/* Generic object operations; and implementation of None (NoObject) */ #include "Python.h" #ifdef macintosh #include "macglue.h" #endif #ifdef Py_REF_DEBUG long _Py_RefTotal; #endif int Py_DivisionWarningFlag; /* Object allocation routines used by NEWOBJ and NEWVAROBJ macros. These are used by the individual routines for object creation. Do not call them otherwise, they do not initialize the object! */ #ifdef COUNT_ALLOCS static PyTypeObject *type_list; extern int tuple_zero_allocs, fast_tuple_allocs; extern int quick_int_allocs, quick_neg_int_allocs; extern int null_strings, one_strings; void dump_counts(void) { PyTypeObject *tp; for (tp = type_list; tp; tp = tp->tp_next) fprintf(stderr, "%s alloc'd: %d, freed: %d, max in use: %d\n", tp->tp_name, tp->tp_allocs, tp->tp_frees, tp->tp_maxalloc); fprintf(stderr, "fast tuple allocs: %d, empty: %d\n", fast_tuple_allocs, tuple_zero_allocs); fprintf(stderr, "fast int allocs: pos: %d, neg: %d\n", quick_int_allocs, quick_neg_int_allocs); fprintf(stderr, "null strings: %d, 1-strings: %d\n", null_strings, one_strings); } PyObject * get_counts(void) { PyTypeObject *tp; PyObject *result; PyObject *v; result = PyList_New(0); if (result == NULL) return NULL; for (tp = type_list; tp; tp = tp->tp_next) { v = Py_BuildValue("(siii)", tp->tp_name, tp->tp_allocs, tp->tp_frees, tp->tp_maxalloc); if (v == NULL) { Py_DECREF(result); return NULL; } if (PyList_Append(result, v) < 0) { Py_DECREF(v); Py_DECREF(result); return NULL; } Py_DECREF(v); } return result; } void inc_count(PyTypeObject *tp) { if (tp->tp_allocs == 0) { /* first time; insert in linked list */ if (tp->tp_next != NULL) /* sanity check */ Py_FatalError("XXX inc_count sanity check"); tp->tp_next = type_list; /* Note that as of Python 2.2, heap-allocated type objects * can go away, but this code requires that they stay alive * until program exit. That's why we're careful with * refcounts here. type_list gets a new reference to tp, * while ownership of the reference type_list used to hold * (if any) was transferred to tp->tp_next in the line above. * tp is thus effectively immortal after this. */ Py_INCREF(tp); type_list = tp; } tp->tp_allocs++; if (tp->tp_allocs - tp->tp_frees > tp->tp_maxalloc) tp->tp_maxalloc = tp->tp_allocs - tp->tp_frees; } #endif #ifdef Py_REF_DEBUG /* Log a fatal error; doesn't return. */ void _Py_NegativeRefcount(const char *fname, int lineno, PyObject *op) { char buf[300]; PyOS_snprintf(buf, sizeof(buf), "%s:%i object at %p has negative ref count %i", fname, lineno, op, op->ob_refcnt); Py_FatalError(buf); } #endif /* Py_REF_DEBUG */ PyObject * PyObject_Init(PyObject *op, PyTypeObject *tp) { if (op == NULL) return PyErr_NoMemory(); /* Any changes should be reflected in PyObject_INIT (objimpl.h) */ op->ob_type = tp; _Py_NewReference(op); return op; } PyVarObject * PyObject_InitVar(PyVarObject *op, PyTypeObject *tp, int size) { if (op == NULL) return (PyVarObject *) PyErr_NoMemory(); /* Any changes should be reflected in PyObject_INIT_VAR */ op->ob_size = size; op->ob_type = tp; _Py_NewReference((PyObject *)op); return op; } PyObject * _PyObject_New(PyTypeObject *tp) { PyObject *op; op = (PyObject *) PyObject_MALLOC(_PyObject_SIZE(tp)); if (op == NULL) return PyErr_NoMemory(); return PyObject_INIT(op, tp); } PyVarObject * _PyObject_NewVar(PyTypeObject *tp, int nitems) { PyVarObject *op; const size_t size = _PyObject_VAR_SIZE(tp, nitems); op = (PyVarObject *) PyObject_MALLOC(size); if (op == NULL) return (PyVarObject *)PyErr_NoMemory(); return PyObject_INIT_VAR(op, tp, nitems); } /* for binary compatibility with 2.2 */ #undef _PyObject_Del void _PyObject_Del(PyObject *op) { PyObject_FREE(op); } /* Implementation of PyObject_Print with recursion checking */ static int internal_print(PyObject *op, FILE *fp, int flags, int nesting) { int ret = 0; if (nesting > 10) { PyErr_SetString(PyExc_RuntimeError, "print recursion"); return -1; } if (PyErr_CheckSignals()) return -1; #ifdef USE_STACKCHECK if (PyOS_CheckStack()) { PyErr_SetString(PyExc_MemoryError, "stack overflow"); return -1; } #endif clearerr(fp); /* Clear any previous error condition */ if (op == NULL) { fprintf(fp, ""); } else { if (op->ob_refcnt <= 0) fprintf(fp, "", op->ob_refcnt, op); else if (op->ob_type->tp_print == NULL) { PyObject *s; if (flags & Py_PRINT_RAW) s = PyObject_Str(op); else s = PyObject_Repr(op); if (s == NULL) ret = -1; else { ret = internal_print(s, fp, Py_PRINT_RAW, nesting+1); } Py_XDECREF(s); } else ret = (*op->ob_type->tp_print)(op, fp, flags); } if (ret == 0) { if (ferror(fp)) { PyErr_SetFromErrno(PyExc_IOError); clearerr(fp); ret = -1; } } return ret; } int PyObject_Print(PyObject *op, FILE *fp, int flags) { return internal_print(op, fp, flags, 0); } /* For debugging convenience. See Misc/gdbinit for some useful gdb hooks */ void _PyObject_Dump(PyObject* op) { if (op == NULL) fprintf(stderr, "NULL\n"); else { fprintf(stderr, "object : "); (void)PyObject_Print(op, stderr, 0); fprintf(stderr, "\n" "type : %s\n" "refcount: %d\n" "address : %p\n", op->ob_type==NULL ? "NULL" : op->ob_type->tp_name, op->ob_refcnt, op); } } PyObject * PyObject_Repr(PyObject *v) { if (PyErr_CheckSignals()) return NULL; #ifdef USE_STACKCHECK if (PyOS_CheckStack()) { PyErr_SetString(PyExc_MemoryError, "stack overflow"); return NULL; } #endif if (v == NULL) return PyString_FromString(""); else if (v->ob_type->tp_repr == NULL) return PyString_FromFormat("<%s object at %p>", v->ob_type->tp_name, v); else { PyObject *res; res = (*v->ob_type->tp_repr)(v); if (res == NULL) return NULL; #ifdef Py_USING_UNICODE if (PyUnicode_Check(res)) { PyObject* str; str = PyUnicode_AsUnicodeEscapeString(res); Py_DECREF(res); if (str) res = str; else return NULL; } #endif if (!PyString_Check(res)) { PyErr_Format(PyExc_TypeError, "__repr__ returned non-string (type %.200s)", res->ob_type->tp_name); Py_DECREF(res); return NULL; } return res; } } PyObject * PyObject_Str(PyObject *v) { PyObject *res; if (v == NULL) return PyString_FromString(""); if (PyString_CheckExact(v)) { Py_INCREF(v); return v; } if (v->ob_type->tp_str == NULL) return PyObject_Repr(v); res = (*v->ob_type->tp_str)(v); if (res == NULL) return NULL; #ifdef Py_USING_UNICODE if (PyUnicode_Check(res)) { PyObject* str; str = PyUnicode_AsEncodedString(res, NULL, NULL); Py_DECREF(res); if (str) res = str; else return NULL; } #endif if (!PyString_Check(res)) { PyErr_Format(PyExc_TypeError, "__str__ returned non-string (type %.200s)", res->ob_type->tp_name); Py_DECREF(res); return NULL; } return res; } #ifdef Py_USING_UNICODE PyObject * PyObject_Unicode(PyObject *v) { PyObject *res; if (v == NULL) res = PyString_FromString(""); if (PyUnicode_CheckExact(v)) { Py_INCREF(v); return v; } if (PyUnicode_Check(v)) { /* For a Unicode subtype that's not a Unicode object, return a true Unicode object with the same data. */ return PyUnicode_FromUnicode(PyUnicode_AS_UNICODE(v), PyUnicode_GET_SIZE(v)); } if (PyString_Check(v)) { Py_INCREF(v); res = v; } else { PyObject *func; static PyObject *unicodestr; /* XXX As soon as we have a tp_unicode slot, we should check this before trying the __unicode__ method. */ if (unicodestr == NULL) { unicodestr= PyString_InternFromString( "__unicode__"); if (unicodestr == NULL) return NULL; } func = PyObject_GetAttr(v, unicodestr); if (func != NULL) { res = PyEval_CallObject(func, (PyObject *)NULL); Py_DECREF(func); } else { PyErr_Clear(); if (v->ob_type->tp_str != NULL) res = (*v->ob_type->tp_str)(v); else res = PyObject_Repr(v); } } if (res == NULL) return NULL; if (!PyUnicode_Check(res)) { PyObject *str; str = PyUnicode_FromEncodedObject(res, NULL, "strict"); Py_DECREF(res); if (str) res = str; else return NULL; } return res; } #endif /* Helper to warn about deprecated tp_compare return values. Return: -2 for an exception; -1 if v < w; 0 if v == w; 1 if v > w. (This function cannot return 2.) */ static int adjust_tp_compare(int c) { if (PyErr_Occurred()) { if (c != -1 && c != -2) { PyObject *t, *v, *tb; PyErr_Fetch(&t, &v, &tb); if (PyErr_Warn(PyExc_RuntimeWarning, "tp_compare didn't return -1 or -2 " "for exception") < 0) { Py_XDECREF(t); Py_XDECREF(v); Py_XDECREF(tb); } else PyErr_Restore(t, v, tb); } return -2; } else if (c < -1 || c > 1) { if (PyErr_Warn(PyExc_RuntimeWarning, "tp_compare didn't return -1, 0 or 1") < 0) return -2; else return c < -1 ? -1 : 1; } else { assert(c >= -1 && c <= 1); return c; } } /* Macro to get the tp_richcompare field of a type if defined */ #define RICHCOMPARE(t) (PyType_HasFeature((t), Py_TPFLAGS_HAVE_RICHCOMPARE) \ ? (t)->tp_richcompare : NULL) /* Map rich comparison operators to their swapped version, e.g. LT --> GT */ static int swapped_op[] = {Py_GT, Py_GE, Py_EQ, Py_NE, Py_LT, Py_LE}; /* Try a genuine rich comparison, returning an object. Return: NULL for exception; NotImplemented if this particular rich comparison is not implemented or undefined; some object not equal to NotImplemented if it is implemented (this latter object may not be a Boolean). */ static PyObject * try_rich_compare(PyObject *v, PyObject *w, int op) { richcmpfunc f; PyObject *res; if (v->ob_type != w->ob_type && PyType_IsSubtype(w->ob_type, v->ob_type) && (f = RICHCOMPARE(w->ob_type)) != NULL) { res = (*f)(w, v, swapped_op[op]); if (res != Py_NotImplemented) return res; Py_DECREF(res); } if ((f = RICHCOMPARE(v->ob_type)) != NULL) { res = (*f)(v, w, op); if (res != Py_NotImplemented) return res; Py_DECREF(res); } if ((f = RICHCOMPARE(w->ob_type)) != NULL) { return (*f)(w, v, swapped_op[op]); } res = Py_NotImplemented; Py_INCREF(res); return res; } /* Try a genuine rich comparison, returning an int. Return: -1 for exception (including the case where try_rich_compare() returns an object that's not a Boolean); 0 if the outcome is false; 1 if the outcome is true; 2 if this particular rich comparison is not implemented or undefined. */ static int try_rich_compare_bool(PyObject *v, PyObject *w, int op) { PyObject *res; int ok; if (RICHCOMPARE(v->ob_type) == NULL && RICHCOMPARE(w->ob_type) == NULL) return 2; /* Shortcut, avoid INCREF+DECREF */ res = try_rich_compare(v, w, op); if (res == NULL) return -1; if (res == Py_NotImplemented) { Py_DECREF(res); return 2; } ok = PyObject_IsTrue(res); Py_DECREF(res); return ok; } /* Try rich comparisons to determine a 3-way comparison. Return: -2 for an exception; -1 if v < w; 0 if v == w; 1 if v > w; 2 if this particular rich comparison is not implemented or undefined. */ static int try_rich_to_3way_compare(PyObject *v, PyObject *w) { static struct { int op; int outcome; } tries[3] = { /* Try this operator, and if it is true, use this outcome: */ {Py_EQ, 0}, {Py_LT, -1}, {Py_GT, 1}, }; int i; if (RICHCOMPARE(v->ob_type) == NULL && RICHCOMPARE(w->ob_type) == NULL) return 2; /* Shortcut */ for (i = 0; i < 3; i++) { switch (try_rich_compare_bool(v, w, tries[i].op)) { case -1: return -2; case 1: return tries[i].outcome; } } return 2; } /* Try a 3-way comparison, returning an int. Return: -2 for an exception; -1 if v < w; 0 if v == w; 1 if v > w; 2 if this particular 3-way comparison is not implemented or undefined. */ static int try_3way_compare(PyObject *v, PyObject *w) { int c; cmpfunc f; /* Comparisons involving instances are given to instance_compare, which has the same return conventions as this function. */ f = v->ob_type->tp_compare; if (PyInstance_Check(v)) return (*f)(v, w); if (PyInstance_Check(w)) return (*w->ob_type->tp_compare)(v, w); /* If both have the same (non-NULL) tp_compare, use it. */ if (f != NULL && f == w->ob_type->tp_compare) { c = (*f)(v, w); return adjust_tp_compare(c); } /* If either tp_compare is _PyObject_SlotCompare, that's safe. */ if (f == _PyObject_SlotCompare || w->ob_type->tp_compare == _PyObject_SlotCompare) return _PyObject_SlotCompare(v, w); /* Try coercion; if it fails, give up */ c = PyNumber_CoerceEx(&v, &w); if (c < 0) return -2; if (c > 0) return 2; /* Try v's comparison, if defined */ if ((f = v->ob_type->tp_compare) != NULL) { c = (*f)(v, w); Py_DECREF(v); Py_DECREF(w); return adjust_tp_compare(c); } /* Try w's comparison, if defined */ if ((f = w->ob_type->tp_compare) != NULL) { c = (*f)(w, v); /* swapped! */ Py_DECREF(v); Py_DECREF(w); c = adjust_tp_compare(c); if (c >= -1) return -c; /* Swapped! */ else return c; } /* No comparison defined */ Py_DECREF(v); Py_DECREF(w); return 2; } /* Final fallback 3-way comparison, returning an int. Return: -2 if an error occurred; -1 if v < w; 0 if v == w; 1 if v > w. */ static int default_3way_compare(PyObject *v, PyObject *w) { int c; char *vname, *wname; if (v->ob_type == w->ob_type) { /* When comparing these pointers, they must be cast to * integer types (i.e. Py_uintptr_t, our spelling of C9X's * uintptr_t). ANSI specifies that pointer compares other * than == and != to non-related structures are undefined. */ Py_uintptr_t vv = (Py_uintptr_t)v; Py_uintptr_t ww = (Py_uintptr_t)w; return (vv < ww) ? -1 : (vv > ww) ? 1 : 0; } #ifdef Py_USING_UNICODE /* Special case for Unicode */ if (PyUnicode_Check(v) || PyUnicode_Check(w)) { c = PyUnicode_Compare(v, w); if (!PyErr_Occurred()) return c; /* TypeErrors are ignored: if Unicode coercion fails due to one of the arguments not having the right type, we continue as defined by the coercion protocol (see above). Luckily, decoding errors are reported as ValueErrors and are not masked by this technique. */ if (!PyErr_ExceptionMatches(PyExc_TypeError)) return -2; PyErr_Clear(); } #endif /* None is smaller than anything */ if (v == Py_None) return -1; if (w == Py_None) return 1; /* different type: compare type names */ if (v->ob_type->tp_as_number) vname = ""; else vname = v->ob_type->tp_name; if (w->ob_type->tp_as_number) wname = ""; else wname = w->ob_type->tp_name; c = strcmp(vname, wname); if (c < 0) return -1; if (c > 0) return 1; /* Same type name, or (more likely) incomparable numeric types */ return ((Py_uintptr_t)(v->ob_type) < ( Py_uintptr_t)(w->ob_type)) ? -1 : 1; } #define CHECK_TYPES(o) PyType_HasFeature((o)->ob_type, Py_TPFLAGS_CHECKTYPES) /* Do a 3-way comparison, by hook or by crook. Return: -2 for an exception (but see below); -1 if v < w; 0 if v == w; 1 if v > w; BUT: if the object implements a tp_compare function, it returns whatever this function returns (whether with an exception or not). */ static int do_cmp(PyObject *v, PyObject *w) { int c; cmpfunc f; if (v->ob_type == w->ob_type && (f = v->ob_type->tp_compare) != NULL) { c = (*f)(v, w); if (PyInstance_Check(v)) { /* Instance tp_compare has a different signature. But if it returns undefined we fall through. */ if (c != 2) return c; /* Else fall through to try_rich_to_3way_compare() */ } else return adjust_tp_compare(c); } /* We only get here if one of the following is true: a) v and w have different types b) v and w have the same type, which doesn't have tp_compare c) v and w are instances, and either __cmp__ is not defined or __cmp__ returns NotImplemented */ c = try_rich_to_3way_compare(v, w); if (c < 2) return c; c = try_3way_compare(v, w); if (c < 2) return c; return default_3way_compare(v, w); } /* compare_nesting is incremented before calling compare (for some types) and decremented on exit. If the count exceeds the nesting limit, enable code to detect circular data structures. This is a tunable parameter that should only affect the performance of comparisons, nothing else. Setting it high makes comparing deeply nested non-cyclical data structures faster, but makes comparing cyclical data structures slower. */ #define NESTING_LIMIT 20 static int compare_nesting = 0; static PyObject* get_inprogress_dict(void) { static PyObject *key; PyObject *tstate_dict, *inprogress; if (key == NULL) { key = PyString_InternFromString("cmp_state"); if (key == NULL) return NULL; } tstate_dict = PyThreadState_GetDict(); if (tstate_dict == NULL) { PyErr_BadInternalCall(); return NULL; } inprogress = PyDict_GetItem(tstate_dict, key); if (inprogress == NULL) { inprogress = PyDict_New(); if (inprogress == NULL) return NULL; if (PyDict_SetItem(tstate_dict, key, inprogress) == -1) { Py_DECREF(inprogress); return NULL; } Py_DECREF(inprogress); } return inprogress; } /* If the comparison "v op w" is already in progress in this thread, returns * a borrowed reference to Py_None (the caller must not decref). * If it's not already in progress, returns "a token" which must eventually * be passed to delete_token(). The caller must not decref this either * (delete_token decrefs it). The token must not survive beyond any point * where v or w may die. * If an error occurs (out-of-memory), returns NULL. */ static PyObject * check_recursion(PyObject *v, PyObject *w, int op) { PyObject *inprogress; PyObject *token; Py_uintptr_t iv = (Py_uintptr_t)v; Py_uintptr_t iw = (Py_uintptr_t)w; PyObject *x, *y, *z; inprogress = get_inprogress_dict(); if (inprogress == NULL) return NULL; token = PyTuple_New(3); if (token == NULL) return NULL; if (iv <= iw) { PyTuple_SET_ITEM(token, 0, x = PyLong_FromVoidPtr((void *)v)); PyTuple_SET_ITEM(token, 1, y = PyLong_FromVoidPtr((void *)w)); if (op >= 0) op = swapped_op[op]; } else { PyTuple_SET_ITEM(token, 0, x = PyLong_FromVoidPtr((void *)w)); PyTuple_SET_ITEM(token, 1, y = PyLong_FromVoidPtr((void *)v)); } PyTuple_SET_ITEM(token, 2, z = PyInt_FromLong((long)op)); if (x == NULL || y == NULL || z == NULL) { Py_DECREF(token); return NULL; } if (PyDict_GetItem(inprogress, token) != NULL) { Py_DECREF(token); return Py_None; /* Without INCREF! */ } if (PyDict_SetItem(inprogress, token, token) < 0) { Py_DECREF(token); return NULL; } return token; } static void delete_token(PyObject *token) { PyObject *inprogress; if (token == NULL || token == Py_None) return; inprogress = get_inprogress_dict(); if (inprogress == NULL) PyErr_Clear(); else PyDict_DelItem(inprogress, token); Py_DECREF(token); } /* Compare v to w. Return -1 if v < w or exception (PyErr_Occurred() true in latter case). 