyBytes_AS_STRING(dot); - } - n = strlen(spec.sep); - if (n > 1 || (n == 1 && !isascii((uchar)spec.sep[0]))) { - /* fix locale dependent non-ascii characters */ - sep = dotsep_as_utf8(spec.sep); - if (sep == NULL) { - goto finish; - } - spec.sep = PyBytes_AS_STRING(sep); - } - } - - - decstring = mpd_qformat_spec(MPD(dec), &spec, CTX(context), &status); - if (decstring == NULL) { - if (status & MPD_Malloc_error) { - PyErr_NoMemory(); - } - else { - PyErr_SetString(PyExc_ValueError, - "format specification exceeds internal limits of _decimal"); - } - goto finish; - } - size = strlen(decstring); - if (replace_fillchar) { - dec_replace_fillchar(decstring); - } - - result = PyUnicode_DecodeUTF8(decstring, size, NULL); - - -finish: - Py_XDECREF(grouping); - Py_XDECREF(sep); - Py_XDECREF(dot); - if (replace_fillchar) PyMem_Free(fmt); - if (decstring) mpd_free(decstring); - return result; -} - -/* Return a PyLongObject from a PyDecObject, using the specified rounding - * mode. The context precision is not observed. */ -static PyObject * -dec_as_long(PyObject *dec, PyObject *context, int round) -{ - PyLongObject *pylong; - digit *ob_digit; - size_t n; - Py_ssize_t i; - mpd_t *x; - mpd_context_t workctx; - uint32_t status = 0; - - if (mpd_isspecial(MPD(dec))) { - if (mpd_isnan(MPD(dec))) { - PyErr_SetString(PyExc_ValueError, - "cannot convert NaN to integer"); - } - else { - PyErr_SetString(PyExc_OverflowError, - "cannot convert Infinity to integer"); - } - return NULL; - } - - x = mpd_qnew(); - if (x == NULL) { - PyErr_NoMemory(); - return NULL; - } - workctx = *CTX(context); - workctx.round = round; - mpd_qround_to_int(x, MPD(dec), &workctx, &status); - if (dec_addstatus(context, status)) { - mpd_del(x); - return NULL; - } - - status = 0; - ob_digit = NULL; -#if PYLONG_BITS_IN_DIGIT == 30 - n = mpd_qexport_u32(&ob_digit, 0, PyLong_BASE, x, &status); -#elif PYLONG_BITS_IN_DIGIT == 15 - n = mpd_qexport_u16(&ob_digit, 0, PyLong_BASE, x, &status); -#else - #error "PYLONG_BITS_IN_DIGIT should be 15 or 30" -#endif - - if (n == SIZE_MAX) { - PyErr_NoMemory(); - mpd_del(x); - return NULL; - } - - assert(n > 0); - pylong = _PyLong_New(n); - if (pylong == NULL) { - mpd_free(ob_digit); - mpd_del(x); - return NULL; - } - - memcpy(pylong->ob_digit, ob_digit, n * sizeof(digit)); - mpd_free(ob_digit); - - i = n; - while ((i > 0) && (pylong->ob_digit[i-1] == 0)) { - i--; - } - - Py_SIZE(pylong) = i; - if (mpd_isnegative(x) && !mpd_iszero(x)) { - Py_SIZE(pylong) = -i; - } - - mpd_del(x); - return (PyObject *) pylong; -} - -/* Convert a Decimal to its exact integer ratio representation. */ -static PyObject * -dec_as_integer_ratio(PyObject *self, PyObject *args UNUSED) -{ - PyObject *numerator = NULL; - PyObject *denominator = NULL; - PyObject *exponent = NULL; - PyObject *result = NULL; - PyObject *tmp; - mpd_ssize_t exp; - PyObject *context; - uint32_t status = 0; - - if (mpd_isspecial(MPD(self))) { - if (mpd_isnan(MPD(self))) { - PyErr_SetString(PyExc_ValueError, - "cannot convert NaN to integer ratio"); - } - else { - PyErr_SetString(PyExc_OverflowError, - "cannot convert Infinity to integer ratio"); - } - return NULL; - } - - CURRENT_CONTEXT(context); - - tmp = dec_alloc(); - if (tmp == NULL) { - return NULL; - } - - if (!mpd_qcopy(MPD(tmp), MPD(self), &status)) { - Py_DECREF(tmp); - PyErr_NoMemory(); - return NULL; - } - - exp = mpd_iszero(MPD(tmp)) ? 0 : MPD(tmp)->exp; - MPD(tmp)->exp = 0; - - /* context and rounding are unused here: the conversion is exact */ - numerator = dec_as_long(tmp, context, MPD_ROUND_FLOOR); - Py_DECREF(tmp); - if (numerator == NULL) { - goto error; - } - - exponent = PyLong_FromSsize_t(exp < 0 ? -exp : exp); - if (exponent == NULL) { - goto error; - } - - tmp = PyLong_FromLong(10); - if (tmp == NULL) { - goto error; - } - - Py_SETREF(exponent, _py_long_power(tmp, exponent, Py_None)); - Py_DECREF(tmp); - if (exponent == NULL) { - goto error; - } - - if (exp >= 0) { - Py_SETREF(numerator, _py_long_multiply(numerator, exponent)); - if (numerator == NULL) { - goto error; - } - denominator = PyLong_FromLong(1); - if (denominator == NULL) { - goto error; - } - } - else { - denominator = exponent; - exponent = NULL; - tmp = _PyLong_GCD(numerator, denominator); - if (tmp == NULL) { - goto error; - } - Py_SETREF(numerator, _py_long_floor_divide(numerator, tmp)); - Py_SETREF(denominator, _py_long_floor_divide(denominator, tmp)); - Py_DECREF(tmp); - if (numerator == NULL || denominator == NULL) { - goto error; - } - } - - result = PyTuple_Pack(2, numerator, denominator); - - -error: - Py_XDECREF(exponent); - Py_XDECREF(denominator); - Py_XDECREF(numerator); - return result; -} - -static PyObject * -PyDec_ToIntegralValue(PyObject *dec, PyObject *args, PyObject *kwds) -{ - static char *kwlist[] = {"rounding", "context", NULL}; - PyObject *result; - PyObject *rounding = Py_None; - PyObject *context = Py_None; - uint32_t status = 0; - mpd_context_t workctx; - - if (!PyArg_ParseTupleAndKeywords(args, kwds, "|OO", kwlist, - &rounding, &context)) { - return NULL; - } - CONTEXT_CHECK_VA(context); - - workctx = *CTX(context); - if (rounding != Py_None) { - int round = getround(rounding); - if (round < 0) { - return NULL; - } - if (!mpd_qsetround(&workctx, round)) { - INTERNAL_ERROR_PTR("PyDec_ToIntegralValue"); /* GCOV_NOT_REACHED */ - } - } - - result = dec_alloc(); - if (result == NULL) { - return NULL; - } - - mpd_qround_to_int(MPD(result), MPD(dec), &workctx, &status); - if (dec_addstatus(context, status)) { - Py_DECREF(result); - return NULL; - } - - return result; -} - -static PyObject * -PyDec_ToIntegralExact(PyObject *dec, PyObject *args, PyObject *kwds) -{ - static char *kwlist[] = {"rounding", "context", NULL}; - PyObject *result; - PyObject *rounding = Py_None; - PyObject *context = Py_None; - uint32_t status = 0; - mpd_context_t workctx; - - if (!PyArg_ParseTupleAndKeywords(args, kwds, "|OO", kwlist, - &rounding, &context)) { - return NULL; - } - CONTEXT_CHECK_VA(context); - - workctx = *CTX(context); - if (rounding != Py_None) { - int round = getround(rounding); - if (round < 0) { - return NULL; - } - if (!mpd_qsetround(&workctx, round)) { - INTERNAL_ERROR_PTR("PyDec_ToIntegralExact"); /* GCOV_NOT_REACHED */ - } - } - - result = dec_alloc(); - if (result == NULL) { - return NULL; - } - - mpd_qround_to_intx(MPD(result), MPD(dec), &workctx, &status); - if (dec_addstatus(context, status)) { - Py_DECREF(result); - return NULL; - } - - return result; -} - -static PyObject * -PyDec_AsFloat(PyObject *dec) -{ - PyObject *f, *s; - - if (mpd_isnan(MPD(dec))) { - if (mpd_issnan(MPD(dec))) { - PyErr_SetString(PyExc_ValueError, - "cannot convert signaling NaN to float"); - return NULL; - } - if (mpd_isnegative(MPD(dec))) { - s = PyUnicode_FromString("-nan"); - } - else { - s = PyUnicode_FromString("nan"); - } - } - else { - s = dec_str(dec); - } - - if (s == NULL) { - return NULL; - } - - f = PyFloat_FromString(s); - Py_DECREF(s); - - return f; -} - -static PyObject * -PyDec_Round(PyObject *dec, PyObject *args) -{ - PyObject *result; - PyObject *x = NULL; - uint32_t status = 0; - PyObject *context; - - - CURRENT_CONTEXT(context); - if (!PyArg_ParseTuple(args, "|O", &x)) { - return NULL; - } - - if (x) { - mpd_uint_t dq[1] = {1}; - mpd_t q = {MPD_STATIC|MPD_CONST_DATA,0,1,1,1,dq}; - mpd_ssize_t y; - - if (!PyLong_Check(x)) { - PyErr_SetString(PyExc_TypeError, - "optional arg must be an integer"); - return NULL; - } - - y = PyLong_AsSsize_t(x); - if (y == -1 && PyErr_Occurred()) { - return NULL; - } - result = dec_alloc(); - if (result == NULL) { - return NULL; - } - - q.exp = (y == MPD_SSIZE_MIN) ? MPD_SSIZE_MAX : -y; - mpd_qquantize(MPD(result), MPD(dec), &q, CTX(context), &status); - if (dec_addstatus(context, status)) { - Py_DECREF(result); - return NULL; - } - - return result; - } - else { - return dec_as_long(dec, context, MPD_ROUND_HALF_EVEN); - } -} - -static PyTypeObject *DecimalTuple = NULL; -/* Return the DecimalTuple representation of a PyDecObject. */ -static PyObject * -PyDec_AsTuple(PyObject *dec, PyObject *dummy UNUSED) -{ - PyObject *result = NULL; - PyObject *sign = NULL; - PyObject *coeff = NULL; - PyObject *expt = NULL; - PyObject *tmp = NULL; - mpd_t *x = NULL; - char *intstring = NULL; - Py_ssize_t intlen, i; - - - x = mpd_qncopy(MPD(dec)); - if (x == NULL) { - PyErr_NoMemory(); - goto out; - } - - sign = PyLong_FromUnsignedLong(mpd_sign(MPD(dec))); - if (sign == NULL) { - goto out; - } - - if (mpd_isinfinite(x)) { - expt = PyUnicode_FromString("F"); - if (expt == NULL) { - goto out; - } - /* decimal.py has non-compliant infinity payloads. */ - coeff = Py_BuildValue("(i)", 0); - if (coeff == NULL) { - goto out; - } - } - else { - if (mpd_isnan(x)) { - expt = PyUnicode_FromString(mpd_isqnan(x)?"n":"N"); - } - else { - expt = PyLong_FromSsize_t(MPD(dec)->exp); - } - if (expt == NULL) { - goto out; - } - - /* coefficient is defined */ - if (x->len > 0) { - - /* make an integer */ - x->exp = 0; - /* clear NaN and sign */ - mpd_clear_flags(x); - intstring = mpd_to_sci(x, 1); - if (intstring == NULL) { - PyErr_NoMemory(); - goto out; - } - - intlen = strlen(intstring); - coeff = PyTuple_New(intlen); - if (coeff == NULL) { - goto out; - } - - for (i = 0; i < intlen; i++) { - tmp = PyLong_FromLong(intstring[i]-'0'); - if (tmp == NULL) { - goto out; - } - PyTuple_SET_ITEM(coeff, i, tmp); - } - } - else { - coeff = PyTuple_New(0); - if (coeff == NULL) { - goto out; - } - } - } - - result = PyObject_CallFunctionObjArgs((PyObject *)DecimalTuple, - sign, coeff, expt, NULL); - -out: - if (x) mpd_del(x); - if (intstring) mpd_free(intstring); - Py_XDECREF(sign); - Py_XDECREF(coeff); - Py_XDECREF(expt); - return result; -} - - -/******************************************************************************/ -/* Macros for converting mpdecimal functions to Decimal methods */ -/******************************************************************************/ - -/* Unary number method that uses the default module context. */ -#define Dec_UnaryNumberMethod(MPDFUNC) \ -static PyObject * \ -nm_##MPDFUNC(PyObject *self) \ -{ \ - PyObject *result; \ - PyObject *context; \ - uint32_t status = 0; \ - \ - CURRENT_CONTEXT(context); \ - if ((result = dec_alloc()) == NULL) { \ - return NULL; \ - } \ - \ - MPDFUNC(MPD(result), MPD(self), CTX(context), &status); \ - if (dec_addstatus(context, status)) { \ - Py_DECREF(result); \ - return NULL; \ - } \ - \ - return result; \ -} - -/* Binary number method that uses default module context. */ -#define Dec_BinaryNumberMethod(MPDFUNC) \ -static PyObject * \ -nm_##MPDFUNC(PyObject *self, PyObject *other) \ -{ \ - PyObject *a, *b; \ - PyObject *result; \ - PyObject *context; \ - uint32_t status = 0; \ - \ - CURRENT_CONTEXT(context) ; \ - CONVERT_BINOP(&a, &b, self, other, context); \ - \ - if ((result = dec_alloc()) == NULL) { \ - Py_DECREF(a); \ - Py_DECREF(b); \ - return NULL; \ - } \ - \ - MPDFUNC(MPD(result), MPD(a), MPD(b), CTX(context), &status); \ - Py_DECREF(a); \ - Py_DECREF(b); \ - if (dec_addstatus(context, status)) { \ - Py_DECREF(result); \ - return NULL; \ - } \ - \ - return result; \ -} - -/* Boolean function without a context arg. */ -#define Dec_BoolFunc(MPDFUNC) \ -static PyObject * \ -dec_##MPDFUNC(PyObject *self, PyObject *dummy UNUSED) \ -{ \ - return MPDFUNC(MPD(self)) ? incr_true() : incr_false(); \ -} - -/* Boolean function with an optional context arg. */ -#define Dec_BoolFuncVA(MPDFUNC) \ -static PyObject * \ -dec_##MPDFUNC(PyObject *self, PyObject *args, PyObject *kwds) \ -{ \ - static char *kwlist[] = {"context", NULL}; \ - PyObject *context = Py_None; \ - \ - if (!PyArg_ParseTupleAndKeywords(args, kwds, "|O", kwlist, \ - &context)) { \ - return NULL; \ - } \ - CONTEXT_CHECK_VA(context); \ - \ - return MPDFUNC(MPD(self), CTX(context)) ? incr_true() : incr_false(); \ -} - -/* Unary function with an optional context arg. */ -#define Dec_UnaryFuncVA(MPDFUNC) \ -static PyObject * \ -dec_##MPDFUNC(PyObject *self, PyObject *args, PyObject *kwds) \ -{ \ - static char *kwlist[] = {"context", NULL}; \ - PyObject *result; \ - PyObject *context = Py_None; \ - uint32_t status = 0; \ - \ - if (!PyArg_ParseTupleAndKeywords(args, kwds, "|O", kwlist, \ - &context)) { \ - return NULL; \ - } \ - CONTEXT_CHECK_VA(context); \ - \ - if ((result = dec_alloc()) == NULL) { \ - return NULL; \ - } \ - \ - MPDFUNC(MPD(result), MPD(self), CTX(context), &status); \ - if (dec_addstatus(context, status)) { \ - Py_DECREF(result); \ - return NULL; \ - } \ - \ - return result; \ -} - -/* Binary function with an optional context arg. */ -#define Dec_BinaryFuncVA(MPDFUNC) \ -static PyObject * \ -dec_##MPDFUNC(PyObject *self, PyObject *args, PyObject *kwds) \ -{ \ - static char *kwlist[] = {"other", "context", NULL}; \ - PyObject *other; \ - PyObject *a, *b; \ - PyObject *result; \ - PyObject *context = Py_None; \ - uint32_t status = 0; \ - \ - if (!PyArg_ParseTupleAndKeywords(args, kwds, "O|O", kwlist, \ - &other, &context)) { \ - return NULL; \ - } \ - CONTEXT_CHECK_VA(context); \ - CONVERT_BINOP_RAISE(&a, &b, self, other, context); \ - \ - if ((result = dec_alloc()) == NULL) { \ - Py_DECREF(a); \ - Py_DECREF(b); \ - return NULL; \ - } \ - \ - MPDFUNC(MPD(result), MPD(a), MPD(b), CTX(context), &status); \ - Py_DECREF(a); \ - Py_DECREF(b); \ - if (dec_addstatus(context, status)) { \ - Py_DECREF(result); \ - return NULL; \ - } \ - \ - return result; \ -} - -/* Binary function with an optional context arg. Actual MPDFUNC does - NOT take a context. The context is used to record InvalidOperation - if the second operand cannot be converted exactly. */ -#define Dec_BinaryFuncVA_NO_CTX(MPDFUNC) \ -static PyObject * \ -dec_##MPDFUNC(PyObject *self, PyObject *args, PyObject *kwds) \ -{ \ - static char *kwlist[] = {"other", "context", NULL}; \ - PyObject *context = Py_None; \ - PyObject *other; \ - PyObject *a, *b; \ - PyObject *result; \ - \ - if (!PyArg_ParseTupleAndKeywords(args, kwds, "O|O", kwlist, \ - &other, &context)) { \ - return NULL; \ - } \ - CONTEXT_CHECK_VA(context); \ - CONVERT_BINOP_RAISE(&a, &b, self, other, context); \ - \ - if ((result = dec_alloc()) == NULL) { \ - Py_DECREF(a); \ - Py_DECREF(b); \ - return NULL; \ - } \ - \ - MPDFUNC(MPD(result), MPD(a), MPD(b)); \ - Py_DECREF(a); \ - Py_DECREF(b); \ - \ - return result; \ -} - -/* Ternary function with an optional context arg. */ -#define Dec_TernaryFuncVA(MPDFUNC) \ -static PyObject * \ -dec_##MPDFUNC(PyObject *self, PyObject *args, PyObject *kwds) \ -{ \ - static char *kwlist[] = {"other", "third", "context", NULL}; \ - PyObject *other, *third; \ - PyObject *a, *b, *c; \ - PyObject *result; \ - PyObject *context = Py_None; \ - uint32_t status = 0; \ - \ - if (!PyArg_ParseTupleAndKeywords(args, kwds, "OO|O", kwlist, \ - &other, &third, &context)) { \ - return NULL; \ - } \ - CONTEXT_CHECK_VA(context); \ - CONVERT_TERNOP_RAISE(&a, &b, &c, self, other, third, context); \ - \ - if ((result = dec_alloc()) == NULL) { \ - Py_DECREF(a); \ - Py_DECREF(b); \ - Py_DECREF(c); \ - return NULL; \ - } \ - \ - MPDFUNC(MPD(result), MPD(a), MPD(b), MPD(c), CTX(context), &status); \ - Py_DECREF(a); \ - Py_DECREF(b); \ - Py_DECREF(c); \ - if (dec_addstatus(context, status)) { \ - Py_DECREF(result); \ - return NULL; \ - } \ - \ - return result; \ -} - - -/**********************************************/ -/* Number methods */ -/**********************************************/ - -Dec_UnaryNumberMethod(mpd_qminus) -Dec_UnaryNumberMethod(mpd_qplus) -Dec_UnaryNumberMethod(mpd_qabs) - -Dec_BinaryNumberMethod(mpd_qadd) -Dec_BinaryNumberMethod(mpd_qsub) -Dec_BinaryNumberMethod(mpd_qmul) -Dec_BinaryNumberMethod(mpd_qdiv) -Dec_BinaryNumberMethod(mpd_qrem) -Dec_BinaryNumberMethod(mpd_qdivint) - -static PyObject * -nm_dec_as_long(PyObject *dec) -{ - PyObject *context; - - CURRENT_CONTEXT(context); - return dec_as_long(dec, context, MPD_ROUND_DOWN); -} - -static int -nm_nonzero(PyObject *v) -{ - return !mpd_iszero(MPD(v)); -} - -static PyObject * -nm_mpd_qdivmod(PyObject *v, PyObject *w) -{ - PyObject *a, *b; - PyObject *q, *r; - PyObject *context; - uint32_t status = 0; - PyObject *ret; - - CURRENT_CONTEXT(context); - CONVERT_BINOP(&a, &b, v, w, context); - - q = dec_alloc(); - if (q == NULL) { - Py_DECREF(a); - Py_DECREF(b); - return NULL; - } - r = dec_alloc(); - if (r == NULL) { - Py_DECREF(a); - Py_DECREF(b); - Py_DECREF(q); - return NULL; - } - - mpd_qdivmod(MPD(q), MPD(r), MPD(a), MPD(b), CTX(context), &status); - Py_DECREF(a); - Py_DECREF(b); - if (dec_addstatus(context, status)) { - Py_DECREF(r); - Py_DECREF(q); - return NULL; - } - - ret = Py_BuildValue("(OO)", q, r); - Py_DECREF(r); - Py_DECREF(q); - return ret; -} - -static PyObject * -nm_mpd_qpow(PyObject *base, PyObject *exp, PyObject *mod) -{ - PyObject *a, *b, *c = NULL; - PyObject *result; - PyObject *context; - uint32_t status = 0; - - CURRENT_CONTEXT(context); - CONVERT_BINOP(&a, &b, base, exp, context); - - if (mod != Py_None) { - if (!convert_op(NOT_IMPL, &c, mod, context)) { - Py_DECREF(a); - Py_DECREF(b); - return c; - } - } - - result = dec_alloc(); - if (result == NULL) { - Py_DECREF(a); - Py_DECREF(b); - Py_XDECREF(c); - return NULL; - } - - if (c == NULL) { - mpd_qpow(MPD(result), MPD(a), MPD(b), - CTX(context), &status); - } - else { - mpd_qpowmod(MPD(result), MPD(a), MPD(b), MPD(c), - CTX(context), &status); - Py_DECREF(c); - } - Py_DECREF(a); - Py_DECREF(b); - if (dec_addstatus(context, status)) { - Py_DECREF(result); - return NULL; - } - - return result; -} - - -/******************************************************************************/ -/* Decimal Methods */ -/******************************************************************************/ - -/* Unary arithmetic functions, optional context arg */ -Dec_UnaryFuncVA(mpd_qexp) -Dec_UnaryFuncVA(mpd_qln) -Dec_UnaryFuncVA(mpd_qlog10) -Dec_UnaryFuncVA(mpd_qnext_minus) -Dec_UnaryFuncVA(mpd_qnext_plus) -Dec_UnaryFuncVA(mpd_qreduce) -Dec_UnaryFuncVA(mpd_qsqrt) - -/* Binary arithmetic functions, optional context arg */ -Dec_BinaryFuncVA(mpd_qcompare) -Dec_BinaryFuncVA(mpd_qcompare_signal) -Dec_BinaryFuncVA(mpd_qmax) -Dec_BinaryFuncVA(mpd_qmax_mag) -Dec_BinaryFuncVA(mpd_qmin) -Dec_BinaryFuncVA(mpd_qmin_mag) -Dec_BinaryFuncVA(mpd_qnext_toward) -Dec_BinaryFuncVA(mpd_qrem_near) - -/* Ternary arithmetic functions, optional context arg */ -Dec_TernaryFuncVA(mpd_qfma) - -/* Boolean functions, no context arg */ -Dec_BoolFunc(mpd_iscanonical) -Dec_BoolFunc(mpd_isfinite) -Dec_BoolFunc(mpd_isinfinite) -Dec_BoolFunc(mpd_isnan) -Dec_BoolFunc(mpd_isqnan) -Dec_BoolFunc(mpd_issnan) -Dec_BoolFunc(mpd_issigned) -Dec_BoolFunc(mpd_iszero) - -/* Boolean functions, optional context arg */ -Dec_BoolFuncVA(mpd_isnormal) -Dec_BoolFuncVA(mpd_issubnormal) - -/* Unary functions, no context arg */ -static PyObject * -dec_mpd_adjexp(PyObject *self, PyObject *dummy UNUSED) -{ - mpd_ssize_t retval; - - if (mpd_isspecial(MPD(self))) { - retval = 0; - } - else { - retval = mpd_adjexp(MPD(self)); - } - - return PyLong_FromSsize_t(retval); -} - -static PyObject * -dec_canonical(PyObject *self, PyObject *dummy UNUSED) -{ - Py_INCREF(self); - return self; -} - -static PyObject * -dec_conjugate(PyObject *self, PyObject *dummy UNUSED) -{ - Py_INCREF(self); - return self; -} - -static PyObject * -dec_mpd_radix(PyObject *self UNUSED, PyObject *dummy UNUSED) -{ - PyObject *result; - - result = dec_alloc(); - if (result == NULL) { - return NULL; - } - - _dec_settriple(result, MPD_POS, 10, 0); - return result; -} - -static PyObject * -dec_mpd_qcopy_abs(PyObject *self, PyObject *dummy UNUSED) -{ - PyObject *result; - uint32_t status = 0; - - if ((result = dec_alloc()) == NULL) { - return NULL; - } - - mpd_qcopy_abs(MPD(result), MPD(self), &status); - if (status & MPD_Malloc_error) { - Py_DECREF(result); - PyErr_NoMemory(); - return NULL; - } - - return result; -} - -static PyObject * -dec_mpd_qcopy_negate(PyObject *self, PyObject *dummy UNUSED) -{ - PyObject *result; - uint32_t status = 0; - - if ((result = dec_alloc()) == NULL) { - return NULL; - } - - mpd_qcopy_negate(MPD(result), MPD(self), &status); - if (status & MPD_Malloc_error) { - Py_DECREF(result); - PyErr_NoMemory(); - return NULL; - } - - return result; -} - -/* Unary functions, optional context arg */ -Dec_UnaryFuncVA(mpd_qinvert) -Dec_UnaryFuncVA(mpd_qlogb) - -static PyObject * -dec_mpd_class(PyObject *self, PyObject *args, PyObject *kwds) -{ - static char *kwlist[] = {"context", NULL}; - PyObject *context = Py_None; - const char *cp; - - if (!PyArg_ParseTupleAndKeywords(args, kwds, "|O", kwlist, - &context)) { - return NULL; - } - CONTEXT_CHECK_VA(context); - - cp = mpd_class(MPD(self), CTX(context)); - return PyUnicode_FromString(cp); -} - -static PyObject * -dec_mpd_to_eng(PyObject *self, PyObject *args, PyObject *kwds) -{ - static char *kwlist[] = {"context", NULL}; - PyObject *result; - PyObject *context = Py_None; - mpd_ssize_t size; - char *s; - - if (!PyArg_ParseTupleAndKeywords(args, kwds, "|O", kwlist, - &context)) { - return NULL; - } - CONTEXT_CHECK_VA(context); - - size = mpd_to_eng_size(&s, MPD(self), CtxCaps(context)); - if (size < 0) { - PyErr_NoMemory(); - return NULL; - } - - result = unicode_fromascii(s, size); - mpd_free(s); - - return result; -} - -/* Binary functions, optional context arg for conversion errors */ -Dec_BinaryFuncVA_NO_CTX(mpd_compare_total) -Dec_BinaryFuncVA_NO_CTX(mpd_compare_total_mag) - -static PyObject * -dec_mpd_qcopy_sign(PyObject *self, PyObject *args, PyObject *kwds) -{ - static char *kwlist[] = {"other", "context", NULL}; - PyObject *other; - PyObject *a, *b; - PyObject *result; - PyObject *context = Py_None; - uint32_t status = 0; - - if (!PyArg_ParseTupleAndKeywords(args, kwds, "O|O", kwlist, - &other, &context)) { - return NULL; - } - CONTEXT_CHECK_VA(context); - CONVERT_BINOP_RAISE(&a, &b, self, other, context); - - result = dec_alloc(); - if (result == NULL) { - Py_DECREF(a); - Py_DECREF(b); - return NULL; - } - - mpd_qcopy_sign(MPD(result), MPD(a), MPD(b), &status); - Py_DECREF(a); - Py_DECREF(b); - if (dec_addstatus(context, status)) { - Py_DECREF(result); - return NULL; - } - - return result; -} - -static PyObject * -dec_mpd_same_quantum(PyObject *self, PyObject *args, PyObject *kwds) -{ - static char *kwlist[] = {"other", "context", NULL}; - PyObject *other; - PyObject *a, *b; - PyObject *result; - PyObject *context = Py_None; - - if (!PyArg_ParseTupleAndKeywords(args, kwds, "O|O", kwlist, - &other, &context)) { - return NULL; - } - CONTEXT_CHECK_VA(context); - CONVERT_BINOP_RAISE(&a, &b, self, other, context); - - result = mpd_same_quantum(MPD(a), MPD(b)) ? incr_true() : incr_false(); - Py_DECREF(a); - Py_DECREF(b); - - return result; -} - -/* Binary functions, optional context arg */ -Dec_BinaryFuncVA(mpd_qand) -Dec_BinaryFuncVA(mpd_qor) -Dec_BinaryFuncVA(mpd_qxor) - -Dec_BinaryFuncVA(mpd_qrotate) -Dec_BinaryFuncVA(mpd_qscaleb) -Dec_BinaryFuncVA(mpd_qshift) - -static PyObject * -dec_mpd_qquantize(PyObject *v, PyObject *args, PyObject *kwds) -{ - static char *kwlist[] = {"exp", "rounding", "context", NULL}; - PyObject *rounding = Py_None; - PyObject *context = Py_None; - PyObject *w, *a, *b; - PyObject *result; - uint32_t status = 0; - mpd_context_t workctx; - - if (!PyArg_ParseTupleAndKeywords(args, kwds, "O|OO", kwlist, - &w, &rounding, &context)) { - return NULL; - } - CONTEXT_CHECK_VA(context); - - workctx = *CTX(context); - if (rounding != Py_None) { - int round = getround(rounding); - if (round < 0) { - return NULL; - } - if (!mpd_qsetround(&workctx, round)) { - INTERNAL_ERROR_PTR("dec_mpd_qquantize"); /* GCOV_NOT_REACHED */ - } - } - - CONVERT_BINOP_RAISE(&a, &b, v, w, context); - - result = dec_alloc(); - if (result == NULL) { - Py_DECREF(a); - Py_DECREF(b); - return NULL; - } - - mpd_qquantize(MPD(result), MPD(a), MPD(b), &workctx, &status); - Py_DECREF(a); - Py_DECREF(b); - if (dec_addstatus(context, status)) { - Py_DECREF(result); - return NULL; - } - - return result; -} - -/* Special methods */ -static PyObject * -dec_richcompare(PyObject *v, PyObject *w, int op) -{ - PyObject *a; - PyObject *b; - PyObject *context; - uint32_t status = 0; - int a_issnan, b_issnan; - int r; - - assert(PyDec_Check(v)); - - CURRENT_CONTEXT(context); - CONVERT_BINOP_CMP(&a, &b, v, w, op, context); - - a_issnan = mpd_issnan(MPD(a)); - b_issnan = mpd_issnan(MPD(b)); - - r = mpd_qcmp(MPD(a), MPD(b), &status); - Py_DECREF(a); - Py_DECREF(b); - if (r == INT_MAX) { - /* sNaNs or op={le,ge,lt,gt} always signal. */ - if (a_issnan || b_issnan || (op != Py_EQ && op != Py_NE)) { - if (dec_addstatus(context, status)) { - return NULL; - } - } - /* qNaN comparison with op={eq,ne} or comparison - * with InvalidOperation disabled. */ - return (op == Py_NE) ? incr_true() : incr_false(); - } - - switch (op) { - case Py_EQ: - r = (r == 0); - break; - case Py_NE: - r = (r != 0); - break; - case Py_LE: - r = (r <= 0); - break; - case Py_GE: - r = (r >= 0); - break; - case Py_LT: - r = (r == -1); - break; - case Py_GT: - r = (r == 1); - break; - } - - return PyBool_FromLong(r); -} - -/* __ceil__ */ -static PyObject * -dec_ceil(PyObject *self, PyObject *dummy UNUSED) -{ - PyObject *context; - - CURRENT_CONTEXT(context); - return dec_as_long(self, context, MPD_ROUND_CEILING); -} - -/* __complex__ */ -static PyObject * -dec_complex(PyObject *self, PyObject *dummy UNUSED) -{ - PyObject *f; - double x; - - f = PyDec_AsFloat(self); - if (f == NULL) { - return NULL; - } - - x = PyFloat_AsDouble(f); - Py_DECREF(f); - if (x == -1.0 && PyErr_Occurred()) { - return NULL; - } - - return PyComplex_FromDoubles(x, 0); -} - -/* __copy__ and __deepcopy__ */ -static PyObject * -dec_copy(PyObject *self, PyObject *dummy UNUSED) -{ - Py_INCREF(self); - return self; -} - -/* __floor__ */ -static PyObject * -dec_floor(PyObject *self, PyObject *dummy UNUSED) -{ - PyObject *context; - - CURRENT_CONTEXT(context); - return dec_as_long(self, context, MPD_ROUND_FLOOR); -} - -/* Always uses the module context */ -static Py_hash_t -_dec_hash(PyDecObject *v) -{ -#if defined(CONFIG_64) && _PyHASH_BITS == 61 - /* 2**61 - 1 */ - mpd_uint_t p_data[1] = {2305843009213693951ULL}; - mpd_t p = {MPD_POS|MPD_STATIC|MPD_CONST_DATA, 0, 19, 1, 1, p_data}; - /* Inverse of 10 modulo p */ - mpd_uint_t inv10_p_data[1] = {2075258708292324556ULL}; - mpd_t inv10_p = {MPD_POS|MPD_STATIC|MPD_CONST_DATA, - 0, 19, 1, 1, inv10_p_data}; -#elif defined(CONFIG_32) && _PyHASH_BITS == 31 - /* 2**31 - 1 */ - mpd_uint_t p_data[2] = {147483647UL, 2}; - mpd_t p = {MPD_POS|MPD_STATIC|MPD_CONST_DATA, 0, 10, 2, 2, p_data}; - /* Inverse of 10 modulo p */ - mpd_uint_t inv10_p_data[2] = {503238553UL, 1}; - mpd_t inv10_p = {MPD_POS|MPD_STATIC|MPD_CONST_DATA, - 0, 10, 2, 2, inv10_p_data}; -#else - #error "No valid combination of CONFIG_64, CONFIG_32 and _PyHASH_BITS" -#endif - const Py_hash_t py_hash_inf = 314159; - const Py_hash_t py_hash_nan = 0; - mpd_uint_t ten_data[1] = {10}; - mpd_t ten = {MPD_POS|MPD_STATIC|MPD_CONST_DATA, - 0, 2, 1, 1, ten_data}; - Py_hash_t result; - mpd_t *exp_hash = NULL; - mpd_t *tmp = NULL; - mpd_ssize_t exp; - uint32_t status = 0; - mpd_context_t maxctx; - PyObject *context; - - - context = current_context(); - if (context == NULL) { - return -1; - } - Py_DECREF(context); - - if (mpd_isspecial(MPD(v))) { - if (mpd_issnan(MPD(v))) { - PyErr_SetString(PyExc_TypeError, - "Cannot hash a signaling NaN value"); - return -1; - } - else if (mpd_isnan(MPD(v))) { - return py_hash_nan; - } - else { - return py_hash_inf * mpd_arith_sign(MPD(v)); - } - } - - mpd_maxcontext(&maxctx); - exp_hash = mpd_qnew(); - if (exp_hash == NULL) { - goto malloc_error; - } - tmp = mpd_qnew(); - if (tmp == NULL) { - goto malloc_error; - } - - /* - * exp(v): exponent of v - * int(v): coefficient of v - */ - exp = MPD(v)->exp; - if (exp >= 0) { - /* 10**exp(v) % p */ - mpd_qsset_ssize(tmp, exp, &maxctx, &status); - mpd_qpowmod(exp_hash, &ten, tmp, &p, &maxctx, &status); - } - else { - /* inv10_p**(-exp(v)) % p */ - mpd_qsset_ssize(tmp, -exp, &maxctx, &status); - mpd_qpowmod(exp_hash, &inv10_p, tmp, &p, &maxctx, &status); - } - - /* hash = (int(v) * exp_hash) % p */ - if (!mpd_qcopy(tmp, MPD(v), &status)) { - goto malloc_error; - } - tmp->exp = 0; - mpd_set_positive(tmp); - - maxctx.prec = MPD_MAX_PREC + 21; - maxctx.emax = MPD_MAX_EMAX + 21; - maxctx.emin = MPD_MIN_EMIN - 21; - - mpd_qmul(tmp, tmp, exp_hash, &maxctx, &status); - mpd_qrem(tmp, tmp, &p, &maxctx, &status); - - result = mpd_qget_ssize(tmp, &status); - result = mpd_ispositive(MPD(v)) ? result : -result; - result = (result == -1) ? -2 : result; - - if (status != 0) { - if (status & MPD_Malloc_error) { - goto malloc_error; - } - else { - PyErr_SetString(PyExc_RuntimeError, /* GCOV_NOT_REACHED */ - "dec_hash: internal error: please report"); /* GCOV_NOT_REACHED */ - } - result = -1; /* GCOV_NOT_REACHED */ - } - - -finish: - if (exp_hash) mpd_del(exp_hash); - if (tmp) mpd_del(tmp); - return result; - -malloc_error: - PyErr_NoMemory(); - result = -1; - goto finish; -} - -static Py_hash_t -dec_hash(PyDecObject *self) -{ - if (self->hash == -1) { - self->hash = _dec_hash(self); - } - - return self->hash; -} - -/* __reduce__ */ -static PyObject * -dec_reduce(PyObject *self, PyObject *dummy UNUSED) -{ - PyObject *result, *str; - - str = dec_str(self); - if (str == NULL) { - return NULL; - } - - result = Py_BuildValue("O(O)", Py_TYPE(self), str); - Py_DECREF(str); - - return result; -} - -/* __sizeof__ */ -static PyObject * -dec_sizeof(PyObject *v, PyObject *dummy UNUSED) -{ - Py_ssize_t res; - - res = _PyObject_SIZE(Py_TYPE(v)); - if (mpd_isdynamic_data(MPD(v))) { - res += MPD(v)->alloc * sizeof(mpd_uint_t); - } - return PyLong_FromSsize_t(res); -} - -/* __trunc__ */ -static PyObject * -dec_trunc(PyObject *self, PyObject *dummy UNUSED) -{ - PyObject *context; - - CURRENT_CONTEXT(context); - return dec_as_long(self, context, MPD_ROUND_DOWN); -} - -/* real and imag */ -static PyObject * -dec_real(PyObject *self, void *closure UNUSED) -{ - Py_INCREF(self); - return self; -} - -static PyObject * -dec_imag(PyObject *self UNUSED, void *closure UNUSED) -{ - PyObject *result; - - result = dec_alloc(); - if (result == NULL) { - return NULL; - } - - _dec_settriple(result, MPD_POS, 0, 0); - return result; -} - - -static PyGetSetDef dec_getsets [] = -{ - { "real", (getter)dec_real, NULL, NULL, NULL}, - { "imag", (getter)dec_imag, NULL, NULL, NULL}, - {NULL} -}; - -static PyNumberMethods dec_number_methods = -{ - (binaryfunc) nm_mpd_qadd, - (binaryfunc) nm_mpd_qsub, - (binaryfunc) nm_mpd_qmul, - (binaryfunc) nm_mpd_qrem, - (binaryfunc) nm_mpd_qdivmod, - (ternaryfunc) nm_mpd_qpow, - (unaryfunc) nm_mpd_qminus, - (unaryfunc) nm_mpd_qplus, - (unaryfunc) nm_mpd_qabs, - (inquiry) nm_nonzero, - (unaryfunc) 0, /* no bit-complement */ - (binaryfunc) 0, /* no shiftl */ - (binaryfunc) 0, /* no shiftr */ - (binaryfunc) 0, /* no bit-and */ - (binaryfunc) 0, /* no bit-xor */ - (binaryfunc) 0, /* no bit-ior */ - (unaryfunc) nm_dec_as_long, - 0, /* nb_reserved */ - (unaryfunc) PyDec_AsFloat, - 0, /* binaryfunc nb_inplace_add; */ - 0, /* binaryfunc nb_inplace_subtract; */ - 0, /* binaryfunc nb_inplace_multiply; */ - 0, /* binaryfunc nb_inplace_remainder; */ - 0, /* ternaryfunc nb_inplace_power; */ - 0, /* binaryfunc nb_inplace_lshift; */ - 0, /* binaryfunc nb_inplace_rshift; */ - 0, /* binaryfunc nb_inplace_and; */ - 0, /* binaryfunc nb_inplace_xor; */ - 0, /* binaryfunc nb_inplace_or; */ - (binaryfunc) nm_mpd_qdivint, /* binaryfunc nb_floor_divide; */ - (binaryfunc) nm_mpd_qdiv, /* binaryfunc nb_true_divide; */ - 0, /* binaryfunc nb_inplace_floor_divide; */ - 0, /* binaryfunc nb_inplace_true_divide; */ -}; - -static PyMethodDef dec_methods [] = -{ - /* Unary arithmetic functions, optional context arg */ - { "exp", (PyCFunction)(void(*)(void))dec_mpd_qexp, METH_VARARGS|METH_KEYWORDS, doc_exp }, - { "ln", (PyCFunction)(void(*)(void))dec_mpd_qln, METH_VARARGS|METH_KEYWORDS, doc_ln }, - { "log10", (PyCFunction)(void(*)(void))dec_mpd_qlog10, METH_VARARGS|METH_KEYWORDS, doc_log10 }, - { "next_minus", (PyCFunction)(void(*)(void))dec_mpd_qnext_minus, METH_VARARGS|METH_KEYWORDS, doc_next_minus }, - { "next_plus", (PyCFunction)(void(*)(void))dec_mpd_qnext_plus, METH_VARARGS|METH_KEYWORDS, doc_next_plus }, - { "normalize", (PyCFunction)(void(*)(void))dec_mpd_qreduce, METH_VARARGS|METH_KEYWORDS, doc_normalize }, - { "to_integral", (PyCFunction)(void(*)(void))PyDec_ToIntegralValue, METH_VARARGS|METH_KEYWORDS, doc_to_integral }, - { "to_integral_exact", (PyCFunction)(void(*)(void))PyDec_ToIntegralExact, METH_VARARGS|METH_KEYWORDS, doc_to_integral_exact }, - { "to_integral_value", (PyCFunction)(void(*)(void))PyDec_ToIntegralValue, METH_VARARGS|METH_KEYWORDS, doc_to_integral_value }, - { "sqrt", (PyCFunction)(void(*)(void))dec_mpd_qsqrt, METH_VARARGS|METH_KEYWORDS, doc_sqrt }, - - /* Binary arithmetic functions, optional context arg */ - { "compare", (PyCFunction)(void(*)(void))dec_mpd_qcompare, METH_VARARGS|METH_KEYWORDS, doc_compare }, - { "compare_signal", (PyCFunction)(void(*)(void))dec_mpd_qcompare_signal, METH_VARARGS|METH_KEYWORDS, doc_compare_signal }, - { "max", (PyCFunction)(void(*)(void))dec_mpd_qmax, METH_VARARGS|METH_KEYWORDS, doc_max }, - { "max_mag", (PyCFunction)(void(*)(void))dec_mpd_qmax_mag, METH_VARARGS|METH_KEYWORDS, doc_max_mag }, - { "min", (PyCFunction)(void(*)(void))dec_mpd_qmin, METH_VARARGS|METH_KEYWORDS, doc_min }, - { "min_mag", (PyCFunction)(void(*)(void))dec_mpd_qmin_mag, METH_VARARGS|METH_KEYWORDS, doc_min_mag }, - { "next_toward", (PyCFunction)(void(*)(void))dec_mpd_qnext_toward, METH_VARARGS|METH_KEYWORDS, doc_next_toward }, - { "quantize", (PyCFunction)(void(*)(void))dec_mpd_qquantize, METH_VARARGS|METH_KEYWORDS, doc_quantize }, - { "remainder_near", (PyCFunction)(void(*)(void))dec_mpd_qrem_near, METH_VARARGS|METH_KEYWORDS, doc_remainder_near }, - - /* Ternary arithmetic functions, optional context arg */ - { "fma", (PyCFunction)(void(*)(void))dec_mpd_qfma, METH_VARARGS|METH_KEYWORDS, doc_fma }, - - /* Boolean functions, no context arg */ - { "is_canonical", dec_mpd_iscanonical, METH_NOARGS, doc_is_canonical }, - { "is_finite", dec_mpd_isfinite, METH_NOARGS, doc_is_finite }, - { "is_infinite", dec_mpd_isinfinite, METH_NOARGS, doc_is_infinite }, - { "is_nan", dec_mpd_isnan, METH_NOARGS, doc_is_nan }, - { "is_qnan", dec_mpd_isqnan, METH_NOARGS, doc_is_qnan }, - { "is_snan", dec_mpd_issnan, METH_NOARGS, doc_is_snan }, - { "is_signed", dec_mpd_issigned, METH_NOARGS, doc_is_signed }, - { "is_zero", dec_mpd_iszero, METH_NOARGS, doc_is_zero }, - - /* Boolean functions, optional context arg */ - { "is_normal", (PyCFunction)(void(*)(void))dec_mpd_isnormal, METH_VARARGS|METH_KEYWORDS, doc_is_normal }, - { "is_subnormal", (PyCFunction)(void(*)(void))dec_mpd_issubnormal, METH_VARARGS|METH_KEYWORDS, doc_is_subnormal }, - - /* Unary functions, no context arg */ - { "adjusted", dec_mpd_adjexp, METH_NOARGS, doc_adjusted }, - { "canonical", dec_canonical, METH_NOARGS, doc_canonical }, - { "conjugate", dec_conjugate, METH_NOARGS, doc_conjugate }, - { "radix", dec_mpd_radix, METH_NOARGS, doc_radix }, - - /* Unary functions, optional context arg for conversion errors */ - { "copy_abs", dec_mpd_qcopy_abs, METH_NOARGS, doc_copy_abs }, - { "copy_negate", dec_mpd_qcopy_negate, METH_NOARGS, doc_copy_negate }, - - /* Unary functions, optional context arg */ - { "logb", (PyCFunction)(void(*)(void))dec_mpd_qlogb, METH_VARARGS|METH_KEYWORDS, doc_logb }, - { "logical_invert", (PyCFunction)(void(*)(void))dec_mpd_qinvert, METH_VARARGS|METH_KEYWORDS, doc_logical_invert }, - { "number_class", (PyCFunction)(void(*)(void))dec_mpd_class, METH_VARARGS|METH_KEYWORDS, doc_number_class }, - { "to_eng_string", (PyCFunction)(void(*)(void))dec_mpd_to_eng, METH_VARARGS|METH_KEYWORDS, doc_to_eng_string }, - - /* Binary functions, optional context arg for conversion errors */ - { "compare_total", (PyCFunction)(void(*)(void))dec_mpd_compare_total, METH_VARARGS|METH_KEYWORDS, doc_compare_total }, - { "compare_total_mag", (PyCFunction)(void(*)(void))dec_mpd_compare_total_mag, METH_VARARGS|METH_KEYWORDS, doc_compare_total_mag }, - { "copy_sign", (PyCFunction)(void(*)(void))dec_mpd_qcopy_sign, METH_VARARGS|METH_KEYWORDS, doc_copy_sign }, - { "same_quantum", (PyCFunction)(void(*)(void))dec_mpd_same_quantum, METH_VARARGS|METH_KEYWORDS, doc_same_quantum }, - - /* Binary functions, optional context arg */ - { "logical_and", (PyCFunction)(void(*)(void))dec_mpd_qand, METH_VARARGS|METH_KEYWORDS, doc_logical_and }, - { "logical_or", (PyCFunction)(void(*)(void))dec_mpd_qor, METH_VARARGS|METH_KEYWORDS, doc_logical_or }, - { "logical_xor", (PyCFunction)(void(*)(void))dec_mpd_qxor, METH_VARARGS|METH_KEYWORDS, doc_logical_xor }, - { "rotate", (PyCFunction)(void(*)(void))dec_mpd_qrotate, METH_VARARGS|METH_KEYWORDS, doc_rotate }, - { "scaleb", (PyCFunction)(void(*)(void))dec_mpd_qscaleb, METH_VARARGS|METH_KEYWORDS, doc_scaleb }, - { "shift", (PyCFunction)(void(*)(void))dec_mpd_qshift, METH_VARARGS|METH_KEYWORDS, doc_shift }, - - /* Miscellaneous */ - { "from_float", dec_from_float, METH_O|METH_CLASS, doc_from_float }, - { "as_tuple", PyDec_AsTuple, METH_NOARGS, doc_as_tuple }, - { "as_integer_ratio", dec_as_integer_ratio, METH_NOARGS, doc_as_integer_ratio }, - - /* Special methods */ - { "__copy__", dec_copy, METH_NOARGS, NULL }, - { "__deepcopy__", dec_copy, METH_O, NULL }, - { "__format__", dec_format, METH_VARARGS, NULL }, - { "__reduce__", dec_reduce, METH_NOARGS, NULL }, - { "__round__", PyDec_Round, METH_VARARGS, NULL }, - { "__ceil__", dec_ceil, METH_NOARGS, NULL }, - { "__floor__", dec_floor, METH_NOARGS, NULL }, - { "__trunc__", dec_trunc, METH_NOARGS, NULL }, - { "__complex__", dec_complex, METH_NOARGS, NULL }, - { "__sizeof__", dec_sizeof, METH_NOARGS, NULL }, - - { NULL, NULL, 1 } -}; - -static PyTypeObject PyDec_Type = -{ - PyVarObject_HEAD_INIT(NULL, 0) - "decimal.Decimal", /* tp_name */ - sizeof(PyDecObject), /* tp_basicsize */ - 0, /* tp_itemsize */ - (destructor) dec_dealloc, /* tp_dealloc */ - 0, /* tp_vectorcall_offset */ - (getattrfunc) 0, /* tp_getattr */ - (setattrfunc) 0, /* tp_setattr */ - 0, /* tp_as_async */ - (reprfunc) dec_repr, /* tp_repr */ - &dec_number_methods, /* tp_as_number */ - 0, /* tp_as_sequence */ - 0, /* tp_as_mapping */ - (hashfunc) dec_hash, /* tp_hash */ - 0, /* tp_call */ - (reprfunc) dec_str, /* tp_str */ - (getattrofunc) PyObject_GenericGetAttr, /* tp_getattro */ - (setattrofunc) 0, /* tp_setattro */ - (PyBufferProcs *) 0, /* tp_as_buffer */ - (Py_TPFLAGS_DEFAULT| - Py_TPFLAGS_BASETYPE), /* tp_flags */ - doc_decimal, /* tp_doc */ - 0, /* tp_traverse */ - 0, /* tp_clear */ - dec_richcompare, /* tp_richcompare */ - 0, /* tp_weaklistoffset */ - 0, /* tp_iter */ - 0, /* tp_iternext */ - dec_methods, /* tp_methods */ - 0, /* tp_members */ - dec_getsets, /* tp_getset */ - 0, /* tp_base */ - 0, /* tp_dict */ - 0, /* tp_descr_get */ - 0, /* tp_descr_set */ - 0, /* tp_dictoffset */ - 0, /* tp_init */ - 0, /* tp_alloc */ - dec_new, /* tp_new */ - PyObject_Del, /* tp_free */ -}; - - -/******************************************************************************/ -/* Context Object, Part 2 */ -/******************************************************************************/ - - -/************************************************************************/ -/* Macros for converting mpdecimal functions to Context methods */ -/************************************************************************/ - -/* Boolean context method. */ -#define DecCtx_BoolFunc(MPDFUNC) \ -static PyObject * \ -ctx_##MPDFUNC(PyObject *context, PyObject *v) \ -{ \ - PyObject *ret; \ - PyObject *a; \ - \ - CONVERT_OP_RAISE(&a, v, context); \ - \ - ret = MPDFUNC(MPD(a), CTX(context)) ? incr_true() : incr_false(); \ - Py_DECREF(a); \ - return ret; \ -} - -/* Boolean context method. MPDFUNC does NOT use a context. */ -#define DecCtx_BoolFunc_NO_CTX(MPDFUNC) \ -static PyObject * \ -ctx_##MPDFUNC(PyObject *context, PyObject *v) \ -{ \ - PyObject *ret; \ - PyObject *a; \ - \ - CONVERT_OP_RAISE(&a, v, context); \ - \ - ret = MPDFUNC(MPD(a)) ? incr_true() : incr_false(); \ - Py_DECREF(a); \ - return ret; \ -} - -/* Unary context method. */ -#define DecCtx_UnaryFunc(MPDFUNC) \ -static PyObject * \ -ctx_##MPDFUNC(PyObject *context, PyObject *v) \ -{ \ - PyObject *result, *a; \ - uint32_t status = 0; \ - \ - CONVERT_OP_RAISE(&a, v, context); \ - \ - if ((result = dec_alloc()) == NULL) { \ - Py_DECREF(a); \ - return NULL; \ - } \ - \ - MPDFUNC(MPD(result), MPD(a), CTX(context), &status); \ - Py_DECREF(a); \ - if (dec_addstatus(context, status)) { \ - Py_DECREF(result); \ - return NULL; \ - } \ - \ - return result; \ -} - -/* Binary context method. */ -#define DecCtx_BinaryFunc(MPDFUNC) \ -static PyObject * \ -ctx_##MPDFUNC(PyObject *context, PyObject *args) \ -{ \ - PyObject *v, *w; \ - PyObject *a, *b; \ - PyObject *result; \ - uint32_t status = 0; \ - \ - if (!PyArg_ParseTuple(args, "OO", &v, &w)) { \ - return NULL; \ - } \ - \ - CONVERT_BINOP_RAISE(&a, &b, v, w, context); \ - \ - if ((result = dec_alloc()) == NULL) { \ - Py_DECREF(a); \ - Py_DECREF(b); \ - return NULL; \ - } \ - \ - MPDFUNC(MPD(result), MPD(a), MPD(b), CTX(context), &status); \ - Py_DECREF(a); \ - Py_DECREF(b); \ - if (dec_addstatus(context, status)) { \ - Py_DECREF(result); \ - return NULL; \ - } \ - \ - return result; \ -} - -/* - * Binary context method. The context is only used for conversion. - * The actual MPDFUNC does NOT take a context arg. - */ -#define DecCtx_BinaryFunc_NO_CTX(MPDFUNC) \ -static PyObject * \ -ctx_##MPDFUNC(PyObject *context, PyObject *args) \ -{ \ - PyObject *v, *w; \ - PyObject *a, *b; \ - PyObject *result; \ - \ - if (!PyArg_ParseTuple(args, "OO", &v, &w)) { \ - return NULL; \ - } \ - \ - CONVERT_BINOP_RAISE(&a, &b, v, w, context); \ - \ - if ((result = dec_alloc()) == NULL) { \ - Py_DECREF(a); \ - Py_DECREF(b); \ - return NULL; \ - } \ - \ - MPDFUNC(MPD(result), MPD(a), MPD(b)); \ - Py_DECREF(a); \ - Py_DECREF(b); \ - \ - return result; \ -} - -/* Ternary context method. */ -#define DecCtx_TernaryFunc(MPDFUNC) \ -static PyObject * \ -ctx_##MPDFUNC(PyObject *context, PyObject *args) \ -{ \ - PyObject *v, *w, *x; \ - PyObject *a, *b, *c; \ - PyObject *result; \ - uint32_t status = 0; \ - \ - if (!PyArg_ParseTuple(args, "OOO", &v, &w, &x)) { \ - return NULL; \ - } \ - \ - CONVERT_TERNOP_RAISE(&a, &b, &c, v, w, x, context); \ - \ - if ((result = dec_alloc()) == NULL) { \ - Py_DECREF(a); \ - Py_DECREF(b); \ - Py_DECREF(c); \ - return NULL; \ - } \ - \ - MPDFUNC(MPD(result), MPD(a), MPD(b), MPD(c), CTX(context), &status); \ - Py_DECREF(a); \ - Py_DECREF(b); \ - Py_DECREF(c); \ - if (dec_addstatus(context, status)) { \ - Py_DECREF(result); \ - return NULL; \ - } \ - \ - return result; \ -} - - -/* Unary arithmetic functions */ -DecCtx_UnaryFunc(mpd_qabs) -DecCtx_UnaryFunc(mpd_qexp) -DecCtx_UnaryFunc(mpd_qln) -DecCtx_UnaryFunc(mpd_qlog10) -DecCtx_UnaryFunc(mpd_qminus) -DecCtx_UnaryFunc(mpd_qnext_minus) -DecCtx_UnaryFunc(mpd_qnext_plus) -DecCtx_UnaryFunc(mpd_qplus) -DecCtx_UnaryFunc(mpd_qreduce) -DecCtx_UnaryFunc(mpd_qround_to_int) -DecCtx_UnaryFunc(mpd_qround_to_intx) -DecCtx_UnaryFunc(mpd_qsqrt) - -/* Binary arithmetic functions */ -DecCtx_BinaryFunc(mpd_qadd) -DecCtx_BinaryFunc(mpd_qcompare) -DecCtx_BinaryFunc(mpd_qcompare_signal) -DecCtx_BinaryFunc(mpd_qdiv) -DecCtx_BinaryFunc(mpd_qdivint) -DecCtx_BinaryFunc(mpd_qmax) -DecCtx_BinaryFunc(mpd_qmax_mag) -DecCtx_BinaryFunc(mpd_qmin) -DecCtx_BinaryFunc(mpd_qmin_mag) -DecCtx_BinaryFunc(mpd_qmul) -DecCtx_BinaryFunc(mpd_qnext_toward) -DecCtx_BinaryFunc(mpd_qquantize) -DecCtx_BinaryFunc(mpd_qrem) -DecCtx_BinaryFunc(mpd_qrem_near) -DecCtx_BinaryFunc(mpd_qsub) - -static PyObject * -ctx_mpd_qdivmod(PyObject *context, PyObject *args) -{ - PyObject *v, *w; - PyObject *a, *b; - PyObject *q, *r; - uint32_t status = 0; - PyObject *ret; - - if (!PyArg_ParseTuple(args, "OO", &v, &w)) { - return NULL; - } - - CONVERT_BINOP_RAISE(&a, &b, v, w, context); - - q = dec_alloc(); - if (q == NULL) { - Py_DECREF(a); - Py_DECREF(b); - return NULL; - } - r = dec_alloc(); - if (r == NULL) { - Py_DECREF(a); - Py_DECREF(b); - Py_DECREF(q); - return NULL; - } - - mpd_qdivmod(MPD(q), MPD(r), MPD(a), MPD(b), CTX(context), &status); - Py_DECREF(a); - Py_DECREF(b); - if (dec_addstatus(context, status)) { - Py_DECREF(r); - Py_DECREF(q); - return NULL; - } - - ret = Py_BuildValue("(OO)", q, r); - Py_DECREF(r); - Py_DECREF(q); - return ret; -} - -/* Binary or ternary arithmetic functions */ -static PyObject * -ctx_mpd_qpow(PyObject *context, PyObject *args, PyObject *kwds) -{ - static char *kwlist[] = {"a", "b", "modulo", NULL}; - PyObject *base, *exp, *mod = Py_None; - PyObject *a, *b, *c = NULL; - PyObject *result; - uint32_t status = 0; - - if (!PyArg_ParseTupleAndKeywords(args, kwds, "OO|O", kwlist, - &base, &exp, &mod)) { - return NULL; - } - - CONVERT_BINOP_RAISE(&a, &b, base, exp, context); - - if (mod != Py_None) { - if (!convert_op(TYPE_ERR, &c, mod, context)) { - Py_DECREF(a); - Py_DECREF(b); - return c; - } - } - - result = dec_alloc(); - if (result == NULL) { - Py_DECREF(a); - Py_DECREF(b); - Py_XDECREF(c); - return NULL; - } - - if (c == NULL) { - mpd_qpow(MPD(result), MPD(a), MPD(b), - CTX(context), &status); - } - else { - mpd_qpowmod(MPD(result), MPD(a), MPD(b), MPD(c), - CTX(context), &status); - Py_DECREF(c); - } - Py_DECREF(a); - Py_DECREF(b); - if (dec_addstatus(context, status)) { - Py_DECREF(result); - return NULL; - } - - return result; -} - -/* Ternary arithmetic functions */ -DecCtx_TernaryFunc(mpd_qfma) - -/* No argument */ -static PyObject * -ctx_mpd_radix(PyObject *context, PyObject *dummy) -{ - return dec_mpd_radix(context, dummy); -} - -/* Boolean functions: single decimal argument */ -DecCtx_BoolFunc(mpd_isnormal) -DecCtx_BoolFunc(mpd_issubnormal) -DecCtx_BoolFunc_NO_CTX(mpd_isfinite) -DecCtx_BoolFunc_NO_CTX(mpd_isinfinite) -DecCtx_BoolFunc_NO_CTX(mpd_isnan) -DecCtx_BoolFunc_NO_CTX(mpd_isqnan) -DecCtx_BoolFunc_NO_CTX(mpd_issigned) -DecCtx_BoolFunc_NO_CTX(mpd_issnan) -DecCtx_BoolFunc_NO_CTX(mpd_iszero) - -static PyObject * -ctx_iscanonical(PyObject *context UNUSED, PyObject *v) -{ - if (!PyDec_Check(v)) { - PyErr_SetString(PyExc_TypeError, - "argument must be a Decimal"); - return NULL; - } - - return mpd_iscanonical(MPD(v)) ? incr_true() : incr_false(); -} - -/* Functions with a single decimal argument */ -static PyObject * -PyDecContext_Apply(PyObject *context, PyObject *v) -{ - PyObject *result, *a; - - CONVERT_OP_RAISE(&a, v, context); - - result = dec_apply(a, context); - Py_DECREF(a); - return result; -} - -static PyObject * -ctx_canonical(PyObject *context UNUSED, PyObject *v) -{ - if (!PyDec_Check(v)) { - PyErr_SetString(PyExc_TypeError, - "argument must be a Decimal"); - return NULL; - } - - Py_INCREF(v); - return v; -} - -static PyObject * -ctx_mpd_qcopy_abs(PyObject *context, PyObject *v) -{ - PyObject *result, *a; - uint32_t status = 0; - - CONVERT_OP_RAISE(&a, v, context); - - result = dec_alloc(); - if (result == NULL) { - Py_DECREF(a); - return NULL; - } - - mpd_qcopy_abs(MPD(result), MPD(a), &status); - Py_DECREF(a); - if (dec_addstatus(context, status)) { - Py_DECREF(result); - return NULL; - } - - return result; -} - -static PyObject * -ctx_copy_decimal(PyObject *context, PyObject *v) -{ - PyObject *result; - - CONVERT_OP_RAISE(&result, v, context); - return result; -} - -static PyObject * -ctx_mpd_qcopy_negate(PyObject *context, PyObject *v) -{ - PyObject *result, *a; - uint32_t status = 0; - - CONVERT_OP_RAISE(&a, v, context); - - result = dec_alloc(); - if (result == NULL) { - Py_DECREF(a); - return NULL; - } - - mpd_qcopy_negate(MPD(result), MPD(a), &status); - Py_DECREF(a); - if (dec_addstatus(context, status)) { - Py_DECREF(result); - return NULL; - } - - return result; -} - -DecCtx_UnaryFunc(mpd_qlogb) -DecCtx_UnaryFunc(mpd_qinvert) - -static PyObject * -ctx_mpd_class(PyObject *context, PyObject *v) -{ - PyObject *a; - const char *cp; - - CONVERT_OP_RAISE(&a, v, context); - - cp = mpd_class(MPD(a), CTX(context)); - Py_DECREF(a); - - return PyUnicode_FromString(cp); -} - -static PyObject * -ctx_mpd_to_sci(PyObject *context, PyObject *v) -{ - PyObject *result; - PyObject *a; - mpd_ssize_t size; - char *s; - - CONVERT_OP_RAISE(&a, v, context); - - size = mpd_to_sci_size(&s, MPD(a), CtxCaps(context)); - Py_DECREF(a); - if (size < 0) { - PyErr_NoMemory(); - return NULL; - } - - result = unicode_fromascii(s, size); - mpd_free(s); - - return result; -} - -static PyObject * -ctx_mpd_to_eng(PyObject *context, PyObject *v) -{ - PyObject *result; - PyObject *a; - mpd_ssize_t size; - char *s; - - CONVERT_OP_RAISE(&a, v, context); - - size = mpd_to_eng_size(&s, MPD(a), CtxCaps(context)); - Py_DECREF(a); - if (size < 0) { - PyErr_NoMemory(); - return NULL; - } - - result = unicode_fromascii(s, size); - mpd_free(s); - - return result; -} - -/* Functions with two decimal arguments */ -DecCtx_BinaryFunc_NO_CTX(mpd_compare_total) -DecCtx_BinaryFunc_NO_CTX(mpd_compare_total_mag) - -static PyObject * -ctx_mpd_qcopy_sign(PyObject *context, PyObject *args) -{ - PyObject *v, *w; - PyObject *a, *b; - PyObject *result; - uint32_t status = 0; - - if (!PyArg_ParseTuple(args, "OO", &v, &w)) { - return NULL; - } - - CONVERT_BINOP_RAISE(&a, &b, v, w, context); - - result = dec_alloc(); - if (result == NULL) { - Py_DECREF(a); - Py_DECREF(b); - return NULL; - } - - mpd_qcopy_sign(MPD(result), MPD(a), MPD(b), &status); - Py_DECREF(a); - Py_DECREF(b); - if (dec_addstatus(context, status)) { - Py_DECREF(result); - return NULL; - } - - return result; -} - -DecCtx_BinaryFunc(mpd_qand) -DecCtx_BinaryFunc(mpd_qor) -DecCtx_BinaryFunc(mpd_qxor) - -DecCtx_BinaryFunc(mpd_qrotate) -DecCtx_BinaryFunc(mpd_qscaleb) -DecCtx_BinaryFunc(mpd_qshift) - -static PyObject * -ctx_mpd_same_quantum(PyObject *context, PyObject *args) -{ - PyObject *v, *w; - PyObject *a, *b; - PyObject *result; - - if (!PyArg_ParseTuple(args, "OO", &v, &w)) { - return NULL; - } - - CONVERT_BINOP_RAISE(&a, &b, v, w, context); - - result = mpd_same_quantum(MPD(a), MPD(b)) ? incr_true() : incr_false(); - Py_DECREF(a); - Py_DECREF(b); - - return result; -} - - -static PyMethodDef context_methods [] = -{ - /* Unary arithmetic functions */ - { "abs", ctx_mpd_qabs, METH_O, doc_ctx_abs }, - { "exp", ctx_mpd_qexp, METH_O, doc_ctx_exp }, - { "ln", ctx_mpd_qln, METH_O, doc_ctx_ln }, - { "log10", ctx_mpd_qlog10, METH_O, doc_ctx_log10 }, - { "minus", ctx_mpd_qminus, METH_O, doc_ctx_minus }, - { "next_minus", ctx_mpd_qnext_minus, METH_O, doc_ctx_next_minus }, - { "next_plus", ctx_mpd_qnext_plus, METH_O, doc_ctx_next_plus }, - { "normalize", ctx_mpd_qreduce, METH_O, doc_ctx_normalize }, - { "plus", ctx_mpd_qplus, METH_O, doc_ctx_plus }, - { "to_integral", ctx_mpd_qround_to_int, METH_O, doc_ctx_to_integral }, - { "to_integral_exact", ctx_mpd_qround_to_intx, METH_O, doc_ctx_to_integral_exact }, - { "to_integral_value", ctx_mpd_qround_to_int, METH_O, doc_ctx_to_integral_value }, - { "sqrt", ctx_mpd_qsqrt, METH_O, doc_ctx_sqrt }, - - /* Binary arithmetic functions */ - { "add", ctx_mpd_qadd, METH_VARARGS, doc_ctx_add }, - { "compare", ctx_mpd_qcompare, METH_VARARGS, doc_ctx_compare }, - { "compare_signal", ctx_mpd_qcompare_signal, METH_VARARGS, doc_ctx_compare_signal }, - { "divide", ctx_mpd_qdiv, METH_VARARGS, doc_ctx_divide }, - { "divide_int", ctx_mpd_qdivint, METH_VARARGS, doc_ctx_divide_int }, - { "divmod", ctx_mpd_qdivmod, METH_VARARGS, doc_ctx_divmod }, - { "max", ctx_mpd_qmax, METH_VARARGS, doc_ctx_max }, - { "max_mag", ctx_mpd_qmax_mag, METH_VARARGS, doc_ctx_max_mag }, - { "min", ctx_mpd_qmin, METH_VARARGS, doc_ctx_min }, - { "min_mag", ctx_mpd_qmin_mag, METH_VARARGS, doc_ctx_min_mag }, - { "multiply", ctx_mpd_qmul, METH_VARARGS, doc_ctx_multiply }, - { "next_toward", ctx_mpd_qnext_toward, METH_VARARGS, doc_ctx_next_toward }, - { "quantize", ctx_mpd_qquantize, METH_VARARGS, doc_ctx_quantize }, - { "remainder", ctx_mpd_qrem, METH_VARARGS, doc_ctx_remainder }, - { "remainder_near", ctx_mpd_qrem_near, METH_VARARGS, doc_ctx_remainder_near }, - { "subtract", ctx_mpd_qsub, METH_VARARGS, doc_ctx_subtract }, - - /* Binary or ternary arithmetic functions */ - { "power", (PyCFunction)(void(*)(void))ctx_mpd_qpow, METH_VARARGS|METH_KEYWORDS, doc_ctx_power }, - - /* Ternary arithmetic functions */ - { "fma", ctx_mpd_qfma, METH_VARARGS, doc_ctx_fma }, - - /* No argument */ - { "Etiny", context_getetiny, METH_NOARGS, doc_ctx_Etiny }, - { "Etop", context_getetop, METH_NOARGS, doc_ctx_Etop }, - { "radix", ctx_mpd_radix, METH_NOARGS, doc_ctx_radix }, - - /* Boolean functions */ - { "is_canonical", ctx_iscanonical, METH_O, doc_ctx_is_canonical }, - { "is_finite", ctx_mpd_isfinite, METH_O, doc_ctx_is_finite }, - { "is_infinite", ctx_mpd_isinfinite, METH_O, doc_ctx_is_infinite }, - { "is_nan", ctx_mpd_isnan, METH_O, doc_ctx_is_nan }, - { "is_normal", ctx_mpd_isnormal, METH_O, doc_ctx_is_normal }, - { "is_qnan", ctx_mpd_isqnan, METH_O, doc_ctx_is_qnan }, - { "is_signed", ctx_mpd_issigned, METH_O, doc_ctx_is_signed }, - { "is_snan", ctx_mpd_issnan, METH_O, doc_ctx_is_snan }, - { "is_subnormal", ctx_mpd_issubnormal, METH_O, doc_ctx_is_subnormal }, - { "is_zero", ctx_mpd_iszero, METH_O, doc_ctx_is_zero }, - - /* Functions with a single decimal argument */ - { "_apply", PyDecContext_Apply, METH_O, NULL }, /* alias for apply */ -#ifdef EXTRA_FUNCTIONALITY - { "apply", PyDecContext_Apply, METH_O, doc_ctx_apply }, -#endif - { "canonical", ctx_canonical, METH_O, doc_ctx_canonical }, - { "copy_abs", ctx_mpd_qcopy_abs, METH_O, doc_ctx_copy_abs }, - { "copy_decimal", ctx_copy_decimal, METH_O, doc_ctx_copy_decimal }, - { "copy_negate", ctx_mpd_qcopy_negate, METH_O, doc_ctx_copy_negate }, - { "logb", ctx_mpd_qlogb, METH_O, doc_ctx_logb }, - { "logical_invert", ctx_mpd_qinvert, METH_O, doc_ctx_logical_invert }, - { "number_class", ctx_mpd_class, METH_O, doc_ctx_number_class }, - { "to_sci_string", ctx_mpd_to_sci, METH_O, doc_ctx_to_sci_string }, - { "to_eng_string", ctx_mpd_to_eng, METH_O, doc_ctx_to_eng_string }, - - /* Functions with two decimal arguments */ - { "compare_total", ctx_mpd_compare_total, METH_VARARGS, doc_ctx_compare_total }, - { "compare_total_mag", ctx_mpd_compare_total_mag, METH_VARARGS, doc_ctx_compare_total_mag }, - { "copy_sign", ctx_mpd_qcopy_sign, METH_VARARGS, doc_ctx_copy_sign }, - { "logical_and", ctx_mpd_qand, METH_VARARGS, doc_ctx_logical_and }, - { "logical_or", ctx_mpd_qor, METH_VARARGS, doc_ctx_logical_or }, - { "logical_xor", ctx_mpd_qxor, METH_VARARGS, doc_ctx_logical_xor }, - { "rotate", ctx_mpd_qrotate, METH_VARARGS, doc_ctx_rotate }, - { "same_quantum", ctx_mpd_same_quantum, METH_VARARGS, doc_ctx_same_quantum }, - { "scaleb", ctx_mpd_qscaleb, METH_VARARGS, doc_ctx_scaleb }, - { "shift", ctx_mpd_qshift, METH_VARARGS, doc_ctx_shift }, - - /* Set context values */ - { "clear_flags", context_clear_flags, METH_NOARGS, doc_ctx_clear_flags }, - { "clear_traps", context_clear_traps, METH_NOARGS, doc_ctx_clear_traps }, - -#ifdef CONFIG_32 - /* Unsafe set functions with relaxed range checks */ - { "_unsafe_setprec", context_unsafe_setprec, METH_O, NULL }, - { "_unsafe_setemin", context_unsafe_setemin, METH_O, NULL }, - { "_unsafe_setemax", context_unsafe_setemax, METH_O, NULL }, -#endif - - /* Miscellaneous */ - { "__copy__", (PyCFunction)context_copy, METH_NOARGS, NULL }, - { "__reduce__", context_reduce, METH_NOARGS, NULL }, - { "copy", (PyCFunction)context_copy, METH_NOARGS, doc_ctx_copy }, - { "create_decimal", ctx_create_decimal, METH_VARARGS, doc_ctx_create_decimal }, - { "create_decimal_from_float", ctx_from_float, METH_O, doc_ctx_create_decimal_from_float }, - - { NULL, NULL, 1 } -}; - -static PyTypeObject PyDecContext_Type = -{ - PyVarObject_HEAD_INIT(NULL, 0) - "decimal.Context", /* tp_name */ - sizeof(PyDecContextObject), /* tp_basicsize */ - 0, /* tp_itemsize */ - (destructor) context_dealloc, /* tp_dealloc */ - 0, /* tp_vectorcall_offset */ - (getattrfunc) 0, /* tp_getattr */ - (setattrfunc) 0, /* tp_setattr */ - 0, /* tp_as_async */ - (reprfunc) context_repr, /* tp_repr */ - 0, /* tp_as_number */ - 0, /* tp_as_sequence */ - 0, /* tp_as_mapping */ - (hashfunc) 0, /* tp_hash */ - 0, /* tp_call */ - 0, /* tp_str */ - (getattrofunc) context_getattr, /* tp_getattro */ - (setattrofunc) context_setattr, /* tp_setattro */ - (PyBufferProcs *) 0, /* tp_as_buffer */ - Py_TPFLAGS_DEFAULT|Py_TPFLAGS_BASETYPE, /* tp_flags */ - doc_context, /* tp_doc */ - 0, /* tp_traverse */ - 0, /* tp_clear */ - 0, /* tp_richcompare */ - 0, /* tp_weaklistoffset */ - 0, /* tp_iter */ - 0, /* tp_iternext */ - context_methods, /* tp_methods */ - 0, /* tp_members */ - context_getsets, /* tp_getset */ - 0, /* tp_base */ - 0, /* tp_dict */ - 0, /* tp_descr_get */ - 0, /* tp_descr_set */ - 0, /* tp_dictoffset */ - context_init, /* tp_init */ - 0, /* tp_alloc */ - context_new, /* tp_new */ - PyObject_Del, /* tp_free */ -}; - - -static PyMethodDef _decimal_methods [] = -{ - { "getcontext", (PyCFunction)PyDec_GetCurrentContext, METH_NOARGS, doc_getcontext}, - { "setcontext", (PyCFunction)PyDec_SetCurrentContext, METH_O, doc_setcontext}, - { "localcontext", (PyCFunction)(void(*)(void))ctxmanager_new, METH_VARARGS|METH_KEYWORDS, doc_localcontext}, -#ifdef EXTRA_FUNCTIONALITY - { "IEEEContext", (PyCFunction)ieee_context, METH_O, doc_ieee_context}, -#endif - { NULL, NULL, 1, NULL } -}; - -static struct PyModuleDef _decimal_module = { - PyModuleDef_HEAD_INIT, - "decimal", - doc__decimal, - -1, - _decimal_methods, - NULL, - NULL, - NULL, - NULL -}; - -struct ssize_constmap { const char *name; mpd_ssize_t val; }; -static struct ssize_constmap ssize_constants [] = { - {"MAX_PREC", MPD_MAX_PREC}, - {"MAX_EMAX", MPD_MAX_EMAX}, - {"MIN_EMIN", MPD_MIN_EMIN}, - {"MIN_ETINY", MPD_MIN_ETINY}, - {NULL} -}; - -struct int_constmap { const char *name; int val; }; -static struct int_constmap int_constants [] = { - /* int constants */ -#ifdef EXTRA_FUNCTIONALITY - {"DECIMAL32", MPD_DECIMAL32}, - {"DECIMAL64", MPD_DECIMAL64}, - {"DECIMAL128", MPD_DECIMAL128}, - {"IEEE_CONTEXT_MAX_BITS", MPD_IEEE_CONTEXT_MAX_BITS}, - /* int condition flags */ - {"DecClamped", MPD_Clamped}, - {"DecConversionSyntax", MPD_Conversion_syntax}, - {"DecDivisionByZero", MPD_Division_by_zero}, - {"DecDivisionImpossible", MPD_Division_impossible}, - {"DecDivisionUndefined", MPD_Division_undefined}, - {"DecFpuError", MPD_Fpu_error}, - {"DecInexact", MPD_Inexact}, - {"DecInvalidContext", MPD_Invalid_context}, - {"DecInvalidOperation", MPD_Invalid_operation}, - {"DecIEEEInvalidOperation", MPD_IEEE_Invalid_operation}, - {"DecMallocError", MPD_Malloc_error}, - {"DecFloatOperation", MPD_Float_operation}, - {"DecOverflow", MPD_Overflow}, - {"DecRounded", MPD_Rounded}, - {"DecSubnormal", MPD_Subnormal}, - {"DecUnderflow", MPD_Underflow}, - {"DecErrors", MPD_Errors}, - {"DecTraps", MPD_Traps}, -#endif - {NULL} -}; - - -#define CHECK_INT(expr) \ - do { if ((expr) < 0) goto error; } while (0) -#define ASSIGN_PTR(result, expr) \ - do { result = (expr); if (result == NULL) goto error; } while (0) -#define CHECK_PTR(expr) \ - do { if ((expr) == NULL) goto error; } while (0) - - -static PyCFunction -cfunc_noargs(PyTypeObject *t, const char *name) -{ - struct PyMethodDef *m; - - if (t->tp_methods == NULL) { - goto error; - } - - for (m = t->tp_methods; m->ml_name != NULL; m++) { - if (strcmp(name, m->ml_name) == 0) { - if (!(m->ml_flags & METH_NOARGS)) { - goto error; - } - return m->ml_meth; - } - } - -error: - PyErr_Format(PyExc_RuntimeError, - "internal error: could not find method %s", name); - return NULL; -} - - -PyMODINIT_FUNC -PyInit__decimal(void) -{ - PyObject *m = NULL; - PyObject *numbers = NULL; - PyObject *Number = NULL; - PyObject *collections = NULL; - PyObject *collections_abc = NULL; - PyObject *MutableMapping = NULL; - PyObject *obj = NULL; - DecCondMap *cm; - struct ssize_constmap *ssize_cm; - struct int_constmap *int_cm; - int i; - - - /* Init libmpdec */ - mpd_traphandler = dec_traphandler; - mpd_mallocfunc = PyMem_Malloc; - mpd_reallocfunc = PyMem_Realloc; - mpd_callocfunc = mpd_callocfunc_em; - mpd_free = PyMem_Free; - mpd_setminalloc(_Py_DEC_MINALLOC); - - /* Init context variable */ - current_context_var = PyContextVar_New("decimal_context", NULL); - if (current_context_var == NULL) { - goto error; - } - - /* Init external C-API functions */ - _py_long_multiply = PyLong_Type.tp_as_number->nb_multiply; - _py_long_floor_divide = PyLong_Type.tp_as_number->nb_floor_divide; - _py_long_power = PyLong_Type.tp_as_number->nb_power; - _py_float_abs = PyFloat_Type.tp_as_number->nb_absolute; - ASSIGN_PTR(_py_float_as_integer_ratio, cfunc_noargs(&PyFloat_Type, - "as_integer_ratio")); - ASSIGN_PTR(_py_long_bit_length, cfunc_noargs(&PyLong_Type, "bit_length")); - - - /* Init types */ - PyDec_Type.tp_base = &PyBaseObject_Type; - PyDecContext_Type.tp_base = &PyBaseObject_Type; - PyDecContextManager_Type.tp_base = &PyBaseObject_Type; - PyDecSignalDictMixin_Type.tp_base = &PyBaseObject_Type; - - CHECK_INT(PyType_Ready(&PyDec_Type)); - CHECK_INT(PyType_Ready(&PyDecContext_Type)); - CHECK_INT(PyType_Ready(&PyDecSignalDictMixin_Type)); - CHECK_INT(PyType_Ready(&PyDecContextManager_Type)); - - ASSIGN_PTR(obj, PyUnicode_FromString("decimal")); - CHECK_INT(PyDict_SetItemString(PyDec_Type.tp_dict, "__module__", obj)); - CHECK_INT(PyDict_SetItemString(PyDecContext_Type.tp_dict, - "__module__", obj)); - Py_CLEAR(obj); - - - /* Numeric abstract base classes */ - ASSIGN_PTR(numbers, PyImport_ImportModule("numbers")); - ASSIGN_PTR(Number, PyObject_GetAttrString(numbers, "Number")); - /* Register Decimal with the Number abstract base class */ - ASSIGN_PTR(obj, PyObject_CallMethod(Number, "register", "(O)", - (PyObject *)&PyDec_Type)); - Py_CLEAR(obj); - /* Rational is a global variable used for fraction comparisons. */ - ASSIGN_PTR(Rational, PyObject_GetAttrString(numbers, "Rational")); - /* Done with numbers, Number */ - Py_CLEAR(numbers); - Py_CLEAR(Number); - - /* DecimalTuple */ - ASSIGN_PTR(collections, PyImport_ImportModule("collections")); - ASSIGN_PTR(DecimalTuple, (PyTypeObject *)PyObject_CallMethod(collections, - "namedtuple", "(ss)", "DecimalTuple", - "sign digits exponent")); - - ASSIGN_PTR(obj, PyUnicode_FromString("decimal")); - CHECK_INT(PyDict_SetItemString(DecimalTuple->tp_dict, "__module__", obj)); - Py_CLEAR(obj); - - /* MutableMapping */ - ASSIGN_PTR(collections_abc, PyImport_ImportModule("collections.abc")); - ASSIGN_PTR(MutableMapping, PyObject_GetAttrString(collections_abc, - "MutableMapping")); - /* Create SignalDict type */ - ASSIGN_PTR(PyDecSignalDict_Type, - (PyTypeObject *)PyObject_CallFunction( - (PyObject *)&PyType_Type, "s(OO){}", - "SignalDict", &PyDecSignalDictMixin_Type, - MutableMapping)); - - /* Done with collections, MutableMapping */ - Py_CLEAR(collections); - Py_CLEAR(collections_abc); - Py_CLEAR(MutableMapping); - - - /* Create the module */ - ASSIGN_PTR(m, PyModule_Create(&_decimal_module)); - - - /* Add types to the module */ - Py_INCREF(&PyDec_Type); - CHECK_INT(PyModule_AddObject(m, "Decimal", (PyObject *)&PyDec_Type)); - Py_INCREF(&PyDecContext_Type); - CHECK_INT(PyModule_AddObject(m, "Context", - (PyObject *)&PyDecContext_Type)); - Py_INCREF(DecimalTuple); - CHECK_INT(PyModule_AddObject(m, "DecimalTuple", (PyObject *)DecimalTuple)); - - - /* Create top level exception */ - ASSIGN_PTR(DecimalException, PyErr_NewException( - "decimal.DecimalException", - PyExc_ArithmeticError, NULL)); - Py_INCREF(DecimalException); - CHECK_INT(PyModule_AddObject(m, "DecimalException", DecimalException)); - - /* Create signal tuple */ - ASSIGN_PTR(SignalTuple, PyTuple_New(SIGNAL_MAP_LEN)); - - /* Add exceptions that correspond to IEEE signals */ - for (i = SIGNAL_MAP_LEN-1; i >= 0; i--) { - PyObject *base; - - cm = signal_map + i; - - switch (cm->flag) { - case MPD_Float_operation: - base = PyTuple_Pack(2, DecimalException, PyExc_TypeError); - break; - case MPD_Division_by_zero: - base = PyTuple_Pack(2, DecimalException, PyExc_ZeroDivisionError); - break; - case MPD_Overflow: - base = PyTuple_Pack(2, signal_map[INEXACT].ex, - signal_map[ROUNDED].ex); - break; - case MPD_Underflow: - base = PyTuple_Pack(3, signal_map[INEXACT].ex, - signal_map[ROUNDED].ex, - signal_map[SUBNORMAL].ex); - break; - default: - base = PyTuple_Pack(1, DecimalException); - break; - } - - if (base == NULL) { - goto error; /* GCOV_NOT_REACHED */ - } - - ASSIGN_PTR(cm->ex, PyErr_NewException(cm->fqname, base, NULL)); - Py_DECREF(base); - - /* add to module */ - Py_INCREF(cm->ex); - CHECK_INT(PyModule_AddObject(m, cm->name, cm->ex)); - - /* add to signal tuple */ - Py_INCREF(cm->ex); - PyTuple_SET_ITEM(SignalTuple, i, cm->ex); - } - - /* - * Unfortunately, InvalidOperation is a signal that comprises - * several conditions, including InvalidOperation! Naming the - * signal IEEEInvalidOperation would prevent the confusion. - */ - cond_map[0].ex = signal_map[0].ex; - - /* Add remaining exceptions, inherit from InvalidOperation */ - for (cm = cond_map+1; cm->name != NULL; cm++) { - PyObject *base; - if (cm->flag == MPD_Division_undefined) { - base = PyTuple_Pack(2, signal_map[0].ex, PyExc_ZeroDivisionError); - } - else { - base = PyTuple_Pack(1, signal_map[0].ex); - } - if (base == NULL) { - goto error; /* GCOV_NOT_REACHED */ - } - - ASSIGN_PTR(cm->ex, PyErr_NewException(cm->fqname, base, NULL)); - Py_DECREF(base); - - Py_INCREF(cm->ex); - CHECK_INT(PyModule_AddObject(m, cm->name, cm->ex)); - } - - - /* Init default context template first */ - ASSIGN_PTR(default_context_template, - PyObject_CallObject((PyObject *)&PyDecContext_Type, NULL)); - Py_INCREF(default_context_template); - CHECK_INT(PyModule_AddObject(m, "DefaultContext", - default_context_template)); - - Py_INCREF(Py_True); - CHECK_INT(PyModule_AddObject(m, "HAVE_THREADS", Py_True)); - - /* Init basic context template */ - ASSIGN_PTR(basic_context_template, - PyObject_CallObject((PyObject *)&PyDecContext_Type, NULL)); - init_basic_context(basic_context_template); - Py_INCREF(basic_context_template); - CHECK_INT(PyModule_AddObject(m, "BasicContext", - basic_context_template)); - - /* Init extended context template */ - ASSIGN_PTR(extended_context_template, - PyObject_CallObject((PyObject *)&PyDecContext_Type, NULL)); - init_extended_context(extended_context_template); - Py_INCREF(extended_context_template); - CHECK_INT(PyModule_AddObject(m, "ExtendedContext", - extended_context_template)); - - - /* Init mpd_ssize_t constants */ - for (ssize_cm = ssize_constants; ssize_cm->name != NULL; ssize_cm++) { - ASSIGN_PTR(obj, PyLong_FromSsize_t(ssize_cm->val)); - CHECK_INT(PyModule_AddObject(m, ssize_cm->name, obj)); - obj = NULL; - } - - /* Init int constants */ - for (int_cm = int_constants; int_cm->name != NULL; int_cm++) { - CHECK_INT(PyModule_AddIntConstant(m, int_cm->name, - int_cm->val)); - } - - /* Init string constants */ - for (i = 0; i < _PY_DEC_ROUND_GUARD; i++) { - ASSIGN_PTR(round_map[i], PyUnicode_InternFromString(mpd_round_string[i])); - Py_INCREF(round_map[i]); - CHECK_INT(PyModule_AddObject(m, mpd_round_string[i], round_map[i])); - } - - /* Add specification version number */ - CHECK_INT(PyModule_AddStringConstant(m, "__version__", "1.70")); - CHECK_INT(PyModule_AddStringConstant(m, "__libmpdec_version__", mpd_version())); - - - return m; - - -error: - Py_CLEAR(obj); /* GCOV_NOT_REACHED */ - Py_CLEAR(numbers); /* GCOV_NOT_REACHED */ - Py_CLEAR(Number); /* GCOV_NOT_REACHED */ - Py_CLEAR(Rational); /* GCOV_NOT_REACHED */ - Py_CLEAR(collections); /* GCOV_NOT_REACHED */ - Py_CLEAR(collections_abc); /* GCOV_NOT_REACHED */ - Py_CLEAR(MutableMapping); /* GCOV_NOT_REACHED */ - Py_CLEAR(SignalTuple); /* GCOV_NOT_REACHED */ - Py_CLEAR(DecimalTuple); /* GCOV_NOT_REACHED */ - Py_CLEAR(default_context_template); /* GCOV_NOT_REACHED */ - Py_CLEAR(basic_context_template); /* GCOV_NOT_REACHED */ - Py_CLEAR(extended_context_template); /* GCOV_NOT_REACHED */ - Py_CLEAR(current_context_var); /* GCOV_NOT_REACHED */ - Py_CLEAR(m); /* GCOV_NOT_REACHED */ - - return NULL; /* GCOV_NOT_REACHED */ -} - - diff --git a/Modules/_decimal/docstrings.h b/Modules/_decimal/docstrings.h deleted file mode 100644 index f7fd6e7..0000000 --- a/Modules/_decimal/docstrings.h +++ /dev/null @@ -1,884 +0,0 @@ -/* - * Copyright (c) 2001-2012 Python Software Foundation. All Rights Reserved. - * Modified and extended by Stefan Krah. - */ - - -#ifndef DOCSTRINGS_H -#define DOCSTRINGS_H - - -#include "pymacro.h" - - -/******************************************************************************/ -/* Module */ -/******************************************************************************/ - - -PyDoc_STRVAR(doc__decimal, -"C decimal arithmetic module"); - -PyDoc_STRVAR(doc_getcontext, -"getcontext($module, /)\n--\n\n\ -Get the current default context.\n\ -\n"); - -PyDoc_STRVAR(doc_setcontext, -"setcontext($module, context, /)\n--\n\n\ -Set a new default context.\n\ -\n"); - -PyDoc_STRVAR(doc_localcontext, -"localcontext($module, /, ctx=None)\n--\n\n\ -Return a context manager that will set the default context to a copy of ctx\n\ -on entry to the with-statement and restore the previous default context when\n\ -exiting the with-statement. If no context is specified, a copy of the current\n\ -default context is used.\n\ -\n"); - -#ifdef EXTRA_FUNCTIONALITY -PyDoc_STRVAR(doc_ieee_context, -"IEEEContext($module, bits, /)\n--\n\n\ -Return a context object initialized to the proper values for one of the\n\ -IEEE interchange formats. The argument must be a multiple of 32 and less\n\ -than IEEE_CONTEXT_MAX_BITS. For the most common values, the constants\n\ -DECIMAL32, DECIMAL64 and DECIMAL128 are provided.\n\ -\n"); -#endif - - -/******************************************************************************/ -/* Decimal Object and Methods */ -/******************************************************************************/ - -PyDoc_STRVAR(doc_decimal, -"Decimal(value=\"0\", context=None)\n--\n\n\ -Construct a new Decimal object. 'value' can be an integer, string, tuple,\n\ -or another Decimal object. If no value is given, return Decimal('0'). The\n\ -context does not affect the conversion and is only passed to determine if\n\ -the InvalidOperation trap is active.\n\ -\n"); - -PyDoc_STRVAR(doc_adjusted, -"adjusted($self, /)\n--\n\n\ -Return the adjusted exponent of the number. Defined as exp + digits - 1.\n\ -\n"); - -PyDoc_STRVAR(doc_as_tuple, -"as_tuple($self, /)\n--\n\n\ -Return a tuple representation of the number.\n\ -\n"); - -PyDoc_STRVAR(doc_as_integer_ratio, -"as_integer_ratio($self, /)\n--\n\n\ -Decimal.as_integer_ratio() -> (int, int)\n\ -\n\ -Return a pair of integers, whose ratio is exactly equal to the original\n\ -Decimal and with a positive denominator. The ratio is in lowest terms.\n\ -Raise OverflowError on infinities and a ValueError on NaNs.\n\ -\n"); - -PyDoc_STRVAR(doc_canonical, -"canonical($self, /)\n--\n\n\ -Return the canonical encoding of the argument. Currently, the encoding\n\ -of a Decimal instance is always canonical, so this operation returns its\n\ -argument unchanged.\n\ -\n"); - -PyDoc_STRVAR(doc_compare, -"compare($self, /, other, context=None)\n--\n\n\ -Compare self to other. Return a decimal value:\n\ -\n\ - a or b is a NaN ==> Decimal('NaN')\n\ - a < b ==> Decimal('-1')\n\ - a == b ==> Decimal('0')\n\ - a > b ==> Decimal('1')\n\ -\n"); - -PyDoc_STRVAR(doc_compare_signal, -"compare_signal($self, /, other, context=None)\n--\n\n\ -Identical to compare, except that all NaNs signal.\n\ -\n"); - -PyDoc_STRVAR(doc_compare_total, -"compare_total($self, /, other, context=None)\n--\n\n\ -Compare two operands using their abstract representation rather than\n\ -their numerical value. Similar to the compare() method, but the result\n\ -gives a total ordering on Decimal instances. Two Decimal instances with\n\ -the same numeric value but different representations compare unequal\n\ -in this ordering:\n\ -\n\ - >>> Decimal('12.0').compare_total(Decimal('12'))\n\ - Decimal('-1')\n\ -\n\ -Quiet and signaling NaNs are also included in the total ordering. The result\n\ -of this function is Decimal('0') if both operands have the same representation,\n\ -Decimal('-1') if the first operand is lower in the total order than the second,\n\ -and Decimal('1') if the first operand is higher in the total order than the\n\ -second operand. See the specification for details of the total order.\n\ -\n\ -This operation is unaffected by context and is quiet: no flags are changed\n\ -and no rounding is performed. As an exception, the C version may raise\n\ -InvalidOperation if the second operand cannot be converted exactly.\n\ -\n"); - -PyDoc_STRVAR(doc_compare_total_mag, -"compare_total_mag($self, /, other, context=None)\n--\n\n\ -Compare two operands using their abstract representation rather than their\n\ -value as in compare_total(), but ignoring the sign of each operand.\n\ -\n\ -x.compare_total_mag(y) is equivalent to x.copy_abs().compare_total(y.copy_abs()).\n\ -\n\ -This operation is unaffected by context and is quiet: no flags are changed\n\ -and no rounding is performed. As an exception, the C version may raise\n\ -InvalidOperation if the second operand cannot be converted exactly.\n\ -\n"); - -PyDoc_STRVAR(doc_conjugate, -"conjugate($self, /)\n--\n\n\ -Return self.\n\ -\n"); - -PyDoc_STRVAR(doc_copy_abs, -"copy_abs($self, /)\n--\n\n\ -Return the absolute value of the argument. This operation is unaffected by\n\ -context and is quiet: no flags are changed and no rounding is performed.\n\ -\n"); - -PyDoc_STRVAR(doc_copy_negate, -"copy_negate($self, /)\n--\n\n\ -Return the negation of the argument. This operation is unaffected by context\n\ -and is quiet: no flags are changed and no rounding is performed.\n\ -\n"); - -PyDoc_STRVAR(doc_copy_sign, -"copy_sign($self, /, other, context=None)\n--\n\n\ -Return a copy of the first operand with the sign set to be the same as the\n\ -sign of the second operand. For example:\n\ -\n\ - >>> Decimal('2.3').copy_sign(Decimal('-1.5'))\n\ - Decimal('-2.3')\n\ -\n\ -This operation is unaffected by context and is quiet: no flags are changed\n\ -and no rounding is performed. As an exception, the C version may raise\n\ -InvalidOperation if the second operand cannot be converted exactly.\n\ -\n"); - -PyDoc_STRVAR(doc_exp, -"exp($self, /, context=None)\n--\n\n\ -Return the value of the (natural) exponential function e**x at the given\n\ -number. The function always uses the ROUND_HALF_EVEN mode and the result\n\ -is correctly rounded.\n\ -\n"); - -PyDoc_STRVAR(doc_from_float, -"from_float($type, f, /)\n--\n\n\ -Class method that converts a float to a decimal number, exactly.\n\ -Since 0.1 is not exactly representable in binary floating point,\n\ -Decimal.from_float(0.1) is not the same as Decimal('0.1').