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use bools
[python.git] / Objects / floatobject.c
blob73d6a1ff417e511811030a474bfcecdafd88396e
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 HAVE_IEEEFP_H
19 #include <ieeefp.h>
20 #endif
21
22 #ifdef _OSF_SOURCE
23 /* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
24 extern int finite(double);
25 #endif
26
27 /* Special free list -- see comments for same code in intobject.c. */
28 #define BLOCK_SIZE 1000 /* 1K less typical malloc overhead */
29 #define BHEAD_SIZE 8 /* Enough for a 64-bit pointer */
30 #define N_FLOATOBJECTS ((BLOCK_SIZE - BHEAD_SIZE) / sizeof(PyFloatObject))
31
32 struct _floatblock {
33 struct _floatblock *next;
34 PyFloatObject objects[N_FLOATOBJECTS];
35 };
36
37 typedef struct _floatblock PyFloatBlock;
38
39 static PyFloatBlock *block_list = NULL;
40 static PyFloatObject *free_list = NULL;
41
42 static PyFloatObject *
43 fill_free_list(void)
44 {
45 PyFloatObject *p, *q;
46 /* XXX Float blocks escape the object heap. Use PyObject_MALLOC ??? */
47 p = (PyFloatObject *) PyMem_MALLOC(sizeof(PyFloatBlock));
48 if (p == NULL)
49 return (PyFloatObject *) PyErr_NoMemory();
50 ((PyFloatBlock *)p)->next = block_list;
51 block_list = (PyFloatBlock *)p;
52 p = &((PyFloatBlock *)p)->objects[0];
53 q = p + N_FLOATOBJECTS;
54 while (--q > p)
55 Py_TYPE(q) = (struct _typeobject *)(q-1);
56 Py_TYPE(q) = NULL;
57 return p + N_FLOATOBJECTS - 1;
58 }
59
60 double
61 PyFloat_GetMax(void)
62 {
63 return DBL_MAX;
64 }
65
66 double
67 PyFloat_GetMin(void)
68 {
69 return DBL_MIN;
70 }
71
72 static PyTypeObject FloatInfoType = {0, 0, 0, 0, 0, 0};
73
74 PyDoc_STRVAR(floatinfo__doc__,
75 "sys.float_info\n\
76 \n\
77 A structseq holding information about the float type. It contains low level\n\
78 information about the precision and internal representation. Please study\n\
79 your system's :file:`float.h` for more information.");
80
81 static PyStructSequence_Field floatinfo_fields[] = {
82 {"max", "DBL_MAX -- maximum representable finite float"},
83 {"max_exp", "DBL_MAX_EXP -- maximum int e such that radix**(e-1) "
84 "is representable"},
85 {"max_10_exp", "DBL_MAX_10_EXP -- maximum int e such that 10**e "
86 "is representable"},
87 {"min", "DBL_MIN -- Minimum positive normalizer float"},
88 {"min_exp", "DBL_MIN_EXP -- minimum int e such that radix**(e-1) "
89 "is a normalized float"},
90 {"min_10_exp", "DBL_MIN_10_EXP -- minimum int e such that 10**e is "
91 "a normalized"},
92 {"dig", "DBL_DIG -- digits"},
93 {"mant_dig", "DBL_MANT_DIG -- mantissa digits"},
94 {"epsilon", "DBL_EPSILON -- Difference between 1 and the next "
95 "representable float"},
96 {"radix", "FLT_RADIX -- radix of exponent"},
97 {"rounds", "FLT_ROUNDS -- addition rounds"},
98 {0}
99 };
100
101 static PyStructSequence_Desc floatinfo_desc = {
102 "sys.float_info", /* name */
103 floatinfo__doc__, /* doc */
104 floatinfo_fields, /* fields */
105 11
106 };
107
108 PyObject *
109 PyFloat_GetInfo(void)
110 {
111 PyObject* floatinfo;
112 int pos = 0;
113
114 floatinfo = PyStructSequence_New(&FloatInfoType);
115 if (floatinfo == NULL) {
116 return NULL;
117 }
118
119 #define SetIntFlag(flag) \
120 PyStructSequence_SET_ITEM(floatinfo, pos++, PyInt_FromLong(flag))
121 #define SetDblFlag(flag) \
122 PyStructSequence_SET_ITEM(floatinfo, pos++, PyFloat_FromDouble(flag))
123
124 SetDblFlag(DBL_MAX);
125 SetIntFlag(DBL_MAX_EXP);
126 SetIntFlag(DBL_MAX_10_EXP);
127 SetDblFlag(DBL_MIN);
128 SetIntFlag(DBL_MIN_EXP);
129 SetIntFlag(DBL_MIN_10_EXP);
130 SetIntFlag(DBL_DIG);
131 SetIntFlag(DBL_MANT_DIG);
132 SetDblFlag(DBL_EPSILON);
133 SetIntFlag(FLT_RADIX);
134 SetIntFlag(FLT_ROUNDS);
135 #undef SetIntFlag
136 #undef SetDblFlag
137
138 if (PyErr_Occurred()) {
139 Py_CLEAR(floatinfo);
140 return NULL;
141 }
142 return floatinfo;
143 }
144
145 PyObject *
146 PyFloat_FromDouble(double fval)
147 {
148 register PyFloatObject *op;
149 if (free_list == NULL) {
150 if ((free_list = fill_free_list()) == NULL)
151 return NULL;
152 }
153 /* Inline PyObject_New */
154 op = free_list;
155 free_list = (PyFloatObject *)Py_TYPE(op);
156 PyObject_INIT(op, &PyFloat_Type);
157 op->ob_fval = fval;
158 return (PyObject *) op;
159 }
160
161 /**************************************************************************
162 RED_FLAG 22-Sep-2000 tim
163 PyFloat_FromString's pend argument is braindead. Prior to this RED_FLAG,
164
165 1. If v was a regular string, *pend was set to point to its terminating
166 null byte. That's useless (the caller can find that without any
167 help from this function!).
168
169 2. If v was a Unicode string, or an object convertible to a character
170 buffer, *pend was set to point into stack trash (the auto temp
171 vector holding the character buffer). That was downright dangerous.
172
173 Since we can't change the interface of a public API function, pend is
174 still supported but now *officially* useless: if pend is not NULL,
175 *pend is set to NULL.
176 **************************************************************************/
177 PyObject *
178 PyFloat_FromString(PyObject *v, char **pend)
179 {
180 const char *s, *last, *end;
181 double x;
182 char buffer[256]; /* for errors */
183 #ifdef Py_USING_UNICODE
184 char s_buffer[256]; /* for objects convertible to a char buffer */
185 #endif
186 Py_ssize_t len;
187
188 if (pend)
189 *pend = NULL;
190 if (PyString_Check(v)) {
191 s = PyString_AS_STRING(v);
192 len = PyString_GET_SIZE(v);
193 }
194 #ifdef Py_USING_UNICODE
195 else if (PyUnicode_Check(v)) {
196 if (PyUnicode_GET_SIZE(v) >= (Py_ssize_t)sizeof(s_buffer)) {
197 PyErr_SetString(PyExc_ValueError,
198 "Unicode float() literal too long to convert");
199 return NULL;
200 }
201 if (PyUnicode_EncodeDecimal(PyUnicode_AS_UNICODE(v),
202 PyUnicode_GET_SIZE(v),
203 s_buffer,
204 NULL))
205 return NULL;
206 s = s_buffer;
207 len = strlen(s);
208 }
209 #endif
210 else if (PyObject_AsCharBuffer(v, &s, &len)) {
211 PyErr_SetString(PyExc_TypeError,
212 "float() argument must be a string or a number");
213 return NULL;
214 }
215 last = s + len;
216
217 while (Py_ISSPACE(*s))
218 s++;
219 /* We don't care about overflow or underflow. If the platform
220 * supports them, infinities and signed zeroes (on underflow) are
221 * fine. */
222 errno = 0;
223 PyFPE_START_PROTECT("strtod", return NULL)
224 x = PyOS_ascii_strtod(s, (char **)&end);
225 PyFPE_END_PROTECT(x)
226 if (end == s) {
227 if (errno == ENOMEM)
228 PyErr_NoMemory();
229 else {
230 PyOS_snprintf(buffer, sizeof(buffer),
231 "invalid literal for float(): %.200s", s);
232 PyErr_SetString(PyExc_ValueError, buffer);
233 }
234 return NULL;
235 }
236 /* Since end != s, the platform made *some* kind of sense out
237 of the input. Trust it. */
238 while (Py_ISSPACE(*end))
239 end++;
240 if (end != last) {
241 if (*end == '\0')
242 PyErr_SetString(PyExc_ValueError,
243 "null byte in argument for float()");
244 else {
245 PyOS_snprintf(buffer, sizeof(buffer),
246 "invalid literal for float(): %.200s", s);
247 PyErr_SetString(PyExc_ValueError, buffer);
248 }
249 return NULL;
250 }
251 return PyFloat_FromDouble(x);
252 }
253
254 static void
255 float_dealloc(PyFloatObject *op)
256 {
257 if (PyFloat_CheckExact(op)) {
258 Py_TYPE(op) = (struct _typeobject *)free_list;
259 free_list = op;
260 }
261 else
262 Py_TYPE(op)->tp_free((PyObject *)op);
263 }
264
265 double
266 PyFloat_AsDouble(PyObject *op)
267 {
268 PyNumberMethods *nb;
269 PyFloatObject *fo;
270 double val;
271
272 if (op && PyFloat_Check(op))
273 return PyFloat_AS_DOUBLE((PyFloatObject*) op);
274
275 if (op == NULL) {
276 PyErr_BadArgument();
277 return -1;
278 }
279
280 if ((nb = Py_TYPE(op)->tp_as_number) == NULL || nb->nb_float == NULL) {
281 PyErr_SetString(PyExc_TypeError, "a float is required");
282 return -1;
283 }
284
285 fo = (PyFloatObject*) (*nb->nb_float) (op);
286 if (fo == NULL)
287 return -1;
288 if (!PyFloat_Check(fo)) {
289 PyErr_SetString(PyExc_TypeError,
290 "nb_float should return float object");
291 return -1;
292 }
293
294 val = PyFloat_AS_DOUBLE(fo);
295 Py_DECREF(fo);
296
297 return val;
298 }
299
300 /* Methods */
301
302 /* XXX PyFloat_AsStringEx should not be a public API function (for one
303 XXX thing, its signature passes a buffer without a length; for another,
304 XXX it isn't useful outside this file).
305 */
306 void
307 PyFloat_AsStringEx(char *buf, PyFloatObject *v, int precision)
308 {
309 _PyOS_double_to_string(buf, 100, v->ob_fval, 'g', precision,
310 Py_DTSF_ADD_DOT_0, NULL);
311 }
312
313 /* Macro and helper that convert PyObject obj to a C double and store
314 the value in dbl; this replaces the functionality of the coercion
315 slot function. If conversion to double raises an exception, obj is
316 set to NULL, and the function invoking this macro returns NULL. If
317 obj is not of float, int or long type, Py_NotImplemented is incref'ed,
318 stored in obj, and returned from the function invoking this macro.