0 if v == w. 1 if v > w. XXX The docs (C API manual) say the return value is undefined in case XXX of error. */ int PyObject_Compare(PyObject *v, PyObject *w) { PyTypeObject *vtp; int result; #if defined(USE_STACKCHECK) if (PyOS_CheckStack()) { PyErr_SetString(PyExc_MemoryError, "Stack overflow"); return -1; } #endif if (v == NULL || w == NULL) { PyErr_BadInternalCall(); return -1; } if (v == w) return 0; vtp = v->ob_type; compare_nesting++; if (compare_nesting > NESTING_LIMIT && (vtp->tp_as_mapping || vtp->tp_as_sequence) && !PyString_CheckExact(v) && !PyTuple_CheckExact(v)) { /* try to detect circular data structures */ PyObject *token = check_recursion(v, w, -1); if (token == NULL) { result = -1; } else if (token == Py_None) { /* already comparing these objects. assume they're equal until shown otherwise */ result = 0; } else { result = do_cmp(v, w); delete_token(token); } } else { result = do_cmp(v, w); } compare_nesting--; return result < 0 ? -1 : result; } /* Return (new reference to) Py_True or Py_False. */ static PyObject * convert_3way_to_object(int op, int c) { PyObject *result; switch (op) { case Py_LT: c = c < 0; break; case Py_LE: c = c <= 0; break; case Py_EQ: c = c == 0; break; case Py_NE: c = c != 0; break; case Py_GT: c = c > 0; break; case Py_GE: c = c >= 0; break; } result = c ? Py_True : Py_False; Py_INCREF(result); return result; } /* We want a rich comparison but don't have one. Try a 3-way cmp instead. Return NULL if error Py_True if v op w Py_False if not (v op w) */ static PyObject * try_3way_to_rich_compare(PyObject *v, PyObject *w, int op) { int c; c = try_3way_compare(v, w); if (c >= 2) c = default_3way_compare(v, w); if (c <= -2) return NULL; return convert_3way_to_object(op, c); } /* Do rich comparison on v and w. Return NULL if error Else a new reference to an object other than Py_NotImplemented, usually(?): Py_True if v op w Py_False if not (v op w) */ static PyObject * do_richcmp(PyObject *v, PyObject *w, int op) { PyObject *res; res = try_rich_compare(v, w, op); if (res != Py_NotImplemented) return res; Py_DECREF(res); return try_3way_to_rich_compare(v, w, op); } /* Return: NULL for exception; some object not equal to NotImplemented if it is implemented (this latter object may not be a Boolean). */ PyObject * PyObject_RichCompare(PyObject *v, PyObject *w, int op) { PyObject *res; assert(Py_LT <= op && op <= Py_GE); compare_nesting++; if (compare_nesting > NESTING_LIMIT && (v->ob_type->tp_as_mapping || v->ob_type->tp_as_sequence) && !PyString_CheckExact(v) && !PyTuple_CheckExact(v)) { /* try to detect circular data structures */ PyObject *token = check_recursion(v, w, op); if (token == NULL) { res = NULL; goto Done; } else if (token == Py_None) { /* already comparing these objects with this operator. assume they're equal until shown otherwise */ if (op == Py_EQ) res = Py_True; else if (op == Py_NE) res = Py_False; else { PyErr_SetString(PyExc_ValueError, "can't order recursive values"); res = NULL; } Py_XINCREF(res); } else { res = do_richcmp(v, w, op); delete_token(token); } goto Done; } /* No nesting extremism. If the types are equal, and not old-style instances, try to get out cheap (don't bother with coercions etc.). */ if (v->ob_type == w->ob_type && !PyInstance_Check(v)) { cmpfunc fcmp; richcmpfunc frich = RICHCOMPARE(v->ob_type); /* If the type has richcmp, try it first. try_rich_compare tries it two-sided, which is not needed since we've a single type only. */ if (frich != NULL) { res = (*frich)(v, w, op); if (res != Py_NotImplemented) goto Done; Py_DECREF(res); } /* No richcmp, or this particular richmp not implemented. Try 3-way cmp. */ fcmp = v->ob_type->tp_compare; if (fcmp != NULL) { int c = (*fcmp)(v, w); c = adjust_tp_compare(c); if (c == -2) { res = NULL; goto Done; } res = convert_3way_to_object(op, c); goto Done; } } /* Fast path not taken, or couldn't deliver a useful result. */ res = do_richcmp(v, w, op); Done: compare_nesting--; return res; } /* Return -1 if error; 1 if v op w; 0 if not (v op w). */ int PyObject_RichCompareBool(PyObject *v, PyObject *w, int op) { PyObject *res = PyObject_RichCompare(v, w, op); int ok; if (res == NULL) return -1; if (PyBool_Check(res)) ok = (res == Py_True); else ok = PyObject_IsTrue(res); Py_DECREF(res); return ok; } /* Set of hash utility functions to help maintaining the invariant that iff a==b then hash(a)==hash(b) All the utility functions (_Py_Hash*()) return "-1" to signify an error. */ long _Py_HashDouble(double v) { double intpart, fractpart; int expo; long hipart; long x; /* the final hash value */ /* This is designed so that Python numbers of different types * that compare equal hash to the same value; otherwise comparisons * of mapping keys will turn out weird. */ #ifdef MPW /* MPW C modf expects pointer to extended as second argument */ { extended e; fractpart = modf(v, &e); intpart = e; } #else fractpart = modf(v, &intpart); #endif if (fractpart == 0.0) { /* This must return the same hash as an equal int or long. */ if (intpart > LONG_MAX || -intpart > LONG_MAX) { /* Convert to long and use its hash. */ PyObject *plong; /* converted to Python long */ if (Py_IS_INFINITY(intpart)) /* can't convert to long int -- arbitrary */ v = v < 0 ? -271828.0 : 314159.0; plong = PyLong_FromDouble(v); if (plong == NULL) return -1; x = PyObject_Hash(plong); Py_DECREF(plong); return x; } /* Fits in a C long == a Python int, so is its own hash. */ x = (long)intpart; if (x == -1) x = -2; return x; } /* The fractional part is non-zero, so we don't have to worry about * making this match the hash of some other type. * Use frexp to get at the bits in the double. * Since the VAX D double format has 56 mantissa bits, which is the * most of any double format in use, each of these parts may have as * many as (but no more than) 56 significant bits. * So, assuming sizeof(long) >= 4, each part can be broken into two * longs; frexp and multiplication are used to do that. * Also, since the Cray double format has 15 exponent bits, which is * the most of any double format in use, shifting the exponent field * left by 15 won't overflow a long (again assuming sizeof(long) >= 4). */ v = frexp(v, &expo); v *= 2147483648.0; /* 2**31 */ hipart = (long)v; /* take the top 32 bits */ v = (v - (double)hipart) * 2147483648.0; /* get the next 32 bits */ x = hipart + (long)v + (expo << 15); if (x == -1) x = -2; return x; } long _Py_HashPointer(void *p) { #if SIZEOF_LONG >= SIZEOF_VOID_P return (long)p; #else /* convert to a Python long and hash that */ PyObject* longobj; long x; if ((longobj = PyLong_FromVoidPtr(p)) == NULL) { x = -1; goto finally; } x = PyObject_Hash(longobj); finally: Py_XDECREF(longobj); return x; #endif } long PyObject_Hash(PyObject *v) { PyTypeObject *tp = v->ob_type; if (tp->tp_hash != NULL) return (*tp->tp_hash)(v); if (tp->tp_compare == NULL && RICHCOMPARE(tp) == NULL) { return _Py_HashPointer(v); /* Use address as hash value */ } /* If there's a cmp but no hash defined, the object can't be hashed */ PyErr_SetString(PyExc_TypeError, "unhashable type"); return -1; } PyObject * PyObject_GetAttrString(PyObject *v, char *name) { PyObject *w, *res; if (v->ob_type->tp_getattr != NULL) return (*v->ob_type->tp_getattr)(v, name); w = PyString_InternFromString(name); if (w == NULL) return NULL; res = PyObject_GetAttr(v, w); Py_XDECREF(w); return res; } int PyObject_HasAttrString(PyObject *v, char *name) { PyObject *res = PyObject_GetAttrString(v, name); if (res != NULL) { Py_DECREF(res); return 1; } PyErr_Clear(); return 0; } int PyObject_SetAttrString(PyObject *v, char *name, PyObject *w) { PyObject *s; int res; if (v->ob_type->tp_setattr != NULL) return (*v->ob_type->tp_setattr)(v, name, w); s = PyString_InternFromString(name); if (s == NULL) return -1; res = PyObject_SetAttr(v, s, w); Py_XDECREF(s); return res; } PyObject * PyObject_GetAttr(PyObject *v, PyObject *name) { PyTypeObject *tp = v->ob_type; if (!PyString_Check(name)) { #ifdef Py_USING_UNICODE /* The Unicode to string conversion is done here because the existing tp_getattro slots expect a string object as name and we wouldn't want to break those. */ if (PyUnicode_Check(name)) { name = _PyUnicode_AsDefaultEncodedString(name, NULL); if (name == NULL) return NULL; } else #endif { PyErr_SetString(PyExc_TypeError, "attribute name must be string"); return NULL; } } if (tp->tp_getattro != NULL) return (*tp->tp_getattro)(v, name); if (tp->tp_getattr != NULL) return (*tp->tp_getattr)(v, PyString_AS_STRING(name)); PyErr_Format(PyExc_AttributeError, "'%.50s' object has no attribute '%.400s'", tp->tp_name, PyString_AS_STRING(name)); return NULL; } int PyObject_HasAttr(PyObject *v, PyObject *name) { PyObject *res = PyObject_GetAttr(v, name); if (res != NULL) { Py_DECREF(res); return 1; } PyErr_Clear(); return 0; } int PyObject_SetAttr(PyObject *v, PyObject *name, PyObject *value) { PyTypeObject *tp = v->ob_type; int err; if (!PyString_Check(name)){ #ifdef Py_USING_UNICODE /* The Unicode to string conversion is done here because the existing tp_setattro slots expect a string object as name and we wouldn't want to break those. */ if (PyUnicode_Check(name)) { name = PyUnicode_AsEncodedString(name, NULL, NULL); if (name == NULL) return -1; } else #endif { PyErr_SetString(PyExc_TypeError, "attribute name must be string"); return -1; } } else Py_INCREF(name); PyString_InternInPlace(&name); if (tp->tp_setattro != NULL) { err = (*tp->tp_setattro)(v, name, value); Py_DECREF(name); return err; } if (tp->tp_setattr != NULL) { err = (*tp->tp_setattr)(v, PyString_AS_STRING(name), value); Py_DECREF(name); return err; } Py_DECREF(name); if (tp->tp_getattr == NULL && tp->tp_getattro == NULL) PyErr_Format(PyExc_TypeError, "'%.100s' object has no attributes " "(%s .%.100s)", tp->tp_name, value==NULL ? "del" : "assign to", PyString_AS_STRING(name)); else PyErr_Format(PyExc_TypeError, "'%.100s' object has only read-only attributes " "(%s .%.100s)", tp->tp_name, value==NULL ? "del" : "assign to", PyString_AS_STRING(name)); return -1; } /* Helper to get a pointer to an object's __dict__ slot, if any */ PyObject ** _PyObject_GetDictPtr(PyObject *obj) { long dictoffset; PyTypeObject *tp = obj->ob_type; if (!(tp->tp_flags & Py_TPFLAGS_HAVE_CLASS)) return NULL; dictoffset = tp->tp_dictoffset; if (dictoffset == 0) return NULL; if (dictoffset < 0) { int tsize; size_t size; tsize = ((PyVarObject *)obj)->ob_size; if (tsize < 0) tsize = -tsize; size = _PyObject_VAR_SIZE(tp, tsize); dictoffset += (long)size; assert(dictoffset > 0); assert(dictoffset % SIZEOF_VOID_P == 0); } return (PyObject **) ((char *)obj + dictoffset); } /* Generic GetAttr functions - put these in your tp_[gs]etattro slot */ PyObject * PyObject_GenericGetAttr(PyObject *obj, PyObject *name) { PyTypeObject *tp = obj->ob_type; PyObject *descr = NULL; PyObject *res = NULL; descrgetfunc f; long dictoffset; PyObject **dictptr; if (!PyString_Check(name)){ #ifdef Py_USING_UNICODE /* The Unicode to string conversion is done here because the existing tp_setattro slots expect a string object as name and we wouldn't want to break those. */ if (PyUnicode_Check(name)) { name = PyUnicode_AsEncodedString(name, NULL, NULL); if (name == NULL) return NULL; } else #endif { PyErr_SetString(PyExc_TypeError, "attribute name must be string"); return NULL; } } else Py_INCREF(name); if (tp->tp_dict == NULL) { if (PyType_Ready(tp) < 0) goto done; } /* Inline _PyType_Lookup */ { int i, n; PyObject *mro, *base, *dict; /* Look in tp_dict of types in MRO */ mro = tp->tp_mro; assert(mro != NULL); assert(PyTuple_Check(mro)); n = PyTuple_GET_SIZE(mro); for (i = 0; i < n; i++) { base = PyTuple_GET_ITEM(mro, i); if (PyClass_Check(base)) dict = ((PyClassObject *)base)->cl_dict; else { assert(PyType_Check(base)); dict = ((PyTypeObject *)base)->tp_dict; } assert(dict && PyDict_Check(dict)); descr = PyDict_GetItem(dict, name); if (descr != NULL) break; } } f = NULL; if (descr != NULL) { f = descr->ob_type->tp_descr_get; if (f != NULL && PyDescr_IsData(descr)) { res = f(descr, obj, (PyObject *)obj->ob_type); goto done; } } /* Inline _PyObject_GetDictPtr */ dictoffset = tp->tp_dictoffset; if (dictoffset != 0) { PyObject *dict; if (dictoffset < 0) { int tsize; size_t size; tsize = ((PyVarObject *)obj)->ob_size; if (tsize < 0) tsize = -tsize; size = _PyObject_VAR_SIZE(tp, tsize); dictoffset += (long)size; assert(dictoffset > 0); assert(dictoffset % SIZEOF_VOID_P == 0); } dictptr = (PyObject **) ((char *)obj + dictoffset); dict = *dictptr; if (dict != NULL) { res = PyDict_GetItem(dict, name); if (res != NULL) { Py_INCREF(res); goto done; } } } if (f != NULL) { res = f(descr, obj, (PyObject *)obj->ob_type); goto done; } if (descr != NULL) { Py_INCREF(descr); res = descr; goto done; } PyErr_Format(PyExc_AttributeError, "'%.50s' object has no attribute '%.400s'", tp->tp_name, PyString_AS_STRING(name)); done: Py_DECREF(name); return res; } int PyObject_GenericSetAttr(PyObject *obj, PyObject *name, PyObject *value) { PyTypeObject *tp = obj->ob_type; PyObject *descr; descrsetfunc f; PyObject **dictptr; int res = -1; if (!PyString_Check(name)){ #ifdef Py_USING_UNICODE /* The Unicode to string conversion is done here because the existing tp_setattro slots expect a string object as name and we wouldn't want to break those. */ if (PyUnicode_Check(name)) { name = PyUnicode_AsEncodedString(name, NULL, NULL); if (name == NULL) return -1; } else #endif { PyErr_SetString(PyExc_TypeError, "attribute name must be string"); return -1; } } else Py_INCREF(name); if (tp->tp_dict == NULL) { if (PyType_Ready(tp) < 0) goto done; } descr = _PyType_Lookup(tp, name); f = NULL; if (descr != NULL) { f = descr->ob_type->tp_descr_set; if (f != NULL && PyDescr_IsData(descr)) { res = f(descr, obj, value); goto done; } } dictptr = _PyObject_GetDictPtr(obj); if (dictptr != NULL) { PyObject *dict = *dictptr; if (dict == NULL && value != NULL) { dict = PyDict_New(); if (dict == NULL) goto done; *dictptr = dict; } if (dict != NULL) { if (value == NULL) res = PyDict_DelItem(dict, name); else res = PyDict_SetItem(dict, name, value); if (res < 0 && PyErr_ExceptionMatches(PyExc_KeyError)) PyErr_SetObject(PyExc_AttributeError, name); goto done; } } if (f != NULL) { res = f(descr, obj, value); goto done; } if (descr == NULL) { PyErr_Format(PyExc_AttributeError, "'%.50s' object has no attribute '%.400s'", tp->tp_name, PyString_AS_STRING(name)); goto done; } PyErr_Format(PyExc_AttributeError, "'%.50s' object attribute '%.400s' is read-only", tp->tp_name, PyString_AS_STRING(name)); done: Py_DECREF(name); return res; } /* Test a value used as condition, e.g., in a for or if statement. Return -1 if an error occurred */ int PyObject_IsTrue(PyObject *v) { int res; if (v == Py_True) return 1; if (v == Py_False) return 0; if (v == Py_None) return 0; else if (v->ob_type->tp_as_number != NULL && v->ob_type->tp_as_number->nb_nonzero != NULL) res = (*v->ob_type->tp_as_number->nb_nonzero)(v); else if (v->ob_type->tp_as_mapping != NULL && v->ob_type->tp_as_mapping->mp_length != NULL) res = (*v->ob_type->tp_as_mapping->mp_length)(v); else if (v->ob_type->tp_as_sequence != NULL && v->ob_type->tp_as_sequence->sq_length != NULL) res = (*v->ob_type->tp_as_sequence->sq_length)(v); else return 1; return (res > 0) ? 