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 */ 20 extern 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 28 struct _floatblock { 29 struct _floatblock *next; 30 PyFloatObject objects[N_FLOATOBJECTS]; 31 }; 32 33 typedef struct _floatblock PyFloatBlock; 34 35 static PyFloatBlock *block_list = NULL; 36 static PyFloatObject *free_list = NULL; 37 38 static PyFloatObject * 39 fill_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 56 double 57 PyFloat_GetMax(void) 58 { 59 return DBL_MAX; 60 } 61 62 double 63 PyFloat_GetMin(void) 64 { 65 return DBL_MIN; 66 } 67 68 static PyTypeObject FloatInfoType = {0, 0, 0, 0, 0, 0}; 69 70 PyDoc_STRVAR(floatinfo__doc__, 71 "sys.float_info\n\ 72 \n\ 73 A structseq holding information about the float type. It contains low level\n\ 74 information about the precision and internal representation. Please study\n\ 75 your system's :file:`float.h` for more information."); 76 77 static 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 97 static PyStructSequence_Desc floatinfo_desc = { 98 "sys.float_info", /* name */ 99 floatinfo__doc__, /* doc */ 100 floatinfo_fields, /* fields */ 101 11 102 }; 103 104 PyObject * 105 PyFloat_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 } 140 141 PyObject * 142 PyFloat_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 PyObject_INIT(op, &PyFloat_Type); 153 op->ob_fval = fval; 154 return (PyObject *) op; 155 } 156 157 /************************************************************************** 158 RED_FLAG 22-Sep-2000 tim 159 PyFloat_FromString's pend argument is braindead. Prior to this RED_FLAG, 160 161 1. 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!). 164 165 2. 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. 168 169 Since we can't change the interface of a public API function, pend is 170 still supported but now *officially* useless: if pend is not NULL, 171 *pend is set to NULL. 172 **************************************************************************/ 173 PyObject * 174 PyFloat_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 *result = NULL; 184 185 if (pend) 186 *pend = NULL; 187 if (PyString_Check(v)) { 188 s = PyString_AS_STRING(v); 189 len = PyString_GET_SIZE(v); 190 } 191 #ifdef Py_USING_UNICODE 192 else if (PyUnicode_Check(v)) { 193 s_buffer = (char *)PyMem_MALLOC(PyUnicode_GET_SIZE(v)+1); 194 if (s_buffer == NULL) 195 return PyErr_NoMemory(); 196 if (PyUnicode_EncodeDecimal(PyUnicode_AS_UNICODE(v), 197 PyUnicode_GET_SIZE(v), 198 s_buffer, 199 NULL)) 200 goto error; 201 s = s_buffer; 202 len = strlen(s); 203 } 204 #endif 205 else if (PyObject_AsCharBuffer(v, &s, &len)) { 206 PyErr_SetString(PyExc_TypeError, 207 "float() argument must be a string or a number"); 208 return NULL; 209 } 210 last = s + len; 211 212 while (Py_ISSPACE(*s)) 213 s++; 214 /* We don't care about overflow or underflow. If the platform 215 * supports them, infinities and signed zeroes (on underflow) are 216 * fine. */ 217 x = PyOS_string_to_double(s, (char **)&end, NULL); 218 if (x == -1.0 && PyErr_Occurred()) 219 goto error; 220 while (Py_ISSPACE(*end)) 221 end++; 222 if (end == last) 223 result = PyFloat_FromDouble(x); 224 else { 225 PyOS_snprintf(buffer, sizeof(buffer), 226 "invalid literal for float(): %.200s", s); 227 PyErr_SetString(PyExc_ValueError, buffer); 228 result = NULL; 229 } 230 231 error: 232 #ifdef Py_USING_UNICODE 233 if (s_buffer) 234 PyMem_FREE(s_buffer); 235 #endif 236 return result; 237 } 238 239 static void 240 float_dealloc(PyFloatObject *op) 241 { 242 if (PyFloat_CheckExact(op)) { 243 Py_TYPE(op) = (struct _typeobject *)free_list; 244 free_list = op; 245 } 246 else 247 Py_TYPE(op)->tp_free((PyObject *)op); 248 } 249 250 double 251 PyFloat_AsDouble(PyObject *op) 252 { 253 PyNumberMethods *nb; 254 PyFloatObject *fo; 255 double val; 256 257 if (op && PyFloat_Check(op)) 258 return PyFloat_AS_DOUBLE((PyFloatObject*) op); 259 260 if (op == NULL) { 261 PyErr_BadArgument(); 262 return -1; 263 } 264 265 if ((nb = Py_TYPE(op)->tp_as_number) == NULL || nb->nb_float == NULL) { 266 PyErr_SetString(PyExc_TypeError, "a float is required"); 267 return -1; 268 } 269 270 fo = (PyFloatObject*) (*nb->nb_float) (op); 271 if (fo == NULL) 272 return -1; 273 if (!PyFloat_Check(fo)) { 274 Py_DECREF(fo); 275 PyErr_SetString(PyExc_TypeError, 276 "nb_float should return float object"); 277 return -1; 278 } 279 280 val = PyFloat_AS_DOUBLE(fo); 281 Py_DECREF(fo); 282 283 return val; 284 } 285 286 /* Methods */ 287 288 /* Macro and helper that convert PyObject obj to a C double and store 289 the value in dbl; this replaces the functionality of the coercion 290 slot function. If conversion to double raises an exception, obj is 291 set to NULL, and the function invoking this macro returns NULL. If 292 obj is not of float, int or long type, Py_NotImplemented is incref'ed, 293 stored in obj, and returned from the function invoking this macro. 294 */ 295 #define CONVERT_TO_DOUBLE(obj, dbl) \ 296 if (PyFloat_Check(obj)) \ 297 dbl = PyFloat_AS_DOUBLE(obj); \ 298 else if (convert_to_double(&(obj), &(dbl)) < 0) \ 299 return obj; 300 301 static int 302 convert_to_double(PyObject **v, double *dbl) 303 { 304 register PyObject *obj = *v; 305 306 if (PyInt_Check(obj)) { 307 *dbl = (double)PyInt_AS_LONG(obj); 308 } 309 else if (PyLong_Check(obj)) { 310 *dbl = PyLong_AsDouble(obj); 311 if (*dbl == -1.0 && PyErr_Occurred()) { 312 *v = NULL; 313 return -1; 314 } 315 } 316 else { 317 Py_INCREF(Py_NotImplemented); 318 *v = Py_NotImplemented; 319 return -1; 320 } 321 return 0; 322 } 323 324 /* XXX PyFloat_AsString and PyFloat_AsReprString are deprecated: 325 XXX they pass a char buffer without passing a length. 326 */ 327 void 328 PyFloat_AsString(char *buf, PyFloatObject *v) 329 { 330 char *tmp = PyOS_double_to_string(v->ob_fval, 'g', 331 PyFloat_STR_PRECISION, 332 Py_DTSF_ADD_DOT_0, NULL); 333 strcpy(buf, tmp); 334 PyMem_Free(tmp); 335 } 336 337 void 338 PyFloat_AsReprString(char *buf, PyFloatObject *v) 339 { 340 char * tmp = PyOS_double_to_string(v->ob_fval, 'r', 0, 341 Py_DTSF_ADD_DOT_0, NULL); 342 strcpy(buf, tmp); 343 PyMem_Free(tmp); 344 } 345 346 /* ARGSUSED */ 347 static int 348 float_print(PyFloatObject *v, FILE *fp, int flags) 349 { 350 char *buf; 351 if (flags & Py_PRINT_RAW) 352 buf = PyOS_double_to_string(v->ob_fval, 353 'g', PyFloat_STR_PRECISION, 354 Py_DTSF_ADD_DOT_0, NULL); 355 else 356 buf = PyOS_double_to_string(v->ob_fval, 357 'r', 0, Py_DTSF_ADD_DOT_0, NULL); 358 Py_BEGIN_ALLOW_THREADS 359 fputs(buf, fp); 360 Py_END_ALLOW_THREADS 361 PyMem_Free(buf); 362 return 0; 363 } 364 365 static PyObject * 366 float_str_or_repr(PyFloatObject *v, int precision, char format_code) 367 { 368 PyObject *result; 369 char *buf = PyOS_double_to_string(PyFloat_AS_DOUBLE(v), 370 format_code, precision, 371 Py_DTSF_ADD_DOT_0, 372 NULL); 373 if (!buf) 374 return PyErr_NoMemory(); 375 result = PyString_FromString(buf); 376 PyMem_Free(buf); 377 return result; 378 } 379 380 static PyObject * 381 float_repr(PyFloatObject *v) 382 { 383 return float_str_or_repr(v, 0, 'r'); 384 } 385 386 static PyObject * 387 float_str(PyFloatObject *v) 388 { 389 return float_str_or_repr(v, PyFloat_STR_PRECISION, 'g'); 390 } 391 392 /* Comparison is pretty much a nightmare. When comparing float to float, 393 * we do it as straightforwardly (and long-windedly) as conceivable, so 394 * that, e.g., Python x == y delivers the same result as the platform 395 * C x == y when x and/or y is a NaN. 396 * When mixing float with an integer type, there's no good *uniform* approach. 397 * Converting the double to an integer obviously doesn't work, since we 398 * may lose info from fractional bits. Converting the integer to a double 399 * also has two failure modes: (1) a long int may trigger overflow (too 400 * large to fit in the dynamic range of a C double); (2) even a C long may have 401 * more bits than fit in a C double (e.g., on a a 64-bit box long may have 402 * 63 bits of precision, but a C double probably has only 53), and then 403 * we can falsely claim equality when low-order integer bits are lost by 404 * coercion to double. So this part is painful too. 405 */ 406 407 static PyObject* 408 float_richcompare(PyObject *v, PyObject *w, int op) 409 { 410 double i, j; 411 int r = 0; 412 413 assert(PyFloat_Check(v)); 414 i = PyFloat_AS_DOUBLE(v); 415 416 /* Switch on the type of w. Set i and j to doubles to be compared, 417 * and op to the richcomp to use. 418 */ 419 if (PyFloat_Check(w)) 420 j = PyFloat_AS_DOUBLE(w); 421 422 else if (!Py_IS_FINITE(i)) { 423 if (PyInt_Check(w) || PyLong_Check(w)) 424 /* If i is an infinity, its magnitude exceeds any 425 * finite integer, so it doesn't matter which int we 426 * compare i with. If i is a NaN, similarly. 