source: python/trunk/Objects/floatobject.c

Last change on this file was 391, checked in by dmik, 11 years ago

python: Merge vendor 2.7.6 to trunk.
  • Property svn:eol-style set to native
File size: 76.7 KB
RevLine 
[2]1
2/* Float object implementation */
3
4/* XXX There should be overflow checks here, but it's hard to check
5 for any kind of float exception without losing portability. */
6
7#include "Python.h"
8#include "structseq.h"
9
10#include <ctype.h>
11#include <float.h>
12
13#undef MAX
14#undef MIN
15#define MAX(x, y) ((x) < (y) ? (y) : (x))
16#define MIN(x, y) ((x) < (y) ? (x) : (y))
17
18#ifdef _OSF_SOURCE
19/* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
20extern int finite(double);
21#endif
22
23/* Special free list -- see comments for same code in intobject.c. */
[391]24#define BLOCK_SIZE 1000 /* 1K less typical malloc overhead */
25#define BHEAD_SIZE 8 /* Enough for a 64-bit pointer */
26#define N_FLOATOBJECTS ((BLOCK_SIZE - BHEAD_SIZE) / sizeof(PyFloatObject))
[2]27
28struct _floatblock {
[391]29 struct _floatblock *next;
30 PyFloatObject objects[N_FLOATOBJECTS];
[2]31};
32
33typedef struct _floatblock PyFloatBlock;
34
35static PyFloatBlock *block_list = NULL;
36static PyFloatObject *free_list = NULL;
37
38static PyFloatObject *
39fill_free_list(void)
40{
[391]41 PyFloatObject *p, *q;
42 /* XXX Float blocks escape the object heap. Use PyObject_MALLOC ??? */
43 p = (PyFloatObject *) PyMem_MALLOC(sizeof(PyFloatBlock));
44 if (p == NULL)
45 return (PyFloatObject *) PyErr_NoMemory();
46 ((PyFloatBlock *)p)->next = block_list;
47 block_list = (PyFloatBlock *)p;
48 p = &((PyFloatBlock *)p)->objects[0];
49 q = p + N_FLOATOBJECTS;
50 while (--q > p)
51 Py_TYPE(q) = (struct _typeobject *)(q-1);
52 Py_TYPE(q) = NULL;
53 return p + N_FLOATOBJECTS - 1;
[2]54}
55
56double
57PyFloat_GetMax(void)
58{
[391]59 return DBL_MAX;
[2]60}
61
62double
63PyFloat_GetMin(void)
64{
[391]65 return DBL_MIN;
[2]66}
67
68static PyTypeObject FloatInfoType = {0, 0, 0, 0, 0, 0};
69
70PyDoc_STRVAR(floatinfo__doc__,
[391]71"sys.float_info\n\
[2]72\n\
73A structseq holding information about the float type. It contains low level\n\
74information about the precision and internal representation. Please study\n\
75your system's :file:`float.h` for more information.");
76
77static PyStructSequence_Field floatinfo_fields[] = {
[391]78 {"max", "DBL_MAX -- maximum representable finite float"},
79 {"max_exp", "DBL_MAX_EXP -- maximum int e such that radix**(e-1) "
80 "is representable"},
81 {"max_10_exp", "DBL_MAX_10_EXP -- maximum int e such that 10**e "
82 "is representable"},
83 {"min", "DBL_MIN -- Minimum positive normalizer float"},
84 {"min_exp", "DBL_MIN_EXP -- minimum int e such that radix**(e-1) "
85 "is a normalized float"},
86 {"min_10_exp", "DBL_MIN_10_EXP -- minimum int e such that 10**e is "
87 "a normalized"},
88 {"dig", "DBL_DIG -- digits"},
89 {"mant_dig", "DBL_MANT_DIG -- mantissa digits"},
90 {"epsilon", "DBL_EPSILON -- Difference between 1 and the next "
91 "representable float"},
92 {"radix", "FLT_RADIX -- radix of exponent"},
93 {"rounds", "FLT_ROUNDS -- addition rounds"},
94 {0}
[2]95};
96
97static PyStructSequence_Desc floatinfo_desc = {
[391]98 "sys.float_info", /* name */
99 floatinfo__doc__, /* doc */
100 floatinfo_fields, /* fields */
101 11
[2]102};
103
104PyObject *
105PyFloat_GetInfo(void)
106{
[391]107 PyObject* floatinfo;
108 int pos = 0;
[2]109
[391]110 floatinfo = PyStructSequence_New(&FloatInfoType);
111 if (floatinfo == NULL) {
112 return NULL;
113 }
[2]114
115#define SetIntFlag(flag) \
[391]116 PyStructSequence_SET_ITEM(floatinfo, pos++, PyInt_FromLong(flag))
[2]117#define SetDblFlag(flag) \
[391]118 PyStructSequence_SET_ITEM(floatinfo, pos++, PyFloat_FromDouble(flag))
[2]119
[391]120 SetDblFlag(DBL_MAX);
121 SetIntFlag(DBL_MAX_EXP);
122 SetIntFlag(DBL_MAX_10_EXP);
123 SetDblFlag(DBL_MIN);
124 SetIntFlag(DBL_MIN_EXP);
125 SetIntFlag(DBL_MIN_10_EXP);
126 SetIntFlag(DBL_DIG);
127 SetIntFlag(DBL_MANT_DIG);
128 SetDblFlag(DBL_EPSILON);
129 SetIntFlag(FLT_RADIX);
130 SetIntFlag(FLT_ROUNDS);
[2]131#undef SetIntFlag
132#undef SetDblFlag
[391]133
134 if (PyErr_Occurred()) {
135 Py_CLEAR(floatinfo);
136 return NULL;
137 }
138 return floatinfo;
[2]139}
140
141PyObject *
142PyFloat_FromDouble(double fval)
143{
[391]144 register PyFloatObject *op;
145 if (free_list == NULL) {
146 if ((free_list = fill_free_list()) == NULL)
147 return NULL;
148 }
149 /* Inline PyObject_New */
150 op = free_list;
151 free_list = (PyFloatObject *)Py_TYPE(op);
152 PyObject_INIT(op, &PyFloat_Type);
153 op->ob_fval = fval;
154 return (PyObject *) op;
[2]155}
156
157/**************************************************************************
158RED_FLAG 22-Sep-2000 tim
159PyFloat_FromString's pend argument is braindead. Prior to this RED_FLAG,
160
1611. If v was a regular string, *pend was set to point to its terminating
162 null byte. That's useless (the caller can find that without any
163 help from this function!).
164
1652. If v was a Unicode string, or an object convertible to a character
166 buffer, *pend was set to point into stack trash (the auto temp
167 vector holding the character buffer). That was downright dangerous.
168
169Since we can't change the interface of a public API function, pend is
170still supported but now *officially* useless: if pend is not NULL,
171*pend is set to NULL.
172**************************************************************************/
173PyObject *
174PyFloat_FromString(PyObject *v, char **pend)
175{
[391]176 const char *s, *last, *end;
177 double x;
178 char buffer[256]; /* for errors */
[2]179#ifdef Py_USING_UNICODE
[391]180 char *s_buffer = NULL;
[2]181#endif
[391]182 Py_ssize_t len;
183 PyObject *result = NULL;
[2]184
[391]185 if (pend)
186 *pend = NULL;
187 if (PyString_Check(v)) {
188 s = PyString_AS_STRING(v);
189 len = PyString_GET_SIZE(v);
190 }
[2]191#ifdef Py_USING_UNICODE
[391]192 else if (PyUnicode_Check(v)) {
193 s_buffer = (char *)PyMem_MALLOC(PyUnicode_GET_SIZE(v)+1);
194 if (s_buffer == NULL)
195 return PyErr_NoMemory();
196 if (PyUnicode_EncodeDecimal(PyUnicode_AS_UNICODE(v),
197 PyUnicode_GET_SIZE(v),
198 s_buffer,
199 NULL))
200 goto error;
201 s = s_buffer;
202 len = strlen(s);
203 }
[2]204#endif
[391]205 else if (PyObject_AsCharBuffer(v, &s, &len)) {
206 PyErr_SetString(PyExc_TypeError,
207 "float() argument must be a string or a number");
208 return NULL;
209 }
210 last = s + len;
[2]211
[391]212 while (Py_ISSPACE(*s))
213 s++;
214 /* We don't care about overflow or underflow. If the platform
215 * supports them, infinities and signed zeroes (on underflow) are
216 * fine. */
217 x = PyOS_string_to_double(s, (char **)&end, NULL);
218 if (x == -1.0 && PyErr_Occurred())
219 goto error;
220 while (Py_ISSPACE(*end))
221 end++;
222 if (end == last)
223 result = PyFloat_FromDouble(x);
224 else {
225 PyOS_snprintf(buffer, sizeof(buffer),
226 "invalid literal for float(): %.200s", s);
227 PyErr_SetString(PyExc_ValueError, buffer);
228 result = NULL;
229 }
[2]230
[391]231 error:
232#ifdef Py_USING_UNICODE
233 if (s_buffer)
234 PyMem_FREE(s_buffer);
[2]235#endif
[391]236 return result;
[2]237}
238
239static void
240float_dealloc(PyFloatObject *op)
241{
[391]242 if (PyFloat_CheckExact(op)) {
243 Py_TYPE(op) = (struct _typeobject *)free_list;
244 free_list = op;
245 }
246 else
247 Py_TYPE(op)->tp_free((PyObject *)op);
[2]248}
249
250double
251PyFloat_AsDouble(PyObject *op)
252{
[391]253 PyNumberMethods *nb;
254 PyFloatObject *fo;
255 double val;
[2]256
[391]257 if (op && PyFloat_Check(op))
258 return PyFloat_AS_DOUBLE((PyFloatObject*) op);
[2]259
[391]260 if (op == NULL) {
261 PyErr_BadArgument();
262 return -1;
263 }
[2]264
[391]265 if ((nb = Py_TYPE(op)->tp_as_number) == NULL || nb->nb_float == NULL) {
266 PyErr_SetString(PyExc_TypeError, "a float is required");
267 return -1;
268 }
[2]269
[391]270 fo = (PyFloatObject*) (*nb->nb_float) (op);
271 if (fo == NULL)
272 return -1;
273 if (!PyFloat_Check(fo)) {
274 PyErr_SetString(PyExc_TypeError,
275 "nb_float should return float object");
276 return -1;
277 }
[2]278
[391]279 val = PyFloat_AS_DOUBLE(fo);
280 Py_DECREF(fo);
[2]281
[391]282 return val;
[2]283}
284
285/* Methods */
286
287/* Macro and helper that convert PyObject obj to a C double and store
288 the value in dbl; this replaces the functionality of the coercion
289 slot function. If conversion to double raises an exception, obj is
290 set to NULL, and the function invoking this macro returns NULL. If
291 obj is not of float, int or long type, Py_NotImplemented is incref'ed,
292 stored in obj, and returned from the function invoking this macro.
293*/
[391]294#define CONVERT_TO_DOUBLE(obj, dbl) \
295 if (PyFloat_Check(obj)) \
296 dbl = PyFloat_AS_DOUBLE(obj); \
297 else if (convert_to_double(&(obj), &(dbl)) < 0) \
298 return obj;
[2]299
300static int
301convert_to_double(PyObject **v, double *dbl)
302{
[391]303 register PyObject *obj = *v;
[2]304
[391]305 if (PyInt_Check(obj)) {
306 *dbl = (double)PyInt_AS_LONG(obj);
307 }
308 else if (PyLong_Check(obj)) {
309 *dbl = PyLong_AsDouble(obj);
310 if (*dbl == -1.0 && PyErr_Occurred()) {
311 *v = NULL;
312 return -1;
313 }
314 }
315 else {
316 Py_INCREF(Py_NotImplemented);
317 *v = Py_NotImplemented;
318 return -1;
319 }
320 return 0;
[2]321}
322
[391]323/* XXX PyFloat_AsString and PyFloat_AsReprString are deprecated:
[2]324 XXX they pass a char buffer without passing a length.