319 */
320 #define CONVERT_TO_DOUBLE(obj, dbl) \
321 if (PyFloat_Check(obj)) \
322 dbl = PyFloat_AS_DOUBLE(obj); \
323 else if (convert_to_double(&(obj), &(dbl)) < 0) \
324 return obj;
325
326 static int
327 convert_to_double(PyObject **v, double *dbl)
328 {
329 register PyObject *obj = *v;
330
331 if (PyInt_Check(obj)) {
332 *dbl = (double)PyInt_AS_LONG(obj);
333 }
334 else if (PyLong_Check(obj)) {
335 *dbl = PyLong_AsDouble(obj);
336 if (*dbl == -1.0 && PyErr_Occurred()) {
337 *v = NULL;
338 return -1;
339 }
340 }
341 else {
342 Py_INCREF(Py_NotImplemented);
343 *v = Py_NotImplemented;
344 return -1;
345 }
346 return 0;
347 }
348
349 /* XXX PyFloat_AsString and PyFloat_AsReprString should be deprecated:
350 XXX they pass a char buffer without passing a length.
351 */
352 void
353 PyFloat_AsString(char *buf, PyFloatObject *v)
354 {
355 _PyOS_double_to_string(buf, 100, v->ob_fval, 'g', PyFloat_STR_PRECISION,
356 Py_DTSF_ADD_DOT_0, NULL);
357 }
358
359 void
360 PyFloat_AsReprString(char *buf, PyFloatObject *v)
361 {
362 _PyOS_double_to_string(buf, 100, v->ob_fval, 'r', 0,
363 Py_DTSF_ADD_DOT_0, NULL);
364 }
365
366 /* ARGSUSED */
367 static int
368 float_print(PyFloatObject *v, FILE *fp, int flags)
369 {
370 char buf[100];
371 if (flags & Py_PRINT_RAW)
372 _PyOS_double_to_string(buf, sizeof(buf), v->ob_fval,
373 'g', PyFloat_STR_PRECISION,
374 Py_DTSF_ADD_DOT_0, NULL);
375 else
376 _PyOS_double_to_string(buf, sizeof(buf), v->ob_fval,
377 'r', 0, Py_DTSF_ADD_DOT_0, NULL);
378 Py_BEGIN_ALLOW_THREADS
379 fputs(buf, fp);
380 Py_END_ALLOW_THREADS
381 return 0;
382 }
383
384 static PyObject *
385 float_repr(PyFloatObject *v)
386 {
387 char buf[100];
388 _PyOS_double_to_string(buf, sizeof(buf), v->ob_fval, 'r', 0,
389 Py_DTSF_ADD_DOT_0, NULL);
390 return PyString_FromString(buf);
391 }
392
393 static PyObject *
394 float_str(PyFloatObject *v)
395 {
396 char buf[100];
397 _PyOS_double_to_string(buf, sizeof(buf), v->ob_fval, 'g',
398 PyFloat_STR_PRECISION,
399 Py_DTSF_ADD_DOT_0, NULL);
400 return PyString_FromString(buf);
401 }
402
403 /* Comparison is pretty much a nightmare. When comparing float to float,
404 * we do it as straightforwardly (and long-windedly) as conceivable, so
405 * that, e.g., Python x == y delivers the same result as the platform
406 * C x == y when x and/or y is a NaN.
407 * When mixing float with an integer type, there's no good *uniform* approach.
408 * Converting the double to an integer obviously doesn't work, since we
409 * may lose info from fractional bits. Converting the integer to a double
410 * also has two failure modes: (1) a long int may trigger overflow (too
411 * large to fit in the dynamic range of a C double); (2) even a C long may have
412 * more bits than fit in a C double (e.g., on a a 64-bit box long may have
413 * 63 bits of precision, but a C double probably has only 53), and then
414 * we can falsely claim equality when low-order integer bits are lost by
415 * coercion to double. So this part is painful too.
416 */
417
418 static PyObject*
419 float_richcompare(PyObject *v, PyObject *w, int op)
420 {
421 double i, j;
422 int r = 0;
423
424 assert(PyFloat_Check(v));
425 i = PyFloat_AS_DOUBLE(v);
426
427 /* Switch on the type of w. Set i and j to doubles to be compared,
428 * and op to the richcomp to use.
429 */
430 if (PyFloat_Check(w))
431 j = PyFloat_AS_DOUBLE(w);
432
433 else if (!Py_IS_FINITE(i)) {
434 if (PyInt_Check(w) || PyLong_Check(w))
435 /* If i is an infinity, its magnitude exceeds any
436 * finite integer, so it doesn't matter which int we
437 * compare i with. If i is a NaN, similarly.
438 */
439 j = 0.0;
440 else
441 goto Unimplemented;
442 }
443
444 else if (PyInt_Check(w)) {
445 long jj = PyInt_AS_LONG(w);
446 /* In the worst realistic case I can imagine, C double is a
447 * Cray single with 48 bits of precision, and long has 64
448 * bits.
449 */
450 #if SIZEOF_LONG > 6
451 unsigned long abs = (unsigned long)(jj < 0 ? -jj : jj);
452 if (abs >> 48) {
453 /* Needs more than 48 bits. Make it take the
454 * PyLong path.
455 */
456 PyObject *result;
457 PyObject *ww = PyLong_FromLong(jj);
458
459 if (ww == NULL)
460 return NULL;
461 result = float_richcompare(v, ww, op);
462 Py_DECREF(ww);
463 return result;
464 }
465 #endif
466 j = (double)jj;
467 assert((long)j == jj);
468 }
469
470 else if (PyLong_Check(w)) {
471 int vsign = i == 0.0 ? 0 : i < 0.0 ? -1 : 1;
472 int wsign = _PyLong_Sign(w);
473 size_t nbits;
474 int exponent;
475
476 if (vsign != wsign) {
477 /* Magnitudes are irrelevant -- the signs alone
478 * determine the outcome.
479 */
480 i = (double)vsign;
481 j = (double)wsign;
482 goto Compare;
483 }
484 /* The signs are the same. */
485 /* Convert w to a double if it fits. In particular, 0 fits. */
486 nbits = _PyLong_NumBits(w);
487 if (nbits == (size_t)-1 && PyErr_Occurred()) {
488 /* This long is so large that size_t isn't big enough
489 * to hold the # of bits. Replace with little doubles
490 * that give the same outcome -- w is so large that
491 * its magnitude must exceed the magnitude of any
492 * finite float.
493 */
494 PyErr_Clear();
495 i = (double)vsign;
496 assert(wsign != 0);
497 j = wsign * 2.0;
498 goto Compare;
499 }
500 if (nbits <= 48) {
501 j = PyLong_AsDouble(w);
502 /* It's impossible that <= 48 bits overflowed. */
503 assert(j != -1.0 || ! PyErr_Occurred());
504 goto Compare;
505 }
506 assert(wsign != 0); /* else nbits was 0 */
507 assert(vsign != 0); /* if vsign were 0, then since wsign is
508 * not 0, we would have taken the
509 * vsign != wsign branch at the start */
510 /* We want to work with non-negative numbers. */
511 if (vsign < 0) {
512 /* "Multiply both sides" by -1; this also swaps the
513 * comparator.
514 */
515 i = -i;
516 op = _Py_SwappedOp[op];
517 }
518 assert(i > 0.0);
519 (void) frexp(i, &exponent);
520 /* exponent is the # of bits in v before the radix point;
521 * we know that nbits (the # of bits in w) > 48 at this point
522 */
523 if (exponent < 0 || (size_t)exponent < nbits) {
524 i = 1.0;
525 j = 2.0;
526 goto Compare;
527 }
528 if ((size_t)exponent > nbits) {
529 i = 2.0;
530 j = 1.0;
531 goto Compare;
532 }
533 /* v and w have the same number of bits before the radix
534 * point. Construct two longs that have the same comparison
535 * outcome.
536 */
537 {
538 double fracpart;
539 double intpart;
540 PyObject *result = NULL;
541 PyObject *one = NULL;
542 PyObject *vv = NULL;
543 PyObject *ww = w;
544
545 if (wsign < 0) {
546 ww = PyNumber_Negative(w);
547 if (ww == NULL)
548 goto Error;
549 }
550 else
551 Py_INCREF(ww);
552
553 fracpart = modf(i, &intpart);
554 vv = PyLong_FromDouble(intpart);
555 if (vv == NULL)
556 goto Error;
557
558 if (fracpart != 0.0) {
559 /* Shift left, and or a 1 bit into vv
560 * to represent the lost fraction.