427 */ 428 j = 0.0; 429 else 430 goto Unimplemented; 431 } 432 433 else if (PyInt_Check(w)) { 434 long jj = PyInt_AS_LONG(w); 435 /* In the worst realistic case I can imagine, C double is a 436 * Cray single with 48 bits of precision, and long has 64 437 * bits. 438 */ 439 #if SIZEOF_LONG > 6 440 unsigned long abs = (unsigned long)(jj < 0 ? -jj : jj); 441 if (abs >> 48) { 442 /* Needs more than 48 bits. Make it take the 443 * PyLong path. 444 */ 445 PyObject *result; 446 PyObject *ww = PyLong_FromLong(jj); 447 448 if (ww == NULL) 449 return NULL; 450 result = float_richcompare(v, ww, op); 451 Py_DECREF(ww); 452 return result; 453 } 454 #endif 455 j = (double)jj; 456 assert((long)j == jj); 457 } 458 459 else if (PyLong_Check(w)) { 460 int vsign = i == 0.0 ? 0 : i < 0.0 ? -1 : 1; 461 int wsign = _PyLong_Sign(w); 462 size_t nbits; 463 int exponent; 464 465 if (vsign != wsign) { 466 /* Magnitudes are irrelevant -- the signs alone 467 * determine the outcome. 468 */ 469 i = (double)vsign; 470 j = (double)wsign; 471 goto Compare; 472 } 473 /* The signs are the same. */ 474 /* Convert w to a double if it fits. In particular, 0 fits. */ 475 nbits = _PyLong_NumBits(w); 476 if (nbits == (size_t)-1 && PyErr_Occurred()) { 477 /* This long is so large that size_t isn't big enough 478 * to hold the # of bits. Replace with little doubles 479 * that give the same outcome -- w is so large that 480 * its magnitude must exceed the magnitude of any 481 * finite float. 482 */ 483 PyErr_Clear(); 484 i = (double)vsign; 485 assert(wsign != 0); 486 j = wsign * 2.0; 487 goto Compare; 488 } 489 if (nbits <= 48) { 490 j = PyLong_AsDouble(w); 491 /* It's impossible that <= 48 bits overflowed. */ 492 assert(j != -1.0 || ! PyErr_Occurred()); 493 goto Compare; 494 } 495 assert(wsign != 0); /* else nbits was 0 */ 496 assert(vsign != 0); /* if vsign were 0, then since wsign is 497 * not 0, we would have taken the 498 * vsign != wsign branch at the start */ 499 /* We want to work with non-negative numbers. */ 500 if (vsign < 0) { 501 /* "Multiply both sides" by -1; this also swaps the 502 * comparator. 503 */ 504 i = -i; 505 op = _Py_SwappedOp[op]; 506 } 507 assert(i > 0.0); 508 (void) frexp(i, &exponent); 509 /* exponent is the # of bits in v before the radix point; 510 * we know that nbits (the # of bits in w) > 48 at this point 511 */ 512 if (exponent < 0 || (size_t)exponent < nbits) { 513 i = 1.0; 514 j = 2.0; 515 goto Compare; 516 } 517 if ((size_t)exponent > nbits) { 518 i = 2.0; 519 j = 1.0; 520 goto Compare; 521 } 522 /* v and w have the same number of bits before the radix 523 * point. Construct two longs that have the same comparison 524 * outcome. 525 */ 526 { 527 double fracpart; 528 double intpart; 529 PyObject *result = NULL; 530 PyObject *one = NULL; 531 PyObject *vv = NULL; 532 PyObject *ww = w; 533 534 if (wsign < 0) { 535 ww = PyNumber_Negative(w); 536 if (ww == NULL) 537 goto Error; 538 } 539 else 540 Py_INCREF(ww); 541 542 fracpart = modf(i, &intpart); 543 vv = PyLong_FromDouble(intpart); 544 if (vv == NULL) 545 goto Error; 546 547 if (fracpart != 0.0) { 548 /* Shift left, and or a 1 bit into vv 549 * to represent the lost fraction. 550 */ 551 PyObject *temp; 552 553 one = PyInt_FromLong(1); 554 if (one == NULL) 555 goto Error; 556 557 temp = PyNumber_Lshift(ww, one); 558 if (temp == NULL) 559 goto Error; 560 Py_DECREF(ww); 561 ww = temp; 562 563 temp = PyNumber_Lshift(vv, one); 564 if (temp == NULL) 565 goto Error; 566 Py_DECREF(vv); 567 vv = temp; 568 569 temp = PyNumber_Or(vv, one); 570 if (temp == NULL) 571 goto Error; 572 Py_DECREF(vv); 573 vv = temp; 574 } 575 576 r = PyObject_RichCompareBool(vv, ww, op); 577 if (r < 0) 578 goto Error; 579 result = PyBool_FromLong(r); 580 Error: 581 Py_XDECREF(vv); 582 Py_XDECREF(ww); 583 Py_XDECREF(one); 584 return result; 585 } 586 } /* else if (PyLong_Check(w)) */ 587 588 else /* w isn't float, int, or long */ 589 goto Unimplemented; 590 591 Compare: 592 PyFPE_START_PROTECT("richcompare", return NULL) 593 switch (op) { 594 case Py_EQ: 595 r = i == j; 596 break; 597 case Py_NE: 598 r = i != j; 599 break; 600 case Py_LE: 601 r = i <= j; 602 break; 603 case Py_GE: 604 r = i >= j; 605 break; 606 case Py_LT: 607 r = i < j; 608 break; 609 case Py_GT: 610 r = i > j; 611 break; 612 } 613 PyFPE_END_PROTECT(r) 614 return PyBool_FromLong(r); 615 616 Unimplemented: 617 Py_INCREF(Py_NotImplemented); 618 return Py_NotImplemented; 619 } 620 621 static long 622 float_hash(PyFloatObject *v) 623 { 624 return _Py_HashDouble(v->ob_fval); 625 } 626 627 static PyObject * 628 float_add(PyObject *v, PyObject *w) 629 { 630 double a,b; 631 CONVERT_TO_DOUBLE(v, a); 632 CONVERT_TO_DOUBLE(w, b); 633 PyFPE_START_PROTECT("add", return 0) 634 a = a + b; 635 PyFPE_END_PROTECT(a) 636 return PyFloat_FromDouble(a); 637 } 638 639 static PyObject * 640 float_sub(PyObject *v, PyObject *w) 641 { 642 double a,b; 643 CONVERT_TO_DOUBLE(v, a); 644 CONVERT_TO_DOUBLE(w, b); 645 PyFPE_START_PROTECT("subtract", return 0) 646 a = a - b; 647 PyFPE_END_PROTECT(a) 648 return PyFloat_FromDouble(a); 649 } 650 651 static PyObject * 652 float_mul(PyObject *v, PyObject *w) 653 { 654 double a,b; 655 CONVERT_TO_DOUBLE(v, a); 656 CONVERT_TO_DOUBLE(w, b); 657 PyFPE_START_PROTECT("multiply", return 0) 658 a = a * b; 659 PyFPE_END_PROTECT(a) 660 return PyFloat_FromDouble(a); 661 } 662 663 static PyObject * 664 float_div(PyObject *v, PyObject *w) 665 { 666 double a,b; 667 CONVERT_TO_DOUBLE(v, a); 668 CONVERT_TO_DOUBLE(w, b); 669 #ifdef Py_NAN 670 if (b == 0.0) { 671 PyErr_SetString(PyExc_ZeroDivisionError, 672 "float division by zero"); 673 return NULL; 674 } 675 #endif 676 PyFPE_START_PROTECT("divide", return 0) 677 a = a / b; 678 PyFPE_END_PROTECT(a) 679 return PyFloat_FromDouble(a); 680 } 681 682 static PyObject * 683 float_classic_div(PyObject *v, PyObject *w) 684 { 685 double a,b; 686 CONVERT_TO_DOUBLE(v, a); 687 CONVERT_TO_DOUBLE(w, b); 688 if (Py_DivisionWarningFlag >= 2 && 689 PyErr_Warn(PyExc_DeprecationWarning, "classic float division") < 0) 690 return NULL; 691 #ifdef Py_NAN 692 if (b == 0.0) { 693 PyErr_SetString(PyExc_ZeroDivisionError, 694 "float division by zero"); 695 return NULL; 696 } 697 #endif 698 PyFPE_START_PROTECT("divide", return 0) 699 a = a / b; 700 PyFPE_END_PROTECT(a) 701 return PyFloat_FromDouble(a); 702 } 703 704 static PyObject * 705 float_rem(PyObject *v, PyObject *w) 706 { 707 double vx, wx; 708 double mod; 709 CONVERT_TO_DOUBLE(v, vx); 710 CONVERT_TO_DOUBLE(w, wx); 711 #ifdef Py_NAN 712 if (wx == 0.0) { 713 PyErr_SetString(PyExc_ZeroDivisionError, 714 "float modulo"); 715 return NULL; 716 } 717 #endif 718 PyFPE_START_PROTECT("modulo", return 0) 719 mod = fmod(vx, wx); 720 if (mod) { 721 /* ensure the remainder has the same sign as the denominator */ 722 if ((wx < 0) != (mod < 0)) { 723 mod += wx; 724 } 725 } 726 else { 727 /* the remainder is zero, and in the presence of signed zeroes 728 fmod returns different results across platforms; ensure 729 it has the same sign as the denominator; we'd like to do 730 "mod = wx * 0.0", but that may get optimized away */ 731 mod *= mod; /* hide "mod = +0" from optimizer */ 732 if (wx < 0.0) 733 mod = -mod; 734 } 735 PyFPE_END_PROTECT(mod) 736 return PyFloat_FromDouble(mod); 737 } 738 739 static PyObject * 740 float_divmod(PyObject *v, PyObject *w) 741 { 742 double vx, wx; 743 double div, mod, floordiv; 744 CONVERT_TO_DOUBLE(v, vx); 745 CONVERT_TO_DOUBLE(w, wx); 746 if (wx == 0.0) { 747 PyErr_SetString(PyExc_ZeroDivisionError, "float divmod()"); 748 return NULL; 749 } 750 PyFPE_START_PROTECT("divmod", return 0) 751 mod = fmod(vx, wx); 752 /* fmod is typically exact, so vx-mod is *mathematically* an 753 exact multiple of wx. But this is fp arithmetic, and fp 754 vx - mod is an approximation; the result is that div may 755 not be an exact integral value after the division, although 756 it will always be very close to one. 757 */ 758 div = (vx - mod) / wx; 759 if (mod) { 760 /* ensure the remainder has the same sign as the denominator */ 761 if ((wx < 0) != (mod < 0)) { 762 mod += wx; 763 div -= 1.0; 764 } 765 } 766 else { 767 /* the remainder is zero, and in the presence of signed zeroes 768 fmod returns different results across platforms; ensure 769 it has the same sign as the denominator; we'd like to do 770 "mod = wx * 0.0", but that may get optimized away */ 771 mod *= mod; /* hide "mod = +0" from optimizer */ 772 if (wx < 0.0) 773 mod = -mod; 774 } 775 /* snap quotient to nearest integral value */ 776 if (div) { 777 floordiv = floor(div); 778 if (div - floordiv > 0.5) 779 floordiv += 1.0; 780 } 781 else { 782 /* div is zero - get the same sign as the true quotient */ 783 div *= div; /* hide "div = +0" from optimizers */ 784 floordiv = div * vx / wx; /* zero w/ sign of vx/wx */ 785 } 786 PyFPE_END_PROTECT(floordiv) 787 return Py_BuildValue("(dd)", floordiv, mod); 788 } 789 790 static PyObject * 791 float_floor_div(PyObject *v, PyObject *w) 792 { 793 PyObject *t, *r; 794 795 t = float_divmod(v, w); 796 if (t == NULL || t == Py_NotImplemented) 797 return t; 798 assert(PyTuple_CheckExact(t)); 799 r = PyTuple_GET_ITEM(t, 0); 800 Py_INCREF(r); 801 Py_DECREF(t); 802 return r; 803 } 804 805 /* determine whether x is an odd integer or not; assumes that 806 x is not an infinity or nan. */ 807 #define DOUBLE_IS_ODD_INTEGER(x) (fmod(fabs(x), 2.0) == 1.0) 808 809 static PyObject * 810 float_pow(PyObject *v, PyObject *w, PyObject *z) 811 { 812 double iv, iw, ix; 813 int negate_result = 0; 814 815 if ((PyObject *)z != Py_None) { 816 PyErr_SetString(PyExc_TypeError, "pow() 3rd argument not " 817 "allowed unless all arguments are integers"); 818 return NULL; 819 } 820 821 CONVERT_TO_DOUBLE(v, iv); 822 CONVERT_TO_DOUBLE(w, iw); 823 824 /* Sort out special cases here instead of relying on pow() */ 825 if (iw == 0) { /* v**0 is 1, even 0**0 */ 826 return PyFloat_FromDouble(1.0); 827 } 828 if (Py_IS_NAN(iv)) { /* nan**w = nan, unless w == 0 */ 829 return PyFloat_FromDouble(iv); 830 } 831 if (Py_IS_NAN(iw)) { /* v**nan = nan, unless v == 1; 1**nan = 1 */ 832 return PyFloat_FromDouble(iv == 1.0 ? 1.0 : iw); 833 } 834 if (Py_IS_INFINITY(iw)) { 835 /* v**inf is: 0.0 if abs(v) < 1; 1.0 if abs(v) == 1; inf if 836 * abs(v) > 1 (including case where v infinite) 837 * 838 * v**-inf is: inf if abs(v) < 1; 1.0 if abs(v) == 1; 0.0 if 839 * abs(v) > 1 (including case where v infinite) 840 */ 841 iv = fabs(iv); 842 if (iv == 1.0) 843 return PyFloat_FromDouble(1.0); 844 else if ((iw > 0.0) == (iv > 1.0)) 845 return PyFloat_FromDouble(fabs(iw)); /* return inf */ 846 else 847 return PyFloat_FromDouble(0.0); 848 } 849 if (Py_IS_INFINITY(iv)) { 850 /* (+-inf)**w is: inf for w positive, 0 for w negative; in 851 * both cases, we need to add the appropriate sign if w is 852 * an odd integer. 853 */ 854 int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw); 855 if (iw > 0.0) 856 return PyFloat_FromDouble(iw_is_odd ? iv : fabs(iv)); 857 else 858 return PyFloat_FromDouble(iw_is_odd ? 859 copysign(0.0, iv) : 0.0); 860 } 861 if (iv == 0.0) { /* 0**w is: 0 for w positive, 1 for w zero 862 (already dealt with above), and an error 863 if w is negative. */ 864 int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw); 865 if (iw < 0.0) { 866 PyErr_SetString(PyExc_ZeroDivisionError, 867 "0.0 cannot be raised to a " 868 "negative power"); 869 return NULL; 870 } 871 /* use correct sign if iw is odd */ 872 return PyFloat_FromDouble(iw_is_odd ? iv : 0.0); 873 } 874 875 if (iv < 0.0) { 876 /* Whether this is an error is a mess, and bumps into libm 877 * bugs so we have to figure it out ourselves. 878 */ 879 if (iw != floor(iw)) { 880 PyErr_SetString(PyExc_ValueError, "negative number " 881 "cannot be raised to a fractional power"); 882 return NULL; 883 } 884 /* iw is an exact integer, albeit perhaps a very large 885 * one. Replace iv by its absolute value and remember 886 * to negate the pow result if iw is odd. 887 */ 888 iv = -iv; 889 negate_result = DOUBLE_IS_ODD_INTEGER(iw); 890 } 891 892 if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */ 893 /* (-1) ** large_integer also ends up here. Here's an 894 * extract from the comments for the previous 895 * implementation explaining why this special case is 896 * necessary: 897 * 898 * -1 raised to an exact integer should never be exceptional. 899 * Alas, some libms (chiefly glibc as of early 2003) return 900 * NaN and set EDOM on pow(-1, large_int) if the int doesn't 901 * happen to be representable in a *C* integer. That's a 902 * bug. 903 */ 904 return PyFloat_FromDouble(negate_result ? -1.0 : 1.0); 905 } 906 907 /* Now iv and iw are finite, iw is nonzero, and iv is 908 * positive and not equal to 1.0. We finally allow 909 * the platform pow to step in and do the rest. 910 */ 911 errno = 0; 912 PyFPE_START_PROTECT("pow", return NULL) 913 ix = pow(iv, iw); 914 PyFPE_END_PROTECT(ix) 915 Py_ADJUST_ERANGE1(ix); 916 if (negate_result) 917 ix = -ix; 918 919 if (errno != 0) { 920 /* We don't expect any errno value other than ERANGE, but 921 * the range of libm bugs appears unbounded. 922 */ 923 PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError : 924 PyExc_ValueError); 925 return NULL; 926 } 927 return PyFloat_FromDouble(ix); 928 } 929 930 #undef DOUBLE_IS_ODD_INTEGER 931 932 static PyObject * 933 float_neg(PyFloatObject *v) 934 { 935 return PyFloat_FromDouble(-v->ob_fval); 936 } 937 938 static PyObject * 939 float_abs(PyFloatObject *v) 940 { 941 return PyFloat_FromDouble(fabs(v->ob_fval)); 942 } 943 944 static int 945 float_nonzero(PyFloatObject *v) 946 { 947 return v->ob_fval != 0.0; 948 } 949 950 static int 951 float_coerce(PyObject **pv, PyObject **pw) 952 { 953 if (PyInt_Check(*pw)) { 954 long x = PyInt_AsLong(*pw); 955 *pw = PyFloat_FromDouble((double)x); 956 Py_INCREF(*pv); 957 return 0; 958 } 959 else if (PyLong_Check(*pw)) { 960 double x = PyLong_AsDouble(*pw); 961 if (x == -1.0 && PyErr_Occurred()) 962 return -1; 963 *pw = PyFloat_FromDouble(x); 964 Py_INCREF(*pv); 965 return 0; 966 } 967 else if (PyFloat_Check(*pw)) { 968 Py_INCREF(*pv); 969 Py_INCREF(*pw); 970 return 0; 971 } 972 return 1; /* Can't do it */ 973 } 974 975 static PyObject * 976 float_is_integer(PyObject *v) 977 { 978 double x = PyFloat_AsDouble(v); 979 PyObject *o; 980 981 if (x == -1.0 && PyErr_Occurred()) 982 return NULL; 983 if (!Py_IS_FINITE(x)) 984 Py_RETURN_FALSE; 985 errno = 0; 986 PyFPE_START_PROTECT("is_integer", return NULL) 987 o = (floor(x) == x) ? Py_True : Py_False; 988 PyFPE_END_PROTECT(x) 989 if (errno != 0) { 990 PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError : 991 PyExc_ValueError); 992 return NULL; 993 } 994 Py_INCREF(o); 995 return o; 996 } 997 998 #if 0 999 static PyObject * 1000 float_is_inf(PyObject *v) 1001 { 1002 double x = PyFloat_AsDouble(v); 1003 if (x == -1.0 && PyErr_Occurred()) 1004 return NULL; 1005 return PyBool_FromLong((long)Py_IS_INFINITY(x)); 1006 } 1007 1008 static PyObject * 1009 float_is_nan(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_NAN(x)); 1015 } 1016 1017 static PyObject * 1018 float_is_finite(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_FINITE(x)); 1024 } 1025 #endif 1026 1027 static PyObject * 1028 float_trunc(PyObject *v) 1029 { 1030 double x = PyFloat_AsDouble(v); 1031 double wholepart; /* integral portion of x, rounded toward 0 */ 1032 1033 (void)modf(x, &wholepart); 1034 /* Try to get out cheap if this fits in a Python int. The attempt 1035 * to cast to long must be protected, as C doesn't define what 1036 * happens if the double is too big to fit in a long. Some rare 1037 * systems raise an exception then (RISCOS was mentioned as one, 1038 * and someone using a non-default option on Sun also bumped into 1039 * that). Note that checking for <= LONG_MAX is unsafe: if a long 1040 * has more bits of precision than a double, casting LONG_MAX to 1041 * double may yield an approximation, and if that's rounded up, 1042 * then, e.g., wholepart=LONG_MAX+1 would yield true from the C 1043 * expression wholepart<=LONG_MAX, despite that wholepart is 1044 * actually greater than LONG_MAX. However, assuming a two's complement 1045 * machine with no trap representation, LONG_MIN will be a power of 2 (and 1046 * hence exactly representable as a double), and LONG_MAX = -1-LONG_MIN, so 1047 * the comparisons with (double)LONG_MIN below should be safe. 1048 */ 1049 if ((double)LONG_MIN <= wholepart && wholepart < -(double)LONG_MIN) { 1050 const long aslong = (long)wholepart; 1051 return PyInt_FromLong(aslong); 1052 } 1053 return PyLong_FromDouble(wholepart); 1054 } 1055 1056 static PyObject * 1057 float_long(PyObject *v) 1058 { 1059 double x = PyFloat_AsDouble(v); 1060 return PyLong_FromDouble(x); 1061 } 1062 1063 /* _Py_double_round: rounds a finite nonzero double to the closest multiple of 1064 10**-ndigits; here ndigits is within reasonable bounds (typically, -308 <= 1065 ndigits <= 323). Returns a Python float, or sets a Python error and 1066 returns NULL on failure (OverflowError and memory errors are possible). */ 1067 1068 #ifndef PY_NO_SHORT_FLOAT_REPR 1069 /* version of _Py_double_round that uses the correctly-rounded string<->double 1070 conversions from Python/dtoa.c */ 1071 1072 /* FIVE_POW_LIMIT is the largest k such that 5**k is exactly representable as 1073 a double. Since we're using the code in Python/dtoa.c, it should be safe 1074 to assume that C doubles are IEEE 754 binary64 format. To be on the safe 1075 side, we check this. */ 1076 #if DBL_MANT_DIG == 53 1077 #define FIVE_POW_LIMIT 22 1078 #else 1079 #error "C doubles do not appear to be IEEE 754 binary64 format" 1080 #endif 1081 1082 PyObject * 1083 _Py_double_round(double x, int ndigits) { 1084 1085 double rounded, m; 1086 Py_ssize_t buflen, mybuflen=100; 1087 char *buf, *buf_end, shortbuf[100], *mybuf=shortbuf; 1088 int decpt, sign, val, halfway_case; 1089 PyObject *result = NULL; 1090 _Py_SET_53BIT_PRECISION_HEADER; 1091 1092 /* Easy path for the common case ndigits == 0. */ 1093 if (ndigits == 0) { 1094 rounded = round(x); 1095 if (fabs(rounded - x) == 0.5) 1096 /* halfway between two integers; use round-away-from-zero */ 1097 rounded = x + (x > 0.0 ? 