\n\ -\n\ - >>> Decimal.from_float(0.1)\n\ - Decimal('0.1000000000000000055511151231257827021181583404541015625')\n\ - >>> Decimal.from_float(float('nan'))\n\ - Decimal('NaN')\n\ - >>> Decimal.from_float(float('inf'))\n\ - Decimal('Infinity')\n\ - >>> Decimal.from_float(float('-inf'))\n\ - Decimal('-Infinity')\n\ -\n\ -\n"); - -PyDoc_STRVAR(doc_fma, -"fma($self, /, other, third, context=None)\n--\n\n\ -Fused multiply-add. Return self*other+third with no rounding of the\n\ -intermediate product self*other.\n\ -\n\ - >>> Decimal(2).fma(3, 5)\n\ - Decimal('11')\n\ -\n\ -\n"); - -PyDoc_STRVAR(doc_is_canonical, -"is_canonical($self, /)\n--\n\n\ -Return True if the argument is canonical and False otherwise. Currently,\n\ -a Decimal instance is always canonical, so this operation always returns\n\ -True.\n\ -\n"); - -PyDoc_STRVAR(doc_is_finite, -"is_finite($self, /)\n--\n\n\ -Return True if the argument is a finite number, and False if the argument\n\ -is infinite or a NaN.\n\ -\n"); - -PyDoc_STRVAR(doc_is_infinite, -"is_infinite($self, /)\n--\n\n\ -Return True if the argument is either positive or negative infinity and\n\ -False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_is_nan, -"is_nan($self, /)\n--\n\n\ -Return True if the argument is a (quiet or signaling) NaN and False\n\ -otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_is_normal, -"is_normal($self, /, context=None)\n--\n\n\ -Return True if the argument is a normal finite non-zero number with an\n\ -adjusted exponent greater than or equal to Emin. Return False if the\n\ -argument is zero, subnormal, infinite or a NaN.\n\ -\n"); - -PyDoc_STRVAR(doc_is_qnan, -"is_qnan($self, /)\n--\n\n\ -Return True if the argument is a quiet NaN, and False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_is_signed, -"is_signed($self, /)\n--\n\n\ -Return True if the argument has a negative sign and False otherwise.\n\ -Note that both zeros and NaNs can carry signs.\n\ -\n"); - -PyDoc_STRVAR(doc_is_snan, -"is_snan($self, /)\n--\n\n\ -Return True if the argument is a signaling NaN and False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_is_subnormal, -"is_subnormal($self, /, context=None)\n--\n\n\ -Return True if the argument is subnormal, and False otherwise. A number is\n\ -subnormal if it is non-zero, finite, and has an adjusted exponent less\n\ -than Emin.\n\ -\n"); - -PyDoc_STRVAR(doc_is_zero, -"is_zero($self, /)\n--\n\n\ -Return True if the argument is a (positive or negative) zero and False\n\ -otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_ln, -"ln($self, /, context=None)\n--\n\n\ -Return the natural (base e) logarithm of the operand. The function always\n\ -uses the ROUND_HALF_EVEN mode and the result is correctly rounded.\n\ -\n"); - -PyDoc_STRVAR(doc_log10, -"log10($self, /, context=None)\n--\n\n\ -Return the base ten logarithm of the operand. The function always uses the\n\ -ROUND_HALF_EVEN mode and the result is correctly rounded.\n\ -\n"); - -PyDoc_STRVAR(doc_logb, -"logb($self, /, context=None)\n--\n\n\ -For a non-zero number, return the adjusted exponent of the operand as a\n\ -Decimal instance. If the operand is a zero, then Decimal('-Infinity') is\n\ -returned and the DivisionByZero condition is raised. If the operand is\n\ -an infinity then Decimal('Infinity') is returned.\n\ -\n"); - -PyDoc_STRVAR(doc_logical_and, -"logical_and($self, /, other, context=None)\n--\n\n\ -Return the digit-wise 'and' of the two (logical) operands.\n\ -\n"); - -PyDoc_STRVAR(doc_logical_invert, -"logical_invert($self, /, context=None)\n--\n\n\ -Return the digit-wise inversion of the (logical) operand.\n\ -\n"); - -PyDoc_STRVAR(doc_logical_or, -"logical_or($self, /, other, context=None)\n--\n\n\ -Return the digit-wise 'or' of the two (logical) operands.\n\ -\n"); - -PyDoc_STRVAR(doc_logical_xor, -"logical_xor($self, /, other, context=None)\n--\n\n\ -Return the digit-wise 'exclusive or' of the two (logical) operands.\n\ -\n"); - -PyDoc_STRVAR(doc_max, -"max($self, /, other, context=None)\n--\n\n\ -Maximum of self and other. If one operand is a quiet NaN and the other is\n\ -numeric, the numeric operand is returned.\n\ -\n"); - -PyDoc_STRVAR(doc_max_mag, -"max_mag($self, /, other, context=None)\n--\n\n\ -Similar to the max() method, but the comparison is done using the absolute\n\ -values of the operands.\n\ -\n"); - -PyDoc_STRVAR(doc_min, -"min($self, /, other, context=None)\n--\n\n\ -Minimum of self and other. If one operand is a quiet NaN and the other is\n\ -numeric, the numeric operand is returned.\n\ -\n"); - -PyDoc_STRVAR(doc_min_mag, -"min_mag($self, /, other, context=None)\n--\n\n\ -Similar to the min() method, but the comparison is done using the absolute\n\ -values of the operands.\n\ -\n"); - -PyDoc_STRVAR(doc_next_minus, -"next_minus($self, /, context=None)\n--\n\n\ -Return the largest number representable in the given context (or in the\n\ -current default context if no context is given) that is smaller than the\n\ -given operand.\n\ -\n"); - -PyDoc_STRVAR(doc_next_plus, -"next_plus($self, /, context=None)\n--\n\n\ -Return the smallest number representable in the given context (or in the\n\ -current default context if no context is given) that is larger than the\n\ -given operand.\n\ -\n"); - -PyDoc_STRVAR(doc_next_toward, -"next_toward($self, /, other, context=None)\n--\n\n\ -If the two operands are unequal, return the number closest to the first\n\ -operand in the direction of the second operand. If both operands are\n\ -numerically equal, return a copy of the first operand with the sign set\n\ -to be the same as the sign of the second operand.\n\ -\n"); - -PyDoc_STRVAR(doc_normalize, -"normalize($self, /, context=None)\n--\n\n\ -Normalize the number by stripping the rightmost trailing zeros and\n\ -converting any result equal to Decimal('0') to Decimal('0e0'). Used\n\ -for producing canonical values for members of an equivalence class.\n\ -For example, Decimal('32.100') and Decimal('0.321000e+2') both normalize\n\ -to the equivalent value Decimal('32.1').\n\ -\n"); - -PyDoc_STRVAR(doc_number_class, -"number_class($self, /, context=None)\n--\n\n\ -Return a string describing the class of the operand. The returned value\n\ -is one of the following ten strings:\n\ -\n\ - * '-Infinity', indicating that the operand is negative infinity.\n\ - * '-Normal', indicating that the operand is a negative normal number.\n\ - * '-Subnormal', indicating that the operand is negative and subnormal.\n\ - * '-Zero', indicating that the operand is a negative zero.\n\ - * '+Zero', indicating that the operand is a positive zero.\n\ - * '+Subnormal', indicating that the operand is positive and subnormal.\n\ - * '+Normal', indicating that the operand is a positive normal number.\n\ - * '+Infinity', indicating that the operand is positive infinity.\n\ - * 'NaN', indicating that the operand is a quiet NaN (Not a Number).\n\ - * 'sNaN', indicating that the operand is a signaling NaN.\n\ -\n\ -\n"); - -PyDoc_STRVAR(doc_quantize, -"quantize($self, /, exp, rounding=None, context=None)\n--\n\n\ -Return a value equal to the first operand after rounding and having the\n\ -exponent of the second operand.\n\ -\n\ - >>> Decimal('1.41421356').quantize(Decimal('1.000'))\n\ - Decimal('1.414')\n\ -\n\ -Unlike other operations, if the length of the coefficient after the quantize\n\ -operation would be greater than precision, then an InvalidOperation is signaled.\n\ -This guarantees that, unless there is an error condition, the quantized exponent\n\ -is always equal to that of the right-hand operand.\n\ -\n\ -Also unlike other operations, quantize never signals Underflow, even if the\n\ -result is subnormal and inexact.\n\ -\n\ -If the exponent of the second operand is larger than that of the first, then\n\ -rounding may be necessary. In this case, the rounding mode is determined by the\n\ -rounding argument if given, else by the given context argument; if neither\n\ -argument is given, the rounding mode of the current thread's context is used.\n\ -\n"); - -PyDoc_STRVAR(doc_radix, -"radix($self, /)\n--\n\n\ -Return Decimal(10), the radix (base) in which the Decimal class does\n\ -all its arithmetic. Included for compatibility with the specification.\n\ -\n"); - -PyDoc_STRVAR(doc_remainder_near, -"remainder_near($self, /, other, context=None)\n--\n\n\ -Return the remainder from dividing self by other. This differs from\n\ -self % other in that the sign of the remainder is chosen so as to minimize\n\ -its absolute value. More precisely, the return value is self - n * other\n\ -where n is the integer nearest to the exact value of self / other, and\n\ -if two integers are equally near then the even one is chosen.\n\ -\n\ -If the result is zero then its sign will be the sign of self.\n\ -\n"); - -PyDoc_STRVAR(doc_rotate, -"rotate($self, /, other, context=None)\n--\n\n\ -Return the result of rotating the digits of the first operand by an amount\n\ -specified by the second operand. The second operand must be an integer in\n\ -the range -precision through precision. The absolute value of the second\n\ -operand gives the number of places to rotate. If the second operand is\n\ -positive then rotation is to the left; otherwise rotation is to the right.\n\ -The coefficient of the first operand is padded on the left with zeros to\n\ -length precision if necessary. The sign and exponent of the first operand are\n\ -unchanged.\n\ -\n"); - -PyDoc_STRVAR(doc_same_quantum, -"same_quantum($self, /, other, context=None)\n--\n\n\ -Test whether self and other have the same exponent or whether both are NaN.\n\ -\n\ -This operation is unaffected by context and is quiet: no flags are changed\n\ -and no rounding is performed. As an exception, the C version may raise\n\ -InvalidOperation if the second operand cannot be converted exactly.\n\ -\n"); - -PyDoc_STRVAR(doc_scaleb, -"scaleb($self, /, other, context=None)\n--\n\n\ -Return the first operand with the exponent adjusted the second. Equivalently,\n\ -return the first operand multiplied by 10**other. The second operand must be\n\ -an integer.\n\ -\n"); - -PyDoc_STRVAR(doc_shift, -"shift($self, /, other, context=None)\n--\n\n\ -Return the result of shifting the digits of the first operand by an amount\n\ -specified by the second operand. The second operand must be an integer in\n\ -the range -precision through precision. The absolute value of the second\n\ -operand gives the number of places to shift. If the second operand is\n\ -positive, then the shift is to the left; otherwise the shift is to the\n\ -right. Digits shifted into the coefficient are zeros. The sign and exponent\n\ -of the first operand are unchanged.\n\ -\n"); - -PyDoc_STRVAR(doc_sqrt, -"sqrt($self, /, context=None)\n--\n\n\ -Return the square root of the argument to full precision. The result is\n\ -correctly rounded using the ROUND_HALF_EVEN rounding mode.\n\ -\n"); - -PyDoc_STRVAR(doc_to_eng_string, -"to_eng_string($self, /, context=None)\n--\n\n\ -Convert to an engineering-type string. Engineering notation has an exponent\n\ -which is a multiple of 3, so there are up to 3 digits left of the decimal\n\ -place. For example, Decimal('123E+1') is converted to Decimal('1.23E+3').\n\ -\n\ -The value of context.capitals determines whether the exponent sign is lower\n\ -or upper case. Otherwise, the context does not affect the operation.\n\ -\n"); - -PyDoc_STRVAR(doc_to_integral, -"to_integral($self, /, rounding=None, context=None)\n--\n\n\ -Identical to the to_integral_value() method. The to_integral() name has been\n\ -kept for compatibility with older versions.\n\ -\n"); - -PyDoc_STRVAR(doc_to_integral_exact, -"to_integral_exact($self, /, rounding=None, context=None)\n--\n\n\ -Round to the nearest integer, signaling Inexact or Rounded as appropriate if\n\ -rounding occurs. The rounding mode is determined by the rounding parameter\n\ -if given, else by the given context. If neither parameter is given, then the\n\ -rounding mode of the current default context is used.\n\ -\n"); - -PyDoc_STRVAR(doc_to_integral_value, -"to_integral_value($self, /, rounding=None, context=None)\n--\n\n\ -Round to the nearest integer without signaling Inexact or Rounded. The\n\ -rounding mode is determined by the rounding parameter if given, else by\n\ -the given context. If neither parameter is given, then the rounding mode\n\ -of the current default context is used.\n\ -\n"); - - -/******************************************************************************/ -/* Context Object and Methods */ -/******************************************************************************/ - -PyDoc_STRVAR(doc_context, -"Context(prec=None, rounding=None, Emin=None, Emax=None, capitals=None, clamp=None, flags=None, traps=None)\n--\n\n\ -The context affects almost all operations and controls rounding,\n\ -Over/Underflow, raising of exceptions and much more. A new context\n\ -can be constructed as follows:\n\ -\n\ - >>> c = Context(prec=28, Emin=-425000000, Emax=425000000,\n\ - ... rounding=ROUND_HALF_EVEN, capitals=1, clamp=1,\n\ - ... traps=[InvalidOperation, DivisionByZero, Overflow],\n\ - ... flags=[])\n\ - >>>\n\ -\n\ -\n"); - -#ifdef EXTRA_FUNCTIONALITY -PyDoc_STRVAR(doc_ctx_apply, -"apply($self, x, /)\n--\n\n\ -Apply self to Decimal x.\n\ -\n"); -#endif - -PyDoc_STRVAR(doc_ctx_clear_flags, -"clear_flags($self, /)\n--\n\n\ -Reset all flags to False.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_clear_traps, -"clear_traps($self, /)\n--\n\n\ -Set all traps to False.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_copy, -"copy($self, /)\n--\n\n\ -Return a duplicate of the context with all flags cleared.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_copy_decimal, -"copy_decimal($self, x, /)\n--\n\n\ -Return a copy of Decimal x.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_create_decimal, -"create_decimal($self, num=\"0\", /)\n--\n\n\ -Create a new Decimal instance from num, using self as the context. Unlike the\n\ -Decimal constructor, this function observes the context limits.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_create_decimal_from_float, -"create_decimal_from_float($self, f, /)\n--\n\n\ -Create a new Decimal instance from float f. Unlike the Decimal.from_float()\n\ -class method, this function observes the context limits.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_Etiny, -"Etiny($self, /)\n--\n\n\ -Return a value equal to Emin - prec + 1, which is the minimum exponent value\n\ -for subnormal results. When underflow occurs, the exponent is set to Etiny.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_Etop, -"Etop($self, /)\n--\n\n\ -Return a value equal to Emax - prec + 1. This is the maximum exponent\n\ -if the _clamp field of the context is set to 1 (IEEE clamp mode). Etop()\n\ -must not be negative.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_abs, -"abs($self, x, /)\n--\n\n\ -Return the absolute value of x.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_add, -"add($self, x, y, /)\n--\n\n\ -Return the sum of x and y.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_canonical, -"canonical($self, x, /)\n--\n\n\ -Return a new instance of x.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_compare, -"compare($self, x, y, /)\n--\n\n\ -Compare x and y numerically.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_compare_signal, -"compare_signal($self, x, y, /)\n--\n\n\ -Compare x and y numerically. All NaNs signal.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_compare_total, -"compare_total($self, x, y, /)\n--\n\n\ -Compare x and y using their abstract representation.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_compare_total_mag, -"compare_total_mag($self, x, y, /)\n--\n\n\ -Compare x and y using their abstract representation, ignoring sign.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_copy_abs, -"copy_abs($self, x, /)\n--\n\n\ -Return a copy of x with the sign set to 0.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_copy_negate, -"copy_negate($self, x, /)\n--\n\n\ -Return a copy of x with the sign inverted.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_copy_sign, -"copy_sign($self, x, y, /)\n--\n\n\ -Copy the sign from y to x.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_divide, -"divide($self, x, y, /)\n--\n\n\ -Return x divided by y.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_divide_int, -"divide_int($self, x, y, /)\n--\n\n\ -Return x divided by y, truncated to an integer.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_divmod, -"divmod($self, x, y, /)\n--\n\n\ -Return quotient and remainder of the division x / y.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_exp, -"exp($self, x, /)\n--\n\n\ -Return e ** x.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_fma, -"fma($self, x, y, z, /)\n--\n\n\ -Return x multiplied by y, plus z.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_is_canonical, -"is_canonical($self, x, /)\n--\n\n\ -Return True if x is canonical, False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_is_finite, -"is_finite($self, x, /)\n--\n\n\ -Return True if x is finite, False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_is_infinite, -"is_infinite($self, x, /)\n--\n\n\ -Return True if x is infinite, False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_is_nan, -"is_nan($self, x, /)\n--\n\n\ -Return True if x is a qNaN or sNaN, False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_is_normal, -"is_normal($self, x, /)\n--\n\n\ -Return True if x is a normal number, False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_is_qnan, -"is_qnan($self, x, /)\n--\n\n\ -Return True if x is a quiet NaN, False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_is_signed, -"is_signed($self, x, /)\n--\n\n\ -Return True if x is negative, False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_is_snan, -"is_snan($self, x, /)\n--\n\n\ -Return True if x is a signaling NaN, False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_is_subnormal, -"is_subnormal($self, x, /)\n--\n\n\ -Return True if x is subnormal, False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_is_zero, -"is_zero($self, x, /)\n--\n\n\ -Return True if x is a zero, False otherwise.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_ln, -"ln($self, x, /)\n--\n\n\ -Return the natural (base e) logarithm of x.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_log10, -"log10($self, x, /)\n--\n\n\ -Return the base 10 logarithm of x.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_logb, -"logb($self, x, /)\n--\n\n\ -Return the exponent of the magnitude of the operand's MSD.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_logical_and, -"logical_and($self, x, y, /)\n--\n\n\ -Digit-wise and of x and y.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_logical_invert, -"logical_invert($self, x, /)\n--\n\n\ -Invert all digits of x.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_logical_or, -"logical_or($self, x, y, /)\n--\n\n\ -Digit-wise or of x and y.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_logical_xor, -"logical_xor($self, x, y, /)\n--\n\n\ -Digit-wise xor of x and y.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_max, -"max($self, x, y, /)\n--\n\n\ -Compare the values numerically and return the maximum.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_max_mag, -"max_mag($self, x, y, /)\n--\n\n\ -Compare the values numerically with their sign ignored.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_min, -"min($self, x, y, /)\n--\n\n\ -Compare the values numerically and return the minimum.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_min_mag, -"min_mag($self, x, y, /)\n--\n\n\ -Compare the values numerically with their sign ignored.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_minus, -"minus($self, x, /)\n--\n\n\ -Minus corresponds to the unary prefix minus operator in Python, but applies\n\ -the context to the result.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_multiply, -"multiply($self, x, y, /)\n--\n\n\ -Return the product of x and y.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_next_minus, -"next_minus($self, x, /)\n--\n\n\ -Return the largest representable number smaller than x.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_next_plus, -"next_plus($self, x, /)\n--\n\n\ -Return the smallest representable number larger than x.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_next_toward, -"next_toward($self, x, y, /)\n--\n\n\ -Return the number closest to x, in the direction towards y.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_normalize, -"normalize($self, x, /)\n--\n\n\ -Reduce x to its simplest form. Alias for reduce(x).\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_number_class, -"number_class($self, x, /)\n--\n\n\ -Return an indication of the class of x.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_plus, -"plus($self, x, /)\n--\n\n\ -Plus corresponds to the unary prefix plus operator in Python, but applies\n\ -the context to the result.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_power, -"power($self, /, a, b, modulo=None)\n--\n\n\ -Compute a**b. If 'a' is negative, then 'b' must be integral. The result\n\ -will be inexact unless 'a' is integral and the result is finite and can\n\ -be expressed exactly in 'precision' digits. In the Python version the\n\ -result is always correctly rounded, in the C version the result is almost\n\ -always correctly rounded.\n\ -\n\ -If modulo is given, compute (a**b) % modulo. The following restrictions\n\ -hold:\n\ -\n\ - * all three arguments must be integral\n\ - * 'b' must be nonnegative\n\ - * at least one of 'a' or 'b' must be nonzero\n\ - * modulo must be nonzero and less than 10**prec in absolute value\n\ -\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_quantize, -"quantize($self, x, y, /)\n--\n\n\ -Return a value equal to x (rounded), having the exponent of y.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_radix, -"radix($self, /)\n--\n\n\ -Return 10.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_remainder, -"remainder($self, x, y, /)\n--\n\n\ -Return the remainder from integer division. The sign of the result,\n\ -if non-zero, is the same as that of the original dividend.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_remainder_near, -"remainder_near($self, x, y, /)\n--\n\n\ -Return x - y * n, where n is the integer nearest the exact value of x / y\n\ -(if the result is 0 then its sign will be the sign of x).\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_rotate, -"rotate($self, x, y, /)\n--\n\n\ -Return a copy of x, rotated by y places.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_same_quantum, -"same_quantum($self, x, y, /)\n--\n\n\ -Return True if the two operands have the same exponent.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_scaleb, -"scaleb($self, x, y, /)\n--\n\n\ -Return the first operand after adding the second value to its exp.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_shift, -"shift($self, x, y, /)\n--\n\n\ -Return a copy of x, shifted by y places.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_sqrt, -"sqrt($self, x, /)\n--\n\n\ -Square root of a non-negative number to context precision.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_subtract, -"subtract($self, x, y, /)\n--\n\n\ -Return the difference between x and y.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_to_eng_string, -"to_eng_string($self, x, /)\n--\n\n\ -Convert a number to a string, using engineering notation.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_to_integral, -"to_integral($self, x, /)\n--\n\n\ -Identical to to_integral_value(x).\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_to_integral_exact, -"to_integral_exact($self, x, /)\n--\n\n\ -Round to an integer. Signal if the result is rounded or inexact.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_to_integral_value, -"to_integral_value($self, x, /)\n--\n\n\ -Round to an integer.\n\ -\n"); - -PyDoc_STRVAR(doc_ctx_to_sci_string, -"to_sci_string($self, x, /)\n--\n\n\ -Convert a number to a string using scientific notation.\n\ -\n"); - - -#endif /* DOCSTRINGS_H */ - - - diff --git a/Modules/_decimal/libmpdec/README.txt b/Modules/_decimal/libmpdec/README.txt deleted file mode 100644 index dc97820..0000000 --- a/Modules/_decimal/libmpdec/README.txt +++ /dev/null @@ -1,89 +0,0 @@ - - -libmpdec -======== - -libmpdec is a fast C/C++ library for correctly-rounded arbitrary precision -decimal floating point arithmetic. It is a complete implementation of -Mike Cowlishaw/IBM's General Decimal Arithmetic Specification. - - -Files required for the Python _decimal module -============================================= - - Core files for small and medium precision arithmetic - ---------------------------------------------------- - - basearith.{c,h} -> Core arithmetic in base 10**9 or 10**19. - bits.h -> Portable detection of least/most significant one-bit. - constants.{c,h} -> Constants that are used in multiple files. - context.c -> Context functions. - io.{c,h} -> Conversions between mpd_t and ASCII strings, - mpd_t formatting (allows UTF-8 fill character). - mpalloc.{c,h} -> Allocation handlers with overflow detection - and functions for switching between static - and dynamic mpd_t. - mpdecimal.{c,h} -> All (quiet) functions of the specification. - typearith.h -> Fast primitives for double word multiplication, - division etc. - - Visual Studio only: - ~~~~~~~~~~~~~~~~~~~ - vccompat.h -> snprintf <==> sprintf_s and similar things. - vcdiv64.asm -> Double word division used in typearith.h. VS 2008 does - not allow inline asm for x64. Also, it does not provide - an intrinsic for double word division. - - Files for bignum arithmetic: - ---------------------------- - - The following files implement the Fast Number Theoretic Transform - used for multiplying coefficients with more than 1024 words (see - mpdecimal.c: _mpd_fntmul()). - - umodarith.h -> Fast low level routines for unsigned modular arithmetic. - numbertheory.{c,h} -> Routines for setting up the Number Theoretic Transform. - difradix2.{c,h} -> Decimation in frequency transform, used as the - "base case" by the following three files: - - fnt.{c,h} -> Transform arrays up to 4096 words. - sixstep.{c,h} -> Transform larger arrays of length 2**n. - fourstep.{c,h} -> Transform larger arrays of length 3 * 2**n. - - convolute.{c,h} -> Fast convolution using one of the three transform - functions. - transpose.{c,h} -> Transpositions needed for the sixstep algorithm. - crt.{c,h} -> Chinese Remainder Theorem: use information from three - transforms modulo three different primes to get the - final result. - - -Pointers to literature, proofs and more -======================================= - - literature/ - ----------- - - REFERENCES.txt -> List of relevant papers. - bignum.txt -> Explanation of the Fast Number Theoretic Transform (FNT). - fnt.py -> Verify constants used in the FNT; Python demo for the - O(N**2) discrete transform. - - matrix-transform.txt -> Proof for the Matrix Fourier Transform used in - fourstep.c. - six-step.txt -> Show that the algorithm used in sixstep.c is - a variant of the Matrix Fourier Transform. - mulmod-64.txt -> Proof for the mulmod64 algorithm from - umodarith.h. - mulmod-ppro.txt -> Proof for the x87 FPU modular multiplication - from umodarith.h. - umodarith.lisp -> ACL2 proofs for many functions from umodarith.h. - - -Library Author -============== - - Stefan Krah <skrah@bytereef.org> - - - diff --git a/Modules/_decimal/libmpdec/basearith.c b/Modules/_decimal/libmpdec/basearith.c deleted file mode 100644 index dfe1523..0000000 --- a/Modules/_decimal/libmpdec/basearith.c +++ /dev/null @@ -1,657 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdio.h> -#include <stdlib.h> -#include <string.h> -#include <assert.h> -#include "constants.h" -#include "typearith.h" -#include "basearith.h" - - -/*********************************************************************/ -/* Calculations in base MPD_RADIX */ -/*********************************************************************/ - - -/* - * Knuth, TAOCP, Volume 2, 4.3.1: - * w := sum of u (len m) and v (len n) - * n > 0 and m >= n - * The calling function has to handle a possible final carry. - */ -mpd_uint_t -_mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t m, mpd_size_t n) -{ - mpd_uint_t s; - mpd_uint_t carry = 0; - mpd_size_t i; - - assert(n > 0 && m >= n); - - /* add n members of u and v */ - for (i = 0; i < n; i++) { - s = u[i] + (v[i] + carry); - carry = (s < u[i]) | (s >= MPD_RADIX); - w[i] = carry ? s-MPD_RADIX : s; - } - /* if there is a carry, propagate it */ - for (; carry && i < m; i++) { - s = u[i] + carry; - carry = (s == MPD_RADIX); - w[i] = carry ? 0 : s; - } - /* copy the rest of u */ - for (; i < m; i++) { - w[i] = u[i]; - } - - return carry; -} - -/* - * Add the contents of u to w. Carries are propagated further. The caller - * has to make sure that w is big enough. - */ -void -_mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n) -{ - mpd_uint_t s; - mpd_uint_t carry = 0; - mpd_size_t i; - - if (n == 0) return; - - /* add n members of u to w */ - for (i = 0; i < n; i++) { - s = w[i] + (u[i] + carry); - carry = (s < w[i]) | (s >= MPD_RADIX); - w[i] = carry ? s-MPD_RADIX : s; - } - /* if there is a carry, propagate it */ - for (; carry; i++) { - s = w[i] + carry; - carry = (s == MPD_RADIX); - w[i] = carry ? 0 : s; - } -} - -/* - * Add v to w (len m). The calling function has to handle a possible - * final carry. Assumption: m > 0. - */ -mpd_uint_t -_mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v) -{ - mpd_uint_t s; - mpd_uint_t carry; - mpd_size_t i; - - assert(m > 0); - - /* add v to w */ - s = w[0] + v; - carry = (s < v) | (s >= MPD_RADIX); - w[0] = carry ? s-MPD_RADIX : s; - - /* if there is a carry, propagate it */ - for (i = 1; carry && i < m; i++) { - s = w[i] + carry; - carry = (s == MPD_RADIX); - w[i] = carry ? 0 : s; - } - - return carry; -} - -/* Increment u. The calling function has to handle a possible carry. */ -mpd_uint_t -_mpd_baseincr(mpd_uint_t *u, mpd_size_t n) -{ - mpd_uint_t s; - mpd_uint_t carry = 1; - mpd_size_t i; - - assert(n > 0); - - /* if there is a carry, propagate it */ - for (i = 0; carry && i < n; i++) { - s = u[i] + carry; - carry = (s == MPD_RADIX); - u[i] = carry ? 0 : s; - } - - return carry; -} - -/* - * Knuth, TAOCP, Volume 2, 4.3.1: - * w := difference of u (len m) and v (len n). - * number in u >= number in v; - */ -void -_mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t m, mpd_size_t n) -{ - mpd_uint_t d; - mpd_uint_t borrow = 0; - mpd_size_t i; - - assert(m > 0 && n > 0); - - /* subtract n members of v from u */ - for (i = 0; i < n; i++) { - d = u[i] - (v[i] + borrow); - borrow = (u[i] < d); - w[i] = borrow ? d + MPD_RADIX : d; - } - /* if there is a borrow, propagate it */ - for (; borrow && i < m; i++) { - d = u[i] - borrow; - borrow = (u[i] == 0); - w[i] = borrow ? MPD_RADIX-1 : d; - } - /* copy the rest of u */ - for (; i < m; i++) { - w[i] = u[i]; - } -} - -/* - * Subtract the contents of u from w. w is larger than u. Borrows are - * propagated further, but eventually w can absorb the final borrow. - */ -void -_mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n) -{ - mpd_uint_t d; - mpd_uint_t borrow = 0; - mpd_size_t i; - - if (n == 0) return; - - /* subtract n members of u from w */ - for (i = 0; i < n; i++) { - d = w[i] - (u[i] + borrow); - borrow = (w[i] < d); - w[i] = borrow ? d + MPD_RADIX : d; - } - /* if there is a borrow, propagate it */ - for (; borrow; i++) { - d = w[i] - borrow; - borrow = (w[i] == 0); - w[i] = borrow ? MPD_RADIX-1 : d; - } -} - -/* w := product of u (len n) and v (single word) */ -void -_mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v) -{ - mpd_uint_t hi, lo; - mpd_uint_t carry = 0; - mpd_size_t i; - - assert(n > 0); - - for (i=0; i < n; i++) { - - _mpd_mul_words(&hi, &lo, u[i], v); - lo = carry + lo; - if (lo < carry) hi++; - - _mpd_div_words_r(&carry, &w[i], hi, lo); - } - w[i] = carry; -} - -/* - * Knuth, TAOCP, Volume 2, 4.3.1: - * w := product of u (len m) and v (len n) - * w must be initialized to zero - */ -void -_mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t m, mpd_size_t n) -{ - mpd_uint_t hi, lo; - mpd_uint_t carry; - mpd_size_t i, j; - - assert(m > 0 && n > 0); - - for (j=0; j < n; j++) { - carry = 0; - for (i=0; i < m; i++) { - - _mpd_mul_words(&hi, &lo, u[i], v[j]); - lo = w[i+j] + lo; - if (lo < w[i+j]) hi++; - lo = carry + lo; - if (lo < carry) hi++; - - _mpd_div_words_r(&carry, &w[i+j], hi, lo); - } - w[j+m] = carry; - } -} - -/* - * Knuth, TAOCP Volume 2, 4.3.1, exercise 16: - * w := quotient of u (len n) divided by a single word v - */ -mpd_uint_t -_mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v) -{ - mpd_uint_t hi, lo; - mpd_uint_t rem = 0; - mpd_size_t i; - - assert(n > 0); - - for (i=n-1; i != MPD_SIZE_MAX; i--) { - - _mpd_mul_words(&hi, &lo, rem, MPD_RADIX); - lo = u[i] + lo; - if (lo < u[i]) hi++; - - _mpd_div_words(&w[i], &rem, hi, lo, v); - } - - return rem; -} - -/* - * Knuth, TAOCP Volume 2, 4.3.1: - * q, r := quotient and remainder of uconst (len nplusm) - * divided by vconst (len n) - * nplusm >= n - * - * If r is not NULL, r will contain the remainder. If r is NULL, the - * return value indicates if there is a remainder: 1 for true, 0 for - * false. A return value of -1 indicates an error. - */ -int -_mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r, - const mpd_uint_t *uconst, const mpd_uint_t *vconst, - mpd_size_t nplusm, mpd_size_t n) -{ - mpd_uint_t ustatic[MPD_MINALLOC_MAX]; - mpd_uint_t vstatic[MPD_MINALLOC_MAX]; - mpd_uint_t *u = ustatic; - mpd_uint_t *v = vstatic; - mpd_uint_t d, qhat, rhat, w2[2]; - mpd_uint_t hi, lo, x; - mpd_uint_t carry; - mpd_size_t i, j, m; - int retval = 0; - - assert(n > 1 && nplusm >= n); - m = sub_size_t(nplusm, n); - - /* D1: normalize */ - d = MPD_RADIX / (vconst[n-1] + 1); - - if (nplusm >= MPD_MINALLOC_MAX) { - if ((u = mpd_alloc(nplusm+1, sizeof *u)) == NULL) { - return -1; - } - } - if (n >= MPD_MINALLOC_MAX) { - if ((v = mpd_alloc(n+1, sizeof *v)) == NULL) { - mpd_free(u); - return -1; - } - } - - _mpd_shortmul(u, uconst, nplusm, d); - _mpd_shortmul(v, vconst, n, d); - - /* D2: loop */ - for (j=m; j != MPD_SIZE_MAX; j--) { - - /* D3: calculate qhat and rhat */ - rhat = _mpd_shortdiv(w2, u+j+n-1, 2, v[n-1]); - qhat = w2[1] * MPD_RADIX + w2[0]; - - while (1) { - if (qhat < MPD_RADIX) { - _mpd_singlemul(w2, qhat, v[n-2]); - if (w2[1] <= rhat) { - if (w2[1] != rhat || w2[0] <= u[j+n-2]) { - break; - } - } - } - qhat -= 1; - rhat += v[n-1]; - if (rhat < v[n-1] || rhat >= MPD_RADIX) { - break; - } - } - /* D4: multiply and subtract */ - carry = 0; - for (i=0; i <= n; i++) { - - _mpd_mul_words(&hi, &lo, qhat, v[i]); - - lo = carry + lo; - if (lo < carry) hi++; - - _mpd_div_words_r(&hi, &lo, hi, lo); - - x = u[i+j] - lo; - carry = (u[i+j] < x); - u[i+j] = carry ? x+MPD_RADIX : x; - carry += hi; - } - q[j] = qhat; - /* D5: test remainder */ - if (carry) { - q[j] -= 1; - /* D6: add back */ - (void)_mpd_baseadd(u+j, u+j, v, n+1, n); - } - } - - /* D8: unnormalize */ - if (r != NULL) { - _mpd_shortdiv(r, u, n, d); - /* we are not interested in the return value here */ - retval = 0; - } - else { - retval = !_mpd_isallzero(u, n); - } - - -if (u != ustatic) mpd_free(u); -if (v != vstatic) mpd_free(v); -return retval; -} - -/* - * Left shift of src by 'shift' digits; src may equal dest. - * - * dest := area of n mpd_uint_t with space for srcdigits+shift digits. - * src := coefficient with length m. - * - * The case splits in the function are non-obvious. The following - * equations might help: - * - * Let msdigits denote the number of digits in the most significant - * word of src. Then 1 <= msdigits <= rdigits. - * - * 1) shift = q * rdigits + r - * 2) srcdigits = qsrc * rdigits + msdigits - * 3) destdigits = shift + srcdigits - * = q * rdigits + r + qsrc * rdigits + msdigits - * = q * rdigits + (qsrc * rdigits + (r + msdigits)) - * - * The result has q zero words, followed by the coefficient that - * is left-shifted by r. The case r == 0 is trivial. For r > 0, it - * is important to keep in mind that we always read m source words, - * but write m+1 destination words if r + msdigits > rdigits, m words - * otherwise. - */ -void -_mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n, mpd_size_t m, - mpd_size_t shift) -{ -#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__) - /* spurious uninitialized warnings */ - mpd_uint_t l=l, lprev=lprev, h=h; -#else - mpd_uint_t l, lprev, h; -#endif - mpd_uint_t q, r; - mpd_uint_t ph; - - assert(m > 0 && n >= m); - - _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS); - - if (r != 0) { - - ph = mpd_pow10[r]; - - --m; --n; - _mpd_divmod_pow10(&h, &lprev, src[m--], MPD_RDIGITS-r); - if (h != 0) { /* r + msdigits > rdigits <==> h != 0 */ - dest[n--] = h; - } - /* write m-1 shifted words */ - for (; m != MPD_SIZE_MAX; m--,n--) { - _mpd_divmod_pow10(&h, &l, src[m], MPD_RDIGITS-r); - dest[n] = ph * lprev + h; - lprev = l; - } - /* write least significant word */ - dest[q] = ph * lprev; - } - else { - while (--m != MPD_SIZE_MAX) { - dest[m+q] = src[m]; - } - } - - mpd_uint_zero(dest, q); -} - -/* - * Right shift of src by 'shift' digits; src may equal dest. - * Assumption: srcdigits-shift > 0. - * - * dest := area with space for srcdigits-shift digits. - * src := coefficient with length 'slen'. - * - * The case splits in the function rely on the following equations: - * - * Let msdigits denote the number of digits in the most significant - * word of src. Then 1 <= msdigits <= rdigits. - * - * 1) shift = q * rdigits + r - * 2) srcdigits = qsrc * rdigits + msdigits - * 3) destdigits = srcdigits - shift - * = qsrc * rdigits + msdigits - (q * rdigits + r) - * = (qsrc - q) * rdigits + msdigits - r - * - * Since destdigits > 0 and 1 <= msdigits <= rdigits: - * - * 4) qsrc >= q - * 5) qsrc == q ==> msdigits > r - * - * The result has slen-q words if msdigits > r, slen-q-1 words otherwise. - */ -mpd_uint_t -_mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen, - mpd_size_t shift) -{ -#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__) - /* spurious uninitialized warnings */ - mpd_uint_t l=l, h=h, hprev=hprev; /* low, high, previous high */ -#else - mpd_uint_t l, h, hprev; /* low, high, previous high */ -#endif - mpd_uint_t rnd, rest; /* rounding digit, rest */ - mpd_uint_t q, r; - mpd_size_t i, j; - mpd_uint_t ph; - - assert(slen > 0); - - _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS); - - rnd = rest = 0; - if (r != 0) { - - ph = mpd_pow10[MPD_RDIGITS-r]; - - _mpd_divmod_pow10(&hprev, &rest, src[q], r); - _mpd_divmod_pow10(&rnd, &rest, rest, r-1); - - if (rest == 0 && q > 0) { - rest = !_mpd_isallzero(src, q); - } - /* write slen-q-1 words */ - for (j=0,i=q+1; i<slen; i++,j++) { - _mpd_divmod_pow10(&h, &l, src[i], r); - dest[j] = ph * l + hprev; - hprev = h; - } - /* write most significant word */ - if (hprev != 0) { /* always the case if slen==q-1 */ - dest[j] = hprev; - } - } - else { - if (q > 0) { - _mpd_divmod_pow10(&rnd, &rest, src[q-1], MPD_RDIGITS-1); - /* is there any non-zero digit below rnd? */ - if (rest == 0) rest = !_mpd_isallzero(src, q-1); - } - for (j = 0; j < slen-q; j++) { - dest[j] = src[q+j]; - } - } - - /* 0-4 ==> rnd+rest < 0.5 */ - /* 5 ==> rnd+rest == 0.5 */ - /* 6-9 ==> rnd+rest > 0.5 */ - return (rnd == 0 || rnd == 5) ? rnd + !!rest : rnd; -} - - -/*********************************************************************/ -/* Calculations in base b */ -/*********************************************************************/ - -/* - * Add v to w (len m). The calling function has to handle a possible - * final carry. Assumption: m > 0. - */ -mpd_uint_t -_mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v, mpd_uint_t b) -{ - mpd_uint_t s; - mpd_uint_t carry; - mpd_size_t i; - - assert(m > 0); - - /* add v to w */ - s = w[0] + v; - carry = (s < v) | (s >= b); - w[0] = carry ? s-b : s; - - /* if there is a carry, propagate it */ - for (i = 1; carry && i < m; i++) { - s = w[i] + carry; - carry = (s == b); - w[i] = carry ? 0 : s; - } - - return carry; -} - -/* w := product of u (len n) and v (single word). Return carry. */ -mpd_uint_t -_mpd_shortmul_c(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v) -{ - mpd_uint_t hi, lo; - mpd_uint_t carry = 0; - mpd_size_t i; - - assert(n > 0); - - for (i=0; i < n; i++) { - - _mpd_mul_words(&hi, &lo, u[i], v); - lo = carry + lo; - if (lo < carry) hi++; - - _mpd_div_words_r(&carry, &w[i], hi, lo); - } - - return carry; -} - -/* w := product of u (len n) and v (single word) */ -mpd_uint_t -_mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v, mpd_uint_t b) -{ - mpd_uint_t hi, lo; - mpd_uint_t carry = 0; - mpd_size_t i; - - assert(n > 0); - - for (i=0; i < n; i++) { - - _mpd_mul_words(&hi, &lo, u[i], v); - lo = carry + lo; - if (lo < carry) hi++; - - _mpd_div_words(&carry, &w[i], hi, lo, b); - } - - return carry; -} - -/* - * Knuth, TAOCP Volume 2, 4.3.1, exercise 16: - * w := quotient of u (len n) divided by a single word v - */ -mpd_uint_t -_mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v, mpd_uint_t b) -{ - mpd_uint_t hi, lo; - mpd_uint_t rem = 0; - mpd_size_t i; - - assert(n > 0); - - for (i=n-1; i != MPD_SIZE_MAX; i--) { - - _mpd_mul_words(&hi, &lo, rem, b); - lo = u[i] + lo; - if (lo < u[i]) hi++; - - _mpd_div_words(&w[i], &rem, hi, lo, v); - } - - return rem; -} - - - diff --git a/Modules/_decimal/libmpdec/basearith.h b/Modules/_decimal/libmpdec/basearith.h deleted file mode 100644 index 976358a..0000000 --- a/Modules/_decimal/libmpdec/basearith.h +++ /dev/null @@ -1,222 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef BASEARITH_H -#define BASEARITH_H - - -#include "mpdecimal.h" -#include <stdio.h> -#include "typearith.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -mpd_uint_t _mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t m, mpd_size_t n); -void _mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n); -mpd_uint_t _mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v); -mpd_uint_t _mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v, - mpd_uint_t b); -mpd_uint_t _mpd_baseincr(mpd_uint_t *u, mpd_size_t n); -void _mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t m, mpd_size_t n); -void _mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n); -void _mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t m, mpd_size_t n); -void _mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v); -mpd_uint_t _mpd_shortmul_c(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v); -mpd_uint_t _mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v, mpd_uint_t b); -mpd_uint_t _mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v); -mpd_uint_t _mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v, mpd_uint_t b); -int _mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r, const mpd_uint_t *uconst, - const mpd_uint_t *vconst, mpd_size_t nplusm, mpd_size_t n); -void _mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n, - mpd_size_t m, mpd_size_t shift); -mpd_uint_t _mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen, - mpd_size_t shift); - - - -#ifdef CONFIG_64 -extern const mpd_uint_t mprime_rdx; - -/* - * Algorithm from: Division by Invariant Integers using Multiplication, - * T. Granlund and P. L. Montgomery, Proceedings of the SIGPLAN '94 - * Conference on Programming Language Design and Implementation. - * - * http://gmplib.org/~tege/divcnst-pldi94.pdf - * - * Variables from the paper and their translations (See section 8): - * - * N := 64 - * d := MPD_RADIX - * l := 64 - * m' := floor((2**(64+64) - 1)/MPD_RADIX) - 2**64 - * - * Since N-l == 0: - * - * dnorm := d - * n2 := hi - * n10 := lo - * - * ACL2 proof: mpd-div-words-r-correct - */ -static inline void -_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo) -{ - mpd_uint_t n_adj, h, l, t; - mpd_uint_t n1_neg; - - /* n1_neg = if lo >= 2**63 then MPD_UINT_MAX else 0 */ - n1_neg = (lo & (1ULL<<63)) ? MPD_UINT_MAX : 0; - /* n_adj = if lo >= 2**63 then lo+MPD_RADIX else lo */ - n_adj = lo + (n1_neg & MPD_RADIX); - - /* (h, l) = if lo >= 2**63 then m'*(hi+1) else m'*hi */ - _mpd_mul_words(&h, &l, mprime_rdx, hi-n1_neg); - l = l + n_adj; - if (l < n_adj) h++; - t = h + hi; - /* At this point t == qest, with q == qest or q == qest+1: - * 1) 0 <= 2**64*hi + lo - qest*MPD_RADIX < 2*MPD_RADIX - */ - - /* t = 2**64-1 - qest = 2**64 - (qest+1) */ - t = MPD_UINT_MAX - t; - - /* (h, l) = 2**64*MPD_RADIX - (qest+1)*MPD_RADIX */ - _mpd_mul_words(&h, &l, t, MPD_RADIX); - l = l + lo; - if (l < lo) h++; - h += hi; - h -= MPD_RADIX; - /* (h, l) = 2**64*hi + lo - (qest+1)*MPD_RADIX (mod 2**128) - * Case q == qest+1: - * a) h == 0, l == r - * b) q := h - t == qest+1 - * c) r := l - * Case q == qest: - * a) h == MPD_UINT_MAX, l == 2**64-(MPD_RADIX-r) - * b) q := h - t == qest - * c) r := l + MPD_RADIX = r - */ - - *q = (h - t); - *r = l + (MPD_RADIX & h); -} -#else -static inline void -_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo) -{ - _mpd_div_words(q, r, hi, lo, MPD_RADIX); -} -#endif - - -/* Multiply two single base MPD_RADIX words, store result in array w[2]. */ -static inline void -_mpd_singlemul(mpd_uint_t w[2], mpd_uint_t u, mpd_uint_t v) -{ - mpd_uint_t hi, lo; - - _mpd_mul_words(&hi, &lo, u, v); - _mpd_div_words_r(&w[1], &w[0], hi, lo); -} - -/* Multiply u (len 2) and v (len m, 1 <= m <= 2). */ -static inline void -_mpd_mul_2_le2(mpd_uint_t w[4], mpd_uint_t u[2], mpd_uint_t v[2], mpd_ssize_t m) -{ - mpd_uint_t hi, lo; - - _mpd_mul_words(&hi, &lo, u[0], v[0]); - _mpd_div_words_r(&w[1], &w[0], hi, lo); - - _mpd_mul_words(&hi, &lo, u[1], v[0]); - lo = w[1] + lo; - if (lo < w[1]) hi++; - _mpd_div_words_r(&w[2], &w[1], hi, lo); - if (m == 1) return; - - _mpd_mul_words(&hi, &lo, u[0], v[1]); - lo = w[1] + lo; - if (lo < w[1]) hi++; - _mpd_div_words_r(&w[3], &w[1], hi, lo); - - _mpd_mul_words(&hi, &lo, u[1], v[1]); - lo = w[2] + lo; - if (lo < w[2]) hi++; - lo = w[3] + lo; - if (lo < w[3]) hi++; - _mpd_div_words_r(&w[3], &w[2], hi, lo); -} - - -/* - * Test if all words from data[len-1] to data[0] are zero. If len is 0, nothing - * is tested and the coefficient is regarded as "all zero". - */ -static inline int -_mpd_isallzero(const mpd_uint_t *data, mpd_ssize_t len) -{ - while (--len >= 0) { - if (data[len] != 0) return 0; - } - return 1; -} - -/* - * Test if all full words from data[len-1] to data[0] are MPD_RADIX-1 - * (all nines). Return true if len == 0. - */ -static inline int -_mpd_isallnine(const mpd_uint_t *data, mpd_ssize_t len) -{ - while (--len >= 0) { - if (data[len] != MPD_RADIX-1) return 0; - } - return 1; -} - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif /* BASEARITH_H */ - - - diff --git a/Modules/_decimal/libmpdec/bits.h b/Modules/_decimal/libmpdec/bits.h deleted file mode 100644 index b5eaa24..0000000 --- a/Modules/_decimal/libmpdec/bits.h +++ /dev/null @@ -1,192 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef BITS_H -#define BITS_H - - -#include "mpdecimal.h" -#include <stdio.h> - - -/* Check if n is a power of 2. */ -static inline int -ispower2(mpd_size_t n) -{ - return n != 0 && (n & (n-1)) == 0; -} - -#if defined(ANSI) -/* - * Return the most significant bit position of n from 0 to 31 (63). - * Assumptions: n != 0. - */ -static inline int -mpd_bsr(mpd_size_t n) -{ - int pos = 0; - mpd_size_t tmp; - -#ifdef CONFIG_64 - tmp = n >> 32; - if (tmp != 0) { n = tmp; pos += 32; } -#endif - tmp = n >> 16; - if (tmp != 0) { n = tmp; pos += 16; } - tmp = n >> 8; - if (tmp != 0) { n = tmp; pos += 8; } - tmp = n >> 4; - if (tmp != 0) { n = tmp; pos += 4; } - tmp = n >> 2; - if (tmp != 0) { n = tmp; pos += 2; } - tmp = n >> 1; - if (tmp != 0) { n = tmp; pos += 1; } - - return pos + (int)n - 1; -} - -/* - * Return the least significant bit position of n from 0 to 31 (63). - * Assumptions: n != 0. - */ -static inline int -mpd_bsf(mpd_size_t n) -{ - int pos; - -#ifdef CONFIG_64 - pos = 63; - if (n & 0x00000000FFFFFFFFULL) { pos -= 32; } else { n >>= 32; } - if (n & 0x000000000000FFFFULL) { pos -= 16; } else { n >>= 16; } - if (n & 0x00000000000000FFULL) { pos -= 8; } else { n >>= 8; } - if (n & 0x000000000000000FULL) { pos -= 4; } else { n >>= 4; } - if (n & 0x0000000000000003ULL) { pos -= 2; } else { n >>= 2; } - if (n & 0x0000000000000001ULL) { pos -= 1; } -#else - pos = 31; - if (n & 0x000000000000FFFFUL) { pos -= 16; } else { n >>= 16; } - if (n & 0x00000000000000FFUL) { pos -= 8; } else { n >>= 8; } - if (n & 0x000000000000000FUL) { pos -= 4; } else { n >>= 4; } - if (n & 0x0000000000000003UL) { pos -= 2; } else { n >>= 2; } - if (n & 0x0000000000000001UL) { pos -= 1; } -#endif - return pos; -} -/* END ANSI */ - -#elif defined(ASM) -/* - * Bit scan reverse. Assumptions: a != 0. - */ -static inline int -mpd_bsr(mpd_size_t a) -{ - mpd_size_t retval; - - __asm__ ( -#ifdef CONFIG_64 - "bsrq %1, %0\n\t" -#else - "bsr %1, %0\n\t" -#endif - :"=r" (retval) - :"r" (a) - :"cc" - ); - - return (int)retval; -} - -/* - * Bit scan forward. Assumptions: a != 0. - */ -static inline int -mpd_bsf(mpd_size_t a) -{ - mpd_size_t retval; - - __asm__ ( -#ifdef CONFIG_64 - "bsfq %1, %0\n\t" -#else - "bsf %1, %0\n\t" -#endif - :"=r" (retval) - :"r" (a) - :"cc" - ); - - return (int)retval; -} -/* END ASM */ - -#elif defined(MASM) -#include <intrin.h> -/* - * Bit scan reverse. Assumptions: a != 0. - */ -static inline int __cdecl -mpd_bsr(mpd_size_t a) -{ - unsigned long retval; - -#ifdef CONFIG_64 - _BitScanReverse64(&retval, a); -#else - _BitScanReverse(&retval, a); -#endif - - return (int)retval; -} - -/* - * Bit scan forward. Assumptions: a != 0. - */ -static inline int __cdecl -mpd_bsf(mpd_size_t a) -{ - unsigned long retval; - -#ifdef CONFIG_64 - _BitScanForward64(&retval, a); -#else - _BitScanForward(&retval, a); -#endif - - return (int)retval; -} -/* END MASM (_MSC_VER) */ -#else - #error "missing preprocessor definitions" -#endif /* BSR/BSF */ - - -#endif /* BITS_H */ - - - diff --git a/Modules/_decimal/libmpdec/constants.c b/Modules/_decimal/libmpdec/constants.c deleted file mode 100644 index 2c2d5ea..0000000 --- a/Modules/_decimal/libmpdec/constants.c +++ /dev/null @@ -1,132 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdio.h> -#include "constants.h" - - -#if defined(CONFIG_64) - - /* number-theory.c */ - const mpd_uint_t mpd_moduli[3] = { - 18446744069414584321ULL, 18446744056529682433ULL, 18446742974197923841ULL - }; - const mpd_uint_t mpd_roots[3] = {7ULL, 10ULL, 19ULL}; - - /* crt.c */ - const mpd_uint_t INV_P1_MOD_P2 = 18446744055098026669ULL; - const mpd_uint_t INV_P1P2_MOD_P3 = 287064143708160ULL; - const mpd_uint_t LH_P1P2 = 18446744052234715137ULL; /* (P1*P2) % 2^64 */ - const mpd_uint_t UH_P1P2 = 18446744052234715141ULL; /* (P1*P2) / 2^64 */ - - /* transpose.c */ - const mpd_size_t mpd_bits[64] = { - 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, - 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, - 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, - 2147483648ULL, 4294967296ULL, 8589934592ULL, 17179869184ULL, 34359738368ULL, - 68719476736ULL, 137438953472ULL, 274877906944ULL, 549755813888ULL, - 1099511627776ULL, 2199023255552ULL, 4398046511104, 8796093022208ULL, - 17592186044416ULL, 35184372088832ULL, 70368744177664ULL, 140737488355328ULL, - 281474976710656ULL, 562949953421312ULL, 1125899906842624ULL, - 2251799813685248ULL, 4503599627370496ULL, 9007199254740992ULL, - 18014398509481984ULL, 36028797018963968ULL, 72057594037927936ULL, - 144115188075855872ULL, 288230376151711744ULL, 576460752303423488ULL, - 1152921504606846976ULL, 2305843009213693952ULL, 4611686018427387904ULL, - 9223372036854775808ULL - }; - - /* mpdecimal.c */ - const mpd_uint_t mpd_pow10[MPD_RDIGITS+1] = { - 1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000, - 10000000000ULL,100000000000ULL,1000000000000ULL,10000000000000ULL, - 100000000000000ULL,1000000000000000ULL,10000000000000000ULL, - 100000000000000000ULL,1000000000000000000ULL,10000000000000000000ULL - }; - - /* magic number for constant division by MPD_RADIX */ - const mpd_uint_t mprime_rdx = 15581492618384294730ULL; - -#elif defined(CONFIG_32) - - /* number-theory.c */ - const mpd_uint_t mpd_moduli[3] = {2113929217UL, 2013265921UL, 1811939329UL}; - const mpd_uint_t mpd_roots[3] = {5UL, 31UL, 13UL}; - - /* PentiumPro modular multiplication: These constants have to be loaded as - * 80 bit long doubles, which are not supported by certain compilers. */ - const uint32_t mpd_invmoduli[3][3] = { - {4293885170U, 2181570688U, 16352U}, /* ((long double) 1 / 2113929217UL) */ - {1698898177U, 2290649223U, 16352U}, /* ((long double) 1 / 2013265921UL) */ - {2716021846U, 2545165803U, 16352U} /* ((long double) 1 / 1811939329UL) */ - }; - - const float MPD_TWO63 = 9223372036854775808.0; /* 2^63 */ - - /* crt.c */ - const mpd_uint_t INV_P1_MOD_P2 = 2013265901UL; - const mpd_uint_t INV_P1P2_MOD_P3 = 54UL; - const mpd_uint_t LH_P1P2 = 4127195137UL; /* (P1*P2) % 2^32 */ - const mpd_uint_t UH_P1P2 = 990904320UL; /* (P1*P2) / 2^32 */ - - /* transpose.c */ - const mpd_size_t mpd_bits[32] = { - 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, - 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, - 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, - 2147483648UL - }; - - /* mpdecimal.c */ - const mpd_uint_t mpd_pow10[MPD_RDIGITS+1] = { - 1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000 - }; - -#else - #error "CONFIG_64 or CONFIG_32 must be defined." -#endif - -const char *mpd_round_string[MPD_ROUND_GUARD] = { - "ROUND_UP", /* round away from 0 */ - "ROUND_DOWN", /* round toward 0 (truncate) */ - "ROUND_CEILING", /* round toward +infinity */ - "ROUND_FLOOR", /* round toward -infinity */ - "ROUND_HALF_UP", /* 0.5 is rounded up */ - "ROUND_HALF_DOWN", /* 0.5 is rounded down */ - "ROUND_HALF_EVEN", /* 0.5 is rounded to even */ - "ROUND_05UP", /* round zero or five away from 0 */ - "ROUND_TRUNC", /* truncate, but set infinity */ -}; - -const char *mpd_clamp_string[MPD_CLAMP_GUARD] = { - "CLAMP_DEFAULT", - "CLAMP_IEEE_754" -}; - - diff --git a/Modules/_decimal/libmpdec/constants.h b/Modules/_decimal/libmpdec/constants.h deleted file mode 100644 index c0febfc..0000000 --- a/Modules/_decimal/libmpdec/constants.h +++ /dev/null @@ -1,90 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef CONSTANTS_H -#define CONSTANTS_H - - -#include "mpdecimal.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -/* choice of optimized functions */ -#if defined(CONFIG_64) -/* x64 */ - #define MULMOD(a, b) x64_mulmod(a, b, umod) - #define MULMOD2C(a0, a1, w) x64_mulmod2c(a0, a1, w, umod) - #define MULMOD2(a0, b0, a1, b1) x64_mulmod2(a0, b0, a1, b1, umod) - #define POWMOD(base, exp) x64_powmod(base, exp, umod) - #define SETMODULUS(modnum) std_setmodulus(modnum, &umod) - #define SIZE3_NTT(x0, x1, x2, w3table) std_size3_ntt(x0, x1, x2, w3table, umod) -#elif defined(PPRO) -/* PentiumPro (or later) gcc inline asm */ - #define MULMOD(a, b) ppro_mulmod(a, b, &dmod, dinvmod) - #define MULMOD2C(a0, a1, w) ppro_mulmod2c(a0, a1, w, &dmod, dinvmod) - #define MULMOD2(a0, b0, a1, b1) ppro_mulmod2(a0, b0, a1, b1, &dmod, dinvmod) - #define POWMOD(base, exp) ppro_powmod(base, exp, &dmod, dinvmod) - #define SETMODULUS(modnum) ppro_setmodulus(modnum, &umod, &dmod, dinvmod) - #define SIZE3_NTT(x0, x1, x2, w3table) ppro_size3_ntt(x0, x1, x2, w3table, umod, &dmod, dinvmod) -#else - /* ANSI C99 */ - #define MULMOD(a, b) std_mulmod(a, b, umod) - #define MULMOD2C(a0, a1, w) std_mulmod2c(a0, a1, w, umod) - #define MULMOD2(a0, b0, a1, b1) std_mulmod2(a0, b0, a1, b1, umod) - #define POWMOD(base, exp) std_powmod(base, exp, umod) - #define SETMODULUS(modnum) std_setmodulus(modnum, &umod) - #define SIZE3_NTT(x0, x1, x2, w3table) std_size3_ntt(x0, x1, x2, w3table, umod) -#endif - -/* PentiumPro (or later) gcc inline asm */ -extern const float MPD_TWO63; -extern const uint32_t mpd_invmoduli[3][3]; - -enum {P1, P2, P3}; - -extern const mpd_uint_t mpd_moduli[]; -extern const mpd_uint_t mpd_roots[]; -extern const mpd_size_t mpd_bits[]; -extern const mpd_uint_t mpd_pow10[]; - -extern const mpd_uint_t INV_P1_MOD_P2; -extern const mpd_uint_t INV_P1P2_MOD_P3; -extern const mpd_uint_t LH_P1P2; -extern const mpd_uint_t UH_P1P2; - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif /* CONSTANTS_H */ - - - diff --git a/Modules/_decimal/libmpdec/context.c b/Modules/_decimal/libmpdec/context.c deleted file mode 100644 index 24c7b89..0000000 --- a/Modules/_decimal/libmpdec/context.c +++ /dev/null @@ -1,286 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdio.h> -#include <string.h> -#include <signal.h> - - -void -mpd_dflt_traphandler(mpd_context_t *ctx UNUSED) -{ - raise(SIGFPE); -} - -void (* mpd_traphandler)(mpd_context_t *) = mpd_dflt_traphandler; - - -/* Set guaranteed minimum number of coefficient words. The function may - be used once at program start. Setting MPD_MINALLOC to out-of-bounds - values is a catastrophic error, so in that case the function exits rather - than relying on the user to check a return value. */ -void -mpd_setminalloc(mpd_ssize_t n) -{ - static int minalloc_is_set = 0; - - if (minalloc_is_set) { - mpd_err_warn("mpd_setminalloc: ignoring request to set " - "MPD_MINALLOC a second time\n"); - return; - } - if (n < MPD_MINALLOC_MIN || n > MPD_MINALLOC_MAX) { - mpd_err_fatal("illegal value for MPD_MINALLOC"); /* GCOV_NOT_REACHED */ - } - MPD_MINALLOC = n; - minalloc_is_set = 1; -} - -void -mpd_init(mpd_context_t *ctx, mpd_ssize_t prec) -{ - mpd_ssize_t ideal_minalloc; - - mpd_defaultcontext(ctx); - - if (!mpd_qsetprec(ctx, prec)) { - mpd_addstatus_raise(ctx, MPD_Invalid_context); - return; - } - - ideal_minalloc = 2 * ((prec+MPD_RDIGITS-1) / MPD_RDIGITS); - if (ideal_minalloc < MPD_MINALLOC_MIN) ideal_minalloc = MPD_MINALLOC_MIN; - if (ideal_minalloc > MPD_MINALLOC_MAX) ideal_minalloc = MPD_MINALLOC_MAX; - - mpd_setminalloc(ideal_minalloc); -} - -void -mpd_maxcontext(mpd_context_t *ctx) -{ - ctx->prec=MPD_MAX_PREC; - ctx->emax=MPD_MAX_EMAX; - ctx->emin=MPD_MIN_EMIN; - ctx->round=MPD_ROUND_HALF_EVEN; - ctx->traps=MPD_Traps; - ctx->status=0; - ctx->newtrap=0; - ctx->clamp=0; - ctx->allcr=1; -} - -void -mpd_defaultcontext(mpd_context_t *ctx) -{ - ctx->prec=2*MPD_RDIGITS; - ctx->emax=MPD_MAX_EMAX; - ctx->emin=MPD_MIN_EMIN; - ctx->round=MPD_ROUND_HALF_UP; - ctx->traps=MPD_Traps; - ctx->status=0; - ctx->newtrap=0; - ctx->clamp=0; - ctx->allcr=1; -} - -void -mpd_basiccontext(mpd_context_t *ctx) -{ - ctx->prec=9; - ctx->emax=MPD_MAX_EMAX; - ctx->emin=MPD_MIN_EMIN; - ctx->round=MPD_ROUND_HALF_UP; - ctx->traps=MPD_Traps|MPD_Clamped; - ctx->status=0; - ctx->newtrap=0; - ctx->clamp=0; - ctx->allcr=1; -} - -int -mpd_ieee_context(mpd_context_t *ctx, int bits) -{ - if (bits <= 0 || bits > MPD_IEEE_CONTEXT_MAX_BITS || bits % 32) { - return -1; - } - - ctx->prec = 9 * (bits/32) - 2; - ctx->emax = 3 * ((mpd_ssize_t)1<<(bits/16+3)); - ctx->emin = 1 - ctx->emax; - ctx->round=MPD_ROUND_HALF_EVEN; - ctx->traps=0; - ctx->status=0; - ctx->newtrap=0; - ctx->clamp=1; - ctx->allcr=1; - - return 0; -} - -mpd_ssize_t -mpd_getprec(const mpd_context_t *ctx) -{ - return ctx->prec; -} - -mpd_ssize_t -mpd_getemax(const mpd_context_t *ctx) -{ - return ctx->emax; -} - -mpd_ssize_t -mpd_getemin(const mpd_context_t *ctx) -{ - return ctx->emin; -} - -int -mpd_getround(const mpd_context_t *ctx) -{ - return ctx->round; -} - -uint32_t -mpd_gettraps(const mpd_context_t *ctx) -{ - return ctx->traps; -} - -uint32_t -mpd_getstatus(const mpd_context_t *ctx) -{ - return ctx->status; -} - -int -mpd_getclamp(const mpd_context_t *ctx) -{ - return ctx->clamp; -} - -int -mpd_getcr(const mpd_context_t *ctx) -{ - return ctx->allcr; -} - - -int -mpd_qsetprec(mpd_context_t *ctx, mpd_ssize_t prec) -{ - if (prec <= 0 || prec > MPD_MAX_PREC) { - return 0; - } - ctx->prec = prec; - return 1; -} - -int -mpd_qsetemax(mpd_context_t *ctx, mpd_ssize_t emax) -{ - if (emax < 0 || emax > MPD_MAX_EMAX) { - return 0; - } - ctx->emax = emax; - return 1; -} - -int -mpd_qsetemin(mpd_context_t *ctx, mpd_ssize_t emin) -{ - if (emin > 0 || emin < MPD_MIN_EMIN) { - return 0; - } - ctx->emin = emin; - return 1; -} - -int -mpd_qsetround(mpd_context_t *ctx, int round) -{ - if (!(0 <= round && round < MPD_ROUND_GUARD)) { - return 0; - } - ctx->round = round; - return 1; -} - -int -mpd_qsettraps(mpd_context_t *ctx, uint32_t traps) -{ - if (traps > MPD_Max_status) { - return 0; - } - ctx->traps = traps; - return 1; -} - -int -mpd_qsetstatus(mpd_context_t *ctx, uint32_t flags) -{ - if (flags > MPD_Max_status) { - return 0; - } - ctx->status = flags; - return 1; -} - -int -mpd_qsetclamp(mpd_context_t *ctx, int c) -{ - if (c != 0 && c != 1) { - return 0; - } - ctx->clamp = c; - return 1; -} - -int -mpd_qsetcr(mpd_context_t *ctx, int c) -{ - if (c != 0 && c != 1) { - return 0; - } - ctx->allcr = c; - return 1; -} - - -void -mpd_addstatus_raise(mpd_context_t *ctx, uint32_t flags) -{ - ctx->status |= flags; - if (flags&ctx->traps) { - ctx->newtrap = (flags&ctx->traps); - mpd_traphandler(ctx); - } -} - - diff --git a/Modules/_decimal/libmpdec/convolute.c b/Modules/_decimal/libmpdec/convolute.c deleted file mode 100644 index 4c62e8b..0000000 --- a/Modules/_decimal/libmpdec/convolute.c +++ /dev/null @@ -1,174 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdio.h> -#include "bits.h" -#include "constants.h" -#include "fnt.h" -#include "fourstep.h" -#include "numbertheory.h" -#include "sixstep.h" -#include "umodarith.h" -#include "convolute.h" - - -/* Bignum: Fast convolution using the Number Theoretic Transform. Used for - the multiplication of very large coefficients. */ - - -/* Convolute the data in c1 and c2. Result is in c1. */ -int -fnt_convolute(mpd_uint_t *c1, mpd_uint_t *c2, mpd_size_t n, int modnum) -{ - int (*fnt)(mpd_uint_t *, mpd_size_t, int); - int (*inv_fnt)(mpd_uint_t *, mpd_size_t, int); -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t n_inv, umod; - mpd_size_t i; - - - SETMODULUS(modnum); - n_inv = POWMOD(n, (umod-2)); - - if (ispower2(n)) { - if (n > SIX_STEP_THRESHOLD) { - fnt = six_step_fnt; - inv_fnt = inv_six_step_fnt; - } - else { - fnt = std_fnt; - inv_fnt = std_inv_fnt; - } - } - else { - fnt = four_step_fnt; - inv_fnt = inv_four_step_fnt; - } - - if (!fnt(c1, n, modnum)) { - return 0; - } - if (!fnt(c2, n, modnum)) { - return 0; - } - for (i = 0; i < n-1; i += 2) { - mpd_uint_t x0 = c1[i]; - mpd_uint_t y0 = c2[i]; - mpd_uint_t x1 = c1[i+1]; - mpd_uint_t y1 = c2[i+1]; - MULMOD2(&x0, y0, &x1, y1); - c1[i] = x0; - c1[i+1] = x1; - } - - if (!inv_fnt(c1, n, modnum)) { - return 0; - } - for (i = 0; i < n-3; i += 4) { - mpd_uint_t x0 = c1[i]; - mpd_uint_t x1 = c1[i+1]; - mpd_uint_t x2 = c1[i+2]; - mpd_uint_t x3 = c1[i+3]; - MULMOD2C(&x0, &x1, n_inv); - MULMOD2C(&x2, &x3, n_inv); - c1[i] = x0; - c1[i+1] = x1; - c1[i+2] = x2; - c1[i+3] = x3; - } - - return 1; -} - -/* Autoconvolute the data in c1. Result is in c1. */ -int -fnt_autoconvolute(mpd_uint_t *c1, mpd_size_t n, int modnum) -{ - int (*fnt)(mpd_uint_t *, mpd_size_t, int); - int (*inv_fnt)(mpd_uint_t *, mpd_size_t, int); -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t n_inv, umod; - mpd_size_t i; - - - SETMODULUS(modnum); - n_inv = POWMOD(n, (umod-2)); - - if (ispower2(n)) { - if (n > SIX_STEP_THRESHOLD) { - fnt = six_step_fnt; - inv_fnt = inv_six_step_fnt; - } - else { - fnt = std_fnt; - inv_fnt = std_inv_fnt; - } - } - else { - fnt = four_step_fnt; - inv_fnt = inv_four_step_fnt; - } - - if (!fnt(c1, n, modnum)) { - return 0; - } - for (i = 0; i < n-1; i += 2) { - mpd_uint_t x0 = c1[i]; - mpd_uint_t x1 = c1[i+1]; - MULMOD2(&x0, x0, &x1, x1); - c1[i] = x0; - c1[i+1] = x1; - } - - if (!inv_fnt(c1, n, modnum)) { - return 0; - } - for (i = 0; i < n-3; i += 4) { - mpd_uint_t x0 = c1[i]; - mpd_uint_t x1 = c1[i+1]; - mpd_uint_t x2 = c1[i+2]; - mpd_uint_t x3 = c1[i+3]; - MULMOD2C(&x0, &x1, n_inv); - MULMOD2C(&x2, &x3, n_inv); - c1[i] = x0; - c1[i+1] = x1; - c1[i+2] = x2; - c1[i+3] = x3; - } - - return 1; -} - - diff --git a/Modules/_decimal/libmpdec/convolute.h b/Modules/_decimal/libmpdec/convolute.h deleted file mode 100644 index f30a177..0000000 --- a/Modules/_decimal/libmpdec/convolute.h +++ /dev/null @@ -1,50 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef CONVOLUTE_H -#define CONVOLUTE_H - - -#include "mpdecimal.h" -#include <stdio.h> - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -#define SIX_STEP_THRESHOLD 4096 - -int fnt_convolute(mpd_uint_t *c1, mpd_uint_t *c2, mpd_size_t n, int modnum); -int fnt_autoconvolute(mpd_uint_t *c1, mpd_size_t n, int modnum); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif diff --git a/Modules/_decimal/libmpdec/crt.c b/Modules/_decimal/libmpdec/crt.c deleted file mode 100644 index 4a1e80a..0000000 --- a/Modules/_decimal/libmpdec/crt.c +++ /dev/null @@ -1,179 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdio.h> -#include <assert.h> -#include "numbertheory.h" -#include "umodarith.h" -#include "crt.h" - - -/* Bignum: Chinese Remainder Theorem, extends the maximum transform length. */ - - -/* Multiply P1P2 by v, store result in w. */ -static inline void -_crt_mulP1P2_3(mpd_uint_t w[3], mpd_uint_t v) -{ - mpd_uint_t hi1, hi2, lo; - - _mpd_mul_words(&hi1, &lo, LH_P1P2, v); - w[0] = lo; - - _mpd_mul_words(&hi2, &lo, UH_P1P2, v); - lo = hi1 + lo; - if (lo < hi1) hi2++; - - w[1] = lo; - w[2] = hi2; -} - -/* Add 3 words from v to w. The result is known to fit in w. */ -static inline void -_crt_add3(mpd_uint_t w[3], mpd_uint_t v[3]) -{ - mpd_uint_t carry; - mpd_uint_t s; - - s = w[0] + v[0]; - carry = (s < w[0]); - w[0] = s; - - s = w[1] + (v[1] + carry); - carry = (s < w[1]); - w[1] = s; - - w[2] = w[2] + (v[2] + carry); -} - -/* Divide 3 words in u by v, store result in w, return remainder. */ -static inline mpd_uint_t -_crt_div3(mpd_uint_t *w, const mpd_uint_t *u, mpd_uint_t v) -{ - mpd_uint_t r1 = u[2]; - mpd_uint_t r2; - - if (r1 < v) { - w[2] = 0; - } - else { - _mpd_div_word(&w[2], &r1, u[2], v); /* GCOV_NOT_REACHED */ - } - - _mpd_div_words(&w[1], &r2, r1, u[1], v); - _mpd_div_words(&w[0], &r1, r2, u[0], v); - - return r1; -} - - -/* - * Chinese Remainder Theorem: - * Algorithm from Joerg Arndt, "Matters Computational", - * Chapter 37.4.1 [http://www.jjj.de/fxt/] - * - * See also Knuth, TAOCP, Volume 2, 4.3.2, exercise 7. - */ - -/* - * CRT with carry: x1, x2, x3 contain numbers modulo p1, p2, p3. For each - * triple of members of the arrays, find the unique z modulo p1*p2*p3, with - * zmax = p1*p2*p3 - 1. - * - * In each iteration of the loop, split z into result[i] = z % MPD_RADIX - * and carry = z / MPD_RADIX. Let N be the size of carry[] and cmax the - * maximum carry. - * - * Limits for the 32-bit build: - * - * N = 2**96 - * cmax = 7711435591312380274 - * - * Limits for the 64 bit build: - * - * N = 2**192 - * cmax = 627710135393475385904124401220046371710 - * - * The following statements hold for both versions: - * - * 1) cmax + zmax < N, so the addition does not overflow. - * - * 2) (cmax + zmax) / MPD_RADIX == cmax. - * - * 3) If c <= cmax, then c_next = (c + zmax) / MPD_RADIX <= cmax. - */ -void -crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t rsize) -{ - mpd_uint_t p1 = mpd_moduli[P1]; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t a1, a2, a3; - mpd_uint_t s; - mpd_uint_t z[3], t[3]; - mpd_uint_t carry[3] = {0,0,0}; - mpd_uint_t hi, lo; - mpd_size_t i; - - for (i = 0; i < rsize; i++) { - - a1 = x1[i]; - a2 = x2[i]; - a3 = x3[i]; - - SETMODULUS(P2); - s = ext_submod(a2, a1, umod); - s = MULMOD(s, INV_P1_MOD_P2); - - _mpd_mul_words(&hi, &lo, s, p1); - lo = lo + a1; - if (lo < a1) hi++; - - SETMODULUS(P3); - s = dw_submod(a3, hi, lo, umod); - s = MULMOD(s, INV_P1P2_MOD_P3); - - z[0] = lo; - z[1] = hi; - z[2] = 0; - - _crt_mulP1P2_3(t, s); - _crt_add3(z, t); - _crt_add3(carry, z); - - x1[i] = _crt_div3(carry, carry, MPD_RADIX); - } - - assert(carry[0] == 0 && carry[1] == 0 && carry[2] == 0); -} - - diff --git a/Modules/_decimal/libmpdec/crt.h b/Modules/_decimal/libmpdec/crt.h deleted file mode 100644 index f61e772..0000000 --- a/Modules/_decimal/libmpdec/crt.h +++ /dev/null @@ -1,47 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef CRT_H -#define CRT_H - - -#include "mpdecimal.h" -#include <stdio.h> - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -void crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t nmemb); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif diff --git a/Modules/_decimal/libmpdec/difradix2.c b/Modules/_decimal/libmpdec/difradix2.c deleted file mode 100644 index 06e5ab5..0000000 --- a/Modules/_decimal/libmpdec/difradix2.c +++ /dev/null @@ -1,173 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdio.h> -#include <assert.h> -#include "bits.h" -#include "numbertheory.h" -#include "umodarith.h" -#include "difradix2.h" - - -/* Bignum: The actual transform routine (decimation in frequency). */ - - -/* - * Generate index pairs (x, bitreverse(x)) and carry out the permutation. - * n must be a power of two. - * Algorithm due to Brent/Lehmann, see Joerg Arndt, "Matters Computational", - * Chapter 1.14.4. [http://www.jjj.de/fxt/] - */ -static inline void -bitreverse_permute(mpd_uint_t a[], mpd_size_t n) -{ - mpd_size_t x = 0; - mpd_size_t r = 0; - mpd_uint_t t; - - do { /* Invariant: r = bitreverse(x) */ - if (r > x) { - t = a[x]; - a[x] = a[r]; - a[r] = t; - } - /* Flip trailing consecutive 1 bits and the first zero bit - * that absorbs a possible carry. */ - x += 1; - /* Mirror the operation on r: Flip n_trailing_zeros(x)+1 - high bits of r. */ - r ^= (n - (n >> (mpd_bsf(x)+1))); - /* The loop invariant is preserved. */ - } while (x < n); -} - - -/* Fast Number Theoretic Transform, decimation in frequency. */ -void -fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams) -{ - mpd_uint_t *wtable = tparams->wtable; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t u0, u1, v0, v1; - mpd_uint_t w, w0, w1, wstep; - mpd_size_t m, mhalf; - mpd_size_t j, r; - - - assert(ispower2(n)); - assert(n >= 4); - - SETMODULUS(tparams->modnum); - - /* m == n */ - mhalf = n / 2; - for (j = 0; j < mhalf; j += 2) { - - w0 = wtable[j]; - w1 = wtable[j+1]; - - u0 = a[j]; - v0 = a[j+mhalf]; - - u1 = a[j+1]; - v1 = a[j+1+mhalf]; - - a[j] = addmod(u0, v0, umod); - v0 = submod(u0, v0, umod); - - a[j+1] = addmod(u1, v1, umod); - v1 = submod(u1, v1, umod); - - MULMOD2(&v0, w0, &v1, w1); - - a[j+mhalf] = v0; - a[j+1+mhalf] = v1; - - } - - wstep = 2; - for (m = n/2; m >= 2; m>>=1, wstep<<=1) { - - mhalf = m / 2; - - /* j == 0 */ - for (r = 0; r < n; r += 2*m) { - - u0 = a[r]; - v0 = a[r+mhalf]; - - u1 = a[m+r]; - v1 = a[m+r+mhalf]; - - a[r] = addmod(u0, v0, umod); - v0 = submod(u0, v0, umod); - - a[m+r] = addmod(u1, v1, umod); - v1 = submod(u1, v1, umod); - - a[r+mhalf] = v0; - a[m+r+mhalf] = v1; - } - - for (j = 1; j < mhalf; j++) { - - w = wtable[j*wstep]; - - for (r = 0; r < n; r += 2*m) { - - u0 = a[r+j]; - v0 = a[r+j+mhalf]; - - u1 = a[m+r+j]; - v1 = a[m+r+j+mhalf]; - - a[r+j] = addmod(u0, v0, umod); - v0 = submod(u0, v0, umod); - - a[m+r+j] = addmod(u1, v1, umod); - v1 = submod(u1, v1, umod); - - MULMOD2C(&v0, &v1, w); - - a[r+j+mhalf] = v0; - a[m+r+j+mhalf] = v1; - } - - } - - } - - bitreverse_permute(a, n); -} - - diff --git a/Modules/_decimal/libmpdec/difradix2.h b/Modules/_decimal/libmpdec/difradix2.h deleted file mode 100644 index 5e22bcf..0000000 --- a/Modules/_decimal/libmpdec/difradix2.h +++ /dev/null @@ -1,48 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef DIF_RADIX2_H -#define DIF_RADIX2_H - - -#include "mpdecimal.h" -#include <stdio.h> -#include "numbertheory.