1 : res; } /* equivalent of 'not v' Return -1 if an error occurred */ int PyObject_Not(PyObject *v) { int res; res = PyObject_IsTrue(v); if (res < 0) return res; return res == 0; } /* Coerce two numeric types to the "larger" one. Increment the reference count on each argument. Return value: -1 if an error occurred; 0 if the coercion succeeded (and then the reference counts are increased); 1 if no coercion is possible (and no error is raised). */ int PyNumber_CoerceEx(PyObject **pv, PyObject **pw) { register PyObject *v = *pv; register PyObject *w = *pw; int res; /* Shortcut only for old-style types */ if (v->ob_type == w->ob_type && !PyType_HasFeature(v->ob_type, Py_TPFLAGS_CHECKTYPES)) { Py_INCREF(v); Py_INCREF(w); return 0; } if (v->ob_type->tp_as_number && v->ob_type->tp_as_number->nb_coerce) { res = (*v->ob_type->tp_as_number->nb_coerce)(pv, pw); if (res <= 0) return res; } if (w->ob_type->tp_as_number && w->ob_type->tp_as_number->nb_coerce) { res = (*w->ob_type->tp_as_number->nb_coerce)(pw, pv); if (res <= 0) return res; } return 1; } /* Coerce two numeric types to the "larger" one. Increment the reference count on each argument. Return -1 and raise an exception if no coercion is possible (and then no reference count is incremented). */ int PyNumber_Coerce(PyObject **pv, PyObject **pw) { int err = PyNumber_CoerceEx(pv, pw); if (err <= 0) return err; PyErr_SetString(PyExc_TypeError, "number coercion failed"); return -1; } /* Test whether an object can be called */ int PyCallable_Check(PyObject *x) { if (x == NULL) return 0; if (PyInstance_Check(x)) { PyObject *call = PyObject_GetAttrString(x, "__call__"); if (call == NULL) { PyErr_Clear(); return 0; } /* Could test recursively but don't, for fear of endless recursion if some joker sets self.__call__ = self */ Py_DECREF(call); return 1; } else { return x->ob_type->tp_call != NULL; } } /* Helper for PyObject_Dir. Merge the __dict__ of aclass into dict, and recursively also all the __dict__s of aclass's base classes. The order of merging isn't defined, as it's expected that only the final set of dict keys is interesting. Return 0 on success, -1 on error. */ static int merge_class_dict(PyObject* dict, PyObject* aclass) { PyObject *classdict; PyObject *bases; assert(PyDict_Check(dict)); assert(aclass); /* Merge in the type's dict (if any). */ classdict = PyObject_GetAttrString(aclass, "__dict__"); if (classdict == NULL) PyErr_Clear(); else { int status = PyDict_Update(dict, classdict); Py_DECREF(classdict); if (status < 0) return -1; } /* Recursively merge in the base types' (if any) dicts. */ bases = PyObject_GetAttrString(aclass, "__bases__"); if (bases == NULL) PyErr_Clear(); else { /* We have no guarantee that bases is a real tuple */ int i, n; n = PySequence_Size(bases); /* This better be right */ if (n < 0) PyErr_Clear(); else { for (i = 0; i < n; i++) { int status; PyObject *base = PySequence_GetItem(bases, i); if (base == NULL) { Py_DECREF(bases); return -1; } status = merge_class_dict(dict, base); Py_DECREF(base); if (status < 0) { Py_DECREF(bases); return -1; } } } Py_DECREF(bases); } return 0; } /* Helper for PyObject_Dir. If obj has an attr named attrname that's a list, merge its string elements into keys of dict. Return 0 on success, -1 on error. Errors due to not finding the attr, or the attr not being a list, are suppressed. */ static int merge_list_attr(PyObject* dict, PyObject* obj, char *attrname) { PyObject *list; int result = 0; assert(PyDict_Check(dict)); assert(obj); assert(attrname); list = PyObject_GetAttrString(obj, attrname); if (list == NULL) PyErr_Clear(); else if (PyList_Check(list)) { int i; for (i = 0; i < PyList_GET_SIZE(list); ++i) { PyObject *item = PyList_GET_ITEM(list, i); if (PyString_Check(item)) { result = PyDict_SetItem(dict, item, Py_None); if (result < 0) break; } } } Py_XDECREF(list); return result; } /* Like __builtin__.dir(arg). See bltinmodule.c's builtin_dir for the docstring, which should be kept in synch with this implementation. */ PyObject * PyObject_Dir(PyObject *arg) { /* Set exactly one of these non-NULL before the end. */ PyObject *result = NULL; /* result list */ PyObject *masterdict = NULL; /* result is masterdict.keys() */ /* If NULL arg, return the locals. */ if (arg == NULL) { PyObject *locals = PyEval_GetLocals(); if (locals == NULL) goto error; result = PyDict_Keys(locals); if (result == NULL) goto error; } /* Elif this is some form of module, we only want its dict. */ else if (PyModule_Check(arg)) { masterdict = PyObject_GetAttrString(arg, "__dict__"); if (masterdict == NULL) goto error; if (!PyDict_Check(masterdict)) { PyErr_SetString(PyExc_TypeError, "module.__dict__ is not a dictionary"); goto error; } } /* Elif some form of type or class, grab its dict and its bases. We deliberately don't suck up its __class__, as methods belonging to the metaclass would probably be more confusing than helpful. */ else if (PyType_Check(arg) || PyClass_Check(arg)) { masterdict = PyDict_New(); if (masterdict == NULL) goto error; if (merge_class_dict(masterdict, arg) < 0) goto error; } /* Else look at its dict, and the attrs reachable from its class. */ else { PyObject *itsclass; /* Create a dict to start with. CAUTION: Not everything responding to __dict__ returns a dict! */ masterdict = PyObject_GetAttrString(arg, "__dict__"); if (masterdict == NULL) { PyErr_Clear(); masterdict = PyDict_New(); } else if (!PyDict_Check(masterdict)) { Py_DECREF(masterdict); masterdict = PyDict_New(); } else { /* The object may have returned a reference to its dict, so copy it to avoid mutating it. */ PyObject *temp = PyDict_Copy(masterdict); Py_DECREF(masterdict); masterdict = temp; } if (masterdict == NULL) goto error; /* Merge in __members__ and __methods__ (if any). XXX Would like this to go away someday; for now, it's XXX needed to get at im_self etc of method objects. */ if (merge_list_attr(masterdict, arg, "__members__") < 0) goto error; if (merge_list_attr(masterdict, arg, "__methods__") < 0) goto error; /* Merge in attrs reachable from its class. CAUTION: Not all objects have a __class__ attr. */ itsclass = PyObject_GetAttrString(arg, "__class__"); if (itsclass == NULL) PyErr_Clear(); else { int status = merge_class_dict(masterdict, itsclass); Py_DECREF(itsclass); if (status < 0) goto error; } } assert((result == NULL) ^ (masterdict == NULL)); if (masterdict != NULL) { /* The result comes from its keys. */ assert(result == NULL); result = PyDict_Keys(masterdict); if (result == NULL) goto error; } assert(result); if (PyList_Sort(result) != 0) goto error; else goto normal_return; error: Py_XDECREF(result); result = NULL; /* fall through */ normal_return: Py_XDECREF(masterdict); return result; } /* NoObject is usable as a non-NULL undefined value, used by the macro None. There is (and should be!) no way to create other objects of this type, so there is exactly one (which is indestructible, by the way). (XXX This type and the type of NotImplemented below should be unified.) */ /* ARGSUSED */ static PyObject * none_repr(PyObject *op) { return PyString_FromString("None"); } /* ARGUSED */ static void none_dealloc(PyObject* ignore) { /* This should never get called, but we also don't want to SEGV if * we accidently decref None out of existance. */ Py_FatalError("deallocating None"); } static PyTypeObject PyNone_Type = { PyObject_HEAD_INIT(&PyType_Type) 0, "NoneType", 0, 0, (destructor)none_dealloc, /*tp_dealloc*/ /*never called*/ 0, /*tp_print*/ 0, /*tp_getattr*/ 0, /*tp_setattr*/ 0, /*tp_compare*/ (reprfunc)none_repr, /*tp_repr*/ 0, /*tp_as_number*/ 0, /*tp_as_sequence*/ 0, /*tp_as_mapping*/ 0, /*tp_hash */ }; PyObject _Py_NoneStruct = { PyObject_HEAD_INIT(&PyNone_Type) }; /* NotImplemented is an object that can be used to signal that an operation is not implemented for the given type combination. */ static PyObject * NotImplemented_repr(PyObject *op) { return PyString_FromString("NotImplemented"); } static PyTypeObject PyNotImplemented_Type = { PyObject_HEAD_INIT(&PyType_Type) 0, "NotImplementedType", 0, 0, (destructor)none_dealloc, /*tp_dealloc*/ /*never called*/ 0, /*tp_print*/ 0, /*tp_getattr*/ 0, /*tp_setattr*/ 0, /*tp_compare*/ (reprfunc)NotImplemented_repr, /*tp_repr*/ 0, /*tp_as_number*/ 0, /*tp_as_sequence*/ 0, /*tp_as_mapping*/ 0, /*tp_hash */ }; PyObject _Py_NotImplementedStruct = { PyObject_HEAD_INIT(&PyNotImplemented_Type) }; void _Py_ReadyTypes(void) { if (PyType_Ready(&PyType_Type) < 0) Py_FatalError("Can't initialize 'type'"); if (PyType_Ready(&PyBool_Type) < 0) Py_FatalError("Can't initialize 'bool'"); if (PyType_Ready(&PyString_Type) < 0) Py_FatalError("Can't initialize 'str'"); if (PyType_Ready(&PyList_Type) < 0) Py_FatalError("Can't initialize 'list'"); if (PyType_Ready(&PyNone_Type) < 0) Py_FatalError("Can't initialize type(None)"); if (PyType_Ready(&PyNotImplemented_Type) < 0) Py_FatalError("Can't initialize type(NotImplemented)"); } #ifdef Py_TRACE_REFS static PyObject refchain = {&refchain, &refchain}; void _Py_NewReference(PyObject *op) { _Py_INC_REFTOTAL; op->ob_refcnt = 1; op->_ob_next = refchain._ob_next; op->_ob_prev = &refchain; refchain._ob_next->_ob_prev = op; refchain._ob_next = op; _Py_INC_TPALLOCS(op); } void _Py_ForgetReference(register PyObject *op) { #ifdef SLOW_UNREF_CHECK register PyObject *p; #endif if (op->ob_refcnt < 0) Py_FatalError("UNREF negative refcnt"); if (op == &refchain || op->_ob_prev->_ob_next != op || op->_ob_next->_ob_prev != op) Py_FatalError("UNREF invalid object"); #ifdef SLOW_UNREF_CHECK for (p = refchain._ob_next; p != &refchain; p = p->_ob_next) { if (p == op) break; } if (p == &refchain) /* Not found */ Py_FatalError("UNREF unknown object"); #endif op->_ob_next->_ob_prev = op->_ob_prev; op->_ob_prev->_ob_next = op->_ob_next; op->_ob_next = op->_ob_prev = NULL; _Py_INC_TPFREES(op); } void _Py_Dealloc(PyObject *op) { destructor dealloc = op->ob_type->tp_dealloc; _Py_ForgetReference(op); (*dealloc)(op); } void _Py_PrintReferences(FILE *fp) { PyObject *op; fprintf(fp, "Remaining objects:\n"); for (op = refchain._ob_next; op != &refchain; op = op->_ob_next) { fprintf(fp, "[%d] ", op->ob_refcnt); if (PyObject_Print(op, fp, 0) != 0) PyErr_Clear(); putc('\n', fp); } } PyObject * _Py_GetObjects(PyObject *self, PyObject *args) { int i, n; PyObject *t = NULL; PyObject *res, *op; if (!PyArg_ParseTuple(args, "i|O", &n, &t)) return NULL; op = refchain._ob_next; res = PyList_New(0); if (res == NULL) return NULL; for (i = 0; (n == 0 || i < n) && op != &refchain; i++) { while (op == self || op == args || op == res || op == t || (t != NULL && op->ob_type != (PyTypeObject *) t)) { op = op->_ob_next; if (op == &refchain) return res; } if (PyList_Append(res, op) < 0) { Py_DECREF(res); return NULL; } op = op->_ob_next; } return res; } #endif /* Hack to force loading of cobject.o */ PyTypeObject *_Py_cobject_hack = &PyCObject_Type; /* Hack to force loading of abstract.o */ int (*_Py_abstract_hack)(PyObject *) = PyObject_Size; /* Python's malloc wrappers (see pymem.h) */ void * PyMem_Malloc(size_t nbytes) { return PyMem_MALLOC(nbytes); } void * PyMem_Realloc(void *p, size_t nbytes) { return PyMem_REALLOC(p, nbytes); } void PyMem_Free(void *p) { PyMem_FREE(p); } /* These methods are used to control infinite recursion in repr, str, print, etc. Container objects that may recursively contain themselves, e.g. builtin dictionaries and lists, should used Py_ReprEnter() and Py_ReprLeave() to avoid infinite recursion. Py_ReprEnter() returns 0 the first time it is called for a particular object and 1 every time thereafter. It returns -1 if an exception occurred. Py_ReprLeave() has no return value. See dictobject.c and listobject.c for examples of use. */ #define KEY "Py_Repr" int Py_ReprEnter(PyObject *obj) { PyObject *dict; PyObject *list; int i; dict = PyThreadState_GetDict(); if (dict == NULL) return -1; list = PyDict_GetItemString(dict, KEY); if (list == NULL) { list = PyList_New(0); if (list == NULL) return -1; if (PyDict_SetItemString(dict, KEY, list) < 0) return -1; Py_DECREF(list); } i = PyList_GET_SIZE(list); while (--i >= 0) { if (PyList_GET_ITEM(list, i) == obj) return 1; } PyList_Append(list, obj); return 0; } void Py_ReprLeave(PyObject *obj) { PyObject *dict; PyObject *list; int i; dict = PyThreadState_GetDict(); if (dict == NULL) return; list = PyDict_GetItemString(dict, KEY); if (list == NULL || !PyList_Check(list)) return; i = PyList_GET_SIZE(list); /* Count backwards because we always expect obj to be list[-1] */ while (--i >= 0) { if (PyList_GET_ITEM(list, i) == obj) { PyList_SetSlice(list, i, i + 1, NULL); break; } } } /* Trashcan support. */ /* Current call-stack depth of tp_dealloc calls. */ int _PyTrash_delete_nesting = 0; /* List of objects that still need to be cleaned up, singly linked via their * gc headers' gc_prev pointers. */ PyObject *_PyTrash_delete_later = NULL; /* Add op to the _PyTrash_delete_later list. Called when the current * call-stack depth gets large. op must be a currently untracked gc'ed * object, with refcount 0. Py_DECREF must already have been called on it. */ void _PyTrash_deposit_object(PyObject *op) { assert(PyObject_IS_GC(op)); assert(_Py_AS_GC(op)->gc.gc_refs == _PyGC_REFS_UNTRACKED); assert(op->ob_refcnt == 0); _Py_AS_GC(op)->gc.gc_prev = (PyGC_Head *)_PyTrash_delete_later; _PyTrash_delete_later = op; } /* Dealloccate all the objects in the _PyTrash_delete_later list. Called when * the call-stack unwinds again. */ void _PyTrash_destroy_chain(void) { while (_PyTrash_delete_later) { PyObject *op = _PyTrash_delete_later; destructor dealloc = op->ob_type->tp_dealloc; _PyTrash_delete_later = (PyObject*) _Py_AS_GC(op)->gc.gc_prev; /* Call the deallocator directly. This used to try to * fool Py_DECREF into calling it indirectly, but * Py_DECREF was already called on this object, and in * assorted non-release builds calling Py_DECREF again ends * up distorting allocation statistics. */ assert(op->ob_refcnt == 0); ++_PyTrash_delete_nesting; (*dealloc)(op); --_PyTrash_delete_nesting; } } ='#n1372'>1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 
/* Math module -- standard C math library functions, pi and e */