0.5 : -0.5); 1098 return PyFloat_FromDouble(rounded); 1099 } 1100 1101 /* The basic idea is very simple: convert and round the double to a 1102 decimal string using _Py_dg_dtoa, then convert that decimal string 1103 back to a double with _Py_dg_strtod. There's one minor difficulty: 1104 Python 2.x expects round to do round-half-away-from-zero, while 1105 _Py_dg_dtoa does round-half-to-even. So we need some way to detect 1106 and correct the halfway cases. 1107 1108 Detection: a halfway value has the form k * 0.5 * 10**-ndigits for 1109 some odd integer k. Or in other words, a rational number x is 1110 exactly halfway between two multiples of 10**-ndigits if its 1111 2-valuation is exactly -ndigits-1 and its 5-valuation is at least 1112 -ndigits. For ndigits >= 0 the latter condition is automatically 1113 satisfied for a binary float x, since any such float has 1114 nonnegative 5-valuation. For 0 > ndigits >= -22, x needs to be an 1115 integral multiple of 5**-ndigits; we can check this using fmod. 1116 For -22 > ndigits, there are no halfway cases: 5**23 takes 54 bits 1117 to represent exactly, so any odd multiple of 0.5 * 10**n for n >= 1118 23 takes at least 54 bits of precision to represent exactly. 1119 1120 Correction: a simple strategy for dealing with halfway cases is to 1121 (for the halfway cases only) call _Py_dg_dtoa with an argument of 1122 ndigits+1 instead of ndigits (thus doing an exact conversion to 1123 decimal), round the resulting string manually, and then convert 1124 back using _Py_dg_strtod. 1125 */ 1126 1127 /* nans, infinities and zeros should have already been dealt 1128 with by the caller (in this case, builtin_round) */ 1129 assert(Py_IS_FINITE(x) && x != 0.0); 1130 1131 /* find 2-valuation val of x */ 1132 m = frexp(x, &val); 1133 while (m != floor(m)) { 1134 m *= 2.0; 1135 val--; 1136 } 1137 1138 /* determine whether this is a halfway case */ 1139 if (val == -ndigits-1) { 1140 if (ndigits >= 0) 1141 halfway_case = 1; 1142 else if (ndigits >= -FIVE_POW_LIMIT) { 1143 double five_pow = 1.0; 1144 int i; 1145 for (i=0; i < -ndigits; i++) 1146 five_pow *= 5.0; 1147 halfway_case = fmod(x, five_pow) == 0.0; 1148 } 1149 else 1150 halfway_case = 0; 1151 } 1152 else 1153 halfway_case = 0; 1154 1155 /* round to a decimal string; use an extra place for halfway case */ 1156 _Py_SET_53BIT_PRECISION_START; 1157 buf = _Py_dg_dtoa(x, 3, ndigits+halfway_case, &decpt, &sign, &buf_end); 1158 _Py_SET_53BIT_PRECISION_END; 1159 if (buf == NULL) { 1160 PyErr_NoMemory(); 1161 return NULL; 1162 } 1163 buflen = buf_end - buf; 1164 1165 /* in halfway case, do the round-half-away-from-zero manually */ 1166 if (halfway_case) { 1167 int i, carry; 1168 /* sanity check: _Py_dg_dtoa should not have stripped 1169 any zeros from the result: there should be exactly 1170 ndigits+1 places following the decimal point, and 1171 the last digit in the buffer should be a '5'.*/ 1172 assert(buflen - decpt == ndigits+1); 1173 assert(buf[buflen-1] == '5'); 1174 1175 /* increment and shift right at the same time. */ 1176 decpt += 1; 1177 carry = 1; 1178 for (i=buflen-1; i-- > 0;) { 1179 carry += buf[i] - '0'; 1180 buf[i+1] = carry % 10 + '0'; 1181 carry /= 10; 1182 } 1183 buf[0] = carry + '0'; 1184 } 1185 1186 /* Get new buffer if shortbuf is too small. Space needed <= buf_end - 1187 buf + 8: (1 extra for '0', 1 for sign, 5 for exp, 1 for '\0'). */ 1188 if (buflen + 8 > mybuflen) { 1189 mybuflen = buflen+8; 1190 mybuf = (char *)PyMem_Malloc(mybuflen); 1191 if (mybuf == NULL) { 1192 PyErr_NoMemory(); 1193 goto exit; 1194 } 1195 } 1196 /* copy buf to mybuf, adding exponent, sign and leading 0 */ 1197 PyOS_snprintf(mybuf, mybuflen, "%s0%se%d", (sign ? "-" : ""), 1198 buf, decpt - (int)buflen); 1199 1200 /* and convert the resulting string back to a double */ 1201 errno = 0; 1202 _Py_SET_53BIT_PRECISION_START; 1203 rounded = _Py_dg_strtod(mybuf, NULL); 1204 _Py_SET_53BIT_PRECISION_END; 1205 if (errno == ERANGE && fabs(rounded) >= 1.) 1206 PyErr_SetString(PyExc_OverflowError, 1207 "rounded value too large to represent"); 1208 else 1209 result = PyFloat_FromDouble(rounded); 1210 1211 /* done computing value; now clean up */ 1212 if (mybuf != shortbuf) 1213 PyMem_Free(mybuf); 1214 exit: 1215 _Py_dg_freedtoa(buf); 1216 return result; 1217 } 1218 1219 #undef FIVE_POW_LIMIT 1220 1221 #else /* PY_NO_SHORT_FLOAT_REPR */ 1222 1223 /* fallback version, to be used when correctly rounded binary<->decimal 1224 conversions aren't available */ 1225 1226 PyObject * 1227 _Py_double_round(double x, int ndigits) { 1228 double pow1, pow2, y, z; 1229 if (ndigits >= 0) { 1230 if (ndigits > 22) { 1231 /* pow1 and pow2 are each safe from overflow, but 1232 pow1*pow2 ~= pow(10.0, ndigits) might overflow */ 1233 pow1 = pow(10.0, (double)(ndigits-22)); 1234 pow2 = 1e22; 1235 } 1236 else { 1237 pow1 = pow(10.0, (double)ndigits); 1238 pow2 = 1.0; 1239 } 1240 y = (x*pow1)*pow2; 1241 /* if y overflows, then rounded value is exactly x */ 1242 if (!Py_IS_FINITE(y)) 1243 return PyFloat_FromDouble(x); 1244 } 1245 else { 1246 pow1 = pow(10.0, (double)-ndigits); 1247 pow2 = 1.0; /* unused; silences a gcc compiler warning */ 1248 y = x / pow1; 1249 } 1250 1251 z = round(y); 1252 if (fabs(y-z) == 0.5) 1253 /* halfway between two integers; use round-away-from-zero */ 1254 z = y + copysign(0.5, y); 1255 1256 if (ndigits >= 0) 1257 z = (z / pow2) / pow1; 1258 else 1259 z *= pow1; 1260 1261 /* if computation resulted in overflow, raise OverflowError */ 1262 if (!Py_IS_FINITE(z)) { 1263 PyErr_SetString(PyExc_OverflowError, 1264 "overflow occurred during round"); 1265 return NULL; 1266 } 1267 1268 return PyFloat_FromDouble(z); 1269 } 1270 1271 #endif /* PY_NO_SHORT_FLOAT_REPR */ 1272 1273 static PyObject * 1274 float_float(PyObject *v) 1275 { 1276 if (PyFloat_CheckExact(v)) 1277 Py_INCREF(v); 1278 else 1279 v = PyFloat_FromDouble(((PyFloatObject *)v)->ob_fval); 1280 return v; 1281 } 1282 1283 /* turn ASCII hex characters into integer values and vice versa */ 1284 1285 static char 1286 char_from_hex(int x) 1287 { 1288 assert(0 <= x && x < 16); 1289 return "0123456789abcdef"[x]; 1290 } 1291 1292 static int 1293 hex_from_char(char c) { 1294 int x; 1295 switch(c) { 1296 case '0': 1297 x = 0; 1298 break; 1299 case '1': 1300 x = 1; 1301 break; 1302 case '2': 1303 x = 2; 1304 break; 1305 case '3': 1306 x = 3; 1307 break; 1308 case '4': 1309 x = 4; 1310 break; 1311 case '5': 1312 x = 5; 1313 break; 1314 case '6': 1315 x = 6; 1316 break; 1317 case '7': 1318 x = 7; 1319 break; 1320 case '8': 1321 x = 8; 1322 break; 1323 case '9': 1324 x = 9; 1325 break; 1326 case 'a': 1327 case 'A': 1328 x = 10; 1329 break; 1330 case 'b': 1331 case 'B': 1332 x = 11; 1333 break; 1334 case 'c': 1335 case 'C': 1336 x = 12; 1337 break; 1338 case 'd': 1339 case 'D': 1340 x = 13; 1341 break; 1342 case 'e': 1343 case 'E': 1344 x = 14; 1345 break; 1346 case 'f': 1347 case 'F': 1348 x = 15; 1349 break; 1350 default: 1351 x = -1; 1352 break; 1353 } 1354 return x; 1355 } 1356 1357 /* convert a float to a hexadecimal string */ 1358 1359 /* TOHEX_NBITS is DBL_MANT_DIG rounded up to the next integer 1360 of the form 4k+1. */ 1361 #define TOHEX_NBITS DBL_MANT_DIG + 3 - (DBL_MANT_DIG+2)%4 1362 1363 static PyObject * 1364 float_hex(PyObject *v) 1365 { 1366 double x, m; 1367 int e, shift, i, si, esign; 1368 /* Space for 1+(TOHEX_NBITS-1)/4 digits, a decimal point, and the 1369 trailing NUL byte. */ 1370 char s[(TOHEX_NBITS-1)/4+3]; 1371 1372 CONVERT_TO_DOUBLE(v, x); 1373 1374 if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) 1375 return float_str((PyFloatObject *)v); 1376 1377 if (x == 0.0) { 1378 if (copysign(1.0, x) == -1.0) 1379 return PyString_FromString("-0x0.0p+0"); 1380 else 1381 return PyString_FromString("0x0.0p+0"); 1382 } 1383 1384 m = frexp(fabs(x), &e); 1385 shift = 1 - MAX(DBL_MIN_EXP - e, 0); 1386 m = ldexp(m, shift); 1387 e -= shift; 1388 1389 si = 0; 1390 s[si] = char_from_hex((int)m); 1391 si++; 1392 m -= (int)m; 1393 s[si] = '.'; 1394 si++; 1395 for (i=0; i < (TOHEX_NBITS-1)/4; i++) { 1396 m *= 16.0; 1397 s[si] = char_from_hex((int)m); 1398 si++; 1399 m -= (int)m; 1400 } 1401 s[si] = '\0'; 1402 1403 if (e < 0) { 1404 esign = (int)'-'; 1405 e = -e; 1406 } 1407 else 1408 esign = (int)'+'; 1409 1410 if (x < 0.0) 1411 return PyString_FromFormat("-0x%sp%c%d", s, esign, e); 1412 else 1413 return PyString_FromFormat("0x%sp%c%d", s, esign, e); 1414 } 1415 1416 PyDoc_STRVAR(float_hex_doc, 1417 "float.hex() -> string\n\ 1418 \n\ 1419 Return a hexadecimal representation of a floating-point number.