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floatobject.c
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2521 lines (2245 loc) · 58.4 KB
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/* Float object implementation */
/* XXX There should be overflow checks here, but it's hard to check
for any kind of float exception without losing portability. */
#include "Python.h"
#include "structseq.h"
#include <ctype.h>
#include <float.h>
#undef MAX
#undef MIN
#define MAX(x, y) ((x) < (y) ? (y) : (x))
#define MIN(x, y) ((x) < (y) ? (x) : (y))
#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif
#ifdef _OSF_SOURCE
/* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
extern int finite(double);
#endif
/* Special free list -- see comments for same code in intobject.c. */
#define BLOCK_SIZE 1000 /* 1K less typical malloc overhead */
#define BHEAD_SIZE 8 /* Enough for a 64-bit pointer */
#define N_FLOATOBJECTS ((BLOCK_SIZE - BHEAD_SIZE) / sizeof(PyFloatObject))
struct _floatblock {
struct _floatblock *next;
PyFloatObject objects[N_FLOATOBJECTS];
};
typedef struct _floatblock PyFloatBlock;
static PyFloatBlock *block_list = NULL;
static PyFloatObject *free_list = NULL;
static PyFloatObject *
fill_free_list(void)
{
PyFloatObject *p, *q;
/* XXX Float blocks escape the object heap. Use PyObject_MALLOC ??? */
p = (PyFloatObject *) PyMem_MALLOC(sizeof(PyFloatBlock));
if (p == NULL)
return (PyFloatObject *) PyErr_NoMemory();
((PyFloatBlock *)p)->next = block_list;
block_list = (PyFloatBlock *)p;
p = &((PyFloatBlock *)p)->objects[0];
q = p + N_FLOATOBJECTS;
while (--q > p)
Py_TYPE(q) = (struct _typeobject *)(q-1);
Py_TYPE(q) = NULL;
return p + N_FLOATOBJECTS - 1;
}
double
PyFloat_GetMax(void)
{
return DBL_MAX;
}
double
PyFloat_GetMin(void)
{
return DBL_MIN;
}
static PyTypeObject FloatInfoType = {0, 0, 0, 0, 0, 0};
PyDoc_STRVAR(floatinfo__doc__,
"sys.floatinfo\n\
\n\
A structseq holding information about the float type. It contains low level\n\
information about the precision and internal representation. Please study\n\
your system's :file:`float.h` for more information.");
static PyStructSequence_Field floatinfo_fields[] = {
{"max", "DBL_MAX -- maximum representable finite float"},
{"max_exp", "DBL_MAX_EXP -- maximum int e such that radix**(e-1) "
"is representable"},
{"max_10_exp", "DBL_MAX_10_EXP -- maximum int e such that 10**e "
"is representable"},
{"min", "DBL_MIN -- Minimum positive normalizer float"},
{"min_exp", "DBL_MIN_EXP -- minimum int e such that radix**(e-1) "
"is a normalized float"},
{"min_10_exp", "DBL_MIN_10_EXP -- minimum int e such that 10**e is "
"a normalized"},
{"dig", "DBL_DIG -- digits"},
{"mant_dig", "DBL_MANT_DIG -- mantissa digits"},
{"epsilon", "DBL_EPSILON -- Difference between 1 and the next "
"representable float"},
{"radix", "FLT_RADIX -- radix of exponent"},
{"rounds", "FLT_ROUNDS -- addition rounds"},
{0}
};
static PyStructSequence_Desc floatinfo_desc = {
"sys.floatinfo", /* name */
floatinfo__doc__, /* doc */
floatinfo_fields, /* fields */
11
};
PyObject *
PyFloat_GetInfo(void)
{
PyObject* floatinfo;
int pos = 0;