325*/
326void
327PyFloat_AsString(char *buf, PyFloatObject *v)
328{
[391]329 char *tmp = PyOS_double_to_string(v->ob_fval, 'g',
330 PyFloat_STR_PRECISION,
331 Py_DTSF_ADD_DOT_0, NULL);
332 strcpy(buf, tmp);
333 PyMem_Free(tmp);
[2]334}
335
336void
337PyFloat_AsReprString(char *buf, PyFloatObject *v)
338{
[391]339 char * tmp = PyOS_double_to_string(v->ob_fval, 'r', 0,
340 Py_DTSF_ADD_DOT_0, NULL);
341 strcpy(buf, tmp);
342 PyMem_Free(tmp);
[2]343}
344
345/* ARGSUSED */
346static int
347float_print(PyFloatObject *v, FILE *fp, int flags)
348{
[391]349 char *buf;
350 if (flags & Py_PRINT_RAW)
351 buf = PyOS_double_to_string(v->ob_fval,
352 'g', PyFloat_STR_PRECISION,
353 Py_DTSF_ADD_DOT_0, NULL);
354 else
355 buf = PyOS_double_to_string(v->ob_fval,
356 'r', 0, Py_DTSF_ADD_DOT_0, NULL);
357 Py_BEGIN_ALLOW_THREADS
358 fputs(buf, fp);
359 Py_END_ALLOW_THREADS
360 PyMem_Free(buf);
361 return 0;
[2]362}
363
364static PyObject *
[391]365float_str_or_repr(PyFloatObject *v, int precision, char format_code)
366{
367 PyObject *result;
368 char *buf = PyOS_double_to_string(PyFloat_AS_DOUBLE(v),
369 format_code, precision,
370 Py_DTSF_ADD_DOT_0,
371 NULL);
372 if (!buf)
373 return PyErr_NoMemory();
374 result = PyString_FromString(buf);
375 PyMem_Free(buf);
376 return result;
377}
378
379static PyObject *
[2]380float_repr(PyFloatObject *v)
381{
[391]382 return float_str_or_repr(v, 0, 'r');
[2]383}
384
385static PyObject *
386float_str(PyFloatObject *v)
387{
[391]388 return float_str_or_repr(v, PyFloat_STR_PRECISION, 'g');
[2]389}
390
391/* Comparison is pretty much a nightmare. When comparing float to float,
392 * we do it as straightforwardly (and long-windedly) as conceivable, so
393 * that, e.g., Python x == y delivers the same result as the platform
394 * C x == y when x and/or y is a NaN.
395 * When mixing float with an integer type, there's no good *uniform* approach.
396 * Converting the double to an integer obviously doesn't work, since we
397 * may lose info from fractional bits. Converting the integer to a double
398 * also has two failure modes: (1) a long int may trigger overflow (too
399 * large to fit in the dynamic range of a C double); (2) even a C long may have
400 * more bits than fit in a C double (e.g., on a a 64-bit box long may have
401 * 63 bits of precision, but a C double probably has only 53), and then
402 * we can falsely claim equality when low-order integer bits are lost by
403 * coercion to double. So this part is painful too.
404 */
405
406static PyObject*
407float_richcompare(PyObject *v, PyObject *w, int op)
408{
[391]409 double i, j;
410 int r = 0;
[2]411
[391]412 assert(PyFloat_Check(v));
413 i = PyFloat_AS_DOUBLE(v);
[2]414
[391]415 /* Switch on the type of w. Set i and j to doubles to be compared,
416 * and op to the richcomp to use.
417 */
418 if (PyFloat_Check(w))
419 j = PyFloat_AS_DOUBLE(w);
[2]420
[391]421 else if (!Py_IS_FINITE(i)) {
422 if (PyInt_Check(w) || PyLong_Check(w))
423 /* If i is an infinity, its magnitude exceeds any
424 * finite integer, so it doesn't matter which int we
425 * compare i with. If i is a NaN, similarly.
426 */
427 j = 0.0;
428 else
429 goto Unimplemented;
430 }
[2]431
[391]432 else if (PyInt_Check(w)) {
433 long jj = PyInt_AS_LONG(w);
434 /* In the worst realistic case I can imagine, C double is a
435 * Cray single with 48 bits of precision, and long has 64
436 * bits.
437 */
[2]438#if SIZEOF_LONG > 6
[391]439 unsigned long abs = (unsigned long)(jj < 0 ? -jj : jj);
440 if (abs >> 48) {
441 /* Needs more than 48 bits. Make it take the
442 * PyLong path.
443 */
444 PyObject *result;
445 PyObject *ww = PyLong_FromLong(jj);
[2]446
[391]447 if (ww == NULL)
448 return NULL;
449 result = float_richcompare(v, ww, op);
450 Py_DECREF(ww);
451 return result;
452 }
[2]453#endif
[391]454 j = (double)jj;
455 assert((long)j == jj);
456 }
[2]457
[391]458 else if (PyLong_Check(w)) {
459 int vsign = i == 0.0 ? 0 : i < 0.0 ? -1 : 1;
460 int wsign = _PyLong_Sign(w);
461 size_t nbits;
462 int exponent;
[2]463
[391]464 if (vsign != wsign) {
465 /* Magnitudes are irrelevant -- the signs alone
466 * determine the outcome.
467 */
468 i = (double)vsign;
469 j = (double)wsign;
470 goto Compare;
471 }
472 /* The signs are the same. */
473 /* Convert w to a double if it fits. In particular, 0 fits. */
474 nbits = _PyLong_NumBits(w);
475 if (nbits == (size_t)-1 && PyErr_Occurred()) {
476 /* This long is so large that size_t isn't big enough
477 * to hold the # of bits. Replace with little doubles
478 * that give the same outcome -- w is so large that
479 * its magnitude must exceed the magnitude of any
480 * finite float.
481 */
482 PyErr_Clear();
483 i = (double)vsign;
484 assert(wsign != 0);
485 j = wsign * 2.0;
486 goto Compare;
487 }
488 if (nbits <= 48) {
489 j = PyLong_AsDouble(w);
490 /* It's impossible that <= 48 bits overflowed. */
491 assert(j != -1.0 || ! PyErr_Occurred());
492 goto Compare;
493 }
494 assert(wsign != 0); /* else nbits was 0 */
495 assert(vsign != 0); /* if vsign were 0, then since wsign is
496 * not 0, we would have taken the
497 * vsign != wsign branch at the start */
498 /* We want to work with non-negative numbers. */
499 if (vsign < 0) {
500 /* "Multiply both sides" by -1; this also swaps the
501 * comparator.
502 */
503 i = -i;
504 op = _Py_SwappedOp[op];
505 }
506 assert(i > 0.0);
507 (void) frexp(i, &exponent);
508 /* exponent is the # of bits in v before the radix point;
509 * we know that nbits (the # of bits in w) > 48 at this point
510 */
511 if (exponent < 0 || (size_t)exponent < nbits) {
512 i = 1.0;
513 j = 2.0;
514 goto Compare;
515 }
516 if ((size_t)exponent > nbits) {
517 i = 2.0;
518 j = 1.0;
519 goto Compare;
520 }
521 /* v and w have the same number of bits before the radix
522 * point. Construct two longs that have the same comparison
523 * outcome.
524 */
525 {
526 double fracpart;
527 double intpart;
528 PyObject *result = NULL;
529 PyObject *one = NULL;
530 PyObject *vv = NULL;
531 PyObject *ww = w;
[2]532
[391]533 if (wsign < 0) {
534 ww = PyNumber_Negative(w);
535 if (ww == NULL)
536 goto Error;
537 }
538 else
539 Py_INCREF(ww);
[2]540
[391]541 fracpart = modf(i, &intpart);
542 vv = PyLong_FromDouble(intpart);
543 if (vv == NULL)
544 goto Error;
[2]545
[391]546 if (fracpart != 0.0) {
547 /* Shift left, and or a 1 bit into vv
548 * to represent the lost fraction.
549 */
550 PyObject *temp;
[2]551
[391]552 one = PyInt_FromLong(1);
553 if (one == NULL)
554 goto Error;
[2]555
[391]556 temp = PyNumber_Lshift(ww, one);
557 if (temp == NULL)
558 goto Error;
559 Py_DECREF(ww);
560 ww = temp;
[2]561
[391]562 temp = PyNumber_Lshift(vv, one);
563 if (temp == NULL)
564 goto Error;
565 Py_DECREF(vv);
566 vv = temp;
[2]567
[391]568 temp = PyNumber_Or(vv, one);
569 if (temp == NULL)
570 goto Error;
571 Py_DECREF(vv);
572 vv = temp;
573 }
[2]574
[391]575 r = PyObject_RichCompareBool(vv, ww, op);
576 if (r < 0)
577 goto Error;
578 result = PyBool_FromLong(r);
579 Error:
580 Py_XDECREF(vv);
581 Py_XDECREF(ww);
582 Py_XDECREF(one);
583 return result;
584 }
585 } /* else if (PyLong_Check(w)) */
[2]586
[391]587 else /* w isn't float, int, or long */
588 goto Unimplemented;
[2]589
590 Compare:
[391]591 PyFPE_START_PROTECT("richcompare", return NULL)
592 switch (op) {
593 case Py_EQ:
594 r = i == j;
595 break;
596 case Py_NE:
597 r = i != j;
598 break;
599 case Py_LE:
600 r = i <= j;
601 break;
602 case Py_GE:
603 r = i >= j;
604 break;
605 case Py_LT:
606 r = i < j;
607 break;
608 case Py_GT:
609 r = i > j;
610 break;
611 }
612 PyFPE_END_PROTECT(r)
613 return PyBool_FromLong(r);
[2]614
615 Unimplemented:
[391]616 Py_INCREF(Py_NotImplemented);
617 return Py_NotImplemented;
[2]618}
619
620static long
621float_hash(PyFloatObject *v)
622{
[391]623 return _Py_HashDouble(v->ob_fval);
[2]624}
625
626static PyObject *
627float_add(PyObject *v, PyObject *w)
628{
[391]629 double a,b;
630 CONVERT_TO_DOUBLE(v, a);
631 CONVERT_TO_DOUBLE(w, b);
632 PyFPE_START_PROTECT("add", return 0)
633 a = a + b;
634 PyFPE_END_PROTECT(a)
635 return PyFloat_FromDouble(a);
[2]636}
637
638static PyObject *
639float_sub(PyObject *v, PyObject *w)
640{
[391]641 double a,b;
642 CONVERT_TO_DOUBLE(v, a);
643 CONVERT_TO_DOUBLE(w, b);
644 PyFPE_START_PROTECT("subtract", return 0)
645 a = a - b;
646 PyFPE_END_PROTECT(a)
647 return PyFloat_FromDouble(a);
[2]648}
649
650static PyObject *
651float_mul(PyObject *v, PyObject *w)
652{
[391]653 double a,b;
654 CONVERT_TO_DOUBLE(v, a);
655 CONVERT_TO_DOUBLE(w, b);
656 PyFPE_START_PROTECT("multiply", return 0)
657 a = a * b;
658 PyFPE_END_PROTECT(a)
659 return PyFloat_FromDouble(a);
[2]660}
661
662static PyObject *
663float_div(PyObject *v, PyObject *w)
664{
[391]665 double a,b;
666 CONVERT_TO_DOUBLE(v, a);
667 CONVERT_TO_DOUBLE(w, b);
[2]668#ifdef Py_NAN
[391]669 if (b == 0.0) {
670 PyErr_SetString(PyExc_ZeroDivisionError,
671 "float division by zero");
672 return NULL;
673 }
[2]674#endif
[391]675 PyFPE_START_PROTECT("divide", return 0)
676 a = a / b;
677 PyFPE_END_PROTECT(a)
678 return PyFloat_FromDouble(a);
[2]679}
680
681static PyObject *
682float_classic_div(PyObject *v, PyObject *w)
683{
[391]684 double a,b;
685 CONVERT_TO_DOUBLE(v, a);
686 CONVERT_TO_DOUBLE(w, b);
687 if (Py_DivisionWarningFlag >= 2 &&
688 PyErr_Warn(PyExc_DeprecationWarning, "classic float division") < 0)
689 return NULL;
[2]690#ifdef Py_NAN
[391]691 if (b == 0.0) {
692 PyErr_SetString(PyExc_ZeroDivisionError,
693 "float division by zero");
694 return NULL;
695 }
[2]696#endif
[391]697 PyFPE_START_PROTECT("divide", return 0)
698 a = a / b;
699 PyFPE_END_PROTECT(a)
700 return PyFloat_FromDouble(a);
[2]701}
702
703static PyObject *
704float_rem(PyObject *v, PyObject *w)
705{
[391]706 double vx, wx;
707 double mod;
708 CONVERT_TO_DOUBLE(v, vx);
709 CONVERT_TO_DOUBLE(w, wx);
[2]710#ifdef Py_NAN
[391]711 if (wx == 0.0) {
712 PyErr_SetString(PyExc_ZeroDivisionError,
713 "float modulo");
714 return NULL;
715 }
[2]716#endif
[391]717 PyFPE_START_PROTECT("modulo", return 0)
718 mod = fmod(vx, wx);
719 if (mod) {
720 /* ensure the remainder has the same sign as the denominator */
721 if ((wx < 0) != (mod < 0)) {
722 mod += wx;
723 }
724 }
725 else {
726 /* the remainder is zero, and in the presence of signed zeroes
727 fmod returns different results across platforms; ensure
728 it has the same sign as the denominator; we'd like to do
729 "mod = wx * 0.0", but that may get optimized away */
730 mod *= mod; /* hide "mod = +0" from optimizer */
731 if (wx < 0.0)
732 mod = -mod;
733 }
734 PyFPE_END_PROTECT(mod)
735 return PyFloat_FromDouble(mod);
[2]736}
737
738static PyObject *
739float_divmod(PyObject *v, PyObject *w)
740{
[391]741 double vx, wx;
742 double div, mod, floordiv;
743 CONVERT_TO_DOUBLE(v, vx);
744 CONVERT_TO_DOUBLE(w, wx);
745 if (wx == 0.0) {
746 PyErr_SetString(PyExc_ZeroDivisionError, "float divmod()");
747 return NULL;
748 }
749 PyFPE_START_PROTECT("divmod", return 0)
750 mod = fmod(vx, wx);
751 /* fmod is typically exact, so vx-mod is *mathematically* an
752 exact multiple of wx. But this is fp arithmetic, and fp
753 vx - mod is an approximation; the result is that div may
754 not be an exact integral value after the division, although
755 it will always be very close to one.