\n\ 1420 >>> (-0.1).hex()\n\ 1421 '-0x1.999999999999ap-4'\n\ 1422 >>> 3.14159.hex()\n\ 1423 '0x1.921f9f01b866ep+1'"); 1424 1425 /* Case-insensitive locale-independent string match used for nan and inf 1426 detection. t should be lower-case and null-terminated. Return a nonzero 1427 result if the first strlen(t) characters of s match t and 0 otherwise. */ 1428 1429 static int 1430 case_insensitive_match(const char *s, const char *t) 1431 { 1432 while(*t && Py_TOLOWER(*s) == *t) { 1433 s++; 1434 t++; 1435 } 1436 return *t ? 0 : 1; 1437 } 1438 1439 /* Convert a hexadecimal string to a float. */ 1440 1441 static PyObject * 1442 float_fromhex(PyObject *cls, PyObject *arg) 1443 { 1444 PyObject *result_as_float, *result; 1445 double x; 1446 long exp, top_exp, lsb, key_digit; 1447 char *s, *coeff_start, *s_store, *coeff_end, *exp_start, *s_end; 1448 int half_eps, digit, round_up, sign=1; 1449 Py_ssize_t length, ndigits, fdigits, i; 1450 1451 /* 1452 * For the sake of simplicity and correctness, we impose an artificial 1453 * limit on ndigits, the total number of hex digits in the coefficient 1454 * The limit is chosen to ensure that, writing exp for the exponent, 1455 * 1456 * (1) if exp > LONG_MAX/2 then the value of the hex string is 1457 * guaranteed to overflow (provided it's nonzero) 1458 * 1459 * (2) if exp < LONG_MIN/2 then the value of the hex string is 1460 * guaranteed to underflow to 0. 1461 * 1462 * (3) if LONG_MIN/2 <= exp <= LONG_MAX/2 then there's no danger of 1463 * overflow in the calculation of exp and top_exp below. 1464 * 1465 * More specifically, ndigits is assumed to satisfy the following 1466 * inequalities: 1467 * 1468 * 4*ndigits <= DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2 1469 * 4*ndigits <= LONG_MAX/2 + 1 - DBL_MAX_EXP 1470 * 1471 * If either of these inequalities is not satisfied, a ValueError is 1472 * raised. Otherwise, write x for the value of the hex string, and 1473 * assume x is nonzero. Then 1474 * 1475 * 2**(exp-4*ndigits) <= |x| < 2**(exp+4*ndigits). 1476 * 1477 * Now if exp > LONG_MAX/2 then: 1478 * 1479 * exp - 4*ndigits >= LONG_MAX/2 + 1 - (LONG_MAX/2 + 1 - DBL_MAX_EXP) 1480 * = DBL_MAX_EXP 1481 * 1482 * so |x| >= 2**DBL_MAX_EXP, which is too large to be stored in C 1483 * double, so overflows. If exp < LONG_MIN/2, then 1484 * 1485 * exp + 4*ndigits <= LONG_MIN/2 - 1 + ( 1486 * DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2) 1487 * = DBL_MIN_EXP - DBL_MANT_DIG - 1 1488 * 1489 * and so |x| < 2**(DBL_MIN_EXP-DBL_MANT_DIG-1), hence underflows to 0 1490 * when converted to a C double. 1491 * 1492 * It's easy to show that if LONG_MIN/2 <= exp <= LONG_MAX/2 then both 1493 * exp+4*ndigits and exp-4*ndigits are within the range of a long. 1494 */ 1495 1496 if (PyString_AsStringAndSize(arg, &s, &length)) 1497 return NULL; 1498 s_end = s + length; 1499 1500 /******************** 1501 * Parse the string * 1502 ********************/ 1503 1504 /* leading whitespace and optional sign */ 1505 while (Py_ISSPACE(*s)) 1506 s++; 1507 if (*s == '-') { 1508 s++; 1509 sign = -1; 1510 } 1511 else if (*s == '+') 1512 s++; 1513 1514 /* infinities and nans */ 1515 if (*s == 'i' || *s == 'I') { 1516 if (!case_insensitive_match(s+1, "nf")) 1517 goto parse_error; 1518 s += 3; 1519 x = Py_HUGE_VAL; 1520 if (case_insensitive_match(s, "inity")) 1521 s += 5; 1522 goto finished; 1523 } 1524 if (*s == 'n' || *s == 'N') { 1525 if (!case_insensitive_match(s+1, "an")) 1526 goto parse_error; 1527 s += 3; 1528 x = Py_NAN; 1529 goto finished; 1530 } 1531 1532 /* [0x] */ 1533 s_store = s; 1534 if (*s == '0') { 1535 s++; 1536 if (*s == 'x' || *s == 'X') 1537 s++; 1538 else 1539 s = s_store; 1540 } 1541 1542 /* coefficient: <integer> [. <fraction>] */ 1543 coeff_start = s; 1544 while (hex_from_char(*s) >= 0) 1545 s++; 1546 s_store = s; 1547 if (*s == '.') { 1548 s++; 1549 while (hex_from_char(*s) >= 0) 1550 s++; 1551 coeff_end = s-1; 1552 } 1553 else 1554 coeff_end = s; 1555 1556 /* ndigits = total # of hex digits; fdigits = # after point */ 1557 ndigits = coeff_end - coeff_start; 1558 fdigits = coeff_end - s_store; 1559 if (ndigits == 0) 1560 goto parse_error; 1561 if (ndigits > MIN(DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2, 1562 LONG_MAX/2 + 1 - DBL_MAX_EXP)/4) 1563 goto insane_length_error; 1564 1565 /* [p <exponent>] */ 1566 if (*s == 'p' || *s == 'P') { 1567 s++; 1568 exp_start = s; 1569 if (*s == '-' || *s == '+') 1570 s++; 1571 if (!('0' <= *s && *s <= '9')) 1572 goto parse_error; 1573 s++; 1574 while ('0' <= *s && *s <= '9') 1575 s++; 1576 exp = strtol(exp_start, NULL, 10); 1577 } 1578 else 1579 exp = 0; 1580 1581 /* for 0 <= j < ndigits, HEX_DIGIT(j) gives the jth most significant digit */ 1582 #define HEX_DIGIT(j) hex_from_char(*((j) < fdigits ? \ 1583 coeff_end-(j) : \ 1584 coeff_end-1-(j))) 1585 1586 /******************************************* 1587 * Compute rounded value of the hex string * 1588 *******************************************/ 1589 1590 /* Discard leading zeros, and catch extreme overflow and underflow */ 1591 while (ndigits > 0 && HEX_DIGIT(ndigits-1) == 0) 1592 ndigits--; 1593 if (ndigits == 0 || exp < LONG_MIN/2) { 1594 x = 0.0; 1595 goto finished; 1596 } 1597 if (exp > LONG_MAX/2) 1598 goto overflow_error; 1599 1600 /* Adjust exponent for fractional part. */ 1601 exp = exp - 4*((long)fdigits); 1602 1603 /* top_exp = 1 more than exponent of most sig. bit of coefficient */ 1604 top_exp = exp + 4*((long)ndigits - 1); 1605 for (digit = HEX_DIGIT(ndigits-1); digit != 0; digit /= 2) 1606 top_exp++; 1607 1608 /* catch almost all nonextreme cases of overflow and underflow here */ 1609 if (top_exp < DBL_MIN_EXP - DBL_MANT_DIG) { 1610 x = 0.0; 1611 goto finished; 1612 } 1613 if (top_exp > DBL_MAX_EXP) 1614 goto overflow_error; 1615 1616 /* lsb = exponent of least significant bit of the *rounded* value. 1617 This is top_exp - DBL_MANT_DIG unless result is subnormal. */ 1618 lsb = MAX(top_exp, (long)DBL_MIN_EXP) - DBL_MANT_DIG; 1619 1620 x = 0.0; 1621 if (exp >= lsb) { 1622 /* no rounding required */ 1623 for (i = ndigits-1; i >= 0; i--) 1624 x = 16.0*x + HEX_DIGIT(i); 1625 x = ldexp(x, (int)(exp)); 1626 goto finished; 1627 } 1628 /* rounding required. key_digit is the index of the hex digit 1629 containing the first bit to be rounded away. */ 1630 half_eps = 1 << (int)((lsb - exp - 1) % 4); 1631 key_digit = (lsb - exp - 1) / 4; 1632 for (i = ndigits-1; i > key_digit; i--) 1633 x = 16.0*x + HEX_DIGIT(i); 1634 digit = HEX_DIGIT(key_digit); 1635 x = 16.0*x + (double)(digit & (16-2*half_eps)); 1636 1637 /* round-half-even: round up if bit lsb-1 is 1 and at least one of 1638 bits lsb, lsb-2, lsb-3, lsb-4, ... is 1. */ 1639 if ((digit & half_eps) != 0) { 1640 round_up = 0; 1641 if ((digit & (3*half_eps-1)) != 0 || 1642 (half_eps == 8 && (HEX_DIGIT(key_digit+1) & 1) != 0)) 1643 round_up = 1; 1644 else 1645 for (i = key_digit-1; i >= 0; i--) 1646 if (HEX_DIGIT(i) != 0) { 1647 round_up = 1; 1648 break; 1649 } 1650 if (round_up == 1) { 1651 x += 2*half_eps; 1652 if (top_exp == DBL_MAX_EXP && 1653 x == ldexp((double)(2*half_eps), DBL_MANT_DIG)) 1654 /* overflow corner case: pre-rounded value < 1655 2**DBL_MAX_EXP; rounded=2**DBL_MAX_EXP. */ 1656 goto overflow_error; 1657 } 1658 } 1659 x = ldexp(x, (int)(exp+4*key_digit)); 1660 1661 finished: 1662 /* optional trailing whitespace leading to the end of the string */ 1663 while (Py_ISSPACE(*s)) 1664 s++; 1665 if (s != s_end) 1666 goto parse_error; 1667 result_as_float = Py_BuildValue("(d)", sign * x); 1668 if (result_as_float == NULL) 1669 return NULL; 1670 result = PyObject_CallObject(cls, result_as_float); 1671 Py_DECREF(result_as_float); 1672 return result; 1673 1674 overflow_error: 1675 PyErr_SetString(PyExc_OverflowError, 1676 "hexadecimal value too large to represent as a float"); 1677 return NULL; 1678 1679 parse_error: 1680 PyErr_SetString(PyExc_ValueError, 1681 "invalid hexadecimal floating-point string"); 1682 return NULL; 1683 1684 insane_length_error: 1685 PyErr_SetString(PyExc_ValueError, 1686 "hexadecimal string too long to convert"); 1687 return NULL; 1688 } 1689 1690 PyDoc_STRVAR(float_fromhex_doc, 1691 "float.fromhex(string) -> float\n\ 1692 \n\ 1693 Create a floating-point number from a hexadecimal string.