cpython/Objects/floatobject.c

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1991-02-19 08:39:46 -04:00
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/* Float object implementation */
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/* XXX There should be overflow checks here, but it's hard to check
for any kind of float exception without losing portability. */
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#include "Python.h"
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#include <ctype.h>
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#if !defined(__STDC__) && !defined(macintosh)
extern double fmod(double, double);
extern double pow(double, double);
#endif
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#if defined(sun) && !defined(__SVR4)
/* On SunOS4.1 only libm.a exists. Make sure that references to all
needed math functions exist in the executable, so that dynamic
loading of mathmodule does not fail. */
double (*_Py_math_funcs_hack[])() = {
acos, asin, atan, atan2, ceil, cos, cosh, exp, fabs, floor,
fmod, log, log10, pow, sin, sinh, sqrt, tan, tanh
};
#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 *
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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)
q->ob_type = (struct _typeobject *)(q-1);
q->ob_type = NULL;
return p + N_FLOATOBJECTS - 1;
}
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PyObject *
PyFloat_FromDouble(double fval)
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{
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 *)op->ob_type;
PyObject_INIT(op, &PyFloat_Type);
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op->ob_fval = fval;
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return (PyObject *) op;
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}
/**************************************************************************
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 *
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PyFloat_FromString(PyObject *v, char **pend)
{
const char *s, *last, *end;
double x;
char buffer[256]; /* for errors */
#ifdef Py_USING_UNICODE
char s_buffer[256]; /* for objects convertible to a char buffer */
#endif
int len;
if (pend)
*pend = NULL;
if (PyString_Check(v)) {
s = PyString_AS_STRING(v);
len = PyString_GET_SIZE(v);
}
#ifdef Py_USING_UNICODE
Marc-Andre's third try at this bulk patch seems to work (except that his copy of test_contains.py seems to be broken -- the lines he deleted were already absent). Checkin messages: New Unicode support for int(), float(), complex() and long(). - new APIs PyInt_FromUnicode() and PyLong_FromUnicode() - added support for Unicode to PyFloat_FromString() - new encoding API PyUnicode_EncodeDecimal() which converts Unicode to a decimal char* string (used in the above new APIs) - shortcuts for calls like int(<int object>) and float(<float obj>) - tests for all of the above Unicode compares and contains checks: - comparing Unicode and non-string types now works; TypeErrors are masked, all other errors such as ValueError during Unicode coercion are passed through (note that PyUnicode_Compare does not implement the masking -- PyObject_Compare does this) - contains now works for non-string types too; TypeErrors are masked and 0 returned; all other errors are passed through Better testing support for the standard codecs. Misc minor enhancements, such as an alias dbcs for the mbcs codec. Changes: - PyLong_FromString() now applies the same error checks as does PyInt_FromString(): trailing garbage is reported as error and not longer silently ignored. The only characters which may be trailing the digits are 'L' and 'l' -- these are still silently ignored. - string.ato?() now directly interface to int(), long() and float(). The error strings are now a little different, but the type still remains the same. These functions are now ready to get declared obsolete ;-) - PyNumber_Int() now also does a check for embedded NULL chars in the input string; PyNumber_Long() already did this (and still does) Followed by: Looks like I've gone a step too far there... (and test_contains.py seem to have a bug too). I've changed back to reporting all errors in PyUnicode_Contains() and added a few more test cases to test_contains.py (plus corrected the join() NameError).
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else if (PyUnicode_Check(v)) {
if (PyUnicode_GET_SIZE(v) >= sizeof(s_buffer)) {
PyErr_SetString(PyExc_ValueError,
"Unicode float() literal too long to convert");
Marc-Andre's third try at this bulk patch seems to work (except that his copy of test_contains.py seems to be broken -- the lines he deleted were already absent). Checkin messages: New Unicode support for int(), float(), complex() and long(). - new APIs PyInt_FromUnicode() and PyLong_FromUnicode() - added support for Unicode to PyFloat_FromString() - new encoding API PyUnicode_EncodeDecimal() which converts Unicode to a decimal char* string (used in the above new APIs) - shortcuts for calls like int(<int object>) and float(<float obj>) - tests for all of the above Unicode compares and contains checks: - comparing Unicode and non-string types now works; TypeErrors are masked, all other errors such as ValueError during Unicode coercion are passed through (note that PyUnicode_Compare does not implement the masking -- PyObject_Compare does this) - contains now works for non-string types too; TypeErrors are masked and 0 returned; all other errors are passed through Better testing support for the standard codecs. Misc minor enhancements, such as an alias dbcs for the mbcs codec. Changes: - PyLong_FromString() now applies the same error checks as does PyInt_FromString(): trailing garbage is reported as error and not longer silently ignored. The only characters which may be trailing the digits are 'L' and 'l' -- these are still silently ignored. - string.ato?() now directly interface to int(), long() and float(). The error strings are now a little different, but the type still remains the same. These functions are now ready to get declared obsolete ;-) - PyNumber_Int() now also does a check for embedded NULL chars in the input string; PyNumber_Long() already did this (and still does) Followed by: Looks like I've gone a step too far there... (and test_contains.py seem to have a bug too). I've changed back to reporting all errors in PyUnicode_Contains() and added a few more test cases to test_contains.py (plus corrected the join() NameError).
