GeezerVisonThe World Wide Web, restored to 800 pixels of glory. |
| Home|About|Gaming cabinet|Archives|How it works|Starter sites |
GeezerVison is showing github.com — cpython/Objects/complexobject.c at main · python/cpython Expand file tree/ Copy pathcomplexobject.cMore file actions 1460 lines (1313 loc) · 43.3 KB / Copy pathcomplexobject.cFile metadata and controls1460 lines (1313 loc) · 43.3 KB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 /* Complex object implementation */ /* Borrows heavily from floatobject.c */ /* Submitted by Jim Hugunin */ #include "Python.h" #include "pycore_call.h" // _PyObject_CallNoArgs() #include "pycore_complexobject.h" // _PyComplex_FormatAdvancedWriter() #include "pycore_floatobject.h" // _Py_convert_int_to_double() #include "pycore_freelist.h" // _Py_FREELIST_FREE(), _Py_FREELIST_POP() #include "pycore_long.h" // _PyLong_GetZero() #include "pycore_object.h" // _PyObject_Init() #include "pycore_pymath.h" // _Py_ADJUST_ERANGE2() #define _PyComplexObject_CAST(op) ((PyComplexObject *)(op)) /*[clinic input] class complex "PyComplexObject *" "&PyComplex_Type" [clinic start generated code]*/ /*[clinic end generated code: output=da39a3ee5e6b4b0d input=819e057d2d10f5ec]*/ #include "clinic/complexobject.c.h" /* elementary operations on complex numbers */ Py_complex _Py_c_sum(Py_complex a, Py_complex b) { Py_complex r; r.real = a.real + b.real; r.imag = a.imag + b.imag; return r; } Py_complex _Py_cr_sum(Py_complex a, double b) { Py_complex r = a; r.real += b; return r; } static inline Py_complex _Py_rc_sum(double a, Py_complex b) { return _Py_cr_sum(b, a); } Py_complex _Py_c_diff(Py_complex a, Py_complex b) { Py_complex r; r.real = a.real - b.real; r.imag = a.imag - b.imag; return r; } Py_complex _Py_cr_diff(Py_complex a, double b) { Py_complex r = a; r.real -= b; return r; } Py_complex _Py_rc_diff(double a, Py_complex b) { Py_complex r; r.real = a - b.real; r.imag = -b.imag; return r; } Py_complex _Py_c_neg(Py_complex a) { Py_complex r; r.real = -a.real; r.imag = -a.imag; return r; } Py_complex _Py_c_prod(Py_complex z, Py_complex w) { double a = z.real, b = z.imag, c = w.real, d = w.imag; double ac = a*c, bd = b*d, ad = a*d, bc = b*c; Py_complex r = {ac - bd, ad + bc}; /* Recover infinities that computed as nan+nanj. See e.g. the C11, Annex G.5.1, routine _Cmultd(). */ if (isnan(r.real) && isnan(r.imag)) { int recalc = 0; if (isinf(a) || isinf(b)) { /* z is infinite */ /* "Box" the infinity and change nans in the other factor to 0 */ a = copysign(isinf(a) ? 1.0 : 0.0, a); b = copysign(isinf(b) ? 1.0 : 0.0, b); if (isnan(c)) { c = copysign(0.0, c); } if (isnan(d)) { d = copysign(0.0, d); } recalc = 1; } if (isinf(c) || isinf(d)) { /* w is infinite */ /* "Box" the infinity and change nans in the other factor to 0 */ c = copysign(isinf(c) ? 1.0 : 0.0, c); d = copysign(isinf(d) ? 1.0 : 0.0, d); if (isnan(a)) { a = copysign(0.0, a); } if (isnan(b)) { b = copysign(0.0, b); } recalc = 1; } if (!recalc && (isinf(ac) || isinf(bd) || isinf(ad) || isinf(bc))) { /* Recover infinities from overflow by changing nans to 0 */ if (isnan(a)) { a = copysign(0.0, a); } if (isnan(b)) { b = copysign(0.0, b); } if (isnan(c)) { c = copysign(0.0, c); } if (isnan(d)) { d = copysign(0.0, d); } recalc = 1; } if (recalc) { r.real = INFINITY*(a*c - b*d); r.imag = INFINITY*(a*d + b*c); } } return r; } Py_complex _Py_cr_prod(Py_complex a, double b) { Py_complex r = a; r.real *= b; r.imag *= b; return r; } static inline Py_complex _Py_rc_prod(double a, Py_complex b) { return _Py_cr_prod(b, a); } /* Avoid bad optimization on Windows ARM64 until the compiler is fixed */ #ifdef _M_ARM64 #pragma optimize("", off) #endif Py_complex _Py_c_quot(Py_complex a, Py_complex b) { /****************************************************************** This was the original algorithm. It's grossly prone to spurious overflow and underflow errors. It also merrily divides by 0 despite checking for that(!). The code still serves a doc purpose here, as the algorithm following is a simple by-cases transformation of this one: Py_complex r; double d = b.real*b.real + b.imag*b.imag; if (d == 0.) errno = EDOM; r.real = (a.real*b.real + a.imag*b.imag)/d; r.imag = (a.imag*b.real - a.real*b.imag)/d; return r; ******************************************************************/ /* This algorithm is better, and is pretty obvious: first divide the * numerators and denominator by whichever of {b.real, b.imag} has * larger magnitude. The earliest reference I found was to CACM * Algorithm 116 (Complex Division, Robert L. Smith, Stanford * University). */ Py_complex r; /* the result */ const double abs_breal = b.real < 0 ? -b.real : b.real; const double abs_bimag = b.imag < 0 ? -b.imag : b.imag; if (abs_breal >= abs_bimag) { /* divide tops and bottom by b.real */ if (abs_breal == 0.0) { errno = EDOM; r.real = r.imag = 0.0; } else { const double ratio = b.imag / b.real; const double denom = b.real + b.imag * ratio; r.real = (a.real + a.imag * ratio) / denom; r.imag = (a.imag - a.real * ratio) / denom; } } else if (abs_bimag >= abs_breal) { /* divide tops and bottom by b.imag */ const double ratio = b.real / b.imag; const double denom = b.real * ratio + b.imag; assert(b.imag != 0.0); r.real = (a.real * ratio + a.imag) / denom; r.imag = (a.imag * ratio - a.real) / denom; } else { /* At least one of b.real or b.imag is a NaN */ r.real = r.imag = Py_NAN; } /* Recover infinities and zeros that computed as nan+nanj. See e.g. the C11, Annex G.5.2, routine _Cdivd(). */ if (isnan(r.real) && isnan(r.imag)) { if ((isinf(a.real) || isinf(a.imag)) && isfinite(b.real) && isfinite(b.imag)) { const double x = copysign(isinf(a.real) ? 1.0 : 0.0, a.real); const double y = copysign(isinf(a.imag) ? 1.0 : 0.0, a.imag); r.real = INFINITY * (x*b.real + y*b.imag); r.imag = INFINITY * (y*b.real - x*b.imag); } else if ((isinf(abs_breal) || isinf(abs_bimag)) && isfinite(a.real) && isfinite(a.imag)) { const double x = copysign(isinf(b.real) ? 1.0 : 0.0, b.real); const double y = copysign(isinf(b.imag) ? 1.0 : 0.0, b.imag); r.real = 0.0 * (a.real*x + a.imag*y); r.imag = 0.0 * (a.imag*x - a.real*y); } } return r; } Py_complex _Py_cr_quot(Py_complex a, double b) { Py_complex r = a; if (b) { r.real /= b; r.imag /= b; } else { errno = EDOM; r.real = r.imag = 0.0; } return r; } /* an equivalent of _Py_c_quot() function, when 1st argument is real */ Py_complex _Py_rc_quot(double a, Py_complex b) { Py_complex r; const double abs_breal = b.real < 0 ? -b.real : b.real; const double abs_bimag = b.imag < 0 ? -b.imag : b.imag; if (abs_breal >= abs_bimag) { if (abs_breal == 0.0) { errno = EDOM; r.real = r.imag = 0.0; } else { const double ratio = b.imag / b.real; const double denom = b.real + b.imag * ratio; r.real = a / denom; r.imag = (-a * ratio) / denom; } } else if (abs_bimag >= abs_breal) { const double ratio = b.real / b.imag; const double denom = b.real * ratio + b.imag; assert(b.imag != 0.0); r.real = (a * ratio) / denom; r.imag = (-a) / denom; } else { r.real = r.imag = Py_NAN; } if (isnan(r.real) && isnan(r.imag) && isfinite(a) && (isinf(abs_breal) || isinf(abs_bimag))) { const double x = copysign(isinf(b.real) ? 1.0 : 0.0, b.real); const double y = copysign(isinf(b.imag) ? 