756 */
757 div = (vx - mod) / wx;
758 if (mod) {
759 /* ensure the remainder has the same sign as the denominator */
760 if ((wx < 0) != (mod < 0)) {
761 mod += wx;
762 div -= 1.0;
763 }
764 }
765 else {
766 /* the remainder is zero, and in the presence of signed zeroes
767 fmod returns different results across platforms; ensure
768 it has the same sign as the denominator; we'd like to do
769 "mod = wx * 0.0", but that may get optimized away */
770 mod *= mod; /* hide "mod = +0" from optimizer */
771 if (wx < 0.0)
772 mod = -mod;
773 }
774 /* snap quotient to nearest integral value */
775 if (div) {
776 floordiv = floor(div);
777 if (div - floordiv > 0.5)
778 floordiv += 1.0;
779 }
780 else {
781 /* div is zero - get the same sign as the true quotient */
782 div *= div; /* hide "div = +0" from optimizers */
783 floordiv = div * vx / wx; /* zero w/ sign of vx/wx */
784 }
785 PyFPE_END_PROTECT(floordiv)
786 return Py_BuildValue("(dd)", floordiv, mod);
[2]787}
788
789static PyObject *
790float_floor_div(PyObject *v, PyObject *w)
791{
[391]792 PyObject *t, *r;
[2]793
[391]794 t = float_divmod(v, w);
795 if (t == NULL || t == Py_NotImplemented)
796 return t;
797 assert(PyTuple_CheckExact(t));
798 r = PyTuple_GET_ITEM(t, 0);
799 Py_INCREF(r);
800 Py_DECREF(t);
801 return r;
[2]802}
803
[391]804/* determine whether x is an odd integer or not; assumes that
805 x is not an infinity or nan. */
806#define DOUBLE_IS_ODD_INTEGER(x) (fmod(fabs(x), 2.0) == 1.0)
807
[2]808static PyObject *
809float_pow(PyObject *v, PyObject *w, PyObject *z)
810{
[391]811 double iv, iw, ix;
812 int negate_result = 0;
[2]813
[391]814 if ((PyObject *)z != Py_None) {
815 PyErr_SetString(PyExc_TypeError, "pow() 3rd argument not "
816 "allowed unless all arguments are integers");
817 return NULL;
818 }
[2]819
[391]820 CONVERT_TO_DOUBLE(v, iv);
821 CONVERT_TO_DOUBLE(w, iw);
[2]822
[391]823 /* Sort out special cases here instead of relying on pow() */
824 if (iw == 0) { /* v**0 is 1, even 0**0 */
825 return PyFloat_FromDouble(1.0);
826 }
827 if (Py_IS_NAN(iv)) { /* nan**w = nan, unless w == 0 */
828 return PyFloat_FromDouble(iv);
829 }
830 if (Py_IS_NAN(iw)) { /* v**nan = nan, unless v == 1; 1**nan = 1 */
831 return PyFloat_FromDouble(iv == 1.0 ? 1.0 : iw);
832 }
833 if (Py_IS_INFINITY(iw)) {
834 /* v**inf is: 0.0 if abs(v) < 1; 1.0 if abs(v) == 1; inf if
835 * abs(v) > 1 (including case where v infinite)
836 *
837 * v**-inf is: inf if abs(v) < 1; 1.0 if abs(v) == 1; 0.0 if
838 * abs(v) > 1 (including case where v infinite)
839 */
840 iv = fabs(iv);
841 if (iv == 1.0)
842 return PyFloat_FromDouble(1.0);
843 else if ((iw > 0.0) == (iv > 1.0))
844 return PyFloat_FromDouble(fabs(iw)); /* return inf */
845 else
846 return PyFloat_FromDouble(0.0);
847 }
848 if (Py_IS_INFINITY(iv)) {
849 /* (+-inf)**w is: inf for w positive, 0 for w negative; in
850 * both cases, we need to add the appropriate sign if w is
851 * an odd integer.
852 */
853 int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw);
854 if (iw > 0.0)
855 return PyFloat_FromDouble(iw_is_odd ? iv : fabs(iv));
856 else
857 return PyFloat_FromDouble(iw_is_odd ?
858 copysign(0.0, iv) : 0.0);
859 }
860 if (iv == 0.0) { /* 0**w is: 0 for w positive, 1 for w zero
861 (already dealt with above), and an error
862 if w is negative. */
863 int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw);
864 if (iw < 0.0) {
865 PyErr_SetString(PyExc_ZeroDivisionError,
866 "0.0 cannot be raised to a "
867 "negative power");
868 return NULL;
869 }
870 /* use correct sign if iw is odd */
871 return PyFloat_FromDouble(iw_is_odd ? iv : 0.0);
872 }
873
874 if (iv < 0.0) {
875 /* Whether this is an error is a mess, and bumps into libm
876 * bugs so we have to figure it out ourselves.
877 */
878 if (iw != floor(iw)) {
879 PyErr_SetString(PyExc_ValueError, "negative number "
880 "cannot be raised to a fractional power");
881 return NULL;
882 }
883 /* iw is an exact integer, albeit perhaps a very large
884 * one. Replace iv by its absolute value and remember
885 * to negate the pow result if iw is odd.
886 */
887 iv = -iv;
888 negate_result = DOUBLE_IS_ODD_INTEGER(iw);
889 }
890
891 if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */
892 /* (-1) ** large_integer also ends up here. Here's an
893 * extract from the comments for the previous
894 * implementation explaining why this special case is
895 * necessary:
896 *
897 * -1 raised to an exact integer should never be exceptional.
898 * Alas, some libms (chiefly glibc as of early 2003) return
899 * NaN and set EDOM on pow(-1, large_int) if the int doesn't
900 * happen to be representable in a *C* integer. That's a
901 * bug.
902 */
903 return PyFloat_FromDouble(negate_result ? -1.0 : 1.0);
904 }
905
906 /* Now iv and iw are finite, iw is nonzero, and iv is
907 * positive and not equal to 1.0. We finally allow
908 * the platform pow to step in and do the rest.
909 */
910 errno = 0;
911 PyFPE_START_PROTECT("pow", return NULL)
912 ix = pow(iv, iw);
913 PyFPE_END_PROTECT(ix)
914 Py_ADJUST_ERANGE1(ix);
915 if (negate_result)
916 ix = -ix;
917
918 if (errno != 0) {
919 /* We don't expect any errno value other than ERANGE, but
920 * the range of libm bugs appears unbounded.
921 */
922 PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError :
923 PyExc_ValueError);
924 return NULL;
925 }
926 return PyFloat_FromDouble(ix);
[2]927}
928
[391]929#undef DOUBLE_IS_ODD_INTEGER
930
[2]931static PyObject *
932float_neg(PyFloatObject *v)
933{
[391]934 return PyFloat_FromDouble(-v->ob_fval);
[2]935}
936
937static PyObject *
938float_abs(PyFloatObject *v)
939{
[391]940 return PyFloat_FromDouble(fabs(v->ob_fval));
[2]941}
942
943static int
944float_nonzero(PyFloatObject *v)
945{
[391]946 return v->ob_fval != 0.0;
[2]947}
948
949static int
950float_coerce(PyObject **pv, PyObject **pw)
951{
[391]952 if (PyInt_Check(*pw)) {
953 long x = PyInt_AsLong(*pw);
954 *pw = PyFloat_FromDouble((double)x);
955 Py_INCREF(*pv);
956 return 0;
957 }
958 else if (PyLong_Check(*pw)) {
959 double x = PyLong_AsDouble(*pw);
960 if (x == -1.0 && PyErr_Occurred())
961 return -1;
962 *pw = PyFloat_FromDouble(x);
963 Py_INCREF(*pv);
964 return 0;
965 }
966 else if (PyFloat_Check(*pw)) {
967 Py_INCREF(*pv);
968 Py_INCREF(*pw);
969 return 0;
970 }
971 return 1; /* Can't do it */
[2]972}
973
974static PyObject *
975float_is_integer(PyObject *v)
976{
[391]977 double x = PyFloat_AsDouble(v);
978 PyObject *o;
979
980 if (x == -1.0 && PyErr_Occurred())
981 return NULL;
982 if (!Py_IS_FINITE(x))
983 Py_RETURN_FALSE;
984 errno = 0;
985 PyFPE_START_PROTECT("is_integer", return NULL)
986 o = (floor(x) == x) ? Py_True : Py_False;
987 PyFPE_END_PROTECT(x)
988 if (errno != 0) {
989 PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError :
990 PyExc_ValueError);
991 return NULL;
992 }
993 Py_INCREF(o);
994 return o;
[2]995}
996
997#if 0
998static PyObject *
999float_is_inf(PyObject *v)
1000{
[391]1001 double x = PyFloat_AsDouble(v);
1002 if (x == -1.0 && PyErr_Occurred())
1003 return NULL;
1004 return PyBool_FromLong((long)Py_IS_INFINITY(x));
[2]1005}
1006
1007static PyObject *
1008float_is_nan(PyObject *v)
1009{
[391]1010 double x = PyFloat_AsDouble(v);
1011 if (x == -1.0 && PyErr_Occurred())
1012 return NULL;
1013 return PyBool_FromLong((long)Py_IS_NAN(x));
[2]1014}
1015
1016static PyObject *
1017float_is_finite(PyObject *v)
1018{
[391]1019 double x = PyFloat_AsDouble(v);
1020 if (x == -1.0 && PyErr_Occurred())
1021 return NULL;
1022 return PyBool_FromLong((long)Py_IS_FINITE(x));
[2]1023}
1024#endif
1025
1026static PyObject *
1027float_trunc(PyObject *v)
1028{
[391]1029 double x = PyFloat_AsDouble(v);
1030 double wholepart; /* integral portion of x, rounded toward 0 */
[2]1031
[391]1032 (void)modf(x, &wholepart);
1033 /* Try to get out cheap if this fits in a Python int. The attempt
1034 * to cast to long must be protected, as C doesn't define what
1035 * happens if the double is too big to fit in a long. Some rare
1036 * systems raise an exception then (RISCOS was mentioned as one,
1037 * and someone using a non-default option on Sun also bumped into
1038 * that). Note that checking for <= LONG_MAX is unsafe: if a long
1039 * has more bits of precision than a double, casting LONG_MAX to
1040 * double may yield an approximation, and if that's rounded up,
1041 * then, e.g., wholepart=LONG_MAX+1 would yield true from the C
1042 * expression wholepart<=LONG_MAX, despite that wholepart is
1043 * actually greater than LONG_MAX. However, assuming a two's complement
1044 * machine with no trap representation, LONG_MIN will be a power of 2 (and
1045 * hence exactly representable as a double), and LONG_MAX = -1-LONG_MIN, so
1046 * the comparisons with (double)LONG_MIN below should be safe.