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return NULL;
}
if (PyUnicode_EncodeDecimal(PyUnicode_AS_UNICODE(v),
Marc-Andre's third try at this bulk patch seems to work (except that his copy of test_contains.py seems to be broken -- the lines he deleted were already absent). Checkin messages: New Unicode support for int(), float(), complex() and long(). - new APIs PyInt_FromUnicode() and PyLong_FromUnicode() - added support for Unicode to PyFloat_FromString() - new encoding API PyUnicode_EncodeDecimal() which converts Unicode to a decimal char* string (used in the above new APIs) - shortcuts for calls like int(<int object>) and float(<float obj>) - tests for all of the above Unicode compares and contains checks: - comparing Unicode and non-string types now works; TypeErrors are masked, all other errors such as ValueError during Unicode coercion are passed through (note that PyUnicode_Compare does not implement the masking -- PyObject_Compare does this) - contains now works for non-string types too; TypeErrors are masked and 0 returned; all other errors are passed through Better testing support for the standard codecs. Misc minor enhancements, such as an alias dbcs for the mbcs codec. Changes: - PyLong_FromString() now applies the same error checks as does PyInt_FromString(): trailing garbage is reported as error and not longer silently ignored. The only characters which may be trailing the digits are 'L' and 'l' -- these are still silently ignored. - string.ato?() now directly interface to int(), long() and float(). The error strings are now a little different, but the type still remains the same. These functions are now ready to get declared obsolete ;-) - PyNumber_Int() now also does a check for embedded NULL chars in the input string; PyNumber_Long() already did this (and still does) Followed by: Looks like I've gone a step too far there... (and test_contains.py seem to have a bug too). I've changed back to reporting all errors in PyUnicode_Contains() and added a few more test cases to test_contains.py (plus corrected the join() NameError).
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PyUnicode_GET_SIZE(v),
s_buffer,
Marc-Andre's third try at this bulk patch seems to work (except that his copy of test_contains.py seems to be broken -- the lines he deleted were already absent). Checkin messages: New Unicode support for int(), float(), complex() and long(). - new APIs PyInt_FromUnicode() and PyLong_FromUnicode() - added support for Unicode to PyFloat_FromString() - new encoding API PyUnicode_EncodeDecimal() which converts Unicode to a decimal char* string (used in the above new APIs) - shortcuts for calls like int(<int object>) and float(<float obj>) - tests for all of the above Unicode compares and contains checks: - comparing Unicode and non-string types now works; TypeErrors are masked, all other errors such as ValueError during Unicode coercion are passed through (note that PyUnicode_Compare does not implement the masking -- PyObject_Compare does this) - contains now works for non-string types too; TypeErrors are masked and 0 returned; all other errors are passed through Better testing support for the standard codecs. Misc minor enhancements, such as an alias dbcs for the mbcs codec. Changes: - PyLong_FromString() now applies the same error checks as does PyInt_FromString(): trailing garbage is reported as error and not longer silently ignored. The only characters which may be trailing the digits are 'L' and 'l' -- these are still silently ignored. - string.ato?() now directly interface to int(), long() and float(). The error strings are now a little different, but the type still remains the same. These functions are now ready to get declared obsolete ;-) - PyNumber_Int() now also does a check for embedded NULL chars in the input string; PyNumber_Long() already did this (and still does) Followed by: Looks like I've gone a step too far there... (and test_contains.py seem to have a bug too). I've changed back to reporting all errors in PyUnicode_Contains() and added a few more test cases to test_contains.py (plus corrected the join() NameError).
2000-04-05 17:11:21 -03:00
NULL))
return NULL;
s = s_buffer;
len = (int)strlen(s);
Marc-Andre's third try at this bulk patch seems to work (except that his copy of test_contains.py seems to be broken -- the lines he deleted were already absent). Checkin messages: New Unicode support for int(), float(), complex() and long(). - new APIs PyInt_FromUnicode() and PyLong_FromUnicode() - added support for Unicode to PyFloat_FromString() - new encoding API PyUnicode_EncodeDecimal() which converts Unicode to a decimal char* string (used in the above new APIs) - shortcuts for calls like int(<int object>) and float(<float obj>) - tests for all of the above Unicode compares and contains checks: - comparing Unicode and non-string types now works; TypeErrors are masked, all other errors such as ValueError during Unicode coercion are passed through (note that PyUnicode_Compare does not implement the masking -- PyObject_Compare does this) - contains now works for non-string types too; TypeErrors are masked and 0 returned; all other errors are passed through Better testing support for the standard codecs. Misc minor enhancements, such as an alias dbcs for the mbcs codec. Changes: - PyLong_FromString() now applies the same error checks as does PyInt_FromString(): trailing garbage is reported as error and not longer silently ignored. The only characters which may be trailing the digits are 'L' and 'l' -- these are still silently ignored. - string.ato?() now directly interface to int(), long() and float(). The error strings are now a little different, but the type still remains the same. These functions are now ready to get declared obsolete ;-) - PyNumber_Int() now also does a check for embedded NULL chars in the input string; PyNumber_Long() already did this (and still does) Followed by: Looks like I've gone a step too far there... (and test_contains.py seem to have a bug too). I've changed back to reporting all errors in PyUnicode_Contains() and added a few more test cases to test_contains.py (plus corrected the join() NameError).