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -void fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif diff --git a/Modules/_decimal/libmpdec/fnt.c b/Modules/_decimal/libmpdec/fnt.c deleted file mode 100644 index 7e924c8..0000000 --- a/Modules/_decimal/libmpdec/fnt.c +++ /dev/null @@ -1,81 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdio.h> -#include <stdlib.h> -#include <assert.h> -#include "bits.h" -#include "difradix2.h" -#include "numbertheory.h" -#include "fnt.h" - - -/* Bignum: Fast transform for medium-sized coefficients. */ - - -/* forward transform, sign = -1 */ -int -std_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) -{ - struct fnt_params *tparams; - - assert(ispower2(n)); - assert(n >= 4); - assert(n <= 3*MPD_MAXTRANSFORM_2N); - - if ((tparams = _mpd_init_fnt_params(n, -1, modnum)) == NULL) { - return 0; - } - fnt_dif2(a, n, tparams); - - mpd_free(tparams); - return 1; -} - -/* reverse transform, sign = 1 */ -int -std_inv_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) -{ - struct fnt_params *tparams; - - assert(ispower2(n)); - assert(n >= 4); - assert(n <= 3*MPD_MAXTRANSFORM_2N); - - if ((tparams = _mpd_init_fnt_params(n, 1, modnum)) == NULL) { - return 0; - } - fnt_dif2(a, n, tparams); - - mpd_free(tparams); - return 1; -} - - - diff --git a/Modules/_decimal/libmpdec/fnt.h b/Modules/_decimal/libmpdec/fnt.h deleted file mode 100644 index fa2154a..0000000 --- a/Modules/_decimal/libmpdec/fnt.h +++ /dev/null @@ -1,49 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef FNT_H -#define FNT_H - - -#include "mpdecimal.h" -#include <stdio.h> - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -int std_fnt(mpd_uint_t a[], mpd_size_t n, int modnum); -int std_inv_fnt(mpd_uint_t a[], mpd_size_t n, int modnum); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif - diff --git a/Modules/_decimal/libmpdec/fourstep.c b/Modules/_decimal/libmpdec/fourstep.c deleted file mode 100644 index 21d3e74..0000000 --- a/Modules/_decimal/libmpdec/fourstep.c +++ /dev/null @@ -1,257 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <assert.h> -#include "numbertheory.h" -#include "sixstep.h" -#include "transpose.h" -#include "umodarith.h" -#include "fourstep.h" - - -/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the - form 3 * 2**n (See literature/matrix-transform.txt). */ - - -#ifndef PPRO -static inline void -std_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, - mpd_uint_t w3table[3], mpd_uint_t umod) -{ - mpd_uint_t r1, r2; - mpd_uint_t w; - mpd_uint_t s, tmp; - - - /* k = 0 -> w = 1 */ - s = *x1; - s = addmod(s, *x2, umod); - s = addmod(s, *x3, umod); - - r1 = s; - - /* k = 1 */ - s = *x1; - - w = w3table[1]; - tmp = MULMOD(*x2, w); - s = addmod(s, tmp, umod); - - w = w3table[2]; - tmp = MULMOD(*x3, w); - s = addmod(s, tmp, umod); - - r2 = s; - - /* k = 2 */ - s = *x1; - - w = w3table[2]; - tmp = MULMOD(*x2, w); - s = addmod(s, tmp, umod); - - w = w3table[1]; - tmp = MULMOD(*x3, w); - s = addmod(s, tmp, umod); - - *x3 = s; - *x2 = r2; - *x1 = r1; -} -#else /* PPRO */ -static inline void -ppro_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_uint_t w3table[3], - mpd_uint_t umod, double *dmod, uint32_t dinvmod[3]) -{ - mpd_uint_t r1, r2; - mpd_uint_t w; - mpd_uint_t s, tmp; - - - /* k = 0 -> w = 1 */ - s = *x1; - s = addmod(s, *x2, umod); - s = addmod(s, *x3, umod); - - r1 = s; - - /* k = 1 */ - s = *x1; - - w = w3table[1]; - tmp = ppro_mulmod(*x2, w, dmod, dinvmod); - s = addmod(s, tmp, umod); - - w = w3table[2]; - tmp = ppro_mulmod(*x3, w, dmod, dinvmod); - s = addmod(s, tmp, umod); - - r2 = s; - - /* k = 2 */ - s = *x1; - - w = w3table[2]; - tmp = ppro_mulmod(*x2, w, dmod, dinvmod); - s = addmod(s, tmp, umod); - - w = w3table[1]; - tmp = ppro_mulmod(*x3, w, dmod, dinvmod); - s = addmod(s, tmp, umod); - - *x3 = s; - *x2 = r2; - *x1 = r1; -} -#endif - - -/* forward transform, sign = -1; transform length = 3 * 2**n */ -int -four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) -{ - mpd_size_t R = 3; /* number of rows */ - mpd_size_t C = n / 3; /* number of columns */ - mpd_uint_t w3table[3]; - mpd_uint_t kernel, w0, w1, wstep; - mpd_uint_t *s, *p0, *p1, *p2; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_size_t i, k; - - - assert(n >= 48); - assert(n <= 3*MPD_MAXTRANSFORM_2N); - - - /* Length R transform on the columns. */ - SETMODULUS(modnum); - _mpd_init_w3table(w3table, -1, modnum); - for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) { - - SIZE3_NTT(p0, p1, p2, w3table); - } - - /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */ - kernel = _mpd_getkernel(n, -1, modnum); - for (i = 1; i < R; i++) { - w0 = 1; /* r**(i*0): initial value for k=0 */ - w1 = POWMOD(kernel, i); /* r**(i*1): initial value for k=1 */ - wstep = MULMOD(w1, w1); /* r**(2*i) */ - for (k = 0; k < C-1; k += 2) { - mpd_uint_t x0 = a[i*C+k]; - mpd_uint_t x1 = a[i*C+k+1]; - MULMOD2(&x0, w0, &x1, w1); - MULMOD2C(&w0, &w1, wstep); /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */ - a[i*C+k] = x0; - a[i*C+k+1] = x1; - } - } - - /* Length C transform on the rows. */ - for (s = a; s < a+n; s += C) { - if (!six_step_fnt(s, C, modnum)) { - return 0; - } - } - -#if 0 - /* An unordered transform is sufficient for convolution. */ - /* Transpose the matrix. */ - transpose_3xpow2(a, R, C); -#endif - - return 1; -} - -/* backward transform, sign = 1; transform length = 3 * 2**n */ -int -inv_four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) -{ - mpd_size_t R = 3; /* number of rows */ - mpd_size_t C = n / 3; /* number of columns */ - mpd_uint_t w3table[3]; - mpd_uint_t kernel, w0, w1, wstep; - mpd_uint_t *s, *p0, *p1, *p2; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_size_t i, k; - - - assert(n >= 48); - assert(n <= 3*MPD_MAXTRANSFORM_2N); - - -#if 0 - /* An unordered transform is sufficient for convolution. */ - /* Transpose the matrix, producing an R*C matrix. */ - transpose_3xpow2(a, C, R); -#endif - - /* Length C transform on the rows. */ - for (s = a; s < a+n; s += C) { - if (!inv_six_step_fnt(s, C, modnum)) { - return 0; - } - } - - /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */ - SETMODULUS(modnum); - kernel = _mpd_getkernel(n, 1, modnum); - for (i = 1; i < R; i++) { - w0 = 1; - w1 = POWMOD(kernel, i); - wstep = MULMOD(w1, w1); - for (k = 0; k < C; k += 2) { - mpd_uint_t x0 = a[i*C+k]; - mpd_uint_t x1 = a[i*C+k+1]; - MULMOD2(&x0, w0, &x1, w1); - MULMOD2C(&w0, &w1, wstep); - a[i*C+k] = x0; - a[i*C+k+1] = x1; - } - } - - /* Length R transform on the columns. */ - _mpd_init_w3table(w3table, 1, modnum); - for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) { - - SIZE3_NTT(p0, p1, p2, w3table); - } - - return 1; -} - - diff --git a/Modules/_decimal/libmpdec/fourstep.h b/Modules/_decimal/libmpdec/fourstep.h deleted file mode 100644 index 80dcd4b..0000000 --- a/Modules/_decimal/libmpdec/fourstep.h +++ /dev/null @@ -1,48 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef FOUR_STEP_H -#define FOUR_STEP_H - - -#include "mpdecimal.h" -#include <stdio.h> - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -int four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum); -int inv_four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif diff --git a/Modules/_decimal/libmpdec/io.c b/Modules/_decimal/libmpdec/io.c deleted file mode 100644 index f45e558..0000000 --- a/Modules/_decimal/libmpdec/io.c +++ /dev/null @@ -1,1583 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdio.h> -#include <stdlib.h> -#include <string.h> -#include <ctype.h> -#include <limits.h> -#include <assert.h> -#include <errno.h> -#include <locale.h> -#include "bits.h" -#include "constants.h" -#include "typearith.h" -#include "io.h" - - -/* This file contains functions for decimal <-> string conversions, including - PEP-3101 formatting for numeric types. */ - - -/* Disable warning that is part of -Wextra since gcc 7.0. */ -#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && __GNUC__ >= 7 - #pragma GCC diagnostic ignored "-Wimplicit-fallthrough" -#endif - - -/* - * Work around the behavior of tolower() and strcasecmp() in certain - * locales. For example, in tr_TR.utf8: - * - * tolower((unsigned char)'I') == 'I' - * - * u is the exact uppercase version of l; n is strlen(l) or strlen(l)+1 - */ -static inline int -_mpd_strneq(const char *s, const char *l, const char *u, size_t n) -{ - while (--n != SIZE_MAX) { - if (*s != *l && *s != *u) { - return 0; - } - s++; u++; l++; - } - - return 1; -} - -static mpd_ssize_t -strtoexp(const char *s) -{ - char *end; - mpd_ssize_t retval; - - errno = 0; - retval = mpd_strtossize(s, &end, 10); - if (errno == 0 && !(*s != '\0' && *end == '\0')) - errno = EINVAL; - - return retval; -} - -/* - * Scan 'len' words. The most significant word contains 'r' digits, - * the remaining words are full words. Skip dpoint. The string 's' must - * consist of digits and an optional single decimal point at 'dpoint'. - */ -static void -string_to_coeff(mpd_uint_t *data, const char *s, const char *dpoint, int r, - size_t len) -{ - int j; - - if (r > 0) { - data[--len] = 0; - for (j = 0; j < r; j++, s++) { - if (s == dpoint) s++; - data[len] = 10 * data[len] + (*s - '0'); - } - } - - while (--len != SIZE_MAX) { - data[len] = 0; - for (j = 0; j < MPD_RDIGITS; j++, s++) { - if (s == dpoint) s++; - data[len] = 10 * data[len] + (*s - '0'); - } - } -} - -/* - * Partially verify a numeric string of the form: - * - * [cdigits][.][cdigits][eE][+-][edigits] - * - * If successful, return a pointer to the location of the first - * relevant coefficient digit. This digit is either non-zero or - * part of one of the following patterns: - * - * ["0\x00", "0.\x00", "0.E", "0.e", "0E", "0e"] - * - * The locations of a single optional dot or indicator are stored - * in 'dpoint' and 'exp'. - * - * The end of the string is stored in 'end'. If an indicator [eE] - * occurs without trailing [edigits], the condition is caught - * later by strtoexp(). - */ -static const char * -scan_dpoint_exp(const char *s, const char **dpoint, const char **exp, - const char **end) -{ - const char *coeff = NULL; - - *dpoint = NULL; - *exp = NULL; - for (; *s != '\0'; s++) { - switch (*s) { - case '.': - if (*dpoint != NULL || *exp != NULL) - return NULL; - *dpoint = s; - break; - case 'E': case 'e': - if (*exp != NULL) - return NULL; - *exp = s; - if (*(s+1) == '+' || *(s+1) == '-') - s++; - break; - default: - if (!isdigit((uchar)*s)) - return NULL; - if (coeff == NULL && *exp == NULL) { - if (*s == '0') { - if (!isdigit((uchar)*(s+1))) - if (!(*(s+1) == '.' && - isdigit((uchar)*(s+2)))) - coeff = s; - } - else { - coeff = s; - } - } - break; - - } - } - - *end = s; - return coeff; -} - -/* scan the payload of a NaN */ -static const char * -scan_payload(const char *s, const char **end) -{ - const char *coeff; - - while (*s == '0') - s++; - coeff = s; - - while (isdigit((uchar)*s)) - s++; - *end = s; - - return (*s == '\0') ? coeff : NULL; -} - -/* convert a character string to a decimal */ -void -mpd_qset_string(mpd_t *dec, const char *s, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_ssize_t q, r, len; - const char *coeff, *end; - const char *dpoint = NULL, *exp = NULL; - size_t digits; - uint8_t sign = MPD_POS; - - mpd_set_flags(dec, 0); - dec->len = 0; - dec->exp = 0; - - /* sign */ - if (*s == '+') { - s++; - } - else if (*s == '-') { - mpd_set_negative(dec); - sign = MPD_NEG; - s++; - } - - if (_mpd_strneq(s, "nan", "NAN", 3)) { /* NaN */ - s += 3; - mpd_setspecial(dec, sign, MPD_NAN); - if (*s == '\0') - return; - /* validate payload: digits only */ - if ((coeff = scan_payload(s, &end)) == NULL) - goto conversion_error; - /* payload consists entirely of zeros */ - if (*coeff == '\0') - return; - digits = end - coeff; - /* prec >= 1, clamp is 0 or 1 */ - if (digits > (size_t)(ctx->prec-ctx->clamp)) - goto conversion_error; - } /* sNaN */ - else if (_mpd_strneq(s, "snan", "SNAN", 4)) { - s += 4; - mpd_setspecial(dec, sign, MPD_SNAN); - if (*s == '\0') - return; - /* validate payload: digits only */ - if ((coeff = scan_payload(s, &end)) == NULL) - goto conversion_error; - /* payload consists entirely of zeros */ - if (*coeff == '\0') - return; - digits = end - coeff; - if (digits > (size_t)(ctx->prec-ctx->clamp)) - goto conversion_error; - } - else if (_mpd_strneq(s, "inf", "INF", 3)) { - s += 3; - if (*s == '\0' || _mpd_strneq(s, "inity", "INITY", 6)) { - /* numeric-value: infinity */ - mpd_setspecial(dec, sign, MPD_INF); - return; - } - goto conversion_error; - } - else { - /* scan for start of coefficient, decimal point, indicator, end */ - if ((coeff = scan_dpoint_exp(s, &dpoint, &exp, &end)) == NULL) - goto conversion_error; - - /* numeric-value: [exponent-part] */ - if (exp) { - /* exponent-part */ - end = exp; exp++; - dec->exp = strtoexp(exp); - if (errno) { - if (!(errno == ERANGE && - (dec->exp == MPD_SSIZE_MAX || - dec->exp == MPD_SSIZE_MIN))) - goto conversion_error; - } - } - - digits = end - coeff; - if (dpoint) { - size_t fracdigits = end-dpoint-1; - if (dpoint > coeff) digits--; - - if (fracdigits > MPD_MAX_PREC) { - goto conversion_error; - } - if (dec->exp < MPD_SSIZE_MIN+(mpd_ssize_t)fracdigits) { - dec->exp = MPD_SSIZE_MIN; - } - else { - dec->exp -= (mpd_ssize_t)fracdigits; - } - } - if (digits > MPD_MAX_PREC) { - goto conversion_error; - } - if (dec->exp > MPD_EXP_INF) { - dec->exp = MPD_EXP_INF; - } - if (dec->exp == MPD_SSIZE_MIN) { - dec->exp = MPD_SSIZE_MIN+1; - } - } - - _mpd_idiv_word(&q, &r, (mpd_ssize_t)digits, MPD_RDIGITS); - - len = (r == 0) ? q : q+1; - if (len == 0) { - goto conversion_error; /* GCOV_NOT_REACHED */ - } - if (!mpd_qresize(dec, len, status)) { - mpd_seterror(dec, MPD_Malloc_error, status); - return; - } - dec->len = len; - - string_to_coeff(dec->data, coeff, dpoint, (int)r, len); - - mpd_setdigits(dec); - mpd_qfinalize(dec, ctx, status); - return; - -conversion_error: - /* standard wants a positive NaN */ - mpd_seterror(dec, MPD_Conversion_syntax, status); -} - -/* Print word x with n decimal digits to string s. dot is either NULL - or the location of a decimal point. */ -#define EXTRACT_DIGIT(s, x, d, dot) \ - if (s == dot) *s++ = '.'; *s++ = '0' + (char)(x / d); x %= d -static inline char * -word_to_string(char *s, mpd_uint_t x, int n, char *dot) -{ - switch(n) { -#ifdef CONFIG_64 - case 20: EXTRACT_DIGIT(s, x, 10000000000000000000ULL, dot); /* GCOV_NOT_REACHED */ - case 19: EXTRACT_DIGIT(s, x, 1000000000000000000ULL, dot); - case 18: EXTRACT_DIGIT(s, x, 100000000000000000ULL, dot); - case 17: EXTRACT_DIGIT(s, x, 10000000000000000ULL, dot); - case 16: EXTRACT_DIGIT(s, x, 1000000000000000ULL, dot); - case 15: EXTRACT_DIGIT(s, x, 100000000000000ULL, dot); - case 14: EXTRACT_DIGIT(s, x, 10000000000000ULL, dot); - case 13: EXTRACT_DIGIT(s, x, 1000000000000ULL, dot); - case 12: EXTRACT_DIGIT(s, x, 100000000000ULL, dot); - case 11: EXTRACT_DIGIT(s, x, 10000000000ULL, dot); -#endif - case 10: EXTRACT_DIGIT(s, x, 1000000000UL, dot); - case 9: EXTRACT_DIGIT(s, x, 100000000UL, dot); - case 8: EXTRACT_DIGIT(s, x, 10000000UL, dot); - case 7: EXTRACT_DIGIT(s, x, 1000000UL, dot); - case 6: EXTRACT_DIGIT(s, x, 100000UL, dot); - case 5: EXTRACT_DIGIT(s, x, 10000UL, dot); - case 4: EXTRACT_DIGIT(s, x, 1000UL, dot); - case 3: EXTRACT_DIGIT(s, x, 100UL, dot); - case 2: EXTRACT_DIGIT(s, x, 10UL, dot); - default: if (s == dot) *s++ = '.'; *s++ = '0' + (char)x; - } - - *s = '\0'; - return s; -} - -/* Print exponent x to string s. Undefined for MPD_SSIZE_MIN. */ -static inline char * -exp_to_string(char *s, mpd_ssize_t x) -{ - char sign = '+'; - - if (x < 0) { - sign = '-'; - x = -x; - } - *s++ = sign; - - return word_to_string(s, x, mpd_word_digits(x), NULL); -} - -/* Print the coefficient of dec to string s. len(dec) > 0. */ -static inline char * -coeff_to_string(char *s, const mpd_t *dec) -{ - mpd_uint_t x; - mpd_ssize_t i; - - /* most significant word */ - x = mpd_msword(dec); - s = word_to_string(s, x, mpd_word_digits(x), NULL); - - /* remaining full words */ - for (i=dec->len-2; i >= 0; --i) { - x = dec->data[i]; - s = word_to_string(s, x, MPD_RDIGITS, NULL); - } - - return s; -} - -/* Print the coefficient of dec to string s. len(dec) > 0. dot is either - NULL or a pointer to the location of a decimal point. */ -static inline char * -coeff_to_string_dot(char *s, char *dot, const mpd_t *dec) -{ - mpd_uint_t x; - mpd_ssize_t i; - - /* most significant word */ - x = mpd_msword(dec); - s = word_to_string(s, x, mpd_word_digits(x), dot); - - /* remaining full words */ - for (i=dec->len-2; i >= 0; --i) { - x = dec->data[i]; - s = word_to_string(s, x, MPD_RDIGITS, dot); - } - - return s; -} - -/* Format type */ -#define MPD_FMT_LOWER 0x00000000 -#define MPD_FMT_UPPER 0x00000001 -#define MPD_FMT_TOSCI 0x00000002 -#define MPD_FMT_TOENG 0x00000004 -#define MPD_FMT_EXP 0x00000008 -#define MPD_FMT_FIXED 0x00000010 -#define MPD_FMT_PERCENT 0x00000020 -#define MPD_FMT_SIGN_SPACE 0x00000040 -#define MPD_FMT_SIGN_PLUS 0x00000080 - -/* Default place of the decimal point for MPD_FMT_TOSCI, MPD_FMT_EXP */ -#define MPD_DEFAULT_DOTPLACE 1 - -/* - * Set *result to the string representation of a decimal. Return the length - * of *result, not including the terminating '\0' character. - * - * Formatting is done according to 'flags'. A return value of -1 with *result - * set to NULL indicates MPD_Malloc_error. - * - * 'dplace' is the default place of the decimal point. It is always set to - * MPD_DEFAULT_DOTPLACE except for zeros in combination with MPD_FMT_EXP. - */ -static mpd_ssize_t -_mpd_to_string(char **result, const mpd_t *dec, int flags, mpd_ssize_t dplace) -{ - char *decstring = NULL, *cp = NULL; - mpd_ssize_t ldigits; - mpd_ssize_t mem = 0, k; - - if (mpd_isspecial(dec)) { - - mem = sizeof "-Infinity%"; - if (mpd_isnan(dec) && dec->len > 0) { - /* diagnostic code */ - mem += dec->digits; - } - cp = decstring = mpd_alloc(mem, sizeof *decstring); - if (cp == NULL) { - *result = NULL; - return -1; - } - - if (mpd_isnegative(dec)) { - *cp++ = '-'; - } - else if (flags&MPD_FMT_SIGN_SPACE) { - *cp++ = ' '; - } - else if (flags&MPD_FMT_SIGN_PLUS) { - *cp++ = '+'; - } - - if (mpd_isnan(dec)) { - if (mpd_isqnan(dec)) { - strcpy(cp, "NaN"); - cp += 3; - } - else { - strcpy(cp, "sNaN"); - cp += 4; - } - if (dec->len > 0) { /* diagnostic code */ - cp = coeff_to_string(cp, dec); - } - } - else if (mpd_isinfinite(dec)) { - strcpy(cp, "Infinity"); - cp += 8; - } - else { /* debug */ - abort(); /* GCOV_NOT_REACHED */ - } - } - else { - assert(dec->len > 0); - - /* - * For easier manipulation of the decimal point's location - * and the exponent that is finally printed, the number is - * rescaled to a virtual representation with exp = 0. Here - * ldigits denotes the number of decimal digits to the left - * of the decimal point and remains constant once initialized. - * - * dplace is the location of the decimal point relative to - * the start of the coefficient. Note that 3) always holds - * when dplace is shifted. - * - * 1) ldigits := dec->digits - dec->exp - * 2) dplace := ldigits (initially) - * 3) exp := ldigits - dplace (initially exp = 0) - * - * 0.00000_.____._____000000. - * ^ ^ ^ ^ - * | | | | - * | | | `- dplace >= digits - * | | `- dplace in the middle of the coefficient - * | ` dplace = 1 (after the first coefficient digit) - * `- dplace <= 0 - */ - - ldigits = dec->digits + dec->exp; - - if (flags&MPD_FMT_EXP) { - ; - } - else if (flags&MPD_FMT_FIXED || (dec->exp <= 0 && ldigits > -6)) { - /* MPD_FMT_FIXED: always use fixed point notation. - * MPD_FMT_TOSCI, MPD_FMT_TOENG: for a certain range, - * override exponent notation. */ - dplace = ldigits; - } - else if (flags&MPD_FMT_TOENG) { - if (mpd_iszero(dec)) { - /* If the exponent is divisible by three, - * dplace = 1. Otherwise, move dplace one - * or two places to the left. */ - dplace = -1 + mod_mpd_ssize_t(dec->exp+2, 3); - } - else { /* ldigits-1 is the adjusted exponent, which - * should be divisible by three. If not, move - * dplace one or two places to the right. */ - dplace += mod_mpd_ssize_t(ldigits-1, 3); - } - } - - /* - * Basic space requirements: - * - * [-][.][coeffdigits][E][-][expdigits+1][%]['\0'] - * - * If the decimal point lies outside of the coefficient digits, - * space is adjusted accordingly. - */ - if (dplace <= 0) { - mem = -dplace + dec->digits + 2; - } - else if (dplace >= dec->digits) { - mem = dplace; - } - else { - mem = dec->digits; - } - mem += (MPD_EXPDIGITS+1+6); - - cp = decstring = mpd_alloc(mem, sizeof *decstring); - if (cp == NULL) { - *result = NULL; - return -1; - } - - - if (mpd_isnegative(dec)) { - *cp++ = '-'; - } - else if (flags&MPD_FMT_SIGN_SPACE) { - *cp++ = ' '; - } - else if (flags&MPD_FMT_SIGN_PLUS) { - *cp++ = '+'; - } - - if (dplace <= 0) { - /* space: -dplace+dec->digits+2 */ - *cp++ = '0'; - *cp++ = '.'; - for (k = 0; k < -dplace; k++) { - *cp++ = '0'; - } - cp = coeff_to_string(cp, dec); - } - else if (dplace >= dec->digits) { - /* space: dplace */ - cp = coeff_to_string(cp, dec); - for (k = 0; k < dplace-dec->digits; k++) { - *cp++ = '0'; - } - } - else { - /* space: dec->digits+1 */ - cp = coeff_to_string_dot(cp, cp+dplace, dec); - } - - /* - * Conditions for printing an exponent: - * - * MPD_FMT_TOSCI, MPD_FMT_TOENG: only if ldigits != dplace - * MPD_FMT_FIXED: never (ldigits == dplace) - * MPD_FMT_EXP: always - */ - if (ldigits != dplace || flags&MPD_FMT_EXP) { - /* space: expdigits+2 */ - *cp++ = (flags&MPD_FMT_UPPER) ? 'E' : 'e'; - cp = exp_to_string(cp, ldigits-dplace); - } - } - - if (flags&MPD_FMT_PERCENT) { - *cp++ = '%'; - } - - assert(cp < decstring+mem); - assert(cp-decstring < MPD_SSIZE_MAX); - - *cp = '\0'; - *result = decstring; - return (mpd_ssize_t)(cp-decstring); -} - -char * -mpd_to_sci(const mpd_t *dec, int fmt) -{ - char *res; - int flags = MPD_FMT_TOSCI; - - flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER; - (void)_mpd_to_string(&res, dec, flags, MPD_DEFAULT_DOTPLACE); - return res; -} - -char * -mpd_to_eng(const mpd_t *dec, int fmt) -{ - char *res; - int flags = MPD_FMT_TOENG; - - flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER; - (void)_mpd_to_string(&res, dec, flags, MPD_DEFAULT_DOTPLACE); - return res; -} - -mpd_ssize_t -mpd_to_sci_size(char **res, const mpd_t *dec, int fmt) -{ - int flags = MPD_FMT_TOSCI; - - flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER; - return _mpd_to_string(res, dec, flags, MPD_DEFAULT_DOTPLACE); -} - -mpd_ssize_t -mpd_to_eng_size(char **res, const mpd_t *dec, int fmt) -{ - int flags = MPD_FMT_TOENG; - - flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER; - return _mpd_to_string(res, dec, flags, MPD_DEFAULT_DOTPLACE); -} - -/* Copy a single UTF-8 char to dest. See: The Unicode Standard, version 5.2, - chapter 3.9: Well-formed UTF-8 byte sequences. */ -static int -_mpd_copy_utf8(char dest[5], const char *s) -{ - const uchar *cp = (const uchar *)s; - uchar lb, ub; - int count, i; - - - if (*cp == 0) { - /* empty string */ - dest[0] = '\0'; - return 0; - } - else if (*cp <= 0x7f) { - /* ascii */ - dest[0] = *cp; - dest[1] = '\0'; - return 1; - } - else if (0xc2 <= *cp && *cp <= 0xdf) { - lb = 0x80; ub = 0xbf; - count = 2; - } - else if (*cp == 0xe0) { - lb = 0xa0; ub = 0xbf; - count = 3; - } - else if (*cp <= 0xec) { - lb = 0x80; ub = 0xbf; - count = 3; - } - else if (*cp == 0xed) { - lb = 0x80; ub = 0x9f; - count = 3; - } - else if (*cp <= 0xef) { - lb = 0x80; ub = 0xbf; - count = 3; - } - else if (*cp == 0xf0) { - lb = 0x90; ub = 0xbf; - count = 4; - } - else if (*cp <= 0xf3) { - lb = 0x80; ub = 0xbf; - count = 4; - } - else if (*cp == 0xf4) { - lb = 0x80; ub = 0x8f; - count = 4; - } - else { - /* invalid */ - goto error; - } - - dest[0] = *cp++; - if (*cp < lb || ub < *cp) { - goto error; - } - dest[1] = *cp++; - for (i = 2; i < count; i++) { - if (*cp < 0x80 || 0xbf < *cp) { - goto error; - } - dest[i] = *cp++; - } - dest[i] = '\0'; - - return count; - -error: - dest[0] = '\0'; - return -1; -} - -int -mpd_validate_lconv(mpd_spec_t *spec) -{ - size_t n; -#if CHAR_MAX == SCHAR_MAX - const char *cp = spec->grouping; - while (*cp != '\0') { - if (*cp++ < 0) { - return -1; - } - } -#endif - n = strlen(spec->dot); - if (n == 0 || n > 4) { - return -1; - } - if (strlen(spec->sep) > 4) { - return -1; - } - - return 0; -} - -int -mpd_parse_fmt_str(mpd_spec_t *spec, const char *fmt, int caps) -{ - char *cp = (char *)fmt; - int have_align = 0, n; - - /* defaults */ - spec->min_width = 0; - spec->prec = -1; - spec->type = caps ? 'G' : 'g'; - spec->align = '>'; - spec->sign = '-'; - spec->dot = ""; - spec->sep = ""; - spec->grouping = ""; - - - /* presume that the first character is a UTF-8 fill character */ - if ((n = _mpd_copy_utf8(spec->fill, cp)) < 0) { - return 0; - } - - /* alignment directive, prefixed by a fill character */ - if (*cp && (*(cp+n) == '<' || *(cp+n) == '>' || - *(cp+n) == '=' || *(cp+n) == '^')) { - cp += n; - spec->align = *cp++; - have_align = 1; - } /* alignment directive */ - else { - /* default fill character */ - spec->fill[0] = ' '; - spec->fill[1] = '\0'; - if (*cp == '<' || *cp == '>' || - *cp == '=' || *cp == '^') { - spec->align = *cp++; - have_align = 1; - } - } - - /* sign formatting */ - if (*cp == '+' || *cp == '-' || *cp == ' ') { - spec->sign = *cp++; - } - - /* zero padding */ - if (*cp == '0') { - /* zero padding implies alignment, which should not be - * specified twice. */ - if (have_align) { - return 0; - } - spec->align = 'z'; - spec->fill[0] = *cp++; - spec->fill[1] = '\0'; - } - - /* minimum width */ - if (isdigit((uchar)*cp)) { - if (*cp == '0') { - return 0; - } - errno = 0; - spec->min_width = mpd_strtossize(cp, &cp, 10); - if (errno == ERANGE || errno == EINVAL) { - return 0; - } - } - - /* thousands separator */ - if (*cp == ',') { - spec->dot = "."; - spec->sep = ","; - spec->grouping = "\003\003"; - cp++; - } - - /* fraction digits or significant digits */ - if (*cp == '.') { - cp++; - if (!isdigit((uchar)*cp)) { - return 0; - } - errno = 0; - spec->prec = mpd_strtossize(cp, &cp, 10); - if (errno == ERANGE || errno == EINVAL) { - return 0; - } - } - - /* type */ - if (*cp == 'E' || *cp == 'e' || *cp == 'F' || *cp == 'f' || - *cp == 'G' || *cp == 'g' || *cp == '%') { - spec->type = *cp++; - } - else if (*cp == 'N' || *cp == 'n') { - /* locale specific conversion */ - struct lconv *lc; - /* separator has already been specified */ - if (*spec->sep) { - return 0; - } - spec->type = *cp++; - spec->type = (spec->type == 'N') ? 'G' : 'g'; - lc = localeconv(); - spec->dot = lc->decimal_point; - spec->sep = lc->thousands_sep; - spec->grouping = lc->grouping; - if (mpd_validate_lconv(spec) < 0) { - return 0; /* GCOV_NOT_REACHED */ - } - } - - /* check correctness */ - if (*cp != '\0') { - return 0; - } - - return 1; -} - -/* - * The following functions assume that spec->min_width <= MPD_MAX_PREC, which - * is made sure in mpd_qformat_spec. Then, even with a spec that inserts a - * four-byte separator after each digit, nbytes in the following struct - * cannot overflow. - */ - -/* Multibyte string */ -typedef struct { - mpd_ssize_t nbytes; /* length in bytes */ - mpd_ssize_t nchars; /* length in chars */ - mpd_ssize_t cur; /* current write index */ - char *data; -} mpd_mbstr_t; - -static inline void -_mpd_bcopy(char *dest, const char *src, mpd_ssize_t n) -{ - while (--n >= 0) { - dest[n] = src[n]; - } -} - -static inline void -_mbstr_copy_char(mpd_mbstr_t *dest, const char *src, mpd_ssize_t n) -{ - dest->nbytes += n; - dest->nchars += (n > 0 ? 1 : 0); - dest->cur -= n; - - if (dest->data != NULL) { - _mpd_bcopy(dest->data+dest->cur, src, n); - } -} - -static inline void -_mbstr_copy_ascii(mpd_mbstr_t *dest, const char *src, mpd_ssize_t n) -{ - dest->nbytes += n; - dest->nchars += n; - dest->cur -= n; - - if (dest->data != NULL) { - _mpd_bcopy(dest->data+dest->cur, src, n); - } -} - -static inline void -_mbstr_copy_pad(mpd_mbstr_t *dest, mpd_ssize_t n) -{ - dest->nbytes += n; - dest->nchars += n; - dest->cur -= n; - - if (dest->data != NULL) { - char *cp = dest->data + dest->cur; - while (--n >= 0) { - cp[n] = '0'; - } - } -} - -/* - * Copy a numeric string to dest->data, adding separators in the integer - * part according to spec->grouping. If leading zero padding is enabled - * and the result is smaller than spec->min_width, continue adding zeros - * and separators until the minimum width is reached. - * - * The final length of dest->data is stored in dest->nbytes. The number - * of UTF-8 characters is stored in dest->nchars. - * - * First run (dest->data == NULL): determine the length of the result - * string and store it in dest->nbytes. - * - * Second run (write to dest->data): data is written in chunks and in - * reverse order, starting with the rest of the numeric string. - */ -static void -_mpd_add_sep_dot(mpd_mbstr_t *dest, - const char *sign, /* location of optional sign */ - const char *src, mpd_ssize_t n_src, /* integer part and length */ - const char *dot, /* location of optional decimal point */ - const char *rest, mpd_ssize_t n_rest, /* remaining part and length */ - const mpd_spec_t *spec) -{ - mpd_ssize_t n_sep, n_sign, consume; - const char *g; - int pad = 0; - - n_sign = sign ? 1 : 0; - n_sep = (mpd_ssize_t)strlen(spec->sep); - /* Initial write index: set to location of '\0' in the output string. - * Irrelevant for the first run. */ - dest->cur = dest->nbytes; - dest->nbytes = dest->nchars = 0; - - _mbstr_copy_ascii(dest, rest, n_rest); - - if (dot) { - _mbstr_copy_char(dest, dot, (mpd_ssize_t)strlen(dot)); - } - - g = spec->grouping; - consume = *g; - while (1) { - /* If the group length is 0 or CHAR_MAX or greater than the - * number of source bytes, consume all remaining bytes. */ - if (*g == 0 || *g == CHAR_MAX || consume > n_src) { - consume = n_src; - } - n_src -= consume; - if (pad) { - _mbstr_copy_pad(dest, consume); - } - else { - _mbstr_copy_ascii(dest, src+n_src, consume); - } - - if (n_src == 0) { - /* Either the real source of intpart digits or the virtual - * source of padding zeros is exhausted. */ - if (spec->align == 'z' && - dest->nchars + n_sign < spec->min_width) { - /* Zero padding is set and length < min_width: - * Generate n_src additional characters. */ - n_src = spec->min_width - (dest->nchars + n_sign); - /* Next iteration: - * case *g == 0 || *g == CHAR_MAX: - * consume all padding characters - * case consume < g*: - * fill remainder of current group - * case consume == g* - * copying is a no-op */ - consume = *g - consume; - /* Switch on virtual source of zeros. */ - pad = 1; - continue; - } - break; - } - - if (n_sep > 0) { - /* If padding is switched on, separators are counted - * as padding characters. This rule does not apply if - * the separator would be the first character of the - * result string. */ - if (pad && n_src > 1) n_src -= 1; - _mbstr_copy_char(dest, spec->sep, n_sep); - } - - /* If non-NUL, use the next value for grouping. */ - if (*g && *(g+1)) g++; - consume = *g; - } - - if (sign) { - _mbstr_copy_ascii(dest, sign, 1); - } - - if (dest->data) { - dest->data[dest->nbytes] = '\0'; - } -} - -/* - * Convert a numeric-string to its locale-specific appearance. - * The string must have one of these forms: - * - * 1) [sign] digits [exponent-part] - * 2) [sign] digits '.' [digits] [exponent-part] - * - * Not allowed, since _mpd_to_string() never returns this form: - * - * 3) [sign] '.' digits [exponent-part] - * - * Input: result->data := original numeric string (ASCII) - * result->bytes := strlen(result->data) - * result->nchars := strlen(result->data) - * - * Output: result->data := modified or original string - * result->bytes := strlen(result->data) - * result->nchars := number of characters (possibly UTF-8) - */ -static int -_mpd_apply_lconv(mpd_mbstr_t *result, const mpd_spec_t *spec, uint32_t *status) -{ - const char *sign = NULL, *intpart = NULL, *dot = NULL; - const char *rest, *dp; - char *decstring; - mpd_ssize_t n_int, n_rest; - - /* original numeric string */ - dp = result->data; - - /* sign */ - if (*dp == '+' || *dp == '-' || *dp == ' ') { - sign = dp++; - } - /* integer part */ - assert(isdigit((uchar)*dp)); - intpart = dp++; - while (isdigit((uchar)*dp)) { - dp++; - } - n_int = (mpd_ssize_t)(dp-intpart); - /* decimal point */ - if (*dp == '.') { - dp++; dot = spec->dot; - } - /* rest */ - rest = dp; - n_rest = result->nbytes - (mpd_ssize_t)(dp-result->data); - - if (dot == NULL && (*spec->sep == '\0' || *spec->grouping == '\0')) { - /* _mpd_add_sep_dot() would not change anything */ - return 1; - } - - /* Determine the size of the new decimal string after inserting the - * decimal point, optional separators and optional padding. */ - decstring = result->data; - result->data = NULL; - _mpd_add_sep_dot(result, sign, intpart, n_int, dot, - rest, n_rest, spec); - - result->data = mpd_alloc(result->nbytes+1, 1); - if (result->data == NULL) { - *status |= MPD_Malloc_error; - mpd_free(decstring); - return 0; - } - - /* Perform actual writes. */ - _mpd_add_sep_dot(result, sign, intpart, n_int, dot, - rest, n_rest, spec); - - mpd_free(decstring); - return 1; -} - -/* Add padding to the formatted string if necessary. */ -static int -_mpd_add_pad(mpd_mbstr_t *result, const mpd_spec_t *spec, uint32_t *status) -{ - if (result->nchars < spec->min_width) { - mpd_ssize_t add_chars, add_bytes; - size_t lpad = 0, rpad = 0; - size_t n_fill, len, i, j; - char align = spec->align; - uint8_t err = 0; - char *cp; - - n_fill = strlen(spec->fill); - add_chars = (spec->min_width - result->nchars); - /* max value: MPD_MAX_PREC * 4 */ - add_bytes = add_chars * (mpd_ssize_t)n_fill; - - cp = result->data = mpd_realloc(result->data, - result->nbytes+add_bytes+1, - sizeof *result->data, &err); - if (err) { - *status |= MPD_Malloc_error; - mpd_free(result->data); - return 0; - } - - if (align == 'z') { - align = '='; - } - - if (align == '<') { - rpad = add_chars; - } - else if (align == '>' || align == '=') { - lpad = add_chars; - } - else { /* align == '^' */ - lpad = add_chars/2; - rpad = add_chars-lpad; - } - - len = result->nbytes; - if (align == '=' && (*cp == '-' || *cp == '+' || *cp == ' ')) { - /* leave sign in the leading position */ - cp++; len--; - } - - memmove(cp+n_fill*lpad, cp, len); - for (i = 0; i < lpad; i++) { - for (j = 0; j < n_fill; j++) { - cp[i*n_fill+j] = spec->fill[j]; - } - } - cp += (n_fill*lpad + len); - for (i = 0; i < rpad; i++) { - for (j = 0; j < n_fill; j++) { - cp[i*n_fill+j] = spec->fill[j]; - } - } - - result->nbytes += add_bytes; - result->nchars += add_chars; - result->data[result->nbytes] = '\0'; - } - - return 1; -} - -/* Round a number to prec digits. The adjusted exponent stays the same - or increases by one if rounding up crosses a power of ten boundary. - If result->digits would exceed MPD_MAX_PREC+1, MPD_Invalid_operation - is set and the result is NaN. */ -static inline void -_mpd_round(mpd_t *result, const mpd_t *a, mpd_ssize_t prec, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_ssize_t exp = a->exp + a->digits - prec; - - if (prec <= 0) { - mpd_seterror(result, MPD_Invalid_operation, status); /* GCOV_NOT_REACHED */ - return; /* GCOV_NOT_REACHED */ - } - if (mpd_isspecial(a) || mpd_iszero(a)) { - mpd_qcopy(result, a, status); /* GCOV_NOT_REACHED */ - return; /* GCOV_NOT_REACHED */ - } - - mpd_qrescale_fmt(result, a, exp, ctx, status); - if (result->digits > prec) { - mpd_qrescale_fmt(result, result, exp+1, ctx, status); - } -} - -/* - * Return the string representation of an mpd_t, formatted according to 'spec'. - * The format specification is assumed to be valid. Memory errors are indicated - * as usual. This function is quiet. - */ -char * -mpd_qformat_spec(const mpd_t *dec, const mpd_spec_t *spec, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_uint_t dt[MPD_MINALLOC_MAX]; - mpd_t tmp = {MPD_STATIC|MPD_STATIC_DATA,0,0,0,MPD_MINALLOC_MAX,dt}; - mpd_ssize_t dplace = MPD_DEFAULT_DOTPLACE; - mpd_mbstr_t result; - mpd_spec_t stackspec; - char type = spec->type; - int flags = 0; - - - if (spec->min_width > MPD_MAX_PREC) { - *status |= MPD_Invalid_operation; - return NULL; - } - - if (isupper((uchar)type)) { - type = tolower((uchar)type); - flags |= MPD_FMT_UPPER; - } - if (spec->sign == ' ') { - flags |= MPD_FMT_SIGN_SPACE; - } - else if (spec->sign == '+') { - flags |= MPD_FMT_SIGN_PLUS; - } - - if (mpd_isspecial(dec)) { - if (spec->align == 'z') { - stackspec = *spec; - stackspec.fill[0] = ' '; - stackspec.fill[1] = '\0'; - stackspec.align = '>'; - spec = &stackspec; - } - if (type == '%') { - flags |= MPD_FMT_PERCENT; - } - } - else { - uint32_t workstatus = 0; - mpd_ssize_t prec; - - switch (type) { - case 'g': flags |= MPD_FMT_TOSCI; break; - case 'e': flags |= MPD_FMT_EXP; break; - case '%': flags |= MPD_FMT_PERCENT; - if (!mpd_qcopy(&tmp, dec, status)) { - return NULL; - } - tmp.exp += 2; - dec = &tmp; - type = 'f'; /* fall through */ - case 'f': flags |= MPD_FMT_FIXED; break; - default: abort(); /* debug: GCOV_NOT_REACHED */ - } - - if (spec->prec >= 0) { - if (spec->prec > MPD_MAX_PREC) { - *status |= MPD_Invalid_operation; - goto error; - } - - switch (type) { - case 'g': - prec = (spec->prec == 0) ? 1 : spec->prec; - if (dec->digits > prec) { - _mpd_round(&tmp, dec, prec, ctx, - &workstatus); - dec = &tmp; - } - break; - case 'e': - if (mpd_iszero(dec)) { - dplace = 1-spec->prec; - } - else { - _mpd_round(&tmp, dec, spec->prec+1, ctx, - &workstatus); - dec = &tmp; - } - break; - case 'f': - mpd_qrescale(&tmp, dec, -spec->prec, ctx, - &workstatus); - dec = &tmp; - break; - } - } - - if (type == 'f') { - if (mpd_iszero(dec) && dec->exp > 0) { - mpd_qrescale(&tmp, dec, 0, ctx, &workstatus); - dec = &tmp; - } - } - - if (workstatus&MPD_Errors) { - *status |= (workstatus&MPD_Errors); - goto error; - } - } - - /* - * At this point, for all scaled or non-scaled decimals: - * 1) 1 <= digits <= MAX_PREC+1 - * 2) adjexp(scaled) = adjexp(orig) [+1] - * 3) case 'g': MIN_ETINY <= exp <= MAX_EMAX+1 - * case 'e': MIN_ETINY-MAX_PREC <= exp <= MAX_EMAX+1 - * case 'f': MIN_ETINY <= exp <= MAX_EMAX+1 - * 4) max memory alloc in _mpd_to_string: - * case 'g': MAX_PREC+36 - * case 'e': MAX_PREC+36 - * case 'f': 2*MPD_MAX_PREC+30 - */ - result.nbytes = _mpd_to_string(&result.data, dec, flags, dplace); - result.nchars = result.nbytes; - if (result.nbytes < 0) { - *status |= MPD_Malloc_error; - goto error; - } - - if (*spec->dot != '\0' && !mpd_isspecial(dec)) { - if (result.nchars > MPD_MAX_PREC+36) { - /* Since a group length of one is not explicitly - * disallowed, ensure that it is always possible to - * insert a four byte separator after each digit. */ - *status |= MPD_Invalid_operation; - mpd_free(result.data); - goto error; - } - if (!_mpd_apply_lconv(&result, spec, status)) { - goto error; - } - } - - if (spec->min_width) { - if (!_mpd_add_pad(&result, spec, status)) { - goto error; - } - } - - mpd_del(&tmp); - return result.data; - -error: - mpd_del(&tmp); - return NULL; -} - -char * -mpd_qformat(const mpd_t *dec, const char *fmt, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_spec_t spec; - - if (!mpd_parse_fmt_str(&spec, fmt, 1)) { - *status |= MPD_Invalid_operation; - return NULL; - } - - return mpd_qformat_spec(dec, &spec, ctx, status); -} - -/* - * The specification has a *condition* called Invalid_operation and an - * IEEE *signal* called Invalid_operation. The former corresponds to - * MPD_Invalid_operation, the latter to MPD_IEEE_Invalid_operation. - * MPD_IEEE_Invalid_operation comprises the following conditions: - * - * [MPD_Conversion_syntax, MPD_Division_impossible, MPD_Division_undefined, - * MPD_Fpu_error, MPD_Invalid_context, MPD_Invalid_operation, - * MPD_Malloc_error] - * - * In the following functions, 'flag' denotes the condition, 'signal' - * denotes the IEEE signal. - */ - -static const char *mpd_flag_string[MPD_NUM_FLAGS] = { - "Clamped", - "Conversion_syntax", - "Division_by_zero", - "Division_impossible", - "Division_undefined", - "Fpu_error", - "Inexact", - "Invalid_context", - "Invalid_operation", - "Malloc_error", - "Not_implemented", - "Overflow", - "Rounded", - "Subnormal", - "Underflow", -}; - -static const char *mpd_signal_string[MPD_NUM_FLAGS] = { - "Clamped", - "IEEE_Invalid_operation", - "Division_by_zero", - "IEEE_Invalid_operation", - "IEEE_Invalid_operation", - "IEEE_Invalid_operation", - "Inexact", - "IEEE_Invalid_operation", - "IEEE_Invalid_operation", - "IEEE_Invalid_operation", - "Not_implemented", - "Overflow", - "Rounded", - "Subnormal", - "Underflow", -}; - -/* print conditions to buffer, separated by spaces */ -int -mpd_snprint_flags(char *dest, int nmemb, uint32_t flags) -{ - char *cp; - int n, j; - - assert(nmemb >= MPD_MAX_FLAG_STRING); - - *dest = '\0'; cp = dest; - for (j = 0; j < MPD_NUM_FLAGS; j++) { - if (flags & (1U<<j)) { - n = snprintf(cp, nmemb, "%s ", mpd_flag_string[j]); - if (n < 0 || n >= nmemb) return -1; - cp += n; nmemb -= n; - } - } - - if (cp != dest) { - *(--cp) = '\0'; - } - - return (int)(cp-dest); -} - -/* print conditions to buffer, in list form */ -int -mpd_lsnprint_flags(char *dest, int nmemb, uint32_t flags, const char *flag_string[]) -{ - char *cp; - int n, j; - - assert(nmemb >= MPD_MAX_FLAG_LIST); - if (flag_string == NULL) { - flag_string = mpd_flag_string; - } - - *dest = '['; - *(dest+1) = '\0'; - cp = dest+1; - --nmemb; - - for (j = 0; j < MPD_NUM_FLAGS; j++) { - if (flags & (1U<<j)) { - n = snprintf(cp, nmemb, "%s, ", flag_string[j]); - if (n < 0 || n >= nmemb) return -1; - cp += n; nmemb -= n; - } - } - - /* erase the last ", " */ - if (cp != dest+1) { - cp -= 2; - } - - *cp++ = ']'; - *cp = '\0'; - - return (int)(cp-dest); /* strlen, without NUL terminator */ -} - -/* print signals to buffer, in list form */ -int -mpd_lsnprint_signals(char *dest, int nmemb, uint32_t flags, const char *signal_string[]) -{ - char *cp; - int n, j; - int ieee_invalid_done = 0; - - assert(nmemb >= MPD_MAX_SIGNAL_LIST); - if (signal_string == NULL) { - signal_string = mpd_signal_string; - } - - *dest = '['; - *(dest+1) = '\0'; - cp = dest+1; - --nmemb; - - for (j = 0; j < MPD_NUM_FLAGS; j++) { - uint32_t f = flags & (1U<<j); - if (f) { - if (f&MPD_IEEE_Invalid_operation) { - if (ieee_invalid_done) { - continue; - } - ieee_invalid_done = 1; - } - n = snprintf(cp, nmemb, "%s, ", signal_string[j]); - if (n < 0 || n >= nmemb) return -1; - cp += n; nmemb -= n; - } - } - - /* erase the last ", " */ - if (cp != dest+1) { - cp -= 2; - } - - *cp++ = ']'; - *cp = '\0'; - - return (int)(cp-dest); /* strlen, without NUL terminator */ -} - -/* The following two functions are mainly intended for debugging. */ -void -mpd_fprint(FILE *file, const mpd_t *dec) -{ - char *decstring; - - decstring = mpd_to_sci(dec, 1); - if (decstring != NULL) { - fprintf(file, "%s\n", decstring); - mpd_free(decstring); - } - else { - fputs("mpd_fprint: output error\n", file); /* GCOV_NOT_REACHED */ - } -} - -void -mpd_print(const mpd_t *dec) -{ - char *decstring; - - decstring = mpd_to_sci(dec, 1); - if (decstring != NULL) { - printf("%s\n", decstring); - mpd_free(decstring); - } - else { - fputs("mpd_fprint: output error\n", stderr); /* GCOV_NOT_REACHED */ - } -} - - diff --git a/Modules/_decimal/libmpdec/io.h b/Modules/_decimal/libmpdec/io.h deleted file mode 100644 index de5486a..0000000 --- a/Modules/_decimal/libmpdec/io.h +++ /dev/null @@ -1,59 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef IO_H -#define IO_H - - -#include <errno.h> -#include "mpdecimal.h" - - -#if SIZE_MAX == MPD_SIZE_MAX - #define mpd_strtossize _mpd_strtossize -#else -static inline mpd_ssize_t -mpd_strtossize(const char *s, char **end, int base) -{ - int64_t retval; - - errno = 0; - retval = _mpd_strtossize(s, end, base); - if (errno == 0 && (retval > MPD_SSIZE_MAX || retval < MPD_SSIZE_MIN)) { - errno = ERANGE; - } - if (errno == ERANGE) { - return (retval < 0) ? MPD_SSIZE_MIN : MPD_SSIZE_MAX; - } - - return (mpd_ssize_t)retval; -} -#endif - - -#endif diff --git a/Modules/_decimal/libmpdec/literature/REFERENCES.txt b/Modules/_decimal/libmpdec/literature/REFERENCES.txt deleted file mode 100644 index 9ed5782..0000000 --- a/Modules/_decimal/libmpdec/literature/REFERENCES.txt +++ /dev/null @@ -1,51 +0,0 @@ - - -This document contains links to the literature used in the process of -creating the library. The list is probably not complete. - - -Mike Cowlishaw: General Decimal Arithmetic Specification -http://speleotrove.com/decimal/decarith.html - - -Jean-Michel Muller: On the definition of ulp (x) -lara.inist.fr/bitstream/2332/518/1/LIP-RR2005-09.pdf - - -T. E. Hull, A. Abrham: Properly rounded variable precision square root -http://portal.acm.org/citation.cfm?id=214413 - - -T. E. Hull, A. Abrham: Variable precision exponential function -http://portal.acm.org/citation.cfm?id=6498 - - -Roman E. Maeder: Storage allocation for the Karatsuba integer multiplication -algorithm. http://www.springerlink.com/content/w15058mj6v59t565/ - - -J. M. Pollard: The fast Fourier transform in a finite field -http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0301966-0/home.html - - -David H. Bailey: FFTs in External or Hierarchical Memory -http://crd.lbl.gov/~dhbailey/dhbpapers/ - - -W. Morven Gentleman: Matrix Multiplication and Fast Fourier Transforms -http://www.alcatel-lucent.com/bstj/vol47-1968/articles/bstj47-6-1099.pdf - - -Mikko Tommila: Apfloat documentation -http://www.apfloat.org/apfloat/2.41/apfloat.pdf - - -Joerg Arndt: "Matters Computational" -http://www.jjj.de/fxt/ - - -Karl Hasselstrom: Fast Division of Large Integers -www.treskal.com/kalle/exjobb/original-report.pdf - - - diff --git a/Modules/_decimal/libmpdec/literature/bignum.txt b/Modules/_decimal/libmpdec/literature/bignum.txt deleted file mode 100644 index f34ff67..0000000 --- a/Modules/_decimal/libmpdec/literature/bignum.txt +++ /dev/null @@ -1,83 +0,0 @@ - - -Bignum support (Fast Number Theoretic Transform or FNT): -======================================================== - -Bignum arithmetic in libmpdec uses the scheme for fast convolution -of integer sequences from: - -J. M. Pollard: The fast Fourier transform in a finite field -http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0301966-0/home.html - - -The transform in a finite field can be used for convolution in the same -way as the Fourier Transform. The main advantages of the Number Theoretic -Transform are that it is both exact and very memory efficient. - - -Convolution in pseudo-code: -~~~~~~~~~~~~~~~~~~~~~~~~~~~ - - fnt_convolute(a, b): - x = fnt(a) # forward transform of a - y = fnt(b) # forward transform of b - z = pairwise multiply x[i] and y[i] - result = inv_fnt(z) # backward transform of z. - - -Extending the maximum transform length (Chinese Remainder Theorem): -------------------------------------------------------------------- - -The maximum transform length is quite limited when using a single -prime field. However, it is possible to use multiple primes and -recover the result using the Chinese Remainder Theorem. - - -Multiplication in pseudo-code: -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - - _mpd_fntmul(u, v): - c1 = fnt_convolute(u, v, P1) # convolute modulo prime1 - c2 = fnt_convolute(u, v, P2) # convolute modulo prime2 - c3 = fnt_convolute(u, v, P3) # convolute modulo prime3 - result = crt3(c1, c2, c3) # Chinese Remainder Theorem - - -Optimized transform functions: ------------------------------- - -There are three different fnt() functions: - - std_fnt: "standard" decimation in frequency transform for array lengths - of 2**n. Performs well up to 1024 words. - - sixstep: Cache-friendly algorithm for array lengths of 2**n. Outperforms - std_fnt for large arrays. - - fourstep: Algorithm for array lengths of 3 * 2**n. Also cache friendly - in large parts. - - -List of bignum-only files: --------------------------- - -Functions from these files are only used in _mpd_fntmul(). - - umodarith.h -> fast low level routines for unsigned modular arithmetic - numbertheory.c -> routines for setting up the FNT - difradix2.c -> decimation in frequency transform, used as the - "base case" by the following three files: - - fnt.c -> standard transform for smaller arrays - sixstep.c -> transform large arrays of length 2**n - fourstep.c -> transform arrays of length 3 * 2**n - - convolute.c -> do the actual fast convolution, using one of - the three transform functions. - transpose.c -> transpositions needed for the sixstep algorithm. - crt.c -> Chinese Remainder Theorem: use information from three - transforms modulo three different primes to get the - final result. - - - diff --git a/Modules/_decimal/libmpdec/literature/fnt.py b/Modules/_decimal/libmpdec/literature/fnt.py deleted file mode 100644 index 6363536..0000000 --- a/Modules/_decimal/libmpdec/literature/fnt.py +++ /dev/null @@ -1,208 +0,0 @@ -# -# Copyright (c) 2008-2016 Stefan Krah. All rights reserved. -# -# Redistribution and use in source and binary forms, with or without -# modification, are permitted provided that the following conditions -# are met: -# -# 1. Redistributions of source code must retain the above copyright -# notice, this list of conditions and the following disclaimer. -# -# 2. Redistributions in binary form must reproduce the above copyright -# notice, this list of conditions and the following disclaimer in the -# documentation and/or other materials provided with the distribution. -# -# THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND -# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE -# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE -# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL -# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS -# OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) -# HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT -# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY -# OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF -# SUCH DAMAGE. -# - - -###################################################################### -# This file lists and checks some of the constants and limits used # -# in libmpdec's Number Theoretic Transform. At the end of the file # -# there is an example function for the plain DFT transform. # -###################################################################### - - -# -# Number theoretic transforms are done in subfields of F(p). P[i] -# are the primes, D[i] = P[i] - 1 are highly composite and w[i] -# are the respective primitive roots of F(p). -# -# The strategy is to convolute two coefficients modulo all three -# primes, then use the Chinese Remainder Theorem on the three -# result arrays to recover the result in the usual base RADIX -# form. -# - -# ====================================================================== -# Primitive roots -# ====================================================================== - -# -# Verify primitive roots: -# -# For a prime field, r is a primitive root if and only if for all prime -# factors f of p-1, r**((p-1)/f) =/= 1 (mod p). -# -def prod(F, E): - """Check that the factorization of P-1 is correct. F is the list of - factors of P-1, E lists the number of occurrences of each factor.""" - x = 1 - for y, z in zip(F, E): - x *= y**z - return x - -def is_primitive_root(r, p, factors, exponents): - """Check if r is a primitive root of F(p).""" - if p != prod(factors, exponents) + 1: - return False - for f in factors: - q, control = divmod(p-1, f) - if control != 0: - return False - if pow(r, q, p) == 1: - return False - return True - - -# ================================================================= -# Constants and limits for the 64-bit version -# ================================================================= - -RADIX = 10**19 - -# Primes P1, P2 and P3: -P = [2**64-2**32+1, 2**64-2**34+1, 2**64-2**40+1] - -# P-1, highly composite. The transform length d is variable and -# must divide D = P-1. Since all D are divisible by 3 * 2**32, -# transform lengths can be 2**n or 3 * 2**n (where n <= 32). -D = [2**32 * 3 * (5 * 17 * 257 * 65537), - 2**34 * 3**2 * (7 * 11 * 31 * 151 * 331), - 2**40 * 3**2 * (5 * 7 * 13 * 17 * 241)] - -# Prime factors of P-1 and their exponents: -F = [(2,3,5,17,257,65537), (2,3,7,11,31,151,331), (2,3,5,7,13,17,241)] -E = [(32,1,1,1,1,1), (34,2,1,1,1,1,1), (40,2,1,1,1,1,1)] - -# Maximum transform length for 2**n. Above that only 3 * 2**31 -# or 3 * 2**32 are possible. -MPD_MAXTRANSFORM_2N = 2**32 - - -# Limits in the terminology of Pollard's paper: -m2 = (MPD_MAXTRANSFORM_2N * 3) // 2 # Maximum length of the smaller array. -M1 = M2 = RADIX-1 # Maximum value per single word. -L = m2 * M1 * M2 -P[0] * P[1] * P[2] > 2 * L - - -# Primitive roots of F(P1), F(P2) and F(P3): -w = [7, 10, 19] - -# The primitive roots are correct: -for i in range(3): - if not is_primitive_root(w[i], P[i], F[i], E[i]): - print("FAIL") - - -# ================================================================= -# Constants and limits for the 32-bit version -# ================================================================= - -RADIX = 10**9 - -# Primes P1, P2 and P3: -P = [2113929217, 2013265921, 1811939329] - -# P-1, highly composite. All D = P-1 are divisible by 3 * 2**25, -# allowing for transform lengths up to 3 * 2**25 words. -D = [2**25 * 3**2 * 7, - 2**27 * 3 * 5, - 2**26 * 3**3] - -# Prime factors of P-1 and their exponents: -F = [(2,3,7), (2,3,5), (2,3)] -E = [(25,2,1), (27,1,1), (26,3)] - -# Maximum transform length for 2**n. Above that only 3 * 2**24 or -# 3 * 2**25 are possible. -MPD_MAXTRANSFORM_2N = 2**25 - - -# Limits in the terminology of Pollard's paper: -m2 = (MPD_MAXTRANSFORM_2N * 3) // 2 # Maximum length of the smaller array. -M1 = M2 = RADIX-1 # Maximum value per single word. -L = m2 * M1 * M2 -P[0] * P[1] * P[2] > 2 * L - - -# Primitive roots of F(P1), F(P2) and F(P3): -w = [5, 31, 13] - -# The primitive roots are correct: -for i in range(3): - if not is_primitive_root(w[i], P[i], F[i], E[i]): - print("FAIL") - - -# ====================================================================== -# Example transform using a single prime -# ====================================================================== - -def ntt(lst, dir): - """Perform a transform on the elements of lst. len(lst) must - be 2**n or 3 * 2**n, where n <= 25. This is the slow DFT.""" - p = 2113929217 # prime - d = len(lst) # transform length - d_prime = pow(d, (p-2), p) # inverse of d - xi = (p-1)//d - w = 5 # primitive root of F(p) - r = pow(w, xi, p) # primitive root of the subfield - r_prime = pow(w, (p-1-xi), p) # inverse of r - if dir == 1: # forward transform - a = lst # input array - A = [0] * d # transformed values - for i in range(d): - s = 0 - for j in range(d): - s += a[j] * pow(r, i*j, p) - A[i] = s % p - return A - elif dir == -1: # backward transform - A = lst # input array - a = [0] * d # transformed values - for j in range(d): - s = 0 - for i in range(d): - s += A[i] * pow(r_prime, i*j, p) - a[j] = (d_prime * s) % p - return a - -def ntt_convolute(a, b): - """convolute arrays a and b.""" - assert(len(a) == len(b)) - x = ntt(a, 1) - y = ntt(b, 1) - for i in range(len(a)): - y[i] = y[i] * x[i] - r = ntt(y, -1) - return r - - -# Example: Two arrays representing 21 and 81 in little-endian: -a = [1, 2, 0, 0] -b = [1, 8, 0, 0] - -assert(ntt_convolute(a, b) == [1, 10, 16, 0]) -assert(21 * 81 == (1*10**0 + 10*10**1 + 16*10**2 + 0*10**3)) diff --git a/Modules/_decimal/libmpdec/literature/matrix-transform.txt b/Modules/_decimal/libmpdec/literature/matrix-transform.txt deleted file mode 100644 index 701d85d..0000000 --- a/Modules/_decimal/libmpdec/literature/matrix-transform.txt +++ /dev/null @@ -1,256 +0,0 @@ - - -(* Copyright (c) 2011 Stefan Krah. All rights reserved. *) - - -The Matrix Fourier Transform: -============================= - -In libmpdec, the Matrix Fourier Transform [1] is called four-step transform -after a variant that appears in [2]. The algorithm requires that the input -array can be viewed as an R*C matrix. - -All operations are done modulo p. For readability, the proofs drop all -instances of (mod p). - - -Algorithm four-step (forward transform): ----------------------------------------- - - a := input array - d := len(a) = R * C - p := prime - w := primitive root of unity of the prime field - r := w**((p-1)/d) - A := output array - - 1) Apply a length R FNT to each column. - - 2) Multiply each matrix element (addressed by j*C+m) by r**(j*m). - - 3) Apply a length C FNT to each row. - - 4) Transpose the matrix. - - -Proof (forward transform): --------------------------- - - The algorithm can be derived starting from the regular definition of - the finite-field transform of length d: - - d-1 - ,---- - \ - A[k] = | a[l] * r**(k * l) - / - `---- - l = 0 - - - The sum can be rearranged into the sum of the sums of columns: - - C-1 R-1 - ,---- ,---- - \ \ - = | | a[i * C + j] * r**(k * (i * C + j)) - / / - `---- `---- - j = 0 i = 0 - - - Extracting a constant from the inner sum: - - C-1 R-1 - ,---- ,---- - \ \ - = | r**k*j * | a[i * C + j] * r**(k * i * C) - / / - `---- `---- - j = 0 i = 0 - - - Without any loss of generality, let k = n * R + m, - where n < C and m < R: - - C-1 R-1 - ,---- ,---- - \ \ - A[n*R+m] = | r**(R*n*j) * r**(m*j) * | a[i*C+j] * r**(R*C*n*i) * r**(C*m*i) - / / - `---- `---- - j = 0 i = 0 - - - Since r = w ** ((p-1) / (R*C)): - - a) r**(R*C*n*i) = w**((p-1)*n*i) = 1 - - b) r**(C*m*i) = w**((p-1) / R) ** (m*i) = r_R ** (m*i) - - c) r**(R*n*j) = w**((p-1) / C) ** (n*j) = r_C ** (n*j) - - r_R := root of the subfield of length R. - r_C := root of the subfield of length C. - - - C-1 R-1 - ,---- ,---- - \ \ - A[n*R+m] = | r_C**(n*j) * [ r**(m*j) * | a[i*C+j] * r_R**(m*i) ] - / ^ / - `---- | `---- 1) transform the columns - j = 0 | i = 0 - ^ | - | `-- 2) multiply - | - `-- 3) transform the rows - - - Note that the entire RHS is a function of n and m and that the results - for each pair (n, m) are stored in Fortran order. - - Let the term in square brackets be f(m, j). Step 1) and 2) precalculate - the term for all (m, j). After that, the original matrix is now a lookup - table with the mth element in the jth column at location m * C + j. - - Let the complete RHS be g(m, n). Step 3) does an in-place transform of - length n on all rows. After that, the original matrix is now a lookup - table with the mth element in the nth column at location m * C + n. - - But each (m, n) pair should be written to location n * R + m. Therefore, - step 4) transposes the result of step 3). - - - -Algorithm four-step (inverse transform): ----------------------------------------- - - A := input array - d := len(A) = R * C - p := prime - d' := d**(p-2) # inverse of d - w := primitive root of unity of the prime field - r := w**((p-1)/d) # root of the subfield - r' := w**((p-1) - (p-1)/d) # inverse of r - a := output array - - 0) View the matrix as a C*R matrix. - - 1) Transpose the matrix, producing an R*C matrix. - - 2) Apply a length C FNT to each row. - - 3) Multiply each matrix element (addressed by i*C+n) by r**(i*n). - - 4) Apply a length R FNT to each column. - - -Proof (inverse transform): --------------------------- - - The algorithm can be derived starting from the regular definition of - the finite-field inverse transform of length d: - - d-1 - ,---- - \ - a[k] = d' * | A[l] * r' ** (k * l) - / - `---- - l = 0 - - - The sum can be rearranged into the sum of the sums of columns. Note - that at this stage we still have a C*R matrix, so C denotes the number - of rows: - - R-1 C-1 - ,---- ,---- - \ \ - = d' * | | a[j * R + i] * r' ** (k * (j * R + i)) - / / - `---- `---- - i = 0 j = 0 - - - Extracting a constant from the inner sum: - - R-1 C-1 - ,---- ,---- - \ \ - = d' * | r' ** (k*i) * | a[j * R + i] * r' ** (k * j * R) - / / - `---- `---- - i = 0 j = 0 - - - Without any loss of generality, let k = m * C + n, - where m < R and n < C: - - R-1 C-1 - ,---- ,---- - \ \ - A[m*C+n] = d' * | r' ** (C*m*i) * r' ** (n*i) * | a[j*R+i] * r' ** (R*C*m*j) * r' ** (R*n*j) - / / - `---- `---- - i = 0 j = 0 - - - Since r' = w**((p-1) - (p-1)/d) and d = R*C: - - a) r' ** (R*C*m*j) = w**((p-1)*R*C*m*j - (p-1)*m*j) = 1 - - b) r' ** (C*m*i) = w**((p-1)*C - (p-1)/R) ** (m*i) = r_R' ** (m*i) - - c) r' ** (R*n*j) = r_C' ** (n*j) - - d) d' = d**(p-2) = (R*C) ** (p-2) = R**(p-2) * C**(p-2) = R' * C' - - r_R' := inverse of the root of the subfield of length R. - r_C' := inverse of the root of the subfield of length C. - R' := inverse of R - C' := inverse of C - - - R-1 C-1 - ,---- ,---- 2) transform the rows of a^T - \ \ - A[m*C+n] = R' * | r_R' ** (m*i) * [ r' ** (n*i) * C' * | a[j*R+i] * r_C' ** (n*j) ] - / ^ / ^ - `---- | `---- | - i = 0 | j = 0 | - ^ | `-- 1) Transpose input matrix - | `-- 3) multiply to address elements by - | i * C + j - `-- 3) transform the columns - - - - Note that the entire RHS is a function of m and n and that the results - for each pair (m, n) are stored in C order. - - Let the term in square brackets be f(n, i). Without step 1), the sum - would perform a length C transform on the columns of the input matrix. - This is a) inefficient and b) the results are needed in C order, so - step 1) exchanges rows and columns. - - Step 2) and 3) precalculate f(n, i) for all (n, i). After that, the - original matrix is now a lookup table with the ith element in the nth - column at location i * C + n. - - Let the complete RHS be g(m, n). Step 4) does an in-place transform of - length m on all columns. After that, the original matrix is now a lookup - table with the mth element in the nth column at location m * C + n, - which means that all A[k] = A[m * C + n] are in the correct order. - - --- - - [1] Joerg Arndt: "Matters Computational" - http://www.jjj.de/fxt/ - [2] David H. Bailey: FFTs in External or Hierarchical Memory - http://crd.lbl.gov/~dhbailey/dhbpapers/ - - - diff --git a/Modules/_decimal/libmpdec/literature/mulmod-64.txt b/Modules/_decimal/libmpdec/literature/mulmod-64.txt deleted file mode 100644 index 029b8de..0000000 --- a/Modules/_decimal/libmpdec/literature/mulmod-64.txt +++ /dev/null @@ -1,127 +0,0 @@ - - -(* Copyright (c) 2011 Stefan Krah. All rights reserved. *) - - -========================================================================== - Calculate (a * b) % p using special primes -========================================================================== - -A description of the algorithm can be found in the apfloat manual by -Tommila [1]. - - -Definitions: ------------- - -In the whole document, "==" stands for "is congruent with". - -Result of a * b in terms of high/low words: - - (1) hi * 2**64 + lo = a * b - -Special primes: - - (2) p = 2**64 - z + 1, where z = 2**n - -Single step modular reduction: - - (3) R(hi, lo) = hi * z - hi + lo - - -Strategy: ---------- - - a) Set (hi, lo) to the result of a * b. - - b) Set (hi', lo') to the result of R(hi, lo). - - c) Repeat step b) until 0 <= hi' * 2**64 + lo' < 2*p. - - d) If the result is less than p, return lo'. Otherwise return lo' - p. - - -The reduction step b) preserves congruence: -------------------------------------------- - - hi * 2**64 + lo == hi * z - hi + lo (mod p) - - Proof: - ~~~~~~ - - hi * 2**64 + lo = (2**64 - z + 1) * hi + z * hi - hi + lo - - = p * hi + z * hi - hi + lo - - == z * hi - hi + lo (mod p) - - -Maximum numbers of step b): ---------------------------- - -# To avoid unnecessary formalism, define: - -def R(hi, lo, z): - return divmod(hi * z - hi + lo, 2**64) - -# For simplicity, assume hi=2**64-1, lo=2**64-1 after the -# initial multiplication a * b. This is of course impossible -# but certainly covers all cases. - -# Then, for p1: -hi=2**64-1; lo=2**64-1; z=2**32 -p1 = 2**64 - z + 1 - -hi, lo = R(hi, lo, z) # First reduction -hi, lo = R(hi, lo, z) # Second reduction -hi * 2**64 + lo < 2 * p1 # True - -# For p2: -hi=2**64-1; lo=2**64-1; z=2**34 -p2 = 2**64 - z + 1 - -hi, lo = R(hi, lo, z) # First reduction -hi, lo = R(hi, lo, z) # Second reduction -hi, lo = R(hi, lo, z) # Third reduction -hi * 2**64 + lo < 2 * p2 # True - -# For p3: -hi=2**64-1; lo=2**64-1; z=2**40 -p3 = 2**64 - z + 1 - -hi, lo = R(hi, lo, z) # First reduction -hi, lo = R(hi, lo, z) # Second reduction -hi, lo = R(hi, lo, z) # Third reduction -hi * 2**64 + lo < 2 * p3 # True - - -Step d) preserves congruence and yields a result < p: ------------------------------------------------------ - - Case hi = 0: - - Case lo < p: trivial. - - Case lo >= p: - - lo == lo - p (mod p) # result is congruent - - p <= lo < 2*p -> 0 <= lo - p < p # result is in the correct range - - Case hi = 1: - - p < 2**64 /\ 2**64 + lo < 2*p -> lo < p # lo is always less than p - - 2**64 + lo == 2**64 + (lo - p) (mod p) # result is congruent - - = lo - p # exactly the same value as the previous RHS - # in uint64_t arithmetic. - - p < 2**64 + lo < 2*p -> 0 < 2**64 + (lo - p) < p # correct range - - - -[1] http://www.apfloat.org/apfloat/2.40/apfloat.pdf - - - diff --git a/Modules/_decimal/libmpdec/literature/mulmod-ppro.txt b/Modules/_decimal/libmpdec/literature/mulmod-ppro.txt deleted file mode 100644 index 4d17a92..0000000 --- a/Modules/_decimal/libmpdec/literature/mulmod-ppro.txt +++ /dev/null @@ -1,269 +0,0 @@ - - -(* Copyright (c) 2011 Stefan Krah. All rights reserved. *) - - -======================================================================== - Calculate (a * b) % p using the 80-bit x87 FPU -======================================================================== - -A description of the algorithm can be found in the apfloat manual by -Tommila [1]. - -The proof follows an argument made by Granlund/Montgomery in [2]. - - -Definitions and assumptions: ----------------------------- - -The 80-bit extended precision format uses 64 bits for the significand: - - (1) F = 64 - -The modulus is prime and less than 2**31: - - (2) 2 <= p < 2**31 - -The factors are less than p: - - (3) 0 <= a < p - (4) 0 <= b < p - -The product a * b is less than 2**62 and is thus exact in 64 bits: - - (5) n = a * b - -The product can be represented in terms of quotient and remainder: - - (6) n = q * p + r - -Using (3), (4) and the fact that p is prime, the remainder is always -greater than zero: - - (7) 0 <= q < p /\ 1 <= r < p - - -Strategy: ---------- - -Precalculate the 80-bit long double inverse of p, with a maximum -relative error of 2**(1-F): - - (8) pinv = (long double)1.0 / p - -Calculate an estimate for q = floor(n/p). The multiplication has another -maximum relative error of 2**(1-F): - - (9) qest = n * pinv - -If we can show that q < qest < q+1, then trunc(qest) = q. It is then -easy to recover the remainder r. The complete algorithm is: - - a) Set the control word to 64-bit precision and truncation mode. - - b) n = a * b # Calculate exact product. - - c) qest = n * pinv # Calculate estimate for the quotient. - - d) q = (qest+2**63)-2**63 # Truncate qest to the exact quotient. - - f) r = n - q * p # Calculate remainder. - - -Proof for q < qest < q+1: -------------------------- - -Using the cumulative error, the error bounds for qest are: - - n n * (1 + 2**(1-F))**2 - (9) --------------------- <= qest <= --------------------- - p * (1 + 2**(1-F))**2 p - - - Lemma 1: - -------- - n q * p + r - (10) q < --------------------- = --------------------- - p * (1 + 2**(1-F))**2 p * (1 + 2**(1-F))**2 - - - Proof: - ~~~~~~ - - (I) q * p * (1 + 2**(1-F))**2 < q * p + r - - (II) q * p * 2**(2-F) + q * p * 2**(2-2*F) < r - - Using (1) and (7), it is sufficient to show that: - - (III) q * p * 2**(-62) + q * p * 2**(-126) < 1 <= r - - (III) can easily be verified by substituting the largest possible - values p = 2**31-1 and q = 2**31-2. - - The critical cases occur when r = 1, n = m * p + 1. These cases - can be exhaustively verified with a test program. - - - Lemma 2: - -------- - - n * (1 + 2**(1-F))**2 (q * p + r) * (1 + 2**(1-F))**2 - (11) --------------------- = ------------------------------- < q + 1 - p p - - Proof: - ~~~~~~ - - (I) (q * p + r) + (q * p + r) * 2**(2-F) + (q * p + r) * 2**(2-2*F) < q * p + p - - (II) (q * p + r) * 2**(2-F) + (q * p + r) * 2**(2-2*F) < p - r - - Using (1) and (7), it is sufficient to show that: - - (III) (q * p + r) * 2**(-62) + (q * p + r) * 2**(-126) < 1 <= p - r - - (III) can easily be verified by substituting the largest possible - values p = 2**31-1, q = 2**31-2 and r = 2**31-2. - - The critical cases occur when r = (p - 1), n = m * p - 1. These cases - can be exhaustively verified with a test program. - - -[1] http://www.apfloat.org/apfloat/2.40/apfloat.pdf -[2] http://gmplib.org/~tege/divcnst-pldi94.pdf - [Section 7: "Use of floating point"] - - - -(* Coq proof for (10) and (11) *) - -Require Import ZArith. -Require Import QArith. -Require Import Qpower. -Require Import Qabs. -Require Import Psatz. - -Open Scope Q_scope. - - -Ltac qreduce T := - rewrite <- (Qred_correct (T)); simpl (Qred (T)). - -Theorem Qlt_move_right : - forall x y z:Q, x + z < y <-> x < y - z. -Proof. - intros. - split. - intros. - psatzl Q. - intros. - psatzl Q. -Qed. - -Theorem Qlt_mult_by_z : - forall x y z:Q, 0 < z -> (x < y <-> x * z < y * z). -Proof. - intros. - split. - intros. - apply Qmult_lt_compat_r. trivial. trivial. - intros. - rewrite <- (Qdiv_mult_l x z). rewrite <- (Qdiv_mult_l y z). - apply Qmult_lt_compat_r. - apply Qlt_shift_inv_l. - trivial. psatzl Q. trivial. psatzl Q. psatzl Q. -Qed. - -Theorem Qle_mult_quad : - forall (a b c d:Q), - 0 <= a -> a <= c -> - 0 <= b -> b <= d -> - a * b <= c * d. - intros. - psatz Q. -Qed. - - -Theorem q_lt_qest: - forall (p q r:Q), - (0 < p) -> (p <= (2#1)^31 - 1) -> - (0 <= q) -> (q <= p - 1) -> - (1 <= r) -> (r <= p - 1) -> - q < (q * p + r) / (p * (1 + (2#1)^(-63))^2). -Proof. - intros. - rewrite Qlt_mult_by_z with (z := (p * (1 + (2#1)^(-63))^2)). - - unfold Qdiv. - rewrite <- Qmult_assoc. - rewrite (Qmult_comm (/ (p * (1 + (2 # 1) ^ (-63)) ^ 2)) (p * (1 + (2 # 1) ^ (-63)) ^ 2)). - rewrite Qmult_inv_r. - rewrite Qmult_1_r. - - assert (q * (p * (1 + (2 # 1) ^ (-63)) ^ 2) == q * p + (q * p) * ((2 # 1) ^ (-62) + (2 # 1) ^ (-126))). - qreduce ((1 + (2 # 1) ^ (-63)) ^ 2). - qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)). - ring_simplify. - reflexivity. - rewrite H5. - - rewrite Qplus_comm. - rewrite Qlt_move_right. - ring_simplify (q * p + r - q * p). - qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)). - - apply Qlt_le_trans with (y := 1). - rewrite Qlt_mult_by_z with (z := 85070591730234615865843651857942052864 # 18446744073709551617). - ring_simplify. - - apply Qle_lt_trans with (y := ((2 # 1) ^ 31 - (2#1)) * ((2 # 1) ^ 31 - 1)). - apply Qle_mult_quad. - assumption. psatzl Q. psatzl Q. psatzl Q. psatzl Q. psatzl Q. assumption. psatzl Q. psatzl Q. -Qed. - -Theorem qest_lt_qplus1: - forall (p q r:Q), - (0 < p) -> (p <= (2#1)^31 - 1) -> - (0 <= q) -> (q <= p - 1) -> - (1 <= r) -> (r <= p - 1) -> - ((q * p + r) * (1 + (2#1)^(-63))^2) / p < q + 1. -Proof. - intros. - rewrite Qlt_mult_by_z with (z := p). - - unfold Qdiv. - rewrite <- Qmult_assoc. - rewrite (Qmult_comm (/ p) p). - rewrite Qmult_inv_r. - rewrite Qmult_1_r. - - assert ((q * p + r) * (1 + (2 # 1) ^ (-63)) ^ 2 == q * p + r + (q * p + r) * ((2 # 1) ^ (-62) + (2 # 1) ^ (-126))). - qreduce ((1 + (2 # 1) ^ (-63)) ^ 2). - qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)). - ring_simplify. reflexivity. - rewrite H5. - - rewrite <- Qplus_assoc. rewrite <- Qplus_comm. rewrite Qlt_move_right. - ring_simplify ((q + 1) * p - q * p). - - rewrite <- Qplus_comm. rewrite Qlt_move_right. - - apply Qlt_le_trans with (y := 1). - qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)). - - rewrite Qlt_mult_by_z with (z := 85070591730234615865843651857942052864 # 18446744073709551617). - ring_simplify. - - ring_simplify in H0. - apply Qle_lt_trans with (y := (2147483646 # 1) * (2147483647 # 1) + (2147483646 # 1)). - - apply Qplus_le_compat. - apply Qle_mult_quad. - assumption. psatzl Q. auto with qarith. assumption. psatzl Q. - auto with qarith. auto with qarith. - psatzl Q. psatzl Q. assumption. -Qed. - - - diff --git a/Modules/_decimal/libmpdec/literature/six-step.txt b/Modules/_decimal/libmpdec/literature/six-step.txt deleted file mode 100644 index 8e45f48..0000000 --- a/Modules/_decimal/libmpdec/literature/six-step.txt +++ /dev/null @@ -1,63 +0,0 @@ - - -(* Copyright (c) 2011 Stefan Krah. All rights reserved. *) - - -The Six Step Transform: -======================= - -In libmpdec, the six-step transform is the Matrix Fourier Transform (See -matrix-transform.txt) in disguise. It is called six-step transform after -a variant that appears in [1]. The algorithm requires that the input -array can be viewed as an R*C matrix. - - -Algorithm six-step (forward transform): ---------------------------------------- - - 1a) Transpose the matrix. - - 1b) Apply a length R FNT to each row. - - 1c) Transpose the matrix. - - 2) Multiply each matrix element (addressed by j*C+m) by r**(j*m). - - 3) Apply a length C FNT to each row. - - 4) Transpose the matrix. - -Note that steps 1a) - 1c) are exactly equivalent to step 1) of the Matrix -Fourier Transform. For large R, it is faster to transpose twice and do -a transform on the rows than to perform a column transpose directly. - - - -Algorithm six-step (inverse transform): ---------------------------------------- - - 0) View the matrix as a C*R matrix. - - 1) Transpose the matrix, producing an R*C matrix. - - 2) Apply a length C FNT to each row. - - 3) Multiply each matrix element (addressed by i*C+n) by r**(i*n). - - 4a) Transpose the matrix. - - 4b) Apply a length R FNT to each row. - - 4c) Transpose the matrix. - -Again, steps 4a) - 4c) are equivalent to step 4) of the Matrix Fourier -Transform. - - - --- - - [1] David H. Bailey: FFTs in External or Hierarchical Memory - http://crd.lbl.gov/~dhbailey/dhbpapers/ - - diff --git a/Modules/_decimal/libmpdec/literature/umodarith.lisp b/Modules/_decimal/libmpdec/literature/umodarith.lisp deleted file mode 100644 index 99d71c3..0000000 --- a/Modules/_decimal/libmpdec/literature/umodarith.lisp +++ /dev/null @@ -1,692 +0,0 @@ -; -; Copyright (c) 2008-2016 Stefan Krah. All rights reserved. -; -; Redistribution and use in source and binary forms, with or without -; modification, are permitted provided that the following conditions -; are met: -; -; 1. Redistributions of source code must retain the above copyright -; notice, this list of conditions and the following disclaimer. -; -; 2. Redistributions in binary form must reproduce the above copyright -; notice, this list of conditions and the following disclaimer in the -; documentation and/or other materials provided with the distribution. -; -; THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND -; ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE -; ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE -; FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL -; DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS -; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) -; HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT -; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY -; OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF -; SUCH DAMAGE. -; - - -(in-package "ACL2") - -(include-book "arithmetic/top-with-meta" :dir :system) -(include-book "arithmetic-2/floor-mod/floor-mod" :dir :system) - - -;; ===================================================================== -;; Proofs for several functions in umodarith.h -;; ===================================================================== - - - -;; ===================================================================== -;; Helper theorems -;; ===================================================================== - -(defthm elim-mod-m<x<2*m - (implies (and (<= m x) - (< x (* 2 m)) - (rationalp x) (rationalp m)) - (equal (mod x m) - (+ x (- m))))) - -(defthm modaux-1a - (implies (and (< x m) (< 0 x) (< 0 m) - (rationalp x) (rationalp m)) - (equal (mod (- x) m) - (+ (- x) m)))) - -(defthm modaux-1b - (implies (and (< (- x) m) (< x 0) (< 0 m) - (rationalp x) (rationalp m)) - (equal (mod x m) - (+ x m))) - :hints (("Goal" :use ((:instance modaux-1a - (x (- x))))))) - -(defthm modaux-1c - (implies (and (< x m) (< 0 x) (< 0 m) - (rationalp x) (rationalp m)) - (equal (mod x m) - x))) - -(defthm modaux-2a - (implies (and (< 0 b) (< b m) - (natp x) (natp b) (natp m) - (< (mod (+ b x) m) b)) - (equal (mod (+ (- m) b x) m) - (+ (- m) b (mod x m))))) - -(defthm modaux-2b - (implies (and (< 0 b) (< b m) - (natp x) (natp b) (natp m) - (< (mod (+ b x) m) b)) - (equal (mod (+ b x) m) - (+ (- m) b (mod x m)))) - :hints (("Goal" :use (modaux-2a)))) - -(defthm linear-mod-1 - (implies (and (< x m) (< b m) - (natp x) (natp b) - (rationalp m)) - (equal (< x (mod (+ (- b) x) m)) - (< x b))) - :hints (("Goal" :use ((:instance modaux-1a - (x (+ b (- x)))))))) - -(defthm linear-mod-2 - (implies (and (< 0 b) (< b m) - (natp x) (natp b) - (natp m)) - (equal (< (mod x m) - (mod (+ (- b) x) m)) - (< (mod x m) b)))) - -(defthm linear-mod-3 - (implies (and (< x m) (< b m) - (natp x) (natp b) - (rationalp m)) - (equal (<= b (mod (+ b x) m)) - (< (+ b x) m))) - :hints (("Goal" :use ((:instance elim-mod-m<x<2*m - (x (+ b x))))))) - -(defthm modaux-2c - (implies (and (< 0 b) (< b m) - (natp x) (natp b) (natp m) - (<= b (mod (+ b x) m))) - (equal (mod (+ b x) m) - (+ b (mod x m)))) - :hints (("Subgoal *1/8''" :use (linear-mod-3)))) - -(defthmd modaux-2d - (implies (and (< x m) (< 0 x) (< 0 m) - (< (- m) b) (< b 0) (rationalp m) - (<= x (mod (+ b x) m)) - (rationalp x) (rationalp b)) - (equal (+ (- m) (mod (+ b x) m)) - (+ b x))) - :hints (("Goal" :cases ((<= 0 (+ b x)))) - ("Subgoal 2'" :use ((:instance modaux-1b - (x (+ b x))))))) - -(defthm mod-m-b - (implies (and (< 0 x) (< 0 b) (< 0 m) - (< x b) (< b m) - (natp x) (natp b) (natp