/* Here are some comments from Tim Peters, extracted from the
   discussion attached to http://bugs.python.org/issue1640.  They
   describe the general aims of the math module with respect to
   special values, IEEE-754 floating-point exceptions, and Python
   exceptions.

These are the "spirit of 754" rules:

1. If the mathematical result is a real number, but of magnitude too
large to approximate by a machine float, overflow is signaled and the
result is an infinity (with the appropriate sign).

2. If the mathematical result is a real number, but of magnitude too
small to approximate by a machine float, underflow is signaled and the
result is a zero (with the appropriate sign).

3. At a singularity (a value x such that the limit of f(y) as y
approaches x exists and is an infinity), "divide by zero" is signaled
and the result is an infinity (with the appropriate sign).  This is
complicated a little by that the left-side and right-side limits may
not be the same; e.g., 1/x approaches +inf or -inf as x approaches 0
from the positive or negative directions.  In that specific case, the
sign of the zero determines the result of 1/0.

4. At a point where a function has no defined result in the extended
reals (i.e., the reals plus an infinity or two), invalid operation is
signaled and a NaN is returned.

And these are what Python has historically /tried/ to do (but not
always successfully, as platform libm behavior varies a lot):

For #1, raise OverflowError.

For #2, return a zero (with the appropriate sign if that happens by
accident ;-)).

For #3 and #4, raise ValueError.  It may have made sense to raise
Python's ZeroDivisionError in #3, but historically that's only been
raised for division by zero and mod by zero.

*/

/*
   In general, on an IEEE-754 platform the aim is to follow the C99
   standard, including Annex 'F', whenever possible.  Where the
   standard recommends raising the 'divide-by-zero' or 'invalid'
   floating-point exceptions, Python should raise a ValueError.  Where
   the standard recommends raising 'overflow', Python should raise an
   OverflowError.  In all other circumstances a value should be
   returned.
 */

#include "Python.h"
#include "_math.h"

/*
   sin(pi*x), giving accurate results for all finite x (especially x
   integral or close to an integer).  This is here for use in the
   reflection formula for the gamma function.  It conforms to IEEE
   754-2008 for finite arguments, but not for infinities or nans.
*/

static const double pi = 3.141592653589793238462643383279502884197;
static const double sqrtpi = 1.772453850905516027298167483341145182798;
static const double logpi = 1.144729885849400174143427351353058711647;

static double
sinpi(double x)
{
    double y, r;
    int n;
    /* this function should only ever be called for finite arguments */
    assert(Py_IS_FINITE(x));
    y = fmod(fabs(x), 2.0);
    n = (int)round(2.0*y);
    assert(0 <= n && n <= 4);
    switch (n) {
    case 0:
        r = sin(pi*y);
        break;
    case 1:
        r = cos(pi*(y-0.5));
        break;
    case 2:
        /* N.B. -sin(pi*(y-1.0)) is *not* equivalent: it would give
           -0.0 instead of 0.0 when y == 1.0. */
        r = sin(pi*(1.0-y));
        break;
    case 3:
        r = -cos(pi*(y-1.5));
        break;
    case 4:
        r = sin(pi*(y-2.0));
        break;
    default:
        assert(0);  /* should never get here */
        r = -1.23e200; /* silence gcc warning */
    }
    return copysign(1.0, x)*r;
}

/* Implementation of the real gamma function.  In extensive but non-exhaustive
   random tests, this function proved accurate to within <= 10 ulps across the
   entire float domain.  Note that accuracy may depend on the quality of the
   system math functions, the pow function in particular.  Special cases
   follow C99 annex F.  The parameters and method are tailored to platforms
   whose double format is the IEEE 754 binary64 format.

   Method: for x > 0.0 we use the Lanczos approximation with parameters N=13
   and g=6.024680040776729583740234375; these parameters are amongst those
   used by the Boost library.  Following Boost (again), we re-express the
   Lanczos sum as a rational function, and compute it that way.  The
   coefficients below were computed independently using MPFR, and have been
   double-checked against the coefficients in the Boost source code.

   For x < 0.0 we use the reflection formula.

   There's one minor tweak that deserves explanation: Lanczos' formula for
   Gamma(x) involves computing pow(x+g-0.5, x-0.5) / exp(x+g-0.5).  For many x
   values, x+g-0.5 can be represented exactly.  However, in cases where it
   can't be represented exactly the small error in x+g-0.5 can be magnified
   significantly by the pow and exp calls, especially for large x.  A cheap
   correction is to multiply by (1 + e*g/(x+g-0.5)), where e is the error
   involved in the computation of x+g-0.5 (that is, e = computed value of
   x+g-0.5 - exact value of x+g-0.5).  Here's the proof:

   Correction factor
   -----------------
   Write x+g-0.5 = y-e, where y is exactly representable as an IEEE 754
   double, and e is tiny.  Then:

     pow(x+g-0.5,x-0.5)/exp(x+g-0.5) = pow(y-e, x-0.5)/exp(y-e)
     = pow(y, x-0.5)/exp(y) * C,

   where the correction_factor C is given by

     C = pow(1-e/y, x-0.5) * exp(e)

   Since e is tiny, pow(1-e/y, x-0.5) ~ 1-(x-0.5)*e/y, and exp(x) ~ 1+e, so:

     C ~ (1-(x-0.5)*e/y) * (1+e) ~ 1 + e*(y-(x-0.5))/y

   But y-(x-0.5) = g+e, and g+e ~ g.  So we get C ~ 1 + e*g/y, and

     pow(x+g-0.5,x-0.5)/exp(x+g-0.5) ~ pow(y, x-0.5)/exp(y) * (1 + e*g/y),

   Note that for accuracy, when computing r*C it's better to do

     r + e*g/y*r;

   than

     r * (1 + e*g/y);

   since the addition in the latter throws away most of the bits of
   information in e*g/y.
*/

#define LANCZOS_N 13
static const double lanczos_g = 6.024680040776729583740234375;
static const double lanczos_g_minus_half = 5.524680040776729583740234375;
static const double lanczos_num_coeffs[LANCZOS_N] = {
    23531376880.410759688572007674451636754734846804940,
    42919803642.649098768957899047001988850926355848959,
    35711959237.355668049440185451547166705960488635843,
    17921034426.037209699919755754458931112671403265390,
    6039542586.3520280050642916443072979210699388420708,
    1439720407.3117216736632230727949123939715485786772,
    248874557.86205415651146038641322942321632125127801,
    31426415.585400194380614231628318205362874684987640,
    2876370.6289353724412254090516208496135991145378768,
    186056.26539522349504029498971604569928220784236328,
    8071.6720023658162106380029022722506138218516325024,
    210.82427775157934587250973392071336271166969580291,
    2.5066282746310002701649081771338373386264310793408
};

/* denominator is x*(x+1)*...*(x+LANCZOS_N-2) */
static const double lanczos_den_coeffs[LANCZOS_N] = {
    0.0, 39916800.0, 120543840.0, 150917976.0, 105258076.0, 45995730.0,
    13339535.0, 2637558.0, 357423.0, 32670.0, 1925.0, 66.0, 1.0};

/* gamma values for small positive integers, 1 though NGAMMA_INTEGRAL */
#define NGAMMA_INTEGRAL 23
static const double gamma_integral[NGAMMA_INTEGRAL] = {
    1.0, 1.0, 2.0, 6.0, 24.0, 120.0, 720.0, 5040.0, 40320.0, 362880.0,
    3628800.0, 39916800.0, 479001600.0, 6227020800.0, 87178291200.0,
    1307674368000.0, 20922789888000.0, 355687428096000.0,
    6402373705728000.0, 121645100408832000.0, 2432902008176640000.0,
    51090942171709440000.0, 1124000727777607680000.0,
};

/* Lanczos' sum L_g(x), for positive x */

static double
lanczos_sum(double x)
{
    double num = 0.0, den = 0.0;
    int i;
    assert(x > 0.0);
    /* evaluate the rational function lanczos_sum(x).  For large
       x, the obvious algorithm risks overflow, so we instead
       rescale the denominator and numerator of the rational
       function by x**(1-LANCZOS_N) and treat this as a
       rational function in 1/x.  This also reduces the error for
       larger x values.  The choice of cutoff point (5.0 below) is
       somewhat arbitrary; in tests, smaller cutoff values than
       this resulted in lower accuracy. */
    if (x < 5.0) {
        for (i = LANCZOS_N; --i >= 0; ) {
            num = num * x + lanczos_num_coeffs[i];
            den = den * x + lanczos_den_coeffs[i];
        }
    }
    else {
        for (i = 0; i < LANCZOS_N; i++) {
            num = num / x + lanczos_num_coeffs[i];
            den = den / x + lanczos_den_coeffs[i];
        }
    }
    return num/den;
}