\n\ 1694 >>> float.fromhex('0x1.ffffp10')\n\ 1695 2047.984375\n\ 1696 >>> float.fromhex('-0x1p-1074')\n\ 1697 -4.9406564584124654e-324"); 1698 1699 1700 static PyObject * 1701 float_as_integer_ratio(PyObject *v, PyObject *unused) 1702 { 1703 double self; 1704 double float_part; 1705 int exponent; 1706 int i; 1707 1708 PyObject *prev; 1709 PyObject *py_exponent = NULL; 1710 PyObject *numerator = NULL; 1711 PyObject *denominator = NULL; 1712 PyObject *result_pair = NULL; 1713 PyNumberMethods *long_methods = PyLong_Type.tp_as_number; 1714 1715 #define INPLACE_UPDATE(obj, call) \ 1716 prev = obj; \ 1717 obj = call; \ 1718 Py_DECREF(prev); \ 1719 1720 CONVERT_TO_DOUBLE(v, self); 1721 1722 if (Py_IS_INFINITY(self)) { 1723 PyErr_SetString(PyExc_OverflowError, 1724 "Cannot pass infinity to float.as_integer_ratio."); 1725 return NULL; 1726 } 1727 #ifdef Py_NAN 1728 if (Py_IS_NAN(self)) { 1729 PyErr_SetString(PyExc_ValueError, 1730 "Cannot pass NaN to float.as_integer_ratio."); 1731 return NULL; 1732 } 1733 #endif 1734 1735 PyFPE_START_PROTECT("as_integer_ratio", goto error); 1736 float_part = frexp(self, &exponent); /* self == float_part * 2**exponent exactly */ 1737 PyFPE_END_PROTECT(float_part); 1738 1739 for (i=0; i<300 && float_part != floor(float_part) ; i++) { 1740 float_part *= 2.0; 1741 exponent--; 1742 } 1743 /* self == float_part * 2**exponent exactly and float_part is integral. 1744 If FLT_RADIX != 2, the 300 steps may leave a tiny fractional part 1745 to be truncated by PyLong_FromDouble(). */ 1746 1747 numerator = PyLong_FromDouble(float_part); 1748 if (numerator == NULL) goto error; 1749 1750 /* fold in 2**exponent */ 1751 denominator = PyLong_FromLong(1); 1752 py_exponent = PyLong_FromLong(labs((long)exponent)); 1753 if (py_exponent == NULL) goto error; 1754 INPLACE_UPDATE(py_exponent, 1755 long_methods->nb_lshift(denominator, py_exponent)); 1756 if (py_exponent == NULL) goto error; 1757 if (exponent > 0) { 1758 INPLACE_UPDATE(numerator, 1759 long_methods->nb_multiply(numerator, py_exponent)); 1760 if (numerator == NULL) goto error; 1761 } 1762 else { 1763 Py_DECREF(denominator); 1764 denominator = py_exponent; 1765 py_exponent = NULL; 1766 } 1767 1768 /* Returns ints instead of longs where possible */ 1769 INPLACE_UPDATE(numerator, PyNumber_Int(numerator)); 1770 if (numerator == NULL) goto error; 1771 INPLACE_UPDATE(denominator, PyNumber_Int(denominator)); 1772 if (denominator == NULL) goto error; 1773 1774 result_pair = PyTuple_Pack(2, numerator, denominator); 1775 1776 #undef INPLACE_UPDATE 1777 error: 1778 Py_XDECREF(py_exponent); 1779 Py_XDECREF(denominator); 1780 Py_XDECREF(numerator); 1781 return result_pair; 1782 } 1783 1784 PyDoc_STRVAR(float_as_integer_ratio_doc, 1785 "float.as_integer_ratio() -> (int, int)\n" 1786 "\n" 1787 "Return a pair of integers, whose ratio is exactly equal to the original\n" 1788 "float and with a positive denominator.\n" 1789 "Raise OverflowError on infinities and a ValueError on NaNs.\n" 1790 "\n" 1791 ">>> (10.0).as_integer_ratio()\n" 1792 "(10, 1)\n" 1793 ">>> (0.0).as_integer_ratio()\n" 1794 "(0, 1)\n" 1795 ">>> (-.25).as_integer_ratio()\n" 1796 "(-1, 4)"); 1797 1798 1799 static PyObject * 1800 float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds); 1801 1802 static PyObject * 1803 float_new(PyTypeObject *type, PyObject *args, PyObject *kwds) 1804 { 1805 PyObject *x = Py_False; /* Integer zero */ 1806 static char *kwlist[] = {"x", 0}; 1807 1808 if (type != &PyFloat_Type) 1809 return float_subtype_new(type, args, kwds); /* Wimp out */ 1810 if (!PyArg_ParseTupleAndKeywords(args, kwds, "|O:float", kwlist, &x)) 1811 return NULL; 1812 /* If it's a string, but not a string subclass, use 1813 PyFloat_FromString. */ 1814 if (PyString_CheckExact(x)) 1815 return PyFloat_FromString(x, NULL); 1816 return PyNumber_Float(x); 1817 } 1818 1819 /* Wimpy, slow approach to tp_new calls for subtypes of float: 1820 first create a regular float from whatever arguments we got, 1821 then allocate a subtype instance and initialize its ob_fval 1822 from the regular float. The regular float is then thrown away. 1823 */ 1824 static PyObject * 1825 float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds) 1826 { 1827 PyObject *tmp, *newobj; 1828 1829 assert(PyType_IsSubtype(type, &PyFloat_Type)); 1830 tmp = float_new(&PyFloat_Type, args, kwds); 1831 if (tmp == NULL) 1832 return NULL; 1833 assert(PyFloat_CheckExact(tmp)); 1834 newobj = type->tp_alloc(type, 0); 1835 if (newobj == NULL) { 1836 Py_DECREF(tmp); 1837 return NULL; 1838 } 1839 ((PyFloatObject *)newobj)->ob_fval = ((PyFloatObject *)tmp)->ob_fval; 1840 Py_DECREF(tmp); 1841 return newobj; 1842 } 1843 1844 static PyObject * 1845 float_getnewargs(PyFloatObject *v) 1846 { 1847 return Py_BuildValue("(d)", v->ob_fval); 1848 } 1849 1850 /* this is for the benefit of the pack/unpack routines below */ 1851 1852 typedef enum { 1853 unknown_format, ieee_big_endian_format, ieee_little_endian_format 1854 } float_format_type; 1855 1856 static float_format_type double_format, float_format; 1857 static float_format_type detected_double_format, detected_float_format; 1858 1859 static PyObject * 1860 float_getformat(PyTypeObject *v, PyObject* arg) 1861 { 1862 char* s; 1863 float_format_type r; 1864 1865 if (!PyString_Check(arg)) { 1866 PyErr_Format(PyExc_TypeError, 1867 "__getformat__() argument must be string, not %.500s", 1868 Py_TYPE(arg)->tp_name); 1869 return NULL; 1870 } 1871 s = PyString_AS_STRING(arg); 1872 if (strcmp(s, "double") == 0) { 1873 r = double_format; 1874 } 1875 else if (strcmp(s, "float") == 0) { 1876 r = float_format; 1877 } 1878 else { 1879 PyErr_SetString(PyExc_ValueError, 1880 "__getformat__() argument 1 must be " 1881 "'double' or 'float'"); 1882 return NULL; 1883 } 1884 1885 switch (r) { 1886 case unknown_format: 1887 return PyString_FromString("unknown"); 1888 case ieee_little_endian_format: 1889 return PyString_FromString("IEEE, little-endian"); 1890 case ieee_big_endian_format: 1891 return PyString_FromString("IEEE, big-endian"); 1892 default: 1893 Py_FatalError("insane float_format or double_format"); 1894 return NULL; 1895 } 1896 } 1897 1898 PyDoc_STRVAR(float_getformat_doc, 1899 "float.__getformat__(typestr) -> string\n" 1900 "\n" 1901 "You probably don't want to use this function. It exists mainly to be\n" 1902 "used in Python's test suite.\n" 1903 "\n" 1904 "typestr must be 'double' or 'float'. This function returns whichever of\n" 1905 "'unknown', 'IEEE, big-endian' or 'IEEE, little-endian' best describes the\n" 1906 "format of floating point numbers used by the C type named by typestr."); 1907 1908 static PyObject * 1909 float_setformat(PyTypeObject *v, PyObject* args) 1910 { 1911 char* typestr; 1912 char* format; 1913 float_format_type f; 1914 float_format_type detected; 1915 float_format_type *p; 1916 1917 if (!PyArg_ParseTuple(args, "ss:__setformat__", &typestr, &format)) 1918 return NULL; 1919 1920 if (strcmp(typestr, "double") == 0) { 1921 p = &double_format; 1922 detected = detected_double_format; 1923 } 1924 else if (strcmp(typestr, "float") == 0) { 1925 p = &float_format; 1926 detected = detected_float_format; 1927 } 1928 else { 1929 PyErr_SetString(PyExc_ValueError, 1930 "__setformat__() argument 1 must " 1931 "be 'double' or 'float'"); 1932 return NULL; 1933 } 1934 1935 if (strcmp(format, "unknown") == 0) { 1936 f = unknown_format; 1937 } 1938 else if (strcmp(format, "IEEE, little-endian") == 0) { 1939 f = ieee_little_endian_format; 1940 } 1941 else if (strcmp(format, "IEEE, big-endian") == 0) { 1942 f = ieee_big_endian_format; 1943 } 1944 else { 1945 PyErr_SetString(PyExc_ValueError, 1946 "__setformat__() argument 2 must be " 1947 "'unknown', 'IEEE, little-endian' or " 1948 "'IEEE, big-endian'"); 1949 return NULL; 1950 1951 } 1952 1953 if (f != unknown_format && f != detected) { 1954 PyErr_Format(PyExc_ValueError, 1955 "can only set %s format to 'unknown' or the " 1956 "detected platform value", typestr); 1957 return NULL; 1958 } 1959 1960 *p = f; 1961 Py_RETURN_NONE; 1962 } 1963 1964 PyDoc_STRVAR(float_setformat_doc, 1965 "float.__setformat__(typestr, fmt) -> None\n" 1966 "\n" 1967 "You probably don't want to use this function. It exists mainly to be\n" 1968 "used in Python's test suite.\n" 1969 "\n" 1970 "typestr must be 'double' or 'float'. fmt must be one of 'unknown',\n" 1971 "'IEEE, big-endian' or 'IEEE, little-endian', and in addition can only be\n" 1972 "one of the latter two if it appears to match the underlying C reality.\n" 1973 "\n" 1974 "Override the automatic determination of C-level floating point type.