m)) - (equal (mod (+ (mod (- x) m) b) m) - (mod (- x) b)))) - - -;; ===================================================================== -;; addmod, submod -;; ===================================================================== - -(defun addmod (a b m base) - (let* ((s (mod (+ a b) base)) - (s (if (< s a) (mod (- s m) base) s)) - (s (if (>= s m) (mod (- s m) base) s))) - s)) - -(defthmd addmod-correct - (implies (and (< 0 m) (< m base) - (< a m) (<= b m) - (natp m) (natp base) - (natp a) (natp b)) - (equal (addmod a b m base) - (mod (+ a b) m))) - :hints (("Goal" :cases ((<= base (+ a b)))) - ("Subgoal 2.1'" :use ((:instance elim-mod-m<x<2*m - (x (+ a b))))))) - -(defun submod (a b m base) - (let* ((d (mod (- a b) base)) - (d (if (< a d) (mod (+ d m) base) d))) - d)) - -(defthmd submod-aux1 - (implies (and (< a (mod (+ a (- b)) base)) - (< 0 base) (< a base) (<= b base) - (natp base) (natp a) (natp b)) - (< a b)) - :rule-classes :forward-chaining) - -(defthmd submod-aux2 - (implies (and (<= (mod (+ a (- b)) base) a) - (< 0 base) (< a base) (< b base) - (natp base) (natp a) (natp b)) - (<= b a)) - :rule-classes :forward-chaining) - -(defthmd submod-correct - (implies (and (< 0 m) (< m base) - (< a m) (<= b m) - (natp m) (natp base) - (natp a) (natp b)) - (equal (submod a b m base) - (mod (- a b) m))) - :hints (("Goal" :cases ((<= base (+ a b)))) - ("Subgoal 2.2" :use ((:instance submod-aux1))) - ("Subgoal 2.2'''" :cases ((and (< 0 (+ a (- b) m)) - (< (+ a (- b) m) m)))) - ("Subgoal 2.1" :use ((:instance submod-aux2))) - ("Subgoal 1.2" :use ((:instance submod-aux1))) - ("Subgoal 1.1" :use ((:instance submod-aux2))))) - - -(defun submod-2 (a b m base) - (let* ((d (mod (- a b) base)) - (d (if (< a b) (mod (+ d m) base) d))) - d)) - -(defthm submod-2-correct - (implies (and (< 0 m) (< m base) - (< a m) (<= b m) - (natp m) (natp base) - (natp a) (natp b)) - (equal (submod-2 a b m base) - (mod (- a b) m))) - :hints (("Subgoal 2'" :cases ((and (< 0 (+ a (- b) m)) - (< (+ a (- b) m) m)))))) - - -;; ========================================================================= -;; ext-submod is correct -;; ========================================================================= - -; a < 2*m, b < 2*m -(defun ext-submod (a b m base) - (let* ((a (if (>= a m) (- a m) a)) - (b (if (>= b m) (- b m) b)) - (d (mod (- a b) base)) - (d (if (< a b) (mod (+ d m) base) d))) - d)) - -; a < 2*m, b < 2*m -(defun ext-submod-2 (a b m base) - (let* ((a (mod a m)) - (b (mod b m)) - (d (mod (- a b) base)) - (d (if (< a b) (mod (+ d m) base) d))) - d)) - -(defthmd ext-submod-ext-submod-2-equal - (implies (and (< 0 m) (< m base) - (< a (* 2 m)) (< b (* 2 m)) - (natp m) (natp base) - (natp a) (natp b)) - (equal (ext-submod a b m base) - (ext-submod-2 a b m base)))) - -(defthmd ext-submod-2-correct - (implies (and (< 0 m) (< m base) - (< a (* 2 m)) (< b (* 2 m)) - (natp m) (natp base) - (natp a) (natp b)) - (equal (ext-submod-2 a b m base) - (mod (- a b) m)))) - - -;; ========================================================================= -;; dw-reduce is correct -;; ========================================================================= - -(defun dw-reduce (hi lo m base) - (let* ((r1 (mod hi m)) - (r2 (mod (+ (* r1 base) lo) m))) - r2)) - -(defthmd dw-reduce-correct - (implies (and (< 0 m) (< m base) - (< hi base) (< lo base) - (natp m) (natp base) - (natp hi) (natp lo)) - (equal (dw-reduce hi lo m base) - (mod (+ (* hi base) lo) m)))) - -(defthmd <=-multiply-both-sides-by-z - (implies (and (rationalp x) (rationalp y) - (< 0 z) (rationalp z)) - (equal (<= x y) - (<= (* z x) (* z y))))) - -(defthmd dw-reduce-aux1 - (implies (and (< 0 m) (< m base) - (natp m) (natp base) - (< lo base) (natp lo) - (< x m) (natp x)) - (< (+ lo (* base x)) (* base m))) - :hints (("Goal" :cases ((<= (+ x 1) m))) - ("Subgoal 1''" :cases ((<= (* base (+ x 1)) (* base m)))) - ("subgoal 1.2" :use ((:instance <=-multiply-both-sides-by-z - (x (+ 1 x)) - (y m) - (z base)))))) - -(defthm dw-reduce-aux2 - (implies (and (< x (* base m)) - (< 0 m) (< m base) - (natp m) (natp base) (natp x)) - (< (floor x m) base))) - -;; This is the necessary condition for using _mpd_div_words(). -(defthmd dw-reduce-second-quotient-fits-in-single-word - (implies (and (< 0 m) (< m base) - (< hi base) (< lo base) - (natp m) (natp base) - (natp hi) (natp lo) - (equal r1 (mod hi m))) - (< (floor (+ (* r1 base) lo) m) - base)) - :hints (("Goal" :cases ((< r1 m))) - ("Subgoal 1''" :cases ((< (+ lo (* base (mod hi m))) (* base m)))) - ("Subgoal 1.2" :use ((:instance dw-reduce-aux1 - (x (mod hi m))))))) - - -;; ========================================================================= -;; dw-submod is correct -;; ========================================================================= - -(defun dw-submod (a hi lo m base) - (let* ((r (dw-reduce hi lo m base)) - (d (mod (- a r) base)) - (d (if (< a r) (mod (+ d m) base) d))) - d)) - -(defthmd dw-submod-aux1 - (implies (and (natp a) (< 0 m) (natp m) - (natp x) (equal r (mod x m))) - (equal (mod (- a x) m) - (mod (- a r) m)))) - -(defthmd dw-submod-correct - (implies (and (< 0 m) (< m base) - (natp a) (< a m) - (< hi base) (< lo base) - (natp m) (natp base) - (natp hi) (natp lo)) - (equal (dw-submod a hi lo m base) - (mod (- a (+ (* base hi) lo)) m))) - :hints (("Goal" :in-theory (disable dw-reduce) - :use ((:instance dw-submod-aux1 - (x (+ lo (* base hi))) - (r (dw-reduce hi lo m base))) - (:instance dw-reduce-correct))))) - - -;; ========================================================================= -;; ANSI C arithmetic for uint64_t -;; ========================================================================= - -(defun add (a b) - (mod (+ a b) - (expt 2 64))) - -(defun sub (a b) - (mod (- a b) - (expt 2 64))) - -(defun << (w n) - (mod (* w (expt 2 n)) - (expt 2 64))) - -(defun >> (w n) - (floor w (expt 2 n))) - -;; join upper and lower half of a double word, yielding a 128 bit number -(defun join (hi lo) - (+ (* (expt 2 64) hi) lo)) - - -;; ============================================================================= -;; Fast modular reduction -;; ============================================================================= - -;; These are the three primes used in the Number Theoretic Transform. -;; A fast modular reduction scheme exists for all of them. -(defmacro p1 () - (+ (expt 2 64) (- (expt 2 32)) 1)) - -(defmacro p2 () - (+ (expt 2 64) (- (expt 2 34)) 1)) - -(defmacro p3 () - (+ (expt 2 64) (- (expt 2 40)) 1)) - - -;; reduce the double word number hi*2**64 + lo (mod p1) -(defun simple-mod-reduce-p1 (hi lo) - (+ (* (expt 2 32) hi) (- hi) lo)) - -;; reduce the double word number hi*2**64 + lo (mod p2) -(defun simple-mod-reduce-p2 (hi lo) - (+ (* (expt 2 34) hi) (- hi) lo)) - -;; reduce the double word number hi*2**64 + lo (mod p3) -(defun simple-mod-reduce-p3 (hi lo) - (+ (* (expt 2 40) hi) (- hi) lo)) - - -; ---------------------------------------------------------- -; The modular reductions given above are correct -; ---------------------------------------------------------- - -(defthmd congruence-p1-aux - (equal (* (expt 2 64) hi) - (+ (* (p1) hi) - (* (expt 2 32) hi) - (- hi)))) - -(defthmd congruence-p2-aux - (equal (* (expt 2 64) hi) - (+ (* (p2) hi) - (* (expt 2 34) hi) - (- hi)))) - -(defthmd congruence-p3-aux - (equal (* (expt 2 64) hi) - (+ (* (p3) hi) - (* (expt 2 40) hi) - (- hi)))) - -(defthmd mod-augment - (implies (and (rationalp x) - (rationalp y) - (rationalp m)) - (equal (mod (+ x y) m) - (mod (+ x (mod y m)) m)))) - -(defthmd simple-mod-reduce-p1-congruent - (implies (and (integerp hi) - (integerp lo)) - (equal (mod (simple-mod-reduce-p1 hi lo) (p1)) - (mod (join hi lo) (p1)))) - :hints (("Goal''" :use ((:instance congruence-p1-aux) - (:instance mod-augment - (m (p1)) - (x (+ (- hi) lo (* (expt 2 32) hi))) - (y (* (p1) hi))))))) - -(defthmd simple-mod-reduce-p2-congruent - (implies (and (integerp hi) - (integerp lo)) - (equal (mod (simple-mod-reduce-p2 hi lo) (p2)) - (mod (join hi lo) (p2)))) - :hints (("Goal''" :use ((:instance congruence-p2-aux) - (:instance mod-augment - (m (p2)) - (x (+ (- hi) lo (* (expt 2 34) hi))) - (y (* (p2) hi))))))) - -(defthmd simple-mod-reduce-p3-congruent - (implies (and (integerp hi) - (integerp lo)) - (equal (mod (simple-mod-reduce-p3 hi lo) (p3)) - (mod (join hi lo) (p3)))) - :hints (("Goal''" :use ((:instance congruence-p3-aux) - (:instance mod-augment - (m (p3)) - (x (+ (- hi) lo (* (expt 2 40) hi))) - (y (* (p3) hi))))))) - - -; --------------------------------------------------------------------- -; We need a number less than 2*p, so that we can use the trick from -; elim-mod-m<x<2*m for the final reduction. -; For p1, two modular reductions are sufficient, for p2 and p3 three. -; --------------------------------------------------------------------- - -;; p1: the first reduction is less than 2**96 -(defthmd simple-mod-reduce-p1-<-2**96 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (natp hi) (natp lo)) - (< (simple-mod-reduce-p1 hi lo) - (expt 2 96)))) - -;; p1: the second reduction is less than 2*p1 -(defthmd simple-mod-reduce-p1-<-2*p1 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (< (join hi lo) (expt 2 96)) - (natp hi) (natp lo)) - (< (simple-mod-reduce-p1 hi lo) - (* 2 (p1))))) - - -;; p2: the first reduction is less than 2**98 -(defthmd simple-mod-reduce-p2-<-2**98 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (natp hi) (natp lo)) - (< (simple-mod-reduce-p2 hi lo) - (expt 2 98)))) - -;; p2: the second reduction is less than 2**69 -(defthmd simple-mod-reduce-p2-<-2*69 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (< (join hi lo) (expt 2 98)) - (natp hi) (natp lo)) - (< (simple-mod-reduce-p2 hi lo) - (expt 2 69)))) - -;; p3: the third reduction is less than 2*p2 -(defthmd simple-mod-reduce-p2-<-2*p2 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (< (join hi lo) (expt 2 69)) - (natp hi) (natp lo)) - (< (simple-mod-reduce-p2 hi lo) - (* 2 (p2))))) - - -;; p3: the first reduction is less than 2**104 -(defthmd simple-mod-reduce-p3-<-2**104 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (natp hi) (natp lo)) - (< (simple-mod-reduce-p3 hi lo) - (expt 2 104)))) - -;; p3: the second reduction is less than 2**81 -(defthmd simple-mod-reduce-p3-<-2**81 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (< (join hi lo) (expt 2 104)) - (natp hi) (natp lo)) - (< (simple-mod-reduce-p3 hi lo) - (expt 2 81)))) - -;; p3: the third reduction is less than 2*p3 -(defthmd simple-mod-reduce-p3-<-2*p3 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (< (join hi lo) (expt 2 81)) - (natp hi) (natp lo)) - (< (simple-mod-reduce-p3 hi lo) - (* 2 (p3))))) - - -; ------------------------------------------------------------------------- -; The simple modular reductions, adapted for compiler friendly C -; ------------------------------------------------------------------------- - -(defun mod-reduce-p1 (hi lo) - (let* ((y hi) - (x y) - (hi (>> hi 32)) - (x (sub lo x)) - (hi (if (> x lo) (+ hi -1) hi)) - (y (<< y 32)) - (lo (add y x)) - (hi (if (< lo y) (+ hi 1) hi))) - (+ (* hi (expt 2 64)) lo))) - -(defun mod-reduce-p2 (hi lo) - (let* ((y hi) - (x y) - (hi (>> hi 30)) - (x (sub lo x)) - (hi (if (> x lo) (+ hi -1) hi)) - (y (<< y 34)) - (lo (add y x)) - (hi (if (< lo y) (+ hi 1) hi))) - (+ (* hi (expt 2 64)) lo))) - -(defun mod-reduce-p3 (hi lo) - (let* ((y hi) - (x y) - (hi (>> hi 24)) - (x (sub lo x)) - (hi (if (> x lo) (+ hi -1) hi)) - (y (<< y 40)) - (lo (add y x)) - (hi (if (< lo y) (+ hi 1) hi))) - (+ (* hi (expt 2 64)) lo))) - - -; ------------------------------------------------------------------------- -; The compiler friendly versions are equal to the simple versions -; ------------------------------------------------------------------------- - -(defthm mod-reduce-aux1 - (implies (and (<= 0 a) (natp a) (natp m) - (< (- m) b) (<= b 0) - (integerp b) - (< (mod (+ b a) m) - (mod a m))) - (equal (mod (+ b a) m) - (+ b (mod a m)))) - :hints (("Subgoal 2" :use ((:instance modaux-1b - (x (+ a b))))))) - -(defthm mod-reduce-aux2 - (implies (and (<= 0 a) (natp a) (natp m) - (< b m) (natp b) - (< (mod (+ b a) m) - (mod a m))) - (equal (+ m (mod (+ b a) m)) - (+ b (mod a m))))) - - -(defthm mod-reduce-aux3 - (implies (and (< 0 a) (natp a) (natp m) - (< (- m) b) (< b 0) - (integerp b) - (<= (mod a m) - (mod (+ b a) m))) - (equal (+ (- m) (mod (+ b a) m)) - (+ b (mod a m)))) - :hints (("Subgoal 1.2'" :use ((:instance modaux-1b - (x b)))) - ("Subgoal 1''" :use ((:instance modaux-2d - (x I)))))) - - -(defthm mod-reduce-aux4 - (implies (and (< 0 a) (natp a) (natp m) - (< b m) (natp b) - (<= (mod a m) - (mod (+ b a) m))) - (equal (mod (+ b a) m) - (+ b (mod a m))))) - - -(defthm mod-reduce-p1==simple-mod-reduce-p1 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (natp hi) (natp lo)) - (equal (mod-reduce-p1 hi lo) - (simple-mod-reduce-p1 hi lo))) - :hints (("Goal" :in-theory (disable expt) - :cases ((< 0 hi))) - ("Subgoal 1.2.2'" :use ((:instance mod-reduce-aux1 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 32) hi))))) - ("Subgoal 1.2.1'" :use ((:instance mod-reduce-aux3 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 32) hi))))) - ("Subgoal 1.1.2'" :use ((:instance mod-reduce-aux2 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 32) hi))))) - ("Subgoal 1.1.1'" :use ((:instance mod-reduce-aux4 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 32) hi))))))) - - -(defthm mod-reduce-p2==simple-mod-reduce-p2 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (natp hi) (natp lo)) - (equal (mod-reduce-p2 hi lo) - (simple-mod-reduce-p2 hi lo))) - :hints (("Goal" :cases ((< 0 hi))) - ("Subgoal 1.2.2'" :use ((:instance mod-reduce-aux1 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 34) hi))))) - ("Subgoal 1.2.1'" :use ((:instance mod-reduce-aux3 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 34) hi))))) - ("Subgoal 1.1.2'" :use ((:instance mod-reduce-aux2 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 34) hi))))) - ("Subgoal 1.1.1'" :use ((:instance mod-reduce-aux4 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 34) hi))))))) - - -(defthm mod-reduce-p3==simple-mod-reduce-p3 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (natp hi) (natp lo)) - (equal (mod-reduce-p3 hi lo) - (simple-mod-reduce-p3 hi lo))) - :hints (("Goal" :cases ((< 0 hi))) - ("Subgoal 1.2.2'" :use ((:instance mod-reduce-aux1 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 40) hi))))) - ("Subgoal 1.2.1'" :use ((:instance mod-reduce-aux3 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 40) hi))))) - ("Subgoal 1.1.2'" :use ((:instance mod-reduce-aux2 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 40) hi))))) - ("Subgoal 1.1.1'" :use ((:instance mod-reduce-aux4 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 40) hi))))))) - - - diff --git a/Modules/_decimal/libmpdec/mpalloc.c b/Modules/_decimal/libmpdec/mpalloc.c deleted file mode 100644 index a854e09..0000000 --- a/Modules/_decimal/libmpdec/mpalloc.c +++ /dev/null @@ -1,297 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdio.h> -#include <stdlib.h> -#include "typearith.h" -#include "mpalloc.h" - - -#if defined(_MSC_VER) - #pragma warning(disable : 4232) -#endif - - -/* Guaranteed minimum allocation for a coefficient. May be changed once - at program start using mpd_setminalloc(). */ -mpd_ssize_t MPD_MINALLOC = MPD_MINALLOC_MIN; - -/* Custom allocation and free functions */ -void *(* mpd_mallocfunc)(size_t size) = malloc; -void *(* mpd_reallocfunc)(void *ptr, size_t size) = realloc; -void *(* mpd_callocfunc)(size_t nmemb, size_t size) = calloc; -void (* mpd_free)(void *ptr) = free; - - -/* emulate calloc if it is not available */ -void * -mpd_callocfunc_em(size_t nmemb, size_t size) -{ - void *ptr; - size_t req; - mpd_size_t overflow; - -#if MPD_SIZE_MAX < SIZE_MAX - /* full_coverage test only */ - if (nmemb > MPD_SIZE_MAX || size > MPD_SIZE_MAX) { - return NULL; - } -#endif - - req = mul_size_t_overflow((mpd_size_t)nmemb, (mpd_size_t)size, - &overflow); - if (overflow) { - return NULL; - } - - ptr = mpd_mallocfunc(req); - if (ptr == NULL) { - return NULL; - } - /* used on uint32_t or uint64_t */ - memset(ptr, 0, req); - - return ptr; -} - - -/* malloc with overflow checking */ -void * -mpd_alloc(mpd_size_t nmemb, mpd_size_t size) -{ - mpd_size_t req, overflow; - - req = mul_size_t_overflow(nmemb, size, &overflow); - if (overflow) { - return NULL; - } - - return mpd_mallocfunc(req); -} - -/* calloc with overflow checking */ -void * -mpd_calloc(mpd_size_t nmemb, mpd_size_t size) -{ - mpd_size_t overflow; - - (void)mul_size_t_overflow(nmemb, size, &overflow); - if (overflow) { - return NULL; - } - - return mpd_callocfunc(nmemb, size); -} - -/* realloc with overflow checking */ -void * -mpd_realloc(void *ptr, mpd_size_t nmemb, mpd_size_t size, uint8_t *err) -{ - void *new; - mpd_size_t req, overflow; - - req = mul_size_t_overflow(nmemb, size, &overflow); - if (overflow) { - *err = 1; - return ptr; - } - - new = mpd_reallocfunc(ptr, req); - if (new == NULL) { - *err = 1; - return ptr; - } - - return new; -} - -/* struct hack malloc with overflow checking */ -void * -mpd_sh_alloc(mpd_size_t struct_size, mpd_size_t nmemb, mpd_size_t size) -{ - mpd_size_t req, overflow; - - req = mul_size_t_overflow(nmemb, size, &overflow); - if (overflow) { - return NULL; - } - - req = add_size_t_overflow(req, struct_size, &overflow); - if (overflow) { - return NULL; - } - - return mpd_mallocfunc(req); -} - - -/* Allocate a new decimal with a coefficient of length 'nwords'. In case - of an error the return value is NULL. */ -mpd_t * -mpd_qnew_size(mpd_ssize_t nwords) -{ - mpd_t *result; - - nwords = (nwords < MPD_MINALLOC) ? MPD_MINALLOC : nwords; - - result = mpd_alloc(1, sizeof *result); - if (result == NULL) { - return NULL; - } - - result->data = mpd_alloc(nwords, sizeof *result->data); - if (result->data == NULL) { - mpd_free(result); - return NULL; - } - - result->flags = 0; - result->exp = 0; - result->digits = 0; - result->len = 0; - result->alloc = nwords; - - return result; -} - -/* Allocate a new decimal with a coefficient of length MPD_MINALLOC. - In case of an error the return value is NULL. */ -mpd_t * -mpd_qnew(void) -{ - return mpd_qnew_size(MPD_MINALLOC); -} - -/* Allocate new decimal. Caller can check for NULL or MPD_Malloc_error. - Raises on error. */ -mpd_t * -mpd_new(mpd_context_t *ctx) -{ - mpd_t *result; - - result = mpd_qnew(); - if (result == NULL) { - mpd_addstatus_raise(ctx, MPD_Malloc_error); - } - return result; -} - -/* - * Input: 'result' is a static mpd_t with a static coefficient. - * Assumption: 'nwords' >= result->alloc. - * - * Resize the static coefficient to a larger dynamic one and copy the - * existing data. If successful, the value of 'result' is unchanged. - * Otherwise, set 'result' to NaN and update 'status' with MPD_Malloc_error. - */ -int -mpd_switch_to_dyn(mpd_t *result, mpd_ssize_t nwords, uint32_t *status) -{ - mpd_uint_t *p = result->data; - - assert(nwords >= result->alloc); - - result->data = mpd_alloc(nwords, sizeof *result->data); - if (result->data == NULL) { - result->data = p; - mpd_set_qnan(result); - mpd_set_positive(result); - result->exp = result->digits = result->len = 0; - *status |= MPD_Malloc_error; - return 0; - } - - memcpy(result->data, p, result->alloc * (sizeof *result->data)); - result->alloc = nwords; - mpd_set_dynamic_data(result); - return 1; -} - -/* - * Input: 'result' is a static mpd_t with a static coefficient. - * - * Convert the coefficient to a dynamic one that is initialized to zero. If - * malloc fails, set 'result' to NaN and update 'status' with MPD_Malloc_error. - */ -int -mpd_switch_to_dyn_zero(mpd_t *result, mpd_ssize_t nwords, uint32_t *status) -{ - mpd_uint_t *p = result->data; - - result->data = mpd_calloc(nwords, sizeof *result->data); - if (result->data == NULL) { - result->data = p; - mpd_set_qnan(result); - mpd_set_positive(result); - result->exp = result->digits = result->len = 0; - *status |= MPD_Malloc_error; - return 0; - } - - result->alloc = nwords; - mpd_set_dynamic_data(result); - - return 1; -} - -/* - * Input: 'result' is a static or a dynamic mpd_t with a dynamic coefficient. - * Resize the coefficient to length 'nwords': - * Case nwords > result->alloc: - * If realloc is successful: - * 'result' has a larger coefficient but the same value. Return 1. - * Otherwise: - * Set 'result' to NaN, update status with MPD_Malloc_error and return 0. - * Case nwords < result->alloc: - * If realloc is successful: - * 'result' has a smaller coefficient. result->len is undefined. Return 1. - * Otherwise (unlikely): - * 'result' is unchanged. Reuse the now oversized coefficient. Return 1. - */ -int -mpd_realloc_dyn(mpd_t *result, mpd_ssize_t nwords, uint32_t *status) -{ - uint8_t err = 0; - - result->data = mpd_realloc(result->data, nwords, sizeof *result->data, &err); - if (!err) { - result->alloc = nwords; - } - else if (nwords > result->alloc) { - mpd_set_qnan(result); - mpd_set_positive(result); - result->exp = result->digits = result->len = 0; - *status |= MPD_Malloc_error; - return 0; - } - - return 1; -} - - diff --git a/Modules/_decimal/libmpdec/mpalloc.h b/Modules/_decimal/libmpdec/mpalloc.h deleted file mode 100644 index efd7119..0000000 --- a/Modules/_decimal/libmpdec/mpalloc.h +++ /dev/null @@ -1,51 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef MPALLOC_H -#define MPALLOC_H - - -#include "mpdecimal.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -int mpd_switch_to_dyn(mpd_t *result, mpd_ssize_t size, uint32_t *status); -int mpd_switch_to_dyn_zero(mpd_t *result, mpd_ssize_t size, uint32_t *status); -int mpd_realloc_dyn(mpd_t *result, mpd_ssize_t size, uint32_t *status); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif - - - diff --git a/Modules/_decimal/libmpdec/mpdecimal.c b/Modules/_decimal/libmpdec/mpdecimal.c deleted file mode 100644 index bfa8bb3..0000000 --- a/Modules/_decimal/libmpdec/mpdecimal.c +++ /dev/null @@ -1,8417 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdio.h> -#include <stdlib.h> -#include <string.h> -#include <limits.h> -#include <math.h> -#include "basearith.h" -#include "bits.h" -#include "convolute.h" -#include "crt.h" -#include "mpalloc.h" -#include "typearith.h" -#include "umodarith.h" - -#ifdef PPRO - #if defined(_MSC_VER) - #include <float.h> - #pragma float_control(precise, on) - #pragma fenv_access(on) - #elif !defined(__OpenBSD__) && !defined(__NetBSD__) - /* C99 */ - #include <fenv.h> - #pragma STDC FENV_ACCESS ON - #endif -#endif - - -/* Disable warning that is part of -Wextra since gcc 7.0. */ -#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && __GNUC__ >= 7 - #pragma GCC diagnostic ignored "-Wimplicit-fallthrough" -#endif - - -#if defined(_MSC_VER) - #define ALWAYS_INLINE __forceinline -#elif defined(LEGACY_COMPILER) - #define ALWAYS_INLINE - #undef inline - #define inline -#else - #ifdef TEST_COVERAGE - #define ALWAYS_INLINE - #else - #define ALWAYS_INLINE inline __attribute__ ((always_inline)) - #endif -#endif - - -#define MPD_NEWTONDIV_CUTOFF 1024L - -#define MPD_NEW_STATIC(name, flags, exp, digits, len) \ - mpd_uint_t name##_data[MPD_MINALLOC_MAX]; \ - mpd_t name = {flags|MPD_STATIC|MPD_STATIC_DATA, exp, digits, \ - len, MPD_MINALLOC_MAX, name##_data} - -#define MPD_NEW_CONST(name, flags, exp, digits, len, alloc, initval) \ - mpd_uint_t name##_data[alloc] = {initval}; \ - mpd_t name = {flags|MPD_STATIC|MPD_CONST_DATA, exp, digits, \ - len, alloc, name##_data} - -#define MPD_NEW_SHARED(name, a) \ - mpd_t name = {(a->flags&~MPD_DATAFLAGS)|MPD_STATIC|MPD_SHARED_DATA, \ - a->exp, a->digits, a->len, a->alloc, a->data} - - -static mpd_uint_t data_one[1] = {1}; -static mpd_uint_t data_zero[1] = {0}; -static const mpd_t one = {MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, data_one}; -static const mpd_t minus_one = {MPD_NEG|MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, - data_one}; -static const mpd_t zero = {MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, data_zero}; - -static inline void _mpd_check_exp(mpd_t *dec, const mpd_context_t *ctx, - uint32_t *status); -static void _settriple(mpd_t *result, uint8_t sign, mpd_uint_t a, - mpd_ssize_t exp); -static inline mpd_ssize_t _mpd_real_size(mpd_uint_t *data, mpd_ssize_t size); - -static int _mpd_cmp_abs(const mpd_t *a, const mpd_t *b); - -static void _mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status); -static inline void _mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status); -static void _mpd_base_ndivmod(mpd_t *q, mpd_t *r, const mpd_t *a, - const mpd_t *b, uint32_t *status); -static inline void _mpd_qpow_uint(mpd_t *result, const mpd_t *base, - mpd_uint_t exp, uint8_t resultsign, - const mpd_context_t *ctx, uint32_t *status); - -static mpd_uint_t mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n); - - -/******************************************************************************/ -/* Version */ -/******************************************************************************/ - -const char * -mpd_version(void) -{ - return MPD_VERSION; -} - - -/******************************************************************************/ -/* Performance critical inline functions */ -/******************************************************************************/ - -#ifdef CONFIG_64 -/* Digits in a word, primarily useful for the most significant word. */ -ALWAYS_INLINE int -mpd_word_digits(mpd_uint_t word) -{ - if (word < mpd_pow10[9]) { - if (word < mpd_pow10[4]) { - if (word < mpd_pow10[2]) { - return (word < mpd_pow10[1]) ? 1 : 2; - } - return (word < mpd_pow10[3]) ? 3 : 4; - } - if (word < mpd_pow10[6]) { - return (word < mpd_pow10[5]) ? 5 : 6; - } - if (word < mpd_pow10[8]) { - return (word < mpd_pow10[7]) ? 7 : 8; - } - return 9; - } - if (word < mpd_pow10[14]) { - if (word < mpd_pow10[11]) { - return (word < mpd_pow10[10]) ? 10 : 11; - } - if (word < mpd_pow10[13]) { - return (word < mpd_pow10[12]) ? 12 : 13; - } - return 14; - } - if (word < mpd_pow10[18]) { - if (word < mpd_pow10[16]) { - return (word < mpd_pow10[15]) ? 15 : 16; - } - return (word < mpd_pow10[17]) ? 17 : 18; - } - - return (word < mpd_pow10[19]) ? 19 : 20; -} -#else -ALWAYS_INLINE int -mpd_word_digits(mpd_uint_t word) -{ - if (word < mpd_pow10[4]) { - if (word < mpd_pow10[2]) { - return (word < mpd_pow10[1]) ? 1 : 2; - } - return (word < mpd_pow10[3]) ? 3 : 4; - } - if (word < mpd_pow10[6]) { - return (word < mpd_pow10[5]) ? 5 : 6; - } - if (word < mpd_pow10[8]) { - return (word < mpd_pow10[7]) ? 7 : 8; - } - - return (word < mpd_pow10[9]) ? 9 : 10; -} -#endif - - -/* Adjusted exponent */ -ALWAYS_INLINE mpd_ssize_t -mpd_adjexp(const mpd_t *dec) -{ - return (dec->exp + dec->digits) - 1; -} - -/* Etiny */ -ALWAYS_INLINE mpd_ssize_t -mpd_etiny(const mpd_context_t *ctx) -{ - return ctx->emin - (ctx->prec - 1); -} - -/* Etop: used for folding down in IEEE clamping */ -ALWAYS_INLINE mpd_ssize_t -mpd_etop(const mpd_context_t *ctx) -{ - return ctx->emax - (ctx->prec - 1); -} - -/* Most significant word */ -ALWAYS_INLINE mpd_uint_t -mpd_msword(const mpd_t *dec) -{ - assert(dec->len > 0); - return dec->data[dec->len-1]; -} - -/* Most significant digit of a word */ -inline mpd_uint_t -mpd_msd(mpd_uint_t word) -{ - int n; - - n = mpd_word_digits(word); - return word / mpd_pow10[n-1]; -} - -/* Least significant digit of a word */ -ALWAYS_INLINE mpd_uint_t -mpd_lsd(mpd_uint_t word) -{ - return word % 10; -} - -/* Coefficient size needed to store 'digits' */ -ALWAYS_INLINE mpd_ssize_t -mpd_digits_to_size(mpd_ssize_t digits) -{ - mpd_ssize_t q, r; - - _mpd_idiv_word(&q, &r, digits, MPD_RDIGITS); - return (r == 0) ? q : q+1; -} - -/* Number of digits in the exponent. Not defined for MPD_SSIZE_MIN. */ -inline int -mpd_exp_digits(mpd_ssize_t exp) -{ - exp = (exp < 0) ? -exp : exp; - return mpd_word_digits(exp); -} - -/* Canonical */ -ALWAYS_INLINE int -mpd_iscanonical(const mpd_t *dec UNUSED) -{ - return 1; -} - -/* Finite */ -ALWAYS_INLINE int -mpd_isfinite(const mpd_t *dec) -{ - return !(dec->flags & MPD_SPECIAL); -} - -/* Infinite */ -ALWAYS_INLINE int -mpd_isinfinite(const mpd_t *dec) -{ - return dec->flags & MPD_INF; -} - -/* NaN */ -ALWAYS_INLINE int -mpd_isnan(const mpd_t *dec) -{ - return dec->flags & (MPD_NAN|MPD_SNAN); -} - -/* Negative */ -ALWAYS_INLINE int -mpd_isnegative(const mpd_t *dec) -{ - return dec->flags & MPD_NEG; -} - -/* Positive */ -ALWAYS_INLINE int -mpd_ispositive(const mpd_t *dec) -{ - return !(dec->flags & MPD_NEG); -} - -/* qNaN */ -ALWAYS_INLINE int -mpd_isqnan(const mpd_t *dec) -{ - return dec->flags & MPD_NAN; -} - -/* Signed */ -ALWAYS_INLINE int -mpd_issigned(const mpd_t *dec) -{ - return dec->flags & MPD_NEG; -} - -/* sNaN */ -ALWAYS_INLINE int -mpd_issnan(const mpd_t *dec) -{ - return dec->flags & MPD_SNAN; -} - -/* Special */ -ALWAYS_INLINE int -mpd_isspecial(const mpd_t *dec) -{ - return dec->flags & MPD_SPECIAL; -} - -/* Zero */ -ALWAYS_INLINE int -mpd_iszero(const mpd_t *dec) -{ - return !mpd_isspecial(dec) && mpd_msword(dec) == 0; -} - -/* Test for zero when specials have been ruled out already */ -ALWAYS_INLINE int -mpd_iszerocoeff(const mpd_t *dec) -{ - return mpd_msword(dec) == 0; -} - -/* Normal */ -inline int -mpd_isnormal(const mpd_t *dec, const mpd_context_t *ctx) -{ - if (mpd_isspecial(dec)) return 0; - if (mpd_iszerocoeff(dec)) return 0; - - return mpd_adjexp(dec) >= ctx->emin; -} - -/* Subnormal */ -inline int -mpd_issubnormal(const mpd_t *dec, const mpd_context_t *ctx) -{ - if (mpd_isspecial(dec)) return 0; - if (mpd_iszerocoeff(dec)) return 0; - - return mpd_adjexp(dec) < ctx->emin; -} - -/* Odd word */ -ALWAYS_INLINE int -mpd_isoddword(mpd_uint_t word) -{ - return word & 1; -} - -/* Odd coefficient */ -ALWAYS_INLINE int -mpd_isoddcoeff(const mpd_t *dec) -{ - return mpd_isoddword(dec->data[0]); -} - -/* 0 if dec is positive, 1 if dec is negative */ -ALWAYS_INLINE uint8_t -mpd_sign(const mpd_t *dec) -{ - return dec->flags & MPD_NEG; -} - -/* 1 if dec is positive, -1 if dec is negative */ -ALWAYS_INLINE int -mpd_arith_sign(const mpd_t *dec) -{ - return 1 - 2 * mpd_isnegative(dec); -} - -/* Radix */ -ALWAYS_INLINE long -mpd_radix(void) -{ - return 10; -} - -/* Dynamic decimal */ -ALWAYS_INLINE int -mpd_isdynamic(const mpd_t *dec) -{ - return !(dec->flags & MPD_STATIC); -} - -/* Static decimal */ -ALWAYS_INLINE int -mpd_isstatic(const mpd_t *dec) -{ - return dec->flags & MPD_STATIC; -} - -/* Data of decimal is dynamic */ -ALWAYS_INLINE int -mpd_isdynamic_data(const mpd_t *dec) -{ - return !(dec->flags & MPD_DATAFLAGS); -} - -/* Data of decimal is static */ -ALWAYS_INLINE int -mpd_isstatic_data(const mpd_t *dec) -{ - return dec->flags & MPD_STATIC_DATA; -} - -/* Data of decimal is shared */ -ALWAYS_INLINE int -mpd_isshared_data(const mpd_t *dec) -{ - return dec->flags & MPD_SHARED_DATA; -} - -/* Data of decimal is const */ -ALWAYS_INLINE int -mpd_isconst_data(const mpd_t *dec) -{ - return dec->flags & MPD_CONST_DATA; -} - - -/******************************************************************************/ -/* Inline memory handling */ -/******************************************************************************/ - -/* Fill destination with zeros */ -ALWAYS_INLINE void -mpd_uint_zero(mpd_uint_t *dest, mpd_size_t len) -{ - mpd_size_t i; - - for (i = 0; i < len; i++) { - dest[i] = 0; - } -} - -/* Free a decimal */ -ALWAYS_INLINE void -mpd_del(mpd_t *dec) -{ - if (mpd_isdynamic_data(dec)) { - mpd_free(dec->data); - } - if (mpd_isdynamic(dec)) { - mpd_free(dec); - } -} - -/* - * Resize the coefficient. Existing data up to 'nwords' is left untouched. - * Return 1 on success, 0 otherwise. - * - * Input invariant: MPD_MINALLOC <= result->alloc. - * - * Case nwords == result->alloc: - * 'result' is unchanged. Return 1. - * - * Case nwords > result->alloc: - * Case realloc success: - * The value of 'result' does not change. Return 1. - * Case realloc failure: - * 'result' is NaN, status is updated with MPD_Malloc_error. Return 0. - * - * Case nwords < result->alloc: - * Case is_static_data or realloc failure [1]: - * 'result' is unchanged. Return 1. - * Case realloc success: - * The value of result is undefined (expected). Return 1. - * - * - * [1] In that case the old (now oversized) area is still valid. - */ -ALWAYS_INLINE int -mpd_qresize(mpd_t *result, mpd_ssize_t nwords, uint32_t *status) -{ - assert(!mpd_isconst_data(result)); /* illegal operation for a const */ - assert(!mpd_isshared_data(result)); /* illegal operation for a shared */ - assert(MPD_MINALLOC <= result->alloc); - - nwords = (nwords <= MPD_MINALLOC) ? MPD_MINALLOC : nwords; - if (nwords == result->alloc) { - return 1; - } - if (mpd_isstatic_data(result)) { - if (nwords > result->alloc) { - return mpd_switch_to_dyn(result, nwords, status); - } - return 1; - } - - return mpd_realloc_dyn(result, nwords, status); -} - -/* Same as mpd_qresize, but the complete coefficient (including the old - * memory area!) is initialized to zero. */ -ALWAYS_INLINE int -mpd_qresize_zero(mpd_t *result, mpd_ssize_t nwords, uint32_t *status) -{ - assert(!mpd_isconst_data(result)); /* illegal operation for a const */ - assert(!mpd_isshared_data(result)); /* illegal operation for a shared */ - assert(MPD_MINALLOC <= result->alloc); - - nwords = (nwords <= MPD_MINALLOC) ? MPD_MINALLOC : nwords; - if (nwords != result->alloc) { - if (mpd_isstatic_data(result)) { - if (nwords > result->alloc) { - return mpd_switch_to_dyn_zero(result, nwords, status); - } - } - else if (!mpd_realloc_dyn(result, nwords, status)) { - return 0; - } - } - - mpd_uint_zero(result->data, nwords); - return 1; -} - -/* - * Reduce memory size for the coefficient to MPD_MINALLOC. In theory, - * realloc may fail even when reducing the memory size. But in that case - * the old memory area is always big enough, so checking for MPD_Malloc_error - * is not imperative. - */ -ALWAYS_INLINE void -mpd_minalloc(mpd_t *result) -{ - assert(!mpd_isconst_data(result)); /* illegal operation for a const */ - assert(!mpd_isshared_data(result)); /* illegal operation for a shared */ - - if (!mpd_isstatic_data(result) && result->alloc > MPD_MINALLOC) { - uint8_t err = 0; - result->data = mpd_realloc(result->data, MPD_MINALLOC, - sizeof *result->data, &err); - if (!err) { - result->alloc = MPD_MINALLOC; - } - } -} - -int -mpd_resize(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx) -{ - uint32_t status = 0; - if (!mpd_qresize(result, nwords, &status)) { - mpd_addstatus_raise(ctx, status); - return 0; - } - return 1; -} - -int -mpd_resize_zero(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx) -{ - uint32_t status = 0; - if (!mpd_qresize_zero(result, nwords, &status)) { - mpd_addstatus_raise(ctx, status); - return 0; - } - return 1; -} - - -/******************************************************************************/ -/* Set attributes of a decimal */ -/******************************************************************************/ - -/* Set digits. Assumption: result->len is initialized and > 0. */ -inline void -mpd_setdigits(mpd_t *result) -{ - mpd_ssize_t wdigits = mpd_word_digits(mpd_msword(result)); - result->digits = wdigits + (result->len-1) * MPD_RDIGITS; -} - -/* Set sign */ -ALWAYS_INLINE void -mpd_set_sign(mpd_t *result, uint8_t sign) -{ - result->flags &= ~MPD_NEG; - result->flags |= sign; -} - -/* Copy sign from another decimal */ -ALWAYS_INLINE void -mpd_signcpy(mpd_t *result, const mpd_t *a) -{ - uint8_t sign = a->flags&MPD_NEG; - - result->flags &= ~MPD_NEG; - result->flags |= sign; -} - -/* Set infinity */ -ALWAYS_INLINE void -mpd_set_infinity(mpd_t *result) -{ - result->flags &= ~MPD_SPECIAL; - result->flags |= MPD_INF; -} - -/* Set qNaN */ -ALWAYS_INLINE void -mpd_set_qnan(mpd_t *result) -{ - result->flags &= ~MPD_SPECIAL; - result->flags |= MPD_NAN; -} - -/* Set sNaN */ -ALWAYS_INLINE void -mpd_set_snan(mpd_t *result) -{ - result->flags &= ~MPD_SPECIAL; - result->flags |= MPD_SNAN; -} - -/* Set to negative */ -ALWAYS_INLINE void -mpd_set_negative(mpd_t *result) -{ - result->flags |= MPD_NEG; -} - -/* Set to positive */ -ALWAYS_INLINE void -mpd_set_positive(mpd_t *result) -{ - result->flags &= ~MPD_NEG; -} - -/* Set to dynamic */ -ALWAYS_INLINE void -mpd_set_dynamic(mpd_t *result) -{ - result->flags &= ~MPD_STATIC; -} - -/* Set to static */ -ALWAYS_INLINE void -mpd_set_static(mpd_t *result) -{ - result->flags |= MPD_STATIC; -} - -/* Set data to dynamic */ -ALWAYS_INLINE void -mpd_set_dynamic_data(mpd_t *result) -{ - result->flags &= ~MPD_DATAFLAGS; -} - -/* Set data to static */ -ALWAYS_INLINE void -mpd_set_static_data(mpd_t *result) -{ - result->flags &= ~MPD_DATAFLAGS; - result->flags |= MPD_STATIC_DATA; -} - -/* Set data to shared */ -ALWAYS_INLINE void -mpd_set_shared_data(mpd_t *result) -{ - result->flags &= ~MPD_DATAFLAGS; - result->flags |= MPD_SHARED_DATA; -} - -/* Set data to const */ -ALWAYS_INLINE void -mpd_set_const_data(mpd_t *result) -{ - result->flags &= ~MPD_DATAFLAGS; - result->flags |= MPD_CONST_DATA; -} - -/* Clear flags, preserving memory attributes. */ -ALWAYS_INLINE void -mpd_clear_flags(mpd_t *result) -{ - result->flags &= (MPD_STATIC|MPD_DATAFLAGS); -} - -/* Set flags, preserving memory attributes. */ -ALWAYS_INLINE void -mpd_set_flags(mpd_t *result, uint8_t flags) -{ - result->flags &= (MPD_STATIC|MPD_DATAFLAGS); - result->flags |= flags; -} - -/* Copy flags, preserving memory attributes of result. */ -ALWAYS_INLINE void -mpd_copy_flags(mpd_t *result, const mpd_t *a) -{ - uint8_t aflags = a->flags; - result->flags &= (MPD_STATIC|MPD_DATAFLAGS); - result->flags |= (aflags & ~(MPD_STATIC|MPD_DATAFLAGS)); -} - -/* Initialize a workcontext from ctx. Set traps, flags and newtrap to 0. */ -static inline void -mpd_workcontext(mpd_context_t *workctx, const mpd_context_t *ctx) -{ - workctx->prec = ctx->prec; - workctx->emax = ctx->emax; - workctx->emin = ctx->emin; - workctx->round = ctx->round; - workctx->traps = 0; - workctx->status = 0; - workctx->newtrap = 0; - workctx->clamp = ctx->clamp; - workctx->allcr = ctx->allcr; -} - - -/******************************************************************************/ -/* Getting and setting parts of decimals */ -/******************************************************************************/ - -/* Flip the sign of a decimal */ -static inline void -_mpd_negate(mpd_t *dec) -{ - dec->flags ^= MPD_NEG; -} - -/* Set coefficient to zero */ -void -mpd_zerocoeff(mpd_t *result) -{ - mpd_minalloc(result); - result->digits = 1; - result->len = 1; - result->data[0] = 0; -} - -/* Set the coefficient to all nines. */ -void -mpd_qmaxcoeff(mpd_t *result, const mpd_context_t *ctx, uint32_t *status) -{ - mpd_ssize_t len, r; - - _mpd_idiv_word(&len, &r, ctx->prec, MPD_RDIGITS); - len = (r == 0) ? len : len+1; - - if (!mpd_qresize(result, len, status)) { - return; - } - - result->len = len; - result->digits = ctx->prec; - - --len; - if (r > 0) { - result->data[len--] = mpd_pow10[r]-1; - } - for (; len >= 0; --len) { - result->data[len] = MPD_RADIX-1; - } -} - -/* - * Cut off the most significant digits so that the rest fits in ctx->prec. - * Cannot fail. - */ -static void -_mpd_cap(mpd_t *result, const mpd_context_t *ctx) -{ - uint32_t dummy; - mpd_ssize_t len, r; - - if (result->len > 0 && result->digits > ctx->prec) { - _mpd_idiv_word(&len, &r, ctx->prec, MPD_RDIGITS); - len = (r == 0) ? len : len+1; - - if (r != 0) { - result->data[len-1] %= mpd_pow10[r]; - } - - len = _mpd_real_size(result->data, len); - /* resize to fewer words cannot fail */ - mpd_qresize(result, len, &dummy); - result->len = len; - mpd_setdigits(result); - } - if (mpd_iszero(result)) { - _settriple(result, mpd_sign(result), 0, result->exp); - } -} - -/* - * Cut off the most significant digits of a NaN payload so that the rest - * fits in ctx->prec - ctx->clamp. Cannot fail. - */ -static void -_mpd_fix_nan(mpd_t *result, const mpd_context_t *ctx) -{ - uint32_t dummy; - mpd_ssize_t prec; - mpd_ssize_t len, r; - - prec = ctx->prec - ctx->clamp; - if (result->len > 0 && result->digits > prec) { - if (prec == 0) { - mpd_minalloc(result); - result->len = result->digits = 0; - } - else { - _mpd_idiv_word(&len, &r, prec, MPD_RDIGITS); - len = (r == 0) ? len : len+1; - - if (r != 0) { - result->data[len-1] %= mpd_pow10[r]; - } - - len = _mpd_real_size(result->data, len); - /* resize to fewer words cannot fail */ - mpd_qresize(result, len, &dummy); - result->len = len; - mpd_setdigits(result); - if (mpd_iszerocoeff(result)) { - /* NaN0 is not a valid representation */ - result->len = result->digits = 0; - } - } - } -} - -/* - * Get n most significant digits from a decimal, where 0 < n <= MPD_UINT_DIGITS. - * Assumes MPD_UINT_DIGITS == MPD_RDIGITS+1, which is true for 32 and 64 bit - * machines. - * - * The result of the operation will be in lo. If the operation is impossible, - * hi will be nonzero. This is used to indicate an error. - */ -static inline void -_mpd_get_msdigits(mpd_uint_t *hi, mpd_uint_t *lo, const mpd_t *dec, - unsigned int n) -{ - mpd_uint_t r, tmp; - - assert(0 < n && n <= MPD_RDIGITS+1); - - _mpd_div_word(&tmp, &r, dec->digits, MPD_RDIGITS); - r = (r == 0) ? MPD_RDIGITS : r; /* digits in the most significant word */ - - *hi = 0; - *lo = dec->data[dec->len-1]; - if (n <= r) { - *lo /= mpd_pow10[r-n]; - } - else if (dec->len > 1) { - /* at this point 1 <= r < n <= MPD_RDIGITS+1 */ - _mpd_mul_words(hi, lo, *lo, mpd_pow10[n-r]); - tmp = dec->data[dec->len-2] / mpd_pow10[MPD_RDIGITS-(n-r)]; - *lo = *lo + tmp; - if (*lo < tmp) (*hi)++; - } -} - - -/******************************************************************************/ -/* Gathering information about a decimal */ -/******************************************************************************/ - -/* The real size of the coefficient without leading zero words. */ -static inline mpd_ssize_t -_mpd_real_size(mpd_uint_t *data, mpd_ssize_t size) -{ - while (size > 1 && data[size-1] == 0) { - size--; - } - - return size; -} - -/* Return number of trailing zeros. No errors are possible. */ -mpd_ssize_t -mpd_trail_zeros(const mpd_t *dec) -{ - mpd_uint_t word; - mpd_ssize_t i, tz = 0; - - for (i=0; i < dec->len; ++i) { - if (dec->data[i] != 0) { - word = dec->data[i]; - tz = i * MPD_RDIGITS; - while (word % 10 == 0) { - word /= 10; - tz++; - } - break; - } - } - - return tz; -} - -/* Integer: Undefined for specials */ -static int -_mpd_isint(const mpd_t *dec) -{ - mpd_ssize_t tz; - - if (mpd_iszerocoeff(dec)) { - return 1; - } - - tz = mpd_trail_zeros(dec); - return (dec->exp + tz >= 0); -} - -/* Integer */ -int -mpd_isinteger(const mpd_t *dec) -{ - if (mpd_isspecial(dec)) { - return 0; - } - return _mpd_isint(dec); -} - -/* Word is a power of 10 */ -static int -mpd_word_ispow10(mpd_uint_t word) -{ - int n; - - n = mpd_word_digits(word); - if (word == mpd_pow10[n-1]) { - return 1; - } - - return 0; -} - -/* Coefficient is a power of 10 */ -static int -mpd_coeff_ispow10(const mpd_t *dec) -{ - if (mpd_word_ispow10(mpd_msword(dec))) { - if (_mpd_isallzero(dec->data, dec->len-1)) { - return 1; - } - } - - return 0; -} - -/* All digits of a word are nines */ -static int -mpd_word_isallnine(mpd_uint_t word) -{ - int n; - - n = mpd_word_digits(word); - if (word == mpd_pow10[n]-1) { - return 1; - } - - return 0; -} - -/* All digits of the coefficient are nines */ -static int -mpd_coeff_isallnine(const mpd_t *dec) -{ - if (mpd_word_isallnine(mpd_msword(dec))) { - if (_mpd_isallnine(dec->data, dec->len-1)) { - return 1; - } - } - - return 0; -} - -/* Odd decimal: Undefined for non-integers! */ -int -mpd_isodd(const mpd_t *dec) -{ - mpd_uint_t q, r; - assert(mpd_isinteger(dec)); - if (mpd_iszerocoeff(dec)) return 0; - if (dec->exp < 0) { - _mpd_div_word(&q, &r, -dec->exp, MPD_RDIGITS); - q = dec->data[q] / mpd_pow10[r]; - return mpd_isoddword(q); - } - return dec->exp == 0 && mpd_isoddword(dec->data[0]); -} - -/* Even: Undefined for non-integers! */ -int -mpd_iseven(const mpd_t *dec) -{ - return !mpd_isodd(dec); -} - -/******************************************************************************/ -/* Getting and setting decimals */ -/******************************************************************************/ - -/* Internal function: Set a static decimal from a triple, no error checking. */ -static void -_ssettriple(mpd_t *result, uint8_t sign, mpd_uint_t a, mpd_ssize_t exp) -{ - mpd_set_flags(result, sign); - result->exp = exp; - _mpd_div_word(&result->data[1], &result->data[0], a, MPD_RADIX); - result->len = (result->data[1] == 0) ? 1 : 2; - mpd_setdigits(result); -} - -/* Internal function: Set a decimal from a triple, no error checking. */ -static void -_settriple(mpd_t *result, uint8_t sign, mpd_uint_t a, mpd_ssize_t exp) -{ - mpd_minalloc(result); - mpd_set_flags(result, sign); - result->exp = exp; - _mpd_div_word(&result->data[1], &result->data[0], a, MPD_RADIX); - result->len = (result->data[1] == 0) ? 1 : 2; - mpd_setdigits(result); -} - -/* Set a special number from a triple */ -void -mpd_setspecial(mpd_t *result, uint8_t sign, uint8_t type) -{ - mpd_minalloc(result); - result->flags &= ~(MPD_NEG|MPD_SPECIAL); - result->flags |= (sign|type); - result->exp = result->digits = result->len = 0; -} - -/* Set result of NaN with an error status */ -void -mpd_seterror(mpd_t *result, uint32_t flags, uint32_t *status) -{ - mpd_minalloc(result); - mpd_set_qnan(result); - mpd_set_positive(result); - result->exp = result->digits = result->len = 0; - *status |= flags; -} - -/* quietly set a static decimal from an mpd_ssize_t */ -void -mpd_qsset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_uint_t u; - uint8_t sign = MPD_POS; - - if (a < 0) { - if (a == MPD_SSIZE_MIN) { - u = (mpd_uint_t)MPD_SSIZE_MAX + - (-(MPD_SSIZE_MIN+MPD_SSIZE_MAX)); - } - else { - u = -a; - } - sign = MPD_NEG; - } - else { - u = a; - } - _ssettriple(result, sign, u, 0); - mpd_qfinalize(result, ctx, status); -} - -/* quietly set a static decimal from an mpd_uint_t */ -void -mpd_qsset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - _ssettriple(result, MPD_POS, a, 0); - mpd_qfinalize(result, ctx, status); -} - -/* quietly set a static decimal from an int32_t */ -void -mpd_qsset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_qsset_ssize(result, a, ctx, status); -} - -/* quietly set a static decimal from a uint32_t */ -void -mpd_qsset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_qsset_uint(result, a, ctx, status); -} - -#ifdef CONFIG_64 -/* quietly set a static decimal from an int64_t */ -void -mpd_qsset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_qsset_ssize(result, a, ctx, status); -} - -/* quietly set a static decimal from a uint64_t */ -void -mpd_qsset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_qsset_uint(result, a, ctx, status); -} -#endif - -/* quietly set a decimal from an mpd_ssize_t */ -void -mpd_qset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_minalloc(result); - mpd_qsset_ssize(result, a, ctx, status); -} - -/* quietly set a decimal from an mpd_uint_t */ -void -mpd_qset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - _settriple(result, MPD_POS, a, 0); - mpd_qfinalize(result, ctx, status); -} - -/* quietly set a decimal from an int32_t */ -void -mpd_qset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_qset_ssize(result, a, ctx, status); -} - -/* quietly set a decimal from a uint32_t */ -void -mpd_qset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_qset_uint(result, a, ctx, status); -} - -#if defined(CONFIG_32) && !defined(LEGACY_COMPILER) -/* set a decimal from a uint64_t */ -static void -_c32setu64(mpd_t *result, uint64_t u, uint8_t sign, uint32_t *status) -{ - mpd_uint_t w[3]; - uint64_t q; - int i, len; - - len = 0; - do { - q = u / MPD_RADIX; - w[len] = (mpd_uint_t)(u - q * MPD_RADIX); - u = q; len++; - } while (u != 0); - - if (!mpd_qresize(result, len, status)) { - return; - } - for (i = 0; i < len; i++) { - result->data[i] = w[i]; - } - - mpd_set_sign(result, sign); - result->exp = 0; - result->len = len; - mpd_setdigits(result); -} - -static void -_c32_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - _c32setu64(result, a, MPD_POS, status); - mpd_qfinalize(result, ctx, status); -} - -/* set a decimal from an int64_t */ -static void -_c32_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - uint64_t u; - uint8_t sign = MPD_POS; - - if (a < 0) { - if (a == INT64_MIN) { - u = (uint64_t)INT64_MAX + (-(INT64_MIN+INT64_MAX)); - } - else { - u = -a; - } - sign = MPD_NEG; - } - else { - u = a; - } - _c32setu64(result, u, sign, status); - mpd_qfinalize(result, ctx, status); -} -#endif /* CONFIG_32 && !LEGACY_COMPILER */ - -#ifndef LEGACY_COMPILER -/* quietly set a decimal from an int64_t */ -void -mpd_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, - uint32_t *status) -{ -#ifdef CONFIG_64 - mpd_qset_ssize(result, a, ctx, status); -#else - _c32_qset_i64(result, a, ctx, status); -#endif -} - -/* quietly set a decimal from a uint64_t */ -void -mpd_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, - uint32_t *status) -{ -#ifdef CONFIG_64 - mpd_qset_uint(result, a, ctx, status); -#else - _c32_qset_u64(result, a, ctx, status); -#endif -} -#endif /* !LEGACY_COMPILER */ - - -/* - * Quietly get an mpd_uint_t from a decimal. Assumes - * MPD_UINT_DIGITS == MPD_RDIGITS+1, which is true for - * 32 and 64 bit machines. - * - * If the operation is impossible, MPD_Invalid_operation is set. - */ -static mpd_uint_t -_mpd_qget_uint(int use_sign, const mpd_t *a, uint32_t *status) -{ - mpd_t tmp; - mpd_uint_t tmp_data[2]; - mpd_uint_t lo, hi; - - if (mpd_isspecial(a)) { - *status |= MPD_Invalid_operation; - return MPD_UINT_MAX; - } - if (mpd_iszero(a)) { - return 0; - } - if (use_sign && mpd_isnegative(a)) { - *status |= MPD_Invalid_operation; - return MPD_UINT_MAX; - } - - if (a->digits+a->exp > MPD_RDIGITS+1) { - *status |= MPD_Invalid_operation; - return MPD_UINT_MAX; - } - - if (a->exp < 0) { - if (!_mpd_isint(a)) { - *status |= MPD_Invalid_operation; - return MPD_UINT_MAX; - } - /* At this point a->digits+a->exp <= MPD_RDIGITS+1, - * so the shift fits. */ - tmp.data = tmp_data; - tmp.flags = MPD_STATIC|MPD_STATIC_DATA; - tmp.alloc = 2; - mpd_qsshiftr(&tmp, a, -a->exp); - tmp.exp = 0; - a = &tmp; - } - - _mpd_get_msdigits(&hi, &lo, a, MPD_RDIGITS+1); - if (hi) { - *status |= MPD_Invalid_operation; - return MPD_UINT_MAX; - } - - if (a->exp > 0) { - _mpd_mul_words(&hi, &lo, lo, mpd_pow10[a->exp]); - if (hi) { - *status |= MPD_Invalid_operation; - return MPD_UINT_MAX; - } - } - - return lo; -} - -/* - * Sets Invalid_operation for: - * - specials - * - negative numbers (except negative zero) - * - non-integers - * - overflow - */ -mpd_uint_t -mpd_qget_uint(const mpd_t *a, uint32_t *status) -{ - return _mpd_qget_uint(1, a, status); -} - -/* Same as above, but gets the absolute value, i.e. the sign is ignored. */ -mpd_uint_t -mpd_qabs_uint(const mpd_t *a, uint32_t *status) -{ - return _mpd_qget_uint(0, a, status); -} - -/* quietly get an mpd_ssize_t from a decimal */ -mpd_ssize_t -mpd_qget_ssize(const mpd_t *a, uint32_t *status) -{ - mpd_uint_t u; - int isneg; - - u = mpd_qabs_uint(a, status); - if (*status&MPD_Invalid_operation) { - return MPD_SSIZE_MAX; - } - - isneg = mpd_isnegative(a); - if (u <= MPD_SSIZE_MAX) { - return isneg ? -((mpd_ssize_t)u) : (mpd_ssize_t)u; - } - else if (isneg && u+(MPD_SSIZE_MIN+MPD_SSIZE_MAX) == MPD_SSIZE_MAX) { - return MPD_SSIZE_MIN; - } - - *status |= MPD_Invalid_operation; - return MPD_SSIZE_MAX; -} - -#if defined(CONFIG_32) && !defined(LEGACY_COMPILER) -/* - * Quietly get a uint64_t from a decimal. If the operation is impossible, - * MPD_Invalid_operation is set. - */ -static uint64_t -_c32_qget_u64(int use_sign, const mpd_t *a, uint32_t *status) -{ - MPD_NEW_STATIC(tmp,0,0,20,3); - mpd_context_t maxcontext; - uint64_t ret; - - tmp_data[0] = 709551615; - tmp_data[1] = 446744073; - tmp_data[2] = 18; - - if (mpd_isspecial(a)) { - *status |= MPD_Invalid_operation; - return UINT64_MAX; - } - if (mpd_iszero(a)) { - return 0; - } - if (use_sign && mpd_isnegative(a)) { - *status |= MPD_Invalid_operation; - return UINT64_MAX; - } - if (!_mpd_isint(a)) { - *status |= MPD_Invalid_operation; - return UINT64_MAX; - } - - if (_mpd_cmp_abs(a, &tmp) > 0) { - *status |= MPD_Invalid_operation; - return UINT64_MAX; - } - - mpd_maxcontext(&maxcontext); - mpd_qrescale(&tmp, a, 0, &maxcontext, &maxcontext.status); - maxcontext.status &= ~MPD_Rounded; - if (maxcontext.status != 0) { - *status |= (maxcontext.status|MPD_Invalid_operation); /* GCOV_NOT_REACHED */ - return UINT64_MAX; /* GCOV_NOT_REACHED */ - } - - ret = 0; - switch (tmp.len) { - case 3: - ret += (uint64_t)tmp_data[2] * 1000000000000000000ULL; - case 2: - ret += (uint64_t)tmp_data[1] * 1000000000ULL; - case 1: - ret += tmp_data[0]; - break; - default: - abort(); /* GCOV_NOT_REACHED */ - } - - return ret; -} - -static int64_t -_c32_qget_i64(const mpd_t *a, uint32_t *status) -{ - uint64_t u; - int isneg; - - u = _c32_qget_u64(0, a, status); - if (*status&MPD_Invalid_operation) { - return INT64_MAX; - } - - isneg = mpd_isnegative(a); - if (u <= INT64_MAX) { - return isneg ? -((int64_t)u) : (int64_t)u; - } - else if (isneg && u+(INT64_MIN+INT64_MAX) == INT64_MAX) { - return INT64_MIN; - } - - *status |= MPD_Invalid_operation; - return INT64_MAX; -} -#endif /* CONFIG_32 && !LEGACY_COMPILER */ - -#ifdef CONFIG_64 -/* quietly get a uint64_t from a decimal */ -uint64_t -mpd_qget_u64(const mpd_t *a, uint32_t *status) -{ - return mpd_qget_uint(a, status); -} - -/* quietly get an int64_t from a decimal */ -int64_t -mpd_qget_i64(const mpd_t *a, uint32_t *status) -{ - return mpd_qget_ssize(a, status); -} - -/* quietly get a uint32_t from a decimal */ -uint32_t -mpd_qget_u32(const mpd_t *a, uint32_t *status) -{ - uint64_t x = mpd_qget_uint(a, status); - - if (*status&MPD_Invalid_operation) { - return UINT32_MAX; - } - if (x > UINT32_MAX) { - *status |= MPD_Invalid_operation; - return UINT32_MAX; - } - - return (uint32_t)x; -} - -/* quietly get an int32_t from a decimal */ -int32_t -mpd_qget_i32(const mpd_t *a, uint32_t *status) -{ - int64_t x = mpd_qget_ssize(a, status); - - if (*status&MPD_Invalid_operation) { - return INT32_MAX; - } - if (x < INT32_MIN || x > INT32_MAX) { - *status |= MPD_Invalid_operation; - return INT32_MAX; - } - - return (int32_t)x; -} -#else -#ifndef LEGACY_COMPILER -/* quietly get a uint64_t from a decimal */ -uint64_t -mpd_qget_u64(const mpd_t *a, uint32_t *status) -{ - return _c32_qget_u64(1, a, status); -} - -/* quietly get an int64_t from a decimal */ -int64_t -mpd_qget_i64(const mpd_t *a, uint32_t *status) -{ - return _c32_qget_i64(a, status); -} -#endif - -/* quietly get a uint32_t from a decimal */ -uint32_t -mpd_qget_u32(const mpd_t *a, uint32_t *status) -{ - return mpd_qget_uint(a, status); -} - -/* quietly get an int32_t from a decimal */ -int32_t -mpd_qget_i32(const mpd_t *a, uint32_t *status) -{ - return mpd_qget_ssize(a, status); -} -#endif - - -/******************************************************************************/ -/* Filtering input of functions, finalizing output of functions */ -/******************************************************************************/ - -/* - * Check if the operand is NaN, copy to result and return 1 if this is - * the case. Copying can fail since NaNs are allowed to have a payload that - * does not fit in MPD_MINALLOC. - */ -int -mpd_qcheck_nan(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isnan(a)) { - *status |= mpd_issnan(a) ? MPD_Invalid_operation : 0; - mpd_qcopy(result, a, status); - mpd_set_qnan(result); - _mpd_fix_nan(result, ctx); - return 1; - } - return 0; -} - -/* - * Check if either operand is NaN, copy to result and return 1 if this - * is the case. Copying can fail since NaNs are allowed to have a payload - * that does not fit in MPD_MINALLOC. - */ -int -mpd_qcheck_nans(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - if ((a->flags|b->flags)&(MPD_NAN|MPD_SNAN)) { - const mpd_t *choice = b; - if (mpd_issnan(a)) { - choice = a; - *status |= MPD_Invalid_operation; - } - else if (mpd_issnan(b)) { - *status |= MPD_Invalid_operation; - } - else if (mpd_isqnan(a)) { - choice = a; - } - mpd_qcopy(result, choice, status); - mpd_set_qnan(result); - _mpd_fix_nan(result, ctx); - return 1; - } - return 0; -} - -/* - * Check if one of the operands is NaN, copy to result and return 1 if this - * is the case. Copying can fail since NaNs are allowed to have a payload - * that does not fit in MPD_MINALLOC. - */ -static int -mpd_qcheck_3nans(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, - const mpd_context_t *ctx, uint32_t *status) -{ - if ((a->flags|b->flags|c->flags)&(MPD_NAN|MPD_SNAN)) { - const mpd_t *choice = c; - if (mpd_issnan(a)) { - choice = a; - *status |= MPD_Invalid_operation; - } - else if (mpd_issnan(b)) { - choice = b; - *status |= MPD_Invalid_operation; - } - else if (mpd_issnan(c)) { - *status |= MPD_Invalid_operation; - } - else if (mpd_isqnan(a)) { - choice = a; - } - else if (mpd_isqnan(b)) { - choice = b; - } - mpd_qcopy(result, choice, status); - mpd_set_qnan(result); - _mpd_fix_nan(result, ctx); - return 1; - } - return 0; -} - -/* Check if rounding digit 'rnd' leads to an increment. */ -static inline int -_mpd_rnd_incr(const mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx) -{ - int ld; - - switch (ctx->round) { - case MPD_ROUND_DOWN: case MPD_ROUND_TRUNC: - return 0; - case MPD_ROUND_HALF_UP: - return (rnd >= 5); - case MPD_ROUND_HALF_EVEN: - return (rnd > 5) || ((rnd == 5) && mpd_isoddcoeff(dec)); - case MPD_ROUND_CEILING: - return !(rnd == 0 || mpd_isnegative(dec)); - case MPD_ROUND_FLOOR: - return !(rnd == 0 || mpd_ispositive(dec)); - case MPD_ROUND_HALF_DOWN: - return (rnd > 5); - case MPD_ROUND_UP: - return !(rnd == 0); - case MPD_ROUND_05UP: - ld = (int)mpd_lsd(dec->data[0]); - return (!(rnd == 0) && (ld == 0 || ld == 5)); - default: - /* Without a valid context, further results will be undefined. */ - return 0; /* GCOV_NOT_REACHED */ - } -} - -/* - * Apply rounding to a decimal that has been right-shifted into a full - * precision decimal. If an increment leads to an overflow of the precision, - * adjust the coefficient and the exponent and check the new exponent for - * overflow. - */ -static inline void -_mpd_apply_round(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx, - uint32_t *status) -{ - if (_mpd_rnd_incr(dec, rnd, ctx)) { - /* We have a number with exactly ctx->prec digits. The increment - * can only lead to an overflow if the decimal is all nines. In - * that case, the result is a power of ten with prec+1 digits. - * - * If the precision is a multiple of MPD_RDIGITS, this situation is - * detected by _mpd_baseincr returning a carry. - * If the precision is not a multiple of MPD_RDIGITS, we have to - * check if the result has one digit too many. - */ - mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len); - if (carry) { - dec->data[dec->len-1] = mpd_pow10[MPD_RDIGITS-1]; - dec->exp += 1; - _mpd_check_exp(dec, ctx, status); - return; - } - mpd_setdigits(dec); - if (dec->digits > ctx->prec) { - mpd_qshiftr_inplace(dec, 1); - dec->exp += 1; - dec->digits = ctx->prec; - _mpd_check_exp(dec, ctx, status); - } - } -} - -/* - * Apply rounding to a decimal. Allow overflow of the precision. - */ -static inline void -_mpd_apply_round_excess(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx, - uint32_t *status) -{ - if (_mpd_rnd_incr(dec, rnd, ctx)) { - mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len); - if (carry) { - if (!mpd_qresize(dec, dec->len+1, status)) { - return; - } - dec->data[dec->len] = 1; - dec->len += 1; - } - mpd_setdigits(dec); - } -} - -/* - * Apply rounding to a decimal that has been right-shifted into a decimal - * with full precision or less. Return failure if an increment would - * overflow the precision. - */ -static inline int -_mpd_apply_round_fit(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx, - uint32_t *status) -{ - if (_mpd_rnd_incr(dec, rnd, ctx)) { - mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len); - if (carry) { - if (!mpd_qresize(dec, dec->len+1, status)) { - return 0; - } - dec->data[dec->len] = 1; - dec->len += 1; - } - mpd_setdigits(dec); - if (dec->digits > ctx->prec) { - mpd_seterror(dec, MPD_Invalid_operation, status); - return 0; - } - } - return 1; -} - -/* Check a normal number for overflow, underflow, clamping. If the operand - is modified, it will be zero, special or (sub)normal with a coefficient - that fits into the current context precision. */ -static inline void -_mpd_check_exp(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status) -{ - mpd_ssize_t adjexp, etiny, shift; - int rnd; - - adjexp = mpd_adjexp(dec); - if (adjexp > ctx->emax) { - - if (mpd_iszerocoeff(dec)) { - dec->exp = ctx->emax; - if (ctx->clamp) { - dec->exp -= (ctx->prec-1); - } - mpd_zerocoeff(dec); - *status |= MPD_Clamped; - return; - } - - switch (ctx->round) { - case MPD_ROUND_HALF_UP: case MPD_ROUND_HALF_EVEN: - case MPD_ROUND_HALF_DOWN: case MPD_ROUND_UP: - case MPD_ROUND_TRUNC: - mpd_setspecial(dec, mpd_sign(dec), MPD_INF); - break; - case MPD_ROUND_DOWN: case MPD_ROUND_05UP: - mpd_qmaxcoeff(dec, ctx, status); - dec->exp = ctx->emax - ctx->prec + 1; - break; - case MPD_ROUND_CEILING: - if (mpd_isnegative(dec)) { - mpd_qmaxcoeff(dec, ctx, status); - dec->exp = ctx->emax - ctx->prec + 1; - } - else { - mpd_setspecial(dec, MPD_POS, MPD_INF); - } - break; - case MPD_ROUND_FLOOR: - if (mpd_ispositive(dec)) { - mpd_qmaxcoeff(dec, ctx, status); - dec->exp = ctx->emax - ctx->prec + 1; - } - else { - mpd_setspecial(dec, MPD_NEG, MPD_INF); - } - break; - default: /* debug */ - abort(); /* GCOV_NOT_REACHED */ - } - - *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded; - - } /* fold down */ - else if (ctx->clamp && dec->exp > mpd_etop(ctx)) { - /* At this point adjexp=exp+digits-1 <= emax and exp > etop=emax-prec+1: - * (1) shift = exp -emax+prec-1 > 0 - * (2) digits+shift = exp+digits-1 - emax + prec <= prec */ - shift = dec->exp - mpd_etop(ctx); - if (!mpd_qshiftl(dec, dec, shift, status)) { - return; - } - dec->exp -= shift; - *status |= MPD_Clamped; - if (!mpd_iszerocoeff(dec) && adjexp < ctx->emin) { - /* Underflow is impossible, since exp < etiny=emin-prec+1 - * and exp > etop=emax-prec+1 would imply emax < emin. */ - *status |= MPD_Subnormal; - } - } - else if (adjexp < ctx->emin) { - - etiny = mpd_etiny(ctx); - - if (mpd_iszerocoeff(dec)) { - if (dec->exp < etiny) { - dec->exp = etiny; - mpd_zerocoeff(dec); - *status |= MPD_Clamped; - } - return; - } - - *status |= MPD_Subnormal; - if (dec->exp < etiny) { - /* At this point adjexp=exp+digits-1 < emin and exp < etiny=emin-prec+1: - * (1) shift = emin-prec+1 - exp > 0 - * (2) digits-shift = exp+digits-1 - emin + prec < prec */ - shift = etiny - dec->exp; - rnd = (int)mpd_qshiftr_inplace(dec, shift); - dec->exp = etiny; - /* We always have a spare digit in case of an increment. */ - _mpd_apply_round_excess(dec, rnd, ctx, status); - *status |= MPD_Rounded; - if (rnd) { - *status |= (MPD_Inexact|MPD_Underflow); - if (mpd_iszerocoeff(dec)) { - mpd_zerocoeff(dec); - *status |= MPD_Clamped; - } - } - } - /* Case exp >= etiny=emin-prec+1: - * (1) adjexp=exp+digits-1 < emin - * (2) digits < emin-exp+1 <= prec */ - } -} - -/* Transcendental functions do not always set Underflow reliably, - * since they only use as much precision as is necessary for correct - * rounding. If a result like 1.0000000000e-101 is finalized, there - * is no rounding digit that would trigger Underflow. But we can - * assume Inexact, so a short check suffices. */ -static inline void -mpd_check_underflow(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status) -{ - if (mpd_adjexp(dec) < ctx->emin && !mpd_iszero(dec) && - dec->exp < mpd_etiny(ctx)) { - *status |= MPD_Underflow; - } -} - -/* Check if a normal number must be rounded after the exponent has been checked. */ -static inline void -_mpd_check_round(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status) -{ - mpd_uint_t rnd; - mpd_ssize_t shift; - - /* must handle specials: _mpd_check_exp() can produce infinities or NaNs */ - if (mpd_isspecial(dec)) { - return; - } - - if (dec->digits > ctx->prec) { - shift = dec->digits - ctx->prec; - rnd = mpd_qshiftr_inplace(dec, shift); - dec->exp += shift; - _mpd_apply_round(dec, rnd, ctx, status); - *status |= MPD_Rounded; - if (rnd) { - *status |= MPD_Inexact; - } - } -} - -/* Finalize all operations. */ -void -mpd_qfinalize(mpd_t *result, const mpd_context_t *ctx, uint32_t *status) -{ - if (mpd_isspecial(result)) { - if (mpd_isnan(result)) { - _mpd_fix_nan(result, ctx); - } - return; - } - - _mpd_check_exp(result, ctx, status); - _mpd_check_round(result, ctx, status); -} - - -/******************************************************************************/ -/* Copying */ -/******************************************************************************/ - -/* Internal function: Copy a decimal, share data with src: USE WITH CARE! */ -static inline void -_mpd_copy_shared(mpd_t *dest, const mpd_t *src) -{ - dest->flags = src->flags; - dest->exp = src->exp; - dest->digits = src->digits; - dest->len = src->len; - dest->alloc = src->alloc; - dest->data = src->data; - - mpd_set_shared_data(dest); -} - -/* - * Copy a decimal. In case of an error, status is set to MPD_Malloc_error. - */ -int -mpd_qcopy(mpd_t *result, const mpd_t *a, uint32_t *status) -{ - if (result == a) return 1; - - if (!mpd_qresize(result, a->len, status)) { - return 0; - } - - mpd_copy_flags(result, a); - result->exp = a->exp; - result->digits = a->digits; - result->len = a->len; - memcpy(result->data, a->data, a->len * (sizeof *result->data)); - - return 1; -} - -/* - * Copy to a decimal with a static buffer. The caller has to make sure that - * the buffer is big enough. Cannot fail. - */ -static void -mpd_qcopy_static(mpd_t *result, const mpd_t *a) -{ - if (result == a) return; - - memcpy(result->data, a->data, a->len * (sizeof *result->data)); - - mpd_copy_flags(result, a); - result->exp = a->exp; - result->digits = a->digits; - result->len = a->len; -} - -/* - * Return a newly allocated copy of the operand. In case of an error, - * status is set to MPD_Malloc_error and the return value is NULL. - */ -mpd_t * -mpd_qncopy(const mpd_t *a) -{ - mpd_t *result; - - if ((result = mpd_qnew_size(a->len)) == NULL) { - return NULL; - } - memcpy(result->data, a->data, a->len * (sizeof *result->data)); - mpd_copy_flags(result, a); - result->exp = a->exp; - result->digits = a->digits; - result->len = a->len; - - return result; -} - -/* - * Copy a decimal and set the sign to positive. In case of an error, the - * status is set to MPD_Malloc_error. - */ -int -mpd_qcopy_abs(mpd_t *result, const mpd_t *a, uint32_t *status) -{ - if (!mpd_qcopy(result, a, status)) { - return 0; - } - mpd_set_positive(result); - return 1; -} - -/* - * Copy a decimal and negate the sign. In case of an error, the - * status is set to MPD_Malloc_error. - */ -int -mpd_qcopy_negate(mpd_t *result, const mpd_t *a, uint32_t *status) -{ - if (!mpd_qcopy(result, a, status)) { - return 0; - } - _mpd_negate(result); - return 1; -} - -/* - * Copy a decimal, setting the sign of the first operand to the sign of the - * second operand. In case of an error, the status is set to MPD_Malloc_error. - */ -int -mpd_qcopy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status) -{ - uint8_t sign_b = mpd_sign(b); /* result may equal b! */ - - if (!mpd_qcopy(result, a, status)) { - return 0; - } - mpd_set_sign(result, sign_b); - return 1; -} - - -/******************************************************************************/ -/* Comparisons */ -/******************************************************************************/ - -/* - * For all functions that compare two operands and return an int the usual - * convention applies to the return value: - * - * -1 if op1 < op2 - * 0 if op1 == op2 - * 1 if op1 > op2 - * - * INT_MAX for error - */ - - -/* Convenience macro. If a and b are not equal, return from the calling - * function with the correct comparison value. */ -#define CMP_EQUAL_OR_RETURN(a, b) \ - if (a != b) { \ - if (a < b) { \ - return -1; \ - } \ - return 1; \ - } - -/* - * Compare the data of big and small. This function does the equivalent - * of first shifting small to the left and then comparing the data of - * big and small, except that no allocation for the left shift is needed. - */ -static int -_mpd_basecmp(mpd_uint_t *big, mpd_uint_t *small, mpd_size_t n, mpd_size_t m, - mpd_size_t shift) -{ -#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__) - /* spurious uninitialized warnings */ - mpd_uint_t l=l, lprev=lprev, h=h; -#else - mpd_uint_t l, lprev, h; -#endif - mpd_uint_t q, r; - mpd_uint_t ph, x; - - assert(m > 0 && n >= m && shift > 0); - - _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS); - - if (r != 0) { - - ph = mpd_pow10[r]; - - --m; --n; - _mpd_divmod_pow10(&h, &lprev, small[m--], MPD_RDIGITS-r); - if (h != 0) { - CMP_EQUAL_OR_RETURN(big[n], h) - --n; - } - for (; m != MPD_SIZE_MAX; m--,n--) { - _mpd_divmod_pow10(&h, &l, small[m], MPD_RDIGITS-r); - x = ph * lprev + h; - CMP_EQUAL_OR_RETURN(big[n], x) - lprev = l; - } - x = ph * lprev; - CMP_EQUAL_OR_RETURN(big[q], x) - } - else { - while (--m != MPD_SIZE_MAX) { - CMP_EQUAL_OR_RETURN(big[m+q], small[m]) - } - } - - return !_mpd_isallzero(big, q); -} - -/* Compare two decimals with the same adjusted exponent. */ -static int -_mpd_cmp_same_adjexp(const mpd_t *a, const mpd_t *b) -{ - mpd_ssize_t shift, i; - - if (a->exp != b->exp) { - /* Cannot wrap: a->exp + a->digits = b->exp + b->digits, so - * a->exp - b->exp = b->digits - a->digits. */ - shift = a->exp - b->exp; - if (shift > 0) { - return -1 * _mpd_basecmp(b->data, a->data, b->len, a->len, shift); - } - else { - return _mpd_basecmp(a->data, b->data, a->len, b->len, -shift); - } - } - - /* - * At this point adjexp(a) == adjexp(b) and a->exp == b->exp, - * so a->digits == b->digits, therefore a->len == b->len. - */ - for (i = a->len-1; i >= 0; --i) { - CMP_EQUAL_OR_RETURN(a->data[i], b->data[i]) - } - - return 0; -} - -/* Compare two numerical values. */ -static int -_mpd_cmp(const mpd_t *a, const mpd_t *b) -{ - mpd_ssize_t adjexp_a, adjexp_b; - - /* equal pointers */ - if (a == b) { - return 0; - } - - /* infinities */ - if (mpd_isinfinite(a)) { - if (mpd_isinfinite(b)) { - return mpd_isnegative(b) - mpd_isnegative(a); - } - return mpd_arith_sign(a); - } - if (mpd_isinfinite(b)) { - return -mpd_arith_sign(b); - } - - /* zeros */ - if (mpd_iszerocoeff(a)) { - if (mpd_iszerocoeff(b)) { - return 0; - } - return -mpd_arith_sign(b); - } - if (mpd_iszerocoeff(b)) { - return mpd_arith_sign(a); - } - - /* different signs */ - if (mpd_sign(a) != mpd_sign(b)) { - return mpd_sign(b) - mpd_sign(a); - } - - /* different adjusted exponents */ - adjexp_a = mpd_adjexp(a); - adjexp_b = mpd_adjexp(b); - if (adjexp_a != adjexp_b) { - if (adjexp_a < adjexp_b) { - return -1 * mpd_arith_sign(a); - } - return mpd_arith_sign(a); - } - - /* same adjusted exponents */ - return _mpd_cmp_same_adjexp(a, b) * mpd_arith_sign(a); -} - -/* Compare the absolutes of two numerical values. */ -static int -_mpd_cmp_abs(const mpd_t *a, const mpd_t *b) -{ - mpd_ssize_t adjexp_a, adjexp_b; - - /* equal pointers */ - if (a == b) { - return 0; - } - - /* infinities */ - if (mpd_isinfinite(a)) { - if (mpd_isinfinite(b)) { - return 0; - } - return 1; - } - if (mpd_isinfinite(b)) { - return -1; - } - - /* zeros */ - if (mpd_iszerocoeff(a)) { - if (mpd_iszerocoeff(b)) { - return 0; - } - return -1; - } - if (mpd_iszerocoeff(b)) { - return 1; - } - - /* different adjusted exponents */ - adjexp_a = mpd_adjexp(a); - adjexp_b = mpd_adjexp(b); - if (adjexp_a != adjexp_b) { - if (adjexp_a < adjexp_b) { - return -1; - } - return 1; - } - - /* same adjusted exponents */ - return _mpd_cmp_same_adjexp(a, b); -} - -/* Compare two values and return an integer result. */ -int -mpd_qcmp(const mpd_t *a, const mpd_t *b, uint32_t *status) -{ - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_isnan(a) || mpd_isnan(b)) { - *status |= MPD_Invalid_operation; - return INT_MAX; - } - } - - return _mpd_cmp(a, b); -} - -/* - * Compare a and b, convert the usual integer result to a decimal and - * store it in 'result'. For convenience, the integer result of the comparison - * is returned. Comparisons involving NaNs return NaN/INT_MAX. - */ -int -mpd_qcompare(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return INT_MAX; - } - } - - c = _mpd_cmp(a, b); - _settriple(result, (c < 0), (c != 0), 0); - return c; -} - -/* Same as mpd_compare(), but signal for all NaNs, i.e. also for quiet NaNs. */ -int -mpd_qcompare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - *status |= MPD_Invalid_operation; - return INT_MAX; - } - } - - c = _mpd_cmp(a, b); - _settriple(result, (c < 0), (c != 0), 0); - return c; -} - -/* Compare the operands using a total order. */ -int -mpd_cmp_total(const mpd_t *a, const mpd_t *b) -{ - mpd_t aa, bb; - int nan_a, nan_b; - int c; - - if (mpd_sign(a) != mpd_sign(b)) { - return mpd_sign(b) - mpd_sign(a); - } - - - if (mpd_isnan(a)) { - c = 1; - if (mpd_isnan(b)) { - nan_a = (mpd_isqnan(a)) ? 1 : 0; - nan_b = (mpd_isqnan(b)) ? 