561 */
562 PyObject *temp;
563
564 one = PyInt_FromLong(1);
565 if (one == NULL)
566 goto Error;
567
568 temp = PyNumber_Lshift(ww, one);
569 if (temp == NULL)
570 goto Error;
571 Py_DECREF(ww);
572 ww = temp;
573
574 temp = PyNumber_Lshift(vv, one);
575 if (temp == NULL)
576 goto Error;
577 Py_DECREF(vv);
578 vv = temp;
579
580 temp = PyNumber_Or(vv, one);
581 if (temp == NULL)
582 goto Error;
583 Py_DECREF(vv);
584 vv = temp;
585 }
586
587 r = PyObject_RichCompareBool(vv, ww, op);
588 if (r < 0)
589 goto Error;
590 result = PyBool_FromLong(r);
591 Error:
592 Py_XDECREF(vv);
593 Py_XDECREF(ww);
594 Py_XDECREF(one);
595 return result;
596 }
597 } /* else if (PyLong_Check(w)) */
598
599 else /* w isn't float, int, or long */
600 goto Unimplemented;
601
602 Compare:
603 PyFPE_START_PROTECT("richcompare", return NULL)
604 switch (op) {
605 case Py_EQ:
606 r = i == j;
607 break;
608 case Py_NE:
609 r = i != j;
610 break;
611 case Py_LE:
612 r = i <= j;
613 break;
614 case Py_GE:
615 r = i >= j;
616 break;
617 case Py_LT:
618 r = i < j;
619 break;
620 case Py_GT:
621 r = i > j;
622 break;
623 }
624 PyFPE_END_PROTECT(r)
625 return PyBool_FromLong(r);
626
627 Unimplemented:
628 Py_INCREF(Py_NotImplemented);
629 return Py_NotImplemented;
630 }
631
632 static long
633 float_hash(PyFloatObject *v)
634 {
635 return _Py_HashDouble(v->ob_fval);
636 }
637
638 static PyObject *
639 float_add(PyObject *v, PyObject *w)
640 {
641 double a,b;
642 CONVERT_TO_DOUBLE(v, a);
643 CONVERT_TO_DOUBLE(w, b);
644 PyFPE_START_PROTECT("add", return 0)
645 a = a + b;
646 PyFPE_END_PROTECT(a)
647 return PyFloat_FromDouble(a);
648 }
649
650 static PyObject *
651 float_sub(PyObject *v, PyObject *w)
652 {
653 double a,b;
654 CONVERT_TO_DOUBLE(v, a);
655 CONVERT_TO_DOUBLE(w, b);
656 PyFPE_START_PROTECT("subtract", return 0)
657 a = a - b;
658 PyFPE_END_PROTECT(a)
659 return PyFloat_FromDouble(a);
660 }
661
662 static PyObject *
663 float_mul(PyObject *v, PyObject *w)
664 {
665 double a,b;
666 CONVERT_TO_DOUBLE(v, a);
667 CONVERT_TO_DOUBLE(w, b);
668 PyFPE_START_PROTECT("multiply", return 0)
669 a = a * b;
670 PyFPE_END_PROTECT(a)
671 return PyFloat_FromDouble(a);
672 }
673
674 static PyObject *
675 float_div(PyObject *v, PyObject *w)
676 {
677 double a,b;
678 CONVERT_TO_DOUBLE(v, a);
679 CONVERT_TO_DOUBLE(w, b);
680 #ifdef Py_NAN
681 if (b == 0.0) {
682 PyErr_SetString(PyExc_ZeroDivisionError,
683 "float division");
684 return NULL;
685 }
686 #endif
687 PyFPE_START_PROTECT("divide", return 0)
688 a = a / b;
689 PyFPE_END_PROTECT(a)
690 return PyFloat_FromDouble(a);
691 }
692
693 static PyObject *
694 float_classic_div(PyObject *v, PyObject *w)
695 {
696 double a,b;
697 CONVERT_TO_DOUBLE(v, a);
698 CONVERT_TO_DOUBLE(w, b);
699 if (Py_DivisionWarningFlag >= 2 &&
700 PyErr_Warn(PyExc_DeprecationWarning, "classic float division") < 0)
701 return NULL;
702 #ifdef Py_NAN
703 if (b == 0.0) {
704 PyErr_SetString(PyExc_ZeroDivisionError,
705 "float division");
706 return NULL;
707 }
708 #endif
709 PyFPE_START_PROTECT("divide", return 0)
710 a = a / b;
711 PyFPE_END_PROTECT(a)
712 return PyFloat_FromDouble(a);
713 }
714
715 static PyObject *
716 float_rem(PyObject *v, PyObject *w)
717 {
718 double vx, wx;
719 double mod;
720 CONVERT_TO_DOUBLE(v, vx);
721 CONVERT_TO_DOUBLE(w, wx);
722 #ifdef Py_NAN
723 if (wx == 0.0) {
724 PyErr_SetString(PyExc_ZeroDivisionError,
725 "float modulo");
726 return NULL;
727 }
728 #endif
729 PyFPE_START_PROTECT("modulo", return 0)
730 mod = fmod(vx, wx);
731 /* note: checking mod*wx < 0 is incorrect -- underflows to
732 0 if wx < sqrt(smallest nonzero double) */
733 if (mod && ((wx < 0) != (mod < 0))) {
734 mod += wx;
735 }
736 PyFPE_END_PROTECT(mod)
737 return PyFloat_FromDouble(mod);
738 }
739
740 static PyObject *
741 float_divmod(PyObject *v, PyObject *w)
742 {
743 double vx, wx;
744 double div, mod, floordiv;
745 CONVERT_TO_DOUBLE(v, vx);
746 CONVERT_TO_DOUBLE(w, wx);
747 if (wx == 0.0) {
748 PyErr_SetString(PyExc_ZeroDivisionError, "float divmod()");
749 return NULL;
750 }
751 PyFPE_START_PROTECT("divmod", return 0)
752 mod = fmod(vx, wx);
753 /* fmod is typically exact, so vx-mod is *mathematically* an
754 exact multiple of wx. But this is fp arithmetic, and fp
755 vx - mod is an approximation; the result is that div may
756 not be an exact integral value after the division, although
757 it will always be very close to one.
758 */
759 div = (vx - mod) / wx;
760 if (mod) {
761 /* ensure the remainder has the same sign as the denominator */
762 if ((wx < 0) != (mod < 0)) {
763 mod += wx;
764 div -= 1.0;
765 }
766 }
767 else {
768 /* the remainder is zero, and in the presence of signed zeroes
769 fmod returns different results across platforms; ensure
770 it has the same sign as the denominator; we'd like to do
771 "mod = wx * 0.0", but that may get optimized away */
772 mod *= mod; /* hide "mod = +0" from optimizer */
773 if (wx < 0.0)
774 mod = -mod;
775 }
776 /* snap quotient to nearest integral value */
777 if (div) {
778 floordiv = floor(div);
779 if (div - floordiv > 0.5)
780 floordiv += 1.0;
781 }
782 else {
783 /* div is zero - get the same sign as the true quotient */
784 div *= div; /* hide "div = +0" from optimizers */
785 floordiv = div * vx / wx; /* zero w/ sign of vx/wx */
786 }
787 PyFPE_END_PROTECT(floordiv)
788 return Py_BuildValue("(dd)", floordiv, mod);
789 }
790
791 static PyObject *
792 float_floor_div(PyObject *v, PyObject *w)
793 {
794 PyObject *t, *r;
795
796 t = float_divmod(v, w);
797 if (t == NULL || t == Py_NotImplemented)
798 return t;
799 assert(PyTuple_CheckExact(t));
800 r = PyTuple_GET_ITEM(t, 0);
801 Py_INCREF(r);
802 Py_DECREF(t);
803 return r;
804 }
805
806 static PyObject *
807 float_pow(PyObject *v, PyObject *w, PyObject *z)
808 {
809 double iv, iw, ix;
810
811 if ((PyObject *)z != Py_None) {
812 PyErr_SetString(PyExc_TypeError, "pow() 3rd argument not "
813 "allowed unless all arguments are integers");
814 return NULL;
815 }
816
817 CONVERT_TO_DOUBLE(v, iv);
818 CONVERT_TO_DOUBLE(w, iw);
819
820 /* Sort out special cases here instead of relying on pow() */
821 if (iw == 0) { /* v**0 is 1, even 0**0 */
822 return PyFloat_FromDouble(1.0);
823 }
824 if (iv == 0.0) { /* 0**w is error if w<0, else 1 */
825 if (iw < 0.0) {
826 PyErr_SetString(PyExc_ZeroDivisionError,
827 "0.0 cannot be raised to a negative power");
828 return NULL;
829 }
830 return PyFloat_FromDouble(0.0);
831 }
832 if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */
833 return PyFloat_FromDouble(1.0);
834 }
835 if (iv < 0.0) {
836 /* Whether this is an error is a mess, and bumps into libm
837 * bugs so we have to figure it out ourselves.
838 */
839 if (iw != floor(iw)) {
840 PyErr_SetString(PyExc_ValueError, "negative number "
841 "cannot be raised to a fractional power");
842 return NULL;
843 }
844 /* iw is an exact integer, albeit perhaps a very large one.
845 * -1 raised to an exact integer should never be exceptional.
846 * Alas, some libms (chiefly glibc as of early 2003) return
847 * NaN and set EDOM on pow(-1, large_int) if the int doesn't
848 * happen to be representable in a *C* integer. That's a
849 * bug; we let that slide in math.pow() (which currently
850 * reflects all platform accidents), but not for Python's **.
851 */
852 if (iv == -1.0 && Py_IS_FINITE(iw)) {
853 /* Return 1 if iw is even, -1 if iw is odd; there's
854 * no guarantee that any C integral type is big
855 * enough to hold iw, so we have to check this
856 * indirectly.
857 */
858 ix = floor(iw * 0.5) * 2.0;
859 return PyFloat_FromDouble(ix == iw ? 1.0 : -1.0);
860 }
861 /* Else iv != -1.0, and overflow or underflow are possible.
862 * Unless we're to write pow() ourselves, we have to trust
863 * the platform to do this correctly.
864 */
865 }
866 errno = 0;
867 PyFPE_START_PROTECT("pow", return NULL)
868 ix = pow(iv, iw);
869 PyFPE_END_PROTECT(ix)
870 Py_ADJUST_ERANGE1(ix);
871 if (errno != 0) {
872 /* We don't expect any errno value other than ERANGE, but
873 * the range of libm bugs appears unbounded.
