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. */ 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)) 27 28struct _floatblock { 29 struct _floatblock *next; 30 PyFloatObject objects[N_FLOATOBJECTS]; 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{ 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; 54} 55 56double 57PyFloat_GetMax(void) 58{ 59 return DBL_MAX; 60} 61 62double 63PyFloat_GetMin(void) 64{ 65 return DBL_MIN; 66} 67 68static PyTypeObject FloatInfoType = {0, 0, 0, 0, 0, 0}; 69 70PyDoc_STRVAR(floatinfo__doc__, 71"sys.float_info\n\ 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[] = { 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} 95}; 96 97static PyStructSequence_Desc floatinfo_desc = { 98 "sys.float_info", /* name */ 99 floatinfo__doc__, /* doc */ 100 floatinfo_fields, /* fields */ 101 11 102}; 103 104PyObject * 105PyFloat_GetInfo(void) 106{ 107 PyObject* floatinfo; 108 int pos = 0; 109 110 floatinfo = PyStructSequence_New(&FloatInfoType); 111 if (floatinfo == NULL) { 112 return NULL; 113 } 114 115#define SetIntFlag(flag) \ 116 PyStructSequence_SET_ITEM(floatinfo, pos++, PyInt_FromLong(flag)) 117#define SetDblFlag(flag) \ 118 PyStructSequence_SET_ITEM(floatinfo, pos++, PyFloat_FromDouble(flag)) 119 120 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); 131#undef SetIntFlag 132#undef SetDblFlag 133 134 if (PyErr_Occurred()) { 135 Py_CLEAR(floatinfo); 136 return NULL; 137 } 138 return floatinfo; 139} 140 141PyObject * 142PyFloat_FromDouble(double fval) 143{ 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 (void)PyObject_INIT(op, &PyFloat_Type); 153 op->ob_fval = fval; 154 return (PyObject *) op; 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{ 176 const char *s, *last, *end; 177 double x; 178 char buffer[256]; /* for errors */ 179#ifdef Py_USING_UNICODE 180 char *s_buffer = NULL; 181#endif 182 Py_ssize_t len; 183 PyObject *str = NULL; 184 PyObject *result = NULL; 185 186 if (pend) 187 *pend = NULL; 188 if (PyString_Check(v)) { 189 s = PyString_AS_STRING(v); 190 len = PyString_GET_SIZE(v); 191 } 192#ifdef Py_USING_UNICODE 193 else if (PyUnicode_Check(v)) { 194 s_buffer = (char *)PyMem_MALLOC(PyUnicode_GET_SIZE(v)+1); 195 if (s_buffer == NULL) 196 return PyErr_NoMemory(); 197 if (PyUnicode_EncodeDecimal(PyUnicode_AS_UNICODE(v), 198 PyUnicode_GET_SIZE(v), 199 s_buffer, 200 NULL)) 201 goto error; 202 s = s_buffer; 203 len = strlen(s); 204 } 205#endif 206 else if (!PyObject_AsCharBuffer(v, &s, &len)) { 207 /* Copy to NUL-terminated buffer. */ 208 str = PyString_FromStringAndSize(s, len); 209 if (str == NULL) 210 return NULL; 211 s = PyString_AS_STRING(str); 212 } 213 else { 214 PyErr_SetString(PyExc_TypeError, 215 "float() argument must be a string or a number"); 216 return NULL; 217 } 218 last = s + len; 219 220 while (Py_ISSPACE(*s)) 221 s++; 222 /* We don't care about overflow or underflow. If the platform 223 * supports them, infinities and signed zeroes (on underflow) are 224 * fine. */ 225 x = PyOS_string_to_double(s, (char **)&end, NULL); 226 if (x == -1.0 && PyErr_Occurred()) 227 goto error; 228 while (Py_ISSPACE(*end)) 229 end++; 230 if (end == last) 231 result = PyFloat_FromDouble(x); 232 else { 233 PyOS_snprintf(buffer, sizeof(buffer), 234 "invalid literal for float(): %.200s", s); 235 PyErr_SetString(PyExc_ValueError, buffer); 236 result = NULL; 237 } 238 239 error: 240#ifdef Py_USING_UNICODE 241 if (s_buffer) 242 PyMem_FREE(s_buffer); 243#endif 244 Py_XDECREF(str); 245 return result; 246} 247 248static void 249float_dealloc(PyFloatObject *op) 250{ 251 if (PyFloat_CheckExact(op)) { 252 Py_TYPE(op) = (struct _typeobject *)free_list; 253 free_list = op; 254 } 255 else 256 Py_TYPE(op)->tp_free((PyObject *)op); 257} 258 259double 260PyFloat_AsDouble(PyObject *op) 261{ 262 PyNumberMethods *nb; 263 PyFloatObject *fo; 264 double val; 265 266 if (op && PyFloat_Check(op)) 267 return PyFloat_AS_DOUBLE((PyFloatObject*) op); 268 269 if (op == NULL) { 270 PyErr_BadArgument(); 271 return -1; 272 } 273 274 if ((nb = Py_TYPE(op)->tp_as_number) == NULL || nb->nb_float == NULL) { 275 PyErr_SetString(PyExc_TypeError, "a float is required"); 276 return -1; 277 } 278 279 fo = (PyFloatObject*) (*nb->nb_float) (op); 280 if (fo == NULL) 281 return -1; 282 if (!PyFloat_Check(fo)) { 283 Py_DECREF(fo); 284 PyErr_SetString(PyExc_TypeError, 285 "nb_float should return float object"); 286 return -1; 287 } 288 289 val = PyFloat_AS_DOUBLE(fo); 290 Py_DECREF(fo); 291 292 return val; 293} 294 295/* Methods */ 296 297/* Macro and helper that convert PyObject obj to a C double and store 298 the value in dbl; this replaces the functionality of the coercion 299 slot function. If conversion to double raises an exception, obj is 300 set to NULL, and the function invoking this macro returns NULL. If 301 obj is not of float, int or long type, Py_NotImplemented is incref'ed, 302 stored in obj, and returned from the function invoking this macro. 303*/ 304#define CONVERT_TO_DOUBLE(obj, dbl) \ 305 if (PyFloat_Check(obj)) \ 306 dbl = PyFloat_AS_DOUBLE(obj); \ 307 else if (convert_to_double(&(obj), &(dbl)) < 0) \ 308 return obj; 309 310static int 311convert_to_double(PyObject **v, double *dbl) 312{ 313 register PyObject *obj = *v; 314 315 if (PyInt_Check(obj)) { 316 *dbl = (double)PyInt_AS_LONG(obj); 317 } 318 else if (PyLong_Check(obj)) { 319 *dbl = PyLong_AsDouble(obj); 320 if (*dbl == -1.0 && PyErr_Occurred()) { 321 *v = NULL; 322 return -1; 323 } 324 } 325 else { 326 Py_INCREF(Py_NotImplemented); 327 *v = Py_NotImplemented; 328 return -1; 329 } 330 return 0; 331} 332 333/* XXX PyFloat_AsString and PyFloat_AsReprString are deprecated: 334 XXX they pass a char buffer without passing a length. 335*/ 336void 337PyFloat_AsString(char *buf, PyFloatObject *v) 338{ 339 char *tmp = PyOS_double_to_string(v->ob_fval, 'g', 340 PyFloat_STR_PRECISION, 341 Py_DTSF_ADD_DOT_0, NULL); 342 strcpy(buf, tmp); 343 PyMem_Free(tmp); 344} 345 346void 347PyFloat_AsReprString(char *buf, PyFloatObject *v) 348{ 349 char * tmp = PyOS_double_to_string(v->ob_fval, 'r', 0, 350 Py_DTSF_ADD_DOT_0, NULL); 351 strcpy(buf, tmp); 352 PyMem_Free(tmp); 353} 354 355/* ARGSUSED */ 356static int 357float_print(PyFloatObject *v, FILE *fp, int flags) 358{ 359 char *buf; 360 if (flags & Py_PRINT_RAW) 361 buf = PyOS_double_to_string(v->ob_fval, 362 'g', PyFloat_STR_PRECISION, 363 Py_DTSF_ADD_DOT_0, NULL); 364 else 365 buf = PyOS_double_to_string(v->ob_fval, 366 'r', 0, Py_DTSF_ADD_DOT_0, NULL); 367 Py_BEGIN_ALLOW_THREADS 368 fputs(buf, fp); 369 Py_END_ALLOW_THREADS 370 PyMem_Free(buf); 371 return 0; 372} 373 374static PyObject * 375float_str_or_repr(PyFloatObject *v, int precision, char format_code) 376{ 377 PyObject *result; 378 char *buf = PyOS_double_to_string(PyFloat_AS_DOUBLE(v), 379 format_code, precision, 380 Py_DTSF_ADD_DOT_0, 381 NULL); 382 if (!buf) 383 return PyErr_NoMemory(); 384 result = PyString_FromString(buf); 385 PyMem_Free(buf); 386 return result; 387} 388 389static PyObject * 390float_repr(PyFloatObject *v) 391{ 392 return float_str_or_repr(v, 0, 'r'); 393} 394 395static PyObject * 396float_str(PyFloatObject *v) 397{ 398 return float_str_or_repr(v, PyFloat_STR_PRECISION, 'g'); 399} 400 401/* Comparison is pretty much a nightmare. When comparing float to float, 402 * we do it as straightforwardly (and long-windedly) as conceivable, so 403 * that, e.g., Python x == y delivers the same result as the platform 404 * C x == y when x and/or y is a NaN. 405 * When mixing float with an integer type, there's no good *uniform* approach. 406 * Converting the double to an integer obviously doesn't work, since we 407 * may lose info from fractional bits. Converting the integer to a double 408 * also has two failure modes: (1) a long int may trigger overflow (too 409 * large to fit in the dynamic range of a C double); (2) even a C long may have 410 * more bits than fit in a C double (e.g., on a 64-bit box long may have 411 * 63 bits of precision, but a C double probably has only 53), and then 412 * we can falsely claim equality when low-order integer bits are lost by 413 * coercion to double. So this part is painful too. 414 */ 415 416static PyObject* 417float_richcompare(PyObject *v, PyObject *w, int op) 418{ 419 double i, j; 420 int r = 0; 421 422 assert(PyFloat_Check(v)); 423 i = PyFloat_AS_DOUBLE(v); 424 425 /* Switch on the type of w. Set i and j to doubles to be compared, 426 * and op to the richcomp to use. 427 */ 428 if (PyFloat_Check(w)) 429 j = PyFloat_AS_DOUBLE(w); 430 431 else if (!Py_IS_FINITE(i)) { 432 if (PyInt_Check(w) || PyLong_Check(w)) 433 /* If i is an infinity, its magnitude exceeds any 434 * finite integer, so it doesn't matter which int we 435 * compare i with. If i is a NaN, similarly. 