/* Constant for +infinity, generated in the same way as float('inf'). */

static double
m_inf(void)
{
#ifndef PY_NO_SHORT_FLOAT_REPR
    return _Py_dg_infinity(0);
#else
    return Py_HUGE_VAL;
#endif
}

/* Constant nan value, generated in the same way as float('nan'). */
/* We don't currently assume that Py_NAN is defined everywhere. */

#if !defined(PY_NO_SHORT_FLOAT_REPR) || defined(Py_NAN)

static double
m_nan(void)
{
#ifndef PY_NO_SHORT_FLOAT_REPR
    return _Py_dg_stdnan(0);
#else
    return Py_NAN;
#endif
}

#endif

static double
m_tgamma(double x)
{
    double absx, r, y, z, sqrtpow;

    /* special cases */
    if (!Py_IS_FINITE(x)) {
        if (Py_IS_NAN(x) || x > 0.0)
            return x;  /* tgamma(nan) = nan, tgamma(inf) = inf */
        else {
            errno = EDOM;
            return Py_NAN;  /* tgamma(-inf) = nan, invalid */
        }
    }
    if (x == 0.0) {
        errno = EDOM;
        /* tgamma(+-0.0) = +-inf, divide-by-zero */
        return copysign(Py_HUGE_VAL, x);
    }

    /* integer arguments */
    if (x == floor(x)) {
        if (x < 0.0) {
            errno = EDOM;  /* tgamma(n) = nan, invalid for */
            return Py_NAN; /* negative integers n */
        }
        if (x <= NGAMMA_INTEGRAL)
            return gamma_integral[(int)x - 1];
    }
    absx = fabs(x);

    /* tiny arguments:  tgamma(x) ~ 1/x for x near 0 */
    if (absx < 1e-20) {
        r = 1.0/x;
        if (Py_IS_INFINITY(r))
            errno = ERANGE;
        return r;
    }

    /* large arguments: assuming IEEE 754 doubles, tgamma(x) overflows for
       x > 200, and underflows to +-0.0 for x < -200, not a negative
       integer. */
    if (absx > 200.0) {
        if (x < 0.0) {
            return 0.0/sinpi(x);
        }
        else {
            errno = ERANGE;
            return Py_HUGE_VAL;
        }
    }

    y = absx + lanczos_g_minus_half;
    /* compute error in sum */
    if (absx > lanczos_g_minus_half) {
        /* note: the correction can be foiled by an optimizing
           compiler that (incorrectly) thinks that an expression like
           a + b - a - b can be optimized to 0.0.  This shouldn't
           happen in a standards-conforming compiler. */
        double q = y - absx;
        z = q - lanczos_g_minus_half;
    }
    else {
        double q = y - lanczos_g_minus_half;
        z = q - absx;
    }
    z = z * lanczos_g / y;
    if (x < 0.0) {
        r = -pi / sinpi(absx) / absx * exp(y) / lanczos_sum(absx);
        r -= z * r;
        if (absx < 140.0) {
            r /= pow(y, absx - 0.5);
        }
        else {
            sqrtpow = pow(y, absx / 2.0 - 0.25);
            r /= sqrtpow;
            r /= sqrtpow;
        }
    }
    else {
        r = lanczos_sum(absx) / exp(y);
        r += z * r;
        if (absx < 140.0) {
            r *= pow(y, absx - 0.5);
        }
        else {
            sqrtpow = pow(y, absx / 2.0 - 0.25);
            r *= sqrtpow;
            r *= sqrtpow;
        }
    }
    if (Py_IS_INFINITY(r))
        errno = ERANGE;
    return r;
}

/*
   lgamma:  natural log of the absolute value of the Gamma function.
   For large arguments, Lanczos' formula works extremely well here.
*/

static double
m_lgamma(double x)
{
    double r, absx;

    /* special cases */
    if (!Py_IS_FINITE(x)) {
        if (Py_IS_NAN(x))
            return x;  /* lgamma(nan) = nan */
        else
            return Py_HUGE_VAL; /* lgamma(+-inf) = +inf */
    }

    /* integer arguments */
    if (x == floor(x) && x <= 2.0) {
        if (x <= 0.0) {
            errno = EDOM;  /* lgamma(n) = inf, divide-by-zero for */
            return Py_HUGE_VAL; /* integers n <= 0 */
        }
        else {
            return 0.0; /* lgamma(1) = lgamma(2) = 0.0 */
        }
    }

    absx = fabs(x);
    /* tiny arguments: lgamma(x) ~ -log(fabs(x)) for small x */
    if (absx < 1e-20)
        return -log(absx);

    /* Lanczos' formula.  We could save a fraction of a ulp in accuracy by
       having a second set of numerator coefficients for lanczos_sum that
       absorbed the exp(-lanczos_g) term, and throwing out the lanczos_g
       subtraction below; it's probably not worth it. */
    r = log(lanczos_sum(absx)) - lanczos_g;
    r += (absx - 0.5) * (log(absx + lanczos_g - 0.5) - 1);
    if (x < 0.0)
        /* Use reflection formula to get value for negative x. */
        r = logpi - log(fabs(sinpi(absx))) - log(absx) - r;
    if (Py_IS_INFINITY(r))
        errno = ERANGE;
    return r;
}

/*
   Implementations of the error function erf(x) and the complementary error
   function erfc(x).

   Method: we use a series approximation for erf for small x, and a continued
   fraction approximation for erfc(x) for larger x;
   combined with the relations erf(-x) = -erf(x) and erfc(x) = 1.0 - erf(x),
   this gives us erf(x) and erfc(x) for all x.

   The series expansion used is:

      erf(x) = x*exp(-x*x)/sqrt(pi) * [
                     2/1 + 4/3 x**2 + 8/15 x**4 + 16/105 x**6 + ...]

   The coefficient of x**(2k-2) here is 4**k*factorial(k)/factorial(2*k).
   This series converges well for smallish x, but slowly for larger x.

   The continued fraction expansion used is:

      erfc(x) = x*exp(-x*x)/sqrt(pi) * [1/(0.5 + x**2 -) 0.5/(2.5 + x**2 - )
                              3.0/(4.5 + x**2 - ) 7.5/(6.5 + x**2 - ) ...]

   after the first term, the general term has the form:

      k*(k-0.5)/(2*k+0.5 + x**2 - ...).

   This expansion converges fast for larger x, but convergence becomes
   infinitely slow as x approaches 0.0.  The (somewhat naive) continued
   fraction evaluation algorithm used below also risks overflow for large x;
   but for large x, erfc(x) == 0.0 to within machine precision.  (For
   example, erfc(30.0) is approximately 2.56e-393).

   Parameters: use series expansion for abs(x) < ERF_SERIES_CUTOFF and
   continued fraction expansion for ERF_SERIES_CUTOFF <= abs(x) <
   ERFC_CONTFRAC_CUTOFF.  ERFC_SERIES_TERMS and ERFC_CONTFRAC_TERMS are the
   numbers of terms to use for the relevant expansions.  */

#define ERF_SERIES_CUTOFF 1.5
#define ERF_SERIES_TERMS 25
#define ERFC_CONTFRAC_CUTOFF 30.0
#define ERFC_CONTFRAC_TERMS 50

/*
   Error function, via power series.

   Given a finite float x, return an approximation to erf(x).
   Converges reasonably fast for small x.
*/

static double
m_erf_series(double x)
{
    double x2, acc, fk, result;
    int i, saved_errno;

    x2 = x * x;
    acc = 0.0;
    fk = (double)ERF_SERIES_TERMS + 0.5;
    for (i = 0; i < ERF_SERIES_TERMS; i++) {
        acc = 2.0 + x2 * acc / fk;
        fk -= 1.0;
    }
    /* Make sure the exp call doesn't affect errno;
       see m_erfc_contfrac for more. */
    saved_errno = errno;
    result = acc * x * exp(-x2) / sqrtpi;
    errno = saved_errno;
    return result;
}

/*
   Complementary error function, via continued fraction expansion.

   Given a positive float x, return an approximation to erfc(x).  Converges
   reasonably fast for x large (say, x > 2.0), and should be safe from
   overflow if x and nterms are not too large.  On an IEEE 754 machine, with x
   <= 30.0, we're safe up to nterms = 100.  For x >= 30.0, erfc(x) is smaller
   than the smallest representable nonzero float.  */

static double
m_erfc_contfrac(double x)
{
    double x2, a, da, p, p_last, q, q_last, b, result;
    int i, saved_errno;

    if (x >= ERFC_CONTFRAC_CUTOFF)
        return 0.0;

    x2 = x*x;
    a = 0.0;
    da = 0.5;
    p = 1.0; p_last = 0.0;
    q = da + x2; q_last = 1.0;
    for (i = 0; i < ERFC_CONTFRAC_TERMS; i++) {
        double temp;
        a += da;
        da += 2.0;
        b = da + x2;
        temp = p; p = b*p - a*p_last; p_last = temp;
        temp = q; q = b*q - a*q_last; q_last = temp;
    }
    /* Issue #8986: On some platforms, exp sets errno on underflow to zero;
       save the current errno value so that we can restore it later. */
    saved_errno = errno;
    result = p / q * x * exp(-x2) / sqrtpi;
    errno = saved_errno;
    return result;
}

/* Error function erf(x), for general x */

static double
m_erf(double x)
{
    double absx, cf;

    if (Py_IS_NAN(x))
        return x;
    absx = fabs(x);
    if (absx < ERF_SERIES_CUTOFF)
        return m_erf_series(x);
    else {
        cf = m_erfc_contfrac(absx);
        return x > 0.0 ? 1.0 - cf : cf - 1.0;
    }
}

/* Complementary error function erfc(x), for general x. */

static double
m_erfc(double x)
{
    double absx, cf;

    if (Py_IS_NAN(x))
        return x;
    absx = fabs(x);
    if (absx < ERF_SERIES_CUTOFF)
        return 1.0 - m_erf_series(x);
    else {
        cf = m_erfc_contfrac(absx);
        return x > 0.0 ? cf : 2.0 - cf;
    }
}

/*
   wrapper for atan2 that deals directly with special cases before
   delegating to the platform libm for the remaining cases.  This
   is necessary to get consistent behaviour across platforms.
   Windows, FreeBSD and alpha Tru64 are amongst platforms that don't
   always follow C99.
*/

static double
m_atan2(double y, double x)
{
    if (Py_IS_NAN(x) || Py_IS_NAN(y))
        return Py_NAN;
    if (Py_IS_INFINITY(y)) {
        if (Py_IS_INFINITY(x)) {
            if (copysign(1., x) == 1.)
                /* atan2(+-inf, +inf) == +-pi/4 */
                return copysign(0.25*Py_MATH_PI, y);
            else
                /* atan2(+-inf, -inf) == +-pi*3/4 */
                return copysign(0.75*Py_MATH_PI, y);
        }
        /* atan2(+-inf, x) == +-pi/2 for finite x */
        return copysign(0.5*Py_MATH_PI, y);
    }
    if (Py_IS_INFINITY(x) || y == 0.) {
        if (copysign(1., x) == 1.)
            /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
            return copysign(0., y);
        else
            /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
            return copysign(Py_MATH_PI, y);
    }
    return atan2(y, x);
}

/*
    Various platforms (Solaris, OpenBSD) do nonstandard things for log(0),
    log(-ve), log(NaN).  Here are wrappers for log and log10 that deal with
    special values directly, passing positive non-special values through to
    the system log/log10.
 */

static double
m_log(double x)
{
    if (Py_IS_FINITE(x)) {
        if (x > 0.0)
            return log(x);
        errno = EDOM;
        if (x == 0.0)
            return -Py_HUGE_VAL; /* log(0) = -inf */
        else
            return Py_NAN; /* log(-ve) = nan */
    }
    else if (Py_IS_NAN(x))
        return x; /* log(nan) = nan */
    else if (x > 0.0)
        return x; /* log(inf) = inf */
    else {
        errno = EDOM;
        return Py_NAN; /* log(-inf) = nan */
    }
}

/*
   log2: log to base 2.

   Uses an algorithm that should:

     (a) produce exact results for powers of 2, and
     (b) give a monotonic log2 (for positive finite floats),
         assuming that the system log is monotonic.
*/

static double
m_log2(double x)
{
    if (!Py_IS_FINITE(x)) {
        if (Py_IS_NAN(x))
            return x; /* log2(nan) = nan */
        else if (x > 0.0)
            return x; /* log2(+inf) = +inf */
        else {
            errno = EDOM;
            return Py_NAN; /* log2(-inf) = nan, invalid-operation */
        }
    }

    if (x > 0.0) {
#ifdef HAVE_LOG2
        return log2(x);
#else
        double m;
        int e;
        m = frexp(x, &e);
        /* We want log2(m * 2**e) == log(m) / log(2) + e.  Care is needed when
         * x is just greater than 1.0: in that case e is 1, log(m) is negative,
         * and we get significant cancellation error from the addition of
         * log(m) / log(2) to e.  The slight rewrite of the expression below
         * avoids this problem.
         */
        if (x >= 1.0) {
            return log(2.0 * m) / log(2.0) + (e - 1);
        }
        else {
            return log(m) / log(2.0) + e;
        }
#endif
    }
    else if (x == 0.0) {
        errno = EDOM;
        return -Py_HUGE_VAL; /* log2(0) = -inf, divide-by-zero */
    }
    else {
        errno = EDOM;
        return Py_NAN; /* log2(-inf) = nan, invalid-operation */
    }
}

static double
m_log10(double x)
{
    if (Py_IS_FINITE(x)) {
        if (x > 0.0)
            return log10(x);
        errno = EDOM;
        if (x == 0.0)
            return -Py_HUGE_VAL; /* log10(0) = -inf */
        else
            return Py_NAN; /* log10(-ve) = nan */
    }
    else if (Py_IS_NAN(x))
        return x; /* log10(nan) = nan */
    else if (x > 0.0)
        return x; /* log10(inf) = inf */
    else {
        errno = EDOM;
        return Py_NAN; /* log10(-inf) = nan */
    }
}


static PyObject *
math_gcd(PyObject *self, PyObject *args)
{
    PyObject *a, *b, *g;

    if (!PyArg_ParseTuple(args, "OO:gcd", &a, &b))
        return NULL;

    a = PyNumber_Index(a);
    if (a == NULL)
        return NULL;
    b = PyNumber_Index(b);
    if (b == NULL) {
        Py_DECREF(a);
        return NULL;
    }
    g = _PyLong_GCD(a, b);
    Py_DECREF(a);
    Py_DECREF(b);
    return g;
}

PyDoc_STRVAR(math_gcd_doc,
"gcd(x, y) -> int\n\
greatest common divisor of x and y");


/* Call is_error when errno != 0, and where x is the result libm
 * returned.  is_error will usually set up an exception and return
 * true (1), but may return false (0) without setting up an exception.
 */
static int
is_error(double x)
{
    int result = 1;     /* presumption of guilt */
    assert(errno);      /* non-zero errno is a precondition for calling */
    if (errno == EDOM)
        PyErr_SetString(PyExc_ValueError, "math domain error");

    else if (errno == ERANGE) {
        /* ANSI C generally requires libm functions to set ERANGE
         * on overflow, but also generally *allows* them to set
         * ERANGE on underflow too.  There's no consistency about
         * the latter across platforms.
         * Alas, C99 never requires that errno be set.
         * Here we suppress the underflow errors (libm functions
         * should return a zero on underflow, and +- HUGE_VAL on
         * overflow, so testing the result for zero suffices to
         * distinguish the cases).
         *
         * On some platforms (Ubuntu/ia64) it seems that errno can be
         * set to ERANGE for subnormal results that do *not* underflow
         * to zero.  So to be safe, we'll ignore ERANGE whenever the
         * function result is less than one in absolute value.
         */
        if (fabs(x) < 1.0)
            result = 0;
        else
            PyErr_SetString(PyExc_OverflowError,
                            "math range error");
    }
    else
        /* Unexpected math error */
        PyErr_SetFromErrno(PyExc_ValueError);
    return result;
}

/*
   math_1 is used to wrap a libm function f that takes a double
   arguments and returns a double.