1047 */
1048 if ((double)LONG_MIN <= wholepart && wholepart < -(double)LONG_MIN) {
1049 const long aslong = (long)wholepart;
1050 return PyInt_FromLong(aslong);
1051 }
1052 return PyLong_FromDouble(wholepart);
[2]1053}
1054
1055static PyObject *
1056float_long(PyObject *v)
1057{
[391]1058 double x = PyFloat_AsDouble(v);
1059 return PyLong_FromDouble(x);
[2]1060}
1061
[391]1062/* _Py_double_round: rounds a finite nonzero double to the closest multiple of
1063 10**-ndigits; here ndigits is within reasonable bounds (typically, -308 <=
1064 ndigits <= 323). Returns a Python float, or sets a Python error and
1065 returns NULL on failure (OverflowError and memory errors are possible). */
1066
1067#ifndef PY_NO_SHORT_FLOAT_REPR
1068/* version of _Py_double_round that uses the correctly-rounded string<->double
1069 conversions from Python/dtoa.c */
1070
1071/* FIVE_POW_LIMIT is the largest k such that 5**k is exactly representable as
1072 a double. Since we're using the code in Python/dtoa.c, it should be safe
1073 to assume that C doubles are IEEE 754 binary64 format. To be on the safe
1074 side, we check this. */
1075#if DBL_MANT_DIG == 53
1076#define FIVE_POW_LIMIT 22
1077#else
1078#error "C doubles do not appear to be IEEE 754 binary64 format"
1079#endif
1080
1081PyObject *
1082_Py_double_round(double x, int ndigits) {
1083
1084 double rounded, m;
1085 Py_ssize_t buflen, mybuflen=100;
1086 char *buf, *buf_end, shortbuf[100], *mybuf=shortbuf;
1087 int decpt, sign, val, halfway_case;
1088 PyObject *result = NULL;
1089 _Py_SET_53BIT_PRECISION_HEADER;
1090
1091 /* Easy path for the common case ndigits == 0. */
1092 if (ndigits == 0) {
1093 rounded = round(x);
1094 if (fabs(rounded - x) == 0.5)
1095 /* halfway between two integers; use round-away-from-zero */
1096 rounded = x + (x > 0.0 ? 0.5 : -0.5);
1097 return PyFloat_FromDouble(rounded);
1098 }
1099
1100 /* The basic idea is very simple: convert and round the double to a
1101 decimal string using _Py_dg_dtoa, then convert that decimal string
1102 back to a double with _Py_dg_strtod. There's one minor difficulty:
1103 Python 2.x expects round to do round-half-away-from-zero, while
1104 _Py_dg_dtoa does round-half-to-even. So we need some way to detect
1105 and correct the halfway cases.
1106
1107 Detection: a halfway value has the form k * 0.5 * 10**-ndigits for
1108 some odd integer k. Or in other words, a rational number x is
1109 exactly halfway between two multiples of 10**-ndigits if its
1110 2-valuation is exactly -ndigits-1 and its 5-valuation is at least
1111 -ndigits. For ndigits >= 0 the latter condition is automatically
1112 satisfied for a binary float x, since any such float has
1113 nonnegative 5-valuation. For 0 > ndigits >= -22, x needs to be an
1114 integral multiple of 5**-ndigits; we can check this using fmod.
1115 For -22 > ndigits, there are no halfway cases: 5**23 takes 54 bits
1116 to represent exactly, so any odd multiple of 0.5 * 10**n for n >=
1117 23 takes at least 54 bits of precision to represent exactly.
1118
1119 Correction: a simple strategy for dealing with halfway cases is to
1120 (for the halfway cases only) call _Py_dg_dtoa with an argument of
1121 ndigits+1 instead of ndigits (thus doing an exact conversion to
1122 decimal), round the resulting string manually, and then convert
1123 back using _Py_dg_strtod.
1124 */
1125
1126 /* nans, infinities and zeros should have already been dealt
1127 with by the caller (in this case, builtin_round) */
1128 assert(Py_IS_FINITE(x) && x != 0.0);
1129
1130 /* find 2-valuation val of x */
1131 m = frexp(x, &val);
1132 while (m != floor(m)) {
1133 m *= 2.0;
1134 val--;
1135 }
1136
1137 /* determine whether this is a halfway case */
1138 if (val == -ndigits-1) {
1139 if (ndigits >= 0)
1140 halfway_case = 1;
1141 else if (ndigits >= -FIVE_POW_LIMIT) {
1142 double five_pow = 1.0;
1143 int i;
1144 for (i=0; i < -ndigits; i++)
1145 five_pow *= 5.0;
1146 halfway_case = fmod(x, five_pow) == 0.0;
1147 }
1148 else
1149 halfway_case = 0;
1150 }
1151 else
1152 halfway_case = 0;
1153
1154 /* round to a decimal string; use an extra place for halfway case */
1155 _Py_SET_53BIT_PRECISION_START;
1156 buf = _Py_dg_dtoa(x, 3, ndigits+halfway_case, &decpt, &sign, &buf_end);
1157 _Py_SET_53BIT_PRECISION_END;
1158 if (buf == NULL) {
1159 PyErr_NoMemory();
1160 return NULL;
1161 }
1162 buflen = buf_end - buf;
1163
1164 /* in halfway case, do the round-half-away-from-zero manually */
1165 if (halfway_case) {
1166 int i, carry;
1167 /* sanity check: _Py_dg_dtoa should not have stripped
1168 any zeros from the result: there should be exactly
1169 ndigits+1 places following the decimal point, and
1170 the last digit in the buffer should be a '5'.*/
1171 assert(buflen - decpt == ndigits+1);
1172 assert(buf[buflen-1] == '5');
1173
1174 /* increment and shift right at the same time. */
1175 decpt += 1;
1176 carry = 1;
1177 for (i=buflen-1; i-- > 0;) {
1178 carry += buf[i] - '0';
1179 buf[i+1] = carry % 10 + '0';
1180 carry /= 10;
1181 }
1182 buf[0] = carry + '0';
1183 }
1184
1185 /* Get new buffer if shortbuf is too small. Space needed <= buf_end -
1186 buf + 8: (1 extra for '0', 1 for sign, 5 for exp, 1 for '\0'). */
1187 if (buflen + 8 > mybuflen) {
1188 mybuflen = buflen+8;
1189 mybuf = (char *)PyMem_Malloc(mybuflen);
1190 if (mybuf == NULL) {
1191 PyErr_NoMemory();
1192 goto exit;
1193 }
1194 }
1195 /* copy buf to mybuf, adding exponent, sign and leading 0 */
1196 PyOS_snprintf(mybuf, mybuflen, "%s0%se%d", (sign ? "-" : ""),
1197 buf, decpt - (int)buflen);
1198
1199 /* and convert the resulting string back to a double */
1200 errno = 0;
1201 _Py_SET_53BIT_PRECISION_START;
1202 rounded = _Py_dg_strtod(mybuf, NULL);
1203 _Py_SET_53BIT_PRECISION_END;
1204 if (errno == ERANGE && fabs(rounded) >= 1.)
1205 PyErr_SetString(PyExc_OverflowError,
1206 "rounded value too large to represent");
1207 else
1208 result = PyFloat_FromDouble(rounded);
1209
1210 /* done computing value; now clean up */
1211 if (mybuf != shortbuf)
1212 PyMem_Free(mybuf);
1213 exit:
1214 _Py_dg_freedtoa(buf);
1215 return result;
1216}
1217
1218#undef FIVE_POW_LIMIT
1219
1220#else /* PY_NO_SHORT_FLOAT_REPR */
1221
1222/* fallback version, to be used when correctly rounded binary<->decimal
1223 conversions aren't available */
1224
1225PyObject *
1226_Py_double_round(double x, int ndigits) {
1227 double pow1, pow2, y, z;
1228 if (ndigits >= 0) {
1229 if (ndigits > 22) {
1230 /* pow1 and pow2 are each safe from overflow, but
1231 pow1*pow2 ~= pow(10.0, ndigits) might overflow */
1232 pow1 = pow(10.0, (double)(ndigits-22));
1233 pow2 = 1e22;
1234 }
1235 else {
1236 pow1 = pow(10.0, (double)ndigits);
1237 pow2 = 1.0;
1238 }
1239 y = (x*pow1)*pow2;
1240 /* if y overflows, then rounded value is exactly x */
1241 if (!Py_IS_FINITE(y))
1242 return PyFloat_FromDouble(x);
1243 }
1244 else {
1245 pow1 = pow(10.0, (double)-ndigits);
1246 pow2 = 1.0; /* unused; silences a gcc compiler warning */
1247 y = x / pow1;
1248 }
1249
1250 z = round(y);
1251 if (fabs(y-z) == 0.5)
1252 /* halfway between two integers; use round-away-from-zero */
1253 z = y + copysign(0.5, y);
1254
1255 if (ndigits >= 0)
1256 z = (z / pow2) / pow1;
1257 else
1258 z *= pow1;
1259
1260 /* if computation resulted in overflow, raise OverflowError */
1261 if (!Py_IS_FINITE(z)) {
1262 PyErr_SetString(PyExc_OverflowError,
1263 "overflow occurred during round");
1264 return NULL;
1265 }
1266
1267 return PyFloat_FromDouble(z);
1268}
1269
1270#endif /* PY_NO_SHORT_FLOAT_REPR */
1271
[2]1272static PyObject *
1273float_float(PyObject *v)
1274{
[391]1275 if (PyFloat_CheckExact(v))
1276 Py_INCREF(v);
1277 else
1278 v = PyFloat_FromDouble(((PyFloatObject *)v)->ob_fval);
1279 return v;
[2]1280}
1281
1282/* turn ASCII hex characters into integer values and vice versa */
1283
1284static char
1285char_from_hex(int x)
1286{
[391]1287 assert(0 <= x && x < 16);
1288 return "0123456789abcdef"[x];
[2]1289}
1290
1291static int
1292hex_from_char(char c) {
[391]1293 int x;
1294 switch(c) {
1295 case '0':
1296 x = 0;
1297 break;
1298 case '1':
1299 x = 1;
1300 break;
1301 case '2':
1302 x = 2;
1303 break;
1304 case '3':
1305 x = 3;
1306 break;
1307 case '4':
1308 x = 4;