436 */ 437 j = 0.0; 438 else 439 goto Unimplemented; 440 } 441 442 else if (PyInt_Check(w)) { 443 long jj = PyInt_AS_LONG(w); 444 /* In the worst realistic case I can imagine, C double is a 445 * Cray single with 48 bits of precision, and long has 64 446 * bits. 447 */ 448#if SIZEOF_LONG > 6 449 unsigned long abs = (unsigned long)(jj < 0 ? -jj : jj); 450 if (abs >> 48) { 451 /* Needs more than 48 bits. Make it take the 452 * PyLong path. 453 */ 454 PyObject *result; 455 PyObject *ww = PyLong_FromLong(jj); 456 457 if (ww == NULL) 458 return NULL; 459 result = float_richcompare(v, ww, op); 460 Py_DECREF(ww); 461 return result; 462 } 463#endif 464 j = (double)jj; 465 assert((long)j == jj); 466 } 467 468 else if (PyLong_Check(w)) { 469 int vsign = i == 0.0 ? 0 : i < 0.0 ? -1 : 1; 470 int wsign = _PyLong_Sign(w); 471 size_t nbits; 472 int exponent; 473 474 if (vsign != wsign) { 475 /* Magnitudes are irrelevant -- the signs alone 476 * determine the outcome. 477 */ 478 i = (double)vsign; 479 j = (double)wsign; 480 goto Compare; 481 } 482 /* The signs are the same. */ 483 /* Convert w to a double if it fits. In particular, 0 fits. */ 484 nbits = _PyLong_NumBits(w); 485 if (nbits == (size_t)-1 && PyErr_Occurred()) { 486 /* This long is so large that size_t isn't big enough 487 * to hold the # of bits. Replace with little doubles 488 * that give the same outcome -- w is so large that 489 * its magnitude must exceed the magnitude of any 490 * finite float. 491 */ 492 PyErr_Clear(); 493 i = (double)vsign; 494 assert(wsign != 0); 495 j = wsign * 2.0; 496 goto Compare; 497 } 498 if (nbits <= 48) { 499 j = PyLong_AsDouble(w); 500 /* It's impossible that <= 48 bits overflowed. */ 501 assert(j != -1.0 || ! PyErr_Occurred()); 502 goto Compare; 503 } 504 assert(wsign != 0); /* else nbits was 0 */ 505 assert(vsign != 0); /* if vsign were 0, then since wsign is 506 * not 0, we would have taken the 507 * vsign != wsign branch at the start */ 508 /* We want to work with non-negative numbers. */ 509 if (vsign < 0) { 510 /* "Multiply both sides" by -1; this also swaps the 511 * comparator. 512 */ 513 i = -i; 514 op = _Py_SwappedOp[op]; 515 } 516 assert(i > 0.0); 517 (void) frexp(i, &exponent); 518 /* exponent is the # of bits in v before the radix point; 519 * we know that nbits (the # of bits in w) > 48 at this point 520 */ 521 if (exponent < 0 || (size_t)exponent < nbits) { 522 i = 1.0; 523 j = 2.0; 524 goto Compare; 525 } 526 if ((size_t)exponent > nbits) { 527 i = 2.0; 528 j = 1.0; 529 goto Compare; 530 } 531 /* v and w have the same number of bits before the radix 532 * point. Construct two longs that have the same comparison 533 * outcome. 534 */ 535 { 536 double fracpart; 537 double intpart; 538 PyObject *result = NULL; 539 PyObject *one = NULL; 540 PyObject *vv = NULL; 541 PyObject *ww = w; 542 543 if (wsign < 0) { 544 ww = PyNumber_Negative(w); 545 if (ww == NULL) 546 goto Error; 547 } 548 else 549 Py_INCREF(ww); 550 551 fracpart = modf(i, &intpart); 552 vv = PyLong_FromDouble(intpart); 553 if (vv == NULL) 554 goto Error; 555 556 if (fracpart != 0.0) { 557 /* Shift left, and or a 1 bit into vv 558 * to represent the lost fraction. 559 */ 560 PyObject *temp; 561 562 one = PyInt_FromLong(1); 563 if (one == NULL) 564 goto Error; 565 566 temp = PyNumber_Lshift(ww, one); 567 if (temp == NULL) 568 goto Error; 569 Py_DECREF(ww); 570 ww = temp; 571 572 temp = PyNumber_Lshift(vv, one); 573 if (temp == NULL) 574 goto Error; 575 Py_DECREF(vv); 576 vv = temp; 577 578 temp = PyNumber_Or(vv, one); 579 if (temp == NULL) 580 goto Error; 581 Py_DECREF(vv); 582 vv = temp; 583 } 584 585 r = PyObject_RichCompareBool(vv, ww, op); 586 if (r < 0) 587 goto Error; 588 result = PyBool_FromLong(r); 589 Error: 590 Py_XDECREF(vv); 591 Py_XDECREF(ww); 592 Py_XDECREF(one); 593 return result; 594 } 595 } /* else if (PyLong_Check(w)) */ 596 597 else /* w isn't float, int, or long */ 598 goto Unimplemented; 599 600 Compare: 601 PyFPE_START_PROTECT("richcompare", return NULL) 602 switch (op) { 603 case Py_EQ: 604 r = i == j; 605 break; 606 case Py_NE: 607 r = i != j; 608 break; 609 case Py_LE: 610 r = i <= j; 611 break; 612 case Py_GE: 613 r = i >= j; 614 break; 615 case Py_LT: 616 r = i < j; 617 break; 618 case Py_GT: 619 r = i > j; 620 break; 621 } 622 PyFPE_END_PROTECT(r) 623 return PyBool_FromLong(r); 624 625 Unimplemented: 626 Py_INCREF(Py_NotImplemented); 627 return Py_NotImplemented; 628} 629 630static long 631float_hash(PyFloatObject *v) 632{ 633 return _Py_HashDouble(v->ob_fval); 634} 635 636static PyObject * 637float_add(PyObject *v, PyObject *w) 638{ 639 double a,b; 640 CONVERT_TO_DOUBLE(v, a); 641 CONVERT_TO_DOUBLE(w, b); 642 PyFPE_START_PROTECT("add", return 0) 643 a = a + b; 644 PyFPE_END_PROTECT(a) 645 return PyFloat_FromDouble(a); 646} 647 648static PyObject * 649float_sub(PyObject *v, PyObject *w) 650{ 651 double a,b; 652 CONVERT_TO_DOUBLE(v, a); 653 CONVERT_TO_DOUBLE(w, b); 654 PyFPE_START_PROTECT("subtract", return 0) 655 a = a - b; 656 PyFPE_END_PROTECT(a) 657 return PyFloat_FromDouble(a); 658} 659 660static PyObject * 661float_mul(PyObject *v, PyObject *w) 662{ 663 double a,b; 664 CONVERT_TO_DOUBLE(v, a); 665 CONVERT_TO_DOUBLE(w, b); 666 PyFPE_START_PROTECT("multiply", return 0) 667 a = a * b; 668 PyFPE_END_PROTECT(a) 669 return PyFloat_FromDouble(a); 670} 671 672static PyObject * 673float_div(PyObject *v, PyObject *w) 674{ 675 double a,b; 676 CONVERT_TO_DOUBLE(v, a); 677 CONVERT_TO_DOUBLE(w, b); 678#ifdef Py_NAN 679 if (b == 0.0) { 680 PyErr_SetString(PyExc_ZeroDivisionError, 681 "float division by zero"); 682 return NULL; 683 } 684#endif 685 PyFPE_START_PROTECT("divide", return 0) 686 a = a / b; 687 PyFPE_END_PROTECT(a) 688 return PyFloat_FromDouble(a); 689} 690 691static PyObject * 692float_classic_div(PyObject *v, PyObject *w) 693{ 694 double a,b; 695 CONVERT_TO_DOUBLE(v, a); 696 CONVERT_TO_DOUBLE(w, b); 697 if (Py_DivisionWarningFlag >= 2 && 698 PyErr_Warn(PyExc_DeprecationWarning, "classic float division") < 0) 699 return NULL; 700#ifdef Py_NAN 701 if (b == 0.0) { 702 PyErr_SetString(PyExc_ZeroDivisionError, 703 "float division by zero"); 704 return NULL; 705 } 706#endif 707 PyFPE_START_PROTECT("divide", return 0) 708 a = a / b; 709 PyFPE_END_PROTECT(a) 710 return PyFloat_FromDouble(a); 711} 712 713static PyObject * 714float_rem(PyObject *v, PyObject *w) 715{ 716 double vx, wx; 717 double mod; 718 CONVERT_TO_DOUBLE(v, vx); 719 CONVERT_TO_DOUBLE(w, wx); 720#ifdef Py_NAN 721 if (wx == 0.0) { 722 PyErr_SetString(PyExc_ZeroDivisionError, 723 "float modulo"); 724 return NULL; 725 } 726#endif 727 PyFPE_START_PROTECT("modulo", return 0) 728 mod = fmod(vx, wx); 729 if (mod) { 730 /* ensure the remainder has the same sign as the denominator */ 731 if ((wx < 0) != (mod < 0)) { 732 mod += wx; 733 } 734 } 735 else { 736 /* the remainder is zero, and in the presence of signed zeroes 737 fmod returns different results across platforms; ensure 738 it has the same sign as the denominator; we'd like to do 739 "mod = wx * 0.0", but that may get optimized away */ 740 mod *= mod; /* hide "mod = +0" from optimizer */ 741 if (wx < 0.0) 742 mod = -mod; 743 } 744 PyFPE_END_PROTECT(mod) 745 return PyFloat_FromDouble(mod); 746} 747 748static PyObject * 749float_divmod(PyObject *v, PyObject *w) 750{ 751 double vx, wx; 752 double div, mod, floordiv; 753 CONVERT_TO_DOUBLE(v, vx); 754 CONVERT_TO_DOUBLE(w, wx); 755 if (wx == 0.0) { 756 PyErr_SetString(PyExc_ZeroDivisionError, "float divmod()"); 757 return NULL; 758 } 759 PyFPE_START_PROTECT("divmod", return 0) 760 mod = fmod(vx, wx); 761 /* fmod is typically exact, so vx-mod is *mathematically* an 762 exact multiple of wx. But this is fp arithmetic, and fp 763 vx - mod is an approximation; the result is that div may 764 not be an exact integral value after the division, although 765 it will always be very close to one. 766 */ 767 div = (vx - mod) / wx; 768 if (mod) { 769 /* ensure the remainder has the same sign as the denominator */ 770 if ((wx < 0) != (mod < 0)) { 771 mod += wx; 772 div -= 1.0; 773 } 774 } 775 else { 776 /* the remainder is zero, and in the presence of signed zeroes 777 fmod returns different results across platforms; ensure 778 it has the same sign as the denominator; we'd like to do 779 "mod = wx * 0.0", but that may get optimized away */ 780 mod *= mod; /* hide "mod = +0" from optimizer */ 781 if (wx < 0.0) 782 mod = -mod; 783 } 784 /* snap quotient to nearest integral value */ 785 if (div) { 786 floordiv = floor(div); 787 if (div - floordiv > 0.5) 788 floordiv += 1.0; 789 } 790 else { 791 /* div is zero - get the same sign as the true quotient */ 792 div *= div; /* hide "div = +0" from optimizers */ 793 floordiv = div * vx / wx; /* zero w/ sign of vx/wx */ 794 } 795 PyFPE_END_PROTECT(floordiv) 796 return Py_BuildValue("(dd)", floordiv, mod); 797} 798 799static PyObject * 800float_floor_div(PyObject *v, PyObject *w) 801{ 802 PyObject *t, *r; 803 804 t = float_divmod(v, w); 805 if (t == NULL || t == Py_NotImplemented) 806 return t; 807 assert(PyTuple_CheckExact(t)); 808 r = PyTuple_GET_ITEM(t, 0); 809 Py_INCREF(r); 810 Py_DECREF(t); 811 return r; 812} 813 814/* determine whether x is an odd integer or not; assumes that 815 x is not an infinity or nan. */ 816#define DOUBLE_IS_ODD_INTEGER(x) (fmod(fabs(x), 2.0) == 1.0) 817 818static PyObject * 819float_pow(PyObject *v, PyObject *w, PyObject *z) 820{ 821 double iv, iw, ix; 822 int negate_result = 0; 823 824 if ((PyObject *)z != Py_None) { 825 PyErr_SetString(PyExc_TypeError, "pow() 3rd argument not " 826 "allowed unless all arguments are integers"); 827 return NULL; 828 } 829 830 CONVERT_TO_DOUBLE(v, iv); 831 CONVERT_TO_DOUBLE(w, iw); 832 833 /* Sort out special cases here instead of relying on pow() */ 834 if (iw == 0) { /* v**0 is 1, even 0**0 */ 835 return PyFloat_FromDouble(1.0); 836 } 837 if (Py_IS_NAN(iv)) { /* nan**w = nan, unless w == 0 */ 838 return PyFloat_FromDouble(iv); 839 } 840 if (Py_IS_NAN(iw)) { /* v**nan = nan, unless v == 1; 1**nan = 1 */ 841 return PyFloat_FromDouble(iv == 1.0 ? 1.0 : iw); 842 } 843 if (Py_IS_INFINITY(iw)) { 844 /* v**inf is: 0.0 if abs(v) < 1; 1.0 if abs(v) == 1; inf if 845 * abs(v) > 1 (including case where v infinite) 846 * 847 * v**-inf is: inf if abs(v) < 1; 1.0 if abs(v) == 1; 0.0 if 848 * abs(v) > 1 (including case where v infinite) 849 */ 850 iv = fabs(iv); 851 if (iv == 1.0) 852 return PyFloat_FromDouble(1.0); 853 else if ((iw > 0.0) == (iv > 1.0)) 854 return PyFloat_FromDouble(fabs(iw)); /* return inf */ 855 else 856 return PyFloat_FromDouble(0.0); 857 } 858 if (Py_IS_INFINITY(iv)) { 859 /* (+-inf)**w is: inf for w positive, 0 for w negative; in 860 * both cases, we need to add the appropriate sign if w is 861 * an odd integer. 862 */ 863 int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw); 864 if (iw > 0.0) 865 return PyFloat_FromDouble(iw_is_odd ? iv : fabs(iv)); 866 else 867 return PyFloat_FromDouble(iw_is_odd ? 868 copysign(0.0, iv) : 0.0); 869 } 870 if (iv == 0.0) { /* 0**w is: 0 for w positive, 1 for w zero 871 (already dealt with above), and an error 872 if w is negative. */ 873 int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw); 874 if (iw < 0.0) { 875 PyErr_SetString(PyExc_ZeroDivisionError, 876 "0.0 cannot be raised to a " 877 "negative power"); 878 return NULL; 879 } 880 /* use correct sign if iw is odd */ 881 return PyFloat_FromDouble(iw_is_odd ? iv : 0.0); 882 } 883 884 if (iv < 0.0) { 885 /* Whether this is an error is a mess, and bumps into libm 886 * bugs so we have to figure it out ourselves. 887 */ 888 if (iw != floor(iw)) { 889 PyErr_SetString(PyExc_ValueError, "negative number " 890 "cannot be raised to a fractional power"); 891 return NULL; 892 } 893 /* iw is an exact integer, albeit perhaps a very large 894 * one. Replace iv by its absolute value and remember 895 * to negate the pow result if iw is odd. 896 */ 897 iv = -iv; 898 negate_result = DOUBLE_IS_ODD_INTEGER(iw); 899 } 900 901 if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */ 902 /* (-1) ** large_integer also ends up here. Here's an 903 * extract from the comments for the previous 904 * implementation explaining why this special case is 905 * necessary: 906 * 907 * -1 raised to an exact integer should never be exceptional. 908 * Alas, some libms (chiefly glibc as of early 2003) return 909 * NaN and set EDOM on pow(-1, large_int) if the int doesn't 910 * happen to be representable in a *C* integer. That's a 911 * bug. 912 */ 913 return PyFloat_FromDouble(negate_result ? -1.0 : 1.0); 914 } 915 916 /* Now iv and iw are finite, iw is nonzero, and iv is 917 * positive and not equal to 1.0. We finally allow 918 * the platform pow to step in and do the rest. 919 */ 920 errno = 0; 921 PyFPE_START_PROTECT("pow", return NULL) 922 ix = pow(iv, iw); 923 PyFPE_END_PROTECT(ix) 924 Py_ADJUST_ERANGE1(ix); 925 if (negate_result) 926 ix = -ix; 927 928 if (errno != 0) { 929 /* We don't expect any errno value other than ERANGE, but 930 * the range of libm bugs appears unbounded. 931 */ 932 PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError : 933 PyExc_ValueError); 934 return NULL; 935 } 936 return PyFloat_FromDouble(ix); 937} 938 939#undef DOUBLE_IS_ODD_INTEGER 940 941static PyObject * 942float_neg(PyFloatObject *v) 943{ 944 return PyFloat_FromDouble(-v->ob_fval); 945} 946 947static PyObject * 948float_abs(PyFloatObject *v) 949{ 950 return PyFloat_FromDouble(fabs(v->ob_fval)); 951} 952 953static int 954float_nonzero(PyFloatObject *v) 955{ 956 return v->ob_fval != 0.0; 957} 958 959static int 960float_coerce(PyObject **pv, PyObject **pw) 961{ 962 if (PyInt_Check(*pw)) { 963 long x = PyInt_AsLong(*pw); 964 *pw = PyFloat_FromDouble((double)x); 965 Py_INCREF(*pv); 966 return 0; 967 } 968 else if (PyLong_Check(*pw)) { 969 double x = PyLong_AsDouble(*pw); 970 if (x == -1.0 && PyErr_Occurred()) 971 return -1; 972 *pw = PyFloat_FromDouble(x); 973 Py_INCREF(*pv); 974 return 0; 975 } 976 else if (PyFloat_Check(*pw)) { 977 Py_INCREF(*pv); 978 Py_INCREF(*pw); 979 return 0; 980 } 981 return 1; /* Can't do it */ 982} 983 984static PyObject * 985float_is_integer(PyObject *v) 986{ 987 double x = PyFloat_AsDouble(v); 988 PyObject *o; 989 990 if (x == -1.0 && PyErr_Occurred()) 991 return NULL; 992 if (!Py_IS_FINITE(x)) 993 Py_RETURN_FALSE; 994 errno = 0; 995 PyFPE_START_PROTECT("is_integer", return NULL) 996 o = (floor(x) == x) ? Py_True : Py_False; 997 PyFPE_END_PROTECT(x) 998 if (errno != 0) { 999 PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError : 1000 PyExc_ValueError); 1001 return NULL; 1002 } 1003 Py_INCREF(o); 1004 return o; 1005} 1006 1007#if 0 1008static PyObject * 1009float_is_inf(PyObject *v) 1010{ 1011 double x = PyFloat_AsDouble(v); 1012 if (x == -1.0 && PyErr_Occurred()) 1013 return NULL; 1014 return PyBool_FromLong((long)Py_IS_INFINITY(x)); 1015} 1016 1017static PyObject * 1018float_is_nan(PyObject *v) 1019{ 1020 double x = PyFloat_AsDouble(v); 1021 if (x == -1.0 && PyErr_Occurred()) 1022 return NULL; 1023 return PyBool_FromLong((long)Py_IS_NAN(x)); 1024} 1025 1026static PyObject * 1027float_is_finite(PyObject *v) 1028{ 1029 double x = PyFloat_AsDouble(v); 1030 if (x == -1.0 && PyErr_Occurred()) 1031 return NULL; 1032 return PyBool_FromLong((long)Py_IS_FINITE(x)); 1033} 1034#endif 1035 1036static PyObject * 1037float_trunc(PyObject *v) 1038{ 1039 double x = PyFloat_AsDouble(v); 1040 double wholepart; /* integral portion of x, rounded toward 0 */ 1041 1042 (void)modf(x, &wholepart); 1043 /* Try to get out cheap if this fits in a Python int. The attempt 1044 * to cast to long must be protected, as C doesn't define what 1045 * happens if the double is too big to fit in a long. Some rare 1046 * systems raise an exception then (RISCOS was mentioned as one, 1047 * and someone using a non-default option on Sun also bumped into 1048 * that). Note that checking for <= LONG_MAX is unsafe: if a long 1049 * has more bits of precision than a double, casting LONG_MAX to 1050 * double may yield an approximation, and if that's rounded up, 1051 * then, e.g., wholepart=LONG_MAX+1 would yield true from the C 1052 * expression wholepart<=LONG_MAX, despite that wholepart is 1053 * actually greater than LONG_MAX. However, assuming a two's complement 1054 * machine with no trap representation, LONG_MIN will be a power of 2 (and 1055 * hence exactly representable as a double), and LONG_MAX = -1-LONG_MIN, so 1056 * the comparisons with (double)LONG_MIN below should be safe. 1057 */ 1058 if ((double)LONG_MIN <= wholepart && wholepart < -(double)LONG_MIN) { 1059 const long aslong = (long)wholepart; 1060 return PyInt_FromLong(aslong); 1061 } 1062 return PyLong_FromDouble(wholepart); 1063} 1064 1065static PyObject * 1066float_long(PyObject *v) 1067{ 1068 double x = PyFloat_AsDouble(v); 1069 return PyLong_FromDouble(x); 1070} 1071 1072/* _Py_double_round: rounds a finite nonzero double to the closest multiple of 1073 10**-ndigits; here ndigits is within reasonable bounds (typically, -308 <= 1074 ndigits <= 323). Returns a Python float, or sets a Python error and 1075 returns NULL on failure (OverflowError and memory errors are possible). */ 1076 1077#ifndef PY_NO_SHORT_FLOAT_REPR 1078/* version of _Py_double_round that uses the correctly-rounded string<->double 1079 conversions from Python/dtoa.c */ 1080 1081/* FIVE_POW_LIMIT is the largest k such that 5**k is exactly representable as 1082 a double. Since we're using the code in Python/dtoa.c, it should be safe 1083 to assume that C doubles are IEEE 754 binary64 format. To be on the safe 1084 side, we check this. */ 1085#if DBL_MANT_DIG == 53 1086#define FIVE_POW_LIMIT 22 1087#else 1088#error "C doubles do not appear to be IEEE 754 binary64 format" 1089#endif 1090 1091PyObject * 1092_Py_double_round(double x, int ndigits) { 1093 1094 double rounded, m; 1095 Py_ssize_t buflen, mybuflen=100; 1096 char *buf, *buf_end, shortbuf[100], *mybuf=shortbuf; 1097 int decpt, sign, val, halfway_case; 1098 PyObject *result = NULL; 1099 _Py_SET_53BIT_PRECISION_HEADER; 1100 1101 /* Easy path for the common case ndigits == 0. */ 1102 if (ndigits == 0) { 1103 rounded = round(x); 1104 if (fabs(rounded - x) == 0.5) 1105 /* halfway between two integers; use round-away-from-zero */ 1106 rounded = x + (x > 0.0 ? 