   The error reporting follows these rules, which are designed to do
   the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
   platforms.

   - a NaN result from non-NaN inputs causes ValueError to be raised
   - an infinite result from finite inputs causes OverflowError to be
     raised if can_overflow is 1, or raises ValueError if can_overflow
     is 0.
   - if the result is finite and errno == EDOM then ValueError is
     raised
   - if the result is finite and nonzero and errno == ERANGE then
     OverflowError is raised

   The last rule is used to catch overflow on platforms which follow
   C89 but for which HUGE_VAL is not an infinity.

   For the majority of one-argument functions these rules are enough
   to ensure that Python's functions behave as specified in 'Annex F'
   of the C99 standard, with the 'invalid' and 'divide-by-zero'
   floating-point exceptions mapping to Python's ValueError and the
   'overflow' floating-point exception mapping to OverflowError.
   math_1 only works for functions that don't have singularities *and*
   the possibility of overflow; fortunately, that covers everything we
   care about right now.
*/

static PyObject *
math_1_to_whatever(PyObject *arg, double (*func) (double),
                   PyObject *(*from_double_func) (double),
                   int can_overflow)
{
    double x, r;
    x = PyFloat_AsDouble(arg);
    if (x == -1.0 && PyErr_Occurred())
        return NULL;
    errno = 0;
    PyFPE_START_PROTECT("in math_1", return 0);
    r = (*func)(x);
    PyFPE_END_PROTECT(r);
    if (Py_IS_NAN(r) && !Py_IS_NAN(x)) {
        PyErr_SetString(PyExc_ValueError,
                        "math domain error"); /* invalid arg */
        return NULL;
    }
    if (Py_IS_INFINITY(r) && Py_IS_FINITE(x)) {
        if (can_overflow)
            PyErr_SetString(PyExc_OverflowError,
                            "math range error"); /* overflow */
        else
            PyErr_SetString(PyExc_ValueError,
                            "math domain error"); /* singularity */
        return NULL;
    }
    if (Py_IS_FINITE(r) && errno && is_error(r))
        /* this branch unnecessary on most platforms */
        return NULL;

    return (*from_double_func)(r);
}

/* variant of math_1, to be used when the function being wrapped is known to
   set errno properly (that is, errno = EDOM for invalid or divide-by-zero,
   errno = ERANGE for overflow). */

static PyObject *
math_1a(PyObject *arg, double (*func) (double))
{
    double x, r;
    x = PyFloat_AsDouble(arg);
    if (x == -1.0 && PyErr_Occurred())
        return NULL;
    errno = 0;
    PyFPE_START_PROTECT("in math_1a", return 0);
    r = (*func)(x);
    PyFPE_END_PROTECT(r);
    if (errno && is_error(r))
        return NULL;
    return PyFloat_FromDouble(r);
}

/*
   math_2 is used to wrap a libm function f that takes two double
   arguments and returns a double.

   The error reporting follows these rules, which are designed to do
   the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
   platforms.

   - a NaN result from non-NaN inputs causes ValueError to be raised
   - an infinite result from finite inputs causes OverflowError to be
     raised.
   - if the result is finite and errno == EDOM then ValueError is
     raised
   - if the result is finite and nonzero and errno == ERANGE then
     OverflowError is raised

   The last rule is used to catch overflow on platforms which follow
   C89 but for which HUGE_VAL is not an infinity.

   For most two-argument functions (copysign, fmod, hypot, atan2)
   these rules are enough to ensure that Python's functions behave as
   specified in 'Annex F' of the C99 standard, with the 'invalid' and
   'divide-by-zero' floating-point exceptions mapping to Python's
   ValueError and the 'overflow' floating-point exception mapping to
   OverflowError.
*/

static PyObject *
math_1(PyObject *arg, double (*func) (double), int can_overflow)
{
    return math_1_to_whatever(arg, func, PyFloat_FromDouble, can_overflow);
}

static PyObject *
math_1_to_int(PyObject *arg, double (*func) (double), int can_overflow)
{
    return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow);
}

static PyObject *
math_2(PyObject *args, double (*func) (double, double), const char *funcname)
{
    PyObject *ox, *oy;
    double x, y, r;
    if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
        return NULL;
    x = PyFloat_AsDouble(ox);
    y = PyFloat_AsDouble(oy);
    if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
        return NULL;
    errno = 0;
    PyFPE_START_PROTECT("in math_2", return 0);
    r = (*func)(x, y);
    PyFPE_END_PROTECT(r);
    if (Py_IS_NAN(r)) {
        if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
            errno = EDOM;
        else
            errno = 0;
    }
    else if (Py_IS_INFINITY(r)) {
        if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
            errno = ERANGE;
        else
            errno = 0;
    }
    if (errno && is_error(r))
        return NULL;
    else
        return PyFloat_FromDouble(r);
}

#define FUNC1(funcname, func, can_overflow, docstring)                  \
    static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
        return math_1(args, func, can_overflow);                            \
    }\
    PyDoc_STRVAR(math_##funcname##_doc, docstring);

#define FUNC1A(funcname, func, docstring)                               \
    static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
        return math_1a(args, func);                                     \
    }\
    PyDoc_STRVAR(math_##funcname##_doc, docstring);

#define FUNC2(funcname, func, docstring) \
    static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
        return math_2(args, func, #funcname); \
    }\
    PyDoc_STRVAR(math_##funcname##_doc, docstring);

FUNC1(acos, acos, 0,
      "acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
FUNC1(acosh, m_acosh, 0,
      "acosh(x)\n\nReturn the inverse hyperbolic cosine of x.")
FUNC1(asin, asin, 0,
      "asin(x)\n\nReturn the arc sine (measured in radians) of x.")
FUNC1(asinh, m_asinh, 0,
      "asinh(x)\n\nReturn the inverse hyperbolic sine of x.")
FUNC1(atan, atan, 0,
      "atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
FUNC2(atan2, m_atan2,
      "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"
      "Unlike atan(y/x), the signs of both x and y are considered.")
FUNC1(atanh, m_atanh, 0,
      "atanh(x)\n\nReturn the inverse hyperbolic tangent of x.")

static PyObject * math_ceil(PyObject *self, PyObject *number) {
    _Py_IDENTIFIER(__ceil__);
    PyObject *method, *result;

    method = _PyObject_LookupSpecial(number, &PyId___ceil__);
    if (method == NULL) {
        if (PyErr_Occurred())
            return NULL;
        return math_1_to_int(number, ceil, 0);
    }
    result = _PyObject_CallNoArg(method);
    Py_DECREF(method);
    return result;
}

PyDoc_STRVAR(math_ceil_doc,
             "ceil(x)\n\nReturn the ceiling of x as an Integral.\n"
             "This is the smallest integer >= x.");

FUNC2(copysign, copysign,
      "copysign(x, y)\n\nReturn a float with the magnitude (absolute value) "
      "of x but the sign \nof y. On platforms that support signed zeros, "
      "copysign(1.0, -0.0) \nreturns -1.0.\n")
FUNC1(cos, cos, 0,
      "cos(x)\n\nReturn the cosine of x (measured in radians).")
FUNC1(cosh, cosh, 1,
      "cosh(x)\n\nReturn the hyperbolic cosine of x.")
FUNC1A(erf, m_erf,
       "erf(x)\n\nError function at x.")
FUNC1A(erfc, m_erfc,
       "erfc(x)\n\nComplementary error function at x.")
FUNC1(exp, exp, 1,
      "exp(x)\n\nReturn e raised to the power of x.")
FUNC1(expm1, m_expm1, 1,
      "expm1(x)\n\nReturn exp(x)-1.\n"
      "This function avoids the loss of precision involved in the direct "
      "evaluation of exp(x)-1 for small x.")
FUNC1(fabs, fabs, 0,
      "fabs(x)\n\nReturn the absolute value of the float x.")

static PyObject * math_floor(PyObject *self, PyObject *number) {
    _Py_IDENTIFIER(__floor__);
    PyObject *method, *result;

    method = _PyObject_LookupSpecial(number, &PyId___floor__);
    if (method == NULL) {
        if (PyErr_Occurred())
            return NULL;
        return math_1_to_int(number, floor, 0);
    }
    result = _PyObject_CallNoArg(method);
    Py_DECREF(method);
    return result;
}

PyDoc_STRVAR(math_floor_doc,
             "floor(x)\n\nReturn the floor of x as an Integral.\n"
             "This is the largest integer <= x.");

FUNC1A(gamma, m_tgamma,
      "gamma(x)\n\nGamma function at x.")
FUNC1A(lgamma, m_lgamma,
      "lgamma(x)\n\nNatural logarithm of absolute value of Gamma function at x.")
FUNC1(log1p, m_log1p, 0,
      "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n"
      "The result is computed in a way which is accurate for x near zero.")
FUNC1(sin, sin, 0,
      "sin(x)\n\nReturn the sine of x (measured in radians).")
FUNC1(sinh, sinh, 1,
      "sinh(x)\n\nReturn the hyperbolic sine of x.")
FUNC1(sqrt, sqrt, 0,
      "sqrt(x)\n\nReturn the square root of x.")
FUNC1(tan, tan, 0,
      "tan(x)\n\nReturn the tangent of x (measured in radians).")
FUNC1(tanh, tanh, 0,
      "tanh(x)\n\nReturn the hyperbolic tangent of x.")

/* Precision summation function as msum() by Raymond Hettinger in
   <http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/393090>,
   enhanced with the exact partials sum and roundoff from Mark
   Dickinson's post at <http://bugs.python.org/file10357/msum4.py>.
   See those links for more details, proofs and other references.

   Note 1: IEEE 754R floating point semantics are assumed,
   but the current implementation does not re-establish special
   value semantics across iterations (i.e. handling -Inf + Inf).

   Note 2:  No provision is made for intermediate overflow handling;
   therefore, sum([1e+308, 1e-308, 1e+308]) returns 1e+308 while
   sum([1e+308, 1e+308, 1e-308]) raises an OverflowError due to the
   overflow of the first partial sum.

   Note 3: The intermediate values lo, yr, and hi are declared volatile so
   aggressive compilers won't algebraically reduce lo to always be exactly 0.0.
   Also, the volatile declaration forces the values to be stored in memory as
   regular doubles instead of extended long precision (80-bit) values.  This
   prevents double rounding because any addition or subtraction of two doubles
   can be resolved exactly into double-sized hi and lo values.  As long as the
   hi value gets forced into a double before yr and lo are computed, the extra
   bits in downstream extended precision operations (x87 for example) will be
   exactly zero and therefore can be losslessly stored back into a double,
   thereby preventing double rounding.

   Note 4: A similar implementation is in Modules/cmathmodule.c.
   Be sure to update both when making changes.

   Note 5: The signature of math.fsum() differs from builtins.sum()
   because the start argument doesn't make sense in the context of
   accurate summation.  Since the partials table is collapsed before
   returning a result, sum(seq2, start=sum(seq1)) may not equal the
   accurate result returned by sum(itertools.chain(seq1, seq2)).
*/

#define NUM_PARTIALS  32  /* initial partials array size, on stack */

/* Extend the partials array p[] by doubling its size. */
static int                          /* non-zero on error */
_fsum_realloc(double **p_ptr, Py_ssize_t  n,
             double  *ps,    Py_ssize_t *m_ptr)
{
    void *v = NULL;
    Py_ssize_t m = *m_ptr;

    m += m;  /* double */
    if (n < m && (size_t)m < ((size_t)PY_SSIZE_T_MAX / sizeof(double))) {
        double *p = *p_ptr;
        if (p == ps) {
            v = PyMem_Malloc(sizeof(double) * m);
            if (v != NULL)
                memcpy(v, ps, sizeof(double) * n);
        }
        else
            v = PyMem_Realloc(p, sizeof(double) * m);
    }
    if (v == NULL) {        /* size overflow or no memory */
        PyErr_SetString(PyExc_MemoryError, "math.fsum partials");
        return 1;
    }
    *p_ptr = (double*) v;
    *m_ptr = m;
    return 0;
}

/* Full precision summation of a sequence of floats.

   def msum(iterable):
       partials = []  # sorted, non-overlapping partial sums
       for x in iterable:
           i = 0
           for y in partials:
               if abs(x) < abs(y):
                   x, y = y, x
               hi = x + y
               lo = y - (hi - x)
               if lo:
                   partials[i] = lo
                   i += 1
               x = hi
           partials[i:] = [x]
       return sum_exact(partials)

   Rounded x+y stored in hi with the roundoff stored in lo.  Together hi+lo
   are exactly equal to x+y.  The inner loop applies hi/lo summation to each
   partial so that the list of partial sums remains exact.

   Sum_exact() adds the partial sums exactly and correctly rounds the final
   result (using the round-half-to-even rule).  The items in partials remain
   non-zero, non-special, non-overlapping and strictly increasing in
   magnitude, but possibly not all having the same sign.

   Depends on IEEE 754 arithmetic guarantees and half-even rounding.
*/

static PyObject*
math_fsum(PyObject *self, PyObject *seq)
{
    PyObject *item, *iter, *sum = NULL;
    Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
    double x, y, t, ps[NUM_PARTIALS], *p = ps;
    double xsave, special_sum = 0.0, inf_sum = 0.0;
    volatile double hi, yr, lo;

    iter = PyObject_GetIter(seq);
    if (iter == NULL)
        return NULL;

    PyFPE_START_PROTECT("fsum", Py_DECREF(iter); return NULL)

    for(;;) {           /* for x in iterable */
        assert(0 <= n && n <= m);
        assert((m == NUM_PARTIALS && p == ps) ||
               (m >  NUM_PARTIALS && p != NULL));

        item = PyIter_Next(iter);
        if (item == NULL) {
            if (PyErr_Occurred())
                goto _fsum_error;
            break;
        }
        x = PyFloat_AsDouble(item);
        Py_DECREF(item);
        if (PyErr_Occurred())
            goto _fsum_error;

        xsave = x;
        for (i = j = 0; j < n; j++) {       /* for y in partials */
            y = p[j];
            if (fabs(x) < fabs(y)) {
                t = x; x = y; y = t;
            }
            hi = x + y;
            yr = hi - x;
            lo = y - yr;
            if (lo != 0.0)
                p[i++] = lo;
            x = hi;
        }

        n = i;                              /* ps[i:] = [x] */
        if (x != 0.0) {
            if (! Py_IS_FINITE(x)) {
                /* a nonfinite x could arise either as
                   a result of intermediate overflow, or
                   as a result of a nan or inf in the
                   summands */
                if (Py_IS_FINITE(xsave)) {
                    PyErr_SetString(PyExc_OverflowError,
                          "intermediate overflow in fsum");
                    goto _fsum_error;
                }
                if (Py_IS_INFINITY(xsave))
                    inf_sum += xsave;
                special_sum += xsave;
                /* reset partials */
                n = 0;
            }
            else if (n >= m && _fsum_realloc(&p, n, ps, &m))
                goto _fsum_error;
            else
                p[n++] = x;
        }
    }

    if (special_sum != 0.0) {
        if (Py_IS_NAN(inf_sum))
            PyErr_SetString(PyExc_ValueError,
                            "-inf + inf in fsum");
        else
            sum = PyFloat_FromDouble(special_sum);
        goto _fsum_error;
    }

    hi = 0.0;
    if (n > 0) {
        hi = p[--n];
        /* sum_exact(ps, hi) from the top, stop when the sum becomes
           inexact. */
        while (n > 0) {
            x = hi;
            y = p[--n];
            assert(fabs(y) < fabs(x));
            hi = x + y;
            yr = hi - x;
            lo = y - yr;
            if (lo != 0.0)
                break;
        }
        /* Make half-even rounding work across multiple partials.
           Needed so that sum([1e-16, 1, 1e16]) will round-up the last
           digit to two instead of down to zero (the 1e-16 makes the 1
           slightly closer to two).  With a potential 1 ULP rounding
           error fixed-up, math.fsum() can guarantee commutativity. */
        if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) ||
                      (lo > 0.0 && p[n-1] > 0.0))) {
            y = lo * 2.0;
            x = hi + y;
            yr = x - hi;
            if (y == yr)
                hi = x;
        }
    }
    sum = PyFloat_FromDouble(hi);