874 */
875 PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError :
876 PyExc_ValueError);
877 return NULL;
878 }
879 return PyFloat_FromDouble(ix);
880 }
881
882 static PyObject *
883 float_neg(PyFloatObject *v)
884 {
885 return PyFloat_FromDouble(-v->ob_fval);
886 }
887
888 static PyObject *
889 float_abs(PyFloatObject *v)
890 {
891 return PyFloat_FromDouble(fabs(v->ob_fval));
892 }
893
894 static int
895 float_nonzero(PyFloatObject *v)
896 {
897 return v->ob_fval != 0.0;
898 }
899
900 static int
901 float_coerce(PyObject **pv, PyObject **pw)
902 {
903 if (PyInt_Check(*pw)) {
904 long x = PyInt_AsLong(*pw);
905 *pw = PyFloat_FromDouble((double)x);
906 Py_INCREF(*pv);
907 return 0;
908 }
909 else if (PyLong_Check(*pw)) {
910 double x = PyLong_AsDouble(*pw);
911 if (x == -1.0 && PyErr_Occurred())
912 return -1;
913 *pw = PyFloat_FromDouble(x);
914 Py_INCREF(*pv);
915 return 0;
916 }
917 else if (PyFloat_Check(*pw)) {
918 Py_INCREF(*pv);
919 Py_INCREF(*pw);
920 return 0;
921 }
922 return 1; /* Can't do it */
923 }
924
925 static PyObject *
926 float_is_integer(PyObject *v)
927 {
928 double x = PyFloat_AsDouble(v);
929 PyObject *o;
930
931 if (x == -1.0 && PyErr_Occurred())
932 return NULL;
933 if (!Py_IS_FINITE(x))
934 Py_RETURN_FALSE;
935 errno = 0;
936 PyFPE_START_PROTECT("is_integer", return NULL)
937 o = (floor(x) == x) ? Py_True : Py_False;
938 PyFPE_END_PROTECT(x)
939 if (errno != 0) {
940 PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError :
941 PyExc_ValueError);
942 return NULL;
943 }
944 Py_INCREF(o);
945 return o;
946 }
947
948 #if 0
949 static PyObject *
950 float_is_inf(PyObject *v)
951 {
952 double x = PyFloat_AsDouble(v);
953 if (x == -1.0 && PyErr_Occurred())
954 return NULL;
955 return PyBool_FromLong((long)Py_IS_INFINITY(x));
956 }
957
958 static PyObject *
959 float_is_nan(PyObject *v)
960 {
961 double x = PyFloat_AsDouble(v);
962 if (x == -1.0 && PyErr_Occurred())
963 return NULL;
964 return PyBool_FromLong((long)Py_IS_NAN(x));
965 }
966
967 static PyObject *
968 float_is_finite(PyObject *v)
969 {
970 double x = PyFloat_AsDouble(v);
971 if (x == -1.0 && PyErr_Occurred())
972 return NULL;
973 return PyBool_FromLong((long)Py_IS_FINITE(x));
974 }
975 #endif
976
977 static PyObject *
978 float_trunc(PyObject *v)
979 {
980 double x = PyFloat_AsDouble(v);
981 double wholepart; /* integral portion of x, rounded toward 0 */
982
983 (void)modf(x, &wholepart);
984 /* Try to get out cheap if this fits in a Python int. The attempt
985 * to cast to long must be protected, as C doesn't define what
986 * happens if the double is too big to fit in a long. Some rare
987 * systems raise an exception then (RISCOS was mentioned as one,
988 * and someone using a non-default option on Sun also bumped into
989 * that). Note that checking for >= and <= LONG_{MIN,MAX} would
990 * still be vulnerable: if a long has more bits of precision than
991 * a double, casting MIN/MAX to double may yield an approximation,
992 * and if that's rounded up, then, e.g., wholepart=LONG_MAX+1 would
993 * yield true from the C expression wholepart<=LONG_MAX, despite
994 * that wholepart is actually greater than LONG_MAX.
995 */
996 if (LONG_MIN < wholepart && wholepart < LONG_MAX) {
997 const long aslong = (long)wholepart;
998 return PyInt_FromLong(aslong);
999 }
1000 return PyLong_FromDouble(wholepart);
1001 }
1002
1003 static PyObject *
1004 float_long(PyObject *v)
1005 {
1006 double x = PyFloat_AsDouble(v);
1007 return PyLong_FromDouble(x);
1008 }
1009
1010 static PyObject *
1011 float_float(PyObject *v)
1012 {
1013 if (PyFloat_CheckExact(v))
1014 Py_INCREF(v);
1015 else
1016 v = PyFloat_FromDouble(((PyFloatObject *)v)->ob_fval);
1017 return v;
1018 }
1019
1020 /* turn ASCII hex characters into integer values and vice versa */
1021
1022 static char
1023 char_from_hex(int x)
1024 {
1025 assert(0 <= x && x < 16);
1026 return "0123456789abcdef"[x];
1027 }
1028
1029 static int
1030 hex_from_char(char c) {
1031 int x;
1032 switch(c) {
1033 case '0':
1034 x = 0;
1035 break;
1036 case '1':
1037 x = 1;
1038 break;
1039 case '2':
1040 x = 2;
1041 break;
1042 case '3':
1043 x = 3;
1044 break;
1045 case '4':
1046 x = 4;
1047 break;
1048 case '5':
1049 x = 5;
1050 break;
1051 case '6':
1052 x = 6;
1053 break;
1054 case '7':
1055 x = 7;
1056 break;
1057 case '8':
1058 x = 8;
1059 break;
1060 case '9':
1061 x = 9;
1062 break;
1063 case 'a':
1064 case 'A':
1065 x = 10;
1066 break;
1067 case 'b':
1068 case 'B':
1069 x = 11;
1070 break;
1071 case 'c':
1072 case 'C':
1073 x = 12;
1074 break;
1075 case 'd':
1076 case 'D':
1077 x = 13;
1078 break;
1079 case 'e':
1080 case 'E':
1081 x = 14;
1082 break;
1083 case 'f':
1084 case 'F':
1085 x = 15;
1086 break;
1087 default:
1088 x = -1;
1089 break;
1090 }
1091 return x;
1092 }
1093
1094 /* convert a float to a hexadecimal string */
1095
1096 /* TOHEX_NBITS is DBL_MANT_DIG rounded up to the next integer
1097 of the form 4k+1. */
1098 #define TOHEX_NBITS DBL_MANT_DIG + 3 - (DBL_MANT_DIG+2)%4
1099
1100 static PyObject *
1101 float_hex(PyObject *v)
1102 {
1103 double x, m;
1104 int e, shift, i, si, esign;
1105 /* Space for 1+(TOHEX_NBITS-1)/4 digits, a decimal point, and the
1106 trailing NUL byte. */
1107 char s[(TOHEX_NBITS-1)/4+3];
1108
1109 CONVERT_TO_DOUBLE(v, x);
1110
1111 if (Py_IS_NAN(x) || Py_IS_INFINITY(x))
1112 return float_str((PyFloatObject *)v);
1113
1114 if (x == 0.0) {
1115 if(copysign(1.0, x) == -1.0)
1116 return PyString_FromString("-0x0.0p+0");
1117 else
1118 return PyString_FromString("0x0.0p+0");
1119 }
1120
1121 m = frexp(fabs(x), &e);
1122 shift = 1 - MAX(DBL_MIN_EXP - e, 0);
1123 m = ldexp(m, shift);
1124 e -= shift;
1125
1126 si = 0;
1127 s[si] = char_from_hex((int)m);
1128 si++;
1129 m -= (int)m;
1130 s[si] = '.';
1131 si++;
1132 for (i=0; i < (TOHEX_NBITS-1)/4; i++) {
1133 m *= 16.0;
1134 s[si] = char_from_hex((int)m);
1135 si++;
1136 m -= (int)m;
1137 }
1138 s[si] = '\0';
1139
1140 if (e < 0) {
1141 esign = (int)'-';
1142 e = -e;
1143 }
1144 else
1145 esign = (int)'+';
1146
1147 if (x < 0.0)
1148 return PyString_FromFormat("-0x%sp%c%d", s, esign, e);
1149 else
1150 return PyString_FromFormat("0x%sp%c%d", s, esign, e);
1151 }
1152
1153 PyDoc_STRVAR(float_hex_doc,
1154 "float.hex() -> string\n\
1155 \n\
1156 Return a hexadecimal representation of a floating-point number.\n\
1157 >>> (-0.1).hex()\n\
1158 '-0x1.999999999999ap-4'\n\
1159 >>> 3.14159.hex()\n\
1160 '0x1.921f9f01b866ep+1'");
1161
1162 /* Case-insensitive locale-independent string match used for nan and inf
1163 detection. t should be lower-case and null-terminated. Return a nonzero
1164 result if the first strlen(t) characters of s match t and 0 otherwise. */
1165
1166 static int
1167 case_insensitive_match(const char *s, const char *t)
1168 {
1169 while(*t && Py_TOLOWER(*s) == *t) {
1170 s++;
1171 t++;
1172 }
1173 return *t ? 0 : 1;
1174 }
1175
1176 /* Convert a hexadecimal string to a float. */
1177
1178 static PyObject *
1179 float_fromhex(PyObject *cls, PyObject *arg)
1180 {
1181 PyObject *result_as_float, *result;
1182 double x;
1183 long exp, top_exp, lsb, key_digit;
1184 char *s, *coeff_start, *s_store, *coeff_end, *exp_start, *s_end;
1185 int half_eps, digit, round_up, sign=1;
1186 Py_ssize_t length, ndigits, fdigits, i;
1187
1188 /*
1189 * For the sake of simplicity and correctness, we impose an artificial
1190 * limit on ndigits, the total number of hex digits in the coefficient
1191 * The limit is chosen to ensure that, writing exp for the exponent,
1192 *
1193 * (1) if exp > LONG_MAX/2 then the value of the hex string is
1194 * guaranteed to overflow (provided it's nonzero)
1195 *
1196 * (2) if exp < LONG_MIN/2 then the value of the hex string is
1197 * guaranteed to underflow to 0.
1198 *
1199 * (3) if LONG_MIN/2 <= exp <= LONG_MAX/2 then there's no danger of
1200 * overflow in the calculation of exp and top_exp below.
1201 *
1202 * More specifically, ndigits is assumed to satisfy the following
1203 * inequalities:
1204 *
1205 * 4*ndigits <= DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2
1206 * 4*ndigits <= LONG_MAX/2 + 1 - DBL_MAX_EXP
1207 *
1208 * If either of these inequalities is not satisfied, a ValueError is
1209 * raised. Otherwise, write x for the value of the hex string, and
1210 * assume x is nonzero. Then
1211 *
1212 * 2**(exp-4*ndigits) <= |x| < 2**(exp+4*ndigits).
1213 *
1214 * Now if exp > LONG_MAX/2 then:
1215 *
1216 * exp - 4*ndigits >= LONG_MAX/2 + 1 - (LONG_MAX/2 + 1 - DBL_MAX_EXP)
1217 * = DBL_MAX_EXP
1218 *
1219 * so |x| >= 2**DBL_MAX_EXP, which is too large to be stored in C
1220 * double, so overflows. If exp < LONG_MIN/2, then
1221 *
1222 * exp + 4*ndigits <= LONG_MIN/2 - 1 + (
1223 * DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2)
1224 * = DBL_MIN_EXP - DBL_MANT_DIG - 1
1225 *
1226 * and so |x| < 2**(DBL_MIN_EXP-DBL_MANT_DIG-1), hence underflows to 0
1227 * when converted to a C double.