0.5 : -0.5); 1107 return PyFloat_FromDouble(rounded); 1108 } 1109 1110 /* The basic idea is very simple: convert and round the double to a 1111 decimal string using _Py_dg_dtoa, then convert that decimal string 1112 back to a double with _Py_dg_strtod. There's one minor difficulty: 1113 Python 2.x expects round to do round-half-away-from-zero, while 1114 _Py_dg_dtoa does round-half-to-even. So we need some way to detect 1115 and correct the halfway cases. 1116 1117 Detection: a halfway value has the form k * 0.5 * 10**-ndigits for 1118 some odd integer k. Or in other words, a rational number x is 1119 exactly halfway between two multiples of 10**-ndigits if its 1120 2-valuation is exactly -ndigits-1 and its 5-valuation is at least 1121 -ndigits. For ndigits >= 0 the latter condition is automatically 1122 satisfied for a binary float x, since any such float has 1123 nonnegative 5-valuation. For 0 > ndigits >= -22, x needs to be an 1124 integral multiple of 5**-ndigits; we can check this using fmod. 1125 For -22 > ndigits, there are no halfway cases: 5**23 takes 54 bits 1126 to represent exactly, so any odd multiple of 0.5 * 10**n for n >= 1127 23 takes at least 54 bits of precision to represent exactly. 1128 1129 Correction: a simple strategy for dealing with halfway cases is to 1130 (for the halfway cases only) call _Py_dg_dtoa with an argument of 1131 ndigits+1 instead of ndigits (thus doing an exact conversion to 1132 decimal), round the resulting string manually, and then convert 1133 back using _Py_dg_strtod. 1134 */ 1135 1136 /* nans, infinities and zeros should have already been dealt 1137 with by the caller (in this case, builtin_round) */ 1138 assert(Py_IS_FINITE(x) && x != 0.0); 1139 1140 /* find 2-valuation val of x */ 1141 m = frexp(x, &val); 1142 while (m != floor(m)) { 1143 m *= 2.0; 1144 val--; 1145 } 1146 1147 /* determine whether this is a halfway case */ 1148 if (val == -ndigits-1) { 1149 if (ndigits >= 0) 1150 halfway_case = 1; 1151 else if (ndigits >= -FIVE_POW_LIMIT) { 1152 double five_pow = 1.0; 1153 int i; 1154 for (i=0; i < -ndigits; i++) 1155 five_pow *= 5.0; 1156 halfway_case = fmod(x, five_pow) == 0.0; 1157 } 1158 else 1159 halfway_case = 0; 1160 } 1161 else 1162 halfway_case = 0; 1163 1164 /* round to a decimal string; use an extra place for halfway case */ 1165 _Py_SET_53BIT_PRECISION_START; 1166 buf = _Py_dg_dtoa(x, 3, ndigits+halfway_case, &decpt, &sign, &buf_end); 1167 _Py_SET_53BIT_PRECISION_END; 1168 if (buf == NULL) { 1169 PyErr_NoMemory(); 1170 return NULL; 1171 } 1172 buflen = buf_end - buf; 1173 1174 /* in halfway case, do the round-half-away-from-zero manually */ 1175 if (halfway_case) { 1176 int i, carry; 1177 /* sanity check: _Py_dg_dtoa should not have stripped 1178 any zeros from the result: there should be exactly 1179 ndigits+1 places following the decimal point, and 1180 the last digit in the buffer should be a '5'.*/ 1181 assert(buflen - decpt == ndigits+1); 1182 assert(buf[buflen-1] == '5'); 1183 1184 /* increment and shift right at the same time. */ 1185 decpt += 1; 1186 carry = 1; 1187 for (i=buflen-1; i-- > 0;) { 1188 carry += buf[i] - '0'; 1189 buf[i+1] = carry % 10 + '0'; 1190 carry /= 10; 1191 } 1192 buf[0] = carry + '0'; 1193 } 1194 1195 /* Get new buffer if shortbuf is too small. Space needed <= buf_end - 1196 buf + 8: (1 extra for '0', 1 for sign, 5 for exp, 1 for '\0'). */ 1197 if (buflen + 8 > mybuflen) { 1198 mybuflen = buflen+8; 1199 mybuf = (char *)PyMem_Malloc(mybuflen); 1200 if (mybuf == NULL) { 1201 PyErr_NoMemory(); 1202 goto exit; 1203 } 1204 } 1205 /* copy buf to mybuf, adding exponent, sign and leading 0 */ 1206 PyOS_snprintf(mybuf, mybuflen, "%s0%se%d", (sign ? "-" : ""), 1207 buf, decpt - (int)buflen); 1208 1209 /* and convert the resulting string back to a double */ 1210 errno = 0; 1211 _Py_SET_53BIT_PRECISION_START; 1212 rounded = _Py_dg_strtod(mybuf, NULL); 1213 _Py_SET_53BIT_PRECISION_END; 1214 if (errno == ERANGE && fabs(rounded) >= 1.) 1215 PyErr_SetString(PyExc_OverflowError, 1216 "rounded value too large to represent"); 1217 else 1218 result = PyFloat_FromDouble(rounded); 1219 1220 /* done computing value; now clean up */ 1221 if (mybuf != shortbuf) 1222 PyMem_Free(mybuf); 1223 exit: 1224 _Py_dg_freedtoa(buf); 1225 return result; 1226} 1227 1228#undef FIVE_POW_LIMIT 1229 1230#else /* PY_NO_SHORT_FLOAT_REPR */ 1231 1232/* fallback version, to be used when correctly rounded binary<->decimal 1233 conversions aren't available */ 1234 1235PyObject * 1236_Py_double_round(double x, int ndigits) { 1237 double pow1, pow2, y, z; 1238 if (ndigits >= 0) { 1239 if (ndigits > 22) { 1240 /* pow1 and pow2 are each safe from overflow, but 1241 pow1*pow2 ~= pow(10.0, ndigits) might overflow */ 1242 pow1 = pow(10.0, (double)(ndigits-22)); 1243 pow2 = 1e22; 1244 } 1245 else { 1246 pow1 = pow(10.0, (double)ndigits); 1247 pow2 = 1.0; 1248 } 1249 y = (x*pow1)*pow2; 1250 /* if y overflows, then rounded value is exactly x */ 1251 if (!Py_IS_FINITE(y)) 1252 return PyFloat_FromDouble(x); 1253 } 1254 else { 1255 pow1 = pow(10.0, (double)-ndigits); 1256 pow2 = 1.0; /* unused; silences a gcc compiler warning */ 1257 y = x / pow1; 1258 } 1259 1260 z = round(y); 1261 if (fabs(y-z) == 0.5) 1262 /* halfway between two integers; use round-away-from-zero */ 1263 z = y + copysign(0.5, y); 1264 1265 if (ndigits >= 0) 1266 z = (z / pow2) / pow1; 1267 else 1268 z *= pow1; 1269 1270 /* if computation resulted in overflow, raise OverflowError */ 1271 if (!Py_IS_FINITE(z)) { 1272 PyErr_SetString(PyExc_OverflowError, 1273 "overflow occurred during round"); 1274 return NULL; 1275 } 1276 1277 return PyFloat_FromDouble(z); 1278} 1279 1280#endif /* PY_NO_SHORT_FLOAT_REPR */ 1281 1282static PyObject * 1283float_float(PyObject *v) 1284{ 1285 if (PyFloat_CheckExact(v)) 1286 Py_INCREF(v); 1287 else 1288 v = PyFloat_FromDouble(((PyFloatObject *)v)->ob_fval); 1289 return v; 1290} 1291 1292/* turn ASCII hex characters into integer values and vice versa */ 1293 1294static char 1295char_from_hex(int x) 1296{ 1297 assert(0 <= x && x < 16); 1298 return "0123456789abcdef"[x]; 1299} 1300 1301static int 1302hex_from_char(char c) { 1303 int x; 1304 switch(c) { 1305 case '0': 1306 x = 0; 1307 break; 1308 case '1': 1309 x = 1; 1310 break; 1311 case '2': 1312 x = 2; 1313 break; 1314 case '3': 1315 x = 3; 1316 break; 1317 case '4': 1318 x = 4; 1319 break; 1320 case '5': 1321 x = 5; 1322 break; 1323 case '6': 1324 x = 6; 1325 break; 1326 case '7': 1327 x = 7; 1328 break; 1329 case '8': 1330 x = 8; 1331 break; 1332 case '9': 1333 x = 9; 1334 break; 1335 case 'a': 1336 case 'A': 1337 x = 10; 1338 break; 1339 case 'b': 1340 case 'B': 1341 x = 11; 1342 break; 1343 case 'c': 1344 case 'C': 1345 x = 12; 1346 break; 1347 case 'd': 1348 case 'D': 1349 x = 13; 1350 break; 1351 case 'e': 1352 case 'E': 1353 x = 14; 1354 break; 1355 case 'f': 1356 case 'F': 1357 x = 15; 1358 break; 1359 default: 1360 x = -1; 1361 break; 1362 } 1363 return x; 1364} 1365 1366/* convert a float to a hexadecimal string */ 1367 1368/* TOHEX_NBITS is DBL_MANT_DIG rounded up to the next integer 1369 of the form 4k+1. */ 1370#define TOHEX_NBITS DBL_MANT_DIG + 3 - (DBL_MANT_DIG+2)%4 1371 1372static PyObject * 1373float_hex(PyObject *v) 1374{ 1375 double x, m; 1376 int e, shift, i, si, esign; 1377 /* Space for 1+(TOHEX_NBITS-1)/4 digits, a decimal point, and the 1378 trailing NUL byte. */ 1379 char s[(TOHEX_NBITS-1)/4+3]; 1380 1381 CONVERT_TO_DOUBLE(v, x); 1382 1383 if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) 1384 return float_str((PyFloatObject *)v); 1385 1386 if (x == 0.0) { 1387 if (copysign(1.0, x) == -1.0) 1388 return PyString_FromString("-0x0.0p+0"); 1389 else 1390 return PyString_FromString("0x0.0p+0"); 1391 } 1392 1393 m = frexp(fabs(x), &e); 1394 shift = 1 - MAX(DBL_MIN_EXP - e, 0); 1395 m = ldexp(m, shift); 1396 e -= shift; 1397 1398 si = 0; 1399 s[si] = char_from_hex((int)m); 1400 si++; 1401 m -= (int)m; 1402 s[si] = '.'; 1403 si++; 1404 for (i=0; i < (TOHEX_NBITS-1)/4; i++) { 1405 m *= 16.0; 1406 s[si] = char_from_hex((int)m); 1407 si++; 1408 m -= (int)m; 1409 } 1410 s[si] = '\0'; 1411 1412 if (e < 0) { 1413 esign = (int)'-'; 1414 e = -e; 1415 } 1416 else 1417 esign = (int)'+'; 1418 1419 if (x < 0.0) 1420 return PyString_FromFormat("-0x%sp%c%d", s, esign, e); 1421 else 1422 return PyString_FromFormat("0x%sp%c%d", s, esign, e); 1423} 1424 1425PyDoc_STRVAR(float_hex_doc, 1426"float.hex() -> string\n\ 1427\n\ 1428Return a hexadecimal representation of a floating-point number.