1309 break;
1310 case '5':
1311 x = 5;
1312 break;
1313 case '6':
1314 x = 6;
1315 break;
1316 case '7':
1317 x = 7;
1318 break;
1319 case '8':
1320 x = 8;
1321 break;
1322 case '9':
1323 x = 9;
1324 break;
1325 case 'a':
1326 case 'A':
1327 x = 10;
1328 break;
1329 case 'b':
1330 case 'B':
1331 x = 11;
1332 break;
1333 case 'c':
1334 case 'C':
1335 x = 12;
1336 break;
1337 case 'd':
1338 case 'D':
1339 x = 13;
1340 break;
1341 case 'e':
1342 case 'E':
1343 x = 14;
1344 break;
1345 case 'f':
1346 case 'F':
1347 x = 15;
1348 break;
1349 default:
1350 x = -1;
1351 break;
1352 }
1353 return x;
[2]1354}
1355
1356/* convert a float to a hexadecimal string */
1357
1358/* TOHEX_NBITS is DBL_MANT_DIG rounded up to the next integer
1359 of the form 4k+1. */
1360#define TOHEX_NBITS DBL_MANT_DIG + 3 - (DBL_MANT_DIG+2)%4
1361
1362static PyObject *
1363float_hex(PyObject *v)
1364{
[391]1365 double x, m;
1366 int e, shift, i, si, esign;
1367 /* Space for 1+(TOHEX_NBITS-1)/4 digits, a decimal point, and the
1368 trailing NUL byte. */
1369 char s[(TOHEX_NBITS-1)/4+3];
[2]1370
[391]1371 CONVERT_TO_DOUBLE(v, x);
[2]1372
[391]1373 if (Py_IS_NAN(x) || Py_IS_INFINITY(x))
1374 return float_str((PyFloatObject *)v);
[2]1375
[391]1376 if (x == 0.0) {
1377 if (copysign(1.0, x) == -1.0)
1378 return PyString_FromString("-0x0.0p+0");
1379 else
1380 return PyString_FromString("0x0.0p+0");
1381 }
[2]1382
[391]1383 m = frexp(fabs(x), &e);
1384 shift = 1 - MAX(DBL_MIN_EXP - e, 0);
1385 m = ldexp(m, shift);
1386 e -= shift;
[2]1387
[391]1388 si = 0;
1389 s[si] = char_from_hex((int)m);
1390 si++;
1391 m -= (int)m;
1392 s[si] = '.';
1393 si++;
1394 for (i=0; i < (TOHEX_NBITS-1)/4; i++) {
1395 m *= 16.0;
1396 s[si] = char_from_hex((int)m);
1397 si++;
1398 m -= (int)m;
1399 }
1400 s[si] = '\0';
[2]1401
[391]1402 if (e < 0) {
1403 esign = (int)'-';
1404 e = -e;
1405 }
1406 else
1407 esign = (int)'+';
[2]1408
[391]1409 if (x < 0.0)
1410 return PyString_FromFormat("-0x%sp%c%d", s, esign, e);
1411 else
1412 return PyString_FromFormat("0x%sp%c%d", s, esign, e);
[2]1413}
1414
1415PyDoc_STRVAR(float_hex_doc,
1416"float.hex() -> string\n\
1417\n\
1418Return a hexadecimal representation of a floating-point number.\n\
1419>>> (-0.1).hex()\n\
1420'-0x1.999999999999ap-4'\n\
1421>>> 3.14159.hex()\n\
1422'0x1.921f9f01b866ep+1'");
1423
[391]1424/* Case-insensitive locale-independent string match used for nan and inf
1425 detection. t should be lower-case and null-terminated. Return a nonzero
1426 result if the first strlen(t) characters of s match t and 0 otherwise. */
[2]1427
1428static int
1429case_insensitive_match(const char *s, const char *t)
1430{
[391]1431 while(*t && Py_TOLOWER(*s) == *t) {
1432 s++;
1433 t++;
1434 }
1435 return *t ? 0 : 1;
[2]1436}
1437
1438/* Convert a hexadecimal string to a float. */
1439
1440static PyObject *
1441float_fromhex(PyObject *cls, PyObject *arg)
1442{
[391]1443 PyObject *result_as_float, *result;
1444 double x;
1445 long exp, top_exp, lsb, key_digit;
1446 char *s, *coeff_start, *s_store, *coeff_end, *exp_start, *s_end;
1447 int half_eps, digit, round_up, sign=1;
1448 Py_ssize_t length, ndigits, fdigits, i;
[2]1449
[391]1450 /*
1451 * For the sake of simplicity and correctness, we impose an artificial
1452 * limit on ndigits, the total number of hex digits in the coefficient
1453 * The limit is chosen to ensure that, writing exp for the exponent,
1454 *
1455 * (1) if exp > LONG_MAX/2 then the value of the hex string is
1456 * guaranteed to overflow (provided it's nonzero)
1457 *
1458 * (2) if exp < LONG_MIN/2 then the value of the hex string is
1459 * guaranteed to underflow to 0.
1460 *
1461 * (3) if LONG_MIN/2 <= exp <= LONG_MAX/2 then there's no danger of
1462 * overflow in the calculation of exp and top_exp below.
1463 *
1464 * More specifically, ndigits is assumed to satisfy the following
1465 * inequalities:
1466 *
1467 * 4*ndigits <= DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2
1468 * 4*ndigits <= LONG_MAX/2 + 1 - DBL_MAX_EXP
1469 *
1470 * If either of these inequalities is not satisfied, a ValueError is
1471 * raised. Otherwise, write x for the value of the hex string, and
1472 * assume x is nonzero. Then
1473 *
1474 * 2**(exp-4*ndigits) <= |x| < 2**(exp+4*ndigits).
1475 *
1476 * Now if exp > LONG_MAX/2 then:
1477 *
1478 * exp - 4*ndigits >= LONG_MAX/2 + 1 - (LONG_MAX/2 + 1 - DBL_MAX_EXP)
1479 * = DBL_MAX_EXP
1480 *
1481 * so |x| >= 2**DBL_MAX_EXP, which is too large to be stored in C
1482 * double, so overflows. If exp < LONG_MIN/2, then
1483 *
1484 * exp + 4*ndigits <= LONG_MIN/2 - 1 + (
1485 * DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2)
1486 * = DBL_MIN_EXP - DBL_MANT_DIG - 1
1487 *
1488 * and so |x| < 2**(DBL_MIN_EXP-DBL_MANT_DIG-1), hence underflows to 0
1489 * when converted to a C double.
1490 *
1491 * It's easy to show that if LONG_MIN/2 <= exp <= LONG_MAX/2 then both
1492 * exp+4*ndigits and exp-4*ndigits are within the range of a long.
1493 */
[2]1494
[391]1495 if (PyString_AsStringAndSize(arg, &s, &length))
1496 return NULL;
1497 s_end = s + length;
[2]1498
[391]1499 /********************
1500 * Parse the string *
1501 ********************/
[2]1502
[391]1503 /* leading whitespace and optional sign */
1504 while (Py_ISSPACE(*s))
1505 s++;
1506 if (*s == '-') {
1507 s++;
1508 sign = -1;
1509 }
1510 else if (*s == '+')
1511 s++;
[2]1512
[391]1513 /* infinities and nans */
1514 if (*s == 'i' || *s == 'I') {
1515 if (!case_insensitive_match(s+1, "nf"))
1516 goto parse_error;
1517 s += 3;
1518 x = Py_HUGE_VAL;
1519 if (case_insensitive_match(s, "inity"))
1520 s += 5;
1521 goto finished;
1522 }
1523 if (*s == 'n' || *s == 'N') {
1524 if (!case_insensitive_match(s+1, "an"))
1525 goto parse_error;
1526 s += 3;
1527 x = Py_NAN;
1528 goto finished;
1529 }
[2]1530
[391]1531 /* [0x] */
1532 s_store = s;
1533 if (*s == '0') {
1534 s++;
1535 if (*s == 'x' || *s == 'X')
1536 s++;
1537 else
1538 s = s_store;
1539 }
[2]1540
[391]1541 /* coefficient: <integer> [. <fraction>] */
1542 coeff_start = s;
1543 while (hex_from_char(*s) >= 0)
1544 s++;
1545 s_store = s;
1546 if (*s == '.') {
1547 s++;
1548 while (hex_from_char(*s) >= 0)
1549 s++;
1550 coeff_end = s-1;
1551 }
1552 else
1553 coeff_end = s;
[2]1554
[391]1555 /* ndigits = total # of hex digits; fdigits = # after point */
1556 ndigits = coeff_end - coeff_start;
1557 fdigits = coeff_end - s_store;
1558 if (ndigits == 0)
1559 goto parse_error;
1560 if (ndigits > MIN(DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2,
1561 LONG_MAX/2 + 1 - DBL_MAX_EXP)/4)
1562 goto insane_length_error;
[2]1563
[391]1564 /* [p <exponent>] */
1565 if (*s == 'p' || *s == 'P') {
1566 s++;
1567 exp_start = s;
1568 if (*s == '-' || *s == '+')
1569 s++;
1570 if (!('0' <= *s && *s <= '9'))
1571 goto parse_error;
1572 s++;
1573 while ('0' <= *s && *s <= '9')
1574 s++;
1575 exp = strtol(exp_start, NULL, 10);
1576 }
1577 else
1578 exp = 0;
[2]1579
1580/* for 0 <= j < ndigits, HEX_DIGIT(j) gives the jth most significant digit */
[391]1581#define HEX_DIGIT(j) hex_from_char(*((j) < fdigits ? \
1582 coeff_end-(j) : \
1583 coeff_end-1-(j)))
[2]1584
[391]1585 /*******************************************
1586 * Compute rounded value of the hex string *
1587 *******************************************/
[2]1588
[391]1589 /* Discard leading zeros, and catch extreme overflow and underflow */
1590 while (ndigits > 0 && HEX_DIGIT(ndigits-1) == 0)
1591 ndigits--;
1592 if (ndigits == 0 || exp < LONG_MIN/2) {
1593 x = 0.0;
1594 goto finished;
1595 }
1596 if (exp > LONG_MAX/2)
1597 goto overflow_error;
[2]1598
[391]1599 /* Adjust exponent for fractional part. */
1600 exp = exp - 4*((long)fdigits);
[2]1601
[391]1602 /* top_exp = 1 more than exponent of most sig. bit of coefficient */
1603 top_exp = exp + 4*((long)ndigits - 1);
1604 for (digit = HEX_DIGIT(ndigits-1); digit != 0; digit /= 2)
1605 top_exp++;
[2]1606
[391]1607 /* catch almost all nonextreme cases of overflow and underflow here */
1608 if (top_exp < DBL_MIN_EXP - DBL_MANT_DIG) {
1609 x = 0.0;
1610 goto finished;
1611 }
1612 if (top_exp > DBL_MAX_EXP)
1613 goto overflow_error;
[2]1614
[391]1615 /* lsb = exponent of least significant bit of the *rounded* value.