floatinfo = PyStructSequence_New(&FloatInfoType);
if (floatinfo == NULL) {
return NULL;
}
#define SetIntFlag(flag) \
PyStructSequence_SET_ITEM(floatinfo, pos++, PyInt_FromLong(flag))
#define SetDblFlag(flag) \
PyStructSequence_SET_ITEM(floatinfo, pos++, PyFloat_FromDouble(flag))
SetDblFlag(DBL_MAX);
SetIntFlag(DBL_MAX_EXP);
SetIntFlag(DBL_MAX_10_EXP);
SetDblFlag(DBL_MIN);
SetIntFlag(DBL_MIN_EXP);
SetIntFlag(DBL_MIN_10_EXP);
SetIntFlag(DBL_DIG);
SetIntFlag(DBL_MANT_DIG);
SetDblFlag(DBL_EPSILON);
SetIntFlag(FLT_RADIX);
SetIntFlag(FLT_ROUNDS);
#undef SetIntFlag
#undef SetDblFlag
if (PyErr_Occurred()) {
Py_CLEAR(floatinfo);
return NULL;
}
return floatinfo;
}
PyObject *
PyFloat_FromDouble(double fval)
{
register PyFloatObject *op;
if (free_list == NULL) {
if ((free_list = fill_free_list()) == NULL)
return NULL;
}
/* Inline PyObject_New */
op = free_list;
free_list = (PyFloatObject *)Py_TYPE(op);
PyObject_INIT(op, &PyFloat_Type);
op->ob_fval = fval;
return (PyObject *) op;
}
/**************************************************************************
RED_FLAG 22-Sep-2000 tim
PyFloat_FromString's pend argument is braindead. Prior to this RED_FLAG,
1. If v was a regular string, *pend was set to point to its terminating
null byte. That's useless (the caller can find that without any
help from this function!).
2. If v was a Unicode string, or an object convertible to a character
buffer, *pend was set to point into stack trash (the auto temp
vector holding the character buffer). That was downright dangerous.
Since we can't change the interface of a public API function, pend is
still supported but now *officially* useless: if pend is not NULL,
*pend is set to NULL.
**************************************************************************/
PyObject *
PyFloat_FromString(PyObject *v, char **pend)
{
const char *s, *last, *end, *sp;
double x;
char buffer[256]; /* for errors */
#ifdef Py_USING_UNICODE
char s_buffer[256]; /* for objects convertible to a char buffer */
#endif
Py_ssize_t len;
if (pend)
*pend = NULL;
if (PyString_Check(v)) {
s = PyString_AS_STRING(v);
len = PyString_GET_SIZE(v);
}
#ifdef Py_USING_UNICODE
else if (PyUnicode_Check(v)) {
if (PyUnicode_GET_SIZE(v) >= (Py_ssize_t)sizeof(s_buffer)) {
PyErr_SetString(PyExc_ValueError,
"Unicode float() literal too long to convert");
return NULL;
}
if (PyUnicode_EncodeDecimal(PyUnicode_AS_UNICODE(v),
PyUnicode_GET_SIZE(v),
s_buffer,
NULL))
return NULL;
s = s_buffer;
len = strlen(s);
}
#endif
else if (PyObject_AsCharBuffer(v, &s, &len)) {
PyErr_SetString(PyExc_TypeError,
"float() argument must be a string or a number");
return NULL;
}
last = s + len;
while (*s && isspace(Py_CHARMASK(*s)))
s++;
if (*s == '\0') {
PyErr_SetString(PyExc_ValueError, "empty string for float()");
return NULL;
}
sp = s;
/* We don't care about overflow or underflow. If the platform supports
* them, infinities and signed zeroes (on underflow) are fine.
* However, strtod can return 0 for denormalized numbers, where atof
* does not. So (alas!) we special-case a zero result. Note that
* whether strtod sets errno on underflow is not defined, so we can't
* key off errno.