\n\ 1429>>> (-0.1).hex()\n\ 1430'-0x1.999999999999ap-4'\n\ 1431>>> 3.14159.hex()\n\ 1432'0x1.921f9f01b866ep+1'"); 1433 1434/* Case-insensitive locale-independent string match used for nan and inf 1435 detection. t should be lower-case and null-terminated. Return a nonzero 1436 result if the first strlen(t) characters of s match t and 0 otherwise. */ 1437 1438static int 1439case_insensitive_match(const char *s, const char *t) 1440{ 1441 while(*t && Py_TOLOWER(*s) == *t) { 1442 s++; 1443 t++; 1444 } 1445 return *t ? 0 : 1; 1446} 1447 1448/* Convert a hexadecimal string to a float. */ 1449 1450static PyObject * 1451float_fromhex(PyObject *cls, PyObject *arg) 1452{ 1453 PyObject *result_as_float, *result; 1454 double x; 1455 long exp, top_exp, lsb, key_digit; 1456 char *s, *coeff_start, *s_store, *coeff_end, *exp_start, *s_end; 1457 int half_eps, digit, round_up, sign=1; 1458 Py_ssize_t length, ndigits, fdigits, i; 1459 1460 /* 1461 * For the sake of simplicity and correctness, we impose an artificial 1462 * limit on ndigits, the total number of hex digits in the coefficient 1463 * The limit is chosen to ensure that, writing exp for the exponent, 1464 * 1465 * (1) if exp > LONG_MAX/2 then the value of the hex string is 1466 * guaranteed to overflow (provided it's nonzero) 1467 * 1468 * (2) if exp < LONG_MIN/2 then the value of the hex string is 1469 * guaranteed to underflow to 0. 1470 * 1471 * (3) if LONG_MIN/2 <= exp <= LONG_MAX/2 then there's no danger of 1472 * overflow in the calculation of exp and top_exp below. 1473 * 1474 * More specifically, ndigits is assumed to satisfy the following 1475 * inequalities: 1476 * 1477 * 4*ndigits <= DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2 1478 * 4*ndigits <= LONG_MAX/2 + 1 - DBL_MAX_EXP 1479 * 1480 * If either of these inequalities is not satisfied, a ValueError is 1481 * raised. Otherwise, write x for the value of the hex string, and 1482 * assume x is nonzero. Then 1483 * 1484 * 2**(exp-4*ndigits) <= |x| < 2**(exp+4*ndigits). 1485 * 1486 * Now if exp > LONG_MAX/2 then: 1487 * 1488 * exp - 4*ndigits >= LONG_MAX/2 + 1 - (LONG_MAX/2 + 1 - DBL_MAX_EXP) 1489 * = DBL_MAX_EXP 1490 * 1491 * so |x| >= 2**DBL_MAX_EXP, which is too large to be stored in C 1492 * double, so overflows. If exp < LONG_MIN/2, then 1493 * 1494 * exp + 4*ndigits <= LONG_MIN/2 - 1 + ( 1495 * DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2) 1496 * = DBL_MIN_EXP - DBL_MANT_DIG - 1 1497 * 1498 * and so |x| < 2**(DBL_MIN_EXP-DBL_MANT_DIG-1), hence underflows to 0 1499 * when converted to a C double. 1500 * 1501 * It's easy to show that if LONG_MIN/2 <= exp <= LONG_MAX/2 then both 1502 * exp+4*ndigits and exp-4*ndigits are within the range of a long. 1503 */ 1504 1505 if (PyString_AsStringAndSize(arg, &s, &length)) 1506 return NULL; 1507 s_end = s + length; 1508 1509 /******************** 1510 * Parse the string * 1511 ********************/ 1512 1513 /* leading whitespace and optional sign */ 1514 while (Py_ISSPACE(*s)) 1515 s++; 1516 if (*s == '-') { 1517 s++; 1518 sign = -1; 1519 } 1520 else if (*s == '+') 1521 s++; 1522 1523 /* infinities and nans */ 1524 if (*s == 'i' || *s == 'I') { 1525 if (!case_insensitive_match(s+1, "nf")) 1526 goto parse_error; 1527 s += 3; 1528 x = Py_HUGE_VAL; 1529 if (case_insensitive_match(s, "inity")) 1530 s += 5; 1531 goto finished; 1532 } 1533 if (*s == 'n' || *s == 'N') { 1534 if (!case_insensitive_match(s+1, "an")) 1535 goto parse_error; 1536 s += 3; 1537 x = Py_NAN; 1538 goto finished; 1539 } 1540 1541 /* [0x] */ 1542 s_store = s; 1543 if (*s == '0') { 1544 s++; 1545 if (*s == 'x' || *s == 'X') 1546 s++; 1547 else 1548 s = s_store; 1549 } 1550 1551 /* coefficient: <integer> [. <fraction>] */ 1552 coeff_start = s; 1553 while (hex_from_char(*s) >= 0) 1554 s++; 1555 s_store = s; 1556 if (*s == '.') { 1557 s++; 1558 while (hex_from_char(*s) >= 0) 1559 s++; 1560 coeff_end = s-1; 1561 } 1562 else 1563 coeff_end = s; 1564 1565 /* ndigits = total # of hex digits; fdigits = # after point */ 1566 ndigits = coeff_end - coeff_start; 1567 fdigits = coeff_end - s_store; 1568 if (ndigits == 0) 1569 goto parse_error; 1570 if (ndigits > MIN(DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2, 1571 LONG_MAX/2 + 1 - DBL_MAX_EXP)/4) 1572 goto insane_length_error; 1573 1574 /* [p <exponent>] */ 1575 if (*s == 'p' || *s == 'P') { 1576 s++; 1577 exp_start = s; 1578 if (*s == '-' || *s == '+') 1579 s++; 1580 if (!('0' <= *s && *s <= '9')) 1581 goto parse_error; 1582 s++; 1583 while ('0' <= *s && *s <= '9') 1584 s++; 1585 exp = strtol(exp_start, NULL, 10); 1586 } 1587 else 1588 exp = 0; 1589 1590/* for 0 <= j < ndigits, HEX_DIGIT(j) gives the jth most significant digit */ 1591#define HEX_DIGIT(j) hex_from_char(*((j) < fdigits ? \ 1592 coeff_end-(j) : \ 1593 coeff_end-1-(j))) 1594 1595 /******************************************* 1596 * Compute rounded value of the hex string * 1597 *******************************************/ 1598 1599 /* Discard leading zeros, and catch extreme overflow and underflow */ 1600 while (ndigits > 0 && HEX_DIGIT(ndigits-1) == 0) 1601 ndigits--; 1602 if (ndigits == 0 || exp < LONG_MIN/2) { 1603 x = 0.0; 1604 goto finished; 1605 } 1606 if (exp > LONG_MAX/2) 1607 goto overflow_error; 1608 1609 /* Adjust exponent for fractional part. */ 1610 exp = exp - 4*((long)fdigits); 1611 1612 /* top_exp = 1 more than exponent of most sig. bit of coefficient */ 1613 top_exp = exp + 4*((long)ndigits - 1); 1614 for (digit = HEX_DIGIT(ndigits-1); digit != 0; digit /= 2) 1615 top_exp++; 1616 1617 /* catch almost all nonextreme cases of overflow and underflow here */ 1618 if (top_exp < DBL_MIN_EXP - DBL_MANT_DIG) { 1619 x = 0.0; 1620 goto finished; 1621 } 1622 if (top_exp > DBL_MAX_EXP) 1623 goto overflow_error; 1624 1625 /* lsb = exponent of least significant bit of the *rounded* value. 1626 This is top_exp - DBL_MANT_DIG unless result is subnormal. */ 1627 lsb = MAX(top_exp, (long)DBL_MIN_EXP) - DBL_MANT_DIG; 1628 1629 x = 0.0; 1630 if (exp >= lsb) { 1631 /* no rounding required */ 1632 for (i = ndigits-1; i >= 0; i--) 1633 x = 16.0*x + HEX_DIGIT(i); 1634 x = ldexp(x, (int)(exp)); 1635 goto finished; 1636 } 1637 /* rounding required. key_digit is the index of the hex digit 1638 containing the first bit to be rounded away. */ 1639 half_eps = 1 << (int)((lsb - exp - 1) % 4); 1640 key_digit = (lsb - exp - 1) / 4; 1641 for (i = ndigits-1; i > key_digit; i--) 1642 x = 16.0*x + HEX_DIGIT(i); 1643 digit = HEX_DIGIT(key_digit); 1644 x = 16.0*x + (double)(digit & (16-2*half_eps)); 1645 1646 /* round-half-even: round up if bit lsb-1 is 1 and at least one of 1647 bits lsb, lsb-2, lsb-3, lsb-4, ... is 1. */ 1648 if ((digit & half_eps) != 0) { 1649 round_up = 0; 1650 if ((digit & (3*half_eps-1)) != 0 || 1651 (half_eps == 8 && (HEX_DIGIT(key_digit+1) & 1) != 0)) 1652 round_up = 1; 1653 else 1654 for (i = key_digit-1; i >= 0; i--) 1655 if (HEX_DIGIT(i) != 0) { 1656 round_up = 1; 1657 break; 1658 } 1659 if (round_up == 1) { 1660 x += 2*half_eps; 1661 if (top_exp == DBL_MAX_EXP && 1662 x == ldexp((double)(2*half_eps), DBL_MANT_DIG)) 1663 /* overflow corner case: pre-rounded value < 1664 2**DBL_MAX_EXP; rounded=2**DBL_MAX_EXP. */ 1665 goto overflow_error; 1666 } 1667 } 1668 x = ldexp(x, (int)(exp+4*key_digit)); 1669 1670 finished: 1671 /* optional trailing whitespace leading to the end of the string */ 1672 while (Py_ISSPACE(*s)) 1673 s++; 1674 if (s != s_end) 1675 goto parse_error; 1676 result_as_float = Py_BuildValue("(d)", sign * x); 1677 if (result_as_float == NULL) 1678 return NULL; 1679 result = PyObject_CallObject(cls, result_as_float); 1680 Py_DECREF(result_as_float); 1681 return result; 1682 1683 overflow_error: 1684 PyErr_SetString(PyExc_OverflowError, 1685 "hexadecimal value too large to represent as a float"); 1686 return NULL; 1687 1688 parse_error: 1689 PyErr_SetString(PyExc_ValueError, 1690 "invalid hexadecimal floating-point string"); 1691 return NULL; 1692 1693 insane_length_error: 1694 PyErr_SetString(PyExc_ValueError, 1695 "hexadecimal string too long to convert"); 1696 return NULL; 1697} 1698 1699PyDoc_STRVAR(float_fromhex_doc, 1700"float.fromhex(string) -> float\n\ 1701\n\ 1702Create a floating-point number from a hexadecimal string.