1616 This is top_exp - DBL_MANT_DIG unless result is subnormal. */
1617 lsb = MAX(top_exp, (long)DBL_MIN_EXP) - DBL_MANT_DIG;
[2]1618
[391]1619 x = 0.0;
1620 if (exp >= lsb) {
1621 /* no rounding required */
1622 for (i = ndigits-1; i >= 0; i--)
1623 x = 16.0*x + HEX_DIGIT(i);
1624 x = ldexp(x, (int)(exp));
1625 goto finished;
1626 }
1627 /* rounding required. key_digit is the index of the hex digit
1628 containing the first bit to be rounded away. */
1629 half_eps = 1 << (int)((lsb - exp - 1) % 4);
1630 key_digit = (lsb - exp - 1) / 4;
1631 for (i = ndigits-1; i > key_digit; i--)
1632 x = 16.0*x + HEX_DIGIT(i);
1633 digit = HEX_DIGIT(key_digit);
1634 x = 16.0*x + (double)(digit & (16-2*half_eps));
[2]1635
[391]1636 /* round-half-even: round up if bit lsb-1 is 1 and at least one of
1637 bits lsb, lsb-2, lsb-3, lsb-4, ... is 1. */
1638 if ((digit & half_eps) != 0) {
1639 round_up = 0;
1640 if ((digit & (3*half_eps-1)) != 0 ||
1641 (half_eps == 8 && (HEX_DIGIT(key_digit+1) & 1) != 0))
1642 round_up = 1;
1643 else
1644 for (i = key_digit-1; i >= 0; i--)
1645 if (HEX_DIGIT(i) != 0) {
1646 round_up = 1;
1647 break;
1648 }
1649 if (round_up == 1) {
1650 x += 2*half_eps;
1651 if (top_exp == DBL_MAX_EXP &&
1652 x == ldexp((double)(2*half_eps), DBL_MANT_DIG))
1653 /* overflow corner case: pre-rounded value <
1654 2**DBL_MAX_EXP; rounded=2**DBL_MAX_EXP. */
1655 goto overflow_error;
1656 }
1657 }
1658 x = ldexp(x, (int)(exp+4*key_digit));
[2]1659
1660 finished:
[391]1661 /* optional trailing whitespace leading to the end of the string */
1662 while (Py_ISSPACE(*s))
1663 s++;
1664 if (s != s_end)
1665 goto parse_error;
1666 result_as_float = Py_BuildValue("(d)", sign * x);
1667 if (result_as_float == NULL)
1668 return NULL;
1669 result = PyObject_CallObject(cls, result_as_float);
1670 Py_DECREF(result_as_float);
1671 return result;
[2]1672
1673 overflow_error:
[391]1674 PyErr_SetString(PyExc_OverflowError,
1675 "hexadecimal value too large to represent as a float");
1676 return NULL;
[2]1677
1678 parse_error:
[391]1679 PyErr_SetString(PyExc_ValueError,
1680 "invalid hexadecimal floating-point string");
1681 return NULL;
[2]1682
1683 insane_length_error:
[391]1684 PyErr_SetString(PyExc_ValueError,
1685 "hexadecimal string too long to convert");
1686 return NULL;
[2]1687}
1688
1689PyDoc_STRVAR(float_fromhex_doc,
1690"float.fromhex(string) -> float\n\
1691\n\
1692Create a floating-point number from a hexadecimal string.\n\
1693>>> float.fromhex('0x1.ffffp10')\n\
16942047.984375\n\
1695>>> float.fromhex('-0x1p-1074')\n\
1696-4.9406564584124654e-324");
1697
1698
1699static PyObject *
1700float_as_integer_ratio(PyObject *v, PyObject *unused)
1701{
[391]1702 double self;
1703 double float_part;
1704 int exponent;
1705 int i;
[2]1706
[391]1707 PyObject *prev;
1708 PyObject *py_exponent = NULL;
1709 PyObject *numerator = NULL;
1710 PyObject *denominator = NULL;
1711 PyObject *result_pair = NULL;
1712 PyNumberMethods *long_methods = PyLong_Type.tp_as_number;
[2]1713
1714#define INPLACE_UPDATE(obj, call) \
[391]1715 prev = obj; \
1716 obj = call; \
1717 Py_DECREF(prev); \
[2]1718
[391]1719 CONVERT_TO_DOUBLE(v, self);
[2]1720
[391]1721 if (Py_IS_INFINITY(self)) {
1722 PyErr_SetString(PyExc_OverflowError,
1723 "Cannot pass infinity to float.as_integer_ratio.");
1724 return NULL;
1725 }
[2]1726#ifdef Py_NAN
[391]1727 if (Py_IS_NAN(self)) {
1728 PyErr_SetString(PyExc_ValueError,
1729 "Cannot pass NaN to float.as_integer_ratio.");
1730 return NULL;
1731 }
[2]1732#endif
1733
[391]1734 PyFPE_START_PROTECT("as_integer_ratio", goto error);
1735 float_part = frexp(self, &exponent); /* self == float_part * 2**exponent exactly */
1736 PyFPE_END_PROTECT(float_part);
[2]1737
[391]1738 for (i=0; i<300 && float_part != floor(float_part) ; i++) {
1739 float_part *= 2.0;
1740 exponent--;
1741 }
1742 /* self == float_part * 2**exponent exactly and float_part is integral.
1743 If FLT_RADIX != 2, the 300 steps may leave a tiny fractional part
1744 to be truncated by PyLong_FromDouble(). */
[2]1745
[391]1746 numerator = PyLong_FromDouble(float_part);
1747 if (numerator == NULL) goto error;
[2]1748
[391]1749 /* fold in 2**exponent */
1750 denominator = PyLong_FromLong(1);
1751 py_exponent = PyLong_FromLong(labs((long)exponent));
1752 if (py_exponent == NULL) goto error;
1753 INPLACE_UPDATE(py_exponent,
1754 long_methods->nb_lshift(denominator, py_exponent));
1755 if (py_exponent == NULL) goto error;
1756 if (exponent > 0) {
1757 INPLACE_UPDATE(numerator,
1758 long_methods->nb_multiply(numerator, py_exponent));
1759 if (numerator == NULL) goto error;
1760 }
1761 else {
1762 Py_DECREF(denominator);
1763 denominator = py_exponent;
1764 py_exponent = NULL;
1765 }
[2]1766
[391]1767 /* Returns ints instead of longs where possible */
1768 INPLACE_UPDATE(numerator, PyNumber_Int(numerator));
1769 if (numerator == NULL) goto error;
1770 INPLACE_UPDATE(denominator, PyNumber_Int(denominator));
1771 if (denominator == NULL) goto error;
[2]1772
[391]1773 result_pair = PyTuple_Pack(2, numerator, denominator);
1774
[2]1775#undef INPLACE_UPDATE
1776error:
[391]1777 Py_XDECREF(py_exponent);
1778 Py_XDECREF(denominator);
1779 Py_XDECREF(numerator);
1780 return result_pair;
[2]1781}
1782
1783PyDoc_STRVAR(float_as_integer_ratio_doc,
1784"float.as_integer_ratio() -> (int, int)\n"
1785"\n"
[391]1786"Return a pair of integers, whose ratio is exactly equal to the original\n"
[2]1787"float and with a positive denominator.\n"
[391]1788"Raise OverflowError on infinities and a ValueError on NaNs.\n"
[2]1789"\n"
1790">>> (10.0).as_integer_ratio()\n"
1791"(10, 1)\n"
1792">>> (0.0).as_integer_ratio()\n"
1793"(0, 1)\n"
1794">>> (-.25).as_integer_ratio()\n"
1795"(-1, 4)");
1796
1797
1798static PyObject *
1799float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds);
1800
1801static PyObject *
1802float_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
1803{
[391]1804 PyObject *x = Py_False; /* Integer zero */
1805 static char *kwlist[] = {"x", 0};
[2]1806
[391]1807 if (type != &PyFloat_Type)
1808 return float_subtype_new(type, args, kwds); /* Wimp out */
1809 if (!PyArg_ParseTupleAndKeywords(args, kwds, "|O:float", kwlist, &x))
1810 return NULL;
1811 /* If it's a string, but not a string subclass, use
1812 PyFloat_FromString. */
1813 if (PyString_CheckExact(x))
1814 return PyFloat_FromString(x, NULL);
1815 return PyNumber_Float(x);
[2]1816}
1817
1818/* Wimpy, slow approach to tp_new calls for subtypes of float:
1819 first create a regular float from whatever arguments we got,
1820 then allocate a subtype instance and initialize its ob_fval
1821 from the regular float. The regular float is then thrown away.
1822*/
1823static PyObject *
1824float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
1825{
[391]1826 PyObject *tmp, *newobj;
[2]1827
[391]1828 assert(PyType_IsSubtype(type, &PyFloat_Type));
1829 tmp = float_new(&PyFloat_Type, args, kwds);
1830 if (tmp == NULL)
1831 return NULL;
1832 assert(PyFloat_CheckExact(tmp));
1833 newobj = type->tp_alloc(type, 0);
1834 if (newobj == NULL) {
1835 Py_DECREF(tmp);
1836 return NULL;
1837 }
1838 ((PyFloatObject *)newobj)->ob_fval = ((PyFloatObject *)tmp)->ob_fval;
1839 Py_DECREF(tmp);
1840 return newobj;
[2]1841}
1842
1843static PyObject *
1844float_getnewargs(PyFloatObject *v)
1845{
[391]1846 return Py_BuildValue("(d)", v->ob_fval);
[2]1847}
1848
1849/* this is for the benefit of the pack/unpack routines below */
1850
1851typedef enum {
[391]1852 unknown_format, ieee_big_endian_format, ieee_little_endian_format
[2]1853} float_format_type;
1854
1855static float_format_type double_format, float_format;
1856static float_format_type detected_double_format, detected_float_format;
1857
1858static PyObject *
1859float_getformat(PyTypeObject *v, PyObject* arg)
1860{
[391]1861 char* s;
1862 float_format_type r;
[2]1863
[391]1864 if (!PyString_Check(arg)) {
1865 PyErr_Format(PyExc_TypeError,
1866 "__getformat__() argument must be string, not %.500s",
1867 Py_TYPE(arg)->tp_name);
1868 return NULL;
1869 }
1870 s = PyString_AS_STRING(arg);
1871 if (strcmp(s, "double") == 0) {
1872 r = double_format;
1873 }
1874 else if (strcmp(s, "float") == 0) {
1875 r = float_format;
1876 }
1877 else {
1878 PyErr_SetString(PyExc_ValueError,
1879 "__getformat__() argument 1 must be "
1880 "'double' or 'float'");
1881 return NULL;
1882 }
1883
1884 switch (r) {
1885 case unknown_format:
1886 return PyString_FromString("unknown");
1887 case ieee_little_endian_format:
1888 return PyString_FromString("IEEE, little-endian");
1889 case ieee_big_endian_format:
1890 return PyString_FromString("IEEE, big-endian");
1891 default:
1892 Py_FatalError("insane float_format or double_format");
1893 return NULL;
1894 }
[2]1895}
1896
1897PyDoc_STRVAR(float_getformat_doc,
1898"float.__getformat__(typestr) -> string\n"
1899"\n"
1900"You probably don't want to use this function. It exists mainly to be\n"
1901"used in Python's test suite.\n"
1902"\n"
1903"typestr must be 'double' or 'float'. This function returns whichever of\n"
1904"'unknown', 'IEEE, big-endian' or 'IEEE, little-endian' best describes the\n"
1905"format of floating point numbers used by the C type named by typestr.");
1906
1907static PyObject *
1908float_setformat(PyTypeObject *v, PyObject* args)
1909{
[391]1910 char* typestr;
1911 char* format;
1912 float_format_type f;
1913 float_format_type detected;
1914 float_format_type *p;
[2]1915
[391]1916 if (!PyArg_ParseTuple(args, "ss:__setformat__", &typestr, &format))
1917 return NULL;
[2]1918
[391]1919 if (strcmp(typestr, "double") == 0) {
1920 p = &double_format;
1921 detected = detected_double_format;
1922 }
1923 else if (strcmp(typestr, "float") == 0) {
1924 p = &float_format;
1925 detected = detected_float_format;
1926 }
1927 else {
1928 PyErr_SetString(PyExc_ValueError,
1929 "__setformat__() argument 1 must "
1930 "be 'double' or 'float'");
1931 return NULL;
1932 }
[2]1933
[391]1934 if (strcmp(format, "unknown") == 0) {
1935 f = unknown_format;
1936 }
1937 else if (strcmp(format, "IEEE, little-endian") == 0) {
1938 f = ieee_little_endian_format;
1939 }
1940 else if (strcmp(format, "IEEE, big-endian") == 0) {
1941 f = ieee_big_endian_format;
1942 }
1943 else {
1944 PyErr_SetString(PyExc_ValueError,
1945 "__setformat__() argument 2 must be "
1946 "'unknown', 'IEEE, little-endian' or "
1947 "'IEEE, big-endian'");
1948 return NULL;
[2]1949
[391]1950 }
[2]1951
[391]1952 if (f != unknown_format && f != detected) {
1953 PyErr_Format(PyExc_ValueError,
1954 "can only set %s format to 'unknown' or the "