_fsum_error:
    PyFPE_END_PROTECT(hi)
    Py_DECREF(iter);
    if (p != ps)
        PyMem_Free(p);
    return sum;
}

#undef NUM_PARTIALS

PyDoc_STRVAR(math_fsum_doc,
"fsum(iterable)\n\n\
Return an accurate floating point sum of values in the iterable.\n\
Assumes IEEE-754 floating point arithmetic.");

/* Return the smallest integer k such that n < 2**k, or 0 if n == 0.
 * Equivalent to floor(lg(x))+1.  Also equivalent to: bitwidth_of_type -
 * count_leading_zero_bits(x)
 */

/* XXX: This routine does more or less the same thing as
 * bits_in_digit() in Objects/longobject.c.  Someday it would be nice to
 * consolidate them.  On BSD, there's a library function called fls()
 * that we could use, and GCC provides __builtin_clz().
 */

static unsigned long
bit_length(unsigned long n)
{
    unsigned long len = 0;
    while (n != 0) {
        ++len;
        n >>= 1;
    }
    return len;
}

static unsigned long
count_set_bits(unsigned long n)
{
    unsigned long count = 0;
    while (n != 0) {
        ++count;
        n &= n - 1; /* clear least significant bit */
    }
    return count;
}

/* Divide-and-conquer factorial algorithm
 *
 * Based on the formula and pseudo-code provided at:
 * http://www.luschny.de/math/factorial/binarysplitfact.html
 *
 * Faster algorithms exist, but they're more complicated and depend on
 * a fast prime factorization algorithm.
 *
 * Notes on the algorithm
 * ----------------------
 *
 * factorial(n) is written in the form 2**k * m, with m odd.  k and m are
 * computed separately, and then combined using a left shift.
 *
 * The function factorial_odd_part computes the odd part m (i.e., the greatest
 * odd divisor) of factorial(n), using the formula:
 *
 *   factorial_odd_part(n) =
 *
 *        product_{i >= 0} product_{0 < j <= n / 2**i, j odd} j
 *
 * Example: factorial_odd_part(20) =
 *
 *        (1) *
 *        (1) *
 *        (1 * 3 * 5) *
 *        (1 * 3 * 5 * 7 * 9)
 *        (1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19)
 *
 * Here i goes from large to small: the first term corresponds to i=4 (any
 * larger i gives an empty product), and the last term corresponds to i=0.
 * Each term can be computed from the last by multiplying by the extra odd
 * numbers required: e.g., to get from the penultimate term to the last one,
 * we multiply by (11 * 13 * 15 * 17 * 19).
 *
 * To see a hint of why this formula works, here are the same numbers as above
 * but with the even parts (i.e., the appropriate powers of 2) included.  For
 * each subterm in the product for i, we multiply that subterm by 2**i:
 *
 *   factorial(20) =
 *
 *        (16) *
 *        (8) *
 *        (4 * 12 * 20) *
 *        (2 * 6 * 10 * 14 * 18) *
 *        (1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19)
 *
 * The factorial_partial_product function computes the product of all odd j in
 * range(start, stop) for given start and stop.  It's used to compute the
 * partial products like (11 * 13 * 15 * 17 * 19) in the example above.  It
 * operates recursively, repeatedly splitting the range into two roughly equal
 * pieces until the subranges are small enough to be computed using only C
 * integer arithmetic.
 *
 * The two-valuation k (i.e., the exponent of the largest power of 2 dividing
 * the factorial) is computed independently in the main math_factorial
 * function.  By standard results, its value is:
 *
 *    two_valuation = n//2 + n//4 + n//8 + ....
 *
 * It can be shown (e.g., by complete induction on n) that two_valuation is
 * equal to n - count_set_bits(n), where count_set_bits(n) gives the number of
 * '1'-bits in the binary expansion of n.
 */

/* factorial_partial_product: Compute product(range(start, stop, 2)) using
 * divide and conquer.  Assumes start and stop are odd and stop > start.
 * max_bits must be >= bit_length(stop - 2). */

static PyObject *
factorial_partial_product(unsigned long start, unsigned long stop,
                          unsigned long max_bits)
{
    unsigned long midpoint, num_operands;
    PyObject *left = NULL, *right = NULL, *result = NULL;

    /* If the return value will fit an unsigned long, then we can
     * multiply in a tight, fast loop where each multiply is O(1).
     * Compute an upper bound on the number of bits required to store
     * the answer.
     *
     * Storing some integer z requires floor(lg(z))+1 bits, which is
     * conveniently the value returned by bit_length(z).  The
     * product x*y will require at most
     * bit_length(x) + bit_length(y) bits to store, based
     * on the idea that lg product = lg x + lg y.
     *
     * We know that stop - 2 is the largest number to be multiplied.  From
     * there, we have: bit_length(answer) <= num_operands *
     * bit_length(stop - 2)
     */

    num_operands = (stop - start) / 2;
    /* The "num_operands <= 8 * SIZEOF_LONG" check guards against the
     * unlikely case of an overflow in num_operands * max_bits. */
    if (num_operands <= 8 * SIZEOF_LONG &&
        num_operands * max_bits <= 8 * SIZEOF_LONG) {
        unsigned long j, total;
        for (total = start, j = start + 2; j < stop; j += 2)
            total *= j;
        return PyLong_FromUnsignedLong(total);
    }

    /* find midpoint of range(start, stop), rounded up to next odd number. */
    midpoint = (start + num_operands) | 1;
    left = factorial_partial_product(start, midpoint,
                                     bit_length(midpoint - 2));
    if (left == NULL)
        goto error;
    right = factorial_partial_product(midpoint, stop, max_bits);
    if (right == NULL)
        goto error;
    result = PyNumber_Multiply(left, right);

  error:
    Py_XDECREF(left);
    Py_XDECREF(right);
    return result;
}

/* factorial_odd_part:  compute the odd part of factorial(n). */

static PyObject *
factorial_odd_part(unsigned long n)
{
    long i;
    unsigned long v, lower, upper;
    PyObject *partial, *tmp, *inner, *outer;

    inner = PyLong_FromLong(1);
    if (inner == NULL)
        return NULL;
    outer = inner;
    Py_INCREF(outer);

    upper = 3;
    for (i = bit_length(n) - 2; i >= 0; i--) {
        v = n >> i;
        if (v <= 2)
            continue;
        lower = upper;
        /* (v + 1) | 1 = least odd integer strictly larger than n / 2**i */
        upper = (v + 1) | 1;
        /* Here inner is the product of all odd integers j in the range (0,
           n/2**(i+1)].  The factorial_partial_product call below gives the
           product of all odd integers j in the range (n/2**(i+1), n/2**i]. */
        partial = factorial_partial_product(lower, upper, bit_length(upper-2));
        /* inner *= partial */
        if (partial == NULL)
            goto error;
        tmp = PyNumber_Multiply(inner, partial);
        Py_DECREF(partial);
        if (tmp == NULL)
            goto error;
        Py_DECREF(inner);
        inner = tmp;
        /* Now inner is the product of all odd integers j in the range (0,
           n/2**i], giving the inner product in the formula above. */

        /* outer *= inner; */
        tmp = PyNumber_Multiply(outer, inner);
        if (tmp == NULL)
            goto error;
        Py_DECREF(outer);
        outer = tmp;
    }
    Py_DECREF(inner);
    return outer;

  error:
    Py_DECREF(outer);
    Py_DECREF(inner);
    return NULL;
}

/* Lookup table for small factorial values */

static const unsigned long SmallFactorials[] = {
    1, 1, 2, 6, 24, 120, 720, 5040, 40320,
    362880, 3628800, 39916800, 479001600,
#if SIZEOF_LONG >= 8
    6227020800, 87178291200, 1307674368000,
    20922789888000, 355687428096000, 6402373705728000,
    121645100408832000, 2432902008176640000
#endif
};

static PyObject *
math_factorial(PyObject *self, PyObject *arg)
{
    long x;
    int overflow;
    PyObject *result, *odd_part, *two_valuation;

    if (PyFloat_Check(arg)) {
        PyObject *lx;
        double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg);
        if (!(Py_IS_FINITE(dx) && dx == floor(dx))) {
            PyErr_SetString(PyExc_ValueError,
                            "factorial() only accepts integral values");
            return NULL;
        }
        lx = PyLong_FromDouble(dx);
        if (lx == NULL)
            return NULL;
        x = PyLong_AsLongAndOverflow(lx, &overflow);
        Py_DECREF(lx);
    }
    else
        x = PyLong_AsLongAndOverflow(arg, &overflow);

    if (x == -1 && PyErr_Occurred()) {
        return NULL;
    }
    else if (overflow == 1) {
        PyErr_Format(PyExc_OverflowError,
                     "factorial() argument should not exceed %ld",
                     LONG_MAX);
        return NULL;
    }
    else if (overflow == -1 || x < 0) {
        PyErr_SetString(PyExc_ValueError,
                        "factorial() not defined for negative values");
        return NULL;
    }

    /* use lookup table if x is small */
    if (x < (long)Py_ARRAY_LENGTH(SmallFactorials))
        return PyLong_FromUnsignedLong(SmallFactorials[x]);

    /* else express in the form odd_part * 2**two_valuation, and compute as
       odd_part << two_valuation. */
    odd_part = factorial_odd_part(x);
    if (odd_part == NULL)
        return NULL;
    two_valuation = PyLong_FromLong(x - count_set_bits(x));
    if (two_valuation == NULL) {
        Py_DECREF(odd_part);
        return NULL;
    }
    result = PyNumber_Lshift(odd_part, two_valuation);
    Py_DECREF(two_valuation);
    Py_DECREF(odd_part);
    return result;
}

PyDoc_STRVAR(math_factorial_doc,
"factorial(x) -> Integral\n"
"\n"
"Find x!. Raise a ValueError if x is negative or non-integral.");

static PyObject *
math_trunc(PyObject *self, PyObject *number)
{
    _Py_IDENTIFIER(__trunc__);
    PyObject *trunc, *result;

    if (Py_TYPE(number)->tp_dict == NULL) {
        if (PyType_Ready(Py_TYPE(number)) < 0)
            return NULL;
    }

    trunc = _PyObject_LookupSpecial(number, &PyId___trunc__);
    if (trunc == NULL) {
        if (!PyErr_Occurred())
            PyErr_Format(PyExc_TypeError,
                         "type %.100s doesn't define __trunc__ method",
                         Py_TYPE(number)->tp_name);
        return NULL;
    }
    result = _PyObject_CallNoArg(trunc);
    Py_DECREF(trunc);
    return result;
}

PyDoc_STRVAR(math_trunc_doc,
"trunc(x:Real) -> Integral\n"
"\n"
"Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method.");

static PyObject *
math_frexp(PyObject *self, PyObject *arg)
{
    int i;
    double x = PyFloat_AsDouble(arg);
    if (x == -1.0 && PyErr_Occurred())
        return NULL;
    /* deal with special cases directly, to sidestep platform
       differences */
    if (Py_IS_NAN(x) || Py_IS_INFINITY(x) || !x) {
        i = 0;
    }
    else {
        PyFPE_START_PROTECT("in math_frexp", return 0);
        x = frexp(x, &i);
        PyFPE_END_PROTECT(x);
    }
    return Py_BuildValue("(di)", x, i);
}

PyDoc_STRVAR(math_frexp_doc,
"frexp(x)\n"
"\n"
"Return the mantissa and exponent of x, as pair (m, e).\n"
"m is a float and e is an int, such that x = m * 2.**e.\n"
"If x is 0, m and e are both 0.  Else 0.5 <= abs(m) < 1.0.");

static PyObject *
math_ldexp(PyObject *self, PyObject *args)
{
    double x, r;
    PyObject *oexp;
    long exp;
    int overflow;
    if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
        return NULL;

    if (PyLong_Check(oexp)) {
        /* on overflow, replace exponent with either LONG_MAX
           or LONG_MIN, depending on the sign. */
        exp = PyLong_AsLongAndOverflow(oexp, &overflow);
        if (exp == -1 && PyErr_Occurred())
            return NULL;
        if (overflow)
            exp = overflow < 0 ? LONG_MIN : LONG_MAX;
    }
    else {
        PyErr_SetString(PyExc_TypeError,
                        "Expected an int as second argument to ldexp.");
        return NULL;
    }

    if (x == 0. || !Py_IS_FINITE(x)) {
        /* NaNs, zeros and infinities are returned unchanged */
        r = x;
        errno = 0;
    } else if (exp > INT_MAX) {
        /* overflow */
        r = copysign(Py_HUGE_VAL, x);
        errno = ERANGE;
    } else if (exp < INT_MIN) {
        /* underflow to +-0 */
        r = copysign(0., x);
        errno = 0;
    } else {
        errno = 0;
        PyFPE_START_PROTECT("in math_ldexp", return 0);
        r = ldexp(x, (int)exp);
        PyFPE_END_PROTECT(r);
        if (Py_IS_INFINITY(r))
            errno = ERANGE;
    }

    if (errno && is_error(r))
        return NULL;
    return PyFloat_FromDouble(r);
}

PyDoc_STRVAR(math_ldexp_doc,
"ldexp(x, i)\n\n\
Return x * (2**i).");

static PyObject *
math_modf(PyObject *self, PyObject *arg)
{
    double y, x = PyFloat_AsDouble(arg);
    if (x == -1.0 && PyErr_Occurred())
        return NULL;
    /* some platforms don't do the right thing for NaNs and
       infinities, so we take care of special cases directly. */
    if (!Py_IS_FINITE(x)) {
        if (Py_IS_INFINITY(x))
            return Py_BuildValue("(dd)", copysign(0., x), x);
        else if (Py_IS_NAN(x))
            return Py_BuildValue("(dd)", x, x);
    }

    errno = 0;
    PyFPE_START_PROTECT("in math_modf", return 0);
    x = modf(x, &y);
    PyFPE_END_PROTECT(x);
    return Py_BuildValue("(dd)", x, y);
}

PyDoc_STRVAR(math_modf_doc,
"modf(x)\n"
"\n"
"Return the fractional and integer parts of x.  Both results carry the sign\n"
"of x and are floats.");

/* A decent logarithm is easy to compute even for huge ints, but libm can't
   do that by itself -- loghelper can.  func is log or log10, and name is
   "log" or "log10".  Note that overflow of the result isn't possible: an int
   can contain no more than INT_MAX * SHIFT bits, so has value certainly less
   than 2**(2**64 * 2**16) == 2**2**80, and log2 of that is 2**80, which is
   small enough to fit in an IEEE single.  log and log10 are even smaller.
   However, intermediate overflow is possible for an int if the number of bits
   in that int is larger than PY_SSIZE_T_MAX. */

static PyObject*
loghelper(PyObject* arg, double (*func)(double), const char *funcname)
{
    /* If it is int, do it ourselves. */
    if (PyLong_Check(arg)) {
        double x, result;
        Py_ssize_t e;