\n\ 1703>>> float.fromhex('0x1.ffffp10')\n\ 17042047.984375\n\ 1705>>> float.fromhex('-0x1p-1074')\n\ 1706-4.9406564584124654e-324"); 1707 1708 1709static PyObject * 1710float_as_integer_ratio(PyObject *v, PyObject *unused) 1711{ 1712 double self; 1713 double float_part; 1714 int exponent; 1715 int i; 1716 1717 PyObject *prev; 1718 PyObject *py_exponent = NULL; 1719 PyObject *numerator = NULL; 1720 PyObject *denominator = NULL; 1721 PyObject *result_pair = NULL; 1722 PyNumberMethods *long_methods = PyLong_Type.tp_as_number; 1723 1724#define INPLACE_UPDATE(obj, call) \ 1725 prev = obj; \ 1726 obj = call; \ 1727 Py_DECREF(prev); \ 1728 1729 CONVERT_TO_DOUBLE(v, self); 1730 1731 if (Py_IS_INFINITY(self)) { 1732 PyErr_SetString(PyExc_OverflowError, 1733 "Cannot pass infinity to float.as_integer_ratio."); 1734 return NULL; 1735 } 1736#ifdef Py_NAN 1737 if (Py_IS_NAN(self)) { 1738 PyErr_SetString(PyExc_ValueError, 1739 "Cannot pass NaN to float.as_integer_ratio."); 1740 return NULL; 1741 } 1742#endif 1743 1744 PyFPE_START_PROTECT("as_integer_ratio", goto error); 1745 float_part = frexp(self, &exponent); /* self == float_part * 2**exponent exactly */ 1746 PyFPE_END_PROTECT(float_part); 1747 1748 for (i=0; i<300 && float_part != floor(float_part) ; i++) { 1749 float_part *= 2.0; 1750 exponent--; 1751 } 1752 /* self == float_part * 2**exponent exactly and float_part is integral. 1753 If FLT_RADIX != 2, the 300 steps may leave a tiny fractional part 1754 to be truncated by PyLong_FromDouble(). */ 1755 1756 numerator = PyLong_FromDouble(float_part); 1757 if (numerator == NULL) goto error; 1758 1759 /* fold in 2**exponent */ 1760 denominator = PyLong_FromLong(1); 1761 py_exponent = PyLong_FromLong(labs((long)exponent)); 1762 if (py_exponent == NULL) goto error; 1763 INPLACE_UPDATE(py_exponent, 1764 long_methods->nb_lshift(denominator, py_exponent)); 1765 if (py_exponent == NULL) goto error; 1766 if (exponent > 0) { 1767 INPLACE_UPDATE(numerator, 1768 long_methods->nb_multiply(numerator, py_exponent)); 1769 if (numerator == NULL) goto error; 1770 } 1771 else { 1772 Py_DECREF(denominator); 1773 denominator = py_exponent; 1774 py_exponent = NULL; 1775 } 1776 1777 /* Returns ints instead of longs where possible */ 1778 INPLACE_UPDATE(numerator, PyNumber_Int(numerator)); 1779 if (numerator == NULL) goto error; 1780 INPLACE_UPDATE(denominator, PyNumber_Int(denominator)); 1781 if (denominator == NULL) goto error; 1782 1783 result_pair = PyTuple_Pack(2, numerator, denominator); 1784 1785#undef INPLACE_UPDATE 1786error: 1787 Py_XDECREF(py_exponent); 1788 Py_XDECREF(denominator); 1789 Py_XDECREF(numerator); 1790 return result_pair; 1791} 1792 1793PyDoc_STRVAR(float_as_integer_ratio_doc, 1794"float.as_integer_ratio() -> (int, int)\n" 1795"\n" 1796"Return a pair of integers, whose ratio is exactly equal to the original\n" 1797"float and with a positive denominator.\n" 1798"Raise OverflowError on infinities and a ValueError on NaNs.\n" 1799"\n" 1800">>> (10.0).as_integer_ratio()\n" 1801"(10, 1)\n" 1802">>> (0.0).as_integer_ratio()\n" 1803"(0, 1)\n" 1804">>> (-.25).as_integer_ratio()\n" 1805"(-1, 4)"); 1806 1807 1808static PyObject * 1809float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds); 1810 1811static PyObject * 1812float_new(PyTypeObject *type, PyObject *args, PyObject *kwds) 1813{ 1814 PyObject *x = Py_False; /* Integer zero */ 1815 static char *kwlist[] = {"x", 0}; 1816 1817 if (type != &PyFloat_Type) 1818 return float_subtype_new(type, args, kwds); /* Wimp out */ 1819 if (!PyArg_ParseTupleAndKeywords(args, kwds, "|O:float", kwlist, &x)) 1820 return NULL; 1821 /* If it's a string, but not a string subclass, use 1822 PyFloat_FromString. */ 1823 if (PyString_CheckExact(x)) 1824 return PyFloat_FromString(x, NULL); 1825 return PyNumber_Float(x); 1826} 1827 1828/* Wimpy, slow approach to tp_new calls for subtypes of float: 1829 first create a regular float from whatever arguments we got, 1830 then allocate a subtype instance and initialize its ob_fval 1831 from the regular float. The regular float is then thrown away. 1832*/ 1833static PyObject * 1834float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds) 1835{ 1836 PyObject *tmp, *newobj; 1837 1838 assert(PyType_IsSubtype(type, &PyFloat_Type)); 1839 tmp = float_new(&PyFloat_Type, args, kwds); 1840 if (tmp == NULL) 1841 return NULL; 1842 assert(PyFloat_Check(tmp)); 1843 newobj = type->tp_alloc(type, 0); 1844 if (newobj == NULL) { 1845 Py_DECREF(tmp); 1846 return NULL; 1847 } 1848 ((PyFloatObject *)newobj)->ob_fval = ((PyFloatObject *)tmp)->ob_fval; 1849 Py_DECREF(tmp); 1850 return newobj; 1851} 1852 1853static PyObject * 1854float_getnewargs(PyFloatObject *v) 1855{ 1856 return Py_BuildValue("(d)", v->ob_fval); 1857} 1858 1859/* this is for the benefit of the pack/unpack routines below */ 1860 1861typedef enum { 1862 unknown_format, ieee_big_endian_format, ieee_little_endian_format 1863} float_format_type; 1864 1865static float_format_type double_format, float_format; 1866static float_format_type detected_double_format, detected_float_format; 1867 1868static PyObject * 1869float_getformat(PyTypeObject *v, PyObject* arg) 1870{ 1871 char* s; 1872 float_format_type r; 1873 1874 if (!PyString_Check(arg)) { 1875 PyErr_Format(PyExc_TypeError, 1876 "__getformat__() argument must be string, not %.500s", 1877 Py_TYPE(arg)->tp_name); 1878 return NULL; 1879 } 1880 s = PyString_AS_STRING(arg); 1881 if (strcmp(s, "double") == 0) { 1882 r = double_format; 1883 } 1884 else if (strcmp(s, "float") == 0) { 1885 r = float_format; 1886 } 1887 else { 1888 PyErr_SetString(PyExc_ValueError, 1889 "__getformat__() argument 1 must be " 1890 "'double' or 'float'"); 1891 return NULL; 1892 } 1893 1894 switch (r) { 1895 case unknown_format: 1896 return PyString_FromString("unknown"); 1897 case ieee_little_endian_format: 1898 return PyString_FromString("IEEE, little-endian"); 1899 case ieee_big_endian_format: 1900 return PyString_FromString("IEEE, big-endian"); 1901 default: 1902 Py_FatalError("insane float_format or double_format"); 1903 return NULL; 1904 } 1905} 1906 1907PyDoc_STRVAR(float_getformat_doc, 1908"float.__getformat__(typestr) -> string\n" 1909"\n" 1910"You probably don't want to use this function. It exists mainly to be\n" 1911"used in Python's test suite.\n" 1912"\n" 1913"typestr must be 'double' or 'float'. This function returns whichever of\n" 1914"'unknown', 'IEEE, big-endian' or 'IEEE, little-endian' best describes the\n" 1915"format of floating point numbers used by the C type named by typestr."); 1916 1917static PyObject * 1918float_setformat(PyTypeObject *v, PyObject* args) 1919{ 1920 char* typestr; 1921 char* format; 1922 float_format_type f; 1923 float_format_type detected; 1924 float_format_type *p; 1925 1926 if (!PyArg_ParseTuple(args, "ss:__setformat__", &typestr, &format)) 1927 return NULL; 1928 1929 if (strcmp(typestr, "double") == 0) { 1930 p = &double_format; 1931 detected = detected_double_format; 1932 } 1933 else if (strcmp(typestr, "float") == 0) { 1934 p = &float_format; 1935 detected = detected_float_format; 1936 } 1937 else { 1938 PyErr_SetString(PyExc_ValueError, 1939 "__setformat__() argument 1 must " 1940 "be 'double' or 'float'"); 1941 return NULL; 1942 } 1943 1944 if (strcmp(format, "unknown") == 0) { 1945 f = unknown_format; 1946 } 1947 else if (strcmp(format, "IEEE, little-endian") == 0) { 1948 f = ieee_little_endian_format; 1949 } 1950 else if (strcmp(format, "IEEE, big-endian") == 0) { 1951 f = ieee_big_endian_format; 1952 } 1953 else { 1954 PyErr_SetString(PyExc_ValueError, 1955 "__setformat__() argument 2 must be " 1956 "'unknown', 'IEEE, little-endian' or " 1957 "'IEEE, big-endian'"); 1958 return NULL; 1959 1960 } 1961 1962 if (f != unknown_format && f != detected) { 1963 PyErr_Format(PyExc_ValueError, 1964 "can only set %s format to 'unknown' or the " 1965 "detected platform value", typestr); 1966 return NULL; 1967 } 1968 1969 *p = f; 1970 Py_RETURN_NONE; 1971} 1972 1973PyDoc_STRVAR(float_setformat_doc, 1974"float.__setformat__(typestr, fmt) -> None\n" 1975"\n" 1976"You probably don't want to use this function. It exists mainly to be\n" 1977"used in Python's test suite.\n" 1978"\n" 1979"typestr must be 'double' or 'float'. fmt must be one of 'unknown',\n" 1980"'IEEE, big-endian' or 'IEEE, little-endian', and in addition can only be\n" 1981"one of the latter two if it appears to match the underlying C reality.