1228 *
1229 * It's easy to show that if LONG_MIN/2 <= exp <= LONG_MAX/2 then both
1230 * exp+4*ndigits and exp-4*ndigits are within the range of a long.
1231 */
1232
1233 if (PyString_AsStringAndSize(arg, &s, &length))
1234 return NULL;
1235 s_end = s + length;
1236
1237 /********************
1238 * Parse the string *
1239 ********************/
1240
1241 /* leading whitespace and optional sign */
1242 while (Py_ISSPACE(*s))
1243 s++;
1244 if (*s == '-') {
1245 s++;
1246 sign = -1;
1247 }
1248 else if (*s == '+')
1249 s++;
1250
1251 /* infinities and nans */
1252 if (*s == 'i' || *s == 'I') {
1253 if (!case_insensitive_match(s+1, "nf"))
1254 goto parse_error;
1255 s += 3;
1256 x = Py_HUGE_VAL;
1257 if (case_insensitive_match(s, "inity"))
1258 s += 5;
1259 goto finished;
1260 }
1261 if (*s == 'n' || *s == 'N') {
1262 if (!case_insensitive_match(s+1, "an"))
1263 goto parse_error;
1264 s += 3;
1265 x = Py_NAN;
1266 goto finished;
1267 }
1268
1269 /* [0x] */
1270 s_store = s;
1271 if (*s == '0') {
1272 s++;
1273 if (*s == 'x' || *s == 'X')
1274 s++;
1275 else
1276 s = s_store;
1277 }
1278
1279 /* coefficient: <integer> [. <fraction>] */
1280 coeff_start = s;
1281 while (hex_from_char(*s) >= 0)
1282 s++;
1283 s_store = s;
1284 if (*s == '.') {
1285 s++;
1286 while (hex_from_char(*s) >= 0)
1287 s++;
1288 coeff_end = s-1;
1289 }
1290 else
1291 coeff_end = s;
1292
1293 /* ndigits = total # of hex digits; fdigits = # after point */
1294 ndigits = coeff_end - coeff_start;
1295 fdigits = coeff_end - s_store;
1296 if (ndigits == 0)
1297 goto parse_error;
1298 if (ndigits > MIN(DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2,
1299 LONG_MAX/2 + 1 - DBL_MAX_EXP)/4)
1300 goto insane_length_error;
1301
1302 /* [p <exponent>] */
1303 if (*s == 'p' || *s == 'P') {
1304 s++;
1305 exp_start = s;
1306 if (*s == '-' || *s == '+')
1307 s++;
1308 if (!('0' <= *s && *s <= '9'))
1309 goto parse_error;
1310 s++;
1311 while ('0' <= *s && *s <= '9')
1312 s++;
1313 exp = strtol(exp_start, NULL, 10);
1314 }
1315 else
1316 exp = 0;
1317
1318 /* for 0 <= j < ndigits, HEX_DIGIT(j) gives the jth most significant digit */
1319 #define HEX_DIGIT(j) hex_from_char(*((j) < fdigits ? \
1320 coeff_end-(j) : \
1321 coeff_end-1-(j)))
1322
1323 /*******************************************
1324 * Compute rounded value of the hex string *
1325 *******************************************/
1326
1327 /* Discard leading zeros, and catch extreme overflow and underflow */
1328 while (ndigits > 0 && HEX_DIGIT(ndigits-1) == 0)
1329 ndigits--;
1330 if (ndigits == 0 || exp < LONG_MIN/2) {
1331 x = 0.0;
1332 goto finished;
1333 }
1334 if (exp > LONG_MAX/2)
1335 goto overflow_error;
1336
1337 /* Adjust exponent for fractional part. */
1338 exp = exp - 4*((long)fdigits);
1339
1340 /* top_exp = 1 more than exponent of most sig. bit of coefficient */
1341 top_exp = exp + 4*((long)ndigits - 1);
1342 for (digit = HEX_DIGIT(ndigits-1); digit != 0; digit /= 2)
1343 top_exp++;
1344
1345 /* catch almost all nonextreme cases of overflow and underflow here */
1346 if (top_exp < DBL_MIN_EXP - DBL_MANT_DIG) {
1347 x = 0.0;
1348 goto finished;
1349 }
1350 if (top_exp > DBL_MAX_EXP)
1351 goto overflow_error;
1352
1353 /* lsb = exponent of least significant bit of the *rounded* value.
1354 This is top_exp - DBL_MANT_DIG unless result is subnormal. */
1355 lsb = MAX(top_exp, (long)DBL_MIN_EXP) - DBL_MANT_DIG;
1356
1357 x = 0.0;
1358 if (exp >= lsb) {
1359 /* no rounding required */
1360 for (i = ndigits-1; i >= 0; i--)
1361 x = 16.0*x + HEX_DIGIT(i);
1362 x = ldexp(x, (int)(exp));
1363 goto finished;
1364 }
1365 /* rounding required. key_digit is the index of the hex digit
1366 containing the first bit to be rounded away. */
1367 half_eps = 1 << (int)((lsb - exp - 1) % 4);
1368 key_digit = (lsb - exp - 1) / 4;
1369 for (i = ndigits-1; i > key_digit; i--)
1370 x = 16.0*x + HEX_DIGIT(i);
1371 digit = HEX_DIGIT(key_digit);
1372 x = 16.0*x + (double)(digit & (16-2*half_eps));
1373
1374 /* round-half-even: round up if bit lsb-1 is 1 and at least one of
1375 bits lsb, lsb-2, lsb-3, lsb-4, ... is 1. */
1376 if ((digit & half_eps) != 0) {
1377 round_up = 0;
1378 if ((digit & (3*half_eps-1)) != 0 ||
1379 (half_eps == 8 && (HEX_DIGIT(key_digit+1) & 1) != 0))
1380 round_up = 1;
1381 else
1382 for (i = key_digit-1; i >= 0; i--)
1383 if (HEX_DIGIT(i) != 0) {
1384 round_up = 1;
1385 break;
1386 }
1387 if (round_up == 1) {
1388 x += 2*half_eps;
1389 if (top_exp == DBL_MAX_EXP &&
1390 x == ldexp((double)(2*half_eps), DBL_MANT_DIG))
1391 /* overflow corner case: pre-rounded value <
1392 2**DBL_MAX_EXP; rounded=2**DBL_MAX_EXP. */
1393 goto overflow_error;
1394 }
1395 }
1396 x = ldexp(x, (int)(exp+4*key_digit));
1397
1398 finished:
1399 /* optional trailing whitespace leading to the end of the string */
1400 while (Py_ISSPACE(*s))
1401 s++;
1402 if (s != s_end)
1403 goto parse_error;
1404 result_as_float = Py_BuildValue("(d)", sign * x);
1405 if (result_as_float == NULL)
1406 return NULL;
1407 result = PyObject_CallObject(cls, result_as_float);
1408 Py_DECREF(result_as_float);
1409 return result;
1410
1411 overflow_error:
1412 PyErr_SetString(PyExc_OverflowError,
1413 "hexadecimal value too large to represent as a float");
1414 return NULL;
1415
1416 parse_error:
1417 PyErr_SetString(PyExc_ValueError,
1418 "invalid hexadecimal floating-point string");
1419 return NULL;
1420
1421 insane_length_error:
1422 PyErr_SetString(PyExc_ValueError,
1423 "hexadecimal string too long to convert");
1424 return NULL;
1425 }
1426
1427 PyDoc_STRVAR(float_fromhex_doc,
1428 "float.fromhex(string) -> float\n\
1429 \n\
1430 Create a floating-point number from a hexadecimal string.\n\
1431 >>> float.fromhex('0x1.ffffp10')\n\
1432 2047.984375\n\
1433 >>> float.fromhex('-0x1p-1074')\n\
1434 -4.9406564584124654e-324");
1435
1436
1437 static PyObject *
1438 float_as_integer_ratio(PyObject *v, PyObject *unused)
1439 {
1440 double self;
1441 double float_part;
1442 int exponent;
1443 int i;
1444
1445 PyObject *prev;
1446 PyObject *py_exponent = NULL;
1447 PyObject *numerator = NULL;
1448 PyObject *denominator = NULL;
1449 PyObject *result_pair = NULL;
1450 PyNumberMethods *long_methods = PyLong_Type.tp_as_number;
1451
1452 #define INPLACE_UPDATE(obj, call) \
1453 prev = obj; \
1454 obj = call; \
1455 Py_DECREF(prev); \
1456
1457 CONVERT_TO_DOUBLE(v, self);
1458
1459 if (Py_IS_INFINITY(self)) {
1460 PyErr_SetString(PyExc_OverflowError,
1461 "Cannot pass infinity to float.as_integer_ratio.");
1462 return NULL;
1463 }
1464 #ifdef Py_NAN
1465 if (Py_IS_NAN(self)) {
1466 PyErr_SetString(PyExc_ValueError,
1467 "Cannot pass NaN to float.as_integer_ratio.");
1468 return NULL;
1469 }
1470 #endif
1471
1472 PyFPE_START_PROTECT("as_integer_ratio", goto error);
1473 float_part = frexp(self, &exponent); /* self == float_part * 2**exponent exactly */
1474 PyFPE_END_PROTECT(float_part);
1475
1476 for (i=0; i<300 && float_part != floor(float_part) ; i++) {
1477 float_part *= 2.0;
1478 exponent--;
1479 }
1480 /* self == float_part * 2**exponent exactly and float_part is integral.