*/
PyFPE_START_PROTECT("strtod", return NULL)
x = PyOS_ascii_strtod(s, (char **)&end);
PyFPE_END_PROTECT(x)
errno = 0;
/* Believe it or not, Solaris 2.6 can move end *beyond* the null
byte at the end of the string, when the input is inf(inity). */
if (end > last)
end = last;
/* Check for inf and nan. This is done late because it rarely happens. */
if (end == s) {
char *p = (char*)sp;
int sign = 1;
if (*p == '-') {
sign = -1;
p++;
}
if (*p == '+') {
p++;
}
if (PyOS_strnicmp(p, "inf", 4) == 0) {
Py_RETURN_INF(sign);
}
if (PyOS_strnicmp(p, "infinity", 9) == 0) {
Py_RETURN_INF(sign);
}
#ifdef Py_NAN
if(PyOS_strnicmp(p, "nan", 4) == 0) {
Py_RETURN_NAN;
}
#endif
PyOS_snprintf(buffer, sizeof(buffer),
"invalid literal for float(): %.200s", s);
PyErr_SetString(PyExc_ValueError, buffer);
return NULL;
}
/* Since end != s, the platform made *some* kind of sense out
of the input. Trust it. */
while (*end && isspace(Py_CHARMASK(*end)))
end++;
if (*end != '\0') {
PyOS_snprintf(buffer, sizeof(buffer),
"invalid literal for float(): %.200s", s);
PyErr_SetString(PyExc_ValueError, buffer);
return NULL;
}
else if (end != last) {
PyErr_SetString(PyExc_ValueError,
"null byte in argument for float()");
return NULL;
}
if (x == 0.0) {
/* See above -- may have been strtod being anal
about denorms. */
PyFPE_START_PROTECT("atof", return NULL)
x = PyOS_ascii_atof(s);
PyFPE_END_PROTECT(x)
errno = 0; /* whether atof ever set errno is undefined */
}
return PyFloat_FromDouble(x);
}
static void
float_dealloc(PyFloatObject *op)
{
if (PyFloat_CheckExact(op)) {
Py_TYPE(op) = (struct _typeobject *)free_list;
free_list = op;
}
else
Py_TYPE(op)->tp_free((PyObject *)op);
}
double
PyFloat_AsDouble(PyObject *op)
{
PyNumberMethods *nb;
PyFloatObject *fo;
double val;
if (op && PyFloat_Check(op))
return PyFloat_AS_DOUBLE((PyFloatObject*) op);
if (op == NULL) {
PyErr_BadArgument();
return -1;
}
if ((nb = Py_TYPE(op)->tp_as_number) == NULL || nb->nb_float == NULL) {
PyErr_SetString(PyExc_TypeError, "a float is required");
return -1;
}
fo = (PyFloatObject*) (*nb->nb_float) (op);
if (fo == NULL)
return -1;
if (!PyFloat_Check(fo)) {
PyErr_SetString(PyExc_TypeError,
"nb_float should return float object");
return -1;
}
val = PyFloat_AS_DOUBLE(fo);
Py_DECREF(fo);
return val;
}
/* Methods */
static void
format_float(char *buf, size_t buflen, PyFloatObject *v, int precision)
{
register char *cp;
char format[32];
int i;
/* Subroutine for float_repr and float_print.
We want float numbers to be recognizable as such,
i.e., they should contain a decimal point or an exponent.
However, %g may print the number as an integer;
in such cases, we append ".0" to the string. */
assert(PyFloat_Check(v));
PyOS_snprintf(format, 32, "%%.%ig", precision);
PyOS_ascii_formatd(buf, buflen, format, v->ob_fval);
cp = buf;
if (*cp == '-')
cp++;
for (; *cp != '\0'; cp++) {
/* Any non-digit means it's not an integer;
this takes care of NAN and INF as well. */
if (!isdigit(Py_CHARMASK(*cp)))
break;
}
if (*cp == '\0') {
*cp++ = '.';
*cp++ = '0';
*cp++ = '\0';
return;
}
/* Checking the next three chars should be more than enough to
* detect inf or nan, even on Windows. We check for inf or nan
* at last because they are rare cases.
*/
for (i=0; *cp != '\0' && i<3; cp++, i++) {
if (isdigit(Py_CHARMASK(*cp)) || *cp == '.')
continue;
/* found something that is neither a digit nor point
* it might be a NaN or INF
*/
#ifdef Py_NAN
if (Py_IS_NAN(v->ob_fval)) {
strcpy(buf, "nan");
}
else
#endif
if (Py_IS_INFINITY(v->ob_fval)) {
cp = buf;
if (*cp == '-')
cp++;
strcpy(cp, "inf");
}
break;
}
}
/* XXX PyFloat_AsStringEx should not be a public API function (for one
XXX thing, its signature passes a buffer without a length; for another,
XXX it isn't useful outside this file).