\n" 1975 "This affects how floats are converted to and from binary strings."); 1976 1977 static PyObject * 1978 float_getzero(PyObject *v, void *closure) 1979 { 1980 return PyFloat_FromDouble(0.0); 1981 } 1982 1983 static PyObject * 1984 float__format__(PyObject *self, PyObject *args) 1985 { 1986 PyObject *format_spec; 1987 1988 if (!PyArg_ParseTuple(args, "O:__format__", &format_spec)) 1989 return NULL; 1990 if (PyBytes_Check(format_spec)) 1991 return _PyFloat_FormatAdvanced(self, 1992 PyBytes_AS_STRING(format_spec), 1993 PyBytes_GET_SIZE(format_spec)); 1994 if (PyUnicode_Check(format_spec)) { 1995 /* Convert format_spec to a str */ 1996 PyObject *result; 1997 PyObject *str_spec = PyObject_Str(format_spec); 1998 1999 if (str_spec == NULL) 2000 return NULL; 2001 2002 result = _PyFloat_FormatAdvanced(self, 2003 PyBytes_AS_STRING(str_spec), 2004 PyBytes_GET_SIZE(str_spec)); 2005 2006 Py_DECREF(str_spec); 2007 return result; 2008 } 2009 PyErr_SetString(PyExc_TypeError, "__format__ requires str or unicode"); 2010 return NULL; 2011 } 2012 2013 PyDoc_STRVAR(float__format__doc, 2014 "float.__format__(format_spec) -> string\n" 2015 "\n" 2016 "Formats the float according to format_spec."); 2017 2018 2019 static PyMethodDef float_methods[] = { 2020 {"conjugate", (PyCFunction)float_float, METH_NOARGS, 2021 "Return self, the complex conjugate of any float."}, 2022 {"__trunc__", (PyCFunction)float_trunc, METH_NOARGS, 2023 "Return the Integral closest to x between 0 and x."}, 2024 {"as_integer_ratio", (PyCFunction)float_as_integer_ratio, METH_NOARGS, 2025 float_as_integer_ratio_doc}, 2026 {"fromhex", (PyCFunction)float_fromhex, 2027 METH_O|METH_CLASS, float_fromhex_doc}, 2028 {"hex", (PyCFunction)float_hex, 2029 METH_NOARGS, float_hex_doc}, 2030 {"is_integer", (PyCFunction)float_is_integer, METH_NOARGS, 2031 "Return True if the float is an integer."}, 2032 #if 0 2033 {"is_inf", (PyCFunction)float_is_inf, METH_NOARGS, 2034 "Return True if the float is positive or negative infinite."}, 2035 {"is_finite", (PyCFunction)float_is_finite, METH_NOARGS, 2036 "Return True if the float is finite, neither infinite nor NaN."}, 2037 {"is_nan", (PyCFunction)float_is_nan, METH_NOARGS, 2038 "Return True if the float is not a number (NaN)."}, 2039 #endif 2040 {"__getnewargs__", (PyCFunction)float_getnewargs, METH_NOARGS}, 2041 {"__getformat__", (PyCFunction)float_getformat, 2042 METH_O|METH_CLASS, float_getformat_doc}, 2043 {"__setformat__", (PyCFunction)float_setformat, 2044 METH_VARARGS|METH_CLASS, float_setformat_doc}, 2045 {"__format__", (PyCFunction)float__format__, 2046 METH_VARARGS, float__format__doc}, 2047 {NULL, NULL} /* sentinel */ 2048 }; 2049 2050 static PyGetSetDef float_getset[] = { 2051 {"real", 2052 (getter)float_float, (setter)NULL, 2053 "the real part of a complex number", 2054 NULL}, 2055 {"imag", 2056 (getter)float_getzero, (setter)NULL, 2057 "the imaginary part of a complex number", 2058 NULL}, 2059 {NULL} /* Sentinel */ 2060 }; 2061 2062 PyDoc_STRVAR(float_doc, 2063 "float(x) -> floating point number\n\ 2064 \n\ 2065 Convert a string or number to a floating point number, if possible."); 2066 2067 2068 static PyNumberMethods float_as_number = { 2069 float_add, /*nb_add*/ 2070 float_sub, /*nb_subtract*/ 2071 float_mul, /*nb_multiply*/ 2072 float_classic_div, /*nb_divide*/ 2073 float_rem, /*nb_remainder*/ 2074 float_divmod, /*nb_divmod*/ 2075 float_pow, /*nb_power*/ 2076 (unaryfunc)float_neg, /*nb_negative*/ 2077 (unaryfunc)float_float, /*nb_positive*/ 2078 (unaryfunc)float_abs, /*nb_absolute*/ 2079 (inquiry)float_nonzero, /*nb_nonzero*/ 2080 0, /*nb_invert*/ 2081 0, /*nb_lshift*/ 2082 0, /*nb_rshift*/ 2083 0, /*nb_and*/ 2084 0, /*nb_xor*/ 2085 0, /*nb_or*/ 2086 float_coerce, /*nb_coerce*/ 2087 float_trunc, /*nb_int*/ 2088 float_long, /*nb_long*/ 2089 float_float, /*nb_float*/ 2090 0, /* nb_oct */ 2091 0, /* nb_hex */ 2092 0, /* nb_inplace_add */ 2093 0, /* nb_inplace_subtract */ 2094 0, /* nb_inplace_multiply */ 2095 0, /* nb_inplace_divide */ 2096 0, /* nb_inplace_remainder */ 2097 0, /* nb_inplace_power */ 2098 0, /* nb_inplace_lshift */ 2099 0, /* nb_inplace_rshift */ 2100 0, /* nb_inplace_and */ 2101 0, /* nb_inplace_xor */ 2102 0, /* nb_inplace_or */ 2103 float_floor_div, /* nb_floor_divide */ 2104 float_div, /* nb_true_divide */ 2105 0, /* nb_inplace_floor_divide */ 2106 0, /* nb_inplace_true_divide */ 2107 }; 2108 2109 PyTypeObject PyFloat_Type = { 2110 PyVarObject_HEAD_INIT(&PyType_Type, 0) 2111 "float", 2112 sizeof(PyFloatObject), 2113 0, 2114 (destructor)float_dealloc, /* tp_dealloc */ 2115 (printfunc)float_print, /* tp_print */ 2116 0, /* tp_getattr */ 2117 0, /* tp_setattr */ 2118 0, /* tp_compare */ 2119 (reprfunc)float_repr, /* tp_repr */ 2120 &float_as_number, /* tp_as_number */ 2121 0, /* tp_as_sequence */ 2122 0, /* tp_as_mapping */ 2123 (hashfunc)float_hash, /* tp_hash */ 2124 0, /* tp_call */ 2125 (reprfunc)float_str, /* tp_str */ 2126 PyObject_GenericGetAttr, /* tp_getattro */ 2127 0, /* tp_setattro */ 2128 0, /* tp_as_buffer */ 2129 Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES | 2130 Py_TPFLAGS_BASETYPE, /* tp_flags */ 2131 float_doc, /* tp_doc */ 2132 0, /* tp_traverse */ 2133 0, /* tp_clear */ 2134 float_richcompare, /* tp_richcompare */ 2135 0, /* tp_weaklistoffset */ 2136 0, /* tp_iter */ 2137 0, /* tp_iternext */ 2138 float_methods, /* tp_methods */ 2139 0, /* tp_members */ 2140 float_getset, /* tp_getset */ 2141 0, /* tp_base */ 2142 0, /* tp_dict */ 2143 0, /* tp_descr_get */ 2144 0, /* tp_descr_set */ 2145 0, /* tp_dictoffset */ 2146 0, /* tp_init */ 2147 0, /* tp_alloc */ 2148 float_new, /* tp_new */ 2149 }; 2150 2151 void 2152 _PyFloat_Init(void) 2153 { 2154 /* We attempt to determine if this machine is using IEEE 2155 floating point formats by peering at the bits of some 2156 carefully chosen values. If it looks like we are on an 2157 IEEE platform, the float packing/unpacking routines can 2158 just copy bits, if not they resort to arithmetic & shifts 2159 and masks. The shifts & masks approach works on all finite 2160 values, but what happens to infinities, NaNs and signed 2161 zeroes on packing is an accident, and attempting to unpack 2162 a NaN or an infinity will raise an exception. 2163 2164 Note that if we're on some whacked-out platform which uses 2165 IEEE formats but isn't strictly little-endian or big- 2166 endian, we will fall back to the portable shifts & masks 2167 method. */ 2168 2169 #if SIZEOF_DOUBLE == 8 2170 { 2171 double x = 9006104071832581.0; 2172 if (memcmp(&x, "\x43\x3f\xff\x01\x02\x03\x04\x05", 8) == 0) 2173 detected_double_format = ieee_big_endian_format; 2174 else if (memcmp(&x, "\x05\x04\x03\x02\x01\xff\x3f\x43", 8) == 0) 2175 detected_double_format = ieee_little_endian_format; 2176 else 2177 detected_double_format = unknown_format; 2178 } 2179 #else 2180 detected_double_format = unknown_format; 2181 #endif 2182 2183 #if SIZEOF_FLOAT == 4 2184 { 2185 float y = 16711938.0; 2186 if (memcmp(&y, "\x4b\x7f\x01\x02", 4) == 0) 2187 detected_float_format = ieee_big_endian_format; 2188 else if (memcmp(&y, "\x02\x01\x7f\x4b", 4) == 0) 2189 detected_float_format = ieee_little_endian_format; 2190 else 2191 detected_float_format = unknown_format; 2192 } 2193 #else 2194 detected_float_format = unknown_format; 2195 #endif 2196 2197 double_format = detected_double_format; 2198 float_format = detected_float_format; 2199 2200 /* Init float info */ 2201 if (FloatInfoType.tp_name == 0) 2202 PyStructSequence_InitType(&FloatInfoType, &floatinfo_desc); 2203 } 2204 2205 int 2206 PyFloat_ClearFreeList(void) 2207 { 2208 PyFloatObject *p; 2209 PyFloatBlock *list, *next; 2210 int i; 2211 int u; /* remaining unfreed ints per block */ 2212 int freelist_size = 0; 2213 2214 list = block_list; 2215 block_list = NULL; 2216 free_list = NULL; 2217 while (list != NULL) { 2218 u = 0; 2219 for (i = 0, p = &list->objects[0]; 2220 i < N_FLOATOBJECTS; 2221 i++, p++) { 2222 if (PyFloat_CheckExact(p) && Py_REFCNT(p) != 0) 2223 u++; 2224 } 2225 next = list->next; 2226 if (u) { 2227 list->next = block_list; 2228 block_list = list; 2229 for (i = 0, p = &list->objects[0]; 2230 i < N_FLOATOBJECTS; 2231 i++, p++) { 2232 if (!PyFloat_CheckExact(p) || 2233 Py_REFCNT(p) == 0) { 2234 Py_TYPE(p) = (struct _typeobject *) 2235 free_list; 2236 free_list = p; 2237 } 2238 } 2239 } 2240 else { 2241 PyMem_FREE(list); 2242 } 2243 freelist_size += u; 2244 list = next; 2245 } 2246 return freelist_size; 2247 } 2248 2249 void 2250 PyFloat_Fini(void) 2251 { 2252 PyFloatObject *p; 2253 PyFloatBlock *list; 2254 int i; 2255 int u; /* total unfreed floats per block */ 2256 2257 u = PyFloat_ClearFreeList(); 2258 2259 if (!Py_VerboseFlag) 