1481 If FLT_RADIX != 2, the 300 steps may leave a tiny fractional part
1482 to be truncated by PyLong_FromDouble(). */
1483
1484 numerator = PyLong_FromDouble(float_part);
1485 if (numerator == NULL) goto error;
1486
1487 /* fold in 2**exponent */
1488 denominator = PyLong_FromLong(1);
1489 py_exponent = PyLong_FromLong(labs((long)exponent));
1490 if (py_exponent == NULL) goto error;
1491 INPLACE_UPDATE(py_exponent,
1492 long_methods->nb_lshift(denominator, py_exponent));
1493 if (py_exponent == NULL) goto error;
1494 if (exponent > 0) {
1495 INPLACE_UPDATE(numerator,
1496 long_methods->nb_multiply(numerator, py_exponent));
1497 if (numerator == NULL) goto error;
1498 }
1499 else {
1500 Py_DECREF(denominator);
1501 denominator = py_exponent;
1502 py_exponent = NULL;
1503 }
1504
1505 /* Returns ints instead of longs where possible */
1506 INPLACE_UPDATE(numerator, PyNumber_Int(numerator));
1507 if (numerator == NULL) goto error;
1508 INPLACE_UPDATE(denominator, PyNumber_Int(denominator));
1509 if (denominator == NULL) goto error;
1510
1511 result_pair = PyTuple_Pack(2, numerator, denominator);
1512
1513 #undef INPLACE_UPDATE
1514 error:
1515 Py_XDECREF(py_exponent);
1516 Py_XDECREF(denominator);
1517 Py_XDECREF(numerator);
1518 return result_pair;
1519 }
1520
1521 PyDoc_STRVAR(float_as_integer_ratio_doc,
1522 "float.as_integer_ratio() -> (int, int)\n"
1523 "\n"
1524 "Returns a pair of integers, whose ratio is exactly equal to the original\n"
1525 "float and with a positive denominator.\n"
1526 "Raises OverflowError on infinities and a ValueError on NaNs.\n"
1527 "\n"
1528 ">>> (10.0).as_integer_ratio()\n"
1529 "(10, 1)\n"
1530 ">>> (0.0).as_integer_ratio()\n"
1531 "(0, 1)\n"
1532 ">>> (-.25).as_integer_ratio()\n"
1533 "(-1, 4)");
1534
1535
1536 static PyObject *
1537 float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds);
1538
1539 static PyObject *
1540 float_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
1541 {
1542 PyObject *x = Py_False; /* Integer zero */
1543 static char *kwlist[] = {"x", 0};
1544
1545 if (type != &PyFloat_Type)
1546 return float_subtype_new(type, args, kwds); /* Wimp out */
1547 if (!PyArg_ParseTupleAndKeywords(args, kwds, "|O:float", kwlist, &x))
1548 return NULL;
1549 /* If it's a string, but not a string subclass, use
1550 PyFloat_FromString. */
1551 if (PyString_CheckExact(x))
1552 return PyFloat_FromString(x, NULL);
1553 return PyNumber_Float(x);
1554 }
1555
1556 /* Wimpy, slow approach to tp_new calls for subtypes of float:
1557 first create a regular float from whatever arguments we got,
1558 then allocate a subtype instance and initialize its ob_fval
1559 from the regular float. The regular float is then thrown away.
1560 */
1561 static PyObject *
1562 float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
1563 {
1564 PyObject *tmp, *newobj;
1565
1566 assert(PyType_IsSubtype(type, &PyFloat_Type));
1567 tmp = float_new(&PyFloat_Type, args, kwds);
1568 if (tmp == NULL)
1569 return NULL;
1570 assert(PyFloat_CheckExact(tmp));
1571 newobj = type->tp_alloc(type, 0);
1572 if (newobj == NULL) {
1573 Py_DECREF(tmp);
1574 return NULL;
1575 }
1576 ((PyFloatObject *)newobj)->ob_fval = ((PyFloatObject *)tmp)->ob_fval;
1577 Py_DECREF(tmp);
1578 return newobj;
1579 }
1580
1581 static PyObject *
1582 float_getnewargs(PyFloatObject *v)
1583 {
1584 return Py_BuildValue("(d)", v->ob_fval);
1585 }
1586
1587 /* this is for the benefit of the pack/unpack routines below */
1588
1589 typedef enum {
1590 unknown_format, ieee_big_endian_format, ieee_little_endian_format
1591 } float_format_type;
1592
1593 static float_format_type double_format, float_format;
1594 static float_format_type detected_double_format, detected_float_format;
1595
1596 static PyObject *
1597 float_getformat(PyTypeObject *v, PyObject* arg)
1598 {
1599 char* s;
1600 float_format_type r;
1601
1602 if (!PyString_Check(arg)) {
1603 PyErr_Format(PyExc_TypeError,
1604 "__getformat__() argument must be string, not %.500s",
1605 Py_TYPE(arg)->tp_name);
1606 return NULL;
1607 }
1608 s = PyString_AS_STRING(arg);
1609 if (strcmp(s, "double") == 0) {
1610 r = double_format;
1611 }
1612 else if (strcmp(s, "float") == 0) {
1613 r = float_format;
1614 }
1615 else {
1616 PyErr_SetString(PyExc_ValueError,
1617 "__getformat__() argument 1 must be "
1618 "'double' or 'float'");
1619 return NULL;
1620 }
1621
1622 switch (r) {
1623 case unknown_format:
1624 return PyString_FromString("unknown");
1625 case ieee_little_endian_format:
1626 return PyString_FromString("IEEE, little-endian");
1627 case ieee_big_endian_format:
1628 return PyString_FromString("IEEE, big-endian");
1629 default:
1630 Py_FatalError("insane float_format or double_format");
1631 return NULL;
1632 }
1633 }
1634
1635 PyDoc_STRVAR(float_getformat_doc,
1636 "float.__getformat__(typestr) -> string\n"
1637 "\n"
1638 "You probably don't want to use this function. It exists mainly to be\n"
1639 "used in Python's test suite.\n"
1640 "\n"
1641 "typestr must be 'double' or 'float'. This function returns whichever of\n"
1642 "'unknown', 'IEEE, big-endian' or 'IEEE, little-endian' best describes the\n"
1643 "format of floating point numbers used by the C type named by typestr.");
1644
1645 static PyObject *
1646 float_setformat(PyTypeObject *v, PyObject* args)
1647 {
1648 char* typestr;
1649 char* format;
1650 float_format_type f;
1651 float_format_type detected;
1652 float_format_type *p;
1653
1654 if (!PyArg_ParseTuple(args, "ss:__setformat__", &typestr, &format))
1655 return NULL;
1656
1657 if (strcmp(typestr, "double") == 0) {
1658 p = &double_format;
1659 detected = detected_double_format;
1660 }
1661 else if (strcmp(typestr, "float") == 0) {
1662 p = &float_format;
1663 detected = detected_float_format;
1664 }
1665 else {
1666 PyErr_SetString(PyExc_ValueError,
1667 "__setformat__() argument 1 must "
1668 "be 'double' or 'float'");
1669 return NULL;
1670 }
1671
1672 if (strcmp(format, "unknown") == 0) {
1673 f = unknown_format;
1674 }
1675 else if (strcmp(format, "IEEE, little-endian") == 0) {
1676 f = ieee_little_endian_format;
1677 }
1678 else if (strcmp(format, "IEEE, big-endian") == 0) {
1679 f = ieee_big_endian_format;
1680 }
1681 else {
1682 PyErr_SetString(PyExc_ValueError,
1683 "__setformat__() argument 2 must be "
1684 "'unknown', 'IEEE, little-endian' or "
1685 "'IEEE, big-endian'");
1686 return NULL;
1687
1688 }
1689
1690 if (f != unknown_format && f != detected) {
1691 PyErr_Format(PyExc_ValueError,
1692 "can only set %s format to 'unknown' or the "
1693 "detected platform value", typestr);
1694 return NULL;
1695 }
1696
1697 *p = f;
1698 Py_RETURN_NONE;
1699 }
1700
1701 PyDoc_STRVAR(float_setformat_doc,
1702 "float.__setformat__(typestr, fmt) -> None\n"
1703 "\n"
1704 "You probably don't want to use this function. It exists mainly to be\n"
1705 "used in Python's test suite.\n"
1706 "\n"
1707 "typestr must be 'double' or 'float'. fmt must be one of 'unknown',\n"
1708 "'IEEE, big-endian' or 'IEEE, little-endian', and in addition can only be\n"
1709 "one of the latter two if it appears to match the underlying C reality.\n"
1710 "\n"
1711 "Overrides the automatic determination of C-level floating point type.\n"
1712 "This affects how floats are converted to and from binary strings.");
1713
1714 static PyObject *
1715 float_getzero(PyObject *v, void *closure)
1716 {
1717 return PyFloat_FromDouble(0.0);
1718 }
1719
1720 static PyObject *
1721 float__format__(PyObject *self, PyObject *args)
1722 {
1723 PyObject *format_spec;
1724
1725 if (!PyArg_ParseTuple(args, "O:__format__", &format_spec))
1726 return NULL;
1727 if (PyBytes_Check(format_spec))
1728 return _PyFloat_FormatAdvanced(self,
1729 PyBytes_AS_STRING(format_spec),
1730 PyBytes_GET_SIZE(format_spec));
1731 if (PyUnicode_Check(format_spec)) {
1732 /* Convert format_spec to a str */
1733 PyObject *result;
1734 PyObject *str_spec = PyObject_Str(format_spec);
1735
1736 if (str_spec == NULL)
1737 return NULL;
1738
1739 result = _PyFloat_FormatAdvanced(self,
1740 PyBytes_AS_STRING(str_spec),
1741 PyBytes_GET_SIZE(str_spec));
1742
1743 Py_DECREF(str_spec);
1744 return result;
1745 }
1746 PyErr_SetString(PyExc_TypeError, "__format__ requires str or unicode");
1747 return NULL;
1748 }
1749
1750 PyDoc_STRVAR(float__format__doc,
1751 "float.__format__(format_spec) -> string\n"
1752 "\n"
1753 "Formats the float according to format_spec.");