*/
void
PyFloat_AsStringEx(char *buf, PyFloatObject *v, int precision)
{
format_float(buf, 100, v, precision);
}
/* Macro and helper that convert PyObject obj to a C double and store
the value in dbl; this replaces the functionality of the coercion
slot function. If conversion to double raises an exception, obj is
set to NULL, and the function invoking this macro returns NULL. If
obj is not of float, int or long type, Py_NotImplemented is incref'ed,
stored in obj, and returned from the function invoking this macro.
*/
#define CONVERT_TO_DOUBLE(obj, dbl) \
if (PyFloat_Check(obj)) \
dbl = PyFloat_AS_DOUBLE(obj); \
else if (convert_to_double(&(obj), &(dbl)) < 0) \
return obj;
static int
convert_to_double(PyObject **v, double *dbl)
{
register PyObject *obj = *v;
if (PyInt_Check(obj)) {
*dbl = (double)PyInt_AS_LONG(obj);
}
else if (PyLong_Check(obj)) {
*dbl = PyLong_AsDouble(obj);
if (*dbl == -1.0 && PyErr_Occurred()) {
*v = NULL;
return -1;
}
}
else {
Py_INCREF(Py_NotImplemented);
*v = Py_NotImplemented;
return -1;
}
return 0;
}
/* Precisions used by repr() and str(), respectively.
The repr() precision (17 significant decimal digits) is the minimal number
that is guaranteed to have enough precision so that if the number is read
back in the exact same binary value is recreated. This is true for IEEE
floating point by design, and also happens to work for all other modern
hardware.
The str() precision is chosen so that in most cases, the rounding noise
created by various operations is suppressed, while giving plenty of
precision for practical use.
*/
#define PREC_REPR 17
#define PREC_STR 12
/* XXX PyFloat_AsString and PyFloat_AsReprString should be deprecated:
XXX they pass a char buffer without passing a length.
*/
void
PyFloat_AsString(char *buf, PyFloatObject *v)
{
format_float(buf, 100, v, PREC_STR);
}
void
PyFloat_AsReprString(char *buf, PyFloatObject *v)
{
format_float(buf, 100, v, PREC_REPR);
}
/* ARGSUSED */
static int
float_print(PyFloatObject *v, FILE *fp, int flags)
{
char buf[100];
format_float(buf, sizeof(buf), v,
(flags & Py_PRINT_RAW) ? PREC_STR : PREC_REPR);
Py_BEGIN_ALLOW_THREADS
fputs(buf, fp);
Py_END_ALLOW_THREADS
return 0;
}
static PyObject *
float_repr(PyFloatObject *v)
{
char buf[100];
format_float(buf, sizeof(buf), v, PREC_REPR);
return PyString_FromString(buf);
}
static PyObject *
float_str(PyFloatObject *v)
{
char buf[100];
format_float(buf, sizeof(buf), v, PREC_STR);
return PyString_FromString(buf);
}
/* Comparison is pretty much a nightmare. When comparing float to float,
* we do it as straightforwardly (and long-windedly) as conceivable, so
* that, e.g., Python x == y delivers the same result as the platform
* C x == y when x and/or y is a NaN.
* When mixing float with an integer type, there's no good *uniform* approach.
* Converting the double to an integer obviously doesn't work, since we
* may lose info from fractional bits. Converting the integer to a double
* also has two failure modes: (1) a long int may trigger overflow (too
* large to fit in the dynamic range of a C double); (2) even a C long may have
* more bits than fit in a C double (e.g., on a a 64-bit box long may have
* 63 bits of precision, but a C double probably has only 53), and then
* we can falsely claim equality when low-order integer bits are lost by
* coercion to double. So this part is painful too.