2260 return; 2261 fprintf(stderr, "# cleanup floats"); 2262 if (!u) { 2263 fprintf(stderr, "\n"); 2264 } 2265 else { 2266 fprintf(stderr, 2267 ": %d unfreed float%s\n", 2268 u, u == 1 ? "" : "s"); 2269 } 2270 if (Py_VerboseFlag > 1) { 2271 list = block_list; 2272 while (list != NULL) { 2273 for (i = 0, p = &list->objects[0]; 2274 i < N_FLOATOBJECTS; 2275 i++, p++) { 2276 if (PyFloat_CheckExact(p) && 2277 Py_REFCNT(p) != 0) { 2278 char *buf = PyOS_double_to_string( 2279 PyFloat_AS_DOUBLE(p), 'r', 2280 0, 0, NULL); 2281 if (buf) { 2282 /* XXX(twouters) cast 2283 refcount to long 2284 until %zd is 2285 universally 2286 available 2287 */ 2288 fprintf(stderr, 2289 "# <float at %p, refcnt=%ld, val=%s>\n", 2290 p, (long)Py_REFCNT(p), buf); 2291 PyMem_Free(buf); 2292 } 2293 } 2294 } 2295 list = list->next; 2296 } 2297 } 2298 } 2299 2300 /*---------------------------------------------------------------------------- 2301 * _PyFloat_{Pack,Unpack}{4,8}. See floatobject.h. 2302 */ 2303 int 2304 _PyFloat_Pack4(double x, unsigned char *p, int le) 2305 { 2306 if (float_format == unknown_format) { 2307 unsigned char sign; 2308 int e; 2309 double f; 2310 unsigned int fbits; 2311 int incr = 1; 2312 2313 if (le) { 2314 p += 3; 2315 incr = -1; 2316 } 2317 2318 if (x < 0) { 2319 sign = 1; 2320 x = -x; 2321 } 2322 else 2323 sign = 0; 2324 2325 f = frexp(x, &e); 2326 2327 /* Normalize f to be in the range [1.0, 2.0) */ 2328 if (0.5 <= f && f < 1.0) { 2329 f *= 2.0; 2330 e--; 2331 } 2332 else if (f == 0.0) 2333 e = 0; 2334 else { 2335 PyErr_SetString(PyExc_SystemError, 2336 "frexp() result out of range"); 2337 return -1; 2338 } 2339 2340 if (e >= 128) 2341 goto Overflow; 2342 else if (e < -126) { 2343 /* Gradual underflow */ 2344 f = ldexp(f, 126 + e); 2345 e = 0; 2346 } 2347 else if (!(e == 0 && f == 0.0)) { 2348 e += 127; 2349 f -= 1.0; /* Get rid of leading 1 */ 2350 } 2351 2352 f *= 8388608.0; /* 2**23 */ 2353 fbits = (unsigned int)(f + 0.5); /* Round */ 2354 assert(fbits <= 8388608); 2355 if (fbits >> 23) { 2356 /* The carry propagated out of a string of 23 1 bits. */ 2357 fbits = 0; 2358 ++e; 2359 if (e >= 255) 2360 goto Overflow; 2361 } 2362 2363 /* First byte */ 2364 *p = (sign << 7) | (e >> 1); 2365 p += incr; 2366 2367 /* Second byte */ 2368 *p = (char) (((e & 1) << 7) | (fbits >> 16)); 2369 p += incr; 2370 2371 /* Third byte */ 2372 *p = (fbits >> 8) & 0xFF; 2373 p += incr; 2374 2375 /* Fourth byte */ 2376 *p = fbits & 0xFF; 2377 2378 /* Done */ 2379 return 0; 2380 2381 } 2382 else { 2383 float y = (float)x; 2384 const char *s = (char*)&y; 2385 int i, incr = 1; 2386 2387 if (Py_IS_INFINITY(y) && !Py_IS_INFINITY(x)) 2388 goto Overflow; 2389 2390 if ((float_format == ieee_little_endian_format && !le) 2391 || (float_format == ieee_big_endian_format && le)) { 2392 p += 3; 2393 incr = -1; 2394 } 2395 2396 for (i = 0; i < 4; i++) { 2397 *p = *s++; 2398 p += incr; 2399 } 2400 return 0; 2401 } 2402 Overflow: 2403 PyErr_SetString(PyExc_OverflowError, 2404 "float too large to pack with f format"); 2405 return -1; 2406 } 2407 2408 int 2409 _PyFloat_Pack8(double x, unsigned char *p, int le) 2410 { 2411 if (double_format == unknown_format) { 2412 unsigned char sign; 2413 int e; 2414 double f; 2415 unsigned int fhi, flo; 2416 int incr = 1; 2417 2418 if (le) { 2419 p += 7; 2420 incr = -1; 2421 } 2422 2423 if (x < 0) { 2424 sign = 1; 2425 x = -x; 2426 } 2427 else 2428 sign = 0; 2429 2430 f = frexp(x, &e); 2431 2432 /* Normalize f to be in the range [1.0, 2.0) */ 2433 if (0.5 <= f && f < 1.0) { 2434 f *= 2.0; 2435 e--; 2436 } 2437 else if (f == 0.0) 2438 e = 0; 2439 else { 2440 PyErr_SetString(PyExc_SystemError, 2441 "frexp() result out of range"); 2442 return -1; 2443 } 2444 2445 if (e >= 1024) 2446 goto Overflow; 2447 else if (e < -1022) { 2448 /* Gradual underflow */ 2449 f = ldexp(f, 1022 + e); 2450 e = 0; 2451 } 2452 else if (!(e == 0 && f == 0.0)) { 2453 e += 1023; 2454 f -= 1.0; /* Get rid of leading 1 */ 2455 } 2456 2457 /* fhi receives the high 28 bits; flo the low 24 bits (== 52 bits) */ 2458 f *= 268435456.0; /* 2**28 */ 2459 fhi = (unsigned int)f; /* Truncate */ 2460 assert(fhi < 268435456); 2461 2462 f -= (double)fhi; 2463 f *= 16777216.0; /* 2**24 */ 2464 flo = (unsigned int)(f + 0.5); /* Round */ 2465 assert(flo <= 16777216); 2466 if (flo >> 24) { 2467 /* The carry propagated out of a string of 24 1 bits. */ 2468 flo = 0; 2469 ++fhi; 2470 if (fhi >> 28) { 2471 /* And it also progagated out of the next 28 bits. */ 2472 fhi = 0; 2473 ++e; 2474 if (e >= 2047) 2475 goto Overflow; 2476 } 2477 } 2478 2479 /* First byte */ 2480 *p = (sign << 7) | (e >> 4); 2481 p += incr; 2482 2483 /* Second byte */ 2484 *p = (unsigned char) (((e & 0xF) << 4) | (fhi >> 24)); 2485 p += incr; 2486 2487 /* Third byte */ 2488 *p = (fhi >> 16) & 0xFF; 2489 p += incr; 2490 2491 /* Fourth byte */ 2492 *p = (fhi >> 8) & 0xFF; 2493 p += incr; 2494 2495 /* Fifth byte */ 2496 *p = fhi & 0xFF; 2497 p += incr; 2498 2499 /* Sixth byte */ 2500 *p = (flo >> 16) & 0xFF; 2501 p += incr; 2502 2503 /* Seventh byte */ 2504 *p = (flo >> 8) & 0xFF; 2505 p += incr; 2506 2507 /* Eighth byte */ 2508 *p = flo & 0xFF; 2509 /* p += incr; Unneeded (for now) */ 2510 2511 /* Done */ 2512 return 0; 2513 2514 Overflow: 2515 PyErr_SetString(PyExc_OverflowError, 2516 "float too large to pack with d format"); 2517 return -1; 2518 } 2519 else { 2520 const char *s = (char*)&x; 2521 int i, incr = 1; 2522 2523 if ((double_format == ieee_little_endian_format && !le) 2524 || (double_format == ieee_big_endian_format && le)) { 2525 p += 7; 2526 incr = -1; 2527 } 2528 2529 for (i = 0; i < 8; i++) { 2530 *p = *s++; 2531 p += incr; 2532 } 2533 return 0; 2534 } 2535 } 2536 2537 double 2538 _PyFloat_Unpack4(const unsigned char *p, int le) 2539 { 2540 if (float_format == unknown_format) { 2541 unsigned char sign; 2542 int e; 2543 unsigned int f; 2544 double x; 2545 int incr = 1; 2546 2547 if (le) { 2548 p += 3; 2549 incr = -1; 2550 } 2551 2552 /* First byte */ 2553 sign = (*p >> 7) & 1; 2554 e = (*p & 0x7F) << 1; 2555 p += incr; 2556 2557 /* Second byte */ 2558 e |= (*p >> 7) & 1; 2559 f = (*p & 0x7F) << 16; 2560 p += incr; 2561 2562 if (e == 255) { 2563 PyErr_SetString( 2564 PyExc_ValueError, 2565 "can't unpack IEEE 754 special value " 2566 "on non-IEEE platform"); 2567 return -1; 2568 } 2569 2570 /* Third byte */ 2571 f |= *p << 8; 2572 p += incr; 2573 2574 /* Fourth byte */ 2575 f |= *p; 2576 2577 x = (double)f / 8388608.0; 2578 2579 /* XXX This sadly ignores Inf/NaN issues */ 2580 if (e == 0) 2581 e = -126; 2582 else { 2583 x += 1.0; 2584 e -= 127; 2585 } 2586 x = ldexp(x, e); 2587 2588 if (sign) 2589 x = -x; 2590 2591 return x; 2592 } 2593 else { 2594 float x; 2595 2596 if ((float_format == ieee_little_endian_format && !le) 2597 || (float_format == ieee_big_endian_format && le)) { 2598 char buf[4]; 2599 char *d = &buf[3]; 2600 int i; 2601 2602 for (i = 0; i < 4; i++) { 2603 *d-- = *p++; 2604 } 2605 memcpy(&x, buf, 4); 2606 } 2607 else { 2608 memcpy(&x, p, 4); 2609 } 2610 2611 return x; 2612 } 2613 } 2614 2615 double 2616 _PyFloat_Unpack8(const unsigned char *p, int le) 2617 { 2618 if (double_format == unknown_format) { 2619 unsigned char sign; 2620 int e; 2621 unsigned int fhi, flo; 2622 double x; 2623 int incr = 1; 2624 2625 if (le) { 2626 p += 7; 2627 incr = -1; 2628 } 2629 2630 /* First byte */ 2631 sign = (*p >> 7) & 1; 2632 e = (*p & 0x7F) << 4; 2633 2634 p += incr; 2635 2636 /* Second byte */ 2637 e |= (*p >> 4) & 0xF; 2638 fhi = (*p & 0xF) << 24; 2639 p += incr; 2640 2641 if (e == 2047) { 2642 PyErr_SetString( 2643 PyExc_ValueError, 2644 "can't unpack IEEE 754 special value " 2645 "on non-IEEE platform"); 2646 return -1.0; 2647 } 2648 2649 /* Third byte */ 2650 fhi |= *p << 16; 2651 p += incr; 2652 2653 /* Fourth byte */ 2654 fhi |= *p << 8; 2655 p += incr; 2656 2657 /* Fifth byte */ 2658 fhi |= *p; 2659 p += incr; 2660 2661 /* Sixth byte */ 2662 flo = *p << 16; 2663 p += incr; 2664 2665 /* Seventh byte */ 2666 flo |= *p << 8; 2667 p += incr; 2668 2669 /* Eighth byte */ 2670 flo |= *p; 2671 2672 x = (double)fhi + (double)flo / 16777216.0; /* 2**24 */ 2673 x /= 268435456.0; /* 2**28 */ 2674 2675 if (e == 0) 2676 e = -1022; 2677 else { 2678 x += 1.0; 2679 e -= 1023; 2680 } 2681 x = ldexp(x, e); 2682 2683 if (sign) 2684 x = -x; 2685 2686 return x; 2687 } 2688 else { 2689 double x; 2690 2691 if ((double_format == ieee_little_endian_format && !le) 2692 || (double_format == ieee_big_endian_format && le)) { 2693 char buf[8]; 2694 char *d = &buf[7]; 2695 int i; 2696 2697 for (i = 0; i < 8; i++) { 2698 *d-- = *p++; 2699 } 2700 memcpy(&x, buf, 8); 2701 } 2702 else { 2703 memcpy(&x, p, 8); 2704 } 2705 2706 return x; 2707 } 2708 } 2709