1754
1755
1756 static PyMethodDef float_methods[] = {
1757 {"conjugate", (PyCFunction)float_float, METH_NOARGS,
1758 "Returns self, the complex conjugate of any float."},
1759 {"__trunc__", (PyCFunction)float_trunc, METH_NOARGS,
1760 "Returns the Integral closest to x between 0 and x."},
1761 {"as_integer_ratio", (PyCFunction)float_as_integer_ratio, METH_NOARGS,
1762 float_as_integer_ratio_doc},
1763 {"fromhex", (PyCFunction)float_fromhex,
1764 METH_O|METH_CLASS, float_fromhex_doc},
1765 {"hex", (PyCFunction)float_hex,
1766 METH_NOARGS, float_hex_doc},
1767 {"is_integer", (PyCFunction)float_is_integer, METH_NOARGS,
1768 "Returns True if the float is an integer."},
1769 #if 0
1770 {"is_inf", (PyCFunction)float_is_inf, METH_NOARGS,
1771 "Returns True if the float is positive or negative infinite."},
1772 {"is_finite", (PyCFunction)float_is_finite, METH_NOARGS,
1773 "Returns True if the float is finite, neither infinite nor NaN."},
1774 {"is_nan", (PyCFunction)float_is_nan, METH_NOARGS,
1775 "Returns True if the float is not a number (NaN)."},
1776 #endif
1777 {"__getnewargs__", (PyCFunction)float_getnewargs, METH_NOARGS},
1778 {"__getformat__", (PyCFunction)float_getformat,
1779 METH_O|METH_CLASS, float_getformat_doc},
1780 {"__setformat__", (PyCFunction)float_setformat,
1781 METH_VARARGS|METH_CLASS, float_setformat_doc},
1782 {"__format__", (PyCFunction)float__format__,
1783 METH_VARARGS, float__format__doc},
1784 {NULL, NULL} /* sentinel */
1785 };
1786
1787 static PyGetSetDef float_getset[] = {
1788 {"real",
1789 (getter)float_float, (setter)NULL,
1790 "the real part of a complex number",
1791 NULL},
1792 {"imag",
1793 (getter)float_getzero, (setter)NULL,
1794 "the imaginary part of a complex number",
1795 NULL},
1796 {NULL} /* Sentinel */
1797 };
1798
1799 PyDoc_STRVAR(float_doc,
1800 "float(x) -> floating point number\n\
1801 \n\
1802 Convert a string or number to a floating point number, if possible.");
1803
1804
1805 static PyNumberMethods float_as_number = {
1806 float_add, /*nb_add*/
1807 float_sub, /*nb_subtract*/
1808 float_mul, /*nb_multiply*/
1809 float_classic_div, /*nb_divide*/
1810 float_rem, /*nb_remainder*/
1811 float_divmod, /*nb_divmod*/
1812 float_pow, /*nb_power*/
1813 (unaryfunc)float_neg, /*nb_negative*/
1814 (unaryfunc)float_float, /*nb_positive*/
1815 (unaryfunc)float_abs, /*nb_absolute*/
1816 (inquiry)float_nonzero, /*nb_nonzero*/
1817 0, /*nb_invert*/
1818 0, /*nb_lshift*/
1819 0, /*nb_rshift*/
1820 0, /*nb_and*/
1821 0, /*nb_xor*/
1822 0, /*nb_or*/
1823 float_coerce, /*nb_coerce*/
1824 float_trunc, /*nb_int*/
1825 float_long, /*nb_long*/
1826 float_float, /*nb_float*/
1827 0, /* nb_oct */
1828 0, /* nb_hex */
1829 0, /* nb_inplace_add */
1830 0, /* nb_inplace_subtract */
1831 0, /* nb_inplace_multiply */
1832 0, /* nb_inplace_divide */
1833 0, /* nb_inplace_remainder */
1834 0, /* nb_inplace_power */
1835 0, /* nb_inplace_lshift */
1836 0, /* nb_inplace_rshift */
1837 0, /* nb_inplace_and */
1838 0, /* nb_inplace_xor */
1839 0, /* nb_inplace_or */
1840 float_floor_div, /* nb_floor_divide */
1841 float_div, /* nb_true_divide */
1842 0, /* nb_inplace_floor_divide */
1843 0, /* nb_inplace_true_divide */
1844 };
1845
1846 PyTypeObject PyFloat_Type = {
1847 PyVarObject_HEAD_INIT(&PyType_Type, 0)
1848 "float",
1849 sizeof(PyFloatObject),
1850 0,
1851 (destructor)float_dealloc, /* tp_dealloc */
1852 (printfunc)float_print, /* tp_print */
1853 0, /* tp_getattr */
1854 0, /* tp_setattr */
1855 0, /* tp_compare */
1856 (reprfunc)float_repr, /* tp_repr */
1857 &float_as_number, /* tp_as_number */
1858 0, /* tp_as_sequence */
1859 0, /* tp_as_mapping */
1860 (hashfunc)float_hash, /* tp_hash */
1861 0, /* tp_call */
1862 (reprfunc)float_str, /* tp_str */
1863 PyObject_GenericGetAttr, /* tp_getattro */
1864 0, /* tp_setattro */
1865 0, /* tp_as_buffer */
1866 Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES |
1867 Py_TPFLAGS_BASETYPE, /* tp_flags */
1868 float_doc, /* tp_doc */
1869 0, /* tp_traverse */
1870 0, /* tp_clear */
1871 float_richcompare, /* tp_richcompare */
1872 0, /* tp_weaklistoffset */
1873 0, /* tp_iter */
1874 0, /* tp_iternext */
1875 float_methods, /* tp_methods */
1876 0, /* tp_members */
1877 float_getset, /* tp_getset */
1878 0, /* tp_base */
1879 0, /* tp_dict */
1880 0, /* tp_descr_get */
1881 0, /* tp_descr_set */
1882 0, /* tp_dictoffset */
1883 0, /* tp_init */
1884 0, /* tp_alloc */
1885 float_new, /* tp_new */
1886 };
1887
1888 void
1889 _PyFloat_Init(void)
1890 {
1891 /* We attempt to determine if this machine is using IEEE
1892 floating point formats by peering at the bits of some
1893 carefully chosen values. If it looks like we are on an
1894 IEEE platform, the float packing/unpacking routines can
1895 just copy bits, if not they resort to arithmetic & shifts
1896 and masks. The shifts & masks approach works on all finite
1897 values, but what happens to infinities, NaNs and signed
1898 zeroes on packing is an accident, and attempting to unpack
1899 a NaN or an infinity will raise an exception.
1900
1901 Note that if we're on some whacked-out platform which uses
1902 IEEE formats but isn't strictly little-endian or big-
1903 endian, we will fall back to the portable shifts & masks
1904 method. */
1905
1906 #if SIZEOF_DOUBLE == 8
1907 {
1908 double x = 9006104071832581.0;
1909 if (memcmp(&x, "\x43\x3f\xff\x01\x02\x03\x04\x05", 8) == 0)
1910 detected_double_format = ieee_big_endian_format;
1911 else if (memcmp(&x, "\x05\x04\x03\x02\x01\xff\x3f\x43", 8) == 0)
1912 detected_double_format = ieee_little_endian_format;
1913 else
1914 detected_double_format = unknown_format;
1915 }
1916 #else
1917 detected_double_format = unknown_format;
1918 #endif
1919
1920 #if SIZEOF_FLOAT == 4
1921 {
1922 float y = 16711938.0;
1923 if (memcmp(&y, "\x4b\x7f\x01\x02", 4) == 0)
1924 detected_float_format = ieee_big_endian_format;
1925 else if (memcmp(&y, "\x02\x01\x7f\x4b", 4) == 0)
1926 detected_float_format = ieee_little_endian_format;
1927 else
1928 detected_float_format = unknown_format;
1929 }
1930 #else
1931 detected_float_format = unknown_format;
1932 #endif
1933
1934 double_format = detected_double_format;
1935 float_format = detected_float_format;
1936
1937 /* Init float info */
1938 if (FloatInfoType.tp_name == 0)
1939 PyStructSequence_InitType(&FloatInfoType, &floatinfo_desc);
1940 }
1941
1942 int
1943 PyFloat_ClearFreeList(void)
1944 {
1945 PyFloatObject *p;
1946 PyFloatBlock *list, *next;
1947 int i;
1948 int u; /* remaining unfreed ints per block */
1949 int freelist_size = 0;
1950
1951 list = block_list;
1952 block_list = NULL;
1953 free_list = NULL;
1954 while (list != NULL) {
1955 u = 0;
1956 for (i = 0, p = &list->objects[0];
1957 i < N_FLOATOBJECTS;
1958 i++, p++) {
1959 if (PyFloat_CheckExact(p) && Py_REFCNT(p) != 0)
1960 u++;
1961 }
1962 next = list->next;
1963 if (u) {
1964 list->next = block_list;
1965 block_list = list;
1966 for (i = 0, p = &list->objects[0];
1967 i < N_FLOATOBJECTS;
1968 i++, p++) {
1969 if (!PyFloat_CheckExact(p) ||
1970 Py_REFCNT(p) == 0) {
1971 Py_TYPE(p) = (struct _typeobject *)
1972 free_list;
1973 free_list = p;
1974 }
1975 }
1976 }
1977 else {
1978 PyMem_FREE(list);
1979 }
1980 freelist_size += u;
1981 list = next;
1982 }
1983 return freelist_size;
1984 }
1985
1986 void
1987 PyFloat_Fini(void)
1988 {
1989 PyFloatObject *p;
1990 PyFloatBlock *list;
1991 int i;
1992 int u; /* total unfreed floats per block */
1993
1994 u = PyFloat_ClearFreeList();
1995
1996 if (!Py_VerboseFlag)
1997 return;
1998 fprintf(stderr, "# cleanup floats");
1999 if (!u) {
2000 fprintf(stderr, "\n");
2001 }
2002 else {
2003 fprintf(stderr,
2004 ": %d unfreed float%s\n",
2005 u, u == 1 ? "" : "s");
2006 }
2007 if (Py_VerboseFlag > 1) {
2008 list = block_list;
2009 while (list != NULL) {
2010 for (i = 0, p = &list->objects[0];
2011 i < N_FLOATOBJECTS;
2012 i++, p++) {
2013 if (PyFloat_CheckExact(p) &&
2014 Py_REFCNT(p) != 0) {
2015 char buf[100];
2016 PyFloat_AsString(buf, p);
2017 /* XXX(twouters) cast refcount to
2018 long until %zd is universally
2019 available
2020 */
2021 fprintf(stderr,
2022 "# <float at %p, refcnt=%ld, val=%s>\n",
2023 p, (long)Py_REFCNT(p), buf);
2024 }
2025 }
2026 list = list->next;
2027 }
2028 }
2029 }
2030
2031 /*----------------------------------------------------------------------------
2032 * _PyFloat_{Pack,Unpack}{4,8}. See floatobject.h.