1955 "detected platform value", typestr);
1956 return NULL;
1957 }
1958
1959 *p = f;
1960 Py_RETURN_NONE;
[2]1961}
1962
1963PyDoc_STRVAR(float_setformat_doc,
1964"float.__setformat__(typestr, fmt) -> None\n"
1965"\n"
1966"You probably don't want to use this function. It exists mainly to be\n"
1967"used in Python's test suite.\n"
1968"\n"
1969"typestr must be 'double' or 'float'. fmt must be one of 'unknown',\n"
1970"'IEEE, big-endian' or 'IEEE, little-endian', and in addition can only be\n"
1971"one of the latter two if it appears to match the underlying C reality.\n"
1972"\n"
[391]1973"Override the automatic determination of C-level floating point type.\n"
[2]1974"This affects how floats are converted to and from binary strings.");
1975
1976static PyObject *
1977float_getzero(PyObject *v, void *closure)
1978{
[391]1979 return PyFloat_FromDouble(0.0);
[2]1980}
1981
1982static PyObject *
1983float__format__(PyObject *self, PyObject *args)
1984{
[391]1985 PyObject *format_spec;
[2]1986
[391]1987 if (!PyArg_ParseTuple(args, "O:__format__", &format_spec))
1988 return NULL;
1989 if (PyBytes_Check(format_spec))
1990 return _PyFloat_FormatAdvanced(self,
1991 PyBytes_AS_STRING(format_spec),
1992 PyBytes_GET_SIZE(format_spec));
1993 if (PyUnicode_Check(format_spec)) {
1994 /* Convert format_spec to a str */
1995 PyObject *result;
1996 PyObject *str_spec = PyObject_Str(format_spec);
[2]1997
[391]1998 if (str_spec == NULL)
1999 return NULL;
[2]2000
[391]2001 result = _PyFloat_FormatAdvanced(self,
2002 PyBytes_AS_STRING(str_spec),
2003 PyBytes_GET_SIZE(str_spec));
[2]2004
[391]2005 Py_DECREF(str_spec);
2006 return result;
2007 }
2008 PyErr_SetString(PyExc_TypeError, "__format__ requires str or unicode");
2009 return NULL;
[2]2010}
2011
2012PyDoc_STRVAR(float__format__doc,
2013"float.__format__(format_spec) -> string\n"
2014"\n"
2015"Formats the float according to format_spec.");
2016
2017
2018static PyMethodDef float_methods[] = {
[391]2019 {"conjugate", (PyCFunction)float_float, METH_NOARGS,
2020 "Return self, the complex conjugate of any float."},
2021 {"__trunc__", (PyCFunction)float_trunc, METH_NOARGS,
2022 "Return the Integral closest to x between 0 and x."},
2023 {"as_integer_ratio", (PyCFunction)float_as_integer_ratio, METH_NOARGS,
2024 float_as_integer_ratio_doc},
2025 {"fromhex", (PyCFunction)float_fromhex,
2026 METH_O|METH_CLASS, float_fromhex_doc},
2027 {"hex", (PyCFunction)float_hex,
2028 METH_NOARGS, float_hex_doc},
2029 {"is_integer", (PyCFunction)float_is_integer, METH_NOARGS,
2030 "Return True if the float is an integer."},
[2]2031#if 0
[391]2032 {"is_inf", (PyCFunction)float_is_inf, METH_NOARGS,
2033 "Return True if the float is positive or negative infinite."},
2034 {"is_finite", (PyCFunction)float_is_finite, METH_NOARGS,
2035 "Return True if the float is finite, neither infinite nor NaN."},
2036 {"is_nan", (PyCFunction)float_is_nan, METH_NOARGS,
2037 "Return True if the float is not a number (NaN)."},
[2]2038#endif
[391]2039 {"__getnewargs__", (PyCFunction)float_getnewargs, METH_NOARGS},
2040 {"__getformat__", (PyCFunction)float_getformat,
2041 METH_O|METH_CLASS, float_getformat_doc},
2042 {"__setformat__", (PyCFunction)float_setformat,
2043 METH_VARARGS|METH_CLASS, float_setformat_doc},
2044 {"__format__", (PyCFunction)float__format__,
2045 METH_VARARGS, float__format__doc},
2046 {NULL, NULL} /* sentinel */
[2]2047};
2048
2049static PyGetSetDef float_getset[] = {
[391]2050 {"real",
[2]2051 (getter)float_float, (setter)NULL,
2052 "the real part of a complex number",
2053 NULL},
[391]2054 {"imag",
[2]2055 (getter)float_getzero, (setter)NULL,
2056 "the imaginary part of a complex number",
2057 NULL},
2058 {NULL} /* Sentinel */
2059};
2060
2061PyDoc_STRVAR(float_doc,
2062"float(x) -> floating point number\n\
2063\n\
2064Convert a string or number to a floating point number, if possible.");
2065
2066
2067static PyNumberMethods float_as_number = {
[391]2068 float_add, /*nb_add*/
2069 float_sub, /*nb_subtract*/
2070 float_mul, /*nb_multiply*/
2071 float_classic_div, /*nb_divide*/
2072 float_rem, /*nb_remainder*/
2073 float_divmod, /*nb_divmod*/
2074 float_pow, /*nb_power*/
2075 (unaryfunc)float_neg, /*nb_negative*/
2076 (unaryfunc)float_float, /*nb_positive*/
2077 (unaryfunc)float_abs, /*nb_absolute*/
2078 (inquiry)float_nonzero, /*nb_nonzero*/
2079 0, /*nb_invert*/
2080 0, /*nb_lshift*/
2081 0, /*nb_rshift*/
2082 0, /*nb_and*/
2083 0, /*nb_xor*/
2084 0, /*nb_or*/
2085 float_coerce, /*nb_coerce*/
2086 float_trunc, /*nb_int*/
2087 float_long, /*nb_long*/
2088 float_float, /*nb_float*/
2089 0, /* nb_oct */
2090 0, /* nb_hex */
2091 0, /* nb_inplace_add */
2092 0, /* nb_inplace_subtract */
2093 0, /* nb_inplace_multiply */
2094 0, /* nb_inplace_divide */
2095 0, /* nb_inplace_remainder */
2096 0, /* nb_inplace_power */
2097 0, /* nb_inplace_lshift */
2098 0, /* nb_inplace_rshift */
2099 0, /* nb_inplace_and */
2100 0, /* nb_inplace_xor */
2101 0, /* nb_inplace_or */
2102 float_floor_div, /* nb_floor_divide */
2103 float_div, /* nb_true_divide */
2104 0, /* nb_inplace_floor_divide */
2105 0, /* nb_inplace_true_divide */
[2]2106};
2107
2108PyTypeObject PyFloat_Type = {
[391]2109 PyVarObject_HEAD_INIT(&PyType_Type, 0)
2110 "float",
2111 sizeof(PyFloatObject),
2112 0,
2113 (destructor)float_dealloc, /* tp_dealloc */
2114 (printfunc)float_print, /* tp_print */
2115 0, /* tp_getattr */
2116 0, /* tp_setattr */
2117 0, /* tp_compare */
2118 (reprfunc)float_repr, /* tp_repr */
2119 &float_as_number, /* tp_as_number */
2120 0, /* tp_as_sequence */
2121 0, /* tp_as_mapping */
2122 (hashfunc)float_hash, /* tp_hash */
2123 0, /* tp_call */
2124 (reprfunc)float_str, /* tp_str */
2125 PyObject_GenericGetAttr, /* tp_getattro */
2126 0, /* tp_setattro */
2127 0, /* tp_as_buffer */
2128 Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES |
2129 Py_TPFLAGS_BASETYPE, /* tp_flags */
2130 float_doc, /* tp_doc */
2131 0, /* tp_traverse */
2132 0, /* tp_clear */
2133 float_richcompare, /* tp_richcompare */
2134 0, /* tp_weaklistoffset */
2135 0, /* tp_iter */
2136 0, /* tp_iternext */
2137 float_methods, /* tp_methods */
2138 0, /* tp_members */
2139 float_getset, /* tp_getset */
2140 0, /* tp_base */
2141 0, /* tp_dict */
2142 0, /* tp_descr_get */
2143 0, /* tp_descr_set */
2144 0, /* tp_dictoffset */
2145 0, /* tp_init */
2146 0, /* tp_alloc */
2147 float_new, /* tp_new */
[2]2148};
2149
2150void
2151_PyFloat_Init(void)
2152{
[391]2153 /* We attempt to determine if this machine is using IEEE
2154 floating point formats by peering at the bits of some
2155 carefully chosen values. If it looks like we are on an
2156 IEEE platform, the float packing/unpacking routines can
2157 just copy bits, if not they resort to arithmetic & shifts
2158 and masks. The shifts & masks approach works on all finite
2159 values, but what happens to infinities, NaNs and signed
2160 zeroes on packing is an accident, and attempting to unpack
2161 a NaN or an infinity will raise an exception.
[2]2162
[391]2163 Note that if we're on some whacked-out platform which uses
2164 IEEE formats but isn't strictly little-endian or big-
2165 endian, we will fall back to the portable shifts & masks
2166 method. */
[2]2167
2168#if SIZEOF_DOUBLE == 8
[391]2169 {
2170 double x = 9006104071832581.0;
2171 if (memcmp(&x, "\x43\x3f\xff\x01\x02\x03\x04\x05", 8) == 0)
2172 detected_double_format = ieee_big_endian_format;
2173 else if (memcmp(&x, "\x05\x04\x03\x02\x01\xff\x3f\x43", 8) == 0)
2174 detected_double_format = ieee_little_endian_format;
2175 else
2176 detected_double_format = unknown_format;
2177 }
[2]2178#else
[391]2179 detected_double_format = unknown_format;
[2]2180#endif
2181
2182#if SIZEOF_FLOAT == 4
[391]2183 {
2184 float y = 16711938.0;
2185 if (memcmp(&y, "\x4b\x7f\x01\x02", 4) == 0)
2186 detected_float_format = ieee_big_endian_format;
2187 else if (memcmp(&y, "\x02\x01\x7f\x4b", 4) == 0)
2188 detected_float_format = ieee_little_endian_format;
2189 else
2190 detected_float_format = unknown_format;
2191 }
[2]2192#else
[391]2193 detected_float_format = unknown_format;
[2]2194#endif
2195
[391]2196 double_format = detected_double_format;
2197 float_format = detected_float_format;
[2]2198
[391]2199 /* Init float info */
2200 if (FloatInfoType.tp_name == 0)
2201 PyStructSequence_InitType(&FloatInfoType, &floatinfo_desc);
[2]2202}
2203
2204int
2205PyFloat_ClearFreeList(void)
2206{
[391]2207 PyFloatObject *p;
2208 PyFloatBlock *list, *next;
2209 int i;
2210 int u; /* remaining unfreed ints per block */
2211 int freelist_size = 0;
[2]2212
[391]2213 list = block_list;
2214 block_list = NULL;
2215 free_list = NULL;
2216 while (list != NULL) {
2217 u = 0;
2218 for (i = 0, p = &list->objects[0];
2219 i < N_FLOATOBJECTS;
2220 i++, p++) {
2221 if (PyFloat_CheckExact(p) && Py_REFCNT(p) != 0)
2222 u++;
2223 }
2224 next = list->next;
2225 if (u) {
2226 list->next = block_list;
2227 block_list = list;
2228 for (i = 0, p = &list->objects[0];
2229 i < N_FLOATOBJECTS;
2230 i++, p++) {
2231 if (!PyFloat_CheckExact(p) ||
2232 Py_REFCNT(p) == 0) {
2233 Py_TYPE(p) = (struct _typeobject *)
2234 free_list;
2235 free_list = p;
2236 }
2237 }
2238 }
2239 else {
2240 PyMem_FREE(list);
2241 }
2242 freelist_size += u;
2243 list = next;
2244 }
2245 return freelist_size;
[2]2246}
2247
2248void
2249PyFloat_Fini(void)
2250{
[391]2251 PyFloatObject *p;
2252 PyFloatBlock *list;
2253 int i;
2254 int u; /* total unfreed floats per block */
[2]2255
[391]2256 u = PyFloat_ClearFreeList();
[2]2257
[391]2258 if (!Py_VerboseFlag)
2259 return;
2260 fprintf(stderr, "# cleanup floats");
2261 if (!u) {
2262 fprintf(stderr, "\n");
2263 }
2264 else {
2265 fprintf(stderr,
2266 ": %d unfreed float%s\n",
2267 u, u == 1 ? "" : "s");
2268 }
2269 if (Py_VerboseFlag > 1) {
2270 list = block_list;
2271 while (list != NULL) {
2272 for (i = 0, p = &list->objects[0];
2273 i < N_FLOATOBJECTS;
2274 i++, p++) {
2275 if (PyFloat_CheckExact(p) &&
2276 Py_REFCNT(p) != 0) {
2277 char *buf = PyOS_double_to_string(
2278 PyFloat_AS_DOUBLE(p), 'r',
2279 0, 0, NULL);
2280 if (buf) {
2281 /* XXX(twouters) cast
2282 refcount to long
2283 until %zd is
2284 universally
2285 available
2286 */
2287 fprintf(stderr,
2288 "# <float at %p, refcnt=%ld, val=%s>\n",
2289 p, (long)Py_REFCNT(p), buf);
2290 PyMem_Free(buf);
2291 }
2292 }
2293 }
2294 list = list->next;
2295 }
2296 }
[2]2297}
2298
2299/*----------------------------------------------------------------------------
2300 * _PyFloat_{Pack,Unpack}{4,8}. See floatobject.h.