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}
#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;
}
/* 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 = 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;
if (end == s) {
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 = atof(s);
PyFPE_END_PROTECT(x)
errno = 0; /* whether atof ever set errno is undefined */
}
return PyFloat_FromDouble(x);
}
static void
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float_dealloc(PyFloatObject *op)
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{
if (PyFloat_CheckExact(op)) {
op->ob_type = (struct _typeobject *)free_list;
free_list = op;
}
else
op->ob_type->tp_free((PyObject *)op);
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}
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double
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PyFloat_AsDouble(PyObject *op)
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{
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PyNumberMethods *nb;
PyFloatObject *fo;
double val;
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if (op && PyFloat_Check(op))
return PyFloat_AS_DOUBLE((PyFloatObject*) op);
if (op == NULL) {
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PyErr_BadArgument();
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return -1;
}
if ((nb = op->ob_type->tp_as_number) == NULL || nb->nb_float == NULL) {
PyErr_SetString(PyExc_TypeError, "a float is required");
return -1;
}
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fo = (PyFloatObject*) (*nb->nb_float) (op);
if (fo == NULL)
return -1;
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if (!PyFloat_Check(fo)) {
PyErr_SetString(PyExc_TypeError,
"nb_float should return float object");
return -1;
}
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val = PyFloat_AS_DOUBLE(fo);
Py_DECREF(fo);
return val;
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}
/* Methods */
static void
format_float(char *buf, size_t buflen, PyFloatObject *v, int precision)
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{
register char *cp;
/* 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(buf, buflen, "%.*g", precision, v->ob_fval);
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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)))
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break;
}
if (*cp == '\0') {
*cp++ = '.';
*cp++ = '0';
*cp++ = '\0';
}
}
/* 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);
}
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/* 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.
*/
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#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)
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{
register PyObject *obj = *v;
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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;
}
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}
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
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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);
}
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/* ARGSUSED */
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static int
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float_print(PyFloatObject *v, FILE *fp, int flags)
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{
char buf[100];
format_float(buf, sizeof(buf), v,
(flags & Py_PRINT_RAW) ? PREC_STR : PREC_REPR);
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fputs(buf, fp);
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return 0;
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}
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static PyObject *
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float_repr(PyFloatObject *v)
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{
char buf[100];
format_float(buf, sizeof(buf), v, PREC_REPR);
return PyString_FromString(buf);
}
static PyObject *
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float_str(PyFloatObject *v)
{
char buf[100];
format_float(buf, sizeof(buf), v, PREC_STR);
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return PyString_FromString(buf);
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}
static int
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float_compare(PyFloatObject *v, PyFloatObject *w)
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{
double i = v->ob_fval;
double j = w->ob_fval;
return (i < j) ? -1 : (i > j) ? 1 : 0;
}
static long
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float_hash(PyFloatObject *v)
{
return _Py_HashDouble(v->ob_fval);
}
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static PyObject *
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float_add(PyObject *v, PyObject *w)
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{
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double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
PyFPE_START_PROTECT("add", return 0)
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a = a + b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
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}
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static PyObject *
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float_sub(PyObject *v, PyObject *w)
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{
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double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
PyFPE_START_PROTECT("subtract", return 0)
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a = a - b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
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}
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static PyObject *
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float_mul(PyObject *v, PyObject *w)
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{
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double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
PyFPE_START_PROTECT("multiply", return 0)
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a = a * b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
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}
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static PyObject *
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float_div(PyObject *v, PyObject *w)
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{
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double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
if (b == 0.0) {
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PyErr_SetString(PyExc_ZeroDivisionError, "float division");
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return NULL;
}
PyFPE_START_PROTECT("divide", return 0)
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a = a / b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
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}
Add warning mode for classic division, almost exactly as specified in PEP 238. Changes: - add a new flag variable Py_DivisionWarningFlag, declared in pydebug.h, defined in object.c, set in main.c, and used in {int,long,float,complex}object.c. When this flag is set, the classic division operator issues a DeprecationWarning message. - add a new API PyRun_SimpleStringFlags() to match PyRun_SimpleString(). The main() function calls this so that commands run with -c can also benefit from -Dnew. - While I was at it, I changed the usage message in main() somewhat: alphabetized the options, split it in *four* parts to fit in under 512 bytes (not that I still believe this is necessary -- doc strings elsewhere are much longer), and perhaps most visibly, don't display the full list of options on each command line error. Instead, the full list is only displayed when -h is used, and otherwise a brief reminder of -h is displayed. When -h is used, write to stdout so that you can do `python -h | more'. Notes: - I don't want to use the -W option to control whether the classic division warning is issued or not, because the machinery to decide whether to display the warning or not is very expensive (it involves calling into the warnings.py module). You can use -Werror to turn the warnings into exceptions though. - The -Dnew option doesn't select future division for all of the program -- only for the __main__ module. I don't know if I'll ever change this -- it would require changes to the .pyc file magic number to do it right, and a more global notion of compiler flags. - You can usefully combine -Dwarn and -Dnew: this gives the __main__ module new division, and warns about classic division everywhere else.