1 : 0; - if (nan_b == nan_a) { - if (a->len > 0 && b->len > 0) { - _mpd_copy_shared(&aa, a); - _mpd_copy_shared(&bb, b); - aa.exp = bb.exp = 0; - /* compare payload */ - c = _mpd_cmp_abs(&aa, &bb); - } - else { - c = (a->len > 0) - (b->len > 0); - } - } - else { - c = nan_a - nan_b; - } - } - } - else if (mpd_isnan(b)) { - c = -1; - } - else { - c = _mpd_cmp_abs(a, b); - if (c == 0 && a->exp != b->exp) { - c = (a->exp < b->exp) ? -1 : 1; - } - } - - return c * mpd_arith_sign(a); -} - -/* - * Compare a and b according to a total order, convert the usual integer result - * to a decimal and store it in 'result'. For convenience, the integer result - * of the comparison is returned. - */ -int -mpd_compare_total(mpd_t *result, const mpd_t *a, const mpd_t *b) -{ - int c; - - c = mpd_cmp_total(a, b); - _settriple(result, (c < 0), (c != 0), 0); - return c; -} - -/* Compare the magnitude of the operands using a total order. */ -int -mpd_cmp_total_mag(const mpd_t *a, const mpd_t *b) -{ - mpd_t aa, bb; - - _mpd_copy_shared(&aa, a); - _mpd_copy_shared(&bb, b); - - mpd_set_positive(&aa); - mpd_set_positive(&bb); - - return mpd_cmp_total(&aa, &bb); -} - -/* - * Compare the magnitude of a and b according to a total order, convert the - * the usual integer result to a decimal and store it in 'result'. - * For convenience, the integer result of the comparison is returned. - */ -int -mpd_compare_total_mag(mpd_t *result, const mpd_t *a, const mpd_t *b) -{ - int c; - - c = mpd_cmp_total_mag(a, b); - _settriple(result, (c < 0), (c != 0), 0); - return c; -} - -/* Determine an ordering for operands that are numerically equal. */ -static inline int -_mpd_cmp_numequal(const mpd_t *a, const mpd_t *b) -{ - int sign_a, sign_b; - int c; - - sign_a = mpd_sign(a); - sign_b = mpd_sign(b); - if (sign_a != sign_b) { - c = sign_b - sign_a; - } - else { - c = (a->exp < b->exp) ? -1 : 1; - c *= mpd_arith_sign(a); - } - - return c; -} - - -/******************************************************************************/ -/* Shifting the coefficient */ -/******************************************************************************/ - -/* - * Shift the coefficient of the operand to the left, no check for specials. - * Both operands may be the same pointer. If the result length has to be - * increased, mpd_qresize() might fail with MPD_Malloc_error. - */ -int -mpd_qshiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status) -{ - mpd_ssize_t size; - - assert(!mpd_isspecial(a)); - assert(n >= 0); - - if (mpd_iszerocoeff(a) || n == 0) { - return mpd_qcopy(result, a, status); - } - - size = mpd_digits_to_size(a->digits+n); - if (!mpd_qresize(result, size, status)) { - return 0; /* result is NaN */ - } - - _mpd_baseshiftl(result->data, a->data, size, a->len, n); - - mpd_copy_flags(result, a); - result->exp = a->exp; - result->digits = a->digits+n; - result->len = size; - - return 1; -} - -/* Determine the rounding indicator if all digits of the coefficient are shifted - * out of the picture. */ -static mpd_uint_t -_mpd_get_rnd(const mpd_uint_t *data, mpd_ssize_t len, int use_msd) -{ - mpd_uint_t rnd = 0, rest = 0, word; - - word = data[len-1]; - /* special treatment for the most significant digit if shift == digits */ - if (use_msd) { - _mpd_divmod_pow10(&rnd, &rest, word, mpd_word_digits(word)-1); - if (len > 1 && rest == 0) { - rest = !_mpd_isallzero(data, len-1); - } - } - else { - rest = !_mpd_isallzero(data, len); - } - - return (rnd == 0 || rnd == 5) ? rnd + !!rest : rnd; -} - -/* - * Same as mpd_qshiftr(), but 'result' is an mpd_t with a static coefficient. - * It is the caller's responsibility to ensure that the coefficient is big - * enough. The function cannot fail. - */ -static mpd_uint_t -mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n) -{ - mpd_uint_t rnd; - mpd_ssize_t size; - - assert(!mpd_isspecial(a)); - assert(n >= 0); - - if (mpd_iszerocoeff(a) || n == 0) { - mpd_qcopy_static(result, a); - return 0; - } - - if (n >= a->digits) { - rnd = _mpd_get_rnd(a->data, a->len, (n==a->digits)); - mpd_zerocoeff(result); - } - else { - result->digits = a->digits-n; - size = mpd_digits_to_size(result->digits); - rnd = _mpd_baseshiftr(result->data, a->data, a->len, n); - result->len = size; - } - - mpd_copy_flags(result, a); - result->exp = a->exp; - - return rnd; -} - -/* - * Inplace shift of the coefficient to the right, no check for specials. - * Returns the rounding indicator for mpd_rnd_incr(). - * The function cannot fail. - */ -mpd_uint_t -mpd_qshiftr_inplace(mpd_t *result, mpd_ssize_t n) -{ - uint32_t dummy; - mpd_uint_t rnd; - mpd_ssize_t size; - - assert(!mpd_isspecial(result)); - assert(n >= 0); - - if (mpd_iszerocoeff(result) || n == 0) { - return 0; - } - - if (n >= result->digits) { - rnd = _mpd_get_rnd(result->data, result->len, (n==result->digits)); - mpd_zerocoeff(result); - } - else { - rnd = _mpd_baseshiftr(result->data, result->data, result->len, n); - result->digits -= n; - size = mpd_digits_to_size(result->digits); - /* reducing the size cannot fail */ - mpd_qresize(result, size, &dummy); - result->len = size; - } - - return rnd; -} - -/* - * Shift the coefficient of the operand to the right, no check for specials. - * Both operands may be the same pointer. Returns the rounding indicator to - * be used by mpd_rnd_incr(). If the result length has to be increased, - * mpd_qcopy() or mpd_qresize() might fail with MPD_Malloc_error. In those - * cases, MPD_UINT_MAX is returned. - */ -mpd_uint_t -mpd_qshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status) -{ - mpd_uint_t rnd; - mpd_ssize_t size; - - assert(!mpd_isspecial(a)); - assert(n >= 0); - - if (mpd_iszerocoeff(a) || n == 0) { - if (!mpd_qcopy(result, a, status)) { - return MPD_UINT_MAX; - } - return 0; - } - - if (n >= a->digits) { - rnd = _mpd_get_rnd(a->data, a->len, (n==a->digits)); - mpd_zerocoeff(result); - } - else { - result->digits = a->digits-n; - size = mpd_digits_to_size(result->digits); - if (result == a) { - rnd = _mpd_baseshiftr(result->data, a->data, a->len, n); - /* reducing the size cannot fail */ - mpd_qresize(result, size, status); - } - else { - if (!mpd_qresize(result, size, status)) { - return MPD_UINT_MAX; - } - rnd = _mpd_baseshiftr(result->data, a->data, a->len, n); - } - result->len = size; - } - - mpd_copy_flags(result, a); - result->exp = a->exp; - - return rnd; -} - - -/******************************************************************************/ -/* Miscellaneous operations */ -/******************************************************************************/ - -/* Logical And */ -void -mpd_qand(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - const mpd_t *big = a, *small = b; - mpd_uint_t x, y, z, xbit, ybit; - int k, mswdigits; - mpd_ssize_t i; - - if (mpd_isspecial(a) || mpd_isspecial(b) || - mpd_isnegative(a) || mpd_isnegative(b) || - a->exp != 0 || b->exp != 0) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (b->digits > a->digits) { - big = b; - small = a; - } - if (!mpd_qresize(result, big->len, status)) { - return; - } - - - /* full words */ - for (i = 0; i < small->len-1; i++) { - x = small->data[i]; - y = big->data[i]; - z = 0; - for (k = 0; k < MPD_RDIGITS; k++) { - xbit = x % 10; - x /= 10; - ybit = y % 10; - y /= 10; - if (xbit > 1 || ybit > 1) { - goto invalid_operation; - } - z += (xbit&ybit) ? mpd_pow10[k] : 0; - } - result->data[i] = z; - } - /* most significant word of small */ - x = small->data[i]; - y = big->data[i]; - z = 0; - mswdigits = mpd_word_digits(x); - for (k = 0; k < mswdigits; k++) { - xbit = x % 10; - x /= 10; - ybit = y % 10; - y /= 10; - if (xbit > 1 || ybit > 1) { - goto invalid_operation; - } - z += (xbit&ybit) ? mpd_pow10[k] : 0; - } - result->data[i++] = z; - - /* scan the rest of y for digits > 1 */ - for (; k < MPD_RDIGITS; k++) { - ybit = y % 10; - y /= 10; - if (ybit > 1) { - goto invalid_operation; - } - } - /* scan the rest of big for digits > 1 */ - for (; i < big->len; i++) { - y = big->data[i]; - for (k = 0; k < MPD_RDIGITS; k++) { - ybit = y % 10; - y /= 10; - if (ybit > 1) { - goto invalid_operation; - } - } - } - - mpd_clear_flags(result); - result->exp = 0; - result->len = _mpd_real_size(result->data, small->len); - mpd_qresize(result, result->len, status); - mpd_setdigits(result); - _mpd_cap(result, ctx); - return; - -invalid_operation: - mpd_seterror(result, MPD_Invalid_operation, status); -} - -/* Class of an operand. Returns a pointer to the constant name. */ -const char * -mpd_class(const mpd_t *a, const mpd_context_t *ctx) -{ - if (mpd_isnan(a)) { - if (mpd_isqnan(a)) - return "NaN"; - else - return "sNaN"; - } - else if (mpd_ispositive(a)) { - if (mpd_isinfinite(a)) - return "+Infinity"; - else if (mpd_iszero(a)) - return "+Zero"; - else if (mpd_isnormal(a, ctx)) - return "+Normal"; - else - return "+Subnormal"; - } - else { - if (mpd_isinfinite(a)) - return "-Infinity"; - else if (mpd_iszero(a)) - return "-Zero"; - else if (mpd_isnormal(a, ctx)) - return "-Normal"; - else - return "-Subnormal"; - } -} - -/* Logical Xor */ -void -mpd_qinvert(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_uint_t x, z, xbit; - mpd_ssize_t i, digits, len; - mpd_ssize_t q, r; - int k; - - if (mpd_isspecial(a) || mpd_isnegative(a) || a->exp != 0) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - digits = (a->digits < ctx->prec) ? ctx->prec : a->digits; - _mpd_idiv_word(&q, &r, digits, MPD_RDIGITS); - len = (r == 0) ? q : q+1; - if (!mpd_qresize(result, len, status)) { - return; - } - - for (i = 0; i < len; i++) { - x = (i < a->len) ? a->data[i] : 0; - z = 0; - for (k = 0; k < MPD_RDIGITS; k++) { - xbit = x % 10; - x /= 10; - if (xbit > 1) { - goto invalid_operation; - } - z += !xbit ? mpd_pow10[k] : 0; - } - result->data[i] = z; - } - - mpd_clear_flags(result); - result->exp = 0; - result->len = _mpd_real_size(result->data, len); - mpd_qresize(result, result->len, status); - mpd_setdigits(result); - _mpd_cap(result, ctx); - return; - -invalid_operation: - mpd_seterror(result, MPD_Invalid_operation, status); -} - -/* Exponent of the magnitude of the most significant digit of the operand. */ -void -mpd_qlogb(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - mpd_setspecial(result, MPD_POS, MPD_INF); - } - else if (mpd_iszerocoeff(a)) { - mpd_setspecial(result, MPD_NEG, MPD_INF); - *status |= MPD_Division_by_zero; - } - else { - mpd_qset_ssize(result, mpd_adjexp(a), ctx, status); - } -} - -/* Logical Or */ -void -mpd_qor(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - const mpd_t *big = a, *small = b; - mpd_uint_t x, y, z, xbit, ybit; - int k, mswdigits; - mpd_ssize_t i; - - if (mpd_isspecial(a) || mpd_isspecial(b) || - mpd_isnegative(a) || mpd_isnegative(b) || - a->exp != 0 || b->exp != 0) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (b->digits > a->digits) { - big = b; - small = a; - } - if (!mpd_qresize(result, big->len, status)) { - return; - } - - - /* full words */ - for (i = 0; i < small->len-1; i++) { - x = small->data[i]; - y = big->data[i]; - z = 0; - for (k = 0; k < MPD_RDIGITS; k++) { - xbit = x % 10; - x /= 10; - ybit = y % 10; - y /= 10; - if (xbit > 1 || ybit > 1) { - goto invalid_operation; - } - z += (xbit|ybit) ? mpd_pow10[k] : 0; - } - result->data[i] = z; - } - /* most significant word of small */ - x = small->data[i]; - y = big->data[i]; - z = 0; - mswdigits = mpd_word_digits(x); - for (k = 0; k < mswdigits; k++) { - xbit = x % 10; - x /= 10; - ybit = y % 10; - y /= 10; - if (xbit > 1 || ybit > 1) { - goto invalid_operation; - } - z += (xbit|ybit) ? mpd_pow10[k] : 0; - } - - /* scan for digits > 1 and copy the rest of y */ - for (; k < MPD_RDIGITS; k++) { - ybit = y % 10; - y /= 10; - if (ybit > 1) { - goto invalid_operation; - } - z += ybit*mpd_pow10[k]; - } - result->data[i++] = z; - /* scan for digits > 1 and copy the rest of big */ - for (; i < big->len; i++) { - y = big->data[i]; - for (k = 0; k < MPD_RDIGITS; k++) { - ybit = y % 10; - y /= 10; - if (ybit > 1) { - goto invalid_operation; - } - } - result->data[i] = big->data[i]; - } - - mpd_clear_flags(result); - result->exp = 0; - result->len = _mpd_real_size(result->data, big->len); - mpd_qresize(result, result->len, status); - mpd_setdigits(result); - _mpd_cap(result, ctx); - return; - -invalid_operation: - mpd_seterror(result, MPD_Invalid_operation, status); -} - -/* - * Rotate the coefficient of 'a' by 'b' digits. 'b' must be an integer with - * exponent 0. - */ -void -mpd_qrotate(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - MPD_NEW_STATIC(tmp,0,0,0,0); - MPD_NEW_STATIC(big,0,0,0,0); - MPD_NEW_STATIC(small,0,0,0,0); - mpd_ssize_t n, lshift, rshift; - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - } - if (b->exp != 0 || mpd_isinfinite(b)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - n = mpd_qget_ssize(b, &workstatus); - if (workstatus&MPD_Invalid_operation) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (n > ctx->prec || n < -ctx->prec) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mpd_isinfinite(a)) { - mpd_qcopy(result, a, status); - return; - } - - if (n >= 0) { - lshift = n; - rshift = ctx->prec-n; - } - else { - lshift = ctx->prec+n; - rshift = -n; - } - - if (a->digits > ctx->prec) { - if (!mpd_qcopy(&tmp, a, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - goto finish; - } - _mpd_cap(&tmp, ctx); - a = &tmp; - } - - if (!mpd_qshiftl(&big, a, lshift, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - goto finish; - } - _mpd_cap(&big, ctx); - - if (mpd_qshiftr(&small, a, rshift, status) == MPD_UINT_MAX) { - mpd_seterror(result, MPD_Malloc_error, status); - goto finish; - } - _mpd_qadd(result, &big, &small, ctx, status); - - -finish: - mpd_del(&tmp); - mpd_del(&big); - mpd_del(&small); -} - -/* - * b must be an integer with exponent 0 and in the range +-2*(emax + prec). - * XXX: In my opinion +-(2*emax + prec) would be more sensible. - * The result is a with the value of b added to its exponent. - */ -void -mpd_qscaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_uint_t n, maxjump; -#ifndef LEGACY_COMPILER - int64_t exp; -#else - mpd_uint_t x; - int x_sign, n_sign; - mpd_ssize_t exp; -#endif - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - } - if (b->exp != 0 || mpd_isinfinite(b)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - n = mpd_qabs_uint(b, &workstatus); - /* the spec demands this */ - maxjump = 2 * (mpd_uint_t)(ctx->emax + ctx->prec); - - if (n > maxjump || workstatus&MPD_Invalid_operation) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mpd_isinfinite(a)) { - mpd_qcopy(result, a, status); - return; - } - -#ifndef LEGACY_COMPILER - exp = a->exp + (int64_t)n * mpd_arith_sign(b); - exp = (exp > MPD_EXP_INF) ? MPD_EXP_INF : exp; - exp = (exp < MPD_EXP_CLAMP) ? MPD_EXP_CLAMP : exp; -#else - x = (a->exp < 0) ? -a->exp : a->exp; - x_sign = (a->exp < 0) ? 1 : 0; - n_sign = mpd_isnegative(b) ? 1 : 0; - - if (x_sign == n_sign) { - x = x + n; - if (x < n) x = MPD_UINT_MAX; - } - else { - x_sign = (x >= n) ? x_sign : n_sign; - x = (x >= n) ? x - n : n - x; - } - if (!x_sign && x > MPD_EXP_INF) x = MPD_EXP_INF; - if (x_sign && x > -MPD_EXP_CLAMP) x = -MPD_EXP_CLAMP; - exp = x_sign ? -((mpd_ssize_t)x) : (mpd_ssize_t)x; -#endif - - mpd_qcopy(result, a, status); - result->exp = (mpd_ssize_t)exp; - - mpd_qfinalize(result, ctx, status); -} - -/* - * Shift the coefficient by n digits, positive n is a left shift. In the case - * of a left shift, the result is decapitated to fit the context precision. If - * you don't want that, use mpd_shiftl(). - */ -void -mpd_qshiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - mpd_qcopy(result, a, status); - return; - } - - if (n >= 0 && n <= ctx->prec) { - mpd_qshiftl(result, a, n, status); - _mpd_cap(result, ctx); - } - else if (n < 0 && n >= -ctx->prec) { - if (!mpd_qcopy(result, a, status)) { - return; - } - _mpd_cap(result, ctx); - mpd_qshiftr_inplace(result, -n); - } - else { - mpd_seterror(result, MPD_Invalid_operation, status); - } -} - -/* - * Same as mpd_shiftn(), but the shift is specified by the decimal b, which - * must be an integer with a zero exponent. Infinities remain infinities. - */ -void -mpd_qshift(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, - uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_ssize_t n; - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - } - if (b->exp != 0 || mpd_isinfinite(b)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - n = mpd_qget_ssize(b, &workstatus); - if (workstatus&MPD_Invalid_operation) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (n > ctx->prec || n < -ctx->prec) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mpd_isinfinite(a)) { - mpd_qcopy(result, a, status); - return; - } - - if (n >= 0) { - mpd_qshiftl(result, a, n, status); - _mpd_cap(result, ctx); - } - else { - if (!mpd_qcopy(result, a, status)) { - return; - } - _mpd_cap(result, ctx); - mpd_qshiftr_inplace(result, -n); - } -} - -/* Logical Xor */ -void -mpd_qxor(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - const mpd_t *big = a, *small = b; - mpd_uint_t x, y, z, xbit, ybit; - int k, mswdigits; - mpd_ssize_t i; - - if (mpd_isspecial(a) || mpd_isspecial(b) || - mpd_isnegative(a) || mpd_isnegative(b) || - a->exp != 0 || b->exp != 0) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (b->digits > a->digits) { - big = b; - small = a; - } - if (!mpd_qresize(result, big->len, status)) { - return; - } - - - /* full words */ - for (i = 0; i < small->len-1; i++) { - x = small->data[i]; - y = big->data[i]; - z = 0; - for (k = 0; k < MPD_RDIGITS; k++) { - xbit = x % 10; - x /= 10; - ybit = y % 10; - y /= 10; - if (xbit > 1 || ybit > 1) { - goto invalid_operation; - } - z += (xbit^ybit) ? mpd_pow10[k] : 0; - } - result->data[i] = z; - } - /* most significant word of small */ - x = small->data[i]; - y = big->data[i]; - z = 0; - mswdigits = mpd_word_digits(x); - for (k = 0; k < mswdigits; k++) { - xbit = x % 10; - x /= 10; - ybit = y % 10; - y /= 10; - if (xbit > 1 || ybit > 1) { - goto invalid_operation; - } - z += (xbit^ybit) ? mpd_pow10[k] : 0; - } - - /* scan for digits > 1 and copy the rest of y */ - for (; k < MPD_RDIGITS; k++) { - ybit = y % 10; - y /= 10; - if (ybit > 1) { - goto invalid_operation; - } - z += ybit*mpd_pow10[k]; - } - result->data[i++] = z; - /* scan for digits > 1 and copy the rest of big */ - for (; i < big->len; i++) { - y = big->data[i]; - for (k = 0; k < MPD_RDIGITS; k++) { - ybit = y % 10; - y /= 10; - if (ybit > 1) { - goto invalid_operation; - } - } - result->data[i] = big->data[i]; - } - - mpd_clear_flags(result); - result->exp = 0; - result->len = _mpd_real_size(result->data, big->len); - mpd_qresize(result, result->len, status); - mpd_setdigits(result); - _mpd_cap(result, ctx); - return; - -invalid_operation: - mpd_seterror(result, MPD_Invalid_operation, status); -} - - -/******************************************************************************/ -/* Arithmetic operations */ -/******************************************************************************/ - -/* - * The absolute value of a. If a is negative, the result is the same - * as the result of the minus operation. Otherwise, the result is the - * result of the plus operation. - */ -void -mpd_qabs(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - } - - if (mpd_isnegative(a)) { - mpd_qminus(result, a, ctx, status); - } - else { - mpd_qplus(result, a, ctx, status); - } -} - -static inline void -_mpd_ptrswap(const mpd_t **a, const mpd_t **b) -{ - const mpd_t *t = *a; - *a = *b; - *b = t; -} - -/* Add or subtract infinities. */ -static void -_mpd_qaddsub_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, uint8_t sign_b, - uint32_t *status) -{ - if (mpd_isinfinite(a)) { - if (mpd_sign(a) != sign_b && mpd_isinfinite(b)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } - else { - mpd_setspecial(result, mpd_sign(a), MPD_INF); - } - return; - } - assert(mpd_isinfinite(b)); - mpd_setspecial(result, sign_b, MPD_INF); -} - -/* Add or subtract non-special numbers. */ -static void -_mpd_qaddsub(mpd_t *result, const mpd_t *a, const mpd_t *b, uint8_t sign_b, - const mpd_context_t *ctx, uint32_t *status) -{ - const mpd_t *big, *small; - MPD_NEW_STATIC(big_aligned,0,0,0,0); - MPD_NEW_CONST(tiny,0,0,1,1,1,1); - mpd_uint_t carry; - mpd_ssize_t newsize, shift; - mpd_ssize_t exp, i; - int swap = 0; - - - /* compare exponents */ - big = a; small = b; - if (big->exp != small->exp) { - if (small->exp > big->exp) { - _mpd_ptrswap(&big, &small); - swap++; - } - /* align the coefficients */ - if (!mpd_iszerocoeff(big)) { - exp = big->exp - 1; - exp += (big->digits > ctx->prec) ? 0 : big->digits-ctx->prec-1; - if (mpd_adjexp(small) < exp) { - /* - * Avoid huge shifts by substituting a value for small that is - * guaranteed to produce the same results. - * - * adjexp(small) < exp if and only if: - * - * bdigits <= prec AND - * bdigits+shift >= prec+2+sdigits AND - * exp = bexp+bdigits-prec-2 - * - * 1234567000000000 -> bdigits + shift - * ----------XX1234 -> sdigits - * ----------X1 -> tiny-digits - * |- prec -| - * - * OR - * - * bdigits > prec AND - * shift > sdigits AND - * exp = bexp-1 - * - * 1234567892100000 -> bdigits + shift - * ----------XX1234 -> sdigits - * ----------X1 -> tiny-digits - * |- prec -| - * - * If tiny is zero, adding or subtracting is a no-op. - * Otherwise, adding tiny generates a non-zero digit either - * below the rounding digit or the least significant digit - * of big. When subtracting, tiny is in the same position as - * the carry that would be generated by subtracting sdigits. - */ - mpd_copy_flags(&tiny, small); - tiny.exp = exp; - tiny.digits = 1; - tiny.len = 1; - tiny.data[0] = mpd_iszerocoeff(small) ? 0 : 1; - small = &tiny; - } - /* This cannot wrap: the difference is positive and <= maxprec */ - shift = big->exp - small->exp; - if (!mpd_qshiftl(&big_aligned, big, shift, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - goto finish; - } - big = &big_aligned; - } - } - result->exp = small->exp; - - - /* compare length of coefficients */ - if (big->len < small->len) { - _mpd_ptrswap(&big, &small); - swap++; - } - - newsize = big->len; - if (!mpd_qresize(result, newsize, status)) { - goto finish; - } - - if (mpd_sign(a) == sign_b) { - - carry = _mpd_baseadd(result->data, big->data, small->data, - big->len, small->len); - - if (carry) { - newsize = big->len + 1; - if (!mpd_qresize(result, newsize, status)) { - goto finish; - } - result->data[newsize-1] = carry; - } - - result->len = newsize; - mpd_set_flags(result, sign_b); - } - else { - if (big->len == small->len) { - for (i=big->len-1; i >= 0; --i) { - if (big->data[i] != small->data[i]) { - if (big->data[i] < small->data[i]) { - _mpd_ptrswap(&big, &small); - swap++; - } - break; - } - } - } - - _mpd_basesub(result->data, big->data, small->data, - big->len, small->len); - newsize = _mpd_real_size(result->data, big->len); - /* resize to smaller cannot fail */ - (void)mpd_qresize(result, newsize, status); - - result->len = newsize; - sign_b = (swap & 1) ? sign_b : mpd_sign(a); - mpd_set_flags(result, sign_b); - - if (mpd_iszerocoeff(result)) { - mpd_set_positive(result); - if (ctx->round == MPD_ROUND_FLOOR) { - mpd_set_negative(result); - } - } - } - - mpd_setdigits(result); - -finish: - mpd_del(&big_aligned); -} - -/* Add a and b. No specials, no finalizing. */ -static void -_mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - _mpd_qaddsub(result, a, b, mpd_sign(b), ctx, status); -} - -/* Subtract b from a. No specials, no finalizing. */ -static void -_mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - _mpd_qaddsub(result, a, b, !mpd_sign(b), ctx, status); -} - -/* Add a and b. */ -void -mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - _mpd_qaddsub_inf(result, a, b, mpd_sign(b), status); - return; - } - - _mpd_qaddsub(result, a, b, mpd_sign(b), ctx, status); - mpd_qfinalize(result, ctx, status); -} - -/* Add a and b. Set NaN/Invalid_operation if the result is inexact. */ -static void -_mpd_qadd_exact(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - - mpd_qadd(result, a, b, ctx, &workstatus); - *status |= workstatus; - if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } -} - -/* Subtract b from a. */ -void -mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - _mpd_qaddsub_inf(result, a, b, !mpd_sign(b), status); - return; - } - - _mpd_qaddsub(result, a, b, !mpd_sign(b), ctx, status); - mpd_qfinalize(result, ctx, status); -} - -/* Subtract b from a. Set NaN/Invalid_operation if the result is inexact. */ -static void -_mpd_qsub_exact(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - - mpd_qsub(result, a, b, ctx, &workstatus); - *status |= workstatus; - if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } -} - -/* Add decimal and mpd_ssize_t. */ -void -mpd_qadd_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_ssize(&bb, b, &maxcontext, status); - mpd_qadd(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Add decimal and mpd_uint_t. */ -void -mpd_qadd_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_uint(&bb, b, &maxcontext, status); - mpd_qadd(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Subtract mpd_ssize_t from decimal. */ -void -mpd_qsub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_ssize(&bb, b, &maxcontext, status); - mpd_qsub(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Subtract mpd_uint_t from decimal. */ -void -mpd_qsub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_uint(&bb, b, &maxcontext, status); - mpd_qsub(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Add decimal and int32_t. */ -void -mpd_qadd_i32(mpd_t *result, const mpd_t *a, int32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qadd_ssize(result, a, b, ctx, status); -} - -/* Add decimal and uint32_t. */ -void -mpd_qadd_u32(mpd_t *result, const mpd_t *a, uint32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qadd_uint(result, a, b, ctx, status); -} - -#ifdef CONFIG_64 -/* Add decimal and int64_t. */ -void -mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qadd_ssize(result, a, b, ctx, status); -} - -/* Add decimal and uint64_t. */ -void -mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qadd_uint(result, a, b, ctx, status); -} -#elif !defined(LEGACY_COMPILER) -/* Add decimal and int64_t. */ -void -mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_i64(&bb, b, &maxcontext, status); - mpd_qadd(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Add decimal and uint64_t. */ -void -mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_u64(&bb, b, &maxcontext, status); - mpd_qadd(result, a, &bb, ctx, status); - mpd_del(&bb); -} -#endif - -/* Subtract int32_t from decimal. */ -void -mpd_qsub_i32(mpd_t *result, const mpd_t *a, int32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qsub_ssize(result, a, b, ctx, status); -} - -/* Subtract uint32_t from decimal. */ -void -mpd_qsub_u32(mpd_t *result, const mpd_t *a, uint32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qsub_uint(result, a, b, ctx, status); -} - -#ifdef CONFIG_64 -/* Subtract int64_t from decimal. */ -void -mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qsub_ssize(result, a, b, ctx, status); -} - -/* Subtract uint64_t from decimal. */ -void -mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qsub_uint(result, a, b, ctx, status); -} -#elif !defined(LEGACY_COMPILER) -/* Subtract int64_t from decimal. */ -void -mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_i64(&bb, b, &maxcontext, status); - mpd_qsub(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Subtract uint64_t from decimal. */ -void -mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_u64(&bb, b, &maxcontext, status); - mpd_qsub(result, a, &bb, ctx, status); - mpd_del(&bb); -} -#endif - - -/* Divide infinities. */ -static void -_mpd_qdiv_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - if (mpd_isinfinite(a)) { - if (mpd_isinfinite(b)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF); - return; - } - assert(mpd_isinfinite(b)); - _settriple(result, mpd_sign(a)^mpd_sign(b), 0, mpd_etiny(ctx)); - *status |= MPD_Clamped; -} - -enum {NO_IDEAL_EXP, SET_IDEAL_EXP}; -/* Divide a by b. */ -static void -_mpd_qdiv(int action, mpd_t *q, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - MPD_NEW_STATIC(aligned,0,0,0,0); - mpd_uint_t ld; - mpd_ssize_t shift, exp, tz; - mpd_ssize_t newsize; - mpd_ssize_t ideal_exp; - mpd_uint_t rem; - uint8_t sign_a = mpd_sign(a); - uint8_t sign_b = mpd_sign(b); - - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(q, a, b, ctx, status)) { - return; - } - _mpd_qdiv_inf(q, a, b, ctx, status); - return; - } - if (mpd_iszerocoeff(b)) { - if (mpd_iszerocoeff(a)) { - mpd_seterror(q, MPD_Division_undefined, status); - } - else { - mpd_setspecial(q, sign_a^sign_b, MPD_INF); - *status |= MPD_Division_by_zero; - } - return; - } - if (mpd_iszerocoeff(a)) { - exp = a->exp - b->exp; - _settriple(q, sign_a^sign_b, 0, exp); - mpd_qfinalize(q, ctx, status); - return; - } - - shift = (b->digits - a->digits) + ctx->prec + 1; - ideal_exp = a->exp - b->exp; - exp = ideal_exp - shift; - if (shift > 0) { - if (!mpd_qshiftl(&aligned, a, shift, status)) { - mpd_seterror(q, MPD_Malloc_error, status); - goto finish; - } - a = &aligned; - } - else if (shift < 0) { - shift = -shift; - if (!mpd_qshiftl(&aligned, b, shift, status)) { - mpd_seterror(q, MPD_Malloc_error, status); - goto finish; - } - b = &aligned; - } - - - newsize = a->len - b->len + 1; - if ((q != b && q != a) || (q == b && newsize > b->len)) { - if (!mpd_qresize(q, newsize, status)) { - mpd_seterror(q, MPD_Malloc_error, status); - goto finish; - } - } - - - if (b->len == 1) { - rem = _mpd_shortdiv(q->data, a->data, a->len, b->data[0]); - } - else if (b->len <= MPD_NEWTONDIV_CUTOFF) { - int ret = _mpd_basedivmod(q->data, NULL, a->data, b->data, - a->len, b->len); - if (ret < 0) { - mpd_seterror(q, MPD_Malloc_error, status); - goto finish; - } - rem = ret; - } - else { - MPD_NEW_STATIC(r,0,0,0,0); - _mpd_base_ndivmod(q, &r, a, b, status); - if (mpd_isspecial(q) || mpd_isspecial(&r)) { - mpd_setspecial(q, MPD_POS, MPD_NAN); - mpd_del(&r); - goto finish; - } - rem = !mpd_iszerocoeff(&r); - mpd_del(&r); - newsize = q->len; - } - - newsize = _mpd_real_size(q->data, newsize); - /* resize to smaller cannot fail */ - mpd_qresize(q, newsize, status); - mpd_set_flags(q, sign_a^sign_b); - q->len = newsize; - mpd_setdigits(q); - - shift = ideal_exp - exp; - if (rem) { - ld = mpd_lsd(q->data[0]); - if (ld == 0 || ld == 5) { - q->data[0] += 1; - } - } - else if (action == SET_IDEAL_EXP && shift > 0) { - tz = mpd_trail_zeros(q); - shift = (tz > shift) ? shift : tz; - mpd_qshiftr_inplace(q, shift); - exp += shift; - } - - q->exp = exp; - - -finish: - mpd_del(&aligned); - mpd_qfinalize(q, ctx, status); -} - -/* Divide a by b. */ -void -mpd_qdiv(mpd_t *q, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - _mpd_qdiv(SET_IDEAL_EXP, q, a, b, ctx, status); -} - -/* Internal function. */ -static void -_mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - MPD_NEW_STATIC(aligned,0,0,0,0); - mpd_ssize_t qsize, rsize; - mpd_ssize_t ideal_exp, expdiff, shift; - uint8_t sign_a = mpd_sign(a); - uint8_t sign_ab = mpd_sign(a)^mpd_sign(b); - - - ideal_exp = (a->exp > b->exp) ? b->exp : a->exp; - if (mpd_iszerocoeff(a)) { - if (!mpd_qcopy(r, a, status)) { - goto nanresult; /* GCOV_NOT_REACHED */ - } - r->exp = ideal_exp; - _settriple(q, sign_ab, 0, 0); - return; - } - - expdiff = mpd_adjexp(a) - mpd_adjexp(b); - if (expdiff < 0) { - if (a->exp > b->exp) { - /* positive and less than b->digits - a->digits */ - shift = a->exp - b->exp; - if (!mpd_qshiftl(r, a, shift, status)) { - goto nanresult; - } - r->exp = ideal_exp; - } - else { - if (!mpd_qcopy(r, a, status)) { - goto nanresult; - } - } - _settriple(q, sign_ab, 0, 0); - return; - } - if (expdiff > ctx->prec) { - *status |= MPD_Division_impossible; - goto nanresult; - } - - - /* - * At this point we have: - * (1) 0 <= a->exp + a->digits - b->exp - b->digits <= prec - * (2) a->exp - b->exp >= b->digits - a->digits - * (3) a->exp - b->exp <= prec + b->digits - a->digits - */ - if (a->exp != b->exp) { - shift = a->exp - b->exp; - if (shift > 0) { - /* by (3), after the shift a->digits <= prec + b->digits */ - if (!mpd_qshiftl(&aligned, a, shift, status)) { - goto nanresult; - } - a = &aligned; - } - else { - shift = -shift; - /* by (2), after the shift b->digits <= a->digits */ - if (!mpd_qshiftl(&aligned, b, shift, status)) { - goto nanresult; - } - b = &aligned; - } - } - - - qsize = a->len - b->len + 1; - if (!(q == a && qsize < a->len) && !(q == b && qsize < b->len)) { - if (!mpd_qresize(q, qsize, status)) { - goto nanresult; - } - } - - rsize = b->len; - if (!(r == a && rsize < a->len)) { - if (!mpd_qresize(r, rsize, status)) { - goto nanresult; - } - } - - if (b->len == 1) { - if (a->len == 1) { - _mpd_div_word(&q->data[0], &r->data[0], a->data[0], b->data[0]); - } - else { - r->data[0] = _mpd_shortdiv(q->data, a->data, a->len, b->data[0]); - } - } - else if (b->len <= MPD_NEWTONDIV_CUTOFF) { - int ret; - ret = _mpd_basedivmod(q->data, r->data, a->data, b->data, - a->len, b->len); - if (ret == -1) { - *status |= MPD_Malloc_error; - goto nanresult; - } - } - else { - _mpd_base_ndivmod(q, r, a, b, status); - if (mpd_isspecial(q) || mpd_isspecial(r)) { - goto nanresult; - } - qsize = q->len; - rsize = r->len; - } - - qsize = _mpd_real_size(q->data, qsize); - /* resize to smaller cannot fail */ - mpd_qresize(q, qsize, status); - q->len = qsize; - mpd_setdigits(q); - mpd_set_flags(q, sign_ab); - q->exp = 0; - if (q->digits > ctx->prec) { - *status |= MPD_Division_impossible; - goto nanresult; - } - - rsize = _mpd_real_size(r->data, rsize); - /* resize to smaller cannot fail */ - mpd_qresize(r, rsize, status); - r->len = rsize; - mpd_setdigits(r); - mpd_set_flags(r, sign_a); - r->exp = ideal_exp; - -out: - mpd_del(&aligned); - return; - -nanresult: - mpd_setspecial(q, MPD_POS, MPD_NAN); - mpd_setspecial(r, MPD_POS, MPD_NAN); - goto out; -} - -/* Integer division with remainder. */ -void -mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint8_t sign = mpd_sign(a)^mpd_sign(b); - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(q, a, b, ctx, status)) { - mpd_qcopy(r, q, status); - return; - } - if (mpd_isinfinite(a)) { - if (mpd_isinfinite(b)) { - mpd_setspecial(q, MPD_POS, MPD_NAN); - } - else { - mpd_setspecial(q, sign, MPD_INF); - } - mpd_setspecial(r, MPD_POS, MPD_NAN); - *status |= MPD_Invalid_operation; - return; - } - if (mpd_isinfinite(b)) { - if (!mpd_qcopy(r, a, status)) { - mpd_seterror(q, MPD_Malloc_error, status); - return; - } - mpd_qfinalize(r, ctx, status); - _settriple(q, sign, 0, 0); - return; - } - /* debug */ - abort(); /* GCOV_NOT_REACHED */ - } - if (mpd_iszerocoeff(b)) { - if (mpd_iszerocoeff(a)) { - mpd_setspecial(q, MPD_POS, MPD_NAN); - mpd_setspecial(r, MPD_POS, MPD_NAN); - *status |= MPD_Division_undefined; - } - else { - mpd_setspecial(q, sign, MPD_INF); - mpd_setspecial(r, MPD_POS, MPD_NAN); - *status |= (MPD_Division_by_zero|MPD_Invalid_operation); - } - return; - } - - _mpd_qdivmod(q, r, a, b, ctx, status); - mpd_qfinalize(q, ctx, status); - mpd_qfinalize(r, ctx, status); -} - -void -mpd_qdivint(mpd_t *q, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - MPD_NEW_STATIC(r,0,0,0,0); - uint8_t sign = mpd_sign(a)^mpd_sign(b); - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(q, a, b, ctx, status)) { - return; - } - if (mpd_isinfinite(a) && mpd_isinfinite(b)) { - mpd_seterror(q, MPD_Invalid_operation, status); - return; - } - if (mpd_isinfinite(a)) { - mpd_setspecial(q, sign, MPD_INF); - return; - } - if (mpd_isinfinite(b)) { - _settriple(q, sign, 0, 0); - return; - } - /* debug */ - abort(); /* GCOV_NOT_REACHED */ - } - if (mpd_iszerocoeff(b)) { - if (mpd_iszerocoeff(a)) { - mpd_seterror(q, MPD_Division_undefined, status); - } - else { - mpd_setspecial(q, sign, MPD_INF); - *status |= MPD_Division_by_zero; - } - return; - } - - - _mpd_qdivmod(q, &r, a, b, ctx, status); - mpd_del(&r); - mpd_qfinalize(q, ctx, status); -} - -/* Divide decimal by mpd_ssize_t. */ -void -mpd_qdiv_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_ssize(&bb, b, &maxcontext, status); - mpd_qdiv(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Divide decimal by mpd_uint_t. */ -void -mpd_qdiv_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_uint(&bb, b, &maxcontext, status); - mpd_qdiv(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Divide decimal by int32_t. */ -void -mpd_qdiv_i32(mpd_t *result, const mpd_t *a, int32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qdiv_ssize(result, a, b, ctx, status); -} - -/* Divide decimal by uint32_t. */ -void -mpd_qdiv_u32(mpd_t *result, const mpd_t *a, uint32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qdiv_uint(result, a, b, ctx, status); -} - -#ifdef CONFIG_64 -/* Divide decimal by int64_t. */ -void -mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qdiv_ssize(result, a, b, ctx, status); -} - -/* Divide decimal by uint64_t. */ -void -mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qdiv_uint(result, a, b, ctx, status); -} -#elif !defined(LEGACY_COMPILER) -/* Divide decimal by int64_t. */ -void -mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_i64(&bb, b, &maxcontext, status); - mpd_qdiv(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Divide decimal by uint64_t. */ -void -mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_u64(&bb, b, &maxcontext, status); - mpd_qdiv(result, a, &bb, ctx, status); - mpd_del(&bb); -} -#endif - -/* Pad the result with trailing zeros if it has fewer digits than prec. */ -static void -_mpd_zeropad(mpd_t *result, const mpd_context_t *ctx, uint32_t *status) -{ - if (!mpd_isspecial(result) && !mpd_iszero(result) && - result->digits < ctx->prec) { - mpd_ssize_t shift = ctx->prec - result->digits; - mpd_qshiftl(result, result, shift, status); - result->exp -= shift; - } -} - -/* Check if the result is guaranteed to be one. */ -static int -_mpd_qexp_check_one(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - MPD_NEW_CONST(lim,0,-(ctx->prec+1),1,1,1,9); - MPD_NEW_SHARED(aa, a); - - mpd_set_positive(&aa); - - /* abs(a) <= 9 * 10**(-prec-1) */ - if (_mpd_cmp(&aa, &lim) <= 0) { - _settriple(result, 0, 1, 0); - *status |= MPD_Rounded|MPD_Inexact; - return 1; - } - - return 0; -} - -/* - * Get the number of iterations for the Horner scheme in _mpd_qexp(). - */ -static inline mpd_ssize_t -_mpd_get_exp_iterations(const mpd_t *r, mpd_ssize_t p) -{ - mpd_ssize_t log10pbyr; /* lower bound for log10(p / abs(r)) */ - mpd_ssize_t n; - - assert(p >= 10); - assert(!mpd_iszero(r)); - assert(-p < mpd_adjexp(r) && mpd_adjexp(r) <= -1); - -#ifdef CONFIG_64 - if (p > (mpd_ssize_t)(1ULL<<52)) { - return MPD_SSIZE_MAX; - } -#endif - - /* - * Lower bound for log10(p / abs(r)): adjexp(p) - (adjexp(r) + 1) - * At this point (for CONFIG_64, CONFIG_32 is not problematic): - * 1) 10 <= p <= 2**52 - * 2) -p < adjexp(r) <= -1 - * 3) 1 <= log10pbyr <= 2**52 + 14 - */ - log10pbyr = (mpd_word_digits(p)-1) - (mpd_adjexp(r)+1); - - /* - * The numerator in the paper is 1.435 * p - 1.182, calculated - * exactly. We compensate for rounding errors by using 1.43503. - * ACL2 proofs: - * 1) exp-iter-approx-lower-bound: The term below evaluated - * in 53-bit floating point arithmetic is greater than or - * equal to the exact term used in the paper. - * 2) exp-iter-approx-upper-bound: The term below is less than - * or equal to 3/2 * p <= 3/2 * 2**52. - */ - n = (mpd_ssize_t)ceil((1.43503*(double)p - 1.182) / (double)log10pbyr); - return n >= 3 ? n : 3; -} - -/* - * Internal function, specials have been dealt with. Apart from Overflow - * and Underflow, two cases must be considered for the error of the result: - * - * 1) abs(a) <= 9 * 10**(-prec-1) ==> result == 1 - * - * Absolute error: abs(1 - e**x) < 10**(-prec) - * ------------------------------------------- - * - * 2) abs(a) > 9 * 10**(-prec-1) - * - * Relative error: abs(result - e**x) < 0.5 * 10**(-prec) * e**x - * ------------------------------------------------------------- - * - * The algorithm is from Hull&Abrham, Variable Precision Exponential Function, - * ACM Transactions on Mathematical Software, Vol. 12, No. 2, June 1986. - * - * Main differences: - * - * - The number of iterations for the Horner scheme is calculated using - * 53-bit floating point arithmetic. - * - * - In the error analysis for ER (relative error accumulated in the - * evaluation of the truncated series) the reduced operand r may - * have any number of digits. - * ACL2 proof: exponent-relative-error - * - * - The analysis for early abortion has been adapted for the mpd_t - * ranges. - */ -static void -_mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_STATIC(tmp,0,0,0,0); - MPD_NEW_STATIC(sum,0,0,0,0); - MPD_NEW_CONST(word,0,0,1,1,1,1); - mpd_ssize_t j, n, t; - - assert(!mpd_isspecial(a)); - - if (mpd_iszerocoeff(a)) { - _settriple(result, MPD_POS, 1, 0); - return; - } - - /* - * We are calculating e^x = e^(r*10^t) = (e^r)^(10^t), where abs(r) < 1 and t >= 0. - * - * If t > 0, we have: - * - * (1) 0.1 <= r < 1, so e^0.1 <= e^r. If t > MAX_T, overflow occurs: - * - * MAX-EMAX+1 < log10(e^(0.1*10*t)) <= log10(e^(r*10^t)) < adjexp(e^(r*10^t))+1 - * - * (2) -1 < r <= -0.1, so e^r <= e^-0.1. If t > MAX_T, underflow occurs: - * - * adjexp(e^(r*10^t)) <= log10(e^(r*10^t)) <= log10(e^(-0.1*10^t)) < MIN-ETINY - */ -#if defined(CONFIG_64) - #define MPD_EXP_MAX_T 19 -#elif defined(CONFIG_32) - #define MPD_EXP_MAX_T 10 -#endif - t = a->digits + a->exp; - t = (t > 0) ? t : 0; - if (t > MPD_EXP_MAX_T) { - if (mpd_ispositive(a)) { - mpd_setspecial(result, MPD_POS, MPD_INF); - *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded; - } - else { - _settriple(result, MPD_POS, 0, mpd_etiny(ctx)); - *status |= (MPD_Inexact|MPD_Rounded|MPD_Subnormal| - MPD_Underflow|MPD_Clamped); - } - return; - } - - /* abs(a) <= 9 * 10**(-prec-1) */ - if (_mpd_qexp_check_one(result, a, ctx, status)) { - return; - } - - mpd_maxcontext(&workctx); - workctx.prec = ctx->prec + t + 2; - workctx.prec = (workctx.prec < 10) ? 10 : workctx.prec; - workctx.round = MPD_ROUND_HALF_EVEN; - - if (!mpd_qcopy(result, a, status)) { - return; - } - result->exp -= t; - - /* - * At this point: - * 1) 9 * 10**(-prec-1) < abs(a) - * 2) 9 * 10**(-prec-t-1) < abs(r) - * 3) log10(9) - prec - t - 1 < log10(abs(r)) < adjexp(abs(r)) + 1 - * 4) - prec - t - 2 < adjexp(abs(r)) <= -1 - */ - n = _mpd_get_exp_iterations(result, workctx.prec); - if (n == MPD_SSIZE_MAX) { - mpd_seterror(result, MPD_Invalid_operation, status); /* GCOV_UNLIKELY */ - return; /* GCOV_UNLIKELY */ - } - - _settriple(&sum, MPD_POS, 1, 0); - - for (j = n-1; j >= 1; j--) { - word.data[0] = j; - mpd_setdigits(&word); - mpd_qdiv(&tmp, result, &word, &workctx, &workctx.status); - mpd_qfma(&sum, &sum, &tmp, &one, &workctx, &workctx.status); - } - -#ifdef CONFIG_64 - _mpd_qpow_uint(result, &sum, mpd_pow10[t], MPD_POS, &workctx, status); -#else - if (t <= MPD_MAX_POW10) { - _mpd_qpow_uint(result, &sum, mpd_pow10[t], MPD_POS, &workctx, status); - } - else { - t -= MPD_MAX_POW10; - _mpd_qpow_uint(&tmp, &sum, mpd_pow10[MPD_MAX_POW10], MPD_POS, - &workctx, status); - _mpd_qpow_uint(result, &tmp, mpd_pow10[t], MPD_POS, &workctx, status); - } -#endif - - mpd_del(&tmp); - mpd_del(&sum); - *status |= (workctx.status&MPD_Errors); - *status |= (MPD_Inexact|MPD_Rounded); -} - -/* exp(a) */ -void -mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - if (mpd_isnegative(a)) { - _settriple(result, MPD_POS, 0, 0); - } - else { - mpd_setspecial(result, MPD_POS, MPD_INF); - } - return; - } - if (mpd_iszerocoeff(a)) { - _settriple(result, MPD_POS, 1, 0); - return; - } - - workctx = *ctx; - workctx.round = MPD_ROUND_HALF_EVEN; - - if (ctx->allcr) { - MPD_NEW_STATIC(t1, 0,0,0,0); - MPD_NEW_STATIC(t2, 0,0,0,0); - MPD_NEW_STATIC(ulp, 0,0,0,0); - MPD_NEW_STATIC(aa, 0,0,0,0); - mpd_ssize_t prec; - mpd_ssize_t ulpexp; - uint32_t workstatus; - - if (result == a) { - if (!mpd_qcopy(&aa, a, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - a = &aa; - } - - workctx.clamp = 0; - prec = ctx->prec + 3; - while (1) { - workctx.prec = prec; - workstatus = 0; - - _mpd_qexp(result, a, &workctx, &workstatus); - *status |= workstatus; - - ulpexp = result->exp + result->digits - workctx.prec; - if (workstatus & MPD_Underflow) { - /* The effective work precision is result->digits. */ - ulpexp = result->exp; - } - _ssettriple(&ulp, MPD_POS, 1, ulpexp); - - /* - * At this point [1]: - * 1) abs(result - e**x) < 0.5 * 10**(-prec) * e**x - * 2) result - ulp < e**x < result + ulp - * 3) result - ulp < result < result + ulp - * - * If round(result-ulp)==round(result+ulp), then - * round(result)==round(e**x). Therefore the result - * is correctly rounded. - * - * [1] If abs(a) <= 9 * 10**(-prec-1), use the absolute - * error for a similar argument. - */ - workctx.prec = ctx->prec; - mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status); - mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status); - if (mpd_isspecial(result) || mpd_iszerocoeff(result) || - mpd_qcmp(&t1, &t2, status) == 0) { - workctx.clamp = ctx->clamp; - _mpd_zeropad(result, &workctx, status); - mpd_check_underflow(result, &workctx, status); - mpd_qfinalize(result, &workctx, status); - break; - } - prec += MPD_RDIGITS; - } - mpd_del(&t1); - mpd_del(&t2); - mpd_del(&ulp); - mpd_del(&aa); - } - else { - _mpd_qexp(result, a, &workctx, status); - _mpd_zeropad(result, &workctx, status); - mpd_check_underflow(result, &workctx, status); - mpd_qfinalize(result, &workctx, status); - } -} - -/* Fused multiply-add: (a * b) + c, with a single final rounding. */ -void -mpd_qfma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_t *cc = NULL; - - if (result == c) { - if ((cc = mpd_qncopy(c)) == NULL) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - c = cc; - } - - _mpd_qmul(result, a, b, ctx, &workstatus); - if (!(workstatus&MPD_Invalid_operation)) { - mpd_qadd(result, result, c, ctx, &workstatus); - } - - if (cc) mpd_del(cc); - *status |= workstatus; -} - -/* - * Schedule the optimal precision increase for the Newton iteration. - * v := input operand - * z_0 := initial approximation - * initprec := natural number such that abs(log(v) - z_0) < 10**-initprec - * maxprec := target precision - * - * For convenience the output klist contains the elements in reverse order: - * klist := [k_n-1, ..., k_0], where - * 1) k_0 <= initprec and - * 2) abs(log(v) - result) < 10**(-2*k_n-1 + 1) <= 10**-maxprec. - */ -static inline int -ln_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2], mpd_ssize_t maxprec, - mpd_ssize_t initprec) -{ - mpd_ssize_t k; - int i; - - assert(maxprec >= 2 && initprec >= 2); - if (maxprec <= initprec) return -1; - - i = 0; k = maxprec; - do { - k = (k+2) / 2; - klist[i++] = k; - } while (k > initprec); - - return i-1; -} - -/* The constants have been verified with both decimal.py and mpfr. */ -#ifdef CONFIG_64 -#if MPD_RDIGITS != 19 - #error "mpdecimal.c: MPD_RDIGITS must be 19." -#endif -static const mpd_uint_t mpd_ln10_data[MPD_MINALLOC_MAX] = { - 6983716328982174407ULL, 9089704281976336583ULL, 1515961135648465461ULL, - 4416816335727555703ULL, 2900988039194170265ULL, 2307925037472986509ULL, - 107598438319191292ULL, 3466624107184669231ULL, 4450099781311469159ULL, - 9807828059751193854ULL, 7713456862091670584ULL, 1492198849978748873ULL, - 6528728696511086257ULL, 2385392051446341972ULL, 8692180205189339507ULL, - 6518769751037497088ULL, 2375253577097505395ULL, 9095610299291824318ULL, - 982748238504564801ULL, 5438635917781170543ULL, 7547331541421808427ULL, - 752371033310119785ULL, 3171643095059950878ULL, 9785265383207606726ULL, - 2932258279850258550ULL, 5497347726624257094ULL, 2976979522110718264ULL, - 9221477656763693866ULL, 1979650047149510504ULL, 6674183485704422507ULL, - 9702766860595249671ULL, 9278096762712757753ULL, 9314848524948644871ULL, - 6826928280848118428ULL, 754403708474699401ULL, 230105703089634572ULL, - 1929203337658714166ULL, 7589402567763113569ULL, 4208241314695689016ULL, - 2922455440575892572ULL, 9356734206705811364ULL, 2684916746550586856ULL, - 644507064800027750ULL, 9476834636167921018ULL, 5659121373450747856ULL, - 2835522011480466371ULL, 6470806855677432162ULL, 7141748003688084012ULL, - 9619404400222105101ULL, 5504893431493939147ULL, 6674744042432743651ULL, - 2287698219886746543ULL, 7773262884616336622ULL, 1985283935053089653ULL, - 4680843799894826233ULL, 8168948290720832555ULL, 8067566662873690987ULL, - 6248633409525465082ULL, 9829834196778404228ULL, 3524802359972050895ULL, - 3327900967572609677ULL, 110148862877297603ULL, 179914546843642076ULL, - 2302585092994045684ULL -}; -#else -#if MPD_RDIGITS != 9 - #error "mpdecimal.c: MPD_RDIGITS must be 9." -#endif -static const mpd_uint_t mpd_ln10_data[MPD_MINALLOC_MAX] = { - 401682692UL, 708474699UL, 720754403UL, 30896345UL, 602301057UL, 765871416UL, - 192920333UL, 763113569UL, 589402567UL, 956890167UL, 82413146UL, 589257242UL, - 245544057UL, 811364292UL, 734206705UL, 868569356UL, 167465505UL, 775026849UL, - 706480002UL, 18064450UL, 636167921UL, 569476834UL, 734507478UL, 156591213UL, - 148046637UL, 283552201UL, 677432162UL, 470806855UL, 880840126UL, 417480036UL, - 210510171UL, 940440022UL, 939147961UL, 893431493UL, 436515504UL, 440424327UL, - 654366747UL, 821988674UL, 622228769UL, 884616336UL, 537773262UL, 350530896UL, - 319852839UL, 989482623UL, 468084379UL, 720832555UL, 168948290UL, 736909878UL, - 675666628UL, 546508280UL, 863340952UL, 404228624UL, 834196778UL, 508959829UL, - 23599720UL, 967735248UL, 96757260UL, 603332790UL, 862877297UL, 760110148UL, - 468436420UL, 401799145UL, 299404568UL, 230258509UL -}; -#endif -/* _mpd_ln10 is used directly for precisions smaller than MINALLOC_MAX*RDIGITS. - Otherwise, it serves as the initial approximation for calculating ln(10). */ -static const mpd_t _mpd_ln10 = { - MPD_STATIC|MPD_CONST_DATA, -(MPD_MINALLOC_MAX*MPD_RDIGITS-1), - MPD_MINALLOC_MAX*MPD_RDIGITS, MPD_MINALLOC_MAX, MPD_MINALLOC_MAX, - (mpd_uint_t *)mpd_ln10_data -}; - -/* - * Set 'result' to log(10). - * Ulp error: abs(result - log(10)) < ulp(log(10)) - * Relative error: abs(result - log(10)) < 5 * 10**-prec * log(10) - * - * NOTE: The relative error is not derived from the ulp error, but - * calculated separately using the fact that 23/10 < log(10) < 24/10. - */ -void -mpd_qln10(mpd_t *result, mpd_ssize_t prec, uint32_t *status) -{ - mpd_context_t varcontext, maxcontext; - MPD_NEW_STATIC(tmp, 0,0,0,0); - MPD_NEW_CONST(static10, 0,0,2,1,1,10); - mpd_ssize_t klist[MPD_MAX_PREC_LOG2]; - mpd_uint_t rnd; - mpd_ssize_t shift; - int i; - - assert(prec >= 1); - - shift = MPD_MINALLOC_MAX*MPD_RDIGITS-prec; - shift = shift < 0 ? 0 : shift; - - rnd = mpd_qshiftr(result, &_mpd_ln10, shift, status); - if (rnd == MPD_UINT_MAX) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - result->exp = -(result->digits-1); - - mpd_maxcontext(&maxcontext); - if (prec < MPD_MINALLOC_MAX*MPD_RDIGITS) { - maxcontext.prec = prec; - _mpd_apply_round_excess(result, rnd, &maxcontext, status); - *status |= (MPD_Inexact|MPD_Rounded); - return; - } - - mpd_maxcontext(&varcontext); - varcontext.round = MPD_ROUND_TRUNC; - - i = ln_schedule_prec(klist, prec+2, -result->exp); - for (; i >= 0; i--) { - varcontext.prec = 2*klist[i]+3; - result->flags ^= MPD_NEG; - _mpd_qexp(&tmp, result, &varcontext, status); - result->flags ^= MPD_NEG; - mpd_qmul(&tmp, &static10, &tmp, &varcontext, status); - mpd_qsub(&tmp, &tmp, &one, &maxcontext, status); - mpd_qadd(result, result, &tmp, &maxcontext, status); - if (mpd_isspecial(result)) { - break; - } - } - - mpd_del(&tmp); - maxcontext.prec = prec; - mpd_qfinalize(result, &maxcontext, status); -} - -/* - * Initial approximations for the ln() iteration. The values have the - * following properties (established with both decimal.py and mpfr): - * - * Index 0 - 400, logarithms of x in [1.00, 5.00]: - * abs(lnapprox[i] * 10**-3 - log((i+100)/100)) < 10**-2 - * abs(lnapprox[i] * 10**-3 - log((i+1+100)/100)) < 10**-2 - * - * Index 401 - 899, logarithms of x in (0.500, 0.999]: - * abs(-lnapprox[i] * 10**-3 - log((i+100)/1000)) < 10**-2 - * abs(-lnapprox[i] * 10**-3 - log((i+1+100)/1000)) < 10**-2 - */ -static const uint16_t lnapprox[900] = { - /* index 0 - 400: log((i+100)/100) * 1000 */ - 0, 10, 20, 30, 39, 49, 58, 68, 77, 86, 95, 104, 113, 122, 131, 140, 148, 157, - 166, 174, 182, 191, 199, 207, 215, 223, 231, 239, 247, 255, 262, 270, 278, - 285, 293, 300, 308, 315, 322, 329, 336, 344, 351, 358, 365, 372, 378, 385, - 392, 399, 406, 412, 419, 425, 432, 438, 445, 451, 457, 464, 470, 476, 482, - 489, 495, 501, 507, 513, 519, 525, 531, 536, 542, 548, 554, 560, 565, 571, - 577, 582, 588, 593, 599, 604, 610, 615, 621, 626, 631, 637, 642, 647, 652, - 658, 663, 668, 673, 678, 683, 688, 693, 698, 703, 708, 713, 718, 723, 728, - 732, 737, 742, 747, 751, 756, 761, 766, 770, 775, 779, 784, 788, 793, 798, - 802, 806, 811, 815, 820, 824, 829, 833, 837, 842, 846, 850, 854, 859, 863, - 867, 871, 876, 880, 884, 888, 892, 896, 900, 904, 908, 912, 916, 920, 924, - 928, 932, 936, 940, 944, 948, 952, 956, 959, 963, 967, 971, 975, 978, 982, - 986, 990, 993, 997, 1001, 1004, 1008, 1012, 1015, 1019, 1022, 1026, 1030, - 1033, 1037, 1040, 1044, 1047, 1051, 1054, 1058, 1061, 1065, 1068, 1072, 1075, - 1078, 1082, 1085, 1089, 1092, 1095, 1099, 1102, 1105, 1109, 1112, 1115, 1118, - 1122, 1125, 1128, 1131, 1135, 1138, 1141, 1144, 1147, 1151, 1154, 1157, 1160, - 1163, 1166, 1169, 1172, 1176, 1179, 1182, 1185, 1188, 1191, 1194, 1197, 1200, - 1203, 1206, 1209, 1212, 1215, 1218, 1221, 1224, 1227, 1230, 1233, 1235, 1238, - 1241, 1244, 1247, 1250, 1253, 1256, 1258, 1261, 1264, 1267, 1270, 1273, 1275, - 1278, 1281, 1284, 1286, 1289, 1292, 1295, 1297, 1300, 1303, 1306, 1308, 1311, - 1314, 1316, 1319, 1322, 1324, 1327, 1330, 1332, 1335, 1338, 1340, 1343, 1345, - 1348, 1351, 1353, 1356, 1358, 1361, 1364, 1366, 1369, 1371, 1374, 1376, 1379, - 1381, 1384, 1386, 1389, 1391, 1394, 1396, 1399, 1401, 1404, 1406, 1409, 1411, - 1413, 1416, 1418, 1421, 1423, 1426, 1428, 1430, 1433, 1435, 1437, 1440, 1442, - 1445, 1447, 1449, 1452, 1454, 1456, 1459, 1461, 1463, 1466, 1468, 1470, 1472, - 1475, 1477, 1479, 1482, 1484, 1486, 1488, 1491, 1493, 1495, 1497, 1500, 1502, - 1504, 1506, 1509, 1511, 1513, 1515, 1517, 1520, 1522, 1524, 1526, 1528, 1530, - 1533, 1535, 1537, 1539, 1541, 1543, 1545, 1548, 1550, 1552, 1554, 1556, 1558, - 1560, 1562, 1564, 1567, 1569, 1571, 1573, 1575, 1577, 1579, 1581, 1583, 1585, - 1587, 1589, 1591, 1593, 1595, 1597, 1599, 1601, 1603, 1605, 1607, 1609, - /* index 401 - 899: -log((i+100)/1000) * 1000 */ - 691, 689, 687, 685, 683, 681, 679, 677, 675, 673, 671, 669, 668, 666, 664, - 662, 660, 658, 656, 654, 652, 650, 648, 646, 644, 642, 641, 639, 637, 635, - 633, 631, 629, 627, 626, 624, 622, 620, 618, 616, 614, 612, 611, 609, 607, - 605, 603, 602, 600, 598, 596, 594, 592, 591, 589, 587, 585, 583, 582, 580, - 578, 576, 574, 573, 571, 569, 567, 566, 564, 562, 560, 559, 557, 555, 553, - 552, 550, 548, 546, 545, 543, 541, 540, 538, 536, 534, 533, 531, 529, 528, - 526, 524, 523, 521, 519, 518, 516, 514, 512, 511, 509, 508, 506, 504, 502, - 501, 499, 498, 496, 494, 493, 491, 489, 488, 486, 484, 483, 481, 480, 478, - 476, 475, 473, 472, 470, 468, 467, 465, 464, 462, 460, 459, 457, 456, 454, - 453, 451, 449, 448, 446, 445, 443, 442, 440, 438, 437, 435, 434, 432, 431, - 429, 428, 426, 425, 423, 422, 420, 419, 417, 416, 414, 412, 411, 410, 408, - 406, 405, 404, 402, 400, 399, 398, 396, 394, 393, 392, 390, 389, 387, 386, - 384, 383, 381, 380, 378, 377, 375, 374, 372, 371, 370, 368, 367, 365, 364, - 362, 361, 360, 358, 357, 355, 354, 352, 351, 350, 348, 347, 345, 344, 342, - 341, 340, 338, 337, 336, 334, 333, 331, 330, 328, 327, 326, 324, 323, 322, - 320, 319, 318, 316, 315, 313, 312, 311, 309, 308, 306, 305, 304, 302, 301, - 300, 298, 297, 296, 294, 293, 292, 290, 289, 288, 286, 285, 284, 282, 281, - 280, 278, 277, 276, 274, 273, 272, 270, 269, 268, 267, 265, 264, 263, 261, - 260, 259, 258, 256, 255, 254, 252, 251, 250, 248, 247, 246, 245, 243, 242, - 241, 240, 238, 237, 236, 234, 233, 232, 231, 229, 228, 227, 226, 224, 223, - 222, 221, 219, 218, 217, 216, 214, 213, 212, 211, 210, 208, 207, 206, 205, - 203, 202, 201, 200, 198, 197, 196, 195, 194, 192, 191, 190, 189, 188, 186, - 185, 184, 183, 182, 180, 179, 178, 177, 176, 174, 173, 172, 171, 170, 168, - 167, 166, 165, 164, 162, 161, 160, 159, 158, 157, 156, 154, 153, 152, 151, - 150, 148, 147, 146, 145, 144, 143, 142, 140, 139, 138, 137, 136, 135, 134, - 132, 131, 130, 129, 128, 127, 126, 124, 123, 122, 121, 120, 119, 118, 116, - 115, 114, 113, 112, 111, 110, 109, 108, 106, 105, 104, 103, 102, 101, 100, - 99, 98, 97, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 84, 83, 82, 81, 80, 79, - 78, 77, 76, 75, 74, 73, 72, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, - 58, 57, 56, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, - 38, 37, 36, 35, 34, 33, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, - 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 -}; - -/* - * Internal ln() function that does not check for specials, zero or one. - * Relative error: abs(result - log(a)) < 0.1 * 10**-prec * abs(log(a)) - */ -static void -_mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t varcontext, maxcontext; - mpd_t *z = (mpd_t *) result; - MPD_NEW_STATIC(v,0,0,0,0); - MPD_NEW_STATIC(vtmp,0,0,0,0); - MPD_NEW_STATIC(tmp,0,0,0,0); - mpd_ssize_t klist[MPD_MAX_PREC_LOG2]; - mpd_ssize_t maxprec, shift, t; - mpd_ssize_t a_digits, a_exp; - mpd_uint_t dummy, x; - int i; - - assert(!mpd_isspecial(a) && !mpd_iszerocoeff(a)); - - /* - * We are calculating ln(a) = ln(v * 10^t) = ln(v) + t*ln(10), - * where 0.5 < v <= 5. - */ - if (!mpd_qcopy(&v, a, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - goto finish; - } - - /* Initial approximation: we have at least one non-zero digit */ - _mpd_get_msdigits(&dummy, &x, &v, 3); - if (x < 10) x *= 10; - if (x < 100) x *= 10; - x -= 100; - - /* a may equal z */ - a_digits = a->digits; - a_exp = a->exp; - - mpd_minalloc(z); - mpd_clear_flags(z); - z->data[0] = lnapprox[x]; - z->len = 1; - z->exp = -3; - mpd_setdigits(z); - - if (x <= 400) { - /* Reduce the input operand to 1.00 <= v <= 5.00. Let y = x + 100, - * so 100 <= y <= 500. Since y contains the most significant digits - * of v, y/100 <= v < (y+1)/100 and abs(z - log(v)) < 10**-2. */ - v.exp = -(a_digits - 1); - t = a_exp + a_digits - 1; - } - else { - /* Reduce the input operand to 0.500 < v <= 0.999. Let y = x + 100, - * so 500 < y <= 999. Since y contains the most significant digits - * of v, y/1000 <= v < (y+1)/1000 and abs(z - log(v)) < 10**-2. */ - v.exp = -a_digits; - t = a_exp + a_digits; - mpd_set_negative(z); - } - - mpd_maxcontext(&maxcontext); - mpd_maxcontext(&varcontext); - varcontext.round = MPD_ROUND_TRUNC; - - maxprec = ctx->prec + 2; - if (t == 0 && (x <= 15 || x >= 800)) { - /* 0.900 <= v <= 1.15: Estimate the magnitude of the logarithm. - * If ln(v) will underflow, skip the loop. Otherwise, adjust the - * precision upwards in order to obtain a sufficient number of - * significant digits. - * - * Case v > 1: - * abs((v-1)/10) < abs((v-1)/v) < abs(ln(v)) < abs(v-1) - * Case v < 1: - * abs(v-1) < abs(ln(v)) < abs((v-1)/v) < abs((v-1)*10) - */ - int cmp = _mpd_cmp(&v, &one); - - /* Upper bound (assume v > 1): abs(v-1), unrounded */ - _mpd_qsub(&tmp, &v, &one, &maxcontext, &maxcontext.status); - if (maxcontext.status & MPD_Errors) { - mpd_seterror(result, MPD_Malloc_error, status); - goto finish; - } - - if (cmp < 0) { - /* v < 1: abs((v-1)*10) */ - tmp.exp += 1; - } - if (mpd_adjexp(&tmp) < mpd_etiny(ctx)) { - /* The upper bound is less than etiny: Underflow to zero */ - _settriple(result, (cmp<0), 1, mpd_etiny(ctx)-1); - goto finish; - } - /* Lower bound: abs((v-1)/10) or abs(v-1) */ - tmp.exp -= 1; - if (mpd_adjexp(&tmp) < 0) { - /* Absolute error of the loop: abs(z - log(v)) < 10**-p. If - * p = ctx->prec+2-adjexp(lower), then the relative error of - * the result is (using 10**adjexp(x) <= abs(x)): - * - * abs(z - log(v)) / abs(log(v)) < 10**-p / abs(log(v)) - * <= 10**(-ctx->prec-2) - */ - maxprec = maxprec - mpd_adjexp(&tmp); - } - } - - i = ln_schedule_prec(klist, maxprec, 2); - for (; i >= 0; i--) { - varcontext.prec = 2*klist[i]+3; - z->flags ^= MPD_NEG; - _mpd_qexp(&tmp, z, &varcontext, status); - z->flags ^= MPD_NEG; - - if (v.digits > varcontext.prec) { - shift = v.digits - varcontext.prec; - mpd_qshiftr(&vtmp, &v, shift, status); - vtmp.exp += shift; - mpd_qmul(&tmp, &vtmp, &tmp, &varcontext, status); - } - else { - mpd_qmul(&tmp, &v, &tmp, &varcontext, status); - } - - mpd_qsub(&tmp, &tmp, &one, &maxcontext, status); - mpd_qadd(z, z, &tmp, &maxcontext, status); - if (mpd_isspecial(z)) { - break; - } - } - - /* - * Case t == 0: - * t * log(10) == 0, the result does not change and the analysis - * above applies. If v < 0.900 or v > 1.15, the relative error is - * less than 10**(-ctx.prec-1). - * Case t != 0: - * z := approx(log(v)) - * y := approx(log(10)) - * p := maxprec = ctx->prec + 2 - * Absolute errors: - * 1) abs(z - log(v)) < 10**-p - * 2) abs(y - log(10)) < 10**-p - * The multiplication is exact, so: - * 3) abs(t*y - t*log(10)) < t*10**-p - * The sum is exact, so: - * 4) abs((z + t*y) - (log(v) + t*log(10))) < (abs(t) + 1) * 10**-p - * Bounds for log(v) and log(10): - * 5) -7/10 < log(v) < 17/10 - * 6) 23/10 < log(10) < 24/10 - * Using 4), 5), 6) and t != 0, the relative error is: - * - * 7) relerr < ((abs(t) + 1)*10**-p) / abs(log(v) + t*log(10)) - * < 0.5 * 10**(-p + 1) = 0.5 * 10**(-ctx->prec-1) - */ - mpd_qln10(&v, maxprec+1, status); - mpd_qmul_ssize(&tmp, &v, t, &maxcontext, status); - mpd_qadd(result, &tmp, z, &maxcontext, status); - - -finish: - *status |= (MPD_Inexact|MPD_Rounded); - mpd_del(&v); - mpd_del(&vtmp); - mpd_del(&tmp); -} - -/* ln(a) */ -void -mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - mpd_ssize_t adjexp, t; - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - mpd_setspecial(result, MPD_POS, MPD_INF); - return; - } - if (mpd_iszerocoeff(a)) { - mpd_setspecial(result, MPD_NEG, MPD_INF); - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (_mpd_cmp(a, &one) == 0) { - _settriple(result, MPD_POS, 0, 0); - return; - } - /* - * Check if the result will overflow (0 < x, x != 1): - * 1) log10(x) < 0 iff adjexp(x) < 0 - * 2) 0 < x /\ x <= y ==> adjexp(x) <= adjexp(y) - * 3) 0 < x /\ x != 1 ==> 2 * abs(log10(x)) < abs(log(x)) - * 4) adjexp(x) <= log10(x) < adjexp(x) + 1 - * - * Case adjexp(x) >= 0: - * 5) 2 * adjexp(x) < abs(log(x)) - * Case adjexp(x) > 0: - * 6) adjexp(2 * adjexp(x)) <= adjexp(abs(log(x))) - * Case adjexp(x) == 0: - * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered) - * - * Case adjexp(x) < 0: - * 7) 2 * (-adjexp(x) - 1) < abs(log(x)) - * Case adjexp(x) < -1: - * 8) adjexp(2 * (-adjexp(x) - 1)) <= adjexp(abs(log(x))) - * Case adjexp(x) == -1: - * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered) - */ - adjexp = mpd_adjexp(a); - t = (adjexp < 0) ? -adjexp-1 : adjexp; - t *= 2; - if (mpd_exp_digits(t)-1 > ctx->emax) { - *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded; - mpd_setspecial(result, (adjexp<0), MPD_INF); - return; - } - - workctx = *ctx; - workctx.round = MPD_ROUND_HALF_EVEN; - - if (ctx->allcr) { - MPD_NEW_STATIC(t1, 0,0,0,0); - MPD_NEW_STATIC(t2, 0,0,0,0); - MPD_NEW_STATIC(ulp, 0,0,0,0); - MPD_NEW_STATIC(aa, 0,0,0,0); - mpd_ssize_t prec; - - if (result == a) { - if (!mpd_qcopy(&aa, a, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - a = &aa; - } - - workctx.clamp = 0; - prec = ctx->prec + 3; - while (1) { - workctx.prec = prec; - _mpd_qln(result, a, &workctx, status); - _ssettriple(&ulp, MPD_POS, 1, - result->exp + result->digits-workctx.prec); - - workctx.prec = ctx->prec; - mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status); - mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status); - if (mpd_isspecial(result) || mpd_iszerocoeff(result) || - mpd_qcmp(&t1, &t2, status) == 0) { - workctx.clamp = ctx->clamp; - mpd_check_underflow(result, &workctx, status); - mpd_qfinalize(result, &workctx, status); - break; - } - prec += MPD_RDIGITS; - } - mpd_del(&t1); - mpd_del(&t2); - mpd_del(&ulp); - mpd_del(&aa); - } - else { - _mpd_qln(result, a, &workctx, status); - mpd_check_underflow(result, &workctx, status); - mpd_qfinalize(result, &workctx, status); - } -} - -/* - * Internal log10() function that does not check for specials, zero or one. - * Case SKIP_FINALIZE: - * Relative error: abs(result - log10(a)) < 0.1 * 10**-prec * abs(log10(a)) - * Case DO_FINALIZE: - * Ulp error: abs(result - log10(a)) < ulp(log10(a)) - */ -enum {SKIP_FINALIZE, DO_FINALIZE}; -static void -_mpd_qlog10(int action, mpd_t *result, const mpd_t *a, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_STATIC(ln10,0,0,0,0); - - mpd_maxcontext(&workctx); - workctx.prec = ctx->prec + 3; - /* relative error: 0.1 * 10**(-p-3). The specific underflow shortcut - * in _mpd_qln() does not change the final result. */ - _mpd_qln(result, a, &workctx, status); - /* relative error: 5 * 10**(-p-3) */ - mpd_qln10(&ln10, workctx.prec, status); - - if (action == DO_FINALIZE) { - workctx = *ctx; - workctx.round = MPD_ROUND_HALF_EVEN; - } - /* SKIP_FINALIZE: relative error: 5 * 10**(-p-3) */ - _mpd_qdiv(NO_IDEAL_EXP, result, result, &ln10, &workctx, status); - - mpd_del(&ln10); -} - -/* log10(a) */ -void -mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - mpd_ssize_t adjexp, t; - - workctx = *ctx; - workctx.round = MPD_ROUND_HALF_EVEN; - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - mpd_setspecial(result, MPD_POS, MPD_INF); - return; - } - if (mpd_iszerocoeff(a)) { - mpd_setspecial(result, MPD_NEG, MPD_INF); - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mpd_coeff_ispow10(a)) { - uint8_t sign = 0; - adjexp = mpd_adjexp(a); - if (adjexp < 0) { - sign = 1; - adjexp = -adjexp; - } - _settriple(result, sign, adjexp, 0); - mpd_qfinalize(result, &workctx, status); - return; - } - /* - * Check if the result will overflow (0 < x, x != 1): - * 1) log10(x) < 0 iff adjexp(x) < 0 - * 2) 0 < x /\ x <= y ==> adjexp(x) <= adjexp(y) - * 3) adjexp(x) <= log10(x) < adjexp(x) + 1 - * - * Case adjexp(x) >= 0: - * 4) adjexp(x) <= abs(log10(x)) - * Case adjexp(x) > 0: - * 5) adjexp(adjexp(x)) <= adjexp(abs(log10(x))) - * Case adjexp(x) == 0: - * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered) - * - * Case adjexp(x) < 0: - * 6) -adjexp(x) - 1 < abs(log10(x)) - * Case adjexp(x) < -1: - * 7) adjexp(-adjexp(x) - 1) <= adjexp(abs(log(x))) - * Case adjexp(x) == -1: - * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered) - */ - adjexp = mpd_adjexp(a); - t = (adjexp < 0) ? -adjexp-1 : adjexp; - if (mpd_exp_digits(t)-1 > ctx->emax) { - *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded; - mpd_setspecial(result, (adjexp<0), MPD_INF); - return; - } - - if (ctx->allcr) { - MPD_NEW_STATIC(t1, 0,0,0,0); - MPD_NEW_STATIC(t2, 0,0,0,0); - MPD_NEW_STATIC(ulp, 0,0,0,0); - MPD_NEW_STATIC(aa, 0,0,0,0); - mpd_ssize_t prec; - - if (result == a) { - if (!mpd_qcopy(&aa, a, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - a = &aa; - } - - workctx.clamp = 0; - prec = ctx->prec + 3; - while (1) { - workctx.prec = prec; - _mpd_qlog10(SKIP_FINALIZE, result, a, &workctx, status); - _ssettriple(&ulp, MPD_POS, 1, - result->exp + result->digits-workctx.prec); - - workctx.prec = ctx->prec; - mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status); - mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status); - if (mpd_isspecial(result) || mpd_iszerocoeff(result) || - mpd_qcmp(&t1, &t2, status) == 0) { - workctx.clamp = ctx->clamp; - mpd_check_underflow(result, &workctx, status); - mpd_qfinalize(result, &workctx, status); - break; - } - prec += MPD_RDIGITS; - } - mpd_del(&t1); - mpd_del(&t2); - mpd_del(&ulp); - mpd_del(&aa); - } - else { - _mpd_qlog10(DO_FINALIZE, result, a, &workctx, status); - mpd_check_underflow(result, &workctx, status); - } -} - -/* - * Maximum of the two operands. Attention: If one operand is a quiet NaN and the - * other is numeric, the numeric operand is returned. This may not be what one - * expects. - */ -void -mpd_qmax(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_isqnan(a) && !mpd_isnan(b)) { - mpd_qcopy(result, b, status); - } - else if (mpd_isqnan(b) && !mpd_isnan(a)) { - mpd_qcopy(result, a, status); - } - else if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - else { - c = _mpd_cmp(a, b); - if (c == 0) { - c = _mpd_cmp_numequal(a, b); - } - - if (c < 0) { - mpd_qcopy(result, b, status); - } - else { - mpd_qcopy(result, a, status); - } - } - - mpd_qfinalize(result, ctx, status); -} - -/* - * Maximum magnitude: Same as mpd_max(), but compares the operands with their - * sign ignored. - */ -void -mpd_qmax_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_isqnan(a) && !mpd_isnan(b)) { - mpd_qcopy(result, b, status); - } - else if (mpd_isqnan(b) && !mpd_isnan(a)) { - mpd_qcopy(result, a, status); - } - else if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - else { - c = _mpd_cmp_abs(a, b); - if (c == 0) { - c = _mpd_cmp_numequal(a, b); - } - - if (c < 0) { - mpd_qcopy(result, b, status); - } - else { - mpd_qcopy(result, a, status); - } - } - - mpd_qfinalize(result, ctx, status); -} - -/* - * Minimum of the two operands. Attention: If one operand is a quiet NaN and the - * other is numeric, the numeric operand is returned. This may not be what one - * expects. - */ -void -mpd_qmin(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_isqnan(a) && !mpd_isnan(b)) { - mpd_qcopy(result, b, status); - } - else if (mpd_isqnan(b) && !mpd_isnan(a)) { - mpd_qcopy(result, a, status); - } - else if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - else { - c = _mpd_cmp(a, b); - if (c == 0) { - c = _mpd_cmp_numequal(a, b); - } - - if (c < 0) { - mpd_qcopy(result, a, status); - } - else { - mpd_qcopy(result, b, status); - } - } - - mpd_qfinalize(result, ctx, status); -} - -/* - * Minimum magnitude: Same as mpd_min(), but compares the operands with their - * sign ignored. - */ -void -mpd_qmin_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_isqnan(a) && !mpd_isnan(b)) { - mpd_qcopy(result, b, status); - } - else if (mpd_isqnan(b) && !mpd_isnan(a)) { - mpd_qcopy(result, a, status); - } - else if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - else { - c = _mpd_cmp_abs(a, b); - if (c == 0) { - c = _mpd_cmp_numequal(a, b); - } - - if (c < 0) { - mpd_qcopy(result, a, status); - } - else { - mpd_qcopy(result, b, status); - } - } - - mpd_qfinalize(result, ctx, status); -} - -/* Minimum space needed for the result array in _karatsuba_rec(). */ -static inline mpd_size_t -_kmul_resultsize(mpd_size_t la, mpd_size_t lb) -{ - mpd_size_t n, m; - - n = add_size_t(la, lb); - n = add_size_t(n, 1); - - m = (la+1)/2 + 1; - m = mul_size_t(m, 3); - - return (m > n) ? m : n; -} - -/* Work space needed in _karatsuba_rec(). lim >= 4 */ -static inline mpd_size_t -_kmul_worksize(mpd_size_t n, mpd_size_t lim) -{ - mpd_size_t m; - - if (n <= lim) { - return 0; - } - - m = (n+1)/2 + 1; - - return add_size_t(mul_size_t(m, 2), _kmul_worksize(m, lim)); -} - - -#define MPD_KARATSUBA_BASECASE 16 /* must be >= 4 */ - -/* - * Add the product of a and b to c. - * c must be _kmul_resultsize(la, lb) in size. - * w is used as a work array and must be _kmul_worksize(a, lim) in size. - * Roman E. Maeder, Storage Allocation for the Karatsuba Integer Multiplication - * Algorithm. In "Design and implementation of symbolic computation systems", - * Springer, 1993, ISBN 354057235X, 9783540572350. - */ -static void -_karatsuba_rec(mpd_uint_t *c, const mpd_uint_t *a, const mpd_uint_t *b, - mpd_uint_t *w, mpd_size_t la, mpd_size_t lb) -{ - mpd_size_t m, lt; - - assert(la >= lb && lb > 0); - assert(la <= MPD_KARATSUBA_BASECASE || w != NULL); - - if (la <= MPD_KARATSUBA_BASECASE) { - _mpd_basemul(c, a, b, la, lb); - return; - } - - m = (la+1)/2; /* ceil(la/2) */ - - /* lb <= m < la */ - if (lb <= m) { - - /* lb can now be larger than la-m */ - if (lb > la-m) { - lt = lb + lb + 1; /* space needed for result array */ - mpd_uint_zero(w, lt); /* clear result array */ - _karatsuba_rec(w, b, a+m, w+lt, lb, la-m); /* b*ah */ - } - else { - lt = (la-m) + (la-m) + 1; /* space needed for result array */ - mpd_uint_zero(w, lt); /* clear result array */ - _karatsuba_rec(w, a+m, b, w+lt, la-m, lb); /* ah*b */ - } - _mpd_baseaddto(c+m, w, (la-m)+lb); /* add ah*b*B**m */ - - lt = m + m + 1; /* space needed for the result array */ - mpd_uint_zero(w, lt); /* clear result array */ - _karatsuba_rec(w, a, b, w+lt, m, lb); /* al*b */ - _mpd_baseaddto(c, w, m+lb); /* add al*b */ - - return; - } - - /* la >= lb > m */ - memcpy(w, a, m * sizeof *w); - w[m] = 0; - _mpd_baseaddto(w, a+m, la-m); - - memcpy(w+(m+1), b, m * sizeof *w); - w[m+1+m] = 0; - _mpd_baseaddto(w+(m+1), b+m, lb-m); - - _karatsuba_rec(c+m, w, w+(m+1), w+2*(m+1), m+1, m+1); - - lt = (la-m) + (la-m) + 1; - mpd_uint_zero(w, lt); - - _karatsuba_rec(w, a+m, b+m, w+lt, la-m, lb-m); - - _mpd_baseaddto(c+2*m, w, (la-m) + (lb-m)); - _mpd_basesubfrom(c+m, w, (la-m) + (lb-m)); - - lt = m + m + 1; - mpd_uint_zero(w, lt); - - _karatsuba_rec(w, a, b, w+lt, m, m); - _mpd_baseaddto(c, w, m+m); - _mpd_basesubfrom(c+m, w, m+m); - - return; -} - -/* - * Multiply u and v, using Karatsuba multiplication. Returns a pointer - * to the result or NULL in case of failure (malloc error). - * Conditions: ulen >= vlen, ulen >= 4 - */ -static mpd_uint_t * -_mpd_kmul(const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t ulen, mpd_size_t vlen, - mpd_size_t *rsize) -{ - mpd_uint_t *result = NULL, *w = NULL; - mpd_size_t m; - - assert(ulen >= 4); - assert(ulen >= vlen); - - *rsize = _kmul_resultsize(ulen, vlen); - if ((result = mpd_calloc(*rsize, sizeof *result)) == NULL) { - return NULL; - } - - m = _kmul_worksize(ulen, MPD_KARATSUBA_BASECASE); - if (m && ((w = mpd_calloc(m, sizeof *w)) == NULL)) { - mpd_free(result); - return NULL; - } - - _karatsuba_rec(result, u, v, w, ulen, vlen); - - - if (w) mpd_free(w); - return result; -} - - -/* - * Determine the minimum length for the number theoretic transform. Valid - * transform lengths are 2**n or 3*2**n, where 2**n <= MPD_MAXTRANSFORM_2N. - * The function finds the shortest length m such that rsize <= m. - */ -static inline mpd_size_t -_mpd_get_transform_len(mpd_size_t rsize) -{ - mpd_size_t log2rsize; - mpd_size_t x, step; - - assert(rsize >= 4); - log2rsize = mpd_bsr(rsize); - - if (rsize <= 1024) { - /* 2**n is faster in this range. */ - x = ((mpd_size_t)1)<<log2rsize; - return (rsize == x) ? x : x<<1; - } - else if (rsize <= MPD_MAXTRANSFORM_2N) { - x = ((mpd_size_t)1)<<log2rsize; - if (rsize == x) return x; - step = x>>1; - x += step; - return (rsize <= x) ? x : x + step; - } - else if (rsize <= MPD_MAXTRANSFORM_2N+MPD_MAXTRANSFORM_2N/2) { - return MPD_MAXTRANSFORM_2N+MPD_MAXTRANSFORM_2N/2; - } - else if (rsize <= 3*MPD_MAXTRANSFORM_2N) { - return 3*MPD_MAXTRANSFORM_2N; - } - else { - return MPD_SIZE_MAX; - } -} - -#ifdef PPRO -#ifndef _MSC_VER -static inline unsigned short -_mpd_get_control87(void) -{ - unsigned short cw; - - __asm__ __volatile__ ("fnstcw %0" : "=m" (cw)); - return cw; -} - -static inline void -_mpd_set_control87(unsigned short cw) -{ - __asm__ __volatile__ ("fldcw %0" : : "m" (cw)); -} -#endif - -static unsigned int -mpd_set_fenv(void) -{ - unsigned int cw; -#ifdef _MSC_VER - unsigned int flags = - _EM_INVALID|_EM_DENORMAL|_EM_ZERODIVIDE|_EM_OVERFLOW| - _EM_UNDERFLOW|_EM_INEXACT|_RC_CHOP|_PC_64; - unsigned int mask = _MCW_EM|_MCW_RC|_MCW_PC; - unsigned int dummy; - - __control87_2(0, 0, &cw, NULL); - __control87_2(flags, mask, &dummy, NULL); -#else - cw = _mpd_get_control87(); - _mpd_set_control87(cw|0xF3F); -#endif - return cw; -} - -static void -mpd_restore_fenv(unsigned int cw) -{ -#ifdef _MSC_VER - unsigned int mask = _MCW_EM|_MCW_RC|_MCW_PC; - unsigned int dummy; - - __control87_2(cw, mask, &dummy, NULL); -#else - _mpd_set_control87((unsigned short)cw); -#endif -} -#endif /* PPRO */ - -/* - * Multiply u and v, using the fast number theoretic transform. Returns - * a pointer to the result or NULL in case of failure (malloc error). - */ -static mpd_uint_t * -_mpd_fntmul(const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t ulen, mpd_size_t vlen, - mpd_size_t *rsize) -{ - mpd_uint_t *c1 = NULL, *c2 = NULL, *c3 = NULL, *vtmp = NULL; - mpd_size_t n; - -#ifdef PPRO - unsigned int cw; - cw = mpd_set_fenv(); -#endif - - *rsize = add_size_t(ulen, vlen); - if ((n = _mpd_get_transform_len(*rsize)) == MPD_SIZE_MAX) { - goto malloc_error; - } - - if ((c1 = mpd_calloc(n, sizeof *c1)) == NULL) { - goto malloc_error; - } - if ((c2 = mpd_calloc(n, sizeof *c2)) == NULL) { - goto malloc_error; - } - if ((c3 = mpd_calloc(n, sizeof *c3)) == NULL) { - goto malloc_error; - } - - memcpy(c1, u, ulen * (sizeof *c1)); - memcpy(c2, u, ulen * (sizeof *c2)); - memcpy(c3, u, ulen * (sizeof *c3)); - - if (u == v) { - if (!fnt_autoconvolute(c1, n, P1) || - !fnt_autoconvolute(c2, n, P2) || - !fnt_autoconvolute(c3, n, P3)) { - goto malloc_error; - } - } - else { - if ((vtmp = mpd_calloc(n, sizeof *vtmp)) == NULL) { - goto malloc_error; - } - - memcpy(vtmp, v, vlen * (sizeof *vtmp)); - if (!fnt_convolute(c1, vtmp, n, P1)) { - mpd_free(vtmp); - goto malloc_error; - } - - memcpy(vtmp, v, vlen * (sizeof *vtmp)); - mpd_uint_zero(vtmp+vlen, n-vlen); - if (!fnt_convolute(c2, vtmp, n, P2)) { - mpd_free(vtmp); - goto malloc_error; - } - - memcpy(vtmp, v, vlen * (sizeof *vtmp)); - mpd_uint_zero(vtmp+vlen, n-vlen); - if (!fnt_convolute(c3, vtmp, n, P3)) { - mpd_free(vtmp); - goto malloc_error; - } - - mpd_free(vtmp); - } - - crt3(c1, c2, c3, *rsize); - -out: -#ifdef PPRO - mpd_restore_fenv(cw); -#endif - if (c2) mpd_free(c2); - if (c3) mpd_free(c3); - return c1; - -malloc_error: - if (c1) mpd_free(c1); - c1 = NULL; - goto out; -} - - -/* - * Karatsuba multiplication with FNT/basemul as the base case. - */ -static int -_karatsuba_rec_fnt(mpd_uint_t *c, const mpd_uint_t *a, const mpd_uint_t *b, - mpd_uint_t *w, mpd_size_t la, mpd_size_t lb) -{ - mpd_size_t m, lt; - - assert(la >= lb && lb > 0); - assert(la <= 3*(MPD_MAXTRANSFORM_2N/2) || w != NULL); - - if (la <= 3*(MPD_MAXTRANSFORM_2N/2)) { - - if (lb <= 192) { - _mpd_basemul(c, b, a, lb, la); - } - else { - mpd_uint_t *result; - mpd_size_t dummy; - - if ((result = _mpd_fntmul(a, b, la, lb, &dummy)) == NULL) { - return 0; - } - memcpy(c, result, (la+lb) * (sizeof *result)); - mpd_free(result); - } - return 1; - } - - m = (la+1)/2; /* ceil(la/2) */ - - /* lb <= m < la */ - if (lb <= m) { - - /* lb can now be larger than la-m */ - if (lb > la-m) { - lt = lb + lb + 1; /* space needed for result array */ - mpd_uint_zero(w, lt); /* clear result array */ - if (!