*/
static PyObject*
float_richcompare(PyObject *v, PyObject *w, int op)
{
double i, j;
int r = 0;
assert(PyFloat_Check(v));
i = PyFloat_AS_DOUBLE(v);
/* Switch on the type of w. Set i and j to doubles to be compared,
* and op to the richcomp to use.
*/
if (PyFloat_Check(w))
j = PyFloat_AS_DOUBLE(w);
else if (!Py_IS_FINITE(i)) {
if (PyInt_Check(w) || PyLong_Check(w))
/* If i is an infinity, its magnitude exceeds any
* finite integer, so it doesn't matter which int we
* compare i with. If i is a NaN, similarly.
*/
j = 0.0;
else
goto Unimplemented;
}
else if (PyInt_Check(w)) {
long jj = PyInt_AS_LONG(w);
/* In the worst realistic case I can imagine, C double is a
* Cray single with 48 bits of precision, and long has 64
* bits.
*/
#if SIZEOF_LONG > 6
unsigned long abs = (unsigned long)(jj < 0 ? -jj : jj);
if (abs >> 48) {
/* Needs more than 48 bits. Make it take the
* PyLong path.
*/
PyObject *result;
PyObject *ww = PyLong_FromLong(jj);
if (ww == NULL)
return NULL;
result = float_richcompare(v, ww, op);
Py_DECREF(ww);
return result;
}
#endif
j = (double)jj;
assert((long)j == jj);
}
else if (PyLong_Check(w)) {
int vsign = i == 0.0 ? 0 : i < 0.0 ? -1 : 1;
int wsign = _PyLong_Sign(w);
size_t nbits;
int exponent;
if (vsign != wsign) {
/* Magnitudes are irrelevant -- the signs alone
* determine the outcome.
*/
i = (double)vsign;
j = (double)wsign;
goto Compare;
}
/* The signs are the same. */
/* Convert w to a double if it fits. In particular, 0 fits. */
nbits = _PyLong_NumBits(w);
if (nbits == (size_t)-1 && PyErr_Occurred()) {
/* This long is so large that size_t isn't big enough
* to hold the # of bits. Replace with little doubles
* that give the same outcome -- w is so large that
* its magnitude must exceed the magnitude of any
* finite float.
*/
PyErr_Clear();
i = (double)vsign;
assert(wsign != 0);
j = wsign * 2.0;
goto Compare;
}
if (nbits <= 48) {
j = PyLong_AsDouble(w);
/* It's impossible that <= 48 bits overflowed. */
assert(j != -1.0 || ! PyErr_Occurred());
goto Compare;
}
assert(wsign != 0); /* else nbits was 0 */
assert(vsign != 0); /* if vsign were 0, then since wsign is
* not 0, we would have taken the
* vsign != wsign branch at the start */
/* We want to work with non-negative numbers. */
if (vsign < 0) {
/* "Multiply both sides" by -1; this also swaps the
* comparator.
*/
i = -i;
op = _Py_SwappedOp[op];
}
assert(i > 0.0);
(void) frexp(i, &exponent);
/* exponent is the # of bits in v before the radix point;
* we know that nbits (the # of bits in w) > 48 at this point
*/
if (exponent < 0 || (size_t)exponent < nbits) {
i = 1.0;
j = 2.0;
goto Compare;
}
if ((size_t)exponent > nbits) {
i = 2.0;
j = 1.0;
goto Compare;
}
/* v and w have the same number of bits before the radix
* point. Construct two longs that have the same comparison
* outcome.
*/
{
double fracpart;
double intpart;
PyObject *result = NULL;
PyObject *one = NULL;
PyObject *vv = NULL;
PyObject *ww = w;
if (wsign < 0) {
ww = PyNumber_Negative(w);
if (ww == NULL)
goto Error;
}
else
Py_INCREF(ww);
fracpart = modf(i, &intpart);
vv = PyLong_FromDouble(intpart);
if (vv == NULL)
goto Error;
if (fracpart != 0.0) {
/* Shift left, and or a 1 bit into vv
* to represent the lost fraction.