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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 &&
Add warning mode for classic division, almost exactly as specified in PEP 238. Changes: - add a new flag variable Py_DivisionWarningFlag, declared in pydebug.h, defined in object.c, set in main.c, and used in {int,long,float,complex}object.c. When this flag is set, the classic division operator issues a DeprecationWarning message. - add a new API PyRun_SimpleStringFlags() to match PyRun_SimpleString(). The main() function calls this so that commands run with -c can also benefit from -Dnew. - While I was at it, I changed the usage message in main() somewhat: alphabetized the options, split it in *four* parts to fit in under 512 bytes (not that I still believe this is necessary -- doc strings elsewhere are much longer), and perhaps most visibly, don't display the full list of options on each command line error. Instead, the full list is only displayed when -h is used, and otherwise a brief reminder of -h is displayed. When -h is used, write to stdout so that you can do `python -h | more'. Notes: - I don't want to use the -W option to control whether the classic division warning is issued or not, because the machinery to decide whether to display the warning or not is very expensive (it involves calling into the warnings.py module). You can use -Werror to turn the warnings into exceptions though. - The -Dnew option doesn't select future division for all of the program -- only for the __main__ module. I don't know if I'll ever change this -- it would require changes to the .pyc file magic number to do it right, and a more global notion of compiler flags. - You can usefully combine -Dwarn and -Dnew: this gives the __main__ module new division, and warns about classic division everywhere else.
2001-08-31 14:40:15 -03:00
PyErr_Warn(PyExc_DeprecationWarning, "classic float division") < 0)
return NULL;
if (b == 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError, "float division");
return NULL;
}
PyFPE_START_PROTECT("divide", return 0)
a = a / b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
}
1997-05-02 00:12:38 -03:00
static PyObject *
2001-01-03 21:44:34 -04:00
float_rem(PyObject *v, PyObject *w)
1990-10-14 09:07:46 -03:00
{
double vx, wx;
double mod;
2001-01-03 21:44:34 -04:00
CONVERT_TO_DOUBLE(v, vx);
CONVERT_TO_DOUBLE(w, wx);
1990-10-14 09:07:46 -03:00
if (wx == 0.0) {
1997-05-02 00:12:38 -03:00
PyErr_SetString(PyExc_ZeroDivisionError, "float modulo");
1990-10-14 09:07:46 -03:00
return NULL;
}
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;
}
1997-03-14 00:32:50 -04:00
PyFPE_END_PROTECT(mod)
1997-05-02 00:12:38 -03:00
return PyFloat_FromDouble(mod);
1990-10-14 09:07:46 -03:00
}
1997-05-02 00:12:38 -03:00
static PyObject *
2001-01-03 21:44:34 -04:00
float_divmod(PyObject *v, PyObject *w)
{
1991-10-20 17:16:45 -03:00
double vx, wx;
double div, mod, floordiv;
2001-01-03 21:44:34 -04:00
CONVERT_TO_DOUBLE(v, vx);
CONVERT_TO_DOUBLE(w, wx);
1991-10-20 17:16:45 -03:00
if (wx == 0.0) {
1997-05-02 00:12:38 -03:00
PyErr_SetString(PyExc_ZeroDivisionError, "float divmod()");
1991-10-20 17:16:45 -03:00
return NULL;
}
PyFPE_START_PROTECT("divmod", return 0)
1991-10-20 17:16:45 -03:00
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.
*/
1991-10-20 17:16:45 -03:00
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;
1991-10-20 17:16:45 -03:00
}
/* 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;
}
1997-05-02 00:12:38 -03:00
static PyObject *
2001-01-03 21:44:34 -04:00
float_pow(PyObject *v, PyObject *w, PyObject *z)
1990-10-14 09:07:46 -03:00
{
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;
}
2001-01-03 21:44:34 -04:00
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 */
PyFPE_START_PROTECT("pow", return NULL)
if ((PyObject *)z != Py_None) {
2001-01-03 21:44:34 -04:00
double iz;
CONVERT_TO_DOUBLE(z, iz);
ix = fmod(1.0, iz);
if (ix != 0 && iz < 0)
ix += iz;
1996-01-11 21:22:56 -04:00
}
else
ix = 1.0;
PyFPE_END_PROTECT(ix)
return PyFloat_FromDouble(ix);
}
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 < 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_INFINITY(iw) && iw == iw) {
/* XXX the "iw == iw" was to weed out NaNs. This
* XXX doesn't actually work on all platforms.