_karatsuba_rec_fnt(w, b, a+m, w+lt, lb, la-m)) { /* b*ah */ - return 0; /* GCOV_UNLIKELY */ - } - } - else { - lt = (la-m) + (la-m) + 1; /* space needed for result array */ - mpd_uint_zero(w, lt); /* clear result array */ - if (!_karatsuba_rec_fnt(w, a+m, b, w+lt, la-m, lb)) { /* ah*b */ - return 0; /* GCOV_UNLIKELY */ - } - } - _mpd_baseaddto(c+m, w, (la-m)+lb); /* add ah*b*B**m */ - - lt = m + m + 1; /* space needed for the result array */ - mpd_uint_zero(w, lt); /* clear result array */ - if (!_karatsuba_rec_fnt(w, a, b, w+lt, m, lb)) { /* al*b */ - return 0; /* GCOV_UNLIKELY */ - } - _mpd_baseaddto(c, w, m+lb); /* add al*b */ - - return 1; - } - - /* la >= lb > m */ - memcpy(w, a, m * sizeof *w); - w[m] = 0; - _mpd_baseaddto(w, a+m, la-m); - - memcpy(w+(m+1), b, m * sizeof *w); - w[m+1+m] = 0; - _mpd_baseaddto(w+(m+1), b+m, lb-m); - - if (!_karatsuba_rec_fnt(c+m, w, w+(m+1), w+2*(m+1), m+1, m+1)) { - return 0; /* GCOV_UNLIKELY */ - } - - lt = (la-m) + (la-m) + 1; - mpd_uint_zero(w, lt); - - if (!_karatsuba_rec_fnt(w, a+m, b+m, w+lt, la-m, lb-m)) { - return 0; /* GCOV_UNLIKELY */ - } - - _mpd_baseaddto(c+2*m, w, (la-m) + (lb-m)); - _mpd_basesubfrom(c+m, w, (la-m) + (lb-m)); - - lt = m + m + 1; - mpd_uint_zero(w, lt); - - if (!_karatsuba_rec_fnt(w, a, b, w+lt, m, m)) { - return 0; /* GCOV_UNLIKELY */ - } - _mpd_baseaddto(c, w, m+m); - _mpd_basesubfrom(c+m, w, m+m); - - return 1; -} - -/* - * Multiply u and v, using Karatsuba multiplication with the FNT as the - * base case. Returns a pointer to the result or NULL in case of failure - * (malloc error). Conditions: ulen >= vlen, ulen >= 4. - */ -static mpd_uint_t * -_mpd_kmul_fnt(const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t ulen, mpd_size_t vlen, - mpd_size_t *rsize) -{ - mpd_uint_t *result = NULL, *w = NULL; - mpd_size_t m; - - assert(ulen >= 4); - assert(ulen >= vlen); - - *rsize = _kmul_resultsize(ulen, vlen); - if ((result = mpd_calloc(*rsize, sizeof *result)) == NULL) { - return NULL; - } - - m = _kmul_worksize(ulen, 3*(MPD_MAXTRANSFORM_2N/2)); - if (m && ((w = mpd_calloc(m, sizeof *w)) == NULL)) { - mpd_free(result); /* GCOV_UNLIKELY */ - return NULL; /* GCOV_UNLIKELY */ - } - - if (!_karatsuba_rec_fnt(result, u, v, w, ulen, vlen)) { - mpd_free(result); - result = NULL; - } - - - if (w) mpd_free(w); - return result; -} - - -/* Deal with the special cases of multiplying infinities. */ -static void -_mpd_qmul_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status) -{ - if (mpd_isinfinite(a)) { - if (mpd_iszero(b)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } - else { - mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF); - } - return; - } - assert(mpd_isinfinite(b)); - if (mpd_iszero(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } - else { - mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF); - } -} - -/* - * Internal function: Multiply a and b. _mpd_qmul deals with specials but - * does NOT finalize the result. This is for use in mpd_fma(). - */ -static inline void -_mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - const mpd_t *big = a, *small = b; - mpd_uint_t *rdata = NULL; - mpd_uint_t rbuf[MPD_MINALLOC_MAX]; - mpd_size_t rsize, i; - - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - _mpd_qmul_inf(result, a, b, status); - return; - } - - if (small->len > big->len) { - _mpd_ptrswap(&big, &small); - } - - rsize = big->len + small->len; - - if (big->len == 1) { - _mpd_singlemul(result->data, big->data[0], small->data[0]); - goto finish; - } - if (rsize <= (mpd_size_t)MPD_MINALLOC_MAX) { - if (big->len == 2) { - _mpd_mul_2_le2(rbuf, big->data, small->data, small->len); - } - else { - mpd_uint_zero(rbuf, rsize); - if (small->len == 1) { - _mpd_shortmul(rbuf, big->data, big->len, small->data[0]); - } - else { - _mpd_basemul(rbuf, small->data, big->data, small->len, big->len); - } - } - if (!mpd_qresize(result, rsize, status)) { - return; - } - for(i = 0; i < rsize; i++) { - result->data[i] = rbuf[i]; - } - goto finish; - } - - - if (small->len <= 256) { - rdata = mpd_calloc(rsize, sizeof *rdata); - if (rdata != NULL) { - if (small->len == 1) { - _mpd_shortmul(rdata, big->data, big->len, small->data[0]); - } - else { - _mpd_basemul(rdata, small->data, big->data, small->len, big->len); - } - } - } - else if (rsize <= 1024) { - rdata = _mpd_kmul(big->data, small->data, big->len, small->len, &rsize); - } - else if (rsize <= 3*MPD_MAXTRANSFORM_2N) { - rdata = _mpd_fntmul(big->data, small->data, big->len, small->len, &rsize); - } - else { - rdata = _mpd_kmul_fnt(big->data, small->data, big->len, small->len, &rsize); - } - - if (rdata == NULL) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - - if (mpd_isdynamic_data(result)) { - mpd_free(result->data); - } - result->data = rdata; - result->alloc = rsize; - mpd_set_dynamic_data(result); - - -finish: - mpd_set_flags(result, mpd_sign(a)^mpd_sign(b)); - result->exp = big->exp + small->exp; - result->len = _mpd_real_size(result->data, rsize); - /* resize to smaller cannot fail */ - mpd_qresize(result, result->len, status); - mpd_setdigits(result); -} - -/* Multiply a and b. */ -void -mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - _mpd_qmul(result, a, b, ctx, status); - mpd_qfinalize(result, ctx, status); -} - -/* Multiply a and b. Set NaN/Invalid_operation if the result is inexact. */ -static void -_mpd_qmul_exact(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - - mpd_qmul(result, a, b, ctx, &workstatus); - *status |= workstatus; - if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } -} - -/* Multiply decimal and mpd_ssize_t. */ -void -mpd_qmul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_ssize(&bb, b, &maxcontext, status); - mpd_qmul(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Multiply decimal and mpd_uint_t. */ -void -mpd_qmul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_uint(&bb, b, &maxcontext, status); - mpd_qmul(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -void -mpd_qmul_i32(mpd_t *result, const mpd_t *a, int32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qmul_ssize(result, a, b, ctx, status); -} - -void -mpd_qmul_u32(mpd_t *result, const mpd_t *a, uint32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qmul_uint(result, a, b, ctx, status); -} - -#ifdef CONFIG_64 -void -mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qmul_ssize(result, a, b, ctx, status); -} - -void -mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qmul_uint(result, a, b, ctx, status); -} -#elif !defined(LEGACY_COMPILER) -/* Multiply decimal and int64_t. */ -void -mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_i64(&bb, b, &maxcontext, status); - mpd_qmul(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Multiply decimal and uint64_t. */ -void -mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_u64(&bb, b, &maxcontext, status); - mpd_qmul(result, a, &bb, ctx, status); - mpd_del(&bb); -} -#endif - -/* Like the minus operator. */ -void -mpd_qminus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - } - - if (mpd_iszero(a) && ctx->round != MPD_ROUND_FLOOR) { - mpd_qcopy_abs(result, a, status); - } - else { - mpd_qcopy_negate(result, a, status); - } - - mpd_qfinalize(result, ctx, status); -} - -/* Like the plus operator. */ -void -mpd_qplus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - } - - if (mpd_iszero(a) && ctx->round != MPD_ROUND_FLOOR) { - mpd_qcopy_abs(result, a, status); - } - else { - mpd_qcopy(result, a, status); - } - - mpd_qfinalize(result, ctx, status); -} - -/* The largest representable number that is smaller than the operand. */ -void -mpd_qnext_minus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_CONST(tiny,MPD_POS,mpd_etiny(ctx)-1,1,1,1,1); - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - - assert(mpd_isinfinite(a)); - if (mpd_isnegative(a)) { - mpd_qcopy(result, a, status); - return; - } - else { - mpd_clear_flags(result); - mpd_qmaxcoeff(result, ctx, status); - if (mpd_isnan(result)) { - return; - } - result->exp = mpd_etop(ctx); - return; - } - } - - mpd_workcontext(&workctx, ctx); - workctx.round = MPD_ROUND_FLOOR; - - if (!mpd_qcopy(result, a, status)) { - return; - } - - mpd_qfinalize(result, &workctx, &workctx.status); - if (workctx.status&(MPD_Inexact|MPD_Errors)) { - *status |= (workctx.status&MPD_Errors); - return; - } - - workctx.status = 0; - mpd_qsub(result, a, &tiny, &workctx, &workctx.status); - *status |= (workctx.status&MPD_Errors); -} - -/* The smallest representable number that is larger than the operand. */ -void -mpd_qnext_plus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_CONST(tiny,MPD_POS,mpd_etiny(ctx)-1,1,1,1,1); - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - - assert(mpd_isinfinite(a)); - if (mpd_ispositive(a)) { - mpd_qcopy(result, a, status); - } - else { - mpd_clear_flags(result); - mpd_qmaxcoeff(result, ctx, status); - if (mpd_isnan(result)) { - return; - } - mpd_set_flags(result, MPD_NEG); - result->exp = mpd_etop(ctx); - } - return; - } - - mpd_workcontext(&workctx, ctx); - workctx.round = MPD_ROUND_CEILING; - - if (!mpd_qcopy(result, a, status)) { - return; - } - - mpd_qfinalize(result, &workctx, &workctx.status); - if (workctx.status & (MPD_Inexact|MPD_Errors)) { - *status |= (workctx.status&MPD_Errors); - return; - } - - workctx.status = 0; - mpd_qadd(result, a, &tiny, &workctx, &workctx.status); - *status |= (workctx.status&MPD_Errors); -} - -/* - * The number closest to the first operand that is in the direction towards - * the second operand. - */ -void -mpd_qnext_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - - c = _mpd_cmp(a, b); - if (c == 0) { - mpd_qcopy_sign(result, a, b, status); - return; - } - - if (c < 0) { - mpd_qnext_plus(result, a, ctx, status); - } - else { - mpd_qnext_minus(result, a, ctx, status); - } - - if (mpd_isinfinite(result)) { - *status |= (MPD_Overflow|MPD_Rounded|MPD_Inexact); - } - else if (mpd_adjexp(result) < ctx->emin) { - *status |= (MPD_Underflow|MPD_Subnormal|MPD_Rounded|MPD_Inexact); - if (mpd_iszero(result)) { - *status |= MPD_Clamped; - } - } -} - -/* - * Internal function: Integer power with mpd_uint_t exponent. The function - * can fail with MPD_Malloc_error. - * - * The error is equal to the error incurred in k-1 multiplications. Assuming - * the upper bound for the relative error in each operation: - * - * abs(err) = 5 * 10**-prec - * result = x**k * (1 + err)**(k-1) - */ -static inline void -_mpd_qpow_uint(mpd_t *result, const mpd_t *base, mpd_uint_t exp, - uint8_t resultsign, const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_uint_t n; - - if (exp == 0) { - _settriple(result, resultsign, 1, 0); /* GCOV_NOT_REACHED */ - return; /* GCOV_NOT_REACHED */ - } - - if (!mpd_qcopy(result, base, status)) { - return; - } - - n = mpd_bits[mpd_bsr(exp)]; - while (n >>= 1) { - mpd_qmul(result, result, result, ctx, &workstatus); - if (exp & n) { - mpd_qmul(result, result, base, ctx, &workstatus); - } - if (mpd_isspecial(result) || - (mpd_iszerocoeff(result) && (workstatus & MPD_Clamped))) { - break; - } - } - - *status |= workstatus; - mpd_set_sign(result, resultsign); -} - -/* - * Internal function: Integer power with mpd_t exponent, tbase and texp - * are modified!! Function can fail with MPD_Malloc_error. - * - * The error is equal to the error incurred in k multiplications. Assuming - * the upper bound for the relative error in each operation: - * - * abs(err) = 5 * 10**-prec - * result = x**k * (1 + err)**k - */ -static inline void -_mpd_qpow_mpd(mpd_t *result, mpd_t *tbase, mpd_t *texp, uint8_t resultsign, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_context_t maxctx; - MPD_NEW_CONST(two,0,0,1,1,1,2); - - - mpd_maxcontext(&maxctx); - - /* resize to smaller cannot fail */ - mpd_qcopy(result, &one, status); - - while (!mpd_iszero(texp)) { - if (mpd_isodd(texp)) { - mpd_qmul(result, result, tbase, ctx, &workstatus); - *status |= workstatus; - if (mpd_isspecial(result) || - (mpd_iszerocoeff(result) && (workstatus & MPD_Clamped))) { - break; - } - } - mpd_qmul(tbase, tbase, tbase, ctx, &workstatus); - mpd_qdivint(texp, texp, &two, &maxctx, &workstatus); - if (mpd_isnan(tbase) || mpd_isnan(texp)) { - mpd_seterror(result, workstatus&MPD_Errors, status); - return; - } - } - mpd_set_sign(result, resultsign); -} - -/* - * The power function for integer exponents. Relative error _before_ the - * final rounding to prec: - * abs(result - base**exp) < 0.1 * 10**-prec * abs(base**exp) - */ -static void -_mpd_qpow_int(mpd_t *result, const mpd_t *base, const mpd_t *exp, - uint8_t resultsign, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_STATIC(tbase,0,0,0,0); - MPD_NEW_STATIC(texp,0,0,0,0); - mpd_ssize_t n; - - - mpd_workcontext(&workctx, ctx); - workctx.prec += (exp->digits + exp->exp + 2); - workctx.round = MPD_ROUND_HALF_EVEN; - workctx.clamp = 0; - if (mpd_isnegative(exp)) { - workctx.prec += 1; - mpd_qdiv(&tbase, &one, base, &workctx, status); - if (*status&MPD_Errors) { - mpd_setspecial(result, MPD_POS, MPD_NAN); - goto finish; - } - } - else { - if (!mpd_qcopy(&tbase, base, status)) { - mpd_setspecial(result, MPD_POS, MPD_NAN); - goto finish; - } - } - - n = mpd_qabs_uint(exp, &workctx.status); - if (workctx.status&MPD_Invalid_operation) { - if (!mpd_qcopy(&texp, exp, status)) { - mpd_setspecial(result, MPD_POS, MPD_NAN); /* GCOV_UNLIKELY */ - goto finish; /* GCOV_UNLIKELY */ - } - _mpd_qpow_mpd(result, &tbase, &texp, resultsign, &workctx, status); - } - else { - _mpd_qpow_uint(result, &tbase, n, resultsign, &workctx, status); - } - - if (mpd_isinfinite(result)) { - /* for ROUND_DOWN, ROUND_FLOOR, etc. */ - _settriple(result, resultsign, 1, MPD_EXP_INF); - } - -finish: - mpd_del(&tbase); - mpd_del(&texp); - mpd_qfinalize(result, ctx, status); -} - -/* - * If the exponent is infinite and base equals one, the result is one - * with a coefficient of length prec. Otherwise, result is undefined. - * Return the value of the comparison against one. - */ -static int -_qcheck_pow_one_inf(mpd_t *result, const mpd_t *base, uint8_t resultsign, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_ssize_t shift; - int cmp; - - if ((cmp = _mpd_cmp(base, &one)) == 0) { - shift = ctx->prec-1; - mpd_qshiftl(result, &one, shift, status); - result->exp = -shift; - mpd_set_flags(result, resultsign); - *status |= (MPD_Inexact|MPD_Rounded); - } - - return cmp; -} - -/* - * If abs(base) equals one, calculate the correct power of one result. - * Otherwise, result is undefined. Return the value of the comparison - * against 1. - * - * This is an internal function that does not check for specials. - */ -static int -_qcheck_pow_one(mpd_t *result, const mpd_t *base, const mpd_t *exp, - uint8_t resultsign, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_ssize_t shift; - int cmp; - - if ((cmp = _mpd_cmp_abs(base, &one)) == 0) { - if (_mpd_isint(exp)) { - if (mpd_isnegative(exp)) { - _settriple(result, resultsign, 1, 0); - return 0; - } - /* 1.000**3 = 1.000000000 */ - mpd_qmul_ssize(result, exp, -base->exp, ctx, &workstatus); - if (workstatus&MPD_Errors) { - *status |= (workstatus&MPD_Errors); - return 0; - } - /* digits-1 after exponentiation */ - shift = mpd_qget_ssize(result, &workstatus); - /* shift is MPD_SSIZE_MAX if result is too large */ - if (shift > ctx->prec-1) { - shift = ctx->prec-1; - *status |= MPD_Rounded; - } - } - else if (mpd_ispositive(base)) { - shift = ctx->prec-1; - *status |= (MPD_Inexact|MPD_Rounded); - } - else { - return -2; /* GCOV_NOT_REACHED */ - } - if (!mpd_qshiftl(result, &one, shift, status)) { - return 0; - } - result->exp = -shift; - mpd_set_flags(result, resultsign); - } - - return cmp; -} - -/* - * Detect certain over/underflow of x**y. - * ACL2 proof: pow-bounds.lisp. - * - * Symbols: - * - * e: EXP_INF or EXP_CLAMP - * x: base - * y: exponent - * - * omega(e) = log10(abs(e)) - * zeta(x) = log10(abs(log10(x))) - * theta(y) = log10(abs(y)) - * - * Upper and lower bounds: - * - * ub_omega(e) = ceil(log10(abs(e))) - * lb_theta(y) = floor(log10(abs(y))) - * - * | floor(log10(floor(abs(log10(x))))) if x < 1/10 or x >= 10 - * lb_zeta(x) = | floor(log10(abs(x-1)/10)) if 1/10 <= x < 1 - * | floor(log10(abs((x-1)/100))) if 1 < x < 10 - * - * ub_omega(e) and lb_theta(y) are obviously upper and lower bounds - * for omega(e) and theta(y). - * - * lb_zeta is a lower bound for zeta(x): - * - * x < 1/10 or x >= 10: - * - * abs(log10(x)) >= 1, so the outer log10 is well defined. Since log10 - * is strictly increasing, the end result is a lower bound. - * - * 1/10 <= x < 1: - * - * We use: log10(x) <= (x-1)/log(10) - * abs(log10(x)) >= abs(x-1)/log(10) - * abs(log10(x)) >= abs(x-1)/10 - * - * 1 < x < 10: - * - * We use: (x-1)/(x*log(10)) < log10(x) - * abs((x-1)/100) < abs(log10(x)) - * - * XXX: abs((x-1)/10) would work, need ACL2 proof. - * - * - * Let (0 < x < 1 and y < 0) or (x > 1 and y > 0). (H1) - * Let ub_omega(exp_inf) < lb_zeta(x) + lb_theta(y) (H2) - * - * Then: - * log10(abs(exp_inf)) < log10(abs(log10(x))) + log10(abs(y)). (1) - * exp_inf < log10(x) * y (2) - * 10**exp_inf < x**y (3) - * - * Let (0 < x < 1 and y > 0) or (x > 1 and y < 0). (H3) - * Let ub_omega(exp_clamp) < lb_zeta(x) + lb_theta(y) (H4) - * - * Then: - * log10(abs(exp_clamp)) < log10(abs(log10(x))) + log10(abs(y)). (4) - * log10(x) * y < exp_clamp (5) - * x**y < 10**exp_clamp (6) - * - */ -static mpd_ssize_t -_lower_bound_zeta(const mpd_t *x, uint32_t *status) -{ - mpd_context_t maxctx; - MPD_NEW_STATIC(scratch,0,0,0,0); - mpd_ssize_t t, u; - - t = mpd_adjexp(x); - if (t > 0) { - /* x >= 10 -> floor(log10(floor(abs(log10(x))))) */ - return mpd_exp_digits(t) - 1; - } - else if (t < -1) { - /* x < 1/10 -> floor(log10(floor(abs(log10(x))))) */ - return mpd_exp_digits(t+1) - 1; - } - else { - mpd_maxcontext(&maxctx); - mpd_qsub(&scratch, x, &one, &maxctx, status); - if (mpd_isspecial(&scratch)) { - mpd_del(&scratch); - return MPD_SSIZE_MAX; - } - u = mpd_adjexp(&scratch); - mpd_del(&scratch); - - /* t == -1, 1/10 <= x < 1 -> floor(log10(abs(x-1)/10)) - * t == 0, 1 < x < 10 -> floor(log10(abs(x-1)/100)) */ - return (t == 0) ? u-2 : u-1; - } -} - -/* - * Detect cases of certain overflow/underflow in the power function. - * Assumptions: x != 1, y != 0. The proof above is for positive x. - * If x is negative and y is an odd integer, x**y == -(abs(x)**y), - * so the analysis does not change. - */ -static int -_qcheck_pow_bounds(mpd_t *result, const mpd_t *x, const mpd_t *y, - uint8_t resultsign, - const mpd_context_t *ctx, uint32_t *status) -{ - MPD_NEW_SHARED(abs_x, x); - mpd_ssize_t ub_omega, lb_zeta, lb_theta; - uint8_t sign; - - mpd_set_positive(&abs_x); - - lb_theta = mpd_adjexp(y); - lb_zeta = _lower_bound_zeta(&abs_x, status); - if (lb_zeta == MPD_SSIZE_MAX) { - mpd_seterror(result, MPD_Malloc_error, status); - return 1; - } - - sign = (mpd_adjexp(&abs_x) < 0) ^ mpd_sign(y); - if (sign == 0) { - /* (0 < |x| < 1 and y < 0) or (|x| > 1 and y > 0) */ - ub_omega = mpd_exp_digits(ctx->emax); - if (ub_omega < lb_zeta + lb_theta) { - _settriple(result, resultsign, 1, MPD_EXP_INF); - mpd_qfinalize(result, ctx, status); - return 1; - } - } - else { - /* (0 < |x| < 1 and y > 0) or (|x| > 1 and y < 0). */ - ub_omega = mpd_exp_digits(mpd_etiny(ctx)); - if (ub_omega < lb_zeta + lb_theta) { - _settriple(result, resultsign, 1, mpd_etiny(ctx)-1); - mpd_qfinalize(result, ctx, status); - return 1; - } - } - - return 0; -} - -/* - * TODO: Implement algorithm for computing exact powers from decimal.py. - * In order to prevent infinite loops, this has to be called before - * using Ziv's strategy for correct rounding. - */ -/* -static int -_mpd_qpow_exact(mpd_t *result, const mpd_t *base, const mpd_t *exp, - const mpd_context_t *ctx, uint32_t *status) -{ - return 0; -} -*/ - -/* - * The power function for real exponents. - * Relative error: abs(result - e**y) < e**y * 1/5 * 10**(-prec - 1) - */ -static void -_mpd_qpow_real(mpd_t *result, const mpd_t *base, const mpd_t *exp, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_STATIC(texp,0,0,0,0); - - if (!mpd_qcopy(&texp, exp, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - - mpd_maxcontext(&workctx); - workctx.prec = (base->digits > ctx->prec) ? base->digits : ctx->prec; - workctx.prec += (4 + MPD_EXPDIGITS); - workctx.round = MPD_ROUND_HALF_EVEN; - workctx.allcr = ctx->allcr; - - /* - * extra := MPD_EXPDIGITS = MPD_EXP_MAX_T - * wp := prec + 4 + extra - * abs(err) < 5 * 10**-wp - * y := log(base) * exp - * Calculate: - * 1) e**(y * (1 + err)**2) * (1 + err) - * = e**y * e**(y * (2*err + err**2)) * (1 + err) - * ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - * Relative error of the underlined term: - * 2) abs(e**(y * (2*err + err**2)) - 1) - * Case abs(y) >= 10**extra: - * 3) adjexp(y)+1 > log10(abs(y)) >= extra - * This triggers the Overflow/Underflow shortcut in _mpd_qexp(), - * so no further analysis is necessary. - * Case abs(y) < 10**extra: - * 4) abs(y * (2*err + err**2)) < 1/5 * 10**(-prec - 2) - * Use (see _mpd_qexp): - * 5) abs(x) <= 9/10 * 10**-p ==> abs(e**x - 1) < 10**-p - * With 2), 4) and 5): - * 6) abs(e**(y * (2*err + err**2)) - 1) < 10**(-prec - 2) - * The complete relative error of 1) is: - * 7) abs(result - e**y) < e**y * 1/5 * 10**(-prec - 1) - */ - mpd_qln(result, base, &workctx, &workctx.status); - mpd_qmul(result, result, &texp, &workctx, &workctx.status); - mpd_qexp(result, result, &workctx, status); - - mpd_del(&texp); - *status |= (workctx.status&MPD_Errors); - *status |= (MPD_Inexact|MPD_Rounded); -} - -/* The power function: base**exp */ -void -mpd_qpow(mpd_t *result, const mpd_t *base, const mpd_t *exp, - const mpd_context_t *ctx, uint32_t *status) -{ - uint8_t resultsign = 0; - int intexp = 0; - int cmp; - - if (mpd_isspecial(base) || mpd_isspecial(exp)) { - if (mpd_qcheck_nans(result, base, exp, ctx, status)) { - return; - } - } - if (mpd_isinteger(exp)) { - intexp = 1; - resultsign = mpd_isnegative(base) && mpd_isodd(exp); - } - - if (mpd_iszero(base)) { - if (mpd_iszero(exp)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } - else if (mpd_isnegative(exp)) { - mpd_setspecial(result, resultsign, MPD_INF); - } - else { - _settriple(result, resultsign, 0, 0); - } - return; - } - if (mpd_isnegative(base)) { - if (!intexp || mpd_isinfinite(exp)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - } - if (mpd_isinfinite(exp)) { - /* power of one */ - cmp = _qcheck_pow_one_inf(result, base, resultsign, ctx, status); - if (cmp == 0) { - return; - } - else { - cmp *= mpd_arith_sign(exp); - if (cmp < 0) { - _settriple(result, resultsign, 0, 0); - } - else { - mpd_setspecial(result, resultsign, MPD_INF); - } - } - return; - } - if (mpd_isinfinite(base)) { - if (mpd_iszero(exp)) { - _settriple(result, resultsign, 1, 0); - } - else if (mpd_isnegative(exp)) { - _settriple(result, resultsign, 0, 0); - } - else { - mpd_setspecial(result, resultsign, MPD_INF); - } - return; - } - if (mpd_iszero(exp)) { - _settriple(result, resultsign, 1, 0); - return; - } - if (_qcheck_pow_one(result, base, exp, resultsign, ctx, status) == 0) { - return; - } - if (_qcheck_pow_bounds(result, base, exp, resultsign, ctx, status)) { - return; - } - - if (intexp) { - _mpd_qpow_int(result, base, exp, resultsign, ctx, status); - } - else { - _mpd_qpow_real(result, base, exp, ctx, status); - if (!mpd_isspecial(result) && _mpd_cmp(result, &one) == 0) { - mpd_ssize_t shift = ctx->prec-1; - mpd_qshiftl(result, &one, shift, status); - result->exp = -shift; - } - if (mpd_isinfinite(result)) { - /* for ROUND_DOWN, ROUND_FLOOR, etc. */ - _settriple(result, MPD_POS, 1, MPD_EXP_INF); - } - mpd_qfinalize(result, ctx, status); - } -} - -/* - * Internal function: Integer powmod with mpd_uint_t exponent, base is modified! - * Function can fail with MPD_Malloc_error. - */ -static inline void -_mpd_qpowmod_uint(mpd_t *result, mpd_t *base, mpd_uint_t exp, - const mpd_t *mod, uint32_t *status) -{ - mpd_context_t maxcontext; - - mpd_maxcontext(&maxcontext); - - /* resize to smaller cannot fail */ - mpd_qcopy(result, &one, status); - - while (exp > 0) { - if (exp & 1) { - _mpd_qmul_exact(result, result, base, &maxcontext, status); - mpd_qrem(result, result, mod, &maxcontext, status); - } - _mpd_qmul_exact(base, base, base, &maxcontext, status); - mpd_qrem(base, base, mod, &maxcontext, status); - exp >>= 1; - } -} - -/* The powmod function: (base**exp) % mod */ -void -mpd_qpowmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, - const mpd_t *mod, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(tbase,0,0,0,0); - MPD_NEW_STATIC(texp,0,0,0,0); - MPD_NEW_STATIC(tmod,0,0,0,0); - MPD_NEW_STATIC(tmp,0,0,0,0); - MPD_NEW_CONST(two,0,0,1,1,1,2); - mpd_ssize_t tbase_exp, texp_exp; - mpd_ssize_t i; - mpd_t t; - mpd_uint_t r; - uint8_t sign; - - - if (mpd_isspecial(base) || mpd_isspecial(exp) || mpd_isspecial(mod)) { - if (mpd_qcheck_3nans(result, base, exp, mod, ctx, status)) { - return; - } - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - - if (!_mpd_isint(base) || !_mpd_isint(exp) || !_mpd_isint(mod)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mpd_iszerocoeff(mod)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mod->digits+mod->exp > ctx->prec) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - sign = (mpd_isnegative(base)) && (mpd_isodd(exp)); - if (mpd_iszerocoeff(exp)) { - if (mpd_iszerocoeff(base)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - r = (_mpd_cmp_abs(mod, &one)==0) ? 0 : 1; - _settriple(result, sign, r, 0); - return; - } - if (mpd_isnegative(exp)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mpd_iszerocoeff(base)) { - _settriple(result, sign, 0, 0); - return; - } - - mpd_maxcontext(&maxcontext); - - mpd_qrescale(&tmod, mod, 0, &maxcontext, &maxcontext.status); - if (maxcontext.status&MPD_Errors) { - mpd_seterror(result, maxcontext.status&MPD_Errors, status); - goto out; - } - maxcontext.status = 0; - mpd_set_positive(&tmod); - - mpd_qround_to_int(&tbase, base, &maxcontext, status); - mpd_set_positive(&tbase); - tbase_exp = tbase.exp; - tbase.exp = 0; - - mpd_qround_to_int(&texp, exp, &maxcontext, status); - texp_exp = texp.exp; - texp.exp = 0; - - /* base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo */ - mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status); - mpd_qshiftl(result, &one, tbase_exp, status); - mpd_qrem(result, result, &tmod, &maxcontext, status); - _mpd_qmul_exact(&tbase, &tbase, result, &maxcontext, status); - mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status); - if (mpd_isspecial(&tbase) || - mpd_isspecial(&texp) || - mpd_isspecial(&tmod)) { - goto mpd_errors; - } - - for (i = 0; i < texp_exp; i++) { - _mpd_qpowmod_uint(&tmp, &tbase, 10, &tmod, status); - t = tmp; - tmp = tbase; - tbase = t; - } - if (mpd_isspecial(&tbase)) { - goto mpd_errors; /* GCOV_UNLIKELY */ - } - - /* resize to smaller cannot fail */ - mpd_qcopy(result, &one, status); - while (mpd_isfinite(&texp) && !mpd_iszero(&texp)) { - if (mpd_isodd(&texp)) { - _mpd_qmul_exact(result, result, &tbase, &maxcontext, status); - mpd_qrem(result, result, &tmod, &maxcontext, status); - } - _mpd_qmul_exact(&tbase, &tbase, &tbase, &maxcontext, status); - mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status); - mpd_qdivint(&texp, &texp, &two, &maxcontext, status); - } - if (mpd_isspecial(&texp) || mpd_isspecial(&tbase) || - mpd_isspecial(&tmod) || mpd_isspecial(result)) { - /* MPD_Malloc_error */ - goto mpd_errors; - } - else { - mpd_set_sign(result, sign); - } - -out: - mpd_del(&tbase); - mpd_del(&texp); - mpd_del(&tmod); - mpd_del(&tmp); - return; - -mpd_errors: - mpd_setspecial(result, MPD_POS, MPD_NAN); - goto out; -} - -void -mpd_qquantize(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_ssize_t b_exp = b->exp; - mpd_ssize_t expdiff, shift; - mpd_uint_t rnd; - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - if (mpd_isinfinite(a) && mpd_isinfinite(b)) { - mpd_qcopy(result, a, status); - return; - } - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - if (b->exp > ctx->emax || b->exp < mpd_etiny(ctx)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - if (mpd_iszero(a)) { - _settriple(result, mpd_sign(a), 0, b->exp); - mpd_qfinalize(result, ctx, status); - return; - } - - - expdiff = a->exp - b->exp; - if (a->digits + expdiff > ctx->prec) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - if (expdiff >= 0) { - shift = expdiff; - if (!mpd_qshiftl(result, a, shift, status)) { - return; - } - result->exp = b_exp; - } - else { - /* At this point expdiff < 0 and a->digits+expdiff <= prec, - * so the shift before an increment will fit in prec. */ - shift = -expdiff; - rnd = mpd_qshiftr(result, a, shift, status); - if (rnd == MPD_UINT_MAX) { - return; - } - result->exp = b_exp; - if (!_mpd_apply_round_fit(result, rnd, ctx, status)) { - return; - } - workstatus |= MPD_Rounded; - if (rnd) { - workstatus |= MPD_Inexact; - } - } - - if (mpd_adjexp(result) > ctx->emax || - mpd_adjexp(result) < mpd_etiny(ctx)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - *status |= workstatus; - mpd_qfinalize(result, ctx, status); -} - -void -mpd_qreduce(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_ssize_t shift, maxexp, maxshift; - uint8_t sign_a = mpd_sign(a); - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - mpd_qcopy(result, a, status); - return; - } - - if (!mpd_qcopy(result, a, status)) { - return; - } - mpd_qfinalize(result, ctx, status); - if (mpd_isspecial(result)) { - return; - } - if (mpd_iszero(result)) { - _settriple(result, sign_a, 0, 0); - return; - } - - shift = mpd_trail_zeros(result); - maxexp = (ctx->clamp) ? mpd_etop(ctx) : ctx->emax; - /* After the finalizing above result->exp <= maxexp. */ - maxshift = maxexp - result->exp; - shift = (shift > maxshift) ? maxshift : shift; - - mpd_qshiftr_inplace(result, shift); - result->exp += shift; -} - -void -mpd_qrem(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, - uint32_t *status) -{ - MPD_NEW_STATIC(q,0,0,0,0); - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(r, a, b, ctx, status)) { - return; - } - if (mpd_isinfinite(a)) { - mpd_seterror(r, MPD_Invalid_operation, status); - return; - } - if (mpd_isinfinite(b)) { - mpd_qcopy(r, a, status); - mpd_qfinalize(r, ctx, status); - return; - } - /* debug */ - abort(); /* GCOV_NOT_REACHED */ - } - if (mpd_iszerocoeff(b)) { - if (mpd_iszerocoeff(a)) { - mpd_seterror(r, MPD_Division_undefined, status); - } - else { - mpd_seterror(r, MPD_Invalid_operation, status); - } - return; - } - - _mpd_qdivmod(&q, r, a, b, ctx, status); - mpd_del(&q); - mpd_qfinalize(r, ctx, status); -} - -void -mpd_qrem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_STATIC(btmp,0,0,0,0); - MPD_NEW_STATIC(q,0,0,0,0); - mpd_ssize_t expdiff, qdigits; - int cmp, isodd, allnine; - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(r, a, b, ctx, status)) { - return; - } - if (mpd_isinfinite(a)) { - mpd_seterror(r, MPD_Invalid_operation, status); - return; - } - if (mpd_isinfinite(b)) { - mpd_qcopy(r, a, status); - mpd_qfinalize(r, ctx, status); - return; - } - /* debug */ - abort(); /* GCOV_NOT_REACHED */ - } - if (mpd_iszerocoeff(b)) { - if (mpd_iszerocoeff(a)) { - mpd_seterror(r, MPD_Division_undefined, status); - } - else { - mpd_seterror(r, MPD_Invalid_operation, status); - } - return; - } - - if (r == b) { - if (!mpd_qcopy(&btmp, b, status)) { - mpd_seterror(r, MPD_Malloc_error, status); - return; - } - b = &btmp; - } - - _mpd_qdivmod(&q, r, a, b, ctx, status); - if (mpd_isnan(&q) || mpd_isnan(r)) { - goto finish; - } - if (mpd_iszerocoeff(r)) { - goto finish; - } - - expdiff = mpd_adjexp(b) - mpd_adjexp(r); - if (-1 <= expdiff && expdiff <= 1) { - - allnine = mpd_coeff_isallnine(&q); - qdigits = q.digits; - isodd = mpd_isodd(&q); - - mpd_maxcontext(&workctx); - if (mpd_sign(a) == mpd_sign(b)) { - /* sign(r) == sign(b) */ - _mpd_qsub(&q, r, b, &workctx, &workctx.status); - } - else { - /* sign(r) != sign(b) */ - _mpd_qadd(&q, r, b, &workctx, &workctx.status); - } - - if (workctx.status&MPD_Errors) { - mpd_seterror(r, workctx.status&MPD_Errors, status); - goto finish; - } - - cmp = _mpd_cmp_abs(&q, r); - if (cmp < 0 || (cmp == 0 && isodd)) { - /* abs(r) > abs(b)/2 or abs(r) == abs(b)/2 and isodd(quotient) */ - if (allnine && qdigits == ctx->prec) { - /* abs(quotient) + 1 == 10**prec */ - mpd_seterror(r, MPD_Division_impossible, status); - goto finish; - } - mpd_qcopy(r, &q, status); - } - } - - -finish: - mpd_del(&btmp); - mpd_del(&q); - mpd_qfinalize(r, ctx, status); -} - -static void -_mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_ssize_t expdiff, shift; - mpd_uint_t rnd; - - if (mpd_isspecial(a)) { - mpd_qcopy(result, a, status); - return; - } - - if (mpd_iszero(a)) { - _settriple(result, mpd_sign(a), 0, exp); - return; - } - - expdiff = a->exp - exp; - if (expdiff >= 0) { - shift = expdiff; - if (a->digits + shift > MPD_MAX_PREC+1) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (!mpd_qshiftl(result, a, shift, status)) { - return; - } - result->exp = exp; - } - else { - shift = -expdiff; - rnd = mpd_qshiftr(result, a, shift, status); - if (rnd == MPD_UINT_MAX) { - return; - } - result->exp = exp; - _mpd_apply_round_excess(result, rnd, ctx, status); - *status |= MPD_Rounded; - if (rnd) { - *status |= MPD_Inexact; - } - } - - if (mpd_issubnormal(result, ctx)) { - *status |= MPD_Subnormal; - } -} - -/* - * Rescale a number so that it has exponent 'exp'. Does not regard context - * precision, emax, emin, but uses the rounding mode. Special numbers are - * quietly copied. Restrictions: - * - * MPD_MIN_ETINY <= exp <= MPD_MAX_EMAX+1 - * result->digits <= MPD_MAX_PREC+1 - */ -void -mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, - const mpd_context_t *ctx, uint32_t *status) -{ - if (exp > MPD_MAX_EMAX+1 || exp < MPD_MIN_ETINY) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - _mpd_qrescale(result, a, exp, ctx, status); -} - -/* - * Same as mpd_qrescale, but with relaxed restrictions. The result of this - * function should only be used for formatting a number and never as input - * for other operations. - * - * MPD_MIN_ETINY-MPD_MAX_PREC <= exp <= MPD_MAX_EMAX+1 - * result->digits <= MPD_MAX_PREC+1 - */ -void -mpd_qrescale_fmt(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, - const mpd_context_t *ctx, uint32_t *status) -{ - if (exp > MPD_MAX_EMAX+1 || exp < MPD_MIN_ETINY-MPD_MAX_PREC) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - _mpd_qrescale(result, a, exp, ctx, status); -} - -/* Round to an integer according to 'action' and ctx->round. */ -enum {TO_INT_EXACT, TO_INT_SILENT, TO_INT_TRUNC}; -static void -_mpd_qround_to_integral(int action, mpd_t *result, const mpd_t *a, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_uint_t rnd; - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - mpd_qcopy(result, a, status); - return; - } - if (a->exp >= 0) { - mpd_qcopy(result, a, status); - return; - } - if (mpd_iszerocoeff(a)) { - _settriple(result, mpd_sign(a), 0, 0); - return; - } - - rnd = mpd_qshiftr(result, a, -a->exp, status); - if (rnd == MPD_UINT_MAX) { - return; - } - result->exp = 0; - - if (action == TO_INT_EXACT || action == TO_INT_SILENT) { - _mpd_apply_round_excess(result, rnd, ctx, status); - if (action == TO_INT_EXACT) { - *status |= MPD_Rounded; - if (rnd) { - *status |= MPD_Inexact; - } - } - } -} - -void -mpd_qround_to_intx(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - (void)_mpd_qround_to_integral(TO_INT_EXACT, result, a, ctx, status); -} - -void -mpd_qround_to_int(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a, ctx, status); -} - -void -mpd_qtrunc(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - (void)_mpd_qround_to_integral(TO_INT_TRUNC, result, a, ctx, status); -} - -void -mpd_qfloor(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx = *ctx; - workctx.round = MPD_ROUND_FLOOR; - (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a, - &workctx, status); -} - -void -mpd_qceil(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx = *ctx; - workctx.round = MPD_ROUND_CEILING; - (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a, - &workctx, status); -} - -int -mpd_same_quantum(const mpd_t *a, const mpd_t *b) -{ - if (mpd_isspecial(a) || mpd_isspecial(b)) { - return ((mpd_isnan(a) && mpd_isnan(b)) || - (mpd_isinfinite(a) && mpd_isinfinite(b))); - } - - return a->exp == b->exp; -} - -/* Schedule the increase in precision for the Newton iteration. */ -static inline int -recpr_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2], - mpd_ssize_t maxprec, mpd_ssize_t initprec) -{ - mpd_ssize_t k; - int i; - - assert(maxprec > 0 && initprec > 0); - if (maxprec <= initprec) return -1; - - i = 0; k = maxprec; - do { - k = (k+1) / 2; - klist[i++] = k; - } while (k > initprec); - - return i-1; -} - -/* - * Initial approximation for the reciprocal: - * k_0 := MPD_RDIGITS-2 - * z_0 := 10**(-k_0) * floor(10**(2*k_0 + 2) / floor(v * 10**(k_0 + 2))) - * Absolute error: - * |1/v - z_0| < 10**(-k_0) - * ACL2 proof: maxerror-inverse-approx - */ -static void -_mpd_qreciprocal_approx(mpd_t *z, const mpd_t *v, uint32_t *status) -{ - mpd_uint_t p10data[2] = {0, mpd_pow10[MPD_RDIGITS-2]}; - mpd_uint_t dummy, word; - int n; - - assert(v->exp == -v->digits); - - _mpd_get_msdigits(&dummy, &word, v, MPD_RDIGITS); - n = mpd_word_digits(word); - word *= mpd_pow10[MPD_RDIGITS-n]; - - mpd_qresize(z, 2, status); - (void)_mpd_shortdiv(z->data, p10data, 2, word); - - mpd_clear_flags(z); - z->exp = -(MPD_RDIGITS-2); - z->len = (z->data[1] == 0) ? 1 : 2; - mpd_setdigits(z); -} - -/* - * Reciprocal, calculated with Newton's Method. Assumption: result != a. - * NOTE: The comments in the function show that certain operations are - * exact. The proof for the maximum error is too long to fit in here. - * ACL2 proof: maxerror-inverse-complete - */ -static void -_mpd_qreciprocal(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t varcontext, maxcontext; - mpd_t *z = result; /* current approximation */ - mpd_t *v; /* a, normalized to a number between 0.1 and 1 */ - MPD_NEW_SHARED(vtmp, a); /* v shares data with a */ - MPD_NEW_STATIC(s,0,0,0,0); /* temporary variable */ - MPD_NEW_STATIC(t,0,0,0,0); /* temporary variable */ - MPD_NEW_CONST(two,0,0,1,1,1,2); /* const 2 */ - mpd_ssize_t klist[MPD_MAX_PREC_LOG2]; - mpd_ssize_t adj, maxprec, initprec; - uint8_t sign = mpd_sign(a); - int i; - - assert(result != a); - - v = &vtmp; - mpd_clear_flags(v); - adj = v->digits + v->exp; - v->exp = -v->digits; - - /* Initial approximation */ - _mpd_qreciprocal_approx(z, v, status); - - mpd_maxcontext(&varcontext); - mpd_maxcontext(&maxcontext); - varcontext.round = maxcontext.round = MPD_ROUND_TRUNC; - varcontext.emax = maxcontext.emax = MPD_MAX_EMAX + 100; - varcontext.emin = maxcontext.emin = MPD_MIN_EMIN - 100; - maxcontext.prec = MPD_MAX_PREC + 100; - - maxprec = ctx->prec; - maxprec += 2; - initprec = MPD_RDIGITS-3; - - i = recpr_schedule_prec(klist, maxprec, initprec); - for (; i >= 0; i--) { - /* Loop invariant: z->digits <= klist[i]+7 */ - /* Let s := z**2, exact result */ - _mpd_qmul_exact(&s, z, z, &maxcontext, status); - varcontext.prec = 2*klist[i] + 5; - if (v->digits > varcontext.prec) { - /* Let t := v, truncated to n >= 2*k+5 fraction digits */ - mpd_qshiftr(&t, v, v->digits-varcontext.prec, status); - t.exp = -varcontext.prec; - /* Let t := trunc(v)*s, truncated to n >= 2*k+1 fraction digits */ - mpd_qmul(&t, &t, &s, &varcontext, status); - } - else { /* v->digits <= 2*k+5 */ - /* Let t := v*s, truncated to n >= 2*k+1 fraction digits */ - mpd_qmul(&t, v, &s, &varcontext, status); - } - /* Let s := 2*z, exact result */ - _mpd_qmul_exact(&s, z, &two, &maxcontext, status); - /* s.digits < t.digits <= 2*k+5, |adjexp(s)-adjexp(t)| <= 1, - * so the subtraction generates at most 2*k+6 <= klist[i+1]+7 - * digits. The loop invariant is preserved. */ - _mpd_qsub_exact(z, &s, &t, &maxcontext, status); - } - - if (!mpd_isspecial(z)) { - z->exp -= adj; - mpd_set_flags(z, sign); - } - - mpd_del(&s); - mpd_del(&t); - mpd_qfinalize(z, ctx, status); -} - -/* - * Internal function for large numbers: - * - * q, r = divmod(coeff(a), coeff(b)) - * - * Strategy: Multiply the dividend by the reciprocal of the divisor. The - * inexact result is fixed by a small loop, using at most one iteration. - * - * ACL2 proofs: - * ------------ - * 1) q is a natural number. (ndivmod-quotient-natp) - * 2) r is a natural number. (ndivmod-remainder-natp) - * 3) a = q * b + r (ndivmod-q*b+r==a) - * 4) r < b (ndivmod-remainder-<-b) - */ -static void -_mpd_base_ndivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, - uint32_t *status) -{ - mpd_context_t workctx; - mpd_t *qq = q, *rr = r; - mpd_t aa, bb; - int k; - - _mpd_copy_shared(&aa, a); - _mpd_copy_shared(&bb, b); - - mpd_set_positive(&aa); - mpd_set_positive(&bb); - aa.exp = 0; - bb.exp = 0; - - if (q == a || q == b) { - if ((qq = mpd_qnew()) == NULL) { - *status |= MPD_Malloc_error; - goto nanresult; - } - } - if (r == a || r == b) { - if ((rr = mpd_qnew()) == NULL) { - *status |= MPD_Malloc_error; - goto nanresult; - } - } - - mpd_maxcontext(&workctx); - - /* Let prec := adigits - bdigits + 4 */ - workctx.prec = a->digits - b->digits + 1 + 3; - if (a->digits > MPD_MAX_PREC || workctx.prec > MPD_MAX_PREC) { - *status |= MPD_Division_impossible; - goto nanresult; - } - - /* Let x := _mpd_qreciprocal(b, prec) - * Then x is bounded by: - * 1) 1/b - 10**(-prec - bdigits) < x < 1/b + 10**(-prec - bdigits) - * 2) 1/b - 10**(-adigits - 4) < x < 1/b + 10**(-adigits - 4) - */ - _mpd_qreciprocal(rr, &bb, &workctx, &workctx.status); - - /* Get an estimate for the quotient. Let q := a * x - * Then q is bounded by: - * 3) a/b - 10**-4 < q < a/b + 10**-4 - */ - _mpd_qmul(qq, &aa, rr, &workctx, &workctx.status); - /* Truncate q to an integer: - * 4) a/b - 2 < trunc(q) < a/b + 1 - */ - mpd_qtrunc(qq, qq, &workctx, &workctx.status); - - workctx.prec = aa.digits + 3; - workctx.emax = MPD_MAX_EMAX + 3; - workctx.emin = MPD_MIN_EMIN - 3; - /* Multiply the estimate for q by b: - * 5) a - 2 * b < trunc(q) * b < a + b - */ - _mpd_qmul(rr, &bb, qq, &workctx, &workctx.status); - /* Get the estimate for r such that a = q * b + r. */ - _mpd_qsub_exact(rr, &aa, rr, &workctx, &workctx.status); - - /* Fix the result. At this point -b < r < 2*b, so the correction loop - takes at most one iteration. */ - for (k = 0;; k++) { - if (mpd_isspecial(qq) || mpd_isspecial(rr)) { - *status |= (workctx.status&MPD_Errors); - goto nanresult; - } - if (k > 2) { /* Allow two iterations despite the proof. */ - mpd_err_warn("libmpdec: internal error in " /* GCOV_NOT_REACHED */ - "_mpd_base_ndivmod: please report"); /* GCOV_NOT_REACHED */ - *status |= MPD_Invalid_operation; /* GCOV_NOT_REACHED */ - goto nanresult; /* GCOV_NOT_REACHED */ - } - /* r < 0 */ - else if (_mpd_cmp(&zero, rr) == 1) { - _mpd_qadd_exact(rr, rr, &bb, &workctx, &workctx.status); - _mpd_qadd_exact(qq, qq, &minus_one, &workctx, &workctx.status); - } - /* 0 <= r < b */ - else if (_mpd_cmp(rr, &bb) == -1) { - break; - } - /* r >= b */ - else { - _mpd_qsub_exact(rr, rr, &bb, &workctx, &workctx.status); - _mpd_qadd_exact(qq, qq, &one, &workctx, &workctx.status); - } - } - - if (qq != q) { - if (!mpd_qcopy(q, qq, status)) { - goto nanresult; /* GCOV_UNLIKELY */ - } - mpd_del(qq); - } - if (rr != r) { - if (!mpd_qcopy(r, rr, status)) { - goto nanresult; /* GCOV_UNLIKELY */ - } - mpd_del(rr); - } - - *status |= (workctx.status&MPD_Errors); - return; - - -nanresult: - if (qq && qq != q) mpd_del(qq); - if (rr && rr != r) mpd_del(rr); - mpd_setspecial(q, MPD_POS, MPD_NAN); - mpd_setspecial(r, MPD_POS, MPD_NAN); -} - -/* LIBMPDEC_ONLY */ -/* - * Schedule the optimal precision increase for the Newton iteration. - * v := input operand - * z_0 := initial approximation - * initprec := natural number such that abs(sqrt(v) - z_0) < 10**-initprec - * maxprec := target precision - * - * For convenience the output klist contains the elements in reverse order: - * klist := [k_n-1, ..., k_0], where - * 1) k_0 <= initprec and - * 2) abs(sqrt(v) - result) < 10**(-2*k_n-1 + 2) <= 10**-maxprec. - */ -static inline int -invroot_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2], - mpd_ssize_t maxprec, mpd_ssize_t initprec) -{ - mpd_ssize_t k; - int i; - - assert(maxprec >= 3 && initprec >= 3); - if (maxprec <= initprec) return -1; - - i = 0; k = maxprec; - do { - k = (k+3) / 2; - klist[i++] = k; - } while (k > initprec); - - return i-1; -} - -/* - * Initial approximation for the inverse square root function. - * Input: - * v := rational number, with 1 <= v < 100 - * vhat := floor(v * 10**6) - * Output: - * z := approximation to 1/sqrt(v), such that abs(z - 1/sqrt(v)) < 10**-3. - */ -static inline void -_invroot_init_approx(mpd_t *z, mpd_uint_t vhat) -{ - mpd_uint_t lo = 1000; - mpd_uint_t hi = 10000; - mpd_uint_t a, sq; - - assert(lo*lo <= vhat && vhat < (hi+1)*(hi+1)); - - for(;;) { - a = (lo + hi) / 2; - sq = a * a; - if (vhat >= sq) { - if (vhat < sq + 2*a + 1) { - break; - } - lo = a + 1; - } - else { - hi = a - 1; - } - } - - /* - * After the binary search we have: - * 1) a**2 <= floor(v * 10**6) < (a + 1)**2 - * This implies: - * 2) a**2 <= v * 10**6 < (a + 1)**2 - * 3) a <= sqrt(v) * 10**3 < a + 1 - * Since 10**3 <= a: - * 4) 0 <= 10**prec/a - 1/sqrt(v) < 10**-prec - * We have: - * 5) 10**3/a - 10**-3 < floor(10**9/a) * 10**-6 <= 10**3/a - * Merging 4) and 5): - * 6) abs(floor(10**9/a) * 10**-6 - 1/sqrt(v)) < 10**-3 - */ - mpd_minalloc(z); - mpd_clear_flags(z); - z->data[0] = 1000000000UL / a; - z->len = 1; - z->exp = -6; - mpd_setdigits(z); -} - -/* - * Set 'result' to 1/sqrt(a). - * Relative error: abs(result - 1/sqrt(a)) < 10**-prec * 1/sqrt(a) - */ -static void -_mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_context_t varcontext, maxcontext; - mpd_t *z = result; /* current approximation */ - mpd_t *v; /* a, normalized to a number between 1 and 100 */ - MPD_NEW_SHARED(vtmp, a); /* by default v will share data with a */ - MPD_NEW_STATIC(s,0,0,0,0); /* temporary variable */ - MPD_NEW_STATIC(t,0,0,0,0); /* temporary variable */ - MPD_NEW_CONST(one_half,0,-1,1,1,1,5); - MPD_NEW_CONST(three,0,0,1,1,1,3); - mpd_ssize_t klist[MPD_MAX_PREC_LOG2]; - mpd_ssize_t ideal_exp, shift; - mpd_ssize_t adj, tz; - mpd_ssize_t maxprec, fracdigits; - mpd_uint_t vhat, dummy; - int i, n; - - - ideal_exp = -(a->exp - (a->exp & 1)) / 2; - - v = &vtmp; - if (result == a) { - if ((v = mpd_qncopy(a)) == NULL) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - } - - /* normalize a to 1 <= v < 100 */ - if ((v->digits+v->exp) & 1) { - fracdigits = v->digits - 1; - v->exp = -fracdigits; - n = (v->digits > 7) ? 7 : (int)v->digits; - /* Let vhat := floor(v * 10**(2*initprec)) */ - _mpd_get_msdigits(&dummy, &vhat, v, n); - if (n < 7) { - vhat *= mpd_pow10[7-n]; - } - } - else { - fracdigits = v->digits - 2; - v->exp = -fracdigits; - n = (v->digits > 8) ? 8 : (int)v->digits; - /* Let vhat := floor(v * 10**(2*initprec)) */ - _mpd_get_msdigits(&dummy, &vhat, v, n); - if (n < 8) { - vhat *= mpd_pow10[8-n]; - } - } - adj = (a->exp-v->exp) / 2; - - /* initial approximation */ - _invroot_init_approx(z, vhat); - - mpd_maxcontext(&maxcontext); - mpd_maxcontext(&varcontext); - varcontext.round = MPD_ROUND_TRUNC; - maxprec = ctx->prec + 1; - - /* initprec == 3 */ - i = invroot_schedule_prec(klist, maxprec, 3); - for (; i >= 0; i--) { - varcontext.prec = 2*klist[i]+2; - mpd_qmul(&s, z, z, &maxcontext, &workstatus); - if (v->digits > varcontext.prec) { - shift = v->digits - varcontext.prec; - mpd_qshiftr(&t, v, shift, &workstatus); - t.exp += shift; - mpd_qmul(&t, &t, &s, &varcontext, &workstatus); - } - else { - mpd_qmul(&t, v, &s, &varcontext, &workstatus); - } - mpd_qsub(&t, &three, &t, &maxcontext, &workstatus); - mpd_qmul(z, z, &t, &varcontext, &workstatus); - mpd_qmul(z, z, &one_half, &maxcontext, &workstatus); - } - - z->exp -= adj; - - tz = mpd_trail_zeros(result); - shift = ideal_exp - result->exp; - shift = (tz > shift) ? shift : tz; - if (shift > 0) { - mpd_qshiftr_inplace(result, shift); - result->exp += shift; - } - - - mpd_del(&s); - mpd_del(&t); - if (v != &vtmp) mpd_del(v); - *status |= (workstatus&MPD_Errors); - *status |= (MPD_Rounded|MPD_Inexact); -} - -void -mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - /* positive infinity */ - _settriple(result, MPD_POS, 0, mpd_etiny(ctx)); - *status |= MPD_Clamped; - return; - } - if (mpd_iszero(a)) { - mpd_setspecial(result, mpd_sign(a), MPD_INF); - *status |= MPD_Division_by_zero; - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - workctx = *ctx; - workctx.prec += 2; - workctx.round = MPD_ROUND_HALF_EVEN; - _mpd_qinvroot(result, a, &workctx, status); - mpd_qfinalize(result, ctx, status); -} -/* END LIBMPDEC_ONLY */ - -/* Algorithm from decimal.py */ -void -mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(c,0,0,0,0); - MPD_NEW_STATIC(q,0,0,0,0); - MPD_NEW_STATIC(r,0,0,0,0); - MPD_NEW_CONST(two,0,0,1,1,1,2); - mpd_ssize_t prec, ideal_exp; - mpd_ssize_t l, shift; - int exact = 0; - - - ideal_exp = (a->exp - (a->exp & 1)) / 2; - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - mpd_setspecial(result, MPD_POS, MPD_INF); - return; - } - if (mpd_iszero(a)) { - _settriple(result, mpd_sign(a), 0, ideal_exp); - mpd_qfinalize(result, ctx, status); - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - mpd_maxcontext(&maxcontext); - prec = ctx->prec + 1; - - if (!mpd_qcopy(&c, a, status)) { - goto malloc_error; - } - c.exp = 0; - - if (a->exp & 1) { - if (!mpd_qshiftl(&c, &c, 1, status)) { - goto malloc_error; - } - l = (a->digits >> 1) + 1; - } - else { - l = (a->digits + 1) >> 1; - } - - shift = prec - l; - if (shift >= 0) { - if (!mpd_qshiftl(&c, &c, 2*shift, status)) { - goto malloc_error; - } - exact = 1; - } - else { - exact = !mpd_qshiftr_inplace(&c, -2*shift); - } - - ideal_exp -= shift; - - /* find result = floor(sqrt(c)) using Newton's method */ - if (!mpd_qshiftl(result, &one, prec, status)) { - goto malloc_error; - } - - while (1) { - _mpd_qdivmod(&q, &r, &c, result, &maxcontext, &maxcontext.status); - if (mpd_isspecial(result) || mpd_isspecial(&q)) { - mpd_seterror(result, maxcontext.status&MPD_Errors, status); - goto out; - } - if (_mpd_cmp(result, &q) <= 0) { - break; - } - _mpd_qadd_exact(result, result, &q, &maxcontext, &maxcontext.status); - if (mpd_isspecial(result)) { - mpd_seterror(result, maxcontext.status&MPD_Errors, status); - goto out; - } - _mpd_qdivmod(result, &r, result, &two, &maxcontext, &maxcontext.status); - } - - if (exact) { - _mpd_qmul_exact(&r, result, result, &maxcontext, &maxcontext.status); - if (mpd_isspecial(&r)) { - mpd_seterror(result, maxcontext.status&MPD_Errors, status); - goto out; - } - exact = (_mpd_cmp(&r, &c) == 0); - } - - if (exact) { - if (shift >= 0) { - mpd_qshiftr_inplace(result, shift); - } - else { - if (!mpd_qshiftl(result, result, -shift, status)) { - goto malloc_error; - } - } - ideal_exp += shift; - } - else { - int lsd = (int)mpd_lsd(result->data[0]); - if (lsd == 0 || lsd == 5) { - result->data[0] += 1; - } - } - - result->exp = ideal_exp; - - -out: - mpd_del(&c); - mpd_del(&q); - mpd_del(&r); - maxcontext = *ctx; - maxcontext.round = MPD_ROUND_HALF_EVEN; - mpd_qfinalize(result, &maxcontext, status); - return; - -malloc_error: - mpd_seterror(result, MPD_Malloc_error, status); - goto out; -} - - -/******************************************************************************/ -/* Base conversions */ -/******************************************************************************/ - -/* Space needed to represent an integer mpd_t in base 'base'. */ -size_t -mpd_sizeinbase(const mpd_t *a, uint32_t base) -{ - double x; - size_t digits; - - assert(mpd_isinteger(a)); - assert(base >= 2); - - if (mpd_iszero(a)) { - return 1; - } - - digits = a->digits+a->exp; - assert(digits > 0); - -#ifdef CONFIG_64 - /* ceil(2711437152599294 / log10(2)) + 4 == 2**53 */ - if (digits > 2711437152599294ULL) { - return SIZE_MAX; - } -#endif - - x = (double)digits / log10(base); - return (x > SIZE_MAX-1) ? SIZE_MAX : (size_t)x + 1; -} - -/* Space needed to import a base 'base' integer of length 'srclen'. */ -static mpd_ssize_t -_mpd_importsize(size_t srclen, uint32_t base) -{ - double x; - - assert(srclen > 0); - assert(base >= 2); - -#if SIZE_MAX == UINT64_MAX - if (srclen > (1ULL<<53)) { - return MPD_SSIZE_MAX; - } -#endif - - x = (double)srclen * (log10(base)/MPD_RDIGITS); - return (x >= MPD_MAXIMPORT) ? MPD_SSIZE_MAX : (mpd_ssize_t)x + 1; -} - -static uint8_t -mpd_resize_u16(uint16_t **w, size_t nmemb) -{ - uint8_t err = 0; - *w = mpd_realloc(*w, nmemb, sizeof **w, &err); - return !err; -} - -static uint8_t -mpd_resize_u32(uint32_t **w, size_t nmemb) -{ - uint8_t err = 0; - *w = mpd_realloc(*w, nmemb, sizeof **w, &err); - return !err; -} - -static size_t -_baseconv_to_u16(uint16_t **w, size_t wlen, mpd_uint_t wbase, - mpd_uint_t *u, mpd_ssize_t ulen) -{ - size_t n = 0; - - assert(wlen > 0 && ulen > 0); - assert(wbase <= (1U<<16)); - - do { - if (n >= wlen) { - if (!mpd_resize_u16(w, n+1)) { - return SIZE_MAX; - } - wlen = n+1; - } - (*w)[n++] = (uint16_t)_mpd_shortdiv(u, u, ulen, wbase); - /* ulen is at least 1. u[ulen-1] can only be zero if ulen == 1. */ - ulen = _mpd_real_size(u, ulen); - - } while (u[ulen-1] != 0); - - return n; -} - -static size_t -_coeff_from_u16(mpd_t *w, mpd_ssize_t wlen, - const mpd_uint_t *u, size_t ulen, uint32_t ubase, - uint32_t *status) -{ - mpd_ssize_t n = 0; - mpd_uint_t carry; - - assert(wlen > 0 && ulen > 0); - assert(ubase <= (1U<<16)); - - w->data[n++] = u[--ulen]; - while (--ulen != SIZE_MAX) { - carry = _mpd_shortmul_c(w->data, w->data, n, ubase); - if (carry) { - if (n >= wlen) { - if (!mpd_qresize(w, n+1, status)) { - return SIZE_MAX; - } - wlen = n+1; - } - w->data[n++] = carry; - } - carry = _mpd_shortadd(w->data, n, u[ulen]); - if (carry) { - if (n >= wlen) { - if (!mpd_qresize(w, n+1, status)) { - return SIZE_MAX; - } - wlen = n+1; - } - w->data[n++] = carry; - } - } - - return n; -} - -/* target base wbase < source base ubase */ -static size_t -_baseconv_to_smaller(uint32_t **w, size_t wlen, uint32_t wbase, - mpd_uint_t *u, mpd_ssize_t ulen, mpd_uint_t ubase) -{ - size_t n = 0; - - assert(wlen > 0 && ulen > 0); - assert(wbase < ubase); - - do { - if (n >= wlen) { - if (!mpd_resize_u32(w, n+1)) { - return SIZE_MAX; - } - wlen = n+1; - } - (*w)[n++] = (uint32_t)_mpd_shortdiv_b(u, u, ulen, wbase, ubase); - /* ulen is at least 1. u[ulen-1] can only be zero if ulen == 1. */ - ulen = _mpd_real_size(u, ulen); - - } while (u[ulen-1] != 0); - - return n; -} - -#ifdef CONFIG_32 -/* target base 'wbase' == source base 'ubase' */ -static size_t -_copy_equal_base(uint32_t **w, size_t wlen, - const uint32_t *u, size_t ulen) -{ - if (wlen < ulen) { - if (!mpd_resize_u32(w, ulen)) { - return SIZE_MAX; - } - } - - memcpy(*w, u, ulen * (sizeof **w)); - return ulen; -} - -/* target base 'wbase' > source base 'ubase' */ -static size_t -_baseconv_to_larger(uint32_t **w, size_t wlen, mpd_uint_t wbase, - const mpd_uint_t *u, size_t ulen, mpd_uint_t ubase) -{ - size_t n = 0; - mpd_uint_t carry; - - assert(wlen > 0 && ulen > 0); - assert(ubase < wbase); - - (*w)[n++] = u[--ulen]; - while (--ulen != SIZE_MAX) { - carry = _mpd_shortmul_b(*w, *w, n, ubase, wbase); - if (carry) { - if (n >= wlen) { - if (!mpd_resize_u32(w, n+1)) { - return SIZE_MAX; - } - wlen = n+1; - } - (*w)[n++] = carry; - } - carry = _mpd_shortadd_b(*w, n, u[ulen], wbase); - if (carry) { - if (n >= wlen) { - if (!mpd_resize_u32(w, n+1)) { - return SIZE_MAX; - } - wlen = n+1; - } - (*w)[n++] = carry; - } - } - - return n; -} - -/* target base wbase < source base ubase */ -static size_t -_coeff_from_larger_base(mpd_t *w, size_t wlen, mpd_uint_t wbase, - mpd_uint_t *u, mpd_ssize_t ulen, mpd_uint_t ubase, - uint32_t *status) -{ - size_t n = 0; - - assert(wlen > 0 && ulen > 0); - assert(wbase < ubase); - - do { - if (n >= wlen) { - if (!mpd_qresize(w, n+1, status)) { - return SIZE_MAX; - } - wlen = n+1; - } - w->data[n++] = (uint32_t)_mpd_shortdiv_b(u, u, ulen, wbase, ubase); - /* ulen is at least 1. u[ulen-1] can only be zero if ulen == 1. */ - ulen = _mpd_real_size(u, ulen); - - } while (u[ulen-1] != 0); - - return n; -} -#endif - -/* target base 'wbase' > source base 'ubase' */ -static size_t -_coeff_from_smaller_base(mpd_t *w, mpd_ssize_t wlen, mpd_uint_t wbase, - const uint32_t *u, size_t ulen, mpd_uint_t ubase, - uint32_t *status) -{ - mpd_ssize_t n = 0; - mpd_uint_t carry; - - assert(wlen > 0 && ulen > 0); - assert(wbase > ubase); - - w->data[n++] = u[--ulen]; - while (--ulen != SIZE_MAX) { - carry = _mpd_shortmul_b(w->data, w->data, n, ubase, wbase); - if (carry) { - if (n >= wlen) { - if (!mpd_qresize(w, n+1, status)) { - return SIZE_MAX; - } - wlen = n+1; - } - w->data[n++] = carry; - } - carry = _mpd_shortadd_b(w->data, n, u[ulen], wbase); - if (carry) { - if (n >= wlen) { - if (!mpd_qresize(w, n+1, status)) { - return SIZE_MAX; - } - wlen = n+1; - } - w->data[n++] = carry; - } - } - - return n; -} - -/* - * Convert an integer mpd_t to a multiprecision integer with base <= 2**16. - * The least significant word of the result is (*rdata)[0]. - * - * If rdata is NULL, space is allocated by the function and rlen is irrelevant. - * In case of an error any allocated storage is freed and rdata is set back to - * NULL. - * - * If rdata is non-NULL, it MUST be allocated by one of libmpdec's allocation - * functions and rlen MUST be correct. If necessary, the function will resize - * rdata. In case of an error the caller must free rdata. - * - * Return value: In case of success, the exact length of rdata, SIZE_MAX - * otherwise. - */ -size_t -mpd_qexport_u16(uint16_t **rdata, size_t rlen, uint32_t rbase, - const mpd_t *src, uint32_t *status) -{ - MPD_NEW_STATIC(tsrc,0,0,0,0); - int alloc = 0; /* rdata == NULL */ - size_t n; - - assert(rbase <= (1U<<16)); - - if (mpd_isspecial(src) || !_mpd_isint(src)) { - *status |= MPD_Invalid_operation; - return SIZE_MAX; - } - - if (*rdata == NULL) { - rlen = mpd_sizeinbase(src, rbase); - if (rlen == SIZE_MAX) { - *status |= MPD_Invalid_operation; - return SIZE_MAX; - } - *rdata = mpd_alloc(rlen, sizeof **rdata); - if (*rdata == NULL) { - goto malloc_error; - } - alloc = 1; - } - - if (mpd_iszero(src)) { - **rdata = 0; - return 1; - } - - if (src->exp >= 0) { - if (!mpd_qshiftl(&tsrc, src, src->exp, status)) { - goto malloc_error; - } - } - else { - if (mpd_qshiftr(&tsrc, src, -src->exp, status) == MPD_UINT_MAX) { - goto malloc_error; - } - } - - n = _baseconv_to_u16(rdata, rlen, rbase, tsrc.data, tsrc.len); - if (n == SIZE_MAX) { - goto malloc_error; - } - - -out: - mpd_del(&tsrc); - return n; - -malloc_error: - if (alloc) { - mpd_free(*rdata); - *rdata = NULL; - } - n = SIZE_MAX; - *status |= MPD_Malloc_error; - goto out; -} - -/* - * Convert an integer mpd_t to a multiprecision integer with base<=UINT32_MAX. - * The least significant word of the result is (*rdata)[0]. - * - * If rdata is NULL, space is allocated by the function and rlen is irrelevant. - * In case of an error any allocated storage is freed and rdata is set back to - * NULL. - * - * If rdata is non-NULL, it MUST be allocated by one of libmpdec's allocation - * functions and rlen MUST be correct. If necessary, the function will resize - * rdata. In case of an error the caller must free rdata. - * - * Return value: In case of success, the exact length of rdata, SIZE_MAX - * otherwise. - */ -size_t -mpd_qexport_u32(uint32_t **rdata, size_t rlen, uint32_t rbase, - const mpd_t *src, uint32_t *status) -{ - MPD_NEW_STATIC(tsrc,0,0,0,0); - int alloc = 0; /* rdata == NULL */ - size_t n; - - if (mpd_isspecial(src) || !_mpd_isint(src)) { - *status |= MPD_Invalid_operation; - return SIZE_MAX; - } - - if (*rdata == NULL) { - rlen = mpd_sizeinbase(src, rbase); - if (rlen == SIZE_MAX) { - *status |= MPD_Invalid_operation; - return SIZE_MAX; - } - *rdata = mpd_alloc(rlen, sizeof **rdata); - if (*rdata == NULL) { - goto malloc_error; - } - alloc = 1; - } - - if (mpd_iszero(src)) { - **rdata = 0; - return 1; - } - - if (src->exp >= 0) { - if (!mpd_qshiftl(&tsrc, src, src->exp, status)) { - goto malloc_error; - } - } - else { - if (mpd_qshiftr(&tsrc, src, -src->exp, status) == MPD_UINT_MAX) { - goto malloc_error; - } - } - -#ifdef CONFIG_64 - n = _baseconv_to_smaller(rdata, rlen, rbase, - tsrc.data, tsrc.len, MPD_RADIX); -#else - if (rbase == MPD_RADIX) { - n = _copy_equal_base(rdata, rlen, tsrc.data, tsrc.len); - } - else if (rbase < MPD_RADIX) { - n = _baseconv_to_smaller(rdata, rlen, rbase, - tsrc.data, tsrc.len, MPD_RADIX); - } - else { - n = _baseconv_to_larger(rdata, rlen, rbase, - tsrc.data, tsrc.len, MPD_RADIX); - } -#endif - - if (n == SIZE_MAX) { - goto malloc_error; - } - - -out: - mpd_del(&tsrc); - return n; - -malloc_error: - if (alloc) { - mpd_free(*rdata); - *rdata = NULL; - } - n = SIZE_MAX; - *status |= MPD_Malloc_error; - goto out; -} - - -/* - * Converts a multiprecision integer with base <= UINT16_MAX+1 to an mpd_t. - * The least significant word of the source is srcdata[0]. - */ -void -mpd_qimport_u16(mpd_t *result, - const uint16_t *srcdata, size_t srclen, - uint8_t srcsign, uint32_t srcbase, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_uint_t *usrc; /* uint16_t src copied to an mpd_uint_t array */ - mpd_ssize_t rlen; /* length of the result */ - size_t n; - - assert(srclen > 0); - assert(srcbase <= (1U<<16)); - - rlen = _mpd_importsize(srclen, srcbase); - if (rlen == MPD_SSIZE_MAX) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - usrc = mpd_alloc((mpd_size_t)srclen, sizeof *usrc); - if (usrc == NULL) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - for (n = 0; n < srclen; n++) { - usrc[n] = srcdata[n]; - } - - if (!mpd_qresize(result, rlen, status)) { - goto finish; - } - - n = _coeff_from_u16(result, rlen, usrc, srclen, srcbase, status); - if (n == SIZE_MAX) { - goto finish; - } - - mpd_set_flags(result, srcsign); - result->exp = 0; - result->len = n; - mpd_setdigits(result); - - mpd_qresize(result, result->len, status); - mpd_qfinalize(result, ctx, status); - - -finish: - mpd_free(usrc); -} - -/* - * Converts a multiprecision integer with base <= UINT32_MAX to an mpd_t. - * The least significant word of the source is srcdata[0]. - */ -void -mpd_qimport_u32(mpd_t *result, - const uint32_t *srcdata, size_t srclen, - uint8_t srcsign, uint32_t srcbase, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_ssize_t rlen; /* length of the result */ - size_t n; - - assert(srclen > 0); - - rlen = _mpd_importsize(srclen, srcbase); - if (rlen == MPD_SSIZE_MAX) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - if (!mpd_qresize(result, rlen, status)) { - return; - } - -#ifdef CONFIG_64 - n = _coeff_from_smaller_base(result, rlen, MPD_RADIX, - srcdata, srclen, srcbase, - status); -#else - if (srcbase == MPD_RADIX) { - if (!mpd_qresize(result, srclen, status)) { - return; - } - memcpy(result->data, srcdata, srclen * (sizeof *srcdata)); - n = srclen; - } - else if (srcbase < MPD_RADIX) { - n = _coeff_from_smaller_base(result, rlen, MPD_RADIX, - srcdata, srclen, srcbase, - status); - } - else { - mpd_uint_t *usrc = mpd_alloc((mpd_size_t)srclen, sizeof *usrc); - if (usrc == NULL) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - for (n = 0; n < srclen; n++) { - usrc[n] = srcdata[n]; - } - - n = _coeff_from_larger_base(result, rlen, MPD_RADIX, - usrc, (mpd_ssize_t)srclen, srcbase, - status); - mpd_free(usrc); - } -#endif - - if (n == SIZE_MAX) { - return; - } - - mpd_set_flags(result, srcsign); - result->exp = 0; - result->len = n; - mpd_setdigits(result); - - mpd_qresize(result, result->len, status); - mpd_qfinalize(result, ctx, status); -} - - - diff --git a/Modules/_decimal/libmpdec/mpdecimal.h b/Modules/_decimal/libmpdec/mpdecimal.h deleted file mode 100644 index a67dd9b..0000000 --- a/Modules/_decimal/libmpdec/mpdecimal.h +++ /dev/null @@ -1,847 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef MPDECIMAL_H -#define MPDECIMAL_H - - -#ifdef __cplusplus -extern "C" { - #ifndef __STDC_LIMIT_MACROS - #define __STDC_LIMIT_MACROS - #define MPD_CLEAR_STDC_LIMIT_MACROS - #endif -#endif - - -#ifndef _MSC_VER - #include "pyconfig.h" -#endif - -#include <stdio.h> -#include <stdlib.h> -#include <string.h> -#include <limits.h> -#include <assert.h> -#include <stdint.h> -#include <inttypes.h> - -#ifdef _MSC_VER - #include "vccompat.h" - #ifndef UNUSED - #define UNUSED - #endif - #define MPD_PRAGMA(x) - #define MPD_HIDE_SYMBOLS_START - #define MPD_HIDE_SYMBOLS_END - #define EXTINLINE extern inline -#else - #ifndef __GNUC_STDC_INLINE__ - #define __GNUC_STDC_INLINE__ 1 - #endif - #if defined(__GNUC__) && !defined(__INTEL_COMPILER) - #define UNUSED __attribute__((unused)) - #else - #define UNUSED - #endif - #if (defined(__linux__) || defined(__FreeBSD__) || defined(__APPLE__)) && \ - defined(__GNUC__) && __GNUC__ >= 4 && !defined(__INTEL_COMPILER) - #define MPD_PRAGMA(x) _Pragma(x) - #define MPD_HIDE_SYMBOLS_START "GCC visibility push(hidden)" - #define MPD_HIDE_SYMBOLS_END "GCC visibility pop" - #else - #define MPD_PRAGMA(x) - #define MPD_HIDE_SYMBOLS_START - #define MPD_HIDE_SYMBOLS_END - #endif - #define EXTINLINE -#endif - - -/* This header file is internal for the purpose of building _decimal.so. - * All symbols should have local scope in the DSO. */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -#if !defined(LEGACY_COMPILER) - #if !defined(UINT64_MAX) - /* The following #error is just a warning. If the compiler indeed does - * not have uint64_t, it is perfectly safe to comment out the #error. */ - #error "Warning: Compiler without uint64_t. Comment out this line." - #define LEGACY_COMPILER - #endif -#endif - - -/******************************************************************************/ -/* Version */ -/******************************************************************************/ - -#define MPD_MAJOR_VERSION 2 -#define MPD_MINOR_VERSION 4 -#define MPD_MICRO_VERSION 2 - -#define MPD_VERSION "2.4.2" - -#define MPD_VERSION_HEX ((MPD_MAJOR_VERSION << 24) | \ - (MPD_MINOR_VERSION << 16) | \ - (MPD_MICRO_VERSION << 8)) - -const char *mpd_version(void); - - -/******************************************************************************/ -/* Configuration */ -/******************************************************************************/ - -#if defined(UNIVERSAL) - #if defined(CONFIG_64) || defined(CONFIG_32) - #error "cannot use CONFIG_64 or CONFIG_32 with UNIVERSAL." - #endif - #if defined(__ppc__) - #define CONFIG_32 - #define ANSI - #elif defined(__ppc64__) - #define CONFIG_64 - #define ANSI - #elif defined(__i386__) - #define CONFIG_32 - #define ANSI - #elif defined(__x86_64__) - #define CONFIG_64 - #define ASM - #else - #error "unknown architecture for universal build." - #endif -#endif - - -/* BEGIN CONFIG_64 */ -#if defined(CONFIG_64) -/* types for modular and base arithmetic */ -#define MPD_UINT_MAX UINT64_MAX -#define MPD_BITS_PER_UINT 64 -typedef uint64_t mpd_uint_t; /* unsigned mod type */ - -#define MPD_SIZE_MAX SIZE_MAX -typedef size_t mpd_size_t; /* unsigned size type */ - -/* type for exp, digits, len, prec */ -#define MPD_SSIZE_MAX INT64_MAX -#define MPD_SSIZE_MIN INT64_MIN -typedef int64_t mpd_ssize_t; -#define _mpd_strtossize strtoll - -/* decimal arithmetic */ -#define MPD_RADIX 10000000000000000000ULL /* 10**19 */ -#define MPD_RDIGITS 19 -#define MPD_MAX_POW10 19 -#define MPD_EXPDIGITS 19 /* MPD_EXPDIGITS <= MPD_RDIGITS+1 */ - -#define MPD_MAXTRANSFORM_2N 4294967296ULL /* 2**32 */ -#define MPD_MAX_PREC 999999999999999999LL -#define MPD_MAX_PREC_LOG2 64 -#define MPD_ELIMIT 1000000000000000000LL -#define MPD_MAX_EMAX 999999999999999999LL /* ELIMIT-1 */ -#define MPD_MIN_EMIN (-999999999999999999LL) /* -EMAX */ -#define MPD_MIN_ETINY (MPD_MIN_EMIN-(MPD_MAX_PREC-1)) -#define MPD_EXP_INF 2000000000000000001LL -#define MPD_EXP_CLAMP (-4000000000000000001LL) -#define MPD_MAXIMPORT 105263157894736842L /* ceil((2*MPD_MAX_PREC)/MPD_RDIGITS) */ - -/* conversion specifiers */ -#define PRI_mpd_uint_t PRIu64 -#define PRI_mpd_ssize_t PRIi64 -/* END CONFIG_64 */ - - -/* BEGIN CONFIG_32 */ -#elif defined(CONFIG_32) -/* types for modular and base arithmetic */ -#define MPD_UINT_MAX UINT32_MAX -#define MPD_BITS_PER_UINT 32 -typedef uint32_t mpd_uint_t; /* unsigned mod type */ - -#ifndef LEGACY_COMPILER -#define MPD_UUINT_MAX UINT64_MAX -typedef uint64_t mpd_uuint_t; /* double width unsigned mod type */ -#endif - -#define MPD_SIZE_MAX SIZE_MAX -typedef size_t mpd_size_t; /* unsigned size type */ - -/* type for dec->len, dec->exp, ctx->prec */ -#define MPD_SSIZE_MAX INT32_MAX -#define MPD_SSIZE_MIN INT32_MIN -typedef int32_t mpd_ssize_t; -#define _mpd_strtossize strtol - -/* decimal arithmetic */ -#define MPD_RADIX 1000000000UL /* 10**9 */ -#define MPD_RDIGITS 9 -#define MPD_MAX_POW10 9 -#define MPD_EXPDIGITS 10 /* MPD_EXPDIGITS <= MPD_RDIGITS+1 */ - -#define MPD_MAXTRANSFORM_2N 33554432UL /* 2**25 */ -#define MPD_MAX_PREC 425000000L -#define MPD_MAX_PREC_LOG2 32 -#define MPD_ELIMIT 425000001L -#define MPD_MAX_EMAX 425000000L /* ELIMIT-1 */ -#define MPD_MIN_EMIN (-425000000L) /* -EMAX */ -#define MPD_MIN_ETINY (MPD_MIN_EMIN-(MPD_MAX_PREC-1)) -#define MPD_EXP_INF 1000000001L /* allows for emax=999999999 in the tests */ -#define MPD_EXP_CLAMP (-2000000001L) /* allows for emin=-999999999 in the tests */ -#define MPD_MAXIMPORT 94444445L /* ceil((2*MPD_MAX_PREC)/MPD_RDIGITS) */ - -/* conversion specifiers */ -#define PRI_mpd_uint_t PRIu32 -#define PRI_mpd_ssize_t PRIi32 -/* END CONFIG_32 */ - -#else - #error "define CONFIG_64 or CONFIG_32" -#endif -/* END CONFIG */ - - -#if MPD_SIZE_MAX != MPD_UINT_MAX - #error "unsupported platform: need mpd_size_t == mpd_uint_t" -#endif - - -/******************************************************************************/ -/* Context */ -/******************************************************************************/ - -enum { - MPD_ROUND_UP, /* round away from 0 */ - MPD_ROUND_DOWN, /* round toward 0 (truncate) */ - MPD_ROUND_CEILING, /* round toward +infinity */ - MPD_ROUND_FLOOR, /* round toward -infinity */ - MPD_ROUND_HALF_UP, /* 0.5 is rounded up */ - MPD_ROUND_HALF_DOWN, /* 0.5 is rounded down */ - MPD_ROUND_HALF_EVEN, /* 0.5 is rounded to even */ - MPD_ROUND_05UP, /* round zero or five away from 0 */ - MPD_ROUND_TRUNC, /* truncate, but set infinity */ - MPD_ROUND_GUARD -}; - -enum { MPD_CLAMP_DEFAULT, MPD_CLAMP_IEEE_754, MPD_CLAMP_GUARD }; - -extern const char *mpd_round_string[MPD_ROUND_GUARD]; -extern const char *mpd_clamp_string[MPD_CLAMP_GUARD]; - - -typedef struct mpd_context_t { - mpd_ssize_t prec; /* precision */ - mpd_ssize_t emax; /* max positive exp */ - mpd_ssize_t emin; /* min negative exp */ - uint32_t traps; /* status events that should be trapped */ - uint32_t status; /* status flags */ - uint32_t newtrap; /* set by mpd_addstatus_raise() */ - int round; /* rounding mode */ - int clamp; /* clamp mode */ - int allcr; /* all functions correctly rounded */ -} mpd_context_t; - - -/* Status flags */ -#define MPD_Clamped 0x00000001U -#define MPD_Conversion_syntax 0x00000002U -#define MPD_Division_by_zero 0x00000004U -#define MPD_Division_impossible 0x00000008U -#define MPD_Division_undefined 0x00000010U -#define MPD_Fpu_error 0x00000020U -#define MPD_Inexact 0x00000040U -#define MPD_Invalid_context 0x00000080U -#define MPD_Invalid_operation 0x00000100U -#define MPD_Malloc_error 0x00000200U -#define MPD_Not_implemented 0x00000400U -#define MPD_Overflow 0x00000800U -#define MPD_Rounded 0x00001000U -#define MPD_Subnormal 0x00002000U -#define MPD_Underflow 0x00004000U -#define MPD_Max_status (0x00008000U-1U) - -/* Conditions that result in an IEEE 754 exception */ -#define MPD_IEEE_Invalid_operation (MPD_Conversion_syntax | \ - MPD_Division_impossible | \ - MPD_Division_undefined | \ - MPD_Fpu_error | \ - MPD_Invalid_context | \ - MPD_Invalid_operation | \ - MPD_Malloc_error) \ - -/* Errors that require the result of an operation to be set to NaN */ -#define MPD_Errors (MPD_IEEE_Invalid_operation | \ - MPD_Division_by_zero) - -/* Default traps */ -#define MPD_Traps (MPD_IEEE_Invalid_operation | \ - MPD_Division_by_zero | \ - MPD_Overflow | \ - MPD_Underflow) - -/* Official name */ -#define MPD_Insufficient_storage MPD_Malloc_error - -/* IEEE 754 interchange format contexts */ -#define MPD_IEEE_CONTEXT_MAX_BITS 512 /* 16*(log2(MPD_MAX_EMAX / 3)-3) */ -#define MPD_DECIMAL32 32 -#define MPD_DECIMAL64 64 -#define MPD_DECIMAL128 128 - - -#define MPD_MINALLOC_MIN 2 -#define MPD_MINALLOC_MAX 64 -extern mpd_ssize_t MPD_MINALLOC; -extern void (* mpd_traphandler)(mpd_context_t *); -void mpd_dflt_traphandler(mpd_context_t *); - -void mpd_setminalloc(mpd_ssize_t n); -void mpd_init(mpd_context_t *ctx, mpd_ssize_t prec); - -void mpd_maxcontext(mpd_context_t *ctx); -void mpd_defaultcontext(mpd_context_t *ctx); -void mpd_basiccontext(mpd_context_t *ctx); -int mpd_ieee_context(mpd_context_t *ctx, int bits); - -mpd_ssize_t mpd_getprec(const mpd_context_t *ctx); -mpd_ssize_t mpd_getemax(const mpd_context_t *ctx); -mpd_ssize_t mpd_getemin(const mpd_context_t *ctx); -int mpd_getround(const mpd_context_t *ctx); -uint32_t mpd_gettraps(const mpd_context_t *ctx); -uint32_t mpd_getstatus(const mpd_context_t *ctx); -int mpd_getclamp(const mpd_context_t *ctx); -int mpd_getcr(const mpd_context_t *ctx); - -int mpd_qsetprec(mpd_context_t *ctx, mpd_ssize_t prec); -int mpd_qsetemax(mpd_context_t *ctx, mpd_ssize_t emax); -int mpd_qsetemin(mpd_context_t *ctx, mpd_ssize_t emin); -int mpd_qsetround(mpd_context_t *ctx, int newround); -int mpd_qsettraps(mpd_context_t *ctx, uint32_t flags); -int mpd_qsetstatus(mpd_context_t *ctx, uint32_t flags); -int mpd_qsetclamp(mpd_context_t *ctx, int c); -int mpd_qsetcr(mpd_context_t *ctx, int c); -void mpd_addstatus_raise(mpd_context_t *ctx, uint32_t flags); - - -/******************************************************************************/ -/* Decimal Arithmetic */ -/******************************************************************************/ - -/* mpd_t flags */ -#define MPD_POS ((uint8_t)0) -#define MPD_NEG ((uint8_t)1) -#define MPD_INF ((uint8_t)2) -#define MPD_NAN ((uint8_t)4) -#define MPD_SNAN ((uint8_t)8) -#define MPD_SPECIAL (MPD_INF|MPD_NAN|MPD_SNAN) -#define MPD_STATIC ((uint8_t)16) -#define MPD_STATIC_DATA ((uint8_t)32) -#define MPD_SHARED_DATA ((uint8_t)64) -#define MPD_CONST_DATA ((uint8_t)128) -#define MPD_DATAFLAGS (MPD_STATIC_DATA|MPD_SHARED_DATA|MPD_CONST_DATA) - -/* mpd_t */ -typedef struct mpd_t { - uint8_t flags; - mpd_ssize_t exp; - mpd_ssize_t digits; - mpd_ssize_t len; - mpd_ssize_t alloc; - mpd_uint_t *data; -} mpd_t; - - -typedef unsigned char uchar; - - -/******************************************************************************/ -/* Quiet, thread-safe functions */ -/******************************************************************************/ - -/* format specification */ -typedef struct mpd_spec_t { - mpd_ssize_t min_width; /* minimum field width */ - mpd_ssize_t prec; /* fraction digits or significant digits */ - char type; /* conversion specifier */ - char align; /* alignment */ - char sign; /* sign printing/alignment */ - char fill[5]; /* fill character */ - const char *dot; /* decimal point */ - const char *sep; /* thousands separator */ - const char *grouping; /* grouping of digits */ -} mpd_spec_t; - -/* output to a string */ -char *mpd_to_sci(const mpd_t *dec, int fmt); -char *mpd_to_eng(const mpd_t *dec, int fmt); -mpd_ssize_t mpd_to_sci_size(char **res, const mpd_t *dec, int fmt); -mpd_ssize_t mpd_to_eng_size(char **res, const mpd_t *dec, int fmt); -int mpd_validate_lconv(mpd_spec_t *spec); -int mpd_parse_fmt_str(mpd_spec_t *spec, const char *fmt, int caps); -char *mpd_qformat_spec(const mpd_t *dec, const mpd_spec_t *spec, const mpd_context_t *ctx, uint32_t *status); -char *mpd_qformat(const mpd_t *dec, const char *fmt, const mpd_context_t *ctx, uint32_t *status); - -#define MPD_NUM_FLAGS 15 -#define MPD_MAX_FLAG_STRING 208 -#define MPD_MAX_FLAG_LIST (MPD_MAX_FLAG_STRING+18) -#define MPD_MAX_SIGNAL_LIST 121 -int mpd_snprint_flags(char *dest, int nmemb, uint32_t flags); -int mpd_lsnprint_flags(char *dest, int nmemb, uint32_t flags, const char *flag_string[]); -int mpd_lsnprint_signals(char *dest, int nmemb, uint32_t flags, const char *signal_string[]); - -/* output to a file */ -void mpd_fprint(FILE *file, const mpd_t *dec); -void mpd_print(const mpd_t *dec); - -/* assignment from a string */ -void mpd_qset_string(mpd_t *dec, const char *s, const mpd_context_t *ctx, uint32_t *status); - -/* set to NaN with error flags */ -void mpd_seterror(mpd_t *result, uint32_t flags, uint32_t *status); -/* set a special with sign and type */ -void mpd_setspecial(mpd_t *dec, uint8_t sign, uint8_t type); -/* set coefficient to zero or all nines */ -void mpd_zerocoeff(mpd_t *result); -void mpd_qmaxcoeff(mpd_t *result, const mpd_context_t *ctx, uint32_t *status); - -/* quietly assign a C integer type to an mpd_t */ -void mpd_qset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, uint32_t *status); -#ifndef LEGACY_COMPILER -void mpd_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, uint32_t *status); -#endif - -/* quietly assign a C integer type to an mpd_t with a static coefficient */ -void mpd_qsset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, uint32_t *status); - -/* quietly get a C integer type from an mpd_t */ -mpd_ssize_t mpd_qget_ssize(const mpd_t *dec, uint32_t *status); -mpd_uint_t mpd_qget_uint(const mpd_t *dec, uint32_t *status); -mpd_uint_t mpd_qabs_uint(const mpd_t *dec, uint32_t *status); - -int32_t mpd_qget_i32(const mpd_t *dec, uint32_t *status); -uint32_t mpd_qget_u32(const mpd_t *dec, uint32_t *status); -#ifndef LEGACY_COMPILER -int64_t mpd_qget_i64(const mpd_t *dec, uint32_t *status); -uint64_t mpd_qget_u64(const mpd_t *dec, uint32_t *status); -#endif - -/* quiet functions */ -int mpd_qcheck_nan(mpd_t *nanresult, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -int mpd_qcheck_nans(mpd_t *nanresult, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qfinalize(mpd_t *result, const mpd_context_t *ctx, uint32_t *status); - -const char *mpd_class(const mpd_t *a, const mpd_context_t *ctx); - -int mpd_qcopy(mpd_t *result, const mpd_t *a, uint32_t *status); -mpd_t *mpd_qncopy(const mpd_t *a); -int mpd_qcopy_abs(mpd_t *result, const mpd_t *a, uint32_t *status); -int mpd_qcopy_negate(mpd_t *result, const mpd_t *a, uint32_t *status); -int mpd_qcopy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status); - -void mpd_qand(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qinvert(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qlogb(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qor(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qscaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qxor(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -int mpd_same_quantum(const mpd_t *a, const mpd_t *b); - -void mpd_qrotate(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -int mpd_qshiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status); -mpd_uint_t mpd_qshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status); -mpd_uint_t mpd_qshiftr_inplace(mpd_t *result, mpd_ssize_t n); -void mpd_qshift(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qshiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, const mpd_context_t *ctx, uint32_t *status); - -int mpd_qcmp(const mpd_t *a, const mpd_t *b, uint32_t *status); -int mpd_qcompare(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -int mpd_qcompare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -int mpd_cmp_total(const mpd_t *a, const mpd_t *b); -int mpd_cmp_total_mag(const mpd_t *a, const mpd_t *b); -int mpd_compare_total(mpd_t *result, const mpd_t *a, const mpd_t *b); -int mpd_compare_total_mag(mpd_t *result, const mpd_t *a, const mpd_t *b); - -void mpd_qround_to_intx(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qround_to_int(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qtrunc(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qfloor(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qceil(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); - -void mpd_qabs(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmax(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmax_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmin(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmin_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qminus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qplus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qnext_minus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qnext_plus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qnext_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qquantize(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, const mpd_context_t *ctx, uint32_t *status); -void mpd_qrescale_fmt(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, const mpd_context_t *ctx, uint32_t *status); -void mpd_qreduce(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qadd_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qadd_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qadd_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qadd_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qfma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv(mpd_t *q, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdivint(mpd_t *q, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qrem(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qrem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qpow(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_context_t *ctx, uint32_t *status); -void mpd_qpowmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod, const mpd_context_t *ctx, uint32_t *status); -void mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qln10(mpd_t *result, mpd_ssize_t prec, uint32_t *status); -void mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); - -#ifndef LEGACY_COMPILER -void mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status); -#endif - - -size_t mpd_sizeinbase(const mpd_t *a, uint32_t base); -void mpd_qimport_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen, - uint8_t srcsign, uint32_t srcbase, - const mpd_context_t *ctx, uint32_t *status); -void mpd_qimport_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen, - uint8_t srcsign, uint32_t srcbase, - const mpd_context_t *ctx, uint32_t *status); -size_t mpd_qexport_u16(uint16_t **rdata, size_t rlen, uint32_t base, - const mpd_t *src, uint32_t *status); -size_t mpd_qexport_u32(uint32_t **rdata, size_t rlen, uint32_t base, - const mpd_t *src, uint32_t *status); - - -/******************************************************************************/ -/* Signalling functions */ -/******************************************************************************/ - -char *mpd_format(const mpd_t *dec, const char *fmt, mpd_context_t *ctx); -void mpd_import_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen, uint8_t srcsign, uint32_t base, mpd_context_t *ctx); -void mpd_import_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen, uint8_t srcsign, uint32_t base, mpd_context_t *ctx); -size_t mpd_export_u16(uint16_t **rdata, size_t rlen, uint32_t base, const mpd_t *src, mpd_context_t *ctx); -size_t mpd_export_u32(uint32_t **rdata, size_t rlen, uint32_t base, const mpd_t *src, mpd_context_t *ctx); -void mpd_finalize(mpd_t *result, mpd_context_t *ctx); -int mpd_check_nan(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -int mpd_check_nans(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_set_string(mpd_t *result, const char *s, mpd_context_t *ctx); -void mpd_maxcoeff(mpd_t *result, mpd_context_t *ctx); -void mpd_sset_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx); -void mpd_sset_i32(mpd_t *result, int32_t a, mpd_context_t *ctx); -void mpd_sset_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx); -void mpd_sset_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx); -void mpd_set_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx); -void mpd_set_i32(mpd_t *result, int32_t a, mpd_context_t *ctx); -void mpd_set_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx); -void mpd_set_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx); -#ifndef LEGACY_COMPILER -void mpd_set_i64(mpd_t *result, int64_t a, mpd_context_t *ctx); -void mpd_set_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx); -#endif -mpd_ssize_t mpd_get_ssize(const mpd_t *a, mpd_context_t *ctx); -mpd_uint_t mpd_get_uint(const mpd_t *a, mpd_context_t *ctx); -mpd_uint_t mpd_abs_uint(const mpd_t *a, mpd_context_t *ctx); -int32_t mpd_get_i32(const mpd_t *a, mpd_context_t *ctx); -uint32_t mpd_get_u32(const mpd_t *a, mpd_context_t *ctx); -#ifndef LEGACY_COMPILER -int64_t mpd_get_i64(const mpd_t *a, mpd_context_t *ctx); -uint64_t mpd_get_u64(const mpd_t *a, mpd_context_t *ctx); -#endif -void mpd_and(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_copy(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_canonical(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_copy_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_copy_negate(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_copy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_invert(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_logb(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_or(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_rotate(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_scaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_shiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx); -mpd_uint_t mpd_shiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx); -void mpd_shiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx); -void mpd_shift(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_xor(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -int mpd_cmp(const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -int mpd_compare(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -int mpd_compare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_add(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_add_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx); -void mpd_add_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx); -void mpd_add_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx); -void mpd_add_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx); -void mpd_sub(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_sub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx); -void mpd_sub_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx); -void mpd_sub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx); -void mpd_sub_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx); -void mpd_div(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_div_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx); -void mpd_div_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx); -void mpd_div_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx); -void mpd_div_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx); -void mpd_divmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_divint(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_exp(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_fma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, mpd_context_t *ctx); -void mpd_ln(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_log10(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_max(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_max_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_min(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_min_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_mul(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_mul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx); -void mpd_mul_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx); -void mpd_mul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx); -void mpd_mul_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx); -void mpd_next_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_next_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_next_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_pow(mpd_t *result, const mpd_t *base, const mpd_t *exp, mpd_context_t *ctx); -void mpd_powmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod, mpd_context_t *ctx); -void mpd_quantize(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_rescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, mpd_context_t *ctx); -void mpd_reduce(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_rem(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_rem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_round_to_intx(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_round_to_int(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_trunc(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_floor(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_ceil(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_sqrt(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_invroot(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); - -#ifndef LEGACY_COMPILER -void mpd_add_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx); -void mpd_add_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx); -void mpd_sub_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx); -void mpd_sub_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx); -void mpd_div_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx); -void mpd_div_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx); -void mpd_mul_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx); -void mpd_mul_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx); -#endif - - -/******************************************************************************/ -/* Configuration specific */ -/******************************************************************************/ - -#ifdef CONFIG_64 -void mpd_qsset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_sset_i64(mpd_t *result, int64_t a, mpd_context_t *ctx); -void mpd_sset_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx); -#endif - - -/******************************************************************************/ -/* Get attributes of a decimal */ -/******************************************************************************/ - -EXTINLINE mpd_ssize_t mpd_adjexp(const mpd_t *dec); -EXTINLINE mpd_ssize_t mpd_etiny(const mpd_context_t *ctx); -EXTINLINE mpd_ssize_t mpd_etop(const mpd_context_t *ctx); -EXTINLINE mpd_uint_t mpd_msword(const mpd_t *dec); -EXTINLINE int mpd_word_digits(mpd_uint_t word); -/* most significant digit of a word */ -EXTINLINE mpd_uint_t mpd_msd(mpd_uint_t word); -/* least significant digit of a word */ -EXTINLINE mpd_uint_t mpd_lsd(mpd_uint_t word); -/* coefficient size needed to store 'digits' */ -EXTINLINE mpd_ssize_t mpd_digits_to_size(mpd_ssize_t digits); -/* number of digits in the exponent, undefined for MPD_SSIZE_MIN */ -EXTINLINE int mpd_exp_digits(mpd_ssize_t exp); -EXTINLINE int mpd_iscanonical(const mpd_t *dec UNUSED); -EXTINLINE int mpd_isfinite(const mpd_t *dec); -EXTINLINE int mpd_isinfinite(const mpd_t *dec); -EXTINLINE int mpd_isinteger(const mpd_t *dec); -EXTINLINE int mpd_isnan(const mpd_t *dec); -EXTINLINE int mpd_isnegative(const mpd_t *dec); -EXTINLINE int mpd_ispositive(const mpd_t *dec); -EXTINLINE int mpd_isqnan(const mpd_t *dec); -EXTINLINE int mpd_issigned(const mpd_t *dec); -EXTINLINE int mpd_issnan(const mpd_t *dec); -EXTINLINE int mpd_isspecial(const mpd_t *dec); -EXTINLINE int mpd_iszero(const mpd_t *dec); -/* undefined for special numbers */ -EXTINLINE int mpd_iszerocoeff(const mpd_t *dec); -EXTINLINE int mpd_isnormal(const mpd_t *dec, const mpd_context_t *ctx); -EXTINLINE int mpd_issubnormal(const mpd_t *dec, const mpd_context_t *ctx); -/* odd word */ -EXTINLINE int mpd_isoddword(mpd_uint_t word); -/* odd coefficient */ -EXTINLINE int mpd_isoddcoeff(const mpd_t *dec); -/* odd decimal, only defined for integers */ -int mpd_isodd(const mpd_t *dec); -/* even decimal, only defined for integers */ -int mpd_iseven(const mpd_t *dec); -/* 0 if dec is positive, 1 if dec is negative */ -EXTINLINE uint8_t mpd_sign(const mpd_t *dec); -/* 1 if dec is positive, -1 if dec is negative */ -EXTINLINE int mpd_arith_sign(const mpd_t *dec); -EXTINLINE long mpd_radix(void); -EXTINLINE int mpd_isdynamic(const mpd_t *dec); -EXTINLINE int mpd_isstatic(const mpd_t *dec); -EXTINLINE int mpd_isdynamic_data(const mpd_t *dec); -EXTINLINE int mpd_isstatic_data(const mpd_t *dec); -EXTINLINE int mpd_isshared_data(const mpd_t *dec); -EXTINLINE int mpd_isconst_data(const mpd_t *dec); -EXTINLINE mpd_ssize_t mpd_trail_zeros(const mpd_t *dec); - - -/******************************************************************************/ -/* Set attributes of a decimal */ -/******************************************************************************/ - -/* set number of decimal digits in the coefficient */ -EXTINLINE void mpd_setdigits(mpd_t *result); -EXTINLINE void mpd_set_sign(mpd_t *result, uint8_t sign); -/* copy sign from another decimal */ -EXTINLINE void mpd_signcpy(mpd_t *result, const mpd_t *a); -EXTINLINE void mpd_set_infinity(mpd_t *result); -EXTINLINE void mpd_set_qnan(mpd_t *result); -EXTINLINE void mpd_set_snan(mpd_t *result); -EXTINLINE void mpd_set_negative(mpd_t *result); -EXTINLINE void mpd_set_positive(mpd_t *result); -EXTINLINE void mpd_set_dynamic(mpd_t *result); -EXTINLINE void mpd_set_static(mpd_t *result); -EXTINLINE void mpd_set_dynamic_data(mpd_t *result); -EXTINLINE void mpd_set_static_data(mpd_t *result); -EXTINLINE void mpd_set_shared_data(mpd_t *result); -EXTINLINE void mpd_set_const_data(mpd_t *result); -EXTINLINE void mpd_clear_flags(mpd_t *result); -EXTINLINE void mpd_set_flags(mpd_t *result, uint8_t flags); -EXTINLINE void mpd_copy_flags(mpd_t *result, const mpd_t *a); - - -/******************************************************************************/ -/* Error Macros */ -/******************************************************************************/ - -#define mpd_err_fatal(...) \ - do {fprintf(stderr, "%s:%d: error: ", __FILE__, __LINE__); \ - fprintf(stderr, __VA_ARGS__); fputc('\n', stderr); \ - abort(); \ - } while (0) -#define mpd_err_warn(...) \ - do {fprintf(stderr, "%s:%d: warning: ", __FILE__, __LINE__); \ - fprintf(stderr, __VA_ARGS__); fputc('\n', stderr); \ - } while (0) - - -/******************************************************************************/ -/* Memory handling */ -/******************************************************************************/ - -extern void *(* mpd_mallocfunc)(size_t size); -extern void *(* mpd_callocfunc)(size_t nmemb, size_t size); -extern void *(* mpd_reallocfunc)(void *ptr, size_t size); -extern void (* mpd_free)(void *ptr); - -void *mpd_callocfunc_em(size_t nmemb, size_t size); - -void *mpd_alloc(mpd_size_t nmemb, mpd_size_t size); -void *mpd_calloc(mpd_size_t nmemb, mpd_size_t size); -void *mpd_realloc(void *ptr, mpd_size_t nmemb, mpd_size_t size, uint8_t *err); -void *mpd_sh_alloc(mpd_size_t struct_size, mpd_size_t nmemb, mpd_size_t size); - -mpd_t *mpd_qnew(void); -mpd_t *mpd_new(mpd_context_t *ctx); -mpd_t *mpd_qnew_size(mpd_ssize_t size); -EXTINLINE void mpd_del(mpd_t *dec); - -EXTINLINE void mpd_uint_zero(mpd_uint_t *dest, mpd_size_t len); -EXTINLINE int mpd_qresize(mpd_t *result, mpd_ssize_t size, uint32_t *status); -EXTINLINE int mpd_qresize_zero(mpd_t *result, mpd_ssize_t size, uint32_t *status); -EXTINLINE void mpd_minalloc(mpd_t *result); - -int mpd_resize(mpd_t *result, mpd_ssize_t size, mpd_context_t *ctx); -int mpd_resize_zero(mpd_t *result, mpd_ssize_t size, mpd_context_t *ctx); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#ifdef __cplusplus - #ifdef MPD_CLEAR_STDC_LIMIT_MACROS - #undef MPD_CLEAR_STDC_LIMIT_MACROS - #undef __STDC_LIMIT_MACROS - #endif -} /* END extern "C" */ -#endif - - -#endif /* MPDECIMAL_H */ - - - diff --git a/Modules/_decimal/libmpdec/numbertheory.c b/Modules/_decimal/libmpdec/numbertheory.c deleted file mode 100644 index 4e03547..0000000 --- a/Modules/_decimal/libmpdec/numbertheory.c +++ /dev/null @@ -1,132 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdlib.h> -#include <assert.h> -#include "bits.h" -#include "umodarith.h" -#include "numbertheory.h" - - -/* Bignum: Initialize the Number Theoretic Transform. */ - - -/* - * Return the nth root of unity in F(p). This corresponds to e**((2*pi*i)/n) - * in the Fourier transform. We have w**n == 1 (mod p). - * n := transform length. - * sign := -1 for forward transform, 1 for backward transform. - * modnum := one of {P1, P2, P3}. - */ -mpd_uint_t -_mpd_getkernel(mpd_uint_t n, int sign, int modnum) -{ - mpd_uint_t umod, p, r, xi; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - - SETMODULUS(modnum); - r = mpd_roots[modnum]; /* primitive root of F(p) */ - p = umod; - xi = (p-1) / n; - - if (sign == -1) - return POWMOD(r, (p-1-xi)); - else - return POWMOD(r, xi); -} - -/* - * Initialize and return transform parameters. - * n := transform length. - * sign := -1 for forward transform, 1 for backward transform. - * modnum := one of {P1, P2, P3}. - */ -struct fnt_params * -_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum) -{ - struct fnt_params *tparams; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t kernel, w; - mpd_uint_t i; - mpd_size_t nhalf; - - assert(ispower2(n)); - assert(sign == -1 || sign == 1); - assert(P1 <= modnum && modnum <= P3); - - nhalf = n/2; - tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t)); - if (tparams == NULL) { - return NULL; - } - - SETMODULUS(modnum); - kernel = _mpd_getkernel(n, sign, modnum); - - tparams->modnum = modnum; - tparams->modulus = umod; - tparams->kernel = kernel; - - /* wtable[] := w**0, w**1, ..., w**(nhalf-1) */ - w = 1; - for (i = 0; i < nhalf; i++) { - tparams->wtable[i] = w; - w = MULMOD(w, kernel); - } - - return tparams; -} - -/* Initialize wtable of size three. */ -void -_mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum) -{ - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t kernel; - - SETMODULUS(modnum); - kernel = _mpd_getkernel(3, sign, modnum); - - w3table[0] = 1; - w3table[1] = kernel; - w3table[2] = POWMOD(kernel, 2); -} - - diff --git a/Modules/_decimal/libmpdec/numbertheory.h b/Modules/_decimal/libmpdec/numbertheory.h deleted file mode 100644 index e94c157..0000000 --- a/Modules/_decimal/libmpdec/numbertheory.h +++ /dev/null @@ -1,78 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef NUMBER_THEORY_H -#define NUMBER_THEORY_H - - -#include "constants.h" -#include "mpdecimal.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -/* transform parameters */ -struct fnt_params { - int modnum; - mpd_uint_t modulus; - mpd_uint_t kernel; - mpd_uint_t wtable[]; -}; - - -mpd_uint_t _mpd_getkernel(mpd_uint_t n, int sign, int modnum); -struct fnt_params *_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum); -void _mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum); - - -#ifdef PPRO -static inline void -ppro_setmodulus(int modnum, mpd_uint_t *umod, double *dmod, uint32_t dinvmod[3]) -{ - *dmod = *umod = mpd_moduli[modnum]; - dinvmod[0] = mpd_invmoduli[modnum][0]; - dinvmod[1] = mpd_invmoduli[modnum][1]; - dinvmod[2] = mpd_invmoduli[modnum][2]; -} -#else -static inline void -std_setmodulus(int modnum, mpd_uint_t *umod) -{ - *umod = mpd_moduli[modnum]; -} -#endif - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif - - diff --git a/Modules/_decimal/libmpdec/sixstep.c b/Modules/_decimal/libmpdec/sixstep.c deleted file mode 100644 index 92d513e..0000000 --- a/Modules/_decimal/libmpdec/sixstep.c +++ /dev/null @@ -1,214 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdio.h> -#include <stdlib.h> -#include <assert.h> -#include "bits.h" -#include "difradix2.h" -#include "numbertheory.h" -#include "transpose.h" -#include "umodarith.h" -#include "sixstep.h" - - -/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the - form 2**n (See literature/six-step.txt). */ - - -/* forward transform with sign = -1 */ -int -six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) -{ - struct fnt_params *tparams; - mpd_size_t log2n, C, R; - mpd_uint_t kernel; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t *x, w0, w1, wstep; - mpd_size_t i, k; - - - assert(ispower2(n)); - assert(n >= 16); - assert(n <= MPD_MAXTRANSFORM_2N); - - log2n = mpd_bsr(n); - C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */ - R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */ - - - /* Transpose the matrix. */ - if (!transpose_pow2(a, R, C)) { - return 0; - } - - /* Length R transform on the rows. */ - if ((tparams = _mpd_init_fnt_params(R, -1, modnum)) == NULL) { - return 0; - } - for (x = a; x < a+n; x += R) { - fnt_dif2(x, R, tparams); - } - - /* Transpose the matrix. */ - if (!transpose_pow2(a, C, R)) { - mpd_free(tparams); - return 0; - } - - /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */ - SETMODULUS(modnum); - kernel = _mpd_getkernel(n, -1, modnum); - for (i = 1; i < R; i++) { - w0 = 1; /* r**(i*0): initial value for k=0 */ - w1 = POWMOD(kernel, i); /* r**(i*1): initial value for k=1 */ - wstep = MULMOD(w1, w1); /* r**(2*i) */ - for (k = 0; k < C; k += 2) { - mpd_uint_t x0 = a[i*C+k]; - mpd_uint_t x1 = a[i*C+k+1]; - MULMOD2(&x0, w0, &x1, w1); - MULMOD2C(&w0, &w1, wstep); /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */ - a[i*C+k] = x0; - a[i*C+k+1] = x1; - } - } - - /* Length C transform on the rows. */ - if (C != R) { - mpd_free(tparams); - if ((tparams = _mpd_init_fnt_params(C, -1, modnum)) == NULL) { - return 0; - } - } - for (x = a; x < a+n; x += C) { - fnt_dif2(x, C, tparams); - } - mpd_free(tparams); - -#if 0 - /* An unordered transform is sufficient for convolution. */ - /* Transpose the matrix. */ - if (!transpose_pow2(a, R, C)) { - return 0; - } -#endif - - return 1; -} - - -/* reverse transform, sign = 1 */ -int -inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) -{ - struct fnt_params *tparams; - mpd_size_t log2n, C, R; - mpd_uint_t kernel; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t *x, w0, w1, wstep; - mpd_size_t i, k; - - - assert(ispower2(n)); - assert(n >= 16); - assert(n <= MPD_MAXTRANSFORM_2N); - - log2n = mpd_bsr(n); - C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */ - R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */ - - -#if 0 - /* An unordered transform is sufficient for convolution. */ - /* Transpose the matrix, producing an R*C matrix. */ - if (!transpose_pow2(a, C, R)) { - return 0; - } -#endif - - /* Length C transform on the rows. */ - if ((tparams = _mpd_init_fnt_params(C, 1, modnum)) == NULL) { - return 0; - } - for (x = a; x < a+n; x += C) { - fnt_dif2(x, C, tparams); - } - - /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */ - SETMODULUS(modnum); - kernel = _mpd_getkernel(n, 1, modnum); - for (i = 1; i < R; i++) { - w0 = 1; - w1 = POWMOD(kernel, i); - wstep = MULMOD(w1, w1); - for (k = 0; k < C; k += 2) { - mpd_uint_t x0 = a[i*C+k]; - mpd_uint_t x1 = a[i*C+k+1]; - MULMOD2(&x0, w0, &x1, w1); - MULMOD2C(&w0, &w1, wstep); - a[i*C+k] = x0; - a[i*C+k+1] = x1; - } - } - - /* Transpose the matrix. */ - if (!transpose_pow2(a, R, C)) { - mpd_free(tparams); - return 0; - } - - /* Length R transform on the rows. */ - if (R != C) { - mpd_free(tparams); - if ((tparams = _mpd_init_fnt_params(R, 1, modnum)) == NULL) { - return 0; - } - } - for (x = a; x < a+n; x += R) { - fnt_dif2(x, R, tparams); - } - mpd_free(tparams); - - /* Transpose the matrix. */ - if (!transpose_pow2(a, C, R)) { - return 0; - } - - return 1; -} - - diff --git a/Modules/_decimal/libmpdec/sixstep.h b/Modules/_decimal/libmpdec/sixstep.h deleted file mode 100644 index 4a8b015..0000000 --- a/Modules/_decimal/libmpdec/sixstep.h +++ /dev/null @@ -1,48 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef SIX_STEP_H -#define SIX_STEP_H - - -#include "mpdecimal.h" -#include <stdio.h> - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -int six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum); -int inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif diff --git a/Modules/_decimal/libmpdec/transpose.c b/Modules/_decimal/libmpdec/transpose.c deleted file mode 100644 index 55d6d89..0000000 --- a/Modules/_decimal/libmpdec/transpose.c +++ /dev/null @@ -1,276 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include <stdio.h> -#include <stdlib.h> -#include <string.h> -#include <limits.h> -#include <assert.h> -#include "bits.h" -#include "constants.h" -#include "typearith.h" -#include "transpose.h" - - -#define BUFSIZE 4096 -#define SIDE 128 - - -/* Bignum: The transpose functions are used for very large transforms - in sixstep.c and fourstep.c. */ - - -/* Definition of the matrix transpose */ -void -std_trans(mpd_uint_t dest[], mpd_uint_t src[], mpd_size_t rows, mpd_size_t cols) -{ - mpd_size_t idest, isrc; - mpd_size_t r, c; - - for (r = 0; r < rows; r++) { - isrc = r * cols; - idest = r; - for (c = 0; c < cols; c++) { - dest[idest] = src[isrc]; - isrc += 1; - idest += rows; - } - } -} - -/* - * Swap half-rows of 2^n * (2*2^n) matrix. - * FORWARD_CYCLE: even/odd permutation of the halfrows. - * BACKWARD_CYCLE: reverse the even/odd permutation. - */ -static int -swap_halfrows_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols, int dir) -{ - mpd_uint_t buf1[BUFSIZE]; - mpd_uint_t buf2[BUFSIZE]; - mpd_uint_t *readbuf, *writebuf, *hp; - mpd_size_t *done, dbits; - mpd_size_t b = BUFSIZE, stride; - mpd_size_t hn, hmax; /* halfrow number */ - mpd_size_t m, r=0; - mpd_size_t offset; - mpd_size_t next; - - - assert(cols == mul_size_t(2, rows)); - - if (dir == FORWARD_CYCLE) { - r = rows; - } - else if (dir == BACKWARD_CYCLE) { - r = 2; - } - else { - abort(); /* GCOV_NOT_REACHED */ - } - - m = cols - 1; - hmax = rows; /* cycles start at odd halfrows */ - dbits = 8 * sizeof *done; - if ((done = mpd_calloc(hmax/(sizeof *done) + 1, sizeof *done)) == NULL) { - return 0; - } - - for (hn = 1; hn <= hmax; hn += 2) { - - if (done[hn/dbits] & mpd_bits[hn%dbits]) { - continue; - } - - readbuf = buf1; writebuf = buf2; - - for (offset = 0; offset < cols/2; offset += b) { - - stride = (offset + b < cols/2) ? b : cols/2-offset; - - hp = matrix + hn*cols/2; - memcpy(readbuf, hp+offset, stride*(sizeof *readbuf)); - pointerswap(&readbuf, &writebuf); - - next = mulmod_size_t(hn, r, m); - hp = matrix + next*cols/2; - - while (next != hn) { - - memcpy(readbuf, hp+offset, stride*(sizeof *readbuf)); - memcpy(hp+offset, writebuf, stride*(sizeof *writebuf)); - pointerswap(&readbuf, &writebuf); - - done[next/dbits] |= mpd_bits[next%dbits]; - - next = mulmod_size_t(next, r, m); - hp = matrix + next*cols/2; - - } - - memcpy(hp+offset, writebuf, stride*(sizeof *writebuf)); - - done[hn/dbits] |= mpd_bits[hn%dbits]; - } - } - - mpd_free(done); - return 1; -} - -/* In-place transpose of a square matrix */ -static inline void -squaretrans(mpd_uint_t *buf, mpd_size_t cols) -{ - mpd_uint_t tmp; - mpd_size_t idest, isrc; - mpd_size_t r, c; - - for (r = 0; r < cols; r++) { - c = r+1; - isrc = r*cols + c; - idest = c*cols + r; - for (c = r+1; c < cols; c++) { - tmp = buf[isrc]; - buf[isrc] = buf[idest]; - buf[idest] = tmp; - isrc += 1; - idest += cols; - } - } -} - -/* - * Transpose 2^n * 2^n matrix. For cache efficiency, the matrix is split into - * square blocks with side length 'SIDE'. First, the blocks are transposed, - * then a square transposition is done on each individual block. - */ -static void -squaretrans_pow2(mpd_uint_t *matrix, mpd_size_t size) -{ - mpd_uint_t buf1[SIDE*SIDE]; - mpd_uint_t buf2[SIDE*SIDE]; - mpd_uint_t *to, *from; - mpd_size_t b = size; - mpd_size_t r, c; - mpd_size_t i; - - while (b > SIDE) b >>= 1; - - for (r = 0; r < size; r += b) { - - for (c = r; c < size; c += b) { - - from = matrix + r*size + c; - to = buf1; - for (i = 0; i < b; i++) { - memcpy(to, from, b*(sizeof *to)); - from += size; - to += b; - } - squaretrans(buf1, b); - - if (r == c) { - to = matrix + r*size + c; - from = buf1; - for (i = 0; i < b; i++) { - memcpy(to, from, b*(sizeof *to)); - from += b; - to += size; - } - continue; - } - else { - from = matrix + c*size + r; - to = buf2; - for (i = 0; i < b; i++) { - memcpy(to, from, b*(sizeof *to)); - from += size; - to += b; - } - squaretrans(buf2, b); - - to = matrix + c*size + r; - from = buf1; - for (i = 0; i < b; i++) { - memcpy(to, from, b*(sizeof *to)); - from += b; - to += size; - } - - to = matrix + r*size + c; - from = buf2; - for (i = 0; i < b; i++) { - memcpy(to, from, b*(sizeof *to)); - from += b; - to += size; - } - } - } - } - -} - -/* - * In-place transposition of a 2^n x 2^n or a 2^n x (2*2^n) - * or a (2*2^n) x 2^n matrix. - */ -int -transpose_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols) -{ - mpd_size_t size = mul_size_t(rows, cols); - - assert(ispower2(rows)); - assert(ispower2(cols)); - - if (cols == rows) { - squaretrans_pow2(matrix, rows); - } - else if (cols == mul_size_t(2, rows)) { - if (!swap_halfrows_pow2(matrix, rows, cols, FORWARD_CYCLE)) { - return 0; - } - squaretrans_pow2(matrix, rows); - squaretrans_pow2(matrix+(size/2), rows); - } - else if (rows == mul_size_t(2, cols)) { - squaretrans_pow2(matrix, cols); - squaretrans_pow2(matrix+(size/2), cols); - if (!swap_halfrows_pow2(matrix, cols, rows, BACKWARD_CYCLE)) { - return 0; - } - } - else { - abort(); /* GCOV_NOT_REACHED */ - } - - return 1; -} - - diff --git a/Modules/_decimal/libmpdec/transpose.h b/Modules/_decimal/libmpdec/transpose.h deleted file mode 100644 index e1cd1fa..0000000 --- a/Modules/_decimal/libmpdec/transpose.h +++ /dev/null @@ -1,62 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef TRANSPOSE_H -#define TRANSPOSE_H - - -#include "mpdecimal.h" -#include <stdio.h> - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -enum {FORWARD_CYCLE, BACKWARD_CYCLE}; - - -void std_trans(mpd_uint_t dest[], mpd_uint_t src[], mpd_size_t rows, mpd_size_t cols); -int transpose_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols); -void transpose_3xpow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols); - - -static inline void pointerswap(mpd_uint_t **a, mpd_uint_t **b) -{ - mpd_uint_t *tmp; - - tmp = *b; - *b = *a; - *a = tmp; -} - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif diff --git a/Modules/_decimal/libmpdec/typearith.h b/Modules/_decimal/libmpdec/typearith.h deleted file mode 100644 index 405237d..0000000 --- a/Modules/_decimal/libmpdec/typearith.h +++ /dev/null @@ -1,669 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef TYPEARITH_H -#define TYPEARITH_H - - -#include "mpdecimal.h" - - -/*****************************************************************************/ -/* Low level native arithmetic on basic types */ -/*****************************************************************************/ - - -/** ------------------------------------------------------------ - ** Double width multiplication and division - ** ------------------------------------------------------------ - */ - -#if defined(CONFIG_64) -#if defined(ANSI) -#if defined(HAVE_UINT128_T) -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - __uint128_t hl; - - hl = (__uint128_t)a * b; - - *hi = hl >> 64; - *lo = (mpd_uint_t)hl; -} - -static inline void -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo, - mpd_uint_t d) -{ - __uint128_t hl; - - hl = ((__uint128_t)hi<<64) + lo; - *q = (mpd_uint_t)(hl / d); /* quotient is known to fit */ - *r = (mpd_uint_t)(hl - (__uint128_t)(*q) * d); -} -#else -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - uint32_t w[4], carry; - uint32_t ah, al, bh, bl; - uint64_t hl; - - ah = (uint32_t)(a>>32); al = (uint32_t)a; - bh = (uint32_t)(b>>32); bl = (uint32_t)b; - - hl = (uint64_t)al * bl; - w[0] = (uint32_t)hl; - carry = (uint32_t)(hl>>32); - - hl = (uint64_t)ah * bl + carry; - w[1] = (uint32_t)hl; - w[2] = (uint32_t)(hl>>32); - - hl = (uint64_t)al * bh + w[1]; - w[1] = (uint32_t)hl; - carry = (uint32_t)(hl>>32); - - hl = ((uint64_t)ah * bh + w[2]) + carry; - w[2] = (uint32_t)hl; - w[3] = (uint32_t)(hl>>32); - - *hi = ((uint64_t)w[3]<<32) + w[2]; - *lo = ((uint64_t)w[1]<<32) + w[0]; -} - -/* - * By Henry S. Warren: http://www.hackersdelight.org/HDcode/divlu.c.txt - * http://www.hackersdelight.org/permissions.htm: - * "You are free to use, copy, and distribute any of the code on this web - * site, whether modified by you or not. You need not give attribution." - * - * Slightly modified, comments are mine. - */ -static inline int -nlz(uint64_t x) -{ - int n; - - if (x == 0) return(64); - - n = 0; - if (x <= 0x00000000FFFFFFFF) {n = n +32; x = x <<32;} - if (x <= 0x0000FFFFFFFFFFFF) {n = n +16; x = x <<16;} - if (x <= 0x00FFFFFFFFFFFFFF) {n = n + 8; x = x << 8;} - if (x <= 0x0FFFFFFFFFFFFFFF) {n = n + 4; x = x << 4;} - if (x <= 0x3FFFFFFFFFFFFFFF) {n = n + 2; x = x << 2;} - if (x <= 0x7FFFFFFFFFFFFFFF) {n = n + 1;} - - return n; -} - -static inline void -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t u1, mpd_uint_t u0, - mpd_uint_t v) -{ - const mpd_uint_t b = 4294967296; - mpd_uint_t un1, un0, - vn1, vn0, - q1, q0, - un32, un21, un10, - rhat, t; - int s; - - assert(u1 < v); - - s = nlz(v); - v = v << s; - vn1 = v >> 32; - vn0 = v & 0xFFFFFFFF; - - t = (s == 0) ? 0 : u0 >> (64 - s); - un32 = (u1 << s) | t; - un10 = u0 << s; - - un1 = un10 >> 32; - un0 = un10 & 0xFFFFFFFF; - - q1 = un32 / vn1; - rhat = un32 - q1*vn1; -again1: - if (q1 >= b || q1*vn0 > b*rhat + un1) { - q1 = q1 - 1; - rhat = rhat + vn1; - if (rhat < b) goto again1; - } - - /* - * Before again1 we had: - * (1) q1*vn1 + rhat = un32 - * (2) q1*vn1*b + rhat*b + un1 = un32*b + un1 - * - * The statements inside the if-clause do not change the value - * of the left-hand side of (2), and the loop is only exited - * if q1*vn0 <= rhat*b + un1, so: - * - * (3) q1*vn1*b + q1*vn0 <= un32*b + un1 - * (4) q1*v <= un32*b + un1 - * (5) 0 <= un32*b + un1 - q1*v - * - * By (5) we are certain that the possible add-back step from - * Knuth's algorithm D is never required. - * - * Since the final quotient is less than 2**64, the following - * must be true: - * - * (6) un32*b + un1 - q1*v <= UINT64_MAX - * - * This means that in the following line, the high words - * of un32*b and q1*v can be discarded without any effect - * on the result. - */ - un21 = un32*b + un1 - q1*v; - - q0 = un21 / vn1; - rhat = un21 - q0*vn1; -again2: - if (q0 >= b || q0*vn0 > b*rhat + un0) { - q0 = q0 - 1; - rhat = rhat + vn1; - if (rhat < b) goto again2; - } - - *q = q1*b + q0; - *r = (un21*b + un0 - q0*v) >> s; -} -#endif - -/* END ANSI */ -#elif defined(ASM) -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - mpd_uint_t h, l; - - __asm__ ( "mulq %3\n\t" - : "=d" (h), "=a" (l) - : "%a" (a), "rm" (b) - : "cc" - ); - - *hi = h; - *lo = l; -} - -static inline void -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo, - mpd_uint_t d) -{ - mpd_uint_t qq, rr; - - __asm__ ( "divq %4\n\t" - : "=a" (qq), "=d" (rr) - : "a" (lo), "d" (hi), "rm" (d) - : "cc" - ); - - *q = qq; - *r = rr; -} -/* END GCC ASM */ -#elif defined(MASM) -#include <intrin.h> -#pragma intrinsic(_umul128) - -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - *lo = _umul128(a, b, hi); -} - -void _mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo, - mpd_uint_t d); - -/* END MASM (_MSC_VER) */ -#else - #error "need platform specific 128 bit multiplication and division" -#endif - -#define DIVMOD(q, r, v, d) *q = v / d; *r = v - *q * d -static inline void -_mpd_divmod_pow10(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t exp) -{ - assert(exp <= 19); - - if (exp <= 9) { - if (exp <= 4) { - switch (exp) { - case 0: *q = v; *r = 0; break; - case 1: DIVMOD(q, r, v, 10UL); break; - case 2: DIVMOD(q, r, v, 100UL); break; - case 3: DIVMOD(q, r, v, 1000UL); break; - case 4: DIVMOD(q, r, v, 10000UL); break; - } - } - else { - switch (exp) { - case 5: DIVMOD(q, r, v, 100000UL); break; - case 6: DIVMOD(q, r, v, 1000000UL); break; - case 7: DIVMOD(q, r, v, 10000000UL); break; - case 8: DIVMOD(q, r, v, 100000000UL); break; - case 9: DIVMOD(q, r, v, 1000000000UL); break; - } - } - } - else { - if (exp <= 14) { - switch (exp) { - case 10: DIVMOD(q, r, v, 10000000000ULL); break; - case 11: DIVMOD(q, r, v, 100000000000ULL); break; - case 12: DIVMOD(q, r, v, 1000000000000ULL); break; - case 13: DIVMOD(q, r, v, 10000000000000ULL); break; - case 14: DIVMOD(q, r, v, 100000000000000ULL); break; - } - } - else { - switch (exp) { - case 15: DIVMOD(q, r, v, 1000000000000000ULL); break; - case 16: DIVMOD(q, r, v, 10000000000000000ULL); break; - case 17: DIVMOD(q, r, v, 100000000000000000ULL); break; - case 18: DIVMOD(q, r, v, 1000000000000000000ULL); break; - case 19: DIVMOD(q, r, v, 10000000000000000000ULL); break; /* GCOV_NOT_REACHED */ - } - } - } -} - -/* END CONFIG_64 */ -#elif defined(CONFIG_32) -#if defined(ANSI) -#if !defined(LEGACY_COMPILER) -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - mpd_uuint_t hl; - - hl = (mpd_uuint_t)a * b; - - *hi = hl >> 32; - *lo = (mpd_uint_t)hl; -} - -static inline void -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo, - mpd_uint_t d) -{ - mpd_uuint_t hl; - - hl = ((mpd_uuint_t)hi<<32) + lo; - *q = (mpd_uint_t)(hl / d); /* quotient is known to fit */ - *r = (mpd_uint_t)(hl - (mpd_uuint_t)(*q) * d); -} -/* END ANSI + uint64_t */ -#else -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - uint16_t w[4], carry; - uint16_t ah, al, bh, bl; - uint32_t hl; - - ah = (uint16_t)(a>>16); al = (uint16_t)a; - bh = (uint16_t)(b>>16); bl = (uint16_t)b; - - hl = (uint32_t)al * bl; - w[0] = (uint16_t)hl; - carry = (uint16_t)(hl>>16); - - hl = (uint32_t)ah * bl + carry; - w[1] = (uint16_t)hl; - w[2] = (uint16_t)(hl>>16); - - hl = (uint32_t)al * bh + w[1]; - w[1] = (uint16_t)hl; - carry = (uint16_t)(hl>>16); - - hl = ((uint32_t)ah * bh + w[2]) + carry; - w[2] = (uint16_t)hl; - w[3] = (uint16_t)(hl>>16); - - *hi = ((uint32_t)w[3]<<16) + w[2]; - *lo = ((uint32_t)w[1]<<16) + w[0]; -} - -/* - * By Henry S. Warren: http://www.hackersdelight.org/HDcode/divlu.c.txt - * http://www.hackersdelight.org/permissions.htm: - * "You are free to use, copy, and distribute any of the code on this web - * site, whether modified by you or not. You need not give attribution." - * - * Slightly modified, comments are mine. - */ -static inline int -nlz(uint32_t x) -{ - int n; - - if (x == 0) return(32); - - n = 0; - if (x <= 0x0000FFFF) {n = n +16; x = x <<16;} - if (x <= 0x00FFFFFF) {n = n + 8; x = x << 8;} - if (x <= 0x0FFFFFFF) {n = n + 4; x = x << 4;} - if (x <= 0x3FFFFFFF) {n = n + 2; x = x << 2;} - if (x <= 0x7FFFFFFF) {n = n + 1;} - - return n; -} - -static inline void -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t u1, mpd_uint_t u0, - mpd_uint_t v) -{ - const mpd_uint_t b = 65536; - mpd_uint_t un1, un0, - vn1, vn0, - q1, q0, - un32, un21, un10, - rhat, t; - int s; - - assert(u1 < v); - - s = nlz(v); - v = v << s; - vn1 = v >> 16; - vn0 = v & 0xFFFF; - - t = (s == 0) ? 0 : u0 >> (32 - s); - un32 = (u1 << s) | t; - un10 = u0 << s; - - un1 = un10 >> 16; - un0 = un10 & 0xFFFF; - - q1 = un32 / vn1; - rhat = un32 - q1*vn1; -again1: - if (q1 >= b || q1*vn0 > b*rhat + un1) { - q1 = q1 - 1; - rhat = rhat + vn1; - if (rhat < b) goto again1; - } - - /* - * Before again1 we had: - * (1) q1*vn1 + rhat = un32 - * (2) q1*vn1*b + rhat*b + un1 = un32*b + un1 - * - * The statements inside the if-clause do not change the value - * of the left-hand side of (2), and the loop is only exited - * if q1*vn0 <= rhat*b + un1, so: - * - * (3) q1*vn1*b + q1*vn0 <= un32*b + un1 - * (4) q1*v <= un32*b + un1 - * (5) 0 <= un32*b + un1 - q1*v - * - * By (5) we are certain that the possible add-back step from - * Knuth's algorithm D is never required. - * - * Since the final quotient is less than 2**32, the following - * must be true: - * - * (6) un32*b + un1 - q1*v <= UINT32_MAX - * - * This means that in the following line, the high words - * of un32*b and q1*v can be discarded without any effect - * on the result. - */ - un21 = un32*b + un1 - q1*v; - - q0 = un21 / vn1; - rhat = un21 - q0*vn1; -again2: - if (q0 >= b || q0*vn0 > b*rhat + un0) { - q0 = q0 - 1; - rhat = rhat + vn1; - if (rhat < b) goto again2; - } - - *q = q1*b + q0; - *r = (un21*b + un0 - q0*v) >> s; -} -#endif /* END ANSI + LEGACY_COMPILER */ - -/* END ANSI */ -#elif defined(ASM) -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - mpd_uint_t h, l; - - __asm__ ( "mull %3\n\t" - : "=d" (h), "=a" (l) - : "%a" (a), "rm" (b) - : "cc" - ); - - *hi = h; - *lo = l; -} - -static inline void -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo, - mpd_uint_t d) -{ - mpd_uint_t qq, rr; - - __asm__ ( "divl %4\n\t" - : "=a" (qq), "=d" (rr) - : "a" (lo), "d" (hi), "rm" (d) - : "cc" - ); - - *q = qq; - *r = rr; -} -/* END GCC ASM */ -#elif defined(MASM) -static inline void __cdecl -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - mpd_uint_t h, l; - - __asm { - mov eax, a - mul b - mov h, edx - mov l, eax - } - - *hi = h; - *lo = l; -} - -static inline void __cdecl -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo, - mpd_uint_t d) -{ - mpd_uint_t qq, rr; - - __asm { - mov eax, lo - mov edx, hi - div d - mov qq, eax - mov rr, edx - } - - *q = qq; - *r = rr; -} -/* END MASM (_MSC_VER) */ -#else - #error "need platform specific 64 bit multiplication and division" -#endif - -#define DIVMOD(q, r, v, d) *q = v / d; *r = v - *q * d -static inline void -_mpd_divmod_pow10(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t exp) -{ - assert(exp <= 9); - - if (exp <= 4) { - switch (exp) { - case 0: *q = v; *r = 0; break; - case 1: DIVMOD(q, r, v, 10UL); break; - case 2: DIVMOD(q, r, v, 100UL); break; - case 3: DIVMOD(q, r, v, 1000UL); break; - case 4: DIVMOD(q, r, v, 10000UL); break; - } - } - else { - switch (exp) { - case 5: DIVMOD(q, r, v, 100000UL); break; - case 6: DIVMOD(q, r, v, 1000000UL); break; - case 7: DIVMOD(q, r, v, 10000000UL); break; - case 8: DIVMOD(q, r, v, 100000000UL); break; - case 9: DIVMOD(q, r, v, 1000000000UL); break; /* GCOV_NOT_REACHED */ - } - } -} -/* END CONFIG_32 */ - -/* NO CONFIG */ -#else - #error "define CONFIG_64 or CONFIG_32" -#endif /* CONFIG */ - - -static inline void -_mpd_div_word(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t d) -{ - *q = v / d; - *r = v - *q * d; -} - -static inline void -_mpd_idiv_word(mpd_ssize_t *q, mpd_ssize_t *r, mpd_ssize_t v, mpd_ssize_t d) -{ - *q = v / d; - *r = v - *q * d; -} - - -/** ------------------------------------------------------------ - ** Arithmetic with overflow checking - ** ------------------------------------------------------------ - */ - -/* The following macros do call exit() in case of an overflow. - If the library is used correctly (i.e. with valid context - parameters), such overflows cannot occur. The macros are used - as sanity checks in a couple of strategic places and should - be viewed as a handwritten version of gcc's -ftrapv option. */ - -static inline mpd_size_t -add_size_t(mpd_size_t a, mpd_size_t b) -{ - if (a > MPD_SIZE_MAX - b) { - mpd_err_fatal("add_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */ - } - return a + b; -} - -static inline mpd_size_t -sub_size_t(mpd_size_t a, mpd_size_t b) -{ - if (b > a) { - mpd_err_fatal("sub_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */ - } - return a - b; -} - -#if MPD_SIZE_MAX != MPD_UINT_MAX - #error "adapt mul_size_t() and mulmod_size_t()" -#endif - -static inline mpd_size_t -mul_size_t(mpd_size_t a, mpd_size_t b) -{ - mpd_uint_t hi, lo; - - _mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b); - if (hi) { - mpd_err_fatal("mul_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */ - } - return lo; -} - -static inline mpd_size_t -add_size_t_overflow(mpd_size_t a, mpd_size_t b, mpd_size_t *overflow) -{ - mpd_size_t ret; - - *overflow = 0; - ret = a + b; - if (ret < a) *overflow = 1; - return ret; -} - -static inline mpd_size_t -mul_size_t_overflow(mpd_size_t a, mpd_size_t b, mpd_size_t *overflow) -{ - mpd_uint_t lo; - - _mpd_mul_words((mpd_uint_t *)overflow, &lo, (mpd_uint_t)a, - (mpd_uint_t)b); - return lo; -} - -static inline mpd_ssize_t -mod_mpd_ssize_t(mpd_ssize_t a, mpd_ssize_t m) -{ - mpd_ssize_t r = a % m; - return (r < 0) ? r + m : r; -} - -static inline mpd_size_t -mulmod_size_t(mpd_size_t a, mpd_size_t b, mpd_size_t m) -{ - mpd_uint_t hi, lo; - mpd_uint_t q, r; - - _mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b); - _mpd_div_words(&q, &r, hi, lo, (mpd_uint_t)m); - - return r; -} - - -#endif /* TYPEARITH_H */ - - - diff --git a/Modules/_decimal/libmpdec/umodarith.h b/Modules/_decimal/libmpdec/umodarith.h deleted file mode 100644 index 68d1518..0000000 --- a/Modules/_decimal/libmpdec/umodarith.h +++ /dev/null @@ -1,650 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef UMODARITH_H -#define UMODARITH_H - - -#include "constants.h" -#include "mpdecimal.h" -#include "typearith.h" - - -/* Bignum: Low level routines for unsigned modular arithmetic. These are - used in the fast convolution functions for very large coefficients. */ - - -/**************************************************************************/ -/* ANSI modular arithmetic */ -/**************************************************************************/ - - -/* - * Restrictions: a < m and b < m - * ACL2 proof: umodarith.lisp: addmod-correct - */ -static inline mpd_uint_t -addmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m) -{ - mpd_uint_t s; - - s = a + b; - s = (s < a) ? s - m : s; - s = (s >= m) ? s - m : s; - - return s; -} - -/* - * Restrictions: a < m and b < m - * ACL2 proof: umodarith.lisp: submod-2-correct - */ -static inline mpd_uint_t -submod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m) -{ - mpd_uint_t d; - - d = a - b; - d = (a < b) ? d + m : d; - - return d; -} - -/* - * Restrictions: a < 2m and b < 2m - * ACL2 proof: umodarith.lisp: section ext-submod - */ -static inline mpd_uint_t -ext_submod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m) -{ - mpd_uint_t d; - - a = (a >= m) ? a - m : a; - b = (b >= m) ? b - m : b; - - d = a - b; - d = (a < b) ? d + m : d; - - return d; -} - -/* - * Reduce double word modulo m. - * Restrictions: m != 0 - * ACL2 proof: umodarith.lisp: section dw-reduce - */ -static inline mpd_uint_t -dw_reduce(mpd_uint_t hi, mpd_uint_t lo, mpd_uint_t m) -{ - mpd_uint_t r1, r2, w; - - _mpd_div_word(&w, &r1, hi, m); - _mpd_div_words(&w, &r2, r1, lo, m); - - return r2; -} - -/* - * Subtract double word from a. - * Restrictions: a < m - * ACL2 proof: umodarith.lisp: section dw-submod - */ -static inline mpd_uint_t -dw_submod(mpd_uint_t a, mpd_uint_t hi, mpd_uint_t lo, mpd_uint_t m) -{ - mpd_uint_t d, r; - - r = dw_reduce(hi, lo, m); - d = a - r; - d = (a < r) ? d + m : d; - - return d; -} - -#ifdef CONFIG_64 - -/**************************************************************************/ -/* 64-bit modular arithmetic */ -/**************************************************************************/ - -/* - * A proof of the algorithm is in literature/mulmod-64.txt. An ACL2 - * proof is in umodarith.lisp: section "Fast modular reduction". - * - * Algorithm: calculate (a * b) % p: - * - * a) hi, lo <- a * b # Calculate a * b. - * - * b) hi, lo <- R(hi, lo) # Reduce modulo p. - * - * c) Repeat step b) until 0 <= hi * 2**64 + lo < 2*p. - * - * d) If the result is less than p, return lo. Otherwise return lo - p. - */ - -static inline mpd_uint_t -x64_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m) -{ - mpd_uint_t hi, lo, x, y; - - - _mpd_mul_words(&hi, &lo, a, b); - - if (m & (1ULL<<32)) { /* P1 */ - - /* first reduction */ - x = y = hi; - hi >>= 32; - - x = lo - x; - if (x > lo) hi--; - - y <<= 32; - lo = y + x; - if (lo < y) hi++; - - /* second reduction */ - x = y = hi; - hi >>= 32; - - x = lo - x; - if (x > lo) hi--; - - y <<= 32; - lo = y + x; - if (lo < y) hi++; - - return (hi || lo >= m ? lo - m : lo); - } - else if (m & (1ULL<<34)) { /* P2 */ - - /* first reduction */ - x = y = hi; - hi >>= 30; - - x = lo - x; - if (x > lo) hi--; - - y <<= 34; - lo = y + x; - if (lo < y) hi++; - - /* second reduction */ - x = y = hi; - hi >>= 30; - - x = lo - x; - if (x > lo) hi--; - - y <<= 34; - lo = y + x; - if (lo < y) hi++; - - /* third reduction */ - x = y = hi; - hi >>= 30; - - x = lo - x; - if (x > lo) hi--; - - y <<= 34; - lo = y + x; - if (lo < y) hi++; - - return (hi || lo >= m ? lo - m : lo); - } - else { /* P3 */ - - /* first reduction */ - x = y = hi; - hi >>= 24; - - x = lo - x; - if (x > lo) hi--; - - y <<= 40; - lo = y + x; - if (lo < y) hi++; - - /* second reduction */ - x = y = hi; - hi >>= 24; - - x = lo - x; - if (x > lo) hi--; - - y <<= 40; - lo = y + x; - if (lo < y) hi++; - - /* third reduction */ - x = y = hi; - hi >>= 24; - - x = lo - x; - if (x > lo) hi--; - - y <<= 40; - lo = y + x; - if (lo < y) hi++; - - return (hi || lo >= m ? lo - m : lo); - } -} - -static inline void -x64_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m) -{ - *a = x64_mulmod(*a, w, m); - *b = x64_mulmod(*b, w, m); -} - -static inline void -x64_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1, - mpd_uint_t m) -{ - *a0 = x64_mulmod(*a0, b0, m); - *a1 = x64_mulmod(*a1, b1, m); -} - -static inline mpd_uint_t -x64_powmod(mpd_uint_t base, mpd_uint_t exp, mpd_uint_t umod) -{ - mpd_uint_t r = 1; - - while (exp > 0) { - if (exp & 1) - r = x64_mulmod(r, base, umod); - base = x64_mulmod(base, base, umod); - exp >>= 1; - } - - return r; -} - -/* END CONFIG_64 */ -#else /* CONFIG_32 */ - - -/**************************************************************************/ -/* 32-bit modular arithmetic */ -/**************************************************************************/ - -#if defined(ANSI) -#if !defined(LEGACY_COMPILER) -/* HAVE_UINT64_T */ -static inline mpd_uint_t -std_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m) -{ - return ((mpd_uuint_t) a * b) % m; -} - -static inline void -std_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m) -{ - *a = ((mpd_uuint_t) *a * w) % m; - *b = ((mpd_uuint_t) *b * w) % m; -} - -static inline void -std_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1, - mpd_uint_t m) -{ - *a0 = ((mpd_uuint_t) *a0 * b0) % m; - *a1 = ((mpd_uuint_t) *a1 * b1) % m; -} -/* END HAVE_UINT64_T */ -#else -/* LEGACY_COMPILER */ -static inline mpd_uint_t -std_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m) -{ - mpd_uint_t hi, lo, q, r; - _mpd_mul_words(&hi, &lo, a, b); - _mpd_div_words(&q, &r, hi, lo, m); - return r; -} - -static inline void -std_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m) -{ - *a = std_mulmod(*a, w, m); - *b = std_mulmod(*b, w, m); -} - -static inline void -std_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1, - mpd_uint_t m) -{ - *a0 = std_mulmod(*a0, b0, m); - *a1 = std_mulmod(*a1, b1, m); -} -/* END LEGACY_COMPILER */ -#endif - -static inline mpd_uint_t -std_powmod(mpd_uint_t base, mpd_uint_t exp, mpd_uint_t umod) -{ - mpd_uint_t r = 1; - - while (exp > 0) { - if (exp & 1) - r = std_mulmod(r, base, umod); - base = std_mulmod(base, base, umod); - exp >>= 1; - } - - return r; -} -#endif /* ANSI CONFIG_32 */ - - -/**************************************************************************/ -/* Pentium Pro modular arithmetic */ -/**************************************************************************/ - -/* - * A proof of the algorithm is in literature/mulmod-ppro.txt. The FPU - * control word must be set to 64-bit precision and truncation mode - * prior to using these functions. - * - * Algorithm: calculate (a * b) % p: - * - * p := prime < 2**31 - * pinv := (long double)1.0 / p (precalculated) - * - * a) n = a * b # Calculate exact product. - * b) qest = n * pinv # Calculate estimate for q = n / p. - * c) q = (qest+2**63)-2**63 # Truncate qest to the exact quotient. - * d) r = n - q * p # Calculate remainder. - * - * Remarks: - * - * - p = dmod and pinv = dinvmod. - * - dinvmod points to an array of three uint32_t, which is interpreted - * as an 80 bit long double by fldt. - * - Intel compilers prior to version 11 do not seem to handle the - * __GNUC__ inline assembly correctly. - * - random tests are provided in tests/extended/ppro_mulmod.c - */ - -#if defined(PPRO) -#if defined(ASM) - -/* Return (a * b) % dmod */ -static inline mpd_uint_t -ppro_mulmod(mpd_uint_t a, mpd_uint_t b, double *dmod, uint32_t *dinvmod) -{ - mpd_uint_t retval; - - __asm__ ( - "fildl %2\n\t" - "fildl %1\n\t" - "fmulp %%st, %%st(1)\n\t" - "fldt (%4)\n\t" - "fmul %%st(1), %%st\n\t" - "flds %5\n\t" - "fadd %%st, %%st(1)\n\t" - "fsubrp %%st, %%st(1)\n\t" - "fldl (%3)\n\t" - "fmulp %%st, %%st(1)\n\t" - "fsubrp %%st, %%st(1)\n\t" - "fistpl %0\n\t" - : "=m" (retval) - : "m" (a), "m" (b), "r" (dmod), "r" (dinvmod), "m" (MPD_TWO63) - : "st", "memory" - ); - - return retval; -} - -/* - * Two modular multiplications in parallel: - * *a0 = (*a0 * w) % dmod - * *a1 = (*a1 * w) % dmod - */ -static inline void -ppro_mulmod2c(mpd_uint_t *a0, mpd_uint_t *a1, mpd_uint_t w, - double *dmod, uint32_t *dinvmod) -{ - __asm__ ( - "fildl %2\n\t" - "fildl (%1)\n\t" - "fmul %%st(1), %%st\n\t" - "fxch %%st(1)\n\t" - "fildl (%0)\n\t" - "fmulp %%st, %%st(1) \n\t" - "fldt (%4)\n\t" - "flds %5\n\t" - "fld %%st(2)\n\t" - "fmul %%st(2)\n\t" - "fadd %%st(1)\n\t" - "fsub %%st(1)\n\t" - "fmull (%3)\n\t" - "fsubrp %%st, %%st(3)\n\t" - "fxch %%st(2)\n\t" - "fistpl (%0)\n\t" - "fmul %%st(2)\n\t" - "fadd %%st(1)\n\t" - "fsubp %%st, %%st(1)\n\t" - "fmull (%3)\n\t" - "fsubrp %%st, %%st(1)\n\t" - "fistpl (%1)\n\t" - : : "r" (a0), "r" (a1), "m" (w), - "r" (dmod), "r" (dinvmod), - "m" (MPD_TWO63) - : "st", "memory" - ); -} - -/* - * Two modular multiplications in parallel: - * *a0 = (*a0 * b0) % dmod - * *a1 = (*a1 * b1) % dmod - */ -static inline void -ppro_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1, - double *dmod, uint32_t *dinvmod) -{ - __asm__ ( - "fildl %3\n\t" - "fildl (%2)\n\t" - "fmulp %%st, %%st(1)\n\t" - "fildl %1\n\t" - "fildl (%0)\n\t" - "fmulp %%st, %%st(1)\n\t" - "fldt (%5)\n\t" - "fld %%st(2)\n\t" - "fmul %%st(1), %%st\n\t" - "fxch %%st(1)\n\t" - "fmul %%st(2), %%st\n\t" - "flds %6\n\t" - "fldl (%4)\n\t" - "fxch %%st(3)\n\t" - "fadd %%st(1), %%st\n\t" - "fxch %%st(2)\n\t" - "fadd %%st(1), %%st\n\t" - "fxch %%st(2)\n\t" - "fsub %%st(1), %%st\n\t" - "fxch %%st(2)\n\t" - "fsubp %%st, %%st(1)\n\t" - "fxch %%st(1)\n\t" - "fmul %%st(2), %%st\n\t" - "fxch %%st(1)\n\t" - "fmulp %%st, %%st(2)\n\t" - "fsubrp %%st, %%st(3)\n\t" - "fsubrp %%st, %%st(1)\n\t" - "fxch %%st(1)\n\t" - "fistpl (%2)\n\t" - "fistpl (%0)\n\t" - : : "r" (a0), "m" (b0), "r" (a1), "m" (b1), - "r" (dmod), "r" (dinvmod), - "m" (MPD_TWO63) - : "st", "memory" - ); -} -/* END PPRO GCC ASM */ -#elif defined(MASM) - -/* Return (a * b) % dmod */ -static inline mpd_uint_t __cdecl -ppro_mulmod(mpd_uint_t a, mpd_uint_t b, double *dmod, uint32_t *dinvmod) -{ - mpd_uint_t retval; - - __asm { - mov eax, dinvmod - mov edx, dmod - fild b - fild a - fmulp st(1), st - fld TBYTE PTR [eax] - fmul st, st(1) - fld MPD_TWO63 - fadd st(1), st - fsubp st(1), st - fld QWORD PTR [edx] - fmulp st(1), st - fsubp st(1), st - fistp retval - } - - return retval; -} - -/* - * Two modular multiplications in parallel: - * *a0 = (*a0 * w) % dmod - * *a1 = (*a1 * w) % dmod - */ -static inline mpd_uint_t __cdecl -ppro_mulmod2c(mpd_uint_t *a0, mpd_uint_t *a1, mpd_uint_t w, - double *dmod, uint32_t *dinvmod) -{ - __asm { - mov ecx, dmod - mov edx, a1 - mov ebx, dinvmod - mov eax, a0 - fild w - fild DWORD PTR [edx] - fmul st, st(1) - fxch st(1) - fild DWORD PTR [eax] - fmulp st(1), st - fld TBYTE PTR [ebx] - fld MPD_TWO63 - fld st(2) - fmul st, st(2) - fadd st, st(1) - fsub st, st(1) - fmul QWORD PTR [ecx] - fsubp st(3), st - fxch st(2) - fistp DWORD PTR [eax] - fmul st, st(2) - fadd st, st(1) - fsubrp st(1), st - fmul QWORD PTR [ecx] - fsubp st(1), st - fistp DWORD PTR [edx] - } -} - -/* - * Two modular multiplications in parallel: - * *a0 = (*a0 * b0) % dmod - * *a1 = (*a1 * b1) % dmod - */ -static inline void __cdecl -ppro_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1, - double *dmod, uint32_t *dinvmod) -{ - __asm { - mov ecx, dmod - mov edx, a1 - mov ebx, dinvmod - mov eax, a0 - fild b1 - fild DWORD PTR [edx] - fmulp st(1), st - fild b0 - fild DWORD PTR [eax] - fmulp st(1), st - fld TBYTE PTR [ebx] - fld st(2) - fmul st, st(1) - fxch st(1) - fmul st, st(2) - fld DWORD PTR MPD_TWO63 - fld QWORD PTR [ecx] - fxch st(3) - fadd st, st(1) - fxch st(2) - fadd st, st(1) - fxch st(2) - fsub st, st(1) - fxch st(2) - fsubrp st(1), st - fxch st(1) - fmul st, st(2) - fxch st(1) - fmulp st(2), st - fsubp st(3), st - fsubp st(1), st - fxch st(1) - fistp DWORD PTR [edx] - fistp DWORD PTR [eax] - } -} -#endif /* PPRO MASM (_MSC_VER) */ - - -/* Return (base ** exp) % dmod */ -static inline mpd_uint_t -ppro_powmod(mpd_uint_t base, mpd_uint_t exp, double *dmod, uint32_t *dinvmod) -{ - mpd_uint_t r = 1; - - while (exp > 0) { - if (exp & 1) - r = ppro_mulmod(r, base, dmod, dinvmod); - base = ppro_mulmod(base, base, dmod, dinvmod); - exp >>= 1; - } - - return r; -} -#endif /* PPRO */ -#endif /* CONFIG_32 */ - - -#endif /* UMODARITH_H */ - - - diff --git a/Modules/_decimal/libmpdec/vccompat.h b/Modules/_decimal/libmpdec/vccompat.h deleted file mode 100644 index 2ba805d..0000000 --- a/Modules/_decimal/libmpdec/vccompat.h +++ /dev/null @@ -1,57 +0,0 @@ -/* - * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef VCCOMPAT_H -#define VCCOMPAT_H - - -/* Visual C fixes: no snprintf ... */ -#ifdef _MSC_VER - #undef inline - #define inline __inline - #undef random - #define random rand - #undef srandom - #define srandom srand - #undef snprintf - #define snprintf sprintf_s - #define HAVE_SNPRINTF - #undef strncasecmp - #define strncasecmp _strnicmp - #undef strcasecmp - #define strcasecmp _stricmp - #undef strtoll - #define strtoll _strtoi64 - #define strdup _strdup -#endif - - -#endif /* VCCOMPAT_H */ - - - diff --git a/Modules/_decimal/libmpdec/vcdiv64.asm b/Modules/_decimal/libmpdec/vcdiv64.asm deleted file mode 100644 index 6b66456..0000000 --- a/Modules/_decimal/libmpdec/vcdiv64.asm +++ /dev/null @@ -1,48 +0,0 @@ -; -; Copyright (c) 2008-2016 Stefan Krah. All rights reserved. -; -; Redistribution and use in source and binary forms, with or without -; modification, are permitted provided that the following conditions -; are met: -; -; 1. Redistributions of source code must retain the above copyright -; notice, this list of conditions and the following disclaimer. -; -; 2. Redistributions in binary form must reproduce the above copyright -; notice, this list of conditions and the following disclaimer in the -; documentation and/or other materials provided with the distribution. -; -; THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND -; ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE -; ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE -; FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL -; DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS -; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) -; HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT -; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY -; OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF -; SUCH DAMAGE. -; - - -PUBLIC _mpd_div_words -_TEXT SEGMENT -q$ = 8 -r$ = 16 -hi$ = 24 -lo$ = 32 -d$ = 40 -_mpd_div_words PROC - mov r10, rdx - mov rdx, r8 - mov rax, r9 - div QWORD PTR d$[rsp] - mov QWORD PTR [r10], rdx - mov QWORD PTR [rcx], rax - ret 0 -_mpd_div_words ENDP -_TEXT ENDS -END - - diff --git a/Modules/_decimal/tests/README.txt b/Modules/_decimal/tests/README.txt deleted file mode 100644 index 97b6ff6..0000000 --- a/Modules/_decimal/tests/README.txt +++ /dev/null @@ -1,15 +0,0 @@ - - -This directory contains extended tests and a benchmark against decimal.py: - - bench.py -> Benchmark for small and large precisions. - Usage: ../../../python bench.py - - formathelper.py -> - randdec.py -> Generate test cases for deccheck.py. - randfloat.py -> - - deccheck.py -> Run extended tests. - Usage: ../../../python deccheck.py [--short|--medium|--long|--all] - - diff --git a/Modules/_decimal/tests/bench.py b/Modules/_decimal/tests/bench.py deleted file mode 100644 index 3726db1..0000000 --- a/Modules/_decimal/tests/bench.py +++ /dev/null @@ -1,132 +0,0 @@ -# -# Copyright (C) 2001-2012 Python Software Foundation. All Rights Reserved. -# Modified and extended by Stefan Krah. -# - -# Usage: ../../../python bench.py - - -import time -try: - from test.support import import_fresh_module -except ImportError: - from test.test_support import import_fresh_module - -C = import_fresh_module('decimal', fresh=['_decimal']) -P = import_fresh_module('decimal', blocked=['_decimal']) - -# -# NOTE: This is the pi function from the decimal documentation, modified -# for benchmarking purposes. Since floats do not have a context, the higher -# intermediate precision from the original is NOT used, so the modified -# algorithm only gives an approximation to the correctly rounded result. -# For serious use, refer to the documentation or the appropriate literature. -# -def pi_float(): - """native float""" - lasts, t, s, n, na, d, da = 0, 3.0, 3, 1, 0, 0, 24 - while s != lasts: - lasts = s - n, na = n+na, na+8 - d, da = d+da, da+32 - t = (t * n) / d - s += t - return s - -def pi_cdecimal(): - """cdecimal""" - D = C.Decimal - lasts, t, s, n, na, d, da = D(0), D(3), D(3), D(1), D(0), D(0), D(24) - while s != lasts: - lasts = s - n, na = n+na, na+8 - d, da = d+da, da+32 - t = (t * n) / d - s += t - return s - -def pi_decimal(): - """decimal""" - D = P.Decimal - lasts, t, s, n, na, d, da = D(0), D(3), D(3), D(1), D(0), D(0), D(24) - while s != lasts: - lasts = s - n, na = n+na, na+8 - d, da = d+da, da+32 - t = (t * n) / d - s += t - return s - -def factorial(n, m): - if (n > m): - return factorial(m, n) - elif m == 0: - return 1 - elif n == m: - return n - else: - return factorial(n, (n+m)//2) * factorial((n+m)//2 + 1, m) - - -print("\n# ======================================================================") -print("# Calculating pi, 10000 iterations") -print("# ======================================================================\n") - -to_benchmark = [pi_float, pi_decimal] -if C is not None: - to_benchmark.insert(1, pi_cdecimal) - -for prec in [9, 19]: - print("\nPrecision: %d decimal digits\n" % prec) - for func in to_benchmark: - start = time.time() - if C is not None: - C.getcontext().prec = prec - P.getcontext().prec = prec - for i in range(10000): - x = func() - print("%s:" % func.__name__.replace("pi_", "")) - print("result: %s" % str(x)) - print("time: %fs\n" % (time.time()-start)) - - -print("\n# ======================================================================") -print("# Factorial") -print("# ======================================================================\n") - -if C is not None: - c = C.getcontext() - c.prec = C.MAX_PREC - c.Emax = C.MAX_EMAX - c.Emin = C.MIN_EMIN - -for n in [100000, 1000000]: - - print("n = %d\n" % n) - - if C is not None: - # C version of decimal - start_calc = time.time() - x = factorial(C.Decimal(n), 0) - end_calc = time.time() - start_conv = time.time() - sx = str(x) - end_conv = time.time() - print("cdecimal:") - print("calculation time: %fs" % (end_calc-start_calc)) - print("conversion time: %fs\n" % (end_conv-start_conv)) - - # Python integers - start_calc = time.time() - y = factorial(n, 0) - end_calc = time.time() - start_conv = time.time() - sy = str(y) - end_conv = time.time() - - print("int:") - print("calculation time: %fs" % (end_calc-start_calc)) - print("conversion time: %fs\n\n" % (end_conv-start_conv)) - - if C is not None: - assert(sx == sy) diff --git a/Modules/_decimal/tests/bignum.py b/Modules/_decimal/tests/bignum.py deleted file mode 100644 index a67e161..0000000 --- a/Modules/_decimal/tests/bignum.py +++ /dev/null @@ -1,42 +0,0 @@ -# -# These tests require gmpy and test the limits of the 32-bit build. The -# limits of the 64-bit build are so large that they cannot be tested -# on accessible hardware. -# - -import sys -from decimal import * -from gmpy import mpz - - -_PyHASH_MODULUS = sys.hash_info.modulus -# hash values to use for positive and negative infinities, and nans -_PyHASH_INF = sys.hash_info.inf -_PyHASH_NAN = sys.hash_info.nan - -# _PyHASH_10INV is the inverse of 10 modulo the prime _PyHASH_MODULUS -_PyHASH_10INV = pow(10, _PyHASH_MODULUS - 2, _PyHASH_MODULUS) - -def xhash(coeff, exp): - sign = 1 - if coeff < 0: - sign = -1 - coeff = -coeff - if exp >= 0: - exp_hash = pow(10, exp, _PyHASH_MODULUS) - else: - exp_hash = pow(_PyHASH_10INV, -exp, _PyHASH_MODULUS) - hash_ = coeff * exp_hash % _PyHASH_MODULUS - ans = hash_ if sign == 1 else -hash_ - return -2 if ans == -1 else ans - - -x = mpz(10) ** 425000000 - 1 -coeff = int(x) - -d = Decimal('9' * 425000000 + 'e-849999999') - -h1 = xhash(coeff, -849999999) -h2 = hash(d) - -assert h2 == h1 diff --git a/Modules/_decimal/tests/deccheck.py b/Modules/_decimal/tests/deccheck.py deleted file mode 100644 index f907531..0000000 --- a/Modules/_decimal/tests/deccheck.py +++ /dev/null @@ -1,1100 +0,0 @@ -# -# Copyright (c) 2008-2012 Stefan Krah. All rights reserved. -# -# Redistribution and use in source and binary forms, with or without -# modification, are permitted provided that the following conditions -# are met: -# -# 1. Redistributions of source code must retain the above copyright -# notice, this list of conditions and the following disclaimer. -# -# 2. Redistributions in binary form must reproduce the above copyright -# notice, this list of conditions and the following disclaimer in the -# documentation and/or other materials provided with the distribution. -# -# THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND -# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE -# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE -# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL -# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS -# OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) -# HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT -# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY -# OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF -# SUCH DAMAGE. -# - -# -# Usage: python deccheck.py [--short|--medium|--long|--all] -# - -import sys, random -from copy import copy -from collections import defaultdict -from test.support import import_fresh_module -from randdec import randfloat, all_unary, all_binary, all_ternary -from randdec import unary_optarg, binary_optarg, ternary_optarg -from formathelper import rand_format, rand_locale -from _pydecimal import _dec_from_triple - -C = import_fresh_module('decimal', fresh=['_decimal']) -P = import_fresh_module('decimal', blocked=['_decimal']) -EXIT_STATUS = 0 - - -# Contains all categories of Decimal methods. -Functions = { - # Plain unary: - 'unary': ( - '__abs__', '__bool__', '__ceil__', '__complex__', '__copy__', - '__floor__', '__float__', '__hash__', '__int__', '__neg__', - '__pos__', '__reduce__', '__repr__', '__str__', '__trunc__', - 'adjusted', 'as_integer_ratio', 'as_tuple', 'canonical', 'conjugate', - 'copy_abs', 'copy_negate', 'is_canonical', 'is_finite', 'is_infinite', - 'is_nan', 'is_qnan', 'is_signed', 'is_snan', 'is_zero', 'radix' - ), - # Unary with optional context: - 'unary_ctx': ( - 'exp', 'is_normal', 'is_subnormal', 'ln', 'log10', 'logb', - 'logical_invert', 'next_minus', 'next_plus', 'normalize', - 'number_class', 'sqrt', 'to_eng_string' - ), - # Unary with optional rounding mode and context: - 'unary_rnd_ctx': ('to_integral', 'to_integral_exact', 'to_integral_value'), - # Plain binary: - 'binary': ( - '__add__', '__divmod__', '__eq__', '__floordiv__', '__ge__', '__gt__', - '__le__', '__lt__', '__mod__', '__mul__', '__ne__', '__pow__', - '__radd__', '__rdivmod__', '__rfloordiv__', '__rmod__', '__rmul__', - '__rpow__', '__rsub__', '__rtruediv__', '__sub__', '__truediv__', - 'compare_total', 'compare_total_mag', 'copy_sign', 'quantize', - 'same_quantum' - ), - # Binary with optional context: - 'binary_ctx': ( - 'compare', 'compare_signal', 'logical_and', 'logical_or', 'logical_xor', - 'max', 'max_mag', 'min', 'min_mag', 'next_toward', 'remainder_near', - 'rotate', 'scaleb', 'shift' - ), - # Plain ternary: - 'ternary': ('__pow__',), - # Ternary with optional context: - 'ternary_ctx': ('fma',), - # Special: - 'special': ('__format__', '__reduce_ex__', '__round__', 'from_float', - 'quantize'), - # Properties: - 'property': ('real', 'imag') -} - -# Contains all categories of Context methods. The n-ary classification -# applies to the number of Decimal arguments. -ContextFunctions = { - # Plain nullary: - 'nullary': ('context.