1.0 : 0.0, b.imag); r.real = 0.0 * (a*x); r.imag = 0.0 * (-a*y); } return r; } #ifdef _M_ARM64 #pragma optimize("", on) #endif Py_complex _Py_c_pow(Py_complex a, Py_complex b) { Py_complex r; double vabs,len,at,phase; if (b.real == 0. && b.imag == 0.) { r.real = 1.; r.imag = 0.; } else if (a.real == 0. && a.imag == 0.) { if (b.imag != 0. || b.real < 0.) errno = EDOM; r.real = 0.; r.imag = 0.; } else { vabs = hypot(a.real,a.imag); len = pow(vabs,b.real); at = atan2(a.imag, a.real); phase = at*b.real; if (b.imag != 0.0) { len *= exp(-at*b.imag); phase += b.imag*log(vabs); } r.real = len*cos(phase); r.imag = len*sin(phase); /* Don't rely on errno set by the math functions above, for example cos() and sin() set EDOM for an infinite phase. */ errno = 0; if (isfinite(a.real) && isfinite(a.imag) && isfinite(b.real) && isfinite(b.imag)) { _Py_ADJUST_ERANGE2(r.real, r.imag); } } return r; } #define INT_EXP_CUTOFF 100 static Py_complex c_powu(Py_complex x, long n) { assert(0 < n && n <= INT_EXP_CUTOFF); while ((n & 1) == 0) { x = _Py_c_prod(x, x); n >>= 1; } Py_complex r = x; n >>= 1; while (n) { x = _Py_c_prod(x, x); if (n & 1) { r = _Py_c_prod(r, x); } n >>= 1; } return r; } static Py_complex c_powi(Py_complex x, long n) { if (n > 0) return c_powu(x, n); else if (n < 0) return _Py_rc_quot(1.0, c_powu(x, -n)); else return (Py_complex){1., 0.}; } double _Py_c_abs(Py_complex z) { /* sets errno = ERANGE on overflow */ double result; int saved_errno = errno; if (!isfinite(z.real) || !isfinite(z.imag)) { /* C99 rules: if either the real or the imaginary part is an infinity, return infinity, even if the other part is a NaN. */ if (isinf(z.real)) { result = fabs(z.real); errno = saved_errno; return result; } if (isinf(z.imag)) { result = fabs(z.imag); errno = saved_errno; return result; } /* either the real or imaginary part is a NaN, and neither is infinite. Result should be NaN. */ errno = saved_errno; return Py_NAN; } result = hypot(z.real, z.imag); if (!isfinite(result)) errno = ERANGE; else errno = saved_errno; return result; } static PyObject * complex_subtype_from_c_complex(PyTypeObject *type, Py_complex cval) { PyObject *op; op = type->tp_alloc(type, 0); if (op != NULL) ((PyComplexObject *)op)->cval = cval; return op; } PyObject * PyComplex_FromCComplex(Py_complex cval) { PyComplexObject *op = _Py_FREELIST_POP(PyComplexObject, complexes); if (op == NULL) { /* Inline PyObject_New */ op = PyObject_Malloc(sizeof(PyComplexObject)); if (op == NULL) { return PyErr_NoMemory(); } _PyObject_Init((PyObject*)op, &PyComplex_Type); } op->cval = cval; return (PyObject *) op; } static void complex_dealloc(PyObject *op) { assert(PyComplex_Check(op)); if (PyComplex_CheckExact(op)) { _Py_FREELIST_FREE(complexes, op, PyObject_Free); } else { Py_TYPE(op)->tp_free(op); } } static PyObject * complex_subtype_from_doubles(PyTypeObject *type, double real, double imag) { Py_complex c; c.real = real; c.imag = imag; return complex_subtype_from_c_complex(type, c); } PyObject * PyComplex_FromDoubles(double real, double imag) { Py_complex c; c.real = real; c.imag = imag; return PyComplex_FromCComplex(c); } static PyObject * try_complex_special_method(PyObject *); double PyComplex_RealAsDouble(PyObject *op) { double real = -1.0; if (PyComplex_Check(op)) { real = ((PyComplexObject *)op)->cval.real; } else { PyObject* newop = try_complex_special_method(op); if (newop) { real = ((PyComplexObject *)newop)->cval.real; Py_DECREF(newop); } else if (!PyErr_Occurred()) { real = PyFloat_AsDouble(op); } } return real; } double PyComplex_ImagAsDouble(PyObject *op) { double imag = -1.0; if (PyComplex_Check(op)) { imag = ((PyComplexObject *)op)->cval.imag; } else { PyObject* newop = try_complex_special_method(op); if (newop) { imag = ((PyComplexObject *)newop)->cval.imag; Py_DECREF(newop); } else if (!PyErr_Occurred()) { PyFloat_AsDouble(op); if (!PyErr_Occurred()) { imag = 0.0; } } } return imag; } static PyObject * try_complex_special_method(PyObject *op) { PyObject *f; f = _PyObject_LookupSpecial(op, &_Py_ID(__complex__)); if (f) { PyObject *res = _PyObject_CallNoArgs(f); Py_DECREF(f); if (!res || PyComplex_CheckExact(res)) { return res; } if (!PyComplex_Check(res)) { PyErr_Format(PyExc_TypeError, "%T.__complex__() must return a complex, not %T", op, res); Py_DECREF(res); return NULL; } /* Issue #29894: warn if 'res' not of exact type complex. */ if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1, "%T.__complex__() must return a complex, not %T. " "The ability to return an instance of a strict subclass of complex " "is deprecated, and may be removed in a future version of Python.", op, res)) { Py_DECREF(res); return NULL; } return res; } return NULL; } Py_complex PyComplex_AsCComplex(PyObject *op) { Py_complex cv; PyObject *newop = NULL; assert(op); /* If op is already of type PyComplex_Type, return its value */ if (PyComplex_Check(op)) { return ((PyComplexObject *)op)->cval; } /* If not, use op's __complex__ method, if it exists */ /* return -1 on failure */ cv.real = -1.; cv.imag = 0.; newop = try_complex_special_method(op); if (newop) { cv = ((PyComplexObject *)newop)->cval; Py_DECREF(newop); return cv; } else if (PyErr_Occurred()) { return cv; } /* If neither of the above works, interpret op as a float giving the real part of the result, and fill in the imaginary part as 0. */ else { /* PyFloat_AsDouble will return -1 on failure */ cv.real = PyFloat_AsDouble(op); return cv; } } static PyObject * complex_repr(PyObject *op) { int precision = 0; char format_code = 'r'; PyObject *result = NULL; PyComplexObject *v = _PyComplexObject_CAST(op); /* If these are non-NULL, they'll need to be freed. */ char *pre = NULL; char *im = NULL; /* These do not need to be freed. re is either an alias for pre or a pointer to a constant. lead and tail are pointers to constants. */ const char *re = NULL; const char *lead = ""; const char *tail = ""; if (v->cval.real == 0. && copysign(1.0, v->cval.real)==1.0) { /* Real part is +0: just output the imaginary part and do not include parens. */ re = ""; im = PyOS_double_to_string(v->cval.imag, format_code, precision, 0, NULL); if (!im) { PyErr_NoMemory(); goto done; } } else { /* Format imaginary part with sign, real part without. Include parens in the result. */ pre = PyOS_double_to_string(v->cval.real, format_code, precision, 0, NULL); if (!pre) { PyErr_NoMemory(); goto done; } re = pre; im = PyOS_double_to_string(v->cval.imag, format_code, precision, Py_DTSF_SIGN, NULL); if (!im) { PyErr_NoMemory(); goto done; } lead = "("; tail = ")"; } result = PyUnicode_FromFormat("%s%s%sj%s", lead, re, im, tail); done: PyMem_Free(im); PyMem_Free(pre); return result; } static Py_hash_t complex_hash(PyObject *op) { Py_uhash_t hashreal, hashimag, combined; PyComplexObject *v = _PyComplexObject_CAST(op); hashreal = (Py_uhash_t)_Py_HashDouble(op, v->cval.real); if (hashreal == (Py_uhash_t)-1) return -1; hashimag = (Py_uhash_t)_Py_HashDouble(op, v->cval.imag); if (hashimag == (Py_uhash_t)-1) return -1; /* Note: if the imaginary part is 0, hashimag is 0 now, * so the following returns hashreal unchanged. This is * important because numbers of different types that * compare equal must have the same hash value, so that * hash(x + 0*j) must equal hash(x). */ combined = hashreal + PyHASH_IMAG * hashimag; if (combined == (Py_uhash_t)-1) combined = (Py_uhash_t)-2; return (Py_hash_t)combined; } /* This macro may return! */ #define TO_COMPLEX(obj, c) \ if (PyComplex_Check(obj)) \ c = ((PyComplexObject *)(obj))->cval; \ else if (real_to_complex(&(obj), &(c)) < 0) \ return (obj) static int real_to_double(PyObject **pobj, double *dbl) { PyObject *obj = *pobj; if (PyFloat_Check(obj)) { *dbl = PyFloat_AS_DOUBLE(obj); } else if (_Py_convert_int_to_double(pobj, dbl) < 0) { return -1; } return 0; } static int real_to_complex(PyObject **pobj, Py_complex *pc) { pc->imag = 0.0; return real_to_double(pobj, &(pc->real)); } /* Complex arithmetic rules implement special mixed-mode case where combining a pure-real (float or int) value and a complex value is performed directly without first coercing the real value to a complex value. Let us consider the addition as an example, assuming that ints are implicitly converted to floats. We have the following rules (up to variants with changed order of operands): complex(a, b) + complex(c, d) = complex(a + c, b + d) float(a) + complex(b, c) = complex(a + b, c) Similar rules are implemented for subtraction, multiplication and division. See C11's Annex G, sections G.5.1 and G.5.2. */ #define COMPLEX_BINOP(NAME, FUNC) \ static PyObject * \ complex_##NAME(PyObject *v, PyObject *w) \ { \ Py_complex a; \ errno = 0; \ if (PyComplex_Check(w)) { \ Py_complex b = ((PyComplexObject *)w)->cval; \ if (PyComplex_Check(v)) { \ a = ((PyComplexObject *)v)->cval; \ a = _Py_c_##FUNC(a, b); \ } \ else if (real_to_double(&v, &a.real) < 0) { \ return v; \ } \ else { \ a = _Py_rc_##FUNC(a.real, b); \ } \ } \ else if (!PyComplex_Check(v)) { \ Py_RETURN_NOTIMPLEMENTED; \ } \ else { \ a = ((PyComplexObject *)v)->cval; \ double b; \ if (real_to_double(&w, &b) < 0) { \ return w; \ } \ a = _Py_cr_##FUNC(a, b); \ } \ if (errno == EDOM) { \ PyErr_SetString(PyExc_ZeroDivisionError, \ "division by zero"); \ return NULL; \ } \ return PyComplex_FromCComplex(a); \ } COMPLEX_BINOP(add, sum) COMPLEX_BINOP(mul, prod) COMPLEX_BINOP(sub, diff) COMPLEX_BINOP(div, quot) static PyObject * complex_pow(PyObject *v, PyObject *w, PyObject *z) { Py_complex p; Py_complex a, b; TO_COMPLEX(v, a); TO_COMPLEX(w, b); if (z != Py_None) { PyErr_SetString(PyExc_ValueError, "complex modulo"); return NULL; } errno = 0; // Check whether the exponent has a small integer value, and if so use // a faster and more accurate algorithm. if (b.imag == 0.0 && b.real == floor(b.real) && fabs(b.real) <= INT_EXP_CUTOFF) { p = c_powi(a, (long)b.real); if (isfinite(a.real) && isfinite(a.imag)) { _Py_ADJUST_ERANGE2(p.real, p.imag); } } else { p = _Py_c_pow(a, b); } if (errno == EDOM) { PyErr_SetString(PyExc_ZeroDivisionError, "zero to a negative or complex power"); return NULL; } else if (errno == ERANGE) { PyErr_SetString(PyExc_OverflowError, "complex exponentiation"); return NULL; } return PyComplex_FromCComplex(p); } static PyObject * complex_neg(PyObject *op) { PyComplexObject *v = _PyComplexObject_CAST(op); Py_complex neg; neg.real = -v->cval.real; neg.imag = -v->cval.imag; return PyComplex_FromCComplex(neg); } static PyObject * complex_pos(PyObject *op) { PyComplexObject *v = _PyComplexObject_CAST(op); if (PyComplex_CheckExact(v)) { return Py_NewRef(v); } return PyComplex_FromCComplex(v->cval); } static PyObject * complex_abs(PyObject *op) { PyComplexObject *v = _PyComplexObject_CAST(op); double result; errno = 0; result = _Py_c_abs(v->cval); if (errno == ERANGE) { PyErr_SetString(PyExc_OverflowError, "absolute value too large"); return NULL; } return PyFloat_FromDouble(result); } static int