*/
/* 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.
*/
1991-05-28 18:57:39 -03:00
}
errno = 0;
PyFPE_START_PROTECT("pow", return NULL)
ix = pow(iv, iw);
PyFPE_END_PROTECT(ix)
Py_ADJUST_ERANGE1(ix);
1990-10-21 19:15:08 -03:00
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);
1990-10-14 09:07:46 -03:00
return NULL;
1990-10-21 19:15:08 -03:00
}
1997-05-02 00:12:38 -03:00
return PyFloat_FromDouble(ix);
1990-10-14 09:07:46 -03:00
}
1997-05-02 00:12:38 -03:00
static PyObject *
2000-07-09 02:02:18 -03:00
float_neg(PyFloatObject *v)
1990-10-14 09:07:46 -03:00
{
1997-05-02 00:12:38 -03:00
return PyFloat_FromDouble(-v->ob_fval);
1990-10-14 09:07:46 -03:00
}
1997-05-02 00:12:38 -03:00
static PyObject *
2000-07-09 02:02:18 -03:00
float_pos(PyFloatObject *v)
1990-10-14 09:07:46 -03:00
{
if (PyFloat_CheckExact(v)) {
Py_INCREF(v);
return (PyObject *)v;
}
else
return PyFloat_FromDouble(v->ob_fval);
}
1997-05-02 00:12:38 -03:00
static PyObject *
2000-07-09 02:02:18 -03:00
float_abs(PyFloatObject *v)
{
return PyFloat_FromDouble(fabs(v->ob_fval));
1990-10-14 09:07:46 -03:00
}
1991-05-14 08:57:01 -03:00
static int
2000-07-09 02:02:18 -03:00
float_nonzero(PyFloatObject *v)
1991-05-14 08:57:01 -03:00
{
return v->ob_fval != 0.0;
}
static int
2000-07-09 02:02:18 -03:00
float_coerce(PyObject **pv, PyObject **pw)
{
1997-05-02 00:12:38 -03:00
if (PyInt_Check(*pw)) {
long x = PyInt_AsLong(*pw);
*pw = PyFloat_FromDouble((double)x);
Py_INCREF(*pv);
return 0;
}
1997-05-02 00:12:38 -03:00
else if (PyLong_Check(*pw)) {
double x = PyLong_AsDouble(*pw);
if (x == -1.0 && PyErr_Occurred())
return -1;
*pw = PyFloat_FromDouble(x);
1997-05-02 00:12:38 -03:00
Py_INCREF(*pv);
return 0;
}
else if (PyFloat_Check(*pw)) {
Py_INCREF(*pv);
Py_INCREF(*pw);
return 0;
}
return 1; /* Can't do it */
}
static PyObject *
float_long(PyObject *v)
{
double x = PyFloat_AsDouble(v);
return PyLong_FromDouble(x);
}
1997-05-02 00:12:38 -03:00
static PyObject *
2000-07-09 02:02:18 -03:00
float_int(PyObject *v)
{
1997-05-02 00:12:38 -03:00
double x = PyFloat_AsDouble(v);
double wholepart; /* integral portion of x, rounded toward 0 */
(void)modf(x, &wholepart);
/* Try to get out cheap if this fits in a Python int. The attempt
* to cast to long must be protected, as C doesn't define what
* happens if the double is too big to fit in a long. Some rare
* systems raise an exception then (RISCOS was mentioned as one,
* and someone using a non-default option on Sun also bumped into
* that). Note that checking for >= and <= LONG_{MIN,MAX} would
* still be vulnerable: if a long has more bits of precision than
* a double, casting MIN/MAX to double may yield an approximation,
* and if that's rounded up, then, e.g., wholepart=LONG_MAX+1 would
* yield true from the C expression wholepart<=LONG_MAX, despite
* that wholepart is actually greater than LONG_MAX.
*/
if (LONG_MIN < wholepart && wholepart < LONG_MAX) {
const long aslong = (long)wholepart;
return PyInt_FromLong(aslong);
}
return PyLong_FromDouble(wholepart);
}
1997-05-02 00:12:38 -03:00
static PyObject *
2000-07-09 02:02:18 -03:00
float_float(PyObject *v)
{
1997-05-02 00:12:38 -03:00
Py_INCREF(v);
return v;
}
static PyObject *
float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds);
2001-08-02 01:15:00 -03:00
static PyObject *
float_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
{
PyObject *x = Py_False; /* Integer zero */
static char *kwlist[] = {"x", 0};
if (type != &PyFloat_Type)
return float_subtype_new(type, args, kwds); /* Wimp out */
2001-08-02 01:15:00 -03:00
if (!PyArg_ParseTupleAndKeywords(args, kwds, "|O:float", kwlist, &x))
return NULL;
if (PyString_Check(x))
return PyFloat_FromString(x, NULL);
return PyNumber_Float(x);
}
/* Wimpy, slow approach to tp_new calls for subtypes of float:
first create a regular float from whatever arguments we got,
then allocate a subtype instance and initialize its ob_fval
from the regular float. The regular float is then thrown away.