2033 */
2034 int
2035 _PyFloat_Pack4(double x, unsigned char *p, int le)
2036 {
2037 if (float_format == unknown_format) {
2038 unsigned char sign;
2039 int e;
2040 double f;
2041 unsigned int fbits;
2042 int incr = 1;
2043
2044 if (le) {
2045 p += 3;
2046 incr = -1;
2047 }
2048
2049 if (x < 0) {
2050 sign = 1;
2051 x = -x;
2052 }
2053 else
2054 sign = 0;
2055
2056 f = frexp(x, &e);
2057
2058 /* Normalize f to be in the range [1.0, 2.0) */
2059 if (0.5 <= f && f < 1.0) {
2060 f *= 2.0;
2061 e--;
2062 }
2063 else if (f == 0.0)
2064 e = 0;
2065 else {
2066 PyErr_SetString(PyExc_SystemError,
2067 "frexp() result out of range");
2068 return -1;
2069 }
2070
2071 if (e >= 128)
2072 goto Overflow;
2073 else if (e < -126) {
2074 /* Gradual underflow */
2075 f = ldexp(f, 126 + e);
2076 e = 0;
2077 }
2078 else if (!(e == 0 && f == 0.0)) {
2079 e += 127;
2080 f -= 1.0; /* Get rid of leading 1 */
2081 }
2082
2083 f *= 8388608.0; /* 2**23 */
2084 fbits = (unsigned int)(f + 0.5); /* Round */
2085 assert(fbits <= 8388608);
2086 if (fbits >> 23) {
2087 /* The carry propagated out of a string of 23 1 bits. */
2088 fbits = 0;
2089 ++e;
2090 if (e >= 255)
2091 goto Overflow;
2092 }
2093
2094 /* First byte */
2095 *p = (sign << 7) | (e >> 1);
2096 p += incr;
2097
2098 /* Second byte */
2099 *p = (char) (((e & 1) << 7) | (fbits >> 16));
2100 p += incr;
2101
2102 /* Third byte */
2103 *p = (fbits >> 8) & 0xFF;
2104 p += incr;
2105
2106 /* Fourth byte */
2107 *p = fbits & 0xFF;
2108
2109 /* Done */
2110 return 0;
2111
2112 }
2113 else {
2114 float y = (float)x;
2115 const char *s = (char*)&y;
2116 int i, incr = 1;
2117
2118 if (Py_IS_INFINITY(y) && !Py_IS_INFINITY(x))
2119 goto Overflow;
2120
2121 if ((float_format == ieee_little_endian_format && !le)
2122 || (float_format == ieee_big_endian_format && le)) {
2123 p += 3;
2124 incr = -1;
2125 }
2126
2127 for (i = 0; i < 4; i++) {
2128 *p = *s++;
2129 p += incr;
2130 }
2131 return 0;
2132 }
2133 Overflow:
2134 PyErr_SetString(PyExc_OverflowError,
2135 "float too large to pack with f format");
2136 return -1;
2137 }
2138
2139 int
2140 _PyFloat_Pack8(double x, unsigned char *p, int le)
2141 {
2142 if (double_format == unknown_format) {
2143 unsigned char sign;
2144 int e;
2145 double f;
2146 unsigned int fhi, flo;
2147 int incr = 1;
2148
2149 if (le) {
2150 p += 7;
2151 incr = -1;
2152 }
2153
2154 if (x < 0) {
2155 sign = 1;
2156 x = -x;
2157 }
2158 else
2159 sign = 0;
2160
2161 f = frexp(x, &e);
2162
2163 /* Normalize f to be in the range [1.0, 2.0) */
2164 if (0.5 <= f && f < 1.0) {
2165 f *= 2.0;
2166 e--;
2167 }
2168 else if (f == 0.0)
2169 e = 0;
2170 else {
2171 PyErr_SetString(PyExc_SystemError,
2172 "frexp() result out of range");
2173 return -1;
2174 }
2175
2176 if (e >= 1024)
2177 goto Overflow;
2178 else if (e < -1022) {
2179 /* Gradual underflow */
2180 f = ldexp(f, 1022 + e);
2181 e = 0;
2182 }
2183 else if (!(e == 0 && f == 0.0)) {
2184 e += 1023;
2185 f -= 1.0; /* Get rid of leading 1 */
2186 }
2187
2188 /* fhi receives the high 28 bits; flo the low 24 bits (== 52 bits) */
2189 f *= 268435456.0; /* 2**28 */
2190 fhi = (unsigned int)f; /* Truncate */
2191 assert(fhi < 268435456);
2192
2193 f -= (double)fhi;
2194 f *= 16777216.0; /* 2**24 */
2195 flo = (unsigned int)(f + 0.5); /* Round */
2196 assert(flo <= 16777216);
2197 if (flo >> 24) {
2198 /* The carry propagated out of a string of 24 1 bits. */
2199 flo = 0;
2200 ++fhi;
2201 if (fhi >> 28) {
2202 /* And it also progagated out of the next 28 bits. */
2203 fhi = 0;
2204 ++e;
2205 if (e >= 2047)
2206 goto Overflow;
2207 }
2208 }
2209
2210 /* First byte */
2211 *p = (sign << 7) | (e >> 4);
2212 p += incr;
2213
2214 /* Second byte */
2215 *p = (unsigned char) (((e & 0xF) << 4) | (fhi >> 24));
2216 p += incr;
2217
2218 /* Third byte */
2219 *p = (fhi >> 16) & 0xFF;
2220 p += incr;
2221
2222 /* Fourth byte */
2223 *p = (fhi >> 8) & 0xFF;
2224 p += incr;
2225
2226 /* Fifth byte */
2227 *p = fhi & 0xFF;
2228 p += incr;
2229
2230 /* Sixth byte */
2231 *p = (flo >> 16) & 0xFF;
2232 p += incr;
2233
2234 /* Seventh byte */
2235 *p = (flo >> 8) & 0xFF;
2236 p += incr;
2237
2238 /* Eighth byte */
2239 *p = flo & 0xFF;
2240 p += incr;
2241
2242 /* Done */
2243 return 0;
2244
2245 Overflow:
2246 PyErr_SetString(PyExc_OverflowError,
2247 "float too large to pack with d format");
2248 return -1;
2249 }
2250 else {
2251 const char *s = (char*)&x;
2252 int i, incr = 1;
2253
2254 if ((double_format == ieee_little_endian_format && !le)
2255 || (double_format == ieee_big_endian_format && le)) {
2256 p += 7;
2257 incr = -1;
2258 }
2259
2260 for (i = 0; i < 8; i++) {
2261 *p = *s++;
2262 p += incr;
2263 }
2264 return 0;
2265 }
2266 }
2267
2268 double
2269 _PyFloat_Unpack4(const unsigned char *p, int le)
2270 {
2271 if (float_format == unknown_format) {
2272 unsigned char sign;
2273 int e;
2274 unsigned int f;
2275 double x;
2276 int incr = 1;
2277
2278 if (le) {
2279 p += 3;
2280 incr = -1;
2281 }
2282
2283 /* First byte */
2284 sign = (*p >> 7) & 1;
2285 e = (*p & 0x7F) << 1;
2286 p += incr;
2287
2288 /* Second byte */
2289 e |= (*p >> 7) & 1;
2290 f = (*p & 0x7F) << 16;
2291 p += incr;
2292
2293 if (e == 255) {
2294 PyErr_SetString(
2295 PyExc_ValueError,
2296 "can't unpack IEEE 754 special value "
2297 "on non-IEEE platform");
2298 return -1;
2299 }
2300
2301 /* Third byte */
2302 f |= *p << 8;
2303 p += incr;
2304
2305 /* Fourth byte */
2306 f |= *p;
2307
2308 x = (double)f / 8388608.0;
2309
2310 /* XXX This sadly ignores Inf/NaN issues */
2311 if (e == 0)
2312 e = -126;
2313 else {
2314 x += 1.0;
2315 e -= 127;
2316 }
2317 x = ldexp(x, e);
2318
2319 if (sign)
2320 x = -x;
2321
2322 return x;
2323 }
2324 else {
2325 float x;
2326
2327 if ((float_format == ieee_little_endian_format && !le)
2328 || (float_format == ieee_big_endian_format && le)) {
2329 char buf[4];
2330 char *d = &buf[3];
2331 int i;
2332
2333 for (i = 0; i < 4; i++) {
2334 *d-- = *p++;
2335 }
2336 memcpy(&x, buf, 4);
2337 }
2338 else {
2339 memcpy(&x, p, 4);
2340 }
2341
2342 return x;
2343 }
2344 }
2345
2346 double
2347 _PyFloat_Unpack8(const unsigned char *p, int le)
2348 {
2349 if (double_format == unknown_format) {
2350 unsigned char sign;
2351 int e;
2352 unsigned int fhi, flo;
2353 double x;
2354 int incr = 1;
2355
2356 if (le) {
2357 p += 7;
2358 incr = -1;
2359 }
2360
2361 /* First byte */
2362 sign = (*p >> 7) & 1;
2363 e = (*p & 0x7F) << 4;
2364
2365 p += incr;
2366
2367 /* Second byte */
2368 e |= (*p >> 4) & 0xF;
2369 fhi = (*p & 0xF) << 24;
2370 p += incr;
2371
2372 if (e == 2047) {
2373 PyErr_SetString(
2374 PyExc_ValueError,
2375 "can't unpack IEEE 754 special value "
2376 "on non-IEEE platform");
2377 return -1.0;
2378 }
2379
2380 /* Third byte */
2381 fhi |= *p << 16;
2382 p += incr;
2383
2384 /* Fourth byte */
2385 fhi |= *p << 8;
2386 p += incr;
2387
2388 /* Fifth byte */
2389 fhi |= *p;
2390 p += incr;
2391
2392 /* Sixth byte */
2393 flo = *p << 16;
2394 p += incr;
2395
2396 /* Seventh byte */
2397 flo |= *p << 8;
2398 p += incr;
2399
2400 /* Eighth byte */
2401 flo |= *p;
2402
2403 x = (double)fhi + (double)flo / 16777216.0; /* 2**24 */
2404 x /= 268435456.0; /* 2**28 */
2405
2406 if (e == 0)
2407 e = -1022;
2408 else {
2409 x += 1.0;
2410 e -= 1023;
2411 }
2412 x = ldexp(x, e);
2413
2414 if (sign)
2415 x = -x;
2416
2417 return x;
2418 }
2419 else {
2420 double x;
2421
2422 if ((double_format == ieee_little_endian_format && !le)
2423 || (double_format == ieee_big_endian_format && le)) {
2424 char buf[8];
2425 char *d = &buf[7];
2426 int i;
2427
2428 for (i = 0; i < 8; i++) {
2429 *d-- = *p++;
2430 }
2431 memcpy(&x, buf, 8);
2432 }
2433 else {
2434 memcpy(&x, p, 8);
2435 }
2436
2437 return x;
2438 }
2439 }
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