complex_bool(PyObject *op) { PyComplexObject *v = _PyComplexObject_CAST(op); return v->cval.real != 0.0 || v->cval.imag != 0.0; } static PyObject * complex_richcompare(PyObject *v, PyObject *w, int op) { PyObject *res; Py_complex i; int equal; if (op != Py_EQ && op != Py_NE) { goto Unimplemented; } assert(PyComplex_Check(v)); TO_COMPLEX(v, i); if (PyLong_Check(w)) { /* Check for 0.0 imaginary part first to avoid the rich * comparison when possible. */ if (i.imag == 0.0) { PyObject *j, *sub_res; j = PyFloat_FromDouble(i.real); if (j == NULL) return NULL; sub_res = PyObject_RichCompare(j, w, op); Py_DECREF(j); return sub_res; } else { equal = 0; } } else if (PyFloat_Check(w)) { equal = (i.real == PyFloat_AsDouble(w) && i.imag == 0.0); } else if (PyComplex_Check(w)) { Py_complex j; TO_COMPLEX(w, j); equal = (i.real == j.real && i.imag == j.imag); } else { goto Unimplemented; } if (equal == (op == Py_EQ)) res = Py_True; else res = Py_False; return Py_NewRef(res); Unimplemented: Py_RETURN_NOTIMPLEMENTED; } /*[clinic input] @permit_long_summary complex.conjugate Return the complex conjugate of its argument. (3-4j).conjugate() == 3+4j. [clinic start generated code]*/ static PyObject * complex_conjugate_impl(PyComplexObject *self) /*[clinic end generated code: output=5059ef162edfc68e input=71b8ab003e1cec95]*/ { Py_complex c = self->cval; c.imag = -c.imag; return PyComplex_FromCComplex(c); } /*[clinic input] complex.__getnewargs__ [clinic start generated code]*/ static PyObject * complex___getnewargs___impl(PyComplexObject *self) /*[clinic end generated code: output=689b8206e8728934 input=539543e0a50533d7]*/ { Py_complex c = self->cval; return Py_BuildValue("(dd)", c.real, c.imag); } /*[clinic input] complex.__format__ format_spec: unicode / Convert to a string according to format_spec. [clinic start generated code]*/ static PyObject * complex___format___impl(PyComplexObject *self, PyObject *format_spec) /*[clinic end generated code: output=bfcb60df24cafea0 input=014ef5488acbe1d5]*/ { _PyUnicodeWriter writer; int ret; _PyUnicodeWriter_Init(&writer); ret = _PyComplex_FormatAdvancedWriter( &writer, (PyObject *)self, format_spec, 0, PyUnicode_GET_LENGTH(format_spec)); if (ret == -1) { _PyUnicodeWriter_Dealloc(&writer); return NULL; } return _PyUnicodeWriter_Finish(&writer); } /*[clinic input] complex.__complex__ Convert this value to exact type complex. [clinic start generated code]*/ static PyObject * complex___complex___impl(PyComplexObject *self) /*[clinic end generated code: output=e6b35ba3d275dc9c input=3589ada9d27db854]*/ { if (PyComplex_CheckExact(self)) { return Py_NewRef(self); } else { return PyComplex_FromCComplex(self->cval); } } static PyObject * complex_from_string_inner(const char *s, Py_ssize_t len, void *type) { double x=0.0, y=0.0, z; int got_bracket=0; const char *start; char *end; /* position on first nonblank */ start = s; while (Py_ISSPACE(*s)) s++; if (*s == '(') { /* Skip over possible bracket from repr(). */ got_bracket = 1; s++; while (Py_ISSPACE(*s)) s++; } /* a valid complex string usually takes one of the three forms: <float> - real part only <float>j - imaginary part only <float><signed-float>j - real and imaginary parts where <float> represents any numeric string that's accepted by the float constructor (including 'nan', 'inf', 'infinity', etc.), and <signed-float> is any string of the form <float> whose first character is '+' or '-'. For backwards compatibility, the extra forms |
| You are visitor 01402503 — GeezerVison does not store the pages you look up. Best viewed with Netscape Navigator 4.7 or Internet Explorer 6 at 800×600. No cookies required. |