*/
static PyObject *
float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
{
PyObject *tmp, *new;
assert(PyType_IsSubtype(type, &PyFloat_Type));
tmp = float_new(&PyFloat_Type, args, kwds);
if (tmp == NULL)
return NULL;
assert(PyFloat_CheckExact(tmp));
2001-08-30 00:09:31 -03:00
new = type->tp_alloc(type, 0);
if (new == NULL)
return NULL;
((PyFloatObject *)new)->ob_fval = ((PyFloatObject *)tmp)->ob_fval;
Py_DECREF(tmp);
return new;
}
static PyObject *
float_getnewargs(PyFloatObject *v)
{
return Py_BuildValue("(d)", v->ob_fval);
}
static PyMethodDef float_methods[] = {
{"__getnewargs__", (PyCFunction)float_getnewargs, METH_NOARGS},
{NULL, NULL} /* sentinel */
};
2002-06-13 17:33:02 -03:00
PyDoc_STRVAR(float_doc,
2001-08-02 01:15:00 -03:00
"float(x) -> floating point number\n\
\n\
2002-06-13 17:33:02 -03:00
Convert a string or number to a floating point number, if possible.");
2001-08-02 01:15:00 -03:00
1997-05-02 00:12:38 -03:00
static PyNumberMethods float_as_number = {
(binaryfunc)float_add, /*nb_add*/
(binaryfunc)float_sub, /*nb_subtract*/
(binaryfunc)float_mul, /*nb_multiply*/
Add warning mode for classic division, almost exactly as specified in PEP 238. Changes: - add a new flag variable Py_DivisionWarningFlag, declared in pydebug.h, defined in object.c, set in main.c, and used in {int,long,float,complex}object.c. When this flag is set, the classic division operator issues a DeprecationWarning message. - add a new API PyRun_SimpleStringFlags() to match PyRun_SimpleString(). The main() function calls this so that commands run with -c can also benefit from -Dnew. - While I was at it, I changed the usage message in main() somewhat: alphabetized the options, split it in *four* parts to fit in under 512 bytes (not that I still believe this is necessary -- doc strings elsewhere are much longer), and perhaps most visibly, don't display the full list of options on each command line error. Instead, the full list is only displayed when -h is used, and otherwise a brief reminder of -h is displayed. When -h is used, write to stdout so that you can do `python -h | more'. Notes: - I don't want to use the -W option to control whether the classic division warning is issued or not, because the machinery to decide whether to display the warning or not is very expensive (it involves calling into the warnings.py module). You can use -Werror to turn the warnings into exceptions though. - The -Dnew option doesn't select future division for all of the program -- only for the __main__ module. I don't know if I'll ever change this -- it would require changes to the .pyc file magic number to do it right, and a more global notion of compiler flags. - You can usefully combine -Dwarn and -Dnew: this gives the __main__ module new division, and warns about classic division everywhere else.
2001-08-31 14:40:15 -03:00
(binaryfunc)float_classic_div, /*nb_divide*/
(binaryfunc)float_rem, /*nb_remainder*/
(binaryfunc)float_divmod, /*nb_divmod*/
(ternaryfunc)float_pow, /*nb_power*/
(unaryfunc)float_neg, /*nb_negative*/
(unaryfunc)float_pos, /*nb_positive*/
(unaryfunc)float_abs, /*nb_absolute*/
(inquiry)float_nonzero, /*nb_nonzero*/
0, /*nb_invert*/
0, /*nb_lshift*/
0, /*nb_rshift*/
0, /*nb_and*/
0, /*nb_xor*/
0, /*nb_or*/
(coercion)float_coerce, /*nb_coerce*/
(unaryfunc)float_int, /*nb_int*/
(unaryfunc)float_long, /*nb_long*/
(unaryfunc)float_float, /*nb_float*/