__hash__', 'context.__reduce__', 'context.radix'), - # Plain unary: - 'unary': ('context.abs', 'context.canonical', 'context.copy_abs', - 'context.copy_decimal', 'context.copy_negate', - 'context.create_decimal', 'context.exp', 'context.is_canonical', - 'context.is_finite', 'context.is_infinite', 'context.is_nan', - 'context.is_normal', 'context.is_qnan', 'context.is_signed', - 'context.is_snan', 'context.is_subnormal', 'context.is_zero', - 'context.ln', 'context.log10', 'context.logb', - 'context.logical_invert', 'context.minus', 'context.next_minus', - 'context.next_plus', 'context.normalize', 'context.number_class', - 'context.plus', 'context.sqrt', 'context.to_eng_string', - 'context.to_integral', 'context.to_integral_exact', - 'context.to_integral_value', 'context.to_sci_string' - ), - # Plain binary: - 'binary': ('context.add', 'context.compare', 'context.compare_signal', - 'context.compare_total', 'context.compare_total_mag', - 'context.copy_sign', 'context.divide', 'context.divide_int', - 'context.divmod', 'context.logical_and', 'context.logical_or', - 'context.logical_xor', 'context.max', 'context.max_mag', - 'context.min', 'context.min_mag', 'context.multiply', - 'context.next_toward', 'context.power', 'context.quantize', - 'context.remainder', 'context.remainder_near', 'context.rotate', - 'context.same_quantum', 'context.scaleb', 'context.shift', - 'context.subtract' - ), - # Plain ternary: - 'ternary': ('context.fma', 'context.power'), - # Special: - 'special': ('context.__reduce_ex__', 'context.create_decimal_from_float') -} - -# Functions that require a restricted exponent range for reasonable runtimes. -UnaryRestricted = [ - '__ceil__', '__floor__', '__int__', '__trunc__', - 'as_integer_ratio', 'to_integral', 'to_integral_value' -] - -BinaryRestricted = ['__round__'] - -TernaryRestricted = ['__pow__', 'context.power'] - - -# ====================================================================== -# Unified Context -# ====================================================================== - -# Translate symbols. -CondMap = { - C.Clamped: P.Clamped, - C.ConversionSyntax: P.ConversionSyntax, - C.DivisionByZero: P.DivisionByZero, - C.DivisionImpossible: P.InvalidOperation, - C.DivisionUndefined: P.DivisionUndefined, - C.Inexact: P.Inexact, - C.InvalidContext: P.InvalidContext, - C.InvalidOperation: P.InvalidOperation, - C.Overflow: P.Overflow, - C.Rounded: P.Rounded, - C.Subnormal: P.Subnormal, - C.Underflow: P.Underflow, - C.FloatOperation: P.FloatOperation, -} - -RoundModes = [C.ROUND_UP, C.ROUND_DOWN, C.ROUND_CEILING, C.ROUND_FLOOR, - C.ROUND_HALF_UP, C.ROUND_HALF_DOWN, C.ROUND_HALF_EVEN, - C.ROUND_05UP] - - -class Context(object): - """Provides a convenient way of syncing the C and P contexts""" - - __slots__ = ['c', 'p'] - - def __init__(self, c_ctx=None, p_ctx=None): - """Initialization is from the C context""" - self.c = C.getcontext() if c_ctx is None else c_ctx - self.p = P.getcontext() if p_ctx is None else p_ctx - self.p.prec = self.c.prec - self.p.Emin = self.c.Emin - self.p.Emax = self.c.Emax - self.p.rounding = self.c.rounding - self.p.capitals = self.c.capitals - self.settraps([sig for sig in self.c.traps if self.c.traps[sig]]) - self.setstatus([sig for sig in self.c.flags if self.c.flags[sig]]) - self.p.clamp = self.c.clamp - - def __str__(self): - return str(self.c) + '\n' + str(self.p) - - def getprec(self): - assert(self.c.prec == self.p.prec) - return self.c.prec - - def setprec(self, val): - self.c.prec = val - self.p.prec = val - - def getemin(self): - assert(self.c.Emin == self.p.Emin) - return self.c.Emin - - def setemin(self, val): - self.c.Emin = val - self.p.Emin = val - - def getemax(self): - assert(self.c.Emax == self.p.Emax) - return self.c.Emax - - def setemax(self, val): - self.c.Emax = val - self.p.Emax = val - - def getround(self): - assert(self.c.rounding == self.p.rounding) - return self.c.rounding - - def setround(self, val): - self.c.rounding = val - self.p.rounding = val - - def getcapitals(self): - assert(self.c.capitals == self.p.capitals) - return self.c.capitals - - def setcapitals(self, val): - self.c.capitals = val - self.p.capitals = val - - def getclamp(self): - assert(self.c.clamp == self.p.clamp) - return self.c.clamp - - def setclamp(self, val): - self.c.clamp = val - self.p.clamp = val - - prec = property(getprec, setprec) - Emin = property(getemin, setemin) - Emax = property(getemax, setemax) - rounding = property(getround, setround) - clamp = property(getclamp, setclamp) - capitals = property(getcapitals, setcapitals) - - def clear_traps(self): - self.c.clear_traps() - for trap in self.p.traps: - self.p.traps[trap] = False - - def clear_status(self): - self.c.clear_flags() - self.p.clear_flags() - - def settraps(self, lst): - """lst: C signal list""" - self.clear_traps() - for signal in lst: - self.c.traps[signal] = True - self.p.traps[CondMap[signal]] = True - - def setstatus(self, lst): - """lst: C signal list""" - self.clear_status() - for signal in lst: - self.c.flags[signal] = True - self.p.flags[CondMap[signal]] = True - - def assert_eq_status(self): - """assert equality of C and P status""" - for signal in self.c.flags: - if self.c.flags[signal] == (not self.p.flags[CondMap[signal]]): - return False - return True - - -# We don't want exceptions so that we can compare the status flags. -context = Context() -context.Emin = C.MIN_EMIN -context.Emax = C.MAX_EMAX -context.clear_traps() - -# When creating decimals, _decimal is ultimately limited by the maximum -# context values. We emulate this restriction for decimal.py. -maxcontext = P.Context( - prec=C.MAX_PREC, - Emin=C.MIN_EMIN, - Emax=C.MAX_EMAX, - rounding=P.ROUND_HALF_UP, - capitals=1 -) -maxcontext.clamp = 0 - -def RestrictedDecimal(value): - maxcontext.traps = copy(context.p.traps) - maxcontext.clear_flags() - if isinstance(value, str): - value = value.strip() - dec = maxcontext.create_decimal(value) - if maxcontext.flags[P.Inexact] or \ - maxcontext.flags[P.Rounded] or \ - maxcontext.flags[P.Clamped] or \ - maxcontext.flags[P.InvalidOperation]: - return context.p._raise_error(P.InvalidOperation) - if maxcontext.flags[P.FloatOperation]: - context.p.flags[P.FloatOperation] = True - return dec - - -# ====================================================================== -# TestSet: Organize data and events during a single test case -# ====================================================================== - -class RestrictedList(list): - """List that can only be modified by appending items.""" - def __getattribute__(self, name): - if name != 'append': - raise AttributeError("unsupported operation") - return list.__getattribute__(self, name) - def unsupported(self, *_): - raise AttributeError("unsupported operation") - __add__ = __delattr__ = __delitem__ = __iadd__ = __imul__ = unsupported - __mul__ = __reversed__ = __rmul__ = __setattr__ = __setitem__ = unsupported - -class TestSet(object): - """A TestSet contains the original input operands, converted operands, - Python exceptions that occurred either during conversion or during - execution of the actual function, and the final results. - - For safety, most attributes are lists that only support the append - operation. - - If a function name is prefixed with 'context.', the corresponding - context method is called. - """ - def __init__(self, funcname, operands): - if funcname.startswith("context."): - self.funcname = funcname.replace("context.", "") - self.contextfunc = True - else: - self.funcname = funcname - self.contextfunc = False - self.op = operands # raw operand tuple - self.context = context # context used for the operation - self.cop = RestrictedList() # converted C.Decimal operands - self.cex = RestrictedList() # Python exceptions for C.Decimal - self.cresults = RestrictedList() # C.Decimal results - self.pop = RestrictedList() # converted P.Decimal operands - self.pex = RestrictedList() # Python exceptions for P.Decimal - self.presults = RestrictedList() # P.Decimal results - - -# ====================================================================== -# SkipHandler: skip known discrepancies -# ====================================================================== - -class SkipHandler: - """Handle known discrepancies between decimal.py and _decimal.so. - These are either ULP differences in the power function or - extremely minor issues.""" - - def __init__(self): - self.ulpdiff = 0 - self.powmod_zeros = 0 - self.maxctx = P.Context(Emax=10**18, Emin=-10**18) - - def default(self, t): - return False - __ge__ = __gt__ = __le__ = __lt__ = __ne__ = __eq__ = default - __reduce__ = __format__ = __repr__ = __str__ = default - - def harrison_ulp(self, dec): - """ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-5504.pdf""" - a = dec.next_plus() - b = dec.next_minus() - return abs(a - b) - - def standard_ulp(self, dec, prec): - return _dec_from_triple(0, '1', dec._exp+len(dec._int)-prec) - - def rounding_direction(self, x, mode): - """Determine the effective direction of the rounding when - the exact result x is rounded according to mode. - Return -1 for downwards, 0 for undirected, 1 for upwards, - 2 for ROUND_05UP.""" - cmp = 1 if x.compare_total(P.Decimal("+0")) >= 0 else -1 - - if mode in (P.ROUND_HALF_EVEN, P.ROUND_HALF_UP, P.ROUND_HALF_DOWN): - return 0 - elif mode == P.ROUND_CEILING: - return 1 - elif mode == P.ROUND_FLOOR: - return -1 - elif mode == P.ROUND_UP: - return cmp - elif mode == P.ROUND_DOWN: - return -cmp - elif mode == P.ROUND_05UP: - return 2 - else: - raise ValueError("Unexpected rounding mode: %s" % mode) - - def check_ulpdiff(self, exact, rounded): - # current precision - p = context.p.prec - - # Convert infinities to the largest representable number + 1. - x = exact - if exact.is_infinite(): - x = _dec_from_triple(exact._sign, '10', context.p.Emax) - y = rounded - if rounded.is_infinite(): - y = _dec_from_triple(rounded._sign, '10', context.p.Emax) - - # err = (rounded - exact) / ulp(rounded) - self.maxctx.prec = p * 2 - t = self.maxctx.subtract(y, x) - if context.c.flags[C.Clamped] or \ - context.c.flags[C.Underflow]: - # The standard ulp does not work in Underflow territory. - ulp = self.harrison_ulp(y) - else: - ulp = self.standard_ulp(y, p) - # Error in ulps. - err = self.maxctx.divide(t, ulp) - - dir = self.rounding_direction(x, context.p.rounding) - if dir == 0: - if P.Decimal("-0.6") < err < P.Decimal("0.6"): - return True - elif dir == 1: # directed, upwards - if P.Decimal("-0.1") < err < P.Decimal("1.1"): - return True - elif dir == -1: # directed, downwards - if P.Decimal("-1.1") < err < P.Decimal("0.1"): - return True - else: # ROUND_05UP - if P.Decimal("-1.1") < err < P.Decimal("1.1"): - return True - - print("ulp: %s error: %s exact: %s c_rounded: %s" - % (ulp, err, exact, rounded)) - return False - - def bin_resolve_ulp(self, t): - """Check if results of _decimal's power function are within the - allowed ulp ranges.""" - # NaNs are beyond repair. - if t.rc.is_nan() or t.rp.is_nan(): - return False - - # "exact" result, double precision, half_even - self.maxctx.prec = context.p.prec * 2 - - op1, op2 = t.pop[0], t.pop[1] - if t.contextfunc: - exact = getattr(self.maxctx, t.funcname)(op1, op2) - else: - exact = getattr(op1, t.funcname)(op2, context=self.maxctx) - - # _decimal's rounded result - rounded = P.Decimal(t.cresults[0]) - - self.ulpdiff += 1 - return self.check_ulpdiff(exact, rounded) - - ############################ Correct rounding ############################# - def resolve_underflow(self, t): - """In extremely rare cases where the infinite precision result is just - below etiny, cdecimal does not set Subnormal/Underflow. Example: - - setcontext(Context(prec=21, rounding=ROUND_UP, Emin=-55, Emax=85)) - Decimal("1.00000000000000000000000000000000000000000000000" - "0000000100000000000000000000000000000000000000000" - "0000000000000025").ln() - """ - if t.cresults != t.presults: - return False # Results must be identical. - if context.c.flags[C.Rounded] and \ - context.c.flags[C.Inexact] and \ - context.p.flags[P.Rounded] and \ - context.p.flags[P.Inexact]: - return True # Subnormal/Underflow may be missing. - return False - - def exp(self, t): - """Resolve Underflow or ULP difference.""" - return self.resolve_underflow(t) - - def log10(self, t): - """Resolve Underflow or ULP difference.""" - return self.resolve_underflow(t) - - def ln(self, t): - """Resolve Underflow or ULP difference.""" - return self.resolve_underflow(t) - - def __pow__(self, t): - """Always calls the resolve function. C.Decimal does not have correct - rounding for the power function.""" - if context.c.flags[C.Rounded] and \ - context.c.flags[C.Inexact] and \ - context.p.flags[P.Rounded] and \ - context.p.flags[P.Inexact]: - return self.bin_resolve_ulp(t) - else: - return False - power = __rpow__ = __pow__ - - ############################## Technicalities ############################# - def __float__(self, t): - """NaN comparison in the verify() function obviously gives an - incorrect answer: nan == nan -> False""" - if t.cop[0].is_nan() and t.pop[0].is_nan(): - return True - return False - __complex__ = __float__ - - def __radd__(self, t): - """decimal.py gives precedence to the first NaN; this is - not important, as __radd__ will not be called for - two decimal arguments.""" - if t.rc.is_nan() and t.rp.is_nan(): - return True - return False - __rmul__ = __radd__ - - ################################ Various ################################## - def __round__(self, t): - """Exception: Decimal('1').__round__(-100000000000000000000000000) - Should it really be InvalidOperation?""" - if t.rc is None and t.rp.is_nan(): - return True - return False - -shandler = SkipHandler() -def skip_error(t): - return getattr(shandler, t.funcname, shandler.default)(t) - - -# ====================================================================== -# Handling verification errors -# ====================================================================== - -class VerifyError(Exception): - """Verification failed.""" - pass - -def function_as_string(t): - if t.contextfunc: - cargs = t.cop - pargs = t.pop - cfunc = "c_func: %s(" % t.funcname - pfunc = "p_func: %s(" % t.funcname - else: - cself, cargs = t.cop[0], t.cop[1:] - pself, pargs = t.pop[0], t.pop[1:] - cfunc = "c_func: %s.%s(" % (repr(cself), t.funcname) - pfunc = "p_func: %s.%s(" % (repr(pself), t.funcname) - - err = cfunc - for arg in cargs: - err += "%s, " % repr(arg) - err = err.rstrip(", ") - err += ")\n" - - err += pfunc - for arg in pargs: - err += "%s, " % repr(arg) - err = err.rstrip(", ") - err += ")" - - return err - -def raise_error(t): - global EXIT_STATUS - - if skip_error(t): - return - EXIT_STATUS = 1 - - err = "Error in %s:\n\n" % t.funcname - err += "input operands: %s\n\n" % (t.op,) - err += function_as_string(t) - err += "\n\nc_result: %s\np_result: %s\n\n" % (t.cresults, t.presults) - err += "c_exceptions: %s\np_exceptions: %s\n\n" % (t.cex, t.pex) - err += "%s\n\n" % str(t.context) - - raise VerifyError(err) - - -# ====================================================================== -# Main testing functions -# -# The procedure is always (t is the TestSet): -# -# convert(t) -> Initialize the TestSet as necessary. -# -# Return 0 for early abortion (e.g. if a TypeError -# occurs during conversion, there is nothing to test). -# -# Return 1 for continuing with the test case. -# -# callfuncs(t) -> Call the relevant function for each implementation -# and record the results in the TestSet. -# -# verify(t) -> Verify the results. If verification fails, details -# are printed to stdout. -# ====================================================================== - -def convert(t, convstr=True): - """ t is the testset. At this stage the testset contains a tuple of - operands t.op of various types. For decimal methods the first - operand (self) is always converted to Decimal. If 'convstr' is - true, string operands are converted as well. - - Context operands are of type deccheck.Context, rounding mode - operands are given as a tuple (C.rounding, P.rounding). - - Other types (float, int, etc.) are left unchanged. - """ - for i, op in enumerate(t.op): - - context.clear_status() - - if op in RoundModes: - t.cop.append(op) - t.pop.append(op) - - elif not t.contextfunc and i == 0 or \ - convstr and isinstance(op, str): - try: - c = C.Decimal(op) - cex = None - except (TypeError, ValueError, OverflowError) as e: - c = None - cex = e.__class__ - - try: - p = RestrictedDecimal(op) - pex = None - except (TypeError, ValueError, OverflowError) as e: - p = None - pex = e.__class__ - - t.cop.append(c) - t.cex.append(cex) - t.pop.append(p) - t.pex.append(pex) - - if cex is pex: - if str(c) != str(p) or not context.assert_eq_status(): - raise_error(t) - if cex and pex: - # nothing to test - return 0 - else: - raise_error(t) - - elif isinstance(op, Context): - t.context = op - t.cop.append(op.c) - t.pop.append(op.p) - - else: - t.cop.append(op) - t.pop.append(op) - - return 1 - -def callfuncs(t): - """ t is the testset. At this stage the testset contains operand lists - t.cop and t.pop for the C and Python versions of decimal. - For Decimal methods, the first operands are of type C.Decimal and - P.Decimal respectively. The remaining operands can have various types. - For Context methods, all operands can have any type. - - t.rc and t.rp are the results of the operation. - """ - context.clear_status() - - try: - if t.contextfunc: - cargs = t.cop - t.rc = getattr(context.c, t.funcname)(*cargs) - else: - cself = t.cop[0] - cargs = t.cop[1:] - t.rc = getattr(cself, t.funcname)(*cargs) - t.cex.append(None) - except (TypeError, ValueError, OverflowError, MemoryError) as e: - t.rc = None - t.cex.append(e.__class__) - - try: - if t.contextfunc: - pargs = t.pop - t.rp = getattr(context.p, t.funcname)(*pargs) - else: - pself = t.pop[0] - pargs = t.pop[1:] - t.rp = getattr(pself, t.funcname)(*pargs) - t.pex.append(None) - except (TypeError, ValueError, OverflowError, MemoryError) as e: - t.rp = None - t.pex.append(e.__class__) - -def verify(t, stat): - """ t is the testset. At this stage the testset contains the following - tuples: - - t.op: original operands - t.cop: C.Decimal operands (see convert for details) - t.pop: P.Decimal operands (see convert for details) - t.rc: C result - t.rp: Python result - - t.rc and t.rp can have various types. - """ - t.cresults.append(str(t.rc)) - t.presults.append(str(t.rp)) - if isinstance(t.rc, C.Decimal) and isinstance(t.rp, P.Decimal): - # General case: both results are Decimals. - t.cresults.append(t.rc.to_eng_string()) - t.cresults.append(t.rc.as_tuple()) - t.cresults.append(str(t.rc.imag)) - t.cresults.append(str(t.rc.real)) - t.presults.append(t.rp.to_eng_string()) - t.presults.append(t.rp.as_tuple()) - t.presults.append(str(t.rp.imag)) - t.presults.append(str(t.rp.real)) - - nc = t.rc.number_class().lstrip('+-s') - stat[nc] += 1 - else: - # Results from e.g. __divmod__ can only be compared as strings. - if not isinstance(t.rc, tuple) and not isinstance(t.rp, tuple): - if t.rc != t.rp: - raise_error(t) - stat[type(t.rc).__name__] += 1 - - # The return value lists must be equal. - if t.cresults != t.presults: - raise_error(t) - # The Python exception lists (TypeError, etc.) must be equal. - if t.cex != t.pex: - raise_error(t) - # The context flags must be equal. - if not t.context.assert_eq_status(): - raise_error(t) - - -# ====================================================================== -# Main test loops -# -# test_method(method, testspecs, testfunc) -> -# -# Loop through various context settings. The degree of -# thoroughness is determined by 'testspec'. For each -# setting, call 'testfunc'. Generally, 'testfunc' itself -# a loop, iterating through many test cases generated -# by the functions in randdec.py. -# -# test_n-ary(method, prec, exp_range, restricted_range, itr, stat) -> -# -# 'test_unary', 'test_binary' and 'test_ternary' are the -# main test functions passed to 'test_method'. They deal -# with the regular cases. The thoroughness of testing is -# determined by 'itr'. -# -# 'prec', 'exp_range' and 'restricted_range' are passed -# to the test-generating functions and limit the generated -# values. In some cases, for reasonable run times a -# maximum exponent of 9999 is required. -# -# The 'stat' parameter is passed down to the 'verify' -# function, which records statistics for the result values. -# ====================================================================== - -def log(fmt, args=None): - if args: - sys.stdout.write(''.join((fmt, '\n')) % args) - else: - sys.stdout.write(''.join((str(fmt), '\n'))) - sys.stdout.flush() - -def test_method(method, testspecs, testfunc): - """Iterate a test function through many context settings.""" - log("testing %s ...", method) - stat = defaultdict(int) - for spec in testspecs: - if 'samples' in spec: - spec['prec'] = sorted(random.sample(range(1, 101), - spec['samples'])) - for prec in spec['prec']: - context.prec = prec - for expts in spec['expts']: - emin, emax = expts - if emin == 'rand': - context.Emin = random.randrange(-1000, 0) - context.Emax = random.randrange(prec, 1000) - else: - context.Emin, context.Emax = emin, emax - if prec > context.Emax: continue - log(" prec: %d emin: %d emax: %d", - (context.prec, context.Emin, context.Emax)) - restr_range = 9999 if context.Emax > 9999 else context.Emax+99 - for rounding in RoundModes: - context.rounding = rounding - context.capitals = random.randrange(2) - if spec['clamp'] == 'rand': - context.clamp = random.randrange(2) - else: - context.clamp = spec['clamp'] - exprange = context.c.Emax - testfunc(method, prec, exprange, restr_range, - spec['iter'], stat) - log(" result types: %s" % sorted([t for t in stat.items()])) - -def test_unary(method, prec, exp_range, restricted_range, itr, stat): - """Iterate a unary function through many test cases.""" - if method in UnaryRestricted: - exp_range = restricted_range - for op in all_unary(prec, exp_range, itr): - t = TestSet(method, op) - try: - if not convert(t): - continue - callfuncs(t) - verify(t, stat) - except VerifyError as err: - log(err) - - if not method.startswith('__'): - for op in unary_optarg(prec, exp_range, itr): - t = TestSet(method, op) - try: - if not convert(t): - continue - callfuncs(t) - verify(t, stat) - except VerifyError as err: - log(err) - -def test_binary(method, prec, exp_range, restricted_range, itr, stat): - """Iterate a binary function through many test cases.""" - if method in BinaryRestricted: - exp_range = restricted_range - for op in all_binary(prec, exp_range, itr): - t = TestSet(method, op) - try: - if not convert(t): - continue - callfuncs(t) - verify(t, stat) - except VerifyError as err: - log(err) - - if not method.startswith('__'): - for op in binary_optarg(prec, exp_range, itr): - t = TestSet(method, op) - try: - if not convert(t): - continue - callfuncs(t) - verify(t, stat) - except VerifyError as err: - log(err) - -def test_ternary(method, prec, exp_range, restricted_range, itr, stat): - """Iterate a ternary function through many test cases.""" - if method in TernaryRestricted: - exp_range = restricted_range - for op in all_ternary(prec, exp_range, itr): - t = TestSet(method, op) - try: - if not convert(t): - continue - callfuncs(t) - verify(t, stat) - except VerifyError as err: - log(err) - - if not method.startswith('__'): - for op in ternary_optarg(prec, exp_range, itr): - t = TestSet(method, op) - try: - if not convert(t): - continue - callfuncs(t) - verify(t, stat) - except VerifyError as err: - log(err) - -def test_format(method, prec, exp_range, restricted_range, itr, stat): - """Iterate the __format__ method through many test cases.""" - for op in all_unary(prec, exp_range, itr): - fmt1 = rand_format(chr(random.randrange(0, 128)), 'EeGgn') - fmt2 = rand_locale() - for fmt in (fmt1, fmt2): - fmtop = (op[0], fmt) - t = TestSet(method, fmtop) - try: - if not convert(t, convstr=False): - continue - callfuncs(t) - verify(t, stat) - except VerifyError as err: - log(err) - for op in all_unary(prec, 9999, itr): - fmt1 = rand_format(chr(random.randrange(0, 128)), 'Ff%') - fmt2 = rand_locale() - for fmt in (fmt1, fmt2): - fmtop = (op[0], fmt) - t = TestSet(method, fmtop) - try: - if not convert(t, convstr=False): - continue - callfuncs(t) - verify(t, stat) - except VerifyError as err: - log(err) - -def test_round(method, prec, exprange, restricted_range, itr, stat): - """Iterate the __round__ method through many test cases.""" - for op in all_unary(prec, 9999, itr): - n = random.randrange(10) - roundop = (op[0], n) - t = TestSet(method, roundop) - try: - if not convert(t): - continue - callfuncs(t) - verify(t, stat) - except VerifyError as err: - log(err) - -def test_from_float(method, prec, exprange, restricted_range, itr, stat): - """Iterate the __float__ method through many test cases.""" - for rounding in RoundModes: - context.rounding = rounding - for i in range(1000): - f = randfloat() - op = (f,) if method.startswith("context.") else ("sNaN", f) - t = TestSet(method, op) - try: - if not convert(t): - continue - callfuncs(t) - verify(t, stat) - except VerifyError as err: - log(err) - -def randcontext(exprange): - c = Context(C.Context(), P.Context()) - c.Emax = random.randrange(1, exprange+1) - c.Emin = random.randrange(-exprange, 0) - maxprec = 100 if c.Emax >= 100 else c.Emax - c.prec = random.randrange(1, maxprec+1) - c.clamp = random.randrange(2) - c.clear_traps() - return c - -def test_quantize_api(method, prec, exprange, restricted_range, itr, stat): - """Iterate the 'quantize' method through many test cases, using - the optional arguments.""" - for op in all_binary(prec, restricted_range, itr): - for rounding in RoundModes: - c = randcontext(exprange) - quantizeop = (op[0], op[1], rounding, c) - t = TestSet(method, quantizeop) - try: - if not convert(t): - continue - callfuncs(t) - verify(t, stat) - except VerifyError as err: - log(err) - - -def check_untested(funcdict, c_cls, p_cls): - """Determine untested, C-only and Python-only attributes. - Uncomment print lines for debugging.""" - c_attr = set(dir(c_cls)) - p_attr = set(dir(p_cls)) - intersect = c_attr & p_attr - - funcdict['c_only'] = tuple(sorted(c_attr-intersect)) - funcdict['p_only'] = tuple(sorted(p_attr-intersect)) - - tested = set() - for lst in funcdict.values(): - for v in lst: - v = v.replace("context.", "") if c_cls == C.Context else v - tested.add(v) - - funcdict['untested'] = tuple(sorted(intersect-tested)) - - #for key in ('untested', 'c_only', 'p_only'): - # s = 'Context' if c_cls == C.Context else 'Decimal' - # print("\n%s %s:\n%s" % (s, key, funcdict[key])) - - -if __name__ == '__main__': - - import time - - randseed = int(time.time()) - random.seed(randseed) - - # Set up the testspecs list. A testspec is simply a dictionary - # that determines the amount of different contexts that 'test_method' - # will generate. - base_expts = [(C.MIN_EMIN, C.MAX_EMAX)] - if C.MAX_EMAX == 999999999999999999: - base_expts.append((-999999999, 999999999)) - - # Basic contexts. - base = { - 'expts': base_expts, - 'prec': [], - 'clamp': 'rand', - 'iter': None, - 'samples': None, - } - # Contexts with small values for prec, emin, emax. - small = { - 'prec': [1, 2, 3, 4, 5], - 'expts': [(-1, 1), (-2, 2), (-3, 3), (-4, 4), (-5, 5)], - 'clamp': 'rand', - 'iter': None - } - # IEEE interchange format. - ieee = [ - # DECIMAL32 - {'prec': [7], 'expts': [(-95, 96)], 'clamp': 1, 'iter': None}, - # DECIMAL64 - {'prec': [16], 'expts': [(-383, 384)], 'clamp': 1, 'iter': None}, - # DECIMAL128 - {'prec': [34], 'expts': [(-6143, 6144)], 'clamp': 1, 'iter': None} - ] - - if '--medium' in sys.argv: - base['expts'].append(('rand', 'rand')) - # 5 random precisions - base['samples'] = 5 - testspecs = [small] + ieee + [base] - if '--long' in sys.argv: - base['expts'].append(('rand', 'rand')) - # 10 random precisions - base['samples'] = 10 - testspecs = [small] + ieee + [base] - elif '--all' in sys.argv: - base['expts'].append(('rand', 'rand')) - # All precisions in [1, 100] - base['samples'] = 100 - testspecs = [small] + ieee + [base] - else: # --short - rand_ieee = random.choice(ieee) - base['iter'] = small['iter'] = rand_ieee['iter'] = 1 - # 1 random precision and exponent pair - base['samples'] = 1 - base['expts'] = [random.choice(base_expts)] - # 1 random precision and exponent pair - prec = random.randrange(1, 6) - small['prec'] = [prec] - small['expts'] = [(-prec, prec)] - testspecs = [small, rand_ieee, base] - - check_untested(Functions, C.Decimal, P.Decimal) - check_untested(ContextFunctions, C.Context, P.Context) - - - log("\n\nRandom seed: %d\n\n", randseed) - - # Decimal methods: - for method in Functions['unary'] + Functions['unary_ctx'] + \ - Functions['unary_rnd_ctx']: - test_method(method, testspecs, test_unary) - - for method in Functions['binary'] + Functions['binary_ctx']: - test_method(method, testspecs, test_binary) - - for method in Functions['ternary'] + Functions['ternary_ctx']: - test_method(method, testspecs, test_ternary) - - test_method('__format__', testspecs, test_format) - test_method('__round__', testspecs, test_round) - test_method('from_float', testspecs, test_from_float) - test_method('quantize', testspecs, test_quantize_api) - - # Context methods: - for method in ContextFunctions['unary']: - test_method(method, testspecs, test_unary) - - for method in ContextFunctions['binary']: - test_method(method, testspecs, test_binary) - - for method in ContextFunctions['ternary']: - test_method(method, testspecs, test_ternary) - - test_method('context.create_decimal_from_float', testspecs, test_from_float) - - - sys.exit(EXIT_STATUS) diff --git a/Modules/_decimal/tests/formathelper.py b/Modules/_decimal/tests/formathelper.py deleted file mode 100644 index 19b2aad..0000000 --- a/Modules/_decimal/tests/formathelper.py +++ /dev/null @@ -1,342 +0,0 @@ -# -# Copyright (c) 2008-2012 Stefan Krah. All rights reserved. -# -# Redistribution and use in source and binary forms, with or without -# modification, are permitted provided that the following conditions -# are met: -# -# 1. Redistributions of source code must retain the above copyright -# notice, this list of conditions and the following disclaimer. -# -# 2. Redistributions in binary form must reproduce the above copyright -# notice, this list of conditions and the following disclaimer in the -# documentation and/or other materials provided with the distribution. -# -# THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND -# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE -# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE -# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL -# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS -# OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) -# HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT -# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY -# OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF -# SUCH DAMAGE. -# - - -# Generate PEP-3101 format strings. - - -import os, sys, locale, random -import platform, subprocess -from test.support import import_fresh_module -from distutils.spawn import find_executable - -C = import_fresh_module('decimal', fresh=['_decimal']) -P = import_fresh_module('decimal', blocked=['_decimal']) - - -windows_lang_strings = [ - "chinese", "chinese-simplified", "chinese-traditional", "czech", "danish", - "dutch", "belgian", "english", "australian", "canadian", "english-nz", - "english-uk", "english-us", "finnish", "french", "french-belgian", - "french-canadian", "french-swiss", "german", "german-austrian", - "german-swiss", "greek", "hungarian", "icelandic", "italian", "italian-swiss", - "japanese", "korean", "norwegian", "norwegian-bokmal", "norwegian-nynorsk", - "polish", "portuguese", "portuguese-brazil", "russian", "slovak", "spanish", - "spanish-mexican", "spanish-modern", "swedish", "turkish", -] - -preferred_encoding = { - 'cs_CZ': 'ISO8859-2', - 'cs_CZ.iso88592': 'ISO8859-2', - 'czech': 'ISO8859-2', - 'eesti': 'ISO8859-1', - 'estonian': 'ISO8859-1', - 'et_EE': 'ISO8859-15', - 'et_EE.ISO-8859-15': 'ISO8859-15', - 'et_EE.iso885915': 'ISO8859-15', - 'et_EE.iso88591': 'ISO8859-1', - 'fi_FI.iso88591': 'ISO8859-1', - 'fi_FI': 'ISO8859-15', - 'fi_FI@euro': 'ISO8859-15', - 'fi_FI.iso885915@euro': 'ISO8859-15', - 'finnish': 'ISO8859-1', - 'lv_LV': 'ISO8859-13', - 'lv_LV.iso885913': 'ISO8859-13', - 'nb_NO': 'ISO8859-1', - 'nb_NO.iso88591': 'ISO8859-1', - 'bokmal': 'ISO8859-1', - 'nn_NO': 'ISO8859-1', - 'nn_NO.iso88591': 'ISO8859-1', - 'no_NO': 'ISO8859-1', - 'norwegian': 'ISO8859-1', - 'nynorsk': 'ISO8859-1', - 'ru_RU': 'ISO8859-5', - 'ru_RU.iso88595': 'ISO8859-5', - 'russian': 'ISO8859-5', - 'ru_RU.KOI8-R': 'KOI8-R', - 'ru_RU.koi8r': 'KOI8-R', - 'ru_RU.CP1251': 'CP1251', - 'ru_RU.cp1251': 'CP1251', - 'sk_SK': 'ISO8859-2', - 'sk_SK.iso88592': 'ISO8859-2', - 'slovak': 'ISO8859-2', - 'sv_FI': 'ISO8859-1', - 'sv_FI.iso88591': 'ISO8859-1', - 'sv_FI@euro': 'ISO8859-15', - 'sv_FI.iso885915@euro': 'ISO8859-15', - 'uk_UA': 'KOI8-U', - 'uk_UA.koi8u': 'KOI8-U' -} - -integers = [ - "", - "1", - "12", - "123", - "1234", - "12345", - "123456", - "1234567", - "12345678", - "123456789", - "1234567890", - "12345678901", - "123456789012", - "1234567890123", - "12345678901234", - "123456789012345", - "1234567890123456", - "12345678901234567", - "123456789012345678", - "1234567890123456789", - "12345678901234567890", - "123456789012345678901", - "1234567890123456789012", -] - -numbers = [ - "0", "-0", "+0", - "0.0", "-0.0", "+0.0", - "0e0", "-0e0", "+0e0", - ".0", "-.0", - ".1", "-.1", - "1.1", "-1.1", - "1e1", "-1e1" -] - -# Get the list of available locales. -if platform.system() == 'Windows': - locale_list = windows_lang_strings -else: - locale_list = ['C'] - if os.path.isfile("/var/lib/locales/supported.d/local"): - # On Ubuntu, `locale -a` gives the wrong case for some locales, - # so we get the correct names directly: - with open("/var/lib/locales/supported.d/local") as f: - locale_list = [loc.split()[0] for loc in f.readlines() \ - if not loc.startswith('#')] - elif find_executable('locale'): - locale_list = subprocess.Popen(["locale", "-a"], - stdout=subprocess.PIPE).communicate()[0] - try: - locale_list = locale_list.decode() - except UnicodeDecodeError: - # Some distributions insist on using latin-1 characters - # in their locale names. - locale_list = locale_list.decode('latin-1') - locale_list = locale_list.split('\n') -try: - locale_list.remove('') -except ValueError: - pass - -# Debian -if os.path.isfile("/etc/locale.alias"): - with open("/etc/locale.alias") as f: - while 1: - try: - line = f.readline() - except UnicodeDecodeError: - continue - if line == "": - break - if line.startswith('#'): - continue - x = line.split() - if len(x) == 2: - if x[0] in locale_list: - locale_list.remove(x[0]) - -# FreeBSD -if platform.system() == 'FreeBSD': - # http://www.freebsd.org/cgi/query-pr.cgi?pr=142173 - # en_GB.US-ASCII has 163 as the currency symbol. - for loc in ['it_CH.ISO8859-1', 'it_CH.ISO8859-15', 'it_CH.UTF-8', - 'it_IT.ISO8859-1', 'it_IT.ISO8859-15', 'it_IT.UTF-8', - 'sl_SI.ISO8859-2', 'sl_SI.UTF-8', - 'en_GB.US-ASCII']: - try: - locale_list.remove(loc) - except ValueError: - pass - -# Print a testcase in the format of the IBM tests (for runtest.c): -def get_preferred_encoding(): - loc = locale.setlocale(locale.LC_CTYPE) - if loc in preferred_encoding: - return preferred_encoding[loc] - else: - return locale.getpreferredencoding() - -def printit(testno, s, fmt, encoding=None): - if not encoding: - encoding = get_preferred_encoding() - try: - result = format(P.Decimal(s), fmt) - fmt = str(fmt.encode(encoding))[2:-1] - result = str(result.encode(encoding))[2:-1] - if "'" in result: - sys.stdout.write("xfmt%d format %s '%s' -> \"%s\"\n" - % (testno, s, fmt, result)) - else: - sys.stdout.write("xfmt%d format %s '%s' -> '%s'\n" - % (testno, s, fmt, result)) - except Exception as err: - sys.stderr.write("%s %s %s\n" % (err, s, fmt)) - - -# Check if an integer can be converted to a valid fill character. -def check_fillchar(i): - try: - c = chr(i) - c.encode('utf-8').decode() - format(P.Decimal(0), c + '<19g') - return c - except: - return None - -# Generate all unicode characters that are accepted as -# fill characters by decimal.py. -def all_fillchars(): - for i in range(0, 0x110002): - c = check_fillchar(i) - if c: yield c - -# Return random fill character. -def rand_fillchar(): - while 1: - i = random.randrange(0, 0x110002) - c = check_fillchar(i) - if c: return c - -# Generate random format strings -# [[fill]align][sign][#][0][width][.precision][type] -def rand_format(fill, typespec='EeGgFfn%'): - active = sorted(random.sample(range(7), random.randrange(8))) - have_align = 0 - s = '' - for elem in active: - if elem == 0: # fill+align - s += fill - s += random.choice('<>=^') - have_align = 1 - elif elem == 1: # sign - s += random.choice('+- ') - elif elem == 2 and not have_align: # zeropad - s += '0' - elif elem == 3: # width - s += str(random.randrange(1, 100)) - elif elem == 4: # thousands separator - s += ',' - elif elem == 5: # prec - s += '.' - s += str(random.randrange(100)) - elif elem == 6: - if 4 in active: c = typespec.replace('n', '') - else: c = typespec - s += random.choice(c) - return s - -# Partially brute force all possible format strings containing a thousands -# separator. Fall back to random where the runtime would become excessive. -# [[fill]align][sign][#][0][width][,][.precision][type] -def all_format_sep(): - for align in ('', '<', '>', '=', '^'): - for fill in ('', 'x'): - if align == '': fill = '' - for sign in ('', '+', '-', ' '): - for zeropad in ('', '0'): - if align != '': zeropad = '' - for width in ['']+[str(y) for y in range(1, 15)]+['101']: - for prec in ['']+['.'+str(y) for y in range(15)]: - # for type in ('', 'E', 'e', 'G', 'g', 'F', 'f', '%'): - type = random.choice(('', 'E', 'e', 'G', 'g', 'F', 'f', '%')) - yield ''.join((fill, align, sign, zeropad, width, ',', prec, type)) - -# Partially brute force all possible format strings with an 'n' specifier. -# [[fill]align][sign][#][0][width][,][.precision][type] -def all_format_loc(): - for align in ('', '<', '>', '=', '^'): - for fill in ('', 'x'): - if align == '': fill = '' - for sign in ('', '+', '-', ' '): - for zeropad in ('', '0'): - if align != '': zeropad = '' - for width in ['']+[str(y) for y in range(1, 20)]+['101']: - for prec in ['']+['.'+str(y) for y in range(1, 20)]: - yield ''.join((fill, align, sign, zeropad, width, prec, 'n')) - -# Generate random format strings with a unicode fill character -# [[fill]align][sign][#][0][width][,][.precision][type] -def randfill(fill): - active = sorted(random.sample(range(5), random.randrange(6))) - s = '' - s += str(fill) - s += random.choice('<>=^') - for elem in active: - if elem == 0: # sign - s += random.choice('+- ') - elif elem == 1: # width - s += str(random.randrange(1, 100)) - elif elem == 2: # thousands separator - s += ',' - elif elem == 3: # prec - s += '.' - s += str(random.randrange(100)) - elif elem == 4: - if 2 in active: c = 'EeGgFf%' - else: c = 'EeGgFfn%' - s += random.choice(c) - return s - -# Generate random format strings with random locale setting -# [[fill]align][sign][#][0][width][,][.precision][type] -def rand_locale(): - try: - loc = random.choice(locale_list) - locale.setlocale(locale.LC_ALL, loc) - except locale.Error as err: - pass - active = sorted(random.sample(range(5), random.randrange(6))) - s = '' - have_align = 0 - for elem in active: - if elem == 0: # fill+align - s += chr(random.randrange(32, 128)) - s += random.choice('<>=^') - have_align = 1 - elif elem == 1: # sign - s += random.choice('+- ') - elif elem == 2 and not have_align: # zeropad - s += '0' - elif elem == 3: # width - s += str(random.randrange(1, 100)) - elif elem == 4: # prec - s += '.' - s += str(random.randrange(100)) - s += 'n' - return s diff --git a/Modules/_decimal/tests/randdec.py b/Modules/_decimal/tests/randdec.py deleted file mode 100644 index d667f79..0000000 --- a/Modules/_decimal/tests/randdec.py +++ /dev/null @@ -1,575 +0,0 @@ -# -# Copyright (c) 2008-2012 Stefan Krah. All rights reserved. -# -# Redistribution and use in source and binary forms, with or without -# modification, are permitted provided that the following conditions -# are met: -# -# 1. Redistributions of source code must retain the above copyright -# notice, this list of conditions and the following disclaimer. -# -# 2. Redistributions in binary form must reproduce the above copyright -# notice, this list of conditions and the following disclaimer in the -# documentation and/or other materials provided with the distribution. -# -# THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND -# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE -# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE -# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL -# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS -# OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) -# HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT -# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY -# OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF -# SUCH DAMAGE. -# - - -# Generate test cases for deccheck.py. - - -# -# Grammar from http://speleotrove.com/decimal/daconvs.html -# -# sign ::= '+' | '-' -# digit ::= '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | -# '8' | '9' -# indicator ::= 'e' | 'E' -# digits ::= digit [digit]... -# decimal-part ::= digits '.' [digits] | ['.'] digits -# exponent-part ::= indicator [sign] digits -# infinity ::= 'Infinity' | 'Inf' -# nan ::= 'NaN' [digits] | 'sNaN' [digits] -# numeric-value ::= decimal-part [exponent-part] | infinity -# numeric-string ::= [sign] numeric-value | [sign] nan -# - - -from random import randrange, sample -from fractions import Fraction -from randfloat import un_randfloat, bin_randfloat, tern_randfloat - - -def sign(): - if randrange(2): - if randrange(2): return '+' - return '' - return '-' - -def indicator(): - return "eE"[randrange(2)] - -def digits(maxprec): - if maxprec == 0: return '' - return str(randrange(10**maxprec)) - -def dot(): - if randrange(2): return '.' - return '' - -def decimal_part(maxprec): - if randrange(100) > 60: # integers - return digits(maxprec) - if randrange(2): - intlen = randrange(1, maxprec+1) - fraclen = maxprec-intlen - intpart = digits(intlen) - fracpart = digits(fraclen) - return ''.join((intpart, '.', fracpart)) - else: - return ''.join((dot(), digits(maxprec))) - -def expdigits(maxexp): - return str(randrange(maxexp)) - -def exponent_part(maxexp): - return ''.join((indicator(), sign(), expdigits(maxexp))) - -def infinity(): - if randrange(2): return 'Infinity' - return 'Inf' - -def nan(): - d = '' - if randrange(2): - d = digits(randrange(99)) - if randrange(2): - return ''.join(('NaN', d)) - else: - return ''.join(('sNaN', d)) - -def numeric_value(maxprec, maxexp): - if randrange(100) > 90: - return infinity() - exp_part = '' - if randrange(100) > 60: - exp_part = exponent_part(maxexp) - return ''.join((decimal_part(maxprec), exp_part)) - -def numeric_string(maxprec, maxexp): - if randrange(100) > 95: - return ''.join((sign(), nan())) - else: - return ''.join((sign(), numeric_value(maxprec, maxexp))) - -def randdec(maxprec, maxexp): - return numeric_string(maxprec, maxexp) - -def rand_adjexp(maxprec, maxadjexp): - d = digits(maxprec) - maxexp = maxadjexp-len(d)+1 - if maxexp == 0: maxexp = 1 - exp = str(randrange(maxexp-2*(abs(maxexp)), maxexp)) - return ''.join((sign(), d, 'E', exp)) - - -def ndigits(n): - if n < 1: return 0 - return randrange(10**(n-1), 10**n) - -def randtuple(maxprec, maxexp): - n = randrange(100) - sign = randrange(2) - coeff = ndigits(maxprec) - if n >= 95: - coeff = () - exp = 'F' - elif n >= 85: - coeff = tuple(map(int, str(ndigits(maxprec)))) - exp = "nN"[randrange(2)] - else: - coeff = tuple(map(int, str(ndigits(maxprec)))) - exp = randrange(-maxexp, maxexp) - return (sign, coeff, exp) - -def from_triple(sign, coeff, exp): - return ''.join((str(sign*coeff), indicator(), str(exp))) - - -# Close to 10**n -def un_close_to_pow10(prec, maxexp, itr=None): - if itr is None: - lst = range(prec+30) - else: - lst = sample(range(prec+30), itr) - nines = [10**n - 1 for n in lst] - pow10 = [10**n for n in lst] - for coeff in nines: - yield coeff - yield -coeff - yield from_triple(1, coeff, randrange(2*maxexp)) - yield from_triple(-1, coeff, randrange(2*maxexp)) - for coeff in pow10: - yield coeff - yield -coeff - -# Close to 10**n -def bin_close_to_pow10(prec, maxexp, itr=None): - if itr is None: - lst = range(prec+30) - else: - lst = sample(range(prec+30), itr) - nines = [10**n - 1 for n in lst] - pow10 = [10**n for n in lst] - for coeff in nines: - yield coeff, 1 - yield -coeff, -1 - yield 1, coeff - yield -1, -coeff - yield from_triple(1, coeff, randrange(2*maxexp)), 1 - yield from_triple(-1, coeff, randrange(2*maxexp)), -1 - yield 1, from_triple(1, coeff, -randrange(2*maxexp)) - yield -1, from_triple(-1, coeff, -randrange(2*maxexp)) - for coeff in pow10: - yield coeff, -1 - yield -coeff, 1 - yield 1, -coeff - yield -coeff, 1 - -# Close to 1: -def close_to_one_greater(prec, emax, emin): - rprec = 10**prec - return ''.join(("1.", '0'*randrange(prec), - str(randrange(rprec)))) - -def close_to_one_less(prec, emax, emin): - rprec = 10**prec - return ''.join(("0.9", '9'*randrange(prec), - str(randrange(rprec)))) - -# Close to 0: -def close_to_zero_greater(prec, emax, emin): - rprec = 10**prec - return ''.join(("0.", '0'*randrange(prec), - str(randrange(rprec)))) - -def close_to_zero_less(prec, emax, emin): - rprec = 10**prec - return ''.join(("-0.", '0'*randrange(prec), - str(randrange(rprec)))) - -# Close to emax: -def close_to_emax_less(prec, emax, emin): - rprec = 10**prec - return ''.join(("9.", '9'*randrange(prec), - str(randrange(rprec)), "E", str(emax))) - -def close_to_emax_greater(prec, emax, emin): - rprec = 10**prec - return ''.join(("1.", '0'*randrange(prec), - str(randrange(rprec)), "E", str(emax+1))) - -# Close to emin: -def close_to_emin_greater(prec, emax, emin): - rprec = 10**prec - return ''.join(("1.", '0'*randrange(prec), - str(randrange(rprec)), "E", str(emin))) - -def close_to_emin_less(prec, emax, emin): - rprec = 10**prec - return ''.join(("9.", '9'*randrange(prec), - str(randrange(rprec)), "E", str(emin-1))) - -# Close to etiny: -def close_to_etiny_greater(prec, emax, emin): - rprec = 10**prec - etiny = emin - (prec - 1) - return ''.join(("1.", '0'*randrange(prec), - str(randrange(rprec)), "E", str(etiny))) - -def close_to_etiny_less(prec, emax, emin): - rprec = 10**prec - etiny = emin - (prec - 1) - return ''.join(("9.", '9'*randrange(prec), - str(randrange(rprec)), "E", str(etiny-1))) - - -def close_to_min_etiny_greater(prec, max_prec, min_emin): - rprec = 10**prec - etiny = min_emin - (max_prec - 1) - return ''.join(("1.", '0'*randrange(prec), - str(randrange(rprec)), "E", str(etiny))) - -def close_to_min_etiny_less(prec, max_prec, min_emin): - rprec = 10**prec - etiny = min_emin - (max_prec - 1) - return ''.join(("9.", '9'*randrange(prec), - str(randrange(rprec)), "E", str(etiny-1))) - - -close_funcs = [ - close_to_one_greater, close_to_one_less, close_to_zero_greater, - close_to_zero_less, close_to_emax_less, close_to_emax_greater, - close_to_emin_greater, close_to_emin_less, close_to_etiny_greater, - close_to_etiny_less, close_to_min_etiny_greater, close_to_min_etiny_less -] - - -def un_close_numbers(prec, emax, emin, itr=None): - if itr is None: - itr = 1000 - for _ in range(itr): - for func in close_funcs: - yield func(prec, emax, emin) - -def bin_close_numbers(prec, emax, emin, itr=None): - if itr is None: - itr = 1000 - for _ in range(itr): - for func1 in close_funcs: - for func2 in close_funcs: - yield func1(prec, emax, emin), func2(prec, emax, emin) - for func in close_funcs: - yield randdec(prec, emax), func(prec, emax, emin) - yield func(prec, emax, emin), randdec(prec, emax) - -def tern_close_numbers(prec, emax, emin, itr): - if itr is None: - itr = 1000 - for _ in range(itr): - for func1 in close_funcs: - for func2 in close_funcs: - for func3 in close_funcs: - yield (func1(prec, emax, emin), func2(prec, emax, emin), - func3(prec, emax, emin)) - for func in close_funcs: - yield (randdec(prec, emax), func(prec, emax, emin), - func(prec, emax, emin)) - yield (func(prec, emax, emin), randdec(prec, emax), - func(prec, emax, emin)) - yield (func(prec, emax, emin), func(prec, emax, emin), - randdec(prec, emax)) - for func in close_funcs: - yield (randdec(prec, emax), randdec(prec, emax), - func(prec, emax, emin)) - yield (randdec(prec, emax), func(prec, emax, emin), - randdec(prec, emax)) - yield (func(prec, emax, emin), randdec(prec, emax), - randdec(prec, emax)) - - -# If itr == None, test all digit lengths up to prec + 30 -def un_incr_digits(prec, maxexp, itr): - if itr is None: - lst = range(prec+30) - else: - lst = sample(range(prec+30), itr) - for m in lst: - yield from_triple(1, ndigits(m), 0) - yield from_triple(-1, ndigits(m), 0) - yield from_triple(1, ndigits(m), randrange(maxexp)) - yield from_triple(-1, ndigits(m), randrange(maxexp)) - -# If itr == None, test all digit lengths up to prec + 30 -# Also output decimals im tuple form. -def un_incr_digits_tuple(prec, maxexp, itr): - if itr is None: - lst = range(prec+30) - else: - lst = sample(range(prec+30), itr) - for m in lst: - yield from_triple(1, ndigits(m), 0) - yield from_triple(-1, ndigits(m), 0) - yield from_triple(1, ndigits(m), randrange(maxexp)) - yield from_triple(-1, ndigits(m), randrange(maxexp)) - # test from tuple - yield (0, tuple(map(int, str(ndigits(m)))), 0) - yield (1, tuple(map(int, str(ndigits(m)))), 0) - yield (0, tuple(map(int, str(ndigits(m)))), randrange(maxexp)) - yield (1, tuple(map(int, str(ndigits(m)))), randrange(maxexp)) - -# If itr == None, test all combinations of digit lengths up to prec + 30 -def bin_incr_digits(prec, maxexp, itr): - if itr is None: - lst1 = range(prec+30) - lst2 = range(prec+30) - else: - lst1 = sample(range(prec+30), itr) - lst2 = sample(range(prec+30), itr) - for m in lst1: - x = from_triple(1, ndigits(m), 0) - yield x, x - x = from_triple(-1, ndigits(m), 0) - yield x, x - x = from_triple(1, ndigits(m), randrange(maxexp)) - yield x, x - x = from_triple(-1, ndigits(m), randrange(maxexp)) - yield x, x - for m in lst1: - for n in lst2: - x = from_triple(1, ndigits(m), 0) - y = from_triple(1, ndigits(n), 0) - yield x, y - x = from_triple(-1, ndigits(m), 0) - y = from_triple(1, ndigits(n), 0) - yield x, y - x = from_triple(1, ndigits(m), 0) - y = from_triple(-1, ndigits(n), 0) - yield x, y - x = from_triple(-1, ndigits(m), 0) - y = from_triple(-1, ndigits(n), 0) - yield x, y - x = from_triple(1, ndigits(m), randrange(maxexp)) - y = from_triple(1, ndigits(n), randrange(maxexp)) - yield x, y - x = from_triple(-1, ndigits(m), randrange(maxexp)) - y = from_triple(1, ndigits(n), randrange(maxexp)) - yield x, y - x = from_triple(1, ndigits(m), randrange(maxexp)) - y = from_triple(-1, ndigits(n), randrange(maxexp)) - yield x, y - x = from_triple(-1, ndigits(m), randrange(maxexp)) - y = from_triple(-1, ndigits(n), randrange(maxexp)) - yield x, y - - -def randsign(): - return (1, -1)[randrange(2)] - -# If itr == None, test all combinations of digit lengths up to prec + 30 -def tern_incr_digits(prec, maxexp, itr): - if itr is None: - lst1 = range(prec+30) - lst2 = range(prec+30) - lst3 = range(prec+30) - else: - lst1 = sample(range(prec+30), itr) - lst2 = sample(range(prec+30), itr) - lst3 = sample(range(prec+30), itr) - for m in lst1: - for n in lst2: - for p in lst3: - x = from_triple(randsign(), ndigits(m), 0) - y = from_triple(randsign(), ndigits(n), 0) - z = from_triple(randsign(), ndigits(p), 0) - yield x, y, z - - -# Tests for the 'logical' functions -def bindigits(prec): - z = 0 - for i in range(prec): - z += randrange(2) * 10**i - return z - -def logical_un_incr_digits(prec, itr): - if itr is None: - lst = range(prec+30) - else: - lst = sample(range(prec+30), itr) - for m in lst: - yield from_triple(1, bindigits(m), 0) - -def logical_bin_incr_digits(prec, itr): - if itr is None: - lst1 = range(prec+30) - lst2 = range(prec+30) - else: - lst1 = sample(range(prec+30), itr) - lst2 = sample(range(prec+30), itr) - for m in lst1: - x = from_triple(1, bindigits(m), 0) - yield x, x - for m in lst1: - for n in lst2: - x = from_triple(1, bindigits(m), 0) - y = from_triple(1, bindigits(n), 0) - yield x, y - - -def randint(): - p = randrange(1, 100) - return ndigits(p) * (1,-1)[randrange(2)] - -def randfloat(): - p = randrange(1, 100) - s = numeric_value(p, 383) - try: - f = float(numeric_value(p, 383)) - except ValueError: - f = 0.0 - return f - -def randcomplex(): - real = randfloat() - if randrange(100) > 30: - imag = 0.0 - else: - imag = randfloat() - return complex(real, imag) - -def randfraction(): - num = randint() - denom = randint() - if denom == 0: - denom = 1 - return Fraction(num, denom) - -number_funcs = [randint, randfloat, randcomplex, randfraction] - -def un_random_mixed_op(itr=None): - if itr is None: - itr = 1000 - for _ in range(itr): - for func in number_funcs: - yield func() - # Test garbage input - for x in (['x'], ('y',), {'z'}, {1:'z'}): - yield x - -def bin_random_mixed_op(prec, emax, emin, itr=None): - if itr is None: - itr = 1000 - for _ in range(itr): - for func in number_funcs: - yield randdec(prec, emax), func() - yield func(), randdec(prec, emax) - for number in number_funcs: - for dec in close_funcs: - yield dec(prec, emax, emin), number() - # Test garbage input - for x in (['x'], ('y',), {'z'}, {1:'z'}): - for y in (['x'], ('y',), {'z'}, {1:'z'}): - yield x, y - -def tern_random_mixed_op(prec, emax, emin, itr): - if itr is None: - itr = 1000 - for _ in range(itr): - for func in number_funcs: - yield randdec(prec, emax), randdec(prec, emax), func() - yield randdec(prec, emax), func(), func() - yield func(), func(), func() - # Test garbage input - for x in (['x'], ('y',), {'z'}, {1:'z'}): - for y in (['x'], ('y',), {'z'}, {1:'z'}): - for z in (['x'], ('y',), {'z'}, {1:'z'}): - yield x, y, z - -def all_unary(prec, exp_range, itr): - for a in un_close_to_pow10(prec, exp_range, itr): - yield (a,) - for a in un_close_numbers(prec, exp_range, -exp_range, itr): - yield (a,) - for a in un_incr_digits_tuple(prec, exp_range, itr): - yield (a,) - for a in un_randfloat(): - yield (a,) - for a in un_random_mixed_op(itr): - yield (a,) - for a in logical_un_incr_digits(prec, itr): - yield (a,) - for _ in range(100): - yield (randdec(prec, exp_range),) - for _ in range(100): - yield (randtuple(prec, exp_range),) - -def unary_optarg(prec, exp_range, itr): - for _ in range(100): - yield randdec(prec, exp_range), None - yield randdec(prec, exp_range), None, None - -def all_binary(prec, exp_range, itr): - for a, b in bin_close_to_pow10(prec, exp_range, itr): - yield a, b - for a, b in bin_close_numbers(prec, exp_range, -exp_range, itr): - yield a, b - for a, b in bin_incr_digits(prec, exp_range, itr): - yield a, b - for a, b in bin_randfloat(): - yield a, b - for a, b in bin_random_mixed_op(prec, exp_range, -exp_range, itr): - yield a, b - for a, b in logical_bin_incr_digits(prec, itr): - yield a, b - for _ in range(100): - yield randdec(prec, exp_range), randdec(prec, exp_range) - -def binary_optarg(prec, exp_range, itr): - for _ in range(100): - yield randdec(prec, exp_range), randdec(prec, exp_range), None - yield randdec(prec, exp_range), randdec(prec, exp_range), None, None - -def all_ternary(prec, exp_range, itr): - for a, b, c in tern_close_numbers(prec, exp_range, -exp_range, itr): - yield a, b, c - for a, b, c in tern_incr_digits(prec, exp_range, itr): - yield a, b, c - for a, b, c in tern_randfloat(): - yield a, b, c - for a, b, c in tern_random_mixed_op(prec, exp_range, -exp_range, itr): - yield a, b, c - for _ in range(100): - a = randdec(prec, 2*exp_range) - b = randdec(prec, 2*exp_range) - c = randdec(prec, 2*exp_range) - yield a, b, c - -def ternary_optarg(prec, exp_range, itr): - for _ in range(100): - a = randdec(prec, 2*exp_range) - b = randdec(prec, 2*exp_range) - c = randdec(prec, 2*exp_range) - yield a, b, c, None - yield a, b, c, None, None diff --git a/Modules/_decimal/tests/randfloat.py b/Modules/_decimal/tests/randfloat.py deleted file mode 100644 index 1687303..0000000 --- a/Modules/_decimal/tests/randfloat.py +++ /dev/null @@ -1,250 +0,0 @@ -# Copyright (c) 2010 Python Software Foundation. All Rights Reserved. -# Adapted from Python's Lib/test/test_strtod.py (by Mark Dickinson) - -# More test cases for deccheck.py. - -import random - -TEST_SIZE = 2 - - -def test_short_halfway_cases(): - # exact halfway cases with a small number of significant digits - for k in 0, 5, 10, 15, 20: - # upper = smallest integer >= 2**54/5**k - upper = -(-2**54//5**k) - # lower = smallest odd number >= 2**53/5**k - lower = -(-2**53//5**k) - if lower % 2 == 0: - lower += 1 - for i in range(10 * TEST_SIZE): - # Select a random odd n in [2**53/5**k, - # 2**54/5**k). Then n * 10**k gives a halfway case - # with small number of significant digits. - n, e = random.randrange(lower, upper, 2), k - - # Remove any additional powers of 5. - while n % 5 == 0: - n, e = n // 5, e + 1 - assert n % 10 in (1, 3, 7, 9) - - # Try numbers of the form n * 2**p2 * 10**e, p2 >= 0, - # until n * 2**p2 has more than 20 significant digits. - digits, exponent = n, e - while digits < 10**20: - s = '{}e{}'.format(digits, exponent) - yield s - # Same again, but with extra trailing zeros. - s = '{}e{}'.format(digits * 10**40, exponent - 40) - yield s - digits *= 2 - - # Try numbers of the form n * 5**p2 * 10**(e - p5), p5 - # >= 0, with n * 5**p5 < 10**20. - digits, exponent = n, e - while digits < 10**20: - s = '{}e{}'.format(digits, exponent) - yield s - # Same again, but with extra trailing zeros. - s = '{}e{}'.format(digits * 10**40, exponent - 40) - yield s - digits *= 5 - exponent -= 1 - -def test_halfway_cases(): - # test halfway cases for the round-half-to-even rule - for i in range(1000): - for j in range(TEST_SIZE): - # bit pattern for a random finite positive (or +0.0) float - bits = random.randrange(2047*2**52) - - # convert bit pattern to a number of the form m * 2**e - e, m = divmod(bits, 2**52) - if e: - m, e = m + 2**52, e - 1 - e -= 1074 - - # add 0.5 ulps - m, e = 2*m + 1, e - 1 - - # convert to a decimal string - if e >= 0: - digits = m << e - exponent = 0 - else: - # m * 2**e = (m * 5**-e) * 10**e - digits = m * 5**-e - exponent = e - s = '{}e{}'.format(digits, exponent) - yield s - -def test_boundaries(): - # boundaries expressed as triples (n, e, u), where - # n*10**e is an approximation to the boundary value and - # u*10**e is 1ulp - boundaries = [ - (10000000000000000000, -19, 1110), # a power of 2 boundary (1.0) - (17976931348623159077, 289, 1995), # overflow boundary (2.**1024) - (22250738585072013831, -327, 4941), # normal/subnormal (2.**-1022) - (0, -327, 4941), # zero - ] - for n, e, u in boundaries: - for j in range(1000): - for i in range(TEST_SIZE): - digits = n + random.randrange(-3*u, 3*u) - exponent = e - s = '{}e{}'.format(digits, exponent) - yield s - n *= 10 - u *= 10 - e -= 1 - -def test_underflow_boundary(): - # test values close to 2**-1075, the underflow boundary; similar - # to boundary_tests, except that the random error doesn't scale - # with n - for exponent in range(-400, -320): - base = 10**-exponent // 2**1075 - for j in range(TEST_SIZE): - digits = base + random.randrange(-1000, 1000) - s = '{}e{}'.format(digits, exponent) - yield s - -def test_bigcomp(): - for ndigs in 5, 10, 14, 15, 16, 17, 18, 19, 20, 40, 41, 50: - dig10 = 10**ndigs - for i in range(100 * TEST_SIZE): - digits = random.randrange(dig10) - exponent = random.randrange(-400, 400) - s = '{}e{}'.format(digits, exponent) - yield s - -def test_parsing(): - # make '0' more likely to be chosen than other digits - digits = '000000123456789' - signs = ('+', '-', '') - - # put together random short valid strings - # \d*[.\d*]?e - for i in range(1000): - for j in range(TEST_SIZE): - s = random.choice(signs) - intpart_len = random.randrange(5) - s += ''.join(random.choice(digits) for _ in range(intpart_len)) - if random.choice([True, False]): - s += '.' - fracpart_len = random.randrange(5) - s += ''.join(random.choice(digits) - for _ in range(fracpart_len)) - else: - fracpart_len = 0 - if random.choice([True, False]): - s += random.choice(['e', 'E']) - s += random.choice(signs) - exponent_len = random.randrange(1, 4) - s += ''.join(random.choice(digits) - for _ in range(exponent_len)) - - if intpart_len + fracpart_len: - yield s - -test_particular = [ - # squares - '1.00000000100000000025', - '1.0000000000000000000000000100000000000000000000000' #... - '00025', - '1.0000000000000000000000000000000000000000000010000' #... - '0000000000000000000000000000000000000000025', - '1.0000000000000000000000000000000000000000000000000' #... - '000001000000000000000000000000000000000000000000000' #... - '000000000025', - '0.99999999900000000025', - '0.9999999999999999999999999999999999999999999999999' #... - '999000000000000000000000000000000000000000000000000' #... - '000025', - '0.9999999999999999999999999999999999999999999999999' #... - '999999999999999999999999999999999999999999999999999' #... - '999999999999999999999999999999999999999990000000000' #... - '000000000000000000000000000000000000000000000000000' #... - '000000000000000000000000000000000000000000000000000' #... - '0000000000000000000000000000025', - - '1.0000000000000000000000000000000000000000000000000' #... - '000000000000000000000000000000000000000000000000000' #... - '100000000000000000000000000000000000000000000000000' #... - '000000000000000000000000000000000000000000000000001', - '1.0000000000000000000000000000000000000000000000000' #... - '000000000000000000000000000000000000000000000000000' #... - '500000000000000000000000000000000000000000000000000' #... - '000000000000000000000000000000000000000000000000005', - '1.0000000000000000000000000000000000000000000000000' #... - '000000000100000000000000000000000000000000000000000' #... - '000000000000000000250000000000000002000000000000000' #... - '000000000000000000000000000000000000000000010000000' #... - '000000000000000000000000000000000000000000000000000' #... - '0000000000000000001', - '1.0000000000000000000000000000000000000000000000000' #... - '000000000100000000000000000000000000000000000000000' #... - '000000000000000000249999999999999999999999999999999' #... - '999999999999979999999999999999999999999999999999999' #... - '999999999999999999999900000000000000000000000000000' #... - '000000000000000000000000000000000000000000000000000' #... - '00000000000000000000000001', - - '0.9999999999999999999999999999999999999999999999999' #... - '999999999900000000000000000000000000000000000000000' #... - '000000000000000000249999999999999998000000000000000' #... - '000000000000000000000000000000000000000000010000000' #... - '000000000000000000000000000000000000000000000000000' #... - '0000000000000000001', - '0.9999999999999999999999999999999999999999999999999' #... - '999999999900000000000000000000000000000000000000000' #... - '000000000000000000250000001999999999999999999999999' #... - '999999999999999999999999999999999990000000000000000' #... - '000000000000000000000000000000000000000000000000000' #... - '1', - - # tough cases for ln etc. - '1.000000000000000000000000000000000000000000000000' #... - '00000000000000000000000000000000000000000000000000' #... - '00100000000000000000000000000000000000000000000000' #... - '00000000000000000000000000000000000000000000000000' #... - '0001', - '0.999999999999999999999999999999999999999999999999' #... - '99999999999999999999999999999999999999999999999999' #... - '99899999999999999999999999999999999999999999999999' #... - '99999999999999999999999999999999999999999999999999' #... - '99999999999999999999999999999999999999999999999999' #... - '9999' - ] - - -TESTCASES = [ - [x for x in test_short_halfway_cases()], - [x for x in test_halfway_cases()], - [x for x in test_boundaries()], - [x for x in test_underflow_boundary()], - [x for x in test_bigcomp()], - [x for x in test_parsing()], - test_particular -] - -def un_randfloat(): - for i in range(1000): - l = random.choice(TESTCASES[:6]) - yield random.choice(l) - for v in test_particular: - yield v - -def bin_randfloat(): - for i in range(1000): - l1 = random.choice(TESTCASES) - l2 = random.choice(TESTCASES) - yield random.choice(l1), random.choice(l2) - -def tern_randfloat(): - for i in range(1000): - l1 = random.choice(TESTCASES) - l2 = random.choice(TESTCASES) - l3 = random.choice(TESTCASES) - yield random.choice(l1), random.choice(l2), random.choice(l3) diff --git a/Modules/_decimal/tests/runall-memorydebugger.sh b/Modules/_decimal/tests/runall-memorydebugger.sh deleted file mode 100755 index 77c0c9c..0000000 --- a/Modules/_decimal/tests/runall-memorydebugger.sh +++ /dev/null @@ -1,172 +0,0 @@ -#!/bin/sh - -# -# Purpose: test all machine configurations, pydebug, refleaks, release build -# and release build with valgrind. -# -# Synopsis: ./runall-memorydebugger.sh [--all-configs64 | --all-configs32] -# -# Requirements: valgrind -# - -# Set additional CFLAGS and LDFLAGS for ./configure -ADD_CFLAGS= -ADD_LDFLAGS= - - -CONFIGS_64="x64 uint128 ansi64 universal" -CONFIGS_32="ppro ansi32 ansi-legacy universal" - -VALGRIND="valgrind --tool=memcheck --leak-resolution=high \ - --db-attach=yes --suppressions=Misc/valgrind-python.supp" - -# Get args -case $@ in - *--all-configs64*) - CONFIGS=$CONFIGS_64 - ;; - *--all-configs32*) - CONFIGS=$CONFIGS_32 - ;; - *) - CONFIGS="auto" - ;; -esac - -# gmake required -GMAKE=`which gmake` -if [ X"$GMAKE" = X"" ]; then - GMAKE=make -fi - -# Pretty print configurations -print_config () -{ - len=`echo $@ | wc -c` - margin="#%"`expr \( 74 - $len \) / 2`"s" - - echo "" - echo "# ========================================================================" - printf $margin "" - echo $@ - echo "# ========================================================================" - echo "" -} - - -cd .. - -# test_decimal: refleak, regular and Valgrind tests -for config in $CONFIGS; do - - unset PYTHON_DECIMAL_WITH_MACHINE - libmpdec_config=$config - if [ X"$config" != X"auto" ]; then - PYTHON_DECIMAL_WITH_MACHINE=$config - export PYTHON_DECIMAL_WITH_MACHINE - else - libmpdec_config="" - fi - - ############ refleak tests ########### - print_config "refleak tests: config=$config" - printf "\nbuilding python ...\n\n" - - cd ../../ - $GMAKE distclean > /dev/null 2>&1 - ./configure CFLAGS="$ADD_CFLAGS" LDFLAGS="$ADD_LDFLAGS" --with-pydebug > /dev/null 2>&1 - $GMAKE | grep _decimal - - printf "\n\n# ======================== refleak tests ===========================\n\n" - ./python -m test -uall -R 2:2 test_decimal - - - ############ regular tests ########### - print_config "regular tests: config=$config" - printf "\nbuilding python ...\n\n" - - $GMAKE distclean > /dev/null 2>&1 - ./configure CFLAGS="$ADD_CFLAGS" LDFLAGS="$ADD_LDFLAGS" > /dev/null 2>&1 - $GMAKE | grep _decimal - - printf "\n\n# ======================== regular tests ===========================\n\n" - ./python -m test -uall test_decimal - - - ########### valgrind tests ########### - valgrind=$VALGRIND - case "$config" in - # Valgrind has no support for 80 bit long double arithmetic. - ppro) valgrind= ;; - auto) case `uname -m` in - i386|i486|i586|i686) valgrind= ;; - esac - esac - - print_config "valgrind tests: config=$config" - printf "\nbuilding python ...\n\n" - $GMAKE distclean > /dev/null 2>&1 - ./configure CFLAGS="$ADD_CFLAGS" LDFLAGS="$ADD_LDFLAGS" --without-pymalloc > /dev/null 2>&1 - $GMAKE | grep _decimal - - printf "\n\n# ======================== valgrind tests ===========================\n\n" - $valgrind ./python -m test -uall test_decimal - - cd Modules/_decimal -done - -# deccheck -cd ../../ -for config in $CONFIGS; do - - unset PYTHON_DECIMAL_WITH_MACHINE - if [ X"$config" != X"auto" ]; then - PYTHON_DECIMAL_WITH_MACHINE=$config - export PYTHON_DECIMAL_WITH_MACHINE - fi - - ############ debug ############ - print_config "deccheck: config=$config --with-pydebug" - printf "\nbuilding python ...\n\n" - - $GMAKE distclean > /dev/null 2>&1 - ./configure CFLAGS="$ADD_CFLAGS" LDFLAGS="$ADD_LDFLAGS" --with-pydebug > /dev/null 2>&1 - $GMAKE | grep _decimal - - printf "\n\n# ========================== debug ===========================\n\n" - ./python Modules/_decimal/tests/deccheck.py - - ########### regular ########### - print_config "deccheck: config=$config " - printf "\nbuilding python ...\n\n" - - $GMAKE distclean > /dev/null 2>&1 - ./configure CFLAGS="$ADD_CFLAGS" LDFLAGS="$ADD_LDFLAGS" > /dev/null 2>&1 - $GMAKE | grep _decimal - - printf "\n\n# ======================== regular ===========================\n\n" - ./python Modules/_decimal/tests/deccheck.py - - ########### valgrind ########### - valgrind=$VALGRIND - case "$config" in - # Valgrind has no support for 80 bit long double arithmetic. - ppro) valgrind= ;; - auto) case `uname -m` in - i386|i486|i586|i686) valgrind= ;; - esac - esac - - print_config "valgrind deccheck: config=$config " - printf "\nbuilding python ...\n\n" - - $GMAKE distclean > /dev/null 2>&1 - ./configure CFLAGS="$ADD_CFLAGS" LDFLAGS="$ADD_LDFLAGS" --without-pymalloc > /dev/null 2>&1 - $GMAKE | grep _decimal - - printf "\n\n# ======================== valgrind ==========================\n\n" - $valgrind ./python Modules/_decimal/tests/deccheck.py -done - - - diff --git a/Modules/_decimal/tests/runall.bat b/Modules/_decimal/tests/runall.bat deleted file mode 100755 index 5bc872a..0000000 --- a/Modules/_decimal/tests/runall.bat +++ /dev/null @@ -1,111 +0,0 @@ -@ECHO OFF - -rem Test all machine configurations, pydebug, refleaks, release build. - -cd ..\..\..\ - - -echo. -echo # ====================================================================== -echo # Building Python -echo # ====================================================================== -echo. - -call "%VS100COMNTOOLS%\..\..\VC\vcvarsall.bat" x64 -msbuild /noconsolelogger /target:clean PCbuild\pcbuild.sln /p:Configuration=Release /p:PlatformTarget=x64 -msbuild /noconsolelogger /target:clean PCbuild\pcbuild.sln /p:Configuration=Debug /p:PlatformTarget=x64 -msbuild /noconsolelogger PCbuild\pcbuild.sln /p:Configuration=Release /p:Platform=x64 -msbuild /noconsolelogger PCbuild\pcbuild.sln /p:Configuration=Debug /p:Platform=x64 - -call "%VS100COMNTOOLS%\..\..\VC\vcvarsall.bat" x86 -msbuild /noconsolelogger PCbuild\pcbuild.sln /p:Configuration=Release /p:Platform=Win32 -msbuild /noconsolelogger PCbuild\pcbuild.sln /p:Configuration=Debug /p:Platform=Win32 -echo. -echo. - -echo. -echo # ====================================================================== -echo # test_decimal: platform=x64 -echo # ====================================================================== -echo. - -cd PCbuild\amd64 - -echo # ==================== refleak tests ======================= -echo. -python_d.exe -m test -uall -R 2:2 test_decimal -echo. -echo. - -echo # ==================== regular tests ======================= -echo. -python.exe -m test -uall test_decimal -echo. -echo. - -cd .. - -echo. -echo # ====================================================================== -echo # test_decimal: platform=x86 -echo # ====================================================================== -echo. - -echo # ==================== refleak tests ======================= -echo. -python_d.exe -m test -uall -R 2:2 test_decimal -echo. -echo. - -echo # ==================== regular tests ======================= -echo. -python.exe -m test -uall test_decimal -echo. -echo. - -cd amd64 - -echo. -echo # ====================================================================== -echo # deccheck: platform=x64 -echo # ====================================================================== -echo. - -echo # ==================== debug build ======================= -echo. -python_d.exe ..\..\Modules\_decimal\tests\deccheck.py -echo. -echo. - -echo # =================== release build ====================== -echo. -python.exe ..\..\Modules\_decimal\tests\deccheck.py -echo. -echo. - -cd .. - -echo. -echo # ====================================================================== -echo # deccheck: platform=x86 -echo # ====================================================================== -echo. -echo. - -echo # ==================== debug build ======================= -echo. -python_d.exe ..\Modules\_decimal\tests\deccheck.py -echo. -echo. - -echo # =================== release build ====================== -echo. -python.exe ..\Modules\_decimal\tests\deccheck.py -echo. -echo. - - -cd ..\Modules\_decimal\tests - - - |