2301 */
2302int
2303_PyFloat_Pack4(double x, unsigned char *p, int le)
2304{
[391]2305 if (float_format == unknown_format) {
2306 unsigned char sign;
2307 int e;
2308 double f;
2309 unsigned int fbits;
2310 int incr = 1;
[2]2311
[391]2312 if (le) {
2313 p += 3;
2314 incr = -1;
2315 }
[2]2316
[391]2317 if (x < 0) {
2318 sign = 1;
2319 x = -x;
2320 }
2321 else
2322 sign = 0;
[2]2323
[391]2324 f = frexp(x, &e);
[2]2325
[391]2326 /* Normalize f to be in the range [1.0, 2.0) */
2327 if (0.5 <= f && f < 1.0) {
2328 f *= 2.0;
2329 e--;
2330 }
2331 else if (f == 0.0)
2332 e = 0;
2333 else {
2334 PyErr_SetString(PyExc_SystemError,
2335 "frexp() result out of range");
2336 return -1;
2337 }
[2]2338
[391]2339 if (e >= 128)
2340 goto Overflow;
2341 else if (e < -126) {
2342 /* Gradual underflow */
2343 f = ldexp(f, 126 + e);
2344 e = 0;
2345 }
2346 else if (!(e == 0 && f == 0.0)) {
2347 e += 127;
2348 f -= 1.0; /* Get rid of leading 1 */
2349 }
[2]2350
[391]2351 f *= 8388608.0; /* 2**23 */
2352 fbits = (unsigned int)(f + 0.5); /* Round */
2353 assert(fbits <= 8388608);
2354 if (fbits >> 23) {
2355 /* The carry propagated out of a string of 23 1 bits. */
2356 fbits = 0;
2357 ++e;
2358 if (e >= 255)
2359 goto Overflow;
2360 }
[2]2361
[391]2362 /* First byte */
2363 *p = (sign << 7) | (e >> 1);
2364 p += incr;
[2]2365
[391]2366 /* Second byte */
2367 *p = (char) (((e & 1) << 7) | (fbits >> 16));
2368 p += incr;
[2]2369
[391]2370 /* Third byte */
2371 *p = (fbits >> 8) & 0xFF;
2372 p += incr;
[2]2373
[391]2374 /* Fourth byte */
2375 *p = fbits & 0xFF;
[2]2376
[391]2377 /* Done */
2378 return 0;
[2]2379
[391]2380 }
2381 else {
2382 float y = (float)x;
2383 const char *s = (char*)&y;
2384 int i, incr = 1;
[2]2385
[391]2386 if (Py_IS_INFINITY(y) && !Py_IS_INFINITY(x))
2387 goto Overflow;
[2]2388
[391]2389 if ((float_format == ieee_little_endian_format && !le)
2390 || (float_format == ieee_big_endian_format && le)) {
2391 p += 3;
2392 incr = -1;
2393 }
[2]2394
[391]2395 for (i = 0; i < 4; i++) {
2396 *p = *s++;
2397 p += incr;
2398 }
2399 return 0;
2400 }
[2]2401 Overflow:
[391]2402 PyErr_SetString(PyExc_OverflowError,
2403 "float too large to pack with f format");
2404 return -1;
[2]2405}
2406
2407int
2408_PyFloat_Pack8(double x, unsigned char *p, int le)
2409{
[391]2410 if (double_format == unknown_format) {
2411 unsigned char sign;
2412 int e;
2413 double f;
2414 unsigned int fhi, flo;
2415 int incr = 1;
[2]2416
[391]2417 if (le) {
2418 p += 7;
2419 incr = -1;
2420 }
[2]2421
[391]2422 if (x < 0) {
2423 sign = 1;
2424 x = -x;
2425 }
2426 else
2427 sign = 0;
[2]2428
[391]2429 f = frexp(x, &e);
[2]2430
[391]2431 /* Normalize f to be in the range [1.0, 2.0) */
2432 if (0.5 <= f && f < 1.0) {
2433 f *= 2.0;
2434 e--;
2435 }
2436 else if (f == 0.0)
2437 e = 0;
2438 else {
2439 PyErr_SetString(PyExc_SystemError,
2440 "frexp() result out of range");
2441 return -1;
2442 }
[2]2443
[391]2444 if (e >= 1024)
2445 goto Overflow;
2446 else if (e < -1022) {
2447 /* Gradual underflow */
2448 f = ldexp(f, 1022 + e);
2449 e = 0;
2450 }
2451 else if (!(e == 0 && f == 0.0)) {
2452 e += 1023;
2453 f -= 1.0; /* Get rid of leading 1 */
2454 }
[2]2455
[391]2456 /* fhi receives the high 28 bits; flo the low 24 bits (== 52 bits) */
2457 f *= 268435456.0; /* 2**28 */
2458 fhi = (unsigned int)f; /* Truncate */
2459 assert(fhi < 268435456);
[2]2460
[391]2461 f -= (double)fhi;
2462 f *= 16777216.0; /* 2**24 */
2463 flo = (unsigned int)(f + 0.5); /* Round */
2464 assert(flo <= 16777216);
2465 if (flo >> 24) {
2466 /* The carry propagated out of a string of 24 1 bits. */
2467 flo = 0;
2468 ++fhi;
2469 if (fhi >> 28) {
2470 /* And it also progagated out of the next 28 bits. */
2471 fhi = 0;
2472 ++e;
2473 if (e >= 2047)
2474 goto Overflow;
2475 }
2476 }
[2]2477
[391]2478 /* First byte */
2479 *p = (sign << 7) | (e >> 4);
2480 p += incr;
[2]2481
[391]2482 /* Second byte */
2483 *p = (unsigned char) (((e & 0xF) << 4) | (fhi >> 24));
2484 p += incr;
[2]2485
[391]2486 /* Third byte */
2487 *p = (fhi >> 16) & 0xFF;
2488 p += incr;
[2]2489
[391]2490 /* Fourth byte */
2491 *p = (fhi >> 8) & 0xFF;
2492 p += incr;
[2]2493
[391]2494 /* Fifth byte */
2495 *p = fhi & 0xFF;
2496 p += incr;
[2]2497
[391]2498 /* Sixth byte */
2499 *p = (flo >> 16) & 0xFF;
2500 p += incr;
[2]2501
[391]2502 /* Seventh byte */
2503 *p = (flo >> 8) & 0xFF;
2504 p += incr;
[2]2505
[391]2506 /* Eighth byte */
2507 *p = flo & 0xFF;
2508 /* p += incr; Unneeded (for now) */
[2]2509
[391]2510 /* Done */
2511 return 0;
[2]2512
[391]2513 Overflow:
2514 PyErr_SetString(PyExc_OverflowError,
2515 "float too large to pack with d format");
2516 return -1;
2517 }
2518 else {
2519 const char *s = (char*)&x;
2520 int i, incr = 1;
[2]2521
[391]2522 if ((double_format == ieee_little_endian_format && !le)
2523 || (double_format == ieee_big_endian_format && le)) {
2524 p += 7;
2525 incr = -1;
2526 }
2527
2528 for (i = 0; i < 8; i++) {
2529 *p = *s++;
2530 p += incr;
2531 }
2532 return 0;
2533 }
[2]2534}
2535
2536double
2537_PyFloat_Unpack4(const unsigned char *p, int le)
2538{
[391]2539 if (float_format == unknown_format) {
2540 unsigned char sign;
2541 int e;
2542 unsigned int f;
2543 double x;
2544 int incr = 1;
[2]2545
[391]2546 if (le) {
2547 p += 3;
2548 incr = -1;
2549 }
[2]2550
[391]2551 /* First byte */
2552 sign = (*p >> 7) & 1;
2553 e = (*p & 0x7F) << 1;
2554 p += incr;
[2]2555
[391]2556 /* Second byte */
2557 e |= (*p >> 7) & 1;
2558 f = (*p & 0x7F) << 16;
2559 p += incr;
[2]2560
[391]2561 if (e == 255) {
2562 PyErr_SetString(
2563 PyExc_ValueError,
2564 "can't unpack IEEE 754 special value "
2565 "on non-IEEE platform");
2566 return -1;
2567 }
[2]2568
[391]2569 /* Third byte */
2570 f |= *p << 8;
2571 p += incr;
[2]2572
[391]2573 /* Fourth byte */
2574 f |= *p;
[2]2575
[391]2576 x = (double)f / 8388608.0;
[2]2577
[391]2578 /* XXX This sadly ignores Inf/NaN issues */
2579 if (e == 0)
2580 e = -126;
2581 else {
2582 x += 1.0;
2583 e -= 127;
2584 }
2585 x = ldexp(x, e);
[2]2586
[391]2587 if (sign)
2588 x = -x;
[2]2589
[391]2590 return x;
2591 }
2592 else {
2593 float x;
[2]2594
[391]2595 if ((float_format == ieee_little_endian_format && !le)
2596 || (float_format == ieee_big_endian_format && le)) {
2597 char buf[4];
2598 char *d = &buf[3];
2599 int i;
[2]2600
[391]2601 for (i = 0; i < 4; i++) {
2602 *d-- = *p++;
2603 }
2604 memcpy(&x, buf, 4);
2605 }
2606 else {
2607 memcpy(&x, p, 4);
2608 }
[2]2609
[391]2610 return x;
2611 }
[2]2612}
2613
2614double
2615_PyFloat_Unpack8(const unsigned char *p, int le)
2616{
[391]2617 if (double_format == unknown_format) {
2618 unsigned char sign;
2619 int e;
2620 unsigned int fhi, flo;
2621 double x;
2622 int incr = 1;
[2]2623
[391]2624 if (le) {
2625 p += 7;
2626 incr = -1;
2627 }
[2]2628
[391]2629 /* First byte */
2630 sign = (*p >> 7) & 1;
2631 e = (*p & 0x7F) << 4;
[2]2632
[391]2633 p += incr;
[2]2634
[391]2635 /* Second byte */
2636 e |= (*p >> 4) & 0xF;
2637 fhi = (*p & 0xF) << 24;
2638 p += incr;
[2]2639
[391]2640 if (e == 2047) {
2641 PyErr_SetString(
2642 PyExc_ValueError,
2643 "can't unpack IEEE 754 special value "
2644 "on non-IEEE platform");
2645 return -1.0;
2646 }
[2]2647
[391]2648 /* Third byte */
2649 fhi |= *p << 16;
2650 p += incr;
[2]2651
[391]2652 /* Fourth byte */
2653 fhi |= *p << 8;
2654 p += incr;
[2]2655
[391]2656 /* Fifth byte */
2657 fhi |= *p;
2658 p += incr;
[2]2659
[391]2660 /* Sixth byte */
2661 flo = *p << 16;
2662 p += incr;
[2]2663
[391]2664 /* Seventh byte */
2665 flo |= *p << 8;
2666 p += incr;
[2]2667
[391]2668 /* Eighth byte */
2669 flo |= *p;
[2]2670
[391]2671 x = (double)fhi + (double)flo / 16777216.0; /* 2**24 */
2672 x /= 268435456.0; /* 2**28 */
[2]2673
[391]2674 if (e == 0)
2675 e = -1022;
2676 else {
2677 x += 1.0;
2678 e -= 1023;
2679 }
2680 x = ldexp(x, e);
[2]2681
[391]2682 if (sign)
2683 x = -x;
[2]2684
[391]2685 return x;
2686 }
2687 else {
2688 double x;
[2]2689
[391]2690 if ((double_format == ieee_little_endian_format && !le)
2691 || (double_format == ieee_big_endian_format && le)) {
2692 char buf[8];
2693 char *d = &buf[7];
2694 int i;
2695
2696 for (i = 0; i < 8; i++) {
2697 *d-- = *p++;
2698 }
2699 memcpy(&x, buf, 8);
2700 }
2701 else {
2702 memcpy(&x, p, 8);
2703 }
2704
2705 return x;
2706 }
[2]2707}
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