0, /* nb_oct */
0, /* nb_hex */
0, /* nb_inplace_add */
0, /* nb_inplace_subtract */
0, /* nb_inplace_multiply */
0, /* nb_inplace_divide */
0, /* nb_inplace_remainder */
0, /* nb_inplace_power */
0, /* nb_inplace_lshift */
0, /* nb_inplace_rshift */
0, /* nb_inplace_and */
0, /* nb_inplace_xor */
0, /* nb_inplace_or */
float_floor_div, /* nb_floor_divide */
float_div, /* nb_true_divide */
0, /* nb_inplace_floor_divide */
0, /* nb_inplace_true_divide */
1990-10-14 09:07:46 -03:00
};
1997-05-02 00:12:38 -03:00
PyTypeObject PyFloat_Type = {
PyObject_HEAD_INIT(&PyType_Type)
1990-10-14 09:07:46 -03:00
0,
"float",
1997-05-02 00:12:38 -03:00
sizeof(PyFloatObject),
1990-10-14 09:07:46 -03:00
0,
2001-08-02 01:15:00 -03:00
(destructor)float_dealloc, /* tp_dealloc */
(printfunc)float_print, /* tp_print */
0, /* tp_getattr */
0, /* tp_setattr */
(cmpfunc)float_compare, /* tp_compare */
(reprfunc)float_repr, /* tp_repr */
&float_as_number, /* tp_as_number */
0, /* tp_as_sequence */
0, /* tp_as_mapping */
(hashfunc)float_hash, /* tp_hash */
0, /* tp_call */
(reprfunc)float_str, /* tp_str */
PyObject_GenericGetAttr, /* tp_getattro */
0, /* tp_setattro */
0, /* tp_as_buffer */
Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES |
Py_TPFLAGS_BASETYPE, /* tp_flags */
2001-08-02 01:15:00 -03:00
float_doc, /* tp_doc */
0, /* tp_traverse */
0, /* tp_clear */
0, /* tp_richcompare */
0, /* tp_weaklistoffset */
0, /* tp_iter */
0, /* tp_iternext */
float_methods, /* tp_methods */
2001-08-02 01:15:00 -03:00
0, /* tp_members */
0, /* tp_getset */
0, /* tp_base */
0, /* tp_dict */
0, /* tp_descr_get */
0, /* tp_descr_set */
0, /* tp_dictoffset */
0, /* tp_init */
0, /* tp_alloc */
float_new, /* tp_new */
1990-10-14 09:07:46 -03:00
};
void
2000-07-09 02:02:18 -03:00
PyFloat_Fini(void)
{
PyFloatObject *p;
PyFloatBlock *list, *next;
int i;
int bc, bf; /* block count, number of freed blocks */
int frem, fsum; /* remaining unfreed floats per block, total */
bc = 0;
bf = 0;
fsum = 0;
list = block_list;
block_list = NULL;
free_list = NULL;
while (list != NULL) {
bc++;
frem = 0;
for (i = 0, p = &list->objects[0];
i < N_FLOATOBJECTS;
i++, p++) {
if (PyFloat_CheckExact(p) && p->ob_refcnt != 0)
frem++;
}
next = list->next;
if (frem) {
list->next = block_list;
block_list = list;
for (i = 0, p = &list->objects[0];
i < N_FLOATOBJECTS;
i++, p++) {
if (!PyFloat_CheckExact(p) ||
p->ob_refcnt == 0) {
p->ob_type = (struct _typeobject *)
free_list;
free_list = p;
}
}
}
else {
PyMem_FREE(list); /* XXX PyObject_FREE ??? */
bf++;
}
fsum += frem;
list = next;
}
if (!Py_VerboseFlag)
return;
fprintf(stderr, "# cleanup floats");
if (!fsum) {
fprintf(stderr, "\n");
}
else {
fprintf(stderr,
": %d unfreed float%s in %d out of %d block%s\n",
fsum, fsum == 1 ? "" : "s",
bc - bf, bc, bc == 1 ? "" : "s");
}
if (Py_VerboseFlag > 1) {
list = block_list;
while (list != NULL) {
for (i = 0, p = &list->objects[0];
i < N_FLOATOBJECTS;
i++, p++) {
if (PyFloat_CheckExact(p) &&
p->ob_refcnt != 0) {
char buf[100];
PyFloat_AsString(buf, p);
fprintf(stderr,
"# <float at %p, refcnt=%d, val=%s>\n",
p, p->ob_refcnt, buf);
}
}
list = list->next;
}
}
}
/*----------------------------------------------------------------------------
* _PyFloat_{Pack,Unpack}{4,8}. See floatobject.h.
*
* TODO: On platforms that use the standard IEEE-754 single and double
* formats natively, these routines could simply copy the bytes.