        /* Negative or zero inputs give a ValueError. */
        if (Py_SIZE(arg) <= 0) {
            PyErr_SetString(PyExc_ValueError,
                            "math domain error");
            return NULL;
        }

        x = PyLong_AsDouble(arg);
        if (x == -1.0 && PyErr_Occurred()) {
            if (!PyErr_ExceptionMatches(PyExc_OverflowError))
                return NULL;
            /* Here the conversion to double overflowed, but it's possible
               to compute the log anyway.  Clear the exception and continue. */
            PyErr_Clear();
            x = _PyLong_Frexp((PyLongObject *)arg, &e);
            if (x == -1.0 && PyErr_Occurred())
                return NULL;
            /* Value is ~= x * 2**e, so the log ~= log(x) + log(2) * e. */
            result = func(x) + func(2.0) * e;
        }
        else
            /* Successfully converted x to a double. */
            result = func(x);
        return PyFloat_FromDouble(result);
    }

    /* Else let libm handle it by itself. */
    return math_1(arg, func, 0);
}

static PyObject *
math_log(PyObject *self, PyObject *args)
{
    PyObject *arg;
    PyObject *base = NULL;
    PyObject *num, *den;
    PyObject *ans;

    if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
        return NULL;

    num = loghelper(arg, m_log, "log");
    if (num == NULL || base == NULL)
        return num;

    den = loghelper(base, m_log, "log");
    if (den == NULL) {
        Py_DECREF(num);
        return NULL;
    }

    ans = PyNumber_TrueDivide(num, den);
    Py_DECREF(num);
    Py_DECREF(den);
    return ans;
}

PyDoc_STRVAR(math_log_doc,
"log(x[, base])\n\n\
Return the logarithm of x to the given base.\n\
If the base not specified, returns the natural logarithm (base e) of x.");

static PyObject *
math_log2(PyObject *self, PyObject *arg)
{
    return loghelper(arg, m_log2, "log2");
}

PyDoc_STRVAR(math_log2_doc,
"log2(x)\n\nReturn the base 2 logarithm of x.");

static PyObject *
math_log10(PyObject *self, PyObject *arg)
{
    return loghelper(arg, m_log10, "log10");
}

PyDoc_STRVAR(math_log10_doc,
"log10(x)\n\nReturn the base 10 logarithm of x.");

static PyObject *
math_fmod(PyObject *self, PyObject *args)
{
    PyObject *ox, *oy;
    double r, x, y;
    if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
        return NULL;
    x = PyFloat_AsDouble(ox);
    y = PyFloat_AsDouble(oy);
    if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
        return NULL;
    /* fmod(x, +/-Inf) returns x for finite x. */
    if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
        return PyFloat_FromDouble(x);
    errno = 0;
    PyFPE_START_PROTECT("in math_fmod", return 0);
    r = fmod(x, y);
    PyFPE_END_PROTECT(r);
    if (Py_IS_NAN(r)) {
        if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
            errno = EDOM;
        else
            errno = 0;
    }
    if (errno && is_error(r))
        return NULL;
    else
        return PyFloat_FromDouble(r);
}

PyDoc_STRVAR(math_fmod_doc,
"fmod(x, y)\n\nReturn fmod(x, y), according to platform C."
"  x % y may differ.");

static PyObject *
math_hypot(PyObject *self, PyObject *args)
{
    PyObject *ox, *oy;
    double r, x, y;
    if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
        return NULL;
    x = PyFloat_AsDouble(ox);
    y = PyFloat_AsDouble(oy);
    if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
        return NULL;
    /* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
    if (Py_IS_INFINITY(x))
        return PyFloat_FromDouble(fabs(x));
    if (Py_IS_INFINITY(y))
        return PyFloat_FromDouble(fabs(y));
    errno = 0;
    PyFPE_START_PROTECT("in math_hypot", return 0);
    r = hypot(x, y);
    PyFPE_END_PROTECT(r);
    if (Py_IS_NAN(r)) {
        if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
            errno = EDOM;
        else
            errno = 0;
    }
    else if (Py_IS_INFINITY(r)) {
        if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
            errno = ERANGE;
        else
            errno = 0;
    }
    if (errno && is_error(r))
        return NULL;
    else
        return PyFloat_FromDouble(r);
}

PyDoc_STRVAR(math_hypot_doc,
"hypot(x, y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).");

/* pow can't use math_2, but needs its own wrapper: the problem is
   that an infinite result can arise either as a result of overflow
   (in which case OverflowError should be raised) or as a result of
   e.g. 0.**-5. (for which ValueError needs to be raised.)
*/

static PyObject *
math_pow(PyObject *self, PyObject *args)
{
    PyObject *ox, *oy;
    double r, x, y;
    int odd_y;

    if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
        return NULL;
    x = PyFloat_AsDouble(ox);
    y = PyFloat_AsDouble(oy);
    if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
        return NULL;

    /* deal directly with IEEE specials, to cope with problems on various
       platforms whose semantics don't exactly match C99 */
    r = 0.; /* silence compiler warning */
    if (!Py_IS_FINITE(x) || !Py_IS_FINITE(y)) {
        errno = 0;
        if (Py_IS_NAN(x))
            r = y == 0. ? 1. : x; /* NaN**0 = 1 */
        else if (Py_IS_NAN(y))
            r = x == 1. ? 1. : y; /* 1**NaN = 1 */
        else if (Py_IS_INFINITY(x)) {
            odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
            if (y > 0.)
                r = odd_y ? x : fabs(x);
            else if (y == 0.)
                r = 1.;
            else /* y < 0. */
                r = odd_y ? copysign(0., x) : 0.;
        }
        else if (Py_IS_INFINITY(y)) {
            if (fabs(x) == 1.0)
                r = 1.;
            else if (y > 0. && fabs(x) > 1.0)
                r = y;
            else if (y < 0. && fabs(x) < 1.0) {
                r = -y; /* result is +inf */
                if (x == 0.) /* 0**-inf: divide-by-zero */
                    errno = EDOM;
            }
            else
                r = 0.;
        }
    }
    else {
        /* let libm handle finite**finite */
        errno = 0;
        PyFPE_START_PROTECT("in math_pow", return 0);
        r = pow(x, y);
        PyFPE_END_PROTECT(r);
        /* a NaN result should arise only from (-ve)**(finite
           non-integer); in this case we want to raise ValueError. */
        if (!Py_IS_FINITE(r)) {
            if (Py_IS_NAN(r)) {
                errno = EDOM;
            }
            /*
               an infinite result here arises either from:
               (A) (+/-0.)**negative (-> divide-by-zero)
               (B) overflow of x**y with x and y finite
            */
            else if (Py_IS_INFINITY(r)) {
                if (x == 0.)
                    errno = EDOM;
                else
                    errno = ERANGE;
            }
        }
    }

    if (errno && is_error(r))
        return NULL;
    else
        return PyFloat_FromDouble(r);
}

PyDoc_STRVAR(math_pow_doc,
"pow(x, y)\n\nReturn x**y (x to the power of y).");

static const double degToRad = Py_MATH_PI / 180.0;
static const double radToDeg = 180.0 / Py_MATH_PI;

static PyObject *
math_degrees(PyObject *self, PyObject *arg)
{
    double x = PyFloat_AsDouble(arg);
    if (x == -1.0 && PyErr_Occurred())
        return NULL;
    return PyFloat_FromDouble(x * radToDeg);
}

PyDoc_STRVAR(math_degrees_doc,
"degrees(x)\n\n\
Convert angle x from radians to degrees.");

static PyObject *
math_radians(PyObject *self, PyObject *arg)
{
    double x = PyFloat_AsDouble(arg);
    if (x == -1.0 && PyErr_Occurred())
        return NULL;
    return PyFloat_FromDouble(x * degToRad);
}

PyDoc_STRVAR(math_radians_doc,
"radians(x)\n\n\
Convert angle x from degrees to radians.");

static PyObject *
math_isfinite(PyObject *self, PyObject *arg)
{
    double x = PyFloat_AsDouble(arg);
    if (x == -1.0 && PyErr_Occurred())
        return NULL;
    return PyBool_FromLong((long)Py_IS_FINITE(x));
}

PyDoc_STRVAR(math_isfinite_doc,
"isfinite(x) -> bool\n\n\
Return True if x is neither an infinity nor a NaN, and False otherwise.");

static PyObject *
math_isnan(PyObject *self, PyObject *arg)
{
    double x = PyFloat_AsDouble(arg);
    if (x == -1.0 && PyErr_Occurred())
        return NULL;
    return PyBool_FromLong((long)Py_IS_NAN(x));
}

PyDoc_STRVAR(math_isnan_doc,
"isnan(x) -> bool\n\n\
Return True if x is a NaN (not a number), and False otherwise.");

static PyObject *
math_isinf(PyObject *self, PyObject *arg)
{
    double x = PyFloat_AsDouble(arg);
    if (x == -1.0 && PyErr_Occurred())
        return NULL;
    return PyBool_FromLong((long)Py_IS_INFINITY(x));
}

PyDoc_STRVAR(math_isinf_doc,
"isinf(x) -> bool\n\n\
Return True if x is a positive or negative infinity, and False otherwise.");

static PyObject *
math_isclose(PyObject *self, PyObject *args, PyObject *kwargs)
{
    double a, b;
    double rel_tol = 1e-9;
    double abs_tol = 0.0;
    double diff = 0.0;
    long result = 0;

    static char *keywords[] = {"a", "b", "rel_tol", "abs_tol", NULL};


    if (!PyArg_ParseTupleAndKeywords(args, kwargs, "dd|$dd:isclose",
                                     keywords,
                                     &a, &b, &rel_tol, &abs_tol
                                     ))
        return NULL;

    /* sanity check on the inputs */
    if (rel_tol < 0.0 || abs_tol < 0.0 ) {
        PyErr_SetString(PyExc_ValueError,
                        "tolerances must be non-negative");
        return NULL;
    }

    if ( a == b ) {
        /* short circuit exact equality -- needed to catch two infinities of
           the same sign. And perhaps speeds things up a bit sometimes.
        */
        Py_RETURN_TRUE;
    }

    /* This catches the case of two infinities of opposite sign, or
       one infinity and one finite number. Two infinities of opposite
       sign would otherwise have an infinite relative tolerance.
       Two infinities of the same sign are caught by the equality check
       above.
    */

    if (Py_IS_INFINITY(a) || Py_IS_INFINITY(b)) {
        Py_RETURN_FALSE;
    }

    /* now do the regular computation
       this is essentially the "weak" test from the Boost library
    */

    diff = fabs(b - a);

    result = (((diff <= fabs(rel_tol * b)) ||
               (diff <= fabs(rel_tol * a))) ||
              (diff <= abs_tol));

    return PyBool_FromLong(result);
}

PyDoc_STRVAR(math_isclose_doc,
"isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0) -> bool\n"
"\n"
"Determine whether two floating point numbers are close in value.\n"
"\n"
"   rel_tol\n"
"       maximum difference for being considered \"close\", relative to the\n"
"       magnitude of the input values\n"
"    abs_tol\n"
"       maximum difference for being considered \"close\", regardless of the\n"
"       magnitude of the input values\n"
"\n"
"Return True if a is close in value to b, and False otherwise.\n"
"\n"
"For the values to be considered close, the difference between them\n"
"must be smaller than at least one of the tolerances.\n"
"\n"
"-inf, inf and NaN behave similarly to the IEEE 754 Standard.  That\n"
"is, NaN is not close to anything, even itself.  inf and -inf are\n"
"only close to themselves.");

static PyMethodDef math_methods[] = {
    {"acos",            math_acos,      METH_O,         math_acos_doc},
    {"acosh",           math_acosh,     METH_O,         math_acosh_doc},
    {"asin",            math_asin,      METH_O,         math_asin_doc},
    {"asinh",           math_asinh,     METH_O,         math_asinh_doc},
    {"atan",            math_atan,      METH_O,         math_atan_doc},
    {"atan2",           math_atan2,     METH_VARARGS,   math_atan2_doc},
    {"atanh",           math_atanh,     METH_O,         math_atanh_doc},
    {"ceil",            math_ceil,      METH_O,         math_ceil_doc},
    {"copysign",        math_copysign,  METH_VARARGS,   math_copysign_doc},
    {"cos",             math_cos,       METH_O,         math_cos_doc},
    {"cosh",            math_cosh,      METH_O,         math_cosh_doc},
    {"degrees",         math_degrees,   METH_O,         math_degrees_doc},
    {"erf",             math_erf,       METH_O,         math_erf_doc},
    {"erfc",            math_erfc,      METH_O,         math_erfc_doc},
    {"exp",             math_exp,       METH_O,         math_exp_doc},
    {"expm1",           math_expm1,     METH_O,         math_expm1_doc},
    {"fabs",            math_fabs,      METH_O,         math_fabs_doc},
    {"factorial",       math_factorial, METH_O,         math_factorial_doc},
    {"floor",           math_floor,     METH_O,         math_floor_doc},
    {"fmod",            math_fmod,      METH_VARARGS,   math_fmod_doc},
    {"frexp",           math_frexp,     METH_O,         math_frexp_doc},
    {"fsum",            math_fsum,      METH_O,         math_fsum_doc},
    {"gamma",           math_gamma,     METH_O,         math_gamma_doc},
    {"gcd",             math_gcd,       METH_VARARGS,   math_gcd_doc},
    {"hypot",           math_hypot,     METH_VARARGS,   math_hypot_doc},
    {"isclose", (PyCFunction) math_isclose, METH_VARARGS | METH_KEYWORDS,
    math_isclose_doc},
    {"isfinite",        math_isfinite,  METH_O,         math_isfinite_doc},
    {"isinf",           math_isinf,     METH_O,         math_isinf_doc},
    {"isnan",           math_isnan,     METH_O,         math_isnan_doc},
    {"ldexp",           math_ldexp,     METH_VARARGS,   math_ldexp_doc},
    {"lgamma",          math_lgamma,    METH_O,         math_lgamma_doc},
    {"log",             math_log,       METH_VARARGS,   math_log_doc},
    {"log1p",           math_log1p,     METH_O,         math_log1p_doc},
    {"log10",           math_log10,     METH_O,         math_log10_doc},
    {"log2",            math_log2,      METH_O,         math_log2_doc},
    {"modf",            math_modf,      METH_O,         math_modf_doc},
    {"pow",             math_pow,       METH_VARARGS,   math_pow_doc},
    {"radians",         math_radians,   METH_O,         math_radians_doc},
    {"sin",             math_sin,       METH_O,         math_sin_doc},
    {"sinh",            math_sinh,      METH_O,         math_sinh_doc},
    {"sqrt",            math_sqrt,      METH_O,         math_sqrt_doc},
    {"tan",             math_tan,       METH_O,         math_tan_doc},
    {"tanh",            math_tanh,      METH_O,         math_tanh_doc},
    {"trunc",           math_trunc,     METH_O,         math_trunc_doc},
    {NULL,              NULL}           /* sentinel */
};


PyDoc_STRVAR(module_doc,
"This module is always available.  It provides access to the\n"
"mathematical functions defined by the C standard.");


static struct PyModuleDef mathmodule = {
    PyModuleDef_HEAD_INIT,
    "math",
    module_doc,
    -1,
    math_methods,
    NULL,
    NULL,
    NULL,
    NULL
};

PyMODINIT_FUNC
PyInit_math(void)
{
    PyObject *m;

    m = PyModule_Create(&mathmodule);
    if (m == NULL)
        goto finally;

    PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
    PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
    PyModule_AddObject(m, "tau", PyFloat_FromDouble(Py_MATH_TAU));  /* 2pi */
    PyModule_AddObject(m, "inf", PyFloat_FromDouble(m_inf()));
#if !defined(PY_NO_SHORT_FLOAT_REPR) || defined(Py_NAN)
    PyModule_AddObject(m, "nan", PyFloat_FromDouble(m_nan()));
#endif

  finally:
    return m;
}
generated by cgit v0.12 at 2025-12-15 15:40:20 (GMT)