| s_cexp.c (226413) | s_cexp.c (226597) |
|---|---|
| 1/*- 2 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright --- 11 unchanged lines hidden (view full) --- 20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 24 * SUCH DAMAGE. 25 */ 26 27#include <sys/cdefs.h> | 1/*- 2 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright --- 11 unchanged lines hidden (view full) --- 20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 24 * SUCH DAMAGE. 25 */ 26 27#include <sys/cdefs.h> |
| 28__FBSDID("$FreeBSD: head/lib/msun/src/s_cexp.c 226413 2011-10-16 05:37:01Z das $"); | 28__FBSDID("$FreeBSD: head/lib/msun/src/s_cexp.c 226597 2011-10-21 06:27:56Z das $"); |
| 29 30#include <complex.h> 31#include <math.h> 32 33#include "math_private.h" 34 35static const uint32_t 36exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */ | 29 30#include <complex.h> 31#include <math.h> 32 33#include "math_private.h" 34 35static const uint32_t 36exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */ |
| 37cexp_ovfl = 0x4096b8e4, /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ 38k = 1799; /* constant for reduction */ | 37cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ |
| 39 | 38 |
| 40static const double 41kln2 = 1246.97177782734161156; /* k * ln2 */ 42 | |
| 43double complex 44cexp(double complex z) 45{ 46 double x, y, exp_x; 47 uint32_t hx, hy, lx, ly; | 39double complex 40cexp(double complex z) 41{