*/
int
_PyFloat_Pack4(double x, unsigned char *p, int le)
{
unsigned char sign;
int e;
double f;
unsigned int fbits;
int incr = 1;
if (le) {
p += 3;
incr = -1;
}
if (x < 0) {
sign = 1;
x = -x;
}
else
sign = 0;
f = frexp(x, &e);
/* Normalize f to be in the range [1.0, 2.0) */
if (0.5 <= f && f < 1.0) {
f *= 2.0;
e--;
}
else if (f == 0.0)
e = 0;
else {
PyErr_SetString(PyExc_SystemError,
"frexp() result out of range");
return -1;
}
if (e >= 128)
goto Overflow;
else if (e < -126) {
/* Gradual underflow */
f = ldexp(f, 126 + e);
e = 0;
}
else if (!(e == 0 && f == 0.0)) {
e += 127;
f -= 1.0; /* Get rid of leading 1 */
}
f *= 8388608.0; /* 2**23 */
fbits = (unsigned int)(f + 0.5); /* Round */
assert(fbits <= 8388608);
if (fbits >> 23) {
/* The carry propagated out of a string of 23 1 bits. */
fbits = 0;
++e;
if (e >= 255)
goto Overflow;
}
/* First byte */
*p = (sign << 7) | (e >> 1);
p += incr;
/* Second byte */
*p = (char) (((e & 1) << 7) | (fbits >> 16));
p += incr;
/* Third byte */
*p = (fbits >> 8) & 0xFF;
p += incr;
/* Fourth byte */
*p = fbits & 0xFF;
/* Done */
return 0;
Overflow:
PyErr_SetString(PyExc_OverflowError,
"float too large to pack with f format");
return -1;
}
int
_PyFloat_Pack8(double x, unsigned char *p, int le)
{
unsigned char sign;
int e;
double f;
unsigned int fhi, flo;
int incr = 1;
if (le) {
p += 7;
incr = -1;
}
if (x < 0) {
sign = 1;
x = -x;
}
else
sign = 0;
f = frexp(x, &e);
/* Normalize f to be in the range [1.0, 2.0) */
if (0.5 <= f && f < 1.0) {
f *= 2.0;
e--;
}
else if (f == 0.0)
e = 0;
else {
PyErr_SetString(PyExc_SystemError,
"frexp() result out of range");
return -1;
}
if (e >= 1024)
goto Overflow;
else if (e < -1022) {
/* Gradual underflow */
f = ldexp(f, 1022 + e);
e = 0;
}
else if (!(e == 0 && f == 0.0)) {
e += 1023;
f -= 1.0; /* Get rid of leading 1 */
}
/* fhi receives the high 28 bits; flo the low 24 bits (== 52 bits) */
f *= 268435456.0; /* 2**28 */
fhi = (unsigned int)f; /* Truncate */
assert(fhi < 268435456);
f -= (double)fhi;
f *= 16777216.0; /* 2**24 */
flo = (unsigned int)(f + 0.5); /* Round */
assert(flo <= 16777216);
if (flo >> 24) {
/* The carry propagated out of a string of 24 1 bits. */
flo = 0;
++fhi;
if (fhi >> 28) {
/* And it also progagated out of the next 28 bits. */
fhi = 0;
++e;
if (e >= 2047)
goto Overflow;
}
}
/* First byte */
*p = (sign << 7) | (e >> 4);
p += incr;
/* Second byte */
*p = (unsigned char) (((e & 0xF) << 4) | (fhi >> 24));
p += incr;
/* Third byte */
*p = (fhi >> 16) & 0xFF;
p += incr;
/* Fourth byte */
*p = (fhi >> 8) & 0xFF;
p += incr;
/* Fifth byte */
*p = fhi & 0xFF;
p += incr;
/* Sixth byte */
*p = (flo >> 16) & 0xFF;
p += incr;
/* Seventh byte */
*p = (flo >> 8) & 0xFF;
p += incr;
/* Eighth byte */
*p = flo & 0xFF;
p += incr;
/* Done */
return 0;
Overflow:
PyErr_SetString(PyExc_OverflowError,
"float too large to pack with d format");
return -1;
}
double
_PyFloat_Unpack4(const unsigned char *p, int le)
{
unsigned char sign;
int e;
unsigned int f;
double x;
int incr = 1;
if (le) {
p += 3;
incr = -1;
}
/* First byte */
sign = (*p >> 7) & 1;
e = (*p & 0x7F) << 1;
p += incr;
/* Second byte */
e |= (*p >> 7) & 1;
f = (*p & 0x7F) << 16;
p += incr;
/* Third byte */
f |= *p << 8;
p += incr;
/* Fourth byte */
f |= *p;
x = (double)f / 8388608.0;
/* XXX This sadly ignores Inf/NaN issues */
if (e == 0)
e = -126;
else {
x += 1.0;
e -= 127;
}
x = ldexp(x, e);
if (sign)
x = -x;
return x;
}
double
_PyFloat_Unpack8(const unsigned char *p, int le)
{
unsigned char sign;
int e;
unsigned int fhi, flo;
double x;
int incr = 1;
if (le) {
p += 7;
incr = -1;
}
/* First byte */
sign = (*p >> 7) & 1;
e = (*p & 0x7F) << 4;
p += incr;
/* Second byte */
e |= (*p >> 4) & 0xF;
fhi = (*p & 0xF) << 24;
p += incr;
/* Third byte */
fhi |= *p << 16;
p += incr;
/* Fourth byte */
fhi |= *p << 8;
p += incr;
/* Fifth byte */
fhi |= *p;
p += incr;
/* Sixth byte */
flo = *p << 16;
p += incr;
/* Seventh byte */
flo |= *p << 8;
p += incr;
/* Eighth byte */
flo |= *p;
x = (double)fhi + (double)flo / 16777216.0; /* 2**24 */
x /= 268435456.0; /* 2**28 */
/* XXX This sadly ignores Inf/NaN */
if (e == 0)
e = -1022;
else {
x += 1.0;
e -= 1023;
}
x = ldexp(x, e);
if (sign)
x = -x;
return x;
}