*/
PyObject *temp;
one = PyInt_FromLong(1);
if (one == NULL)
goto Error;
temp = PyNumber_Lshift(ww, one);
if (temp == NULL)
goto Error;
Py_DECREF(ww);
ww = temp;
temp = PyNumber_Lshift(vv, one);
if (temp == NULL)
goto Error;
Py_DECREF(vv);
vv = temp;
temp = PyNumber_Or(vv, one);
if (temp == NULL)
goto Error;
Py_DECREF(vv);
vv = temp;
}
r = PyObject_RichCompareBool(vv, ww, op);
if (r < 0)
goto Error;
result = PyBool_FromLong(r);
Error:
Py_XDECREF(vv);
Py_XDECREF(ww);
Py_XDECREF(one);
return result;
}
} /* else if (PyLong_Check(w)) */
else /* w isn't float, int, or long */
goto Unimplemented;
Compare:
PyFPE_START_PROTECT("richcompare", return NULL)
switch (op) {
case Py_EQ:
r = i == j;
break;
case Py_NE:
r = i != j;
break;
case Py_LE:
r = i <= j;
break;
case Py_GE:
r = i >= j;
break;
case Py_LT:
r = i < j;
break;
case Py_GT:
r = i > j;
break;
}
PyFPE_END_PROTECT(r)
return PyBool_FromLong(r);
Unimplemented:
Py_INCREF(Py_NotImplemented);
return Py_NotImplemented;
}
static long
float_hash(PyFloatObject *v)
{
return _Py_HashDouble(v->ob_fval);
}
static PyObject *
float_add(PyObject *v, PyObject *w)
{
double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
PyFPE_START_PROTECT("add", return 0)
a = a + b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
}
static PyObject *
float_sub(PyObject *v, PyObject *w)
{
double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
PyFPE_START_PROTECT("subtract", return 0)
a = a - b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
}
static PyObject *
float_mul(PyObject *v, PyObject *w)
{
double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
PyFPE_START_PROTECT("multiply", return 0)
a = a * b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
}
static PyObject *
float_div(PyObject *v, PyObject *w)
{
double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
#ifdef Py_NAN
if (b == 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError,
"float division");
return NULL;
}
#endif
PyFPE_START_PROTECT("divide", return 0)
a = a / b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
}
static PyObject *
float_classic_div(PyObject *v, PyObject *w)
{
double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
if (Py_DivisionWarningFlag >= 2 &&
PyErr_Warn(PyExc_DeprecationWarning, "classic float division") < 0)
return NULL;
#ifdef Py_NAN
if (b == 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError,
"float division");
return NULL;
}
#endif
PyFPE_START_PROTECT("divide", return 0)
a = a / b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
}
static PyObject *
float_rem(PyObject *v, PyObject *w)
{
double vx, wx;
double mod;
CONVERT_TO_DOUBLE(v, vx);
CONVERT_TO_DOUBLE(w, wx);
#ifdef Py_NAN
if (wx == 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError,
"float modulo");
return NULL;
}
#endif
PyFPE_START_PROTECT("modulo", return 0)
mod = fmod(vx, wx);
/* note: checking mod*wx < 0 is incorrect -- underflows to
0 if wx < sqrt(smallest nonzero double) */
if (mod && ((wx < 0) != (mod < 0))) {
mod += wx;
}
PyFPE_END_PROTECT(mod)
return PyFloat_FromDouble(mod);
}
static PyObject *
float_divmod(PyObject *v, PyObject *w)
{
double vx, wx;
double div, mod, floordiv;
CONVERT_TO_DOUBLE(v, vx);
CONVERT_TO_DOUBLE(w, wx);
if (wx == 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError, "float divmod()");
return NULL;
}
PyFPE_START_PROTECT("divmod", return 0)
mod = fmod(vx, wx);
/* fmod is typically exact, so vx-mod is *mathematically* an
exact multiple of wx. But this is fp arithmetic, and fp
vx - mod is an approximation; the result is that div may
not be an exact integral value after the division, although
it will always be very close to one.