\n" 1982"\n" 1983"Override the automatic determination of C-level floating point type.\n" 1984"This affects how floats are converted to and from binary strings."); 1985 1986static PyObject * 1987float_getzero(PyObject *v, void *closure) 1988{ 1989 return PyFloat_FromDouble(0.0); 1990} 1991 1992static PyObject * 1993float__format__(PyObject *self, PyObject *args) 1994{ 1995 PyObject *format_spec; 1996 1997 if (!PyArg_ParseTuple(args, "O:__format__", &format_spec)) 1998 return NULL; 1999 if (PyBytes_Check(format_spec)) 2000 return _PyFloat_FormatAdvanced(self, 2001 PyBytes_AS_STRING(format_spec), 2002 PyBytes_GET_SIZE(format_spec)); 2003 if (PyUnicode_Check(format_spec)) { 2004 /* Convert format_spec to a str */ 2005 PyObject *result; 2006 PyObject *str_spec = PyObject_Str(format_spec); 2007 2008 if (str_spec == NULL) 2009 return NULL; 2010 2011 result = _PyFloat_FormatAdvanced(self, 2012 PyBytes_AS_STRING(str_spec), 2013 PyBytes_GET_SIZE(str_spec)); 2014 2015 Py_DECREF(str_spec); 2016 return result; 2017 } 2018 PyErr_SetString(PyExc_TypeError, "__format__ requires str or unicode"); 2019 return NULL; 2020} 2021 2022PyDoc_STRVAR(float__format__doc, 2023"float.__format__(format_spec) -> string\n" 2024"\n" 2025"Formats the float according to format_spec."); 2026 2027 2028static PyMethodDef float_methods[] = { 2029 {"conjugate", (PyCFunction)float_float, METH_NOARGS, 2030 "Return self, the complex conjugate of any float."}, 2031 {"__trunc__", (PyCFunction)float_trunc, METH_NOARGS, 2032 "Return the Integral closest to x between 0 and x."}, 2033 {"as_integer_ratio", (PyCFunction)float_as_integer_ratio, METH_NOARGS, 2034 float_as_integer_ratio_doc}, 2035 {"fromhex", (PyCFunction)float_fromhex, 2036 METH_O|METH_CLASS, float_fromhex_doc}, 2037 {"hex", (PyCFunction)float_hex, 2038 METH_NOARGS, float_hex_doc}, 2039 {"is_integer", (PyCFunction)float_is_integer, METH_NOARGS, 2040 "Return True if the float is an integer."}, 2041#if 0 2042 {"is_inf", (PyCFunction)float_is_inf, METH_NOARGS, 2043 "Return True if the float is positive or negative infinite."}, 2044 {"is_finite", (PyCFunction)float_is_finite, METH_NOARGS, 2045 "Return True if the float is finite, neither infinite nor NaN."}, 2046 {"is_nan", (PyCFunction)float_is_nan, METH_NOARGS, 2047 "Return True if the float is not a number (NaN)."}, 2048#endif 2049 {"__getnewargs__", (PyCFunction)float_getnewargs, METH_NOARGS}, 2050 {"__getformat__", (PyCFunction)float_getformat, 2051 METH_O|METH_CLASS, float_getformat_doc}, 2052 {"__setformat__", (PyCFunction)float_setformat, 2053 METH_VARARGS|METH_CLASS, float_setformat_doc}, 2054 {"__format__", (PyCFunction)float__format__, 2055 METH_VARARGS, float__format__doc}, 2056 {NULL, NULL} /* sentinel */ 2057}; 2058 2059static PyGetSetDef float_getset[] = { 2060 {"real", 2061 (getter)float_float, (setter)NULL, 2062 "the real part of a complex number", 2063 NULL}, 2064 {"imag", 2065 (getter)float_getzero, (setter)NULL, 2066 "the imaginary part of a complex number", 2067 NULL}, 2068 {NULL} /* Sentinel */ 2069}; 2070 2071PyDoc_STRVAR(float_doc, 2072"float(x) -> floating point number\n\ 2073\n\ 2074Convert a string or number to a floating point number, if possible."); 2075 2076 2077static PyNumberMethods float_as_number = { 2078 float_add, /*nb_add*/ 2079 float_sub, /*nb_subtract*/ 2080 float_mul, /*nb_multiply*/ 2081 float_classic_div, /*nb_divide*/ 2082 float_rem, /*nb_remainder*/ 2083 float_divmod, /*nb_divmod*/ 2084 float_pow, /*nb_power*/ 2085 (unaryfunc)float_neg, /*nb_negative*/ 2086 (unaryfunc)float_float, /*nb_positive*/ 2087 (unaryfunc)float_abs, /*nb_absolute*/ 2088 (inquiry)float_nonzero, /*nb_nonzero*/ 2089 0, /*nb_invert*/ 2090 0, /*nb_lshift*/ 2091 0, /*nb_rshift*/ 2092 0, /*nb_and*/ 2093 0, /*nb_xor*/ 2094 0, /*nb_or*/ 2095 float_coerce, /*nb_coerce*/ 2096 float_trunc, /*nb_int*/ 2097 float_long, /*nb_long*/ 2098 float_float, /*nb_float*/ 2099 0, /* nb_oct */ 2100 0, /* nb_hex */ 2101 0, /* nb_inplace_add */ 2102 0, /* nb_inplace_subtract */ 2103 0, /* nb_inplace_multiply */ 2104 0, /* nb_inplace_divide */ 2105 0, /* nb_inplace_remainder */ 2106 0, /* nb_inplace_power */ 2107 0, /* nb_inplace_lshift */ 2108 0, /* nb_inplace_rshift */ 2109 0, /* nb_inplace_and */ 2110 0, /* nb_inplace_xor */ 2111 0, /* nb_inplace_or */ 2112 float_floor_div, /* nb_floor_divide */ 2113 float_div, /* nb_true_divide */ 2114 0, /* nb_inplace_floor_divide */ 2115 0, /* nb_inplace_true_divide */ 2116}; 2117 2118PyTypeObject PyFloat_Type = { 2119 PyVarObject_HEAD_INIT(&PyType_Type, 0) 2120 "float", 2121 sizeof(PyFloatObject), 2122 0, 2123 (destructor)float_dealloc, /* tp_dealloc */ 2124 (printfunc)float_print, /* tp_print */ 2125 0, /* tp_getattr */ 2126 0, /* tp_setattr */ 2127 0, /* tp_compare */ 2128 (reprfunc)float_repr, /* tp_repr */ 2129 &float_as_number, /* tp_as_number */ 2130 0, /* tp_as_sequence */ 2131 0, /* tp_as_mapping */ 2132 (hashfunc)float_hash, /* tp_hash */ 2133 0, /* tp_call */ 2134 (reprfunc)float_str, /* tp_str */ 2135 PyObject_GenericGetAttr, /* tp_getattro */ 2136 0, /* tp_setattro */ 2137 0, /* tp_as_buffer */ 2138 Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES | 2139 Py_TPFLAGS_BASETYPE, /* tp_flags */ 2140 float_doc, /* tp_doc */ 2141 0, /* tp_traverse */ 2142 0, /* tp_clear */ 2143 float_richcompare, /* tp_richcompare */ 2144 0, /* tp_weaklistoffset */ 2145 0, /* tp_iter */ 2146 0, /* tp_iternext */ 2147 float_methods, /* tp_methods */ 2148 0, /* tp_members */ 2149 float_getset, /* tp_getset */ 2150 0, /* tp_base */ 2151 0, /* tp_dict */ 2152 0, /* tp_descr_get */ 2153 0, /* tp_descr_set */ 2154 0, /* tp_dictoffset */ 2155 0, /* tp_init */ 2156 0, /* tp_alloc */ 2157 float_new, /* tp_new */ 2158}; 2159 2160void 2161_PyFloat_Init(void) 2162{ 2163 /* We attempt to determine if this machine is using IEEE 2164 floating point formats by peering at the bits of some 2165 carefully chosen values. If it looks like we are on an 2166 IEEE platform, the float packing/unpacking routines can 2167 just copy bits, if not they resort to arithmetic & shifts 2168 and masks. The shifts & masks approach works on all finite 2169 values, but what happens to infinities, NaNs and signed 2170 zeroes on packing is an accident, and attempting to unpack 2171 a NaN or an infinity will raise an exception. 2172 2173 Note that if we're on some whacked-out platform which uses 2174 IEEE formats but isn't strictly little-endian or big- 2175 endian, we will fall back to the portable shifts & masks 2176 method. */ 2177 2178#if SIZEOF_DOUBLE == 8 2179 { 2180 double x = 9006104071832581.0; 2181 if (memcmp(&x, "\x43\x3f\xff\x01\x02\x03\x04\x05", 8) == 0) 2182 detected_double_format = ieee_big_endian_format; 2183 else if (memcmp(&x, "\x05\x04\x03\x02\x01\xff\x3f\x43", 8) == 0) 2184 detected_double_format = ieee_little_endian_format; 2185 else 2186 detected_double_format = unknown_format; 2187 } 2188#else 2189 detected_double_format = unknown_format; 2190#endif 2191 2192#if SIZEOF_FLOAT == 4 2193 { 2194 float y = 16711938.0; 2195 if (memcmp(&y, "\x4b\x7f\x01\x02", 4) == 0) 2196 detected_float_format = ieee_big_endian_format; 2197 else if (memcmp(&y, "\x02\x01\x7f\x4b", 4) == 0) 2198 detected_float_format = ieee_little_endian_format; 2199 else 2200 detected_float_format = unknown_format; 2201 } 2202#else 2203 detected_float_format = unknown_format; 2204#endif 2205 2206 double_format = detected_double_format; 2207 float_format = detected_float_format; 2208 2209 /* Init float info */ 2210 if (FloatInfoType.tp_name == 0) 2211 PyStructSequence_InitType(&FloatInfoType, &floatinfo_desc); 2212} 2213 2214int 2215PyFloat_ClearFreeList(void) 2216{ 2217 PyFloatObject *p; 2218 PyFloatBlock *list, *next; 2219 int i; 2220 int u; /* remaining unfreed ints per block */ 2221 int freelist_size = 0; 2222 2223 list = block_list; 2224 block_list = NULL; 2225 free_list = NULL; 2226 while (list != NULL) { 2227 u = 0; 2228 for (i = 0, p = &list->objects[0]; 2229 i < N_FLOATOBJECTS; 2230 i++, p++) { 2231 if (PyFloat_CheckExact(p) && Py_REFCNT(p) != 0) 2232 u++; 2233 } 2234 next = list->next; 2235 if (u) { 2236 list->next = block_list; 2237 block_list = list; 2238 for (i = 0, p = &list->objects[0]; 2239 i < N_FLOATOBJECTS; 2240 i++, p++) { 2241 if (!PyFloat_CheckExact(p) || 2242 Py_REFCNT(p) == 0) { 2243 Py_TYPE(p) = (struct _typeobject *) 2244 free_list; 2245 free_list = p; 2246 } 2247 } 2248 } 2249 else { 2250 PyMem_FREE(list); 2251 } 2252 freelist_size += u; 2253 list = next; 2254 } 2255 return freelist_size; 2256} 2257 2258void 2259PyFloat_Fini(void) 2260{ 2261 PyFloatObject *p; 2262 PyFloatBlock *list; 2263 int i; 2264 int u; /* total unfreed floats per block */ 2265 2266 u = PyFloat_ClearFreeList(); 2267 2268 if (!Py_VerboseFlag) 2269 return; 2270 fprintf(stderr, "# cleanup floats"); 2271 if (!u) { 2272 fprintf(stderr, "\n"); 2273 } 2274 else { 2275 fprintf(stderr, 2276 ": %d unfreed float%s\n", 2277 u, u == 1 ? "" : "s"); 2278 } 2279 if (Py_VerboseFlag > 1) { 2280 list = block_list; 2281 while (list != NULL) { 2282 for (i = 0, p = &list->objects[0]; 2283 i < N_FLOATOBJECTS; 2284 i++, p++) { 2285 if (PyFloat_CheckExact(p) && 2286 Py_REFCNT(p) != 0) { 2287 char *buf = PyOS_double_to_string( 2288 PyFloat_AS_DOUBLE(p), 'r', 2289 0, 0, NULL); 2290 if (buf) { 2291 /* XXX(twouters) cast 2292 refcount to long 2293 until %zd is 2294 universally 2295 available 2296 */ 2297 fprintf(stderr, 2298 "# <float at %p, refcnt=%ld, val=%s>\n", 2299 p, (long)Py_REFCNT(p), buf); 2300 PyMem_Free(buf); 2301 } 2302 } 2303 } 2304 list = list->next; 2305 } 2306 } 2307} 2308 2309/*---------------------------------------------------------------------------- 2310 * _PyFloat_{Pack,Unpack}{4,8}. See floatobject.h. 2311 */ 2312int 2313_PyFloat_Pack4(double x, unsigned char *p, int le) 2314{ 2315 if (float_format == unknown_format) { 2316 unsigned char sign; 2317 int e; 2318 double f; 2319 unsigned int fbits; 2320 int incr = 1; 2321 2322 if (le) { 2323 p += 3; 2324 incr = -1; 2325 } 2326 2327 if (x < 0) { 2328 sign = 1; 2329 x = -x; 2330 } 2331 else 2332 sign = 0; 2333 2334 f = frexp(x, &e); 2335 2336 /* Normalize f to be in the range [1.0, 2.0) */ 2337 if (0.5 <= f && f < 1.0) { 2338 f *= 2.0; 2339 e--; 2340 } 2341 else if (f == 0.0) 2342 e = 0; 2343 else { 2344 PyErr_SetString(PyExc_SystemError, 2345 "frexp() result out of range"); 2346 return -1; 2347 } 2348 2349 if (e >= 128) 2350 goto Overflow; 2351 else if (e < -126) { 2352 /* Gradual underflow */ 2353 f = ldexp(f, 126 + e); 2354 e = 0; 2355 } 2356 else if (!(e == 0 && f == 0.0)) { 2357 e += 127; 2358 f -= 1.0; /* Get rid of leading 1 */ 2359 } 2360 2361 f *= 8388608.0; /* 2**23 */ 2362 fbits = (unsigned int)(f + 0.5); /* Round */ 2363 assert(fbits <= 8388608); 2364 if (fbits >> 23) { 2365 /* The carry propagated out of a string of 23 1 bits. */ 2366 fbits = 0; 2367 ++e; 2368 if (e >= 255) 2369 goto Overflow; 2370 } 2371 2372 /* First byte */ 2373 *p = (sign << 7) | (e >> 1); 2374 p += incr; 2375 2376 /* Second byte */ 2377 *p = (char) (((e & 1) << 7) | (fbits >> 16)); 2378 p += incr; 2379 2380 /* Third byte */ 2381 *p = (fbits >> 8) & 0xFF; 2382 p += incr; 2383 2384 /* Fourth byte */ 2385 *p = fbits & 0xFF; 2386 2387 /* Done */ 2388 return 0; 2389 2390 } 2391 else { 2392 float y = (float)x; 2393 const char *s = (char*)&y; 2394 int i, incr = 1; 2395 2396 if (Py_IS_INFINITY(y) && !Py_IS_INFINITY(x)) 2397 goto Overflow; 2398 2399 if ((float_format == ieee_little_endian_format && !le) 2400 || (float_format == ieee_big_endian_format && le)) { 2401 p += 3; 2402 incr = -1; 2403 } 2404 2405 for (i = 0; i < 4; i++) { 2406 *p = *s++; 2407 p += incr; 2408 } 2409 return 0; 2410 } 2411 Overflow: 2412 PyErr_SetString(PyExc_OverflowError, 2413 "float too large to pack with f format"); 2414 return -1; 2415} 2416 2417int 2418_PyFloat_Pack8(double x, unsigned char *p, int le) 2419{ 2420 if (double_format == unknown_format) { 2421 unsigned char sign; 2422 int e; 2423 double f; 2424 unsigned int fhi, flo; 2425 int incr = 1; 2426 2427 if (le) { 2428 p += 7; 2429 incr = -1; 2430 } 2431 2432 if (x < 0) { 2433 sign = 1; 2434 x = -x; 2435 } 2436 else 2437 sign = 0; 2438 2439 f = frexp(x, &e); 2440 2441 /* Normalize f to be in the range [1.0, 2.0) */ 2442 if (0.5 <= f && f < 1.0) { 2443 f *= 2.0; 2444 e--; 2445 } 2446 else if (f == 0.0) 2447 e = 0; 2448 else { 2449 PyErr_SetString(PyExc_SystemError, 2450 "frexp() result out of range"); 2451 return -1; 2452 } 2453 2454 if (e >= 1024) 2455 goto Overflow; 2456 else if (e < -1022) { 2457 /* Gradual underflow */ 2458 f = ldexp(f, 1022 + e); 2459 e = 0; 2460 } 2461 else if (!(e == 0 && f == 0.0)) { 2462 e += 1023; 2463 f -= 1.0; /* Get rid of leading 1 */ 2464 } 2465 2466 /* fhi receives the high 28 bits; flo the low 24 bits (== 52 bits) */ 2467 f *= 268435456.0; /* 2**28 */ 2468 fhi = (unsigned int)f; /* Truncate */ 2469 assert(fhi < 268435456); 2470 2471 f -= (double)fhi; 2472 f *= 16777216.0; /* 2**24 */ 2473 flo = (unsigned int)(f + 0.5); /* Round */ 2474 assert(flo <= 16777216); 2475 if (flo >> 24) { 2476 /* The carry propagated out of a string of 24 1 bits. */ 2477 flo = 0; 2478 ++fhi; 2479 if (fhi >> 28) { 2480 /* And it also progagated out of the next 28 bits. */ 2481 fhi = 0; 2482 ++e; 2483 if (e >= 2047) 2484 goto Overflow; 2485 } 2486 } 2487 2488 /* First byte */ 2489 *p = (sign << 7) | (e >> 4); 2490 p += incr; 2491 2492 /* Second byte */ 2493 *p = (unsigned char) (((e & 0xF) << 4) | (fhi >> 24)); 2494 p += incr; 2495 2496 /* Third byte */ 2497 *p = (fhi >> 16) & 0xFF; 2498 p += incr; 2499 2500 /* Fourth byte */ 2501 *p = (fhi >> 8) & 0xFF; 2502 p += incr; 2503 2504 /* Fifth byte */ 2505 *p = fhi & 0xFF; 2506 p += incr; 2507 2508 /* Sixth byte */ 2509 *p = (flo >> 16) & 0xFF; 2510 p += incr; 2511 2512 /* Seventh byte */ 2513 *p = (flo >> 8) & 0xFF; 2514 p += incr; 2515 2516 /* Eighth byte */ 2517 *p = flo & 0xFF; 2518 /* p += incr; Unneeded (for now) */ 2519 2520 /* Done */ 2521 return 0; 2522 2523 Overflow: 2524 PyErr_SetString(PyExc_OverflowError, 2525 "float too large to pack with d format"); 2526 return -1; 2527 } 2528 else { 2529 const char *s = (char*)&x; 2530 int i, incr = 1; 2531 2532 if ((double_format == ieee_little_endian_format && !le) 2533 || (double_format == ieee_big_endian_format && le)) { 2534 p += 7; 2535 incr = -1; 2536 } 2537 2538 for (i = 0; i < 8; i++) { 2539 *p = *s++; 2540 p += incr; 2541 } 2542 return 0; 2543 } 2544} 2545 2546double 2547_PyFloat_Unpack4(const unsigned char *p, int le) 2548{ 2549 if (float_format == unknown_format) { 2550 unsigned char sign; 2551 int e; 2552 unsigned int f; 2553 double x; 2554 int incr = 1; 2555 2556 if (le) { 2557 p += 3; 2558 incr = -1; 2559 } 2560 2561 /* First byte */ 2562 sign = (*p >> 7) & 1; 2563 e = (*p & 0x7F) << 1; 2564 p += incr; 2565 2566 /* Second byte */ 2567 e |= (*p >> 7) & 1; 2568 f = (*p & 0x7F) << 16; 2569 p += incr; 2570 2571 if (e == 255) { 2572 PyErr_SetString( 2573 PyExc_ValueError, 2574 "can't unpack IEEE 754 special value " 2575 "on non-IEEE platform"); 2576 return -1; 2577 } 2578 2579 /* Third byte */ 2580 f |= *p << 8; 2581 p += incr; 2582 2583 /* Fourth byte */ 2584 f |= *p; 2585 2586 x = (double)f / 8388608.0; 2587 2588 /* XXX This sadly ignores Inf/NaN issues */ 2589 if (e == 0) 2590 e = -126; 2591 else { 2592 x += 1.0; 2593 e -= 127; 2594 } 2595 x = ldexp(x, e); 2596 2597 if (sign) 2598 x = -x; 2599 2600 return x; 2601 } 2602 else { 2603 float x; 2604 2605 if ((float_format == ieee_little_endian_format && !le) 2606 || (float_format == ieee_big_endian_format && le)) { 2607 char buf[4]; 2608 char *d = &buf[3]; 2609 int i; 2610 2611 for (i = 0; i < 4; i++) { 2612 *d-- = *p++; 2613 } 2614 memcpy(&x, buf, 4); 2615 } 2616 else { 2617 memcpy(&x, p, 4); 2618 } 2619 2620 return x; 2621 } 2622} 2623 2624double 2625_PyFloat_Unpack8(const unsigned char *p, int le) 2626{ 2627 if (double_format == unknown_format) { 2628 unsigned char sign; 2629 int e; 2630 unsigned int fhi, flo; 2631 double x; 2632 int incr = 1; 2633 2634 if (le) { 2635 p += 7; 2636 incr = -1; 2637 } 2638 2639 /* First byte */ 2640 sign = (*p >> 7) & 1; 2641 e = (*p & 0x7F) << 4; 2642 2643 p += incr; 2644 2645 /* Second byte */ 2646 e |= (*p >> 4) & 0xF; 2647 fhi = (*p & 0xF) << 24; 2648 p += incr; 2649 2650 if (e == 2047) { 2651 PyErr_SetString( 2652 PyExc_ValueError, 2653 "can't unpack IEEE 754 special value " 2654 "on non-IEEE platform"); 2655 return -1.0; 2656 } 2657 2658 /* Third byte */ 2659 fhi |= *p << 16; 2660 p += incr; 2661 2662 /* Fourth byte */ 2663 fhi |= *p << 8; 2664 p += incr; 2665 2666 /* Fifth byte */ 2667 fhi |= *p; 2668 p += incr; 2669 2670 /* Sixth byte */ 2671 flo = *p << 16; 2672 p += incr; 2673 2674 /* Seventh byte */ 2675 flo |= *p << 8; 2676 p += incr; 2677 2678 /* Eighth byte */ 2679 flo |= *p; 2680 2681 x = (double)fhi + (double)flo / 16777216.0; /* 2**24 */ 2682 x /= 268435456.0; /* 2**28 */ 2683 2684 if (e == 0) 2685 e = -1022; 2686 else { 2687 x += 1.0; 2688 e -= 1023; 2689 } 2690 x = ldexp(x, e); 2691 2692 if (sign) 2693 x = -x; 2694 2695 return x; 2696 } 2697 else { 2698 double x; 2699 2700 if ((double_format == ieee_little_endian_format && !le) 2701 || (double_format == ieee_big_endian_format && le)) { 2702 char buf[8]; 2703 char *d = &buf[7]; 2704 int i; 2705 2706 for (i = 0; i < 8; i++) { 2707 *d-- = *p++; 2708 } 2709 memcpy(&x, buf, 8); 2710 } 2711 else { 2712 memcpy(&x, p, 8); 2713 } 2714 2715 return x; 2716 } 2717} 2718