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Diffstat (limited to 'Modules/_decimal/libmpdec/mpdecimal.c')
| -rw-r--r-- | Modules/_decimal/libmpdec/mpdecimal.c | 8417 |
1 files changed, 0 insertions, 8417 deletions
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); -} - - - |