*/
div = (vx - mod) / wx;
if (mod) {
/* ensure the remainder has the same sign as the denominator */
if ((wx < 0) != (mod < 0)) {
mod += wx;
div -= 1.0;
}
}
else {
/* the remainder is zero, and in the presence of signed zeroes
fmod returns different results across platforms; ensure
it has the same sign as the denominator; we'd like to do
"mod = wx * 0.0", but that may get optimized away */
mod *= mod; /* hide "mod = +0" from optimizer */
if (wx < 0.0)
mod = -mod;
}
/* snap quotient to nearest integral value */
if (div) {
floordiv = floor(div);
if (div - floordiv > 0.5)
floordiv += 1.0;
}
else {
/* div is zero - get the same sign as the true quotient */
div *= div; /* hide "div = +0" from optimizers */
floordiv = div * vx / wx; /* zero w/ sign of vx/wx */
}
PyFPE_END_PROTECT(floordiv)
return Py_BuildValue("(dd)", floordiv, mod);
}
static PyObject *
float_floor_div(PyObject *v, PyObject *w)
{
PyObject *t, *r;
t = float_divmod(v, w);
if (t == NULL || t == Py_NotImplemented)
return t;
assert(PyTuple_CheckExact(t));
r = PyTuple_GET_ITEM(t, 0);
Py_INCREF(r);
Py_DECREF(t);
return r;
}
static PyObject *
float_pow(PyObject *v, PyObject *w, PyObject *z)
{
double iv, iw, ix;
if ((PyObject *)z != Py_None) {
PyErr_SetString(PyExc_TypeError, "pow() 3rd argument not "
"allowed unless all arguments are integers");
return NULL;
}
CONVERT_TO_DOUBLE(v, iv);
CONVERT_TO_DOUBLE(w, iw);
/* Sort out special cases here instead of relying on pow() */
if (iw == 0) { /* v**0 is 1, even 0**0 */
return PyFloat_FromDouble(1.0);
}
if (iv == 0.0) { /* 0**w is error if w<0, else 1 */
if (iw < 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError,
"0.0 cannot be raised to a negative power");
return NULL;
}
return PyFloat_FromDouble(0.0);
}
if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */
return PyFloat_FromDouble(1.0);
}
if (iv < 0.0) {
/* Whether this is an error is a mess, and bumps into libm
* bugs so we have to figure it out ourselves.
*/
if (iw != floor(iw)) {
PyErr_SetString(PyExc_ValueError, "negative number "
"cannot be raised to a fractional power");
return NULL;
}
/* iw is an exact integer, albeit perhaps a very large one.
* -1 raised to an exact integer should never be exceptional.
* Alas, some libms (chiefly glibc as of early 2003) return
* NaN and set EDOM on pow(-1, large_int) if the int doesn't
* happen to be representable in a *C* integer. That's a
* bug; we let that slide in math.pow() (which currently
* reflects all platform accidents), but not for Python's **.
*/
if (iv == -1.0 && Py_IS_FINITE(iw)) {
/* Return 1 if iw is even, -1 if iw is odd; there's
* no guarantee that any C integral type is big
* enough to hold iw, so we have to check this
* indirectly.
*/
ix = floor(iw * 0.5) * 2.0;
return PyFloat_FromDouble(ix == iw ? 1.0 : -1.0);
}
/* Else iv != -1.0, and overflow or underflow are possible.
* Unless we're to write pow() ourselves, we have to trust
* the platform to do this correctly.
*/
}
errno = 0;
PyFPE_START_PROTECT("pow", return NULL)
ix = pow(iv, iw);
PyFPE_END_PROTECT(ix)
Py_ADJUST_ERANGE1(ix);
if (errno != 0) {
/* We don't expect any errno value other than ERANGE, but
* the range of libm bugs appears unbounded.
*/
PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError :
PyExc_ValueError);
return NULL;
}
return PyFloat_FromDouble(ix);
}
static PyObject *
float_neg(PyFloatObject *v)
{
return PyFloat_FromDouble(-v->ob_fval);
}
static PyObject *
float_abs(PyFloatObject *v)
{
return PyFloat_FromDouble(fabs(v->ob_fval));
}
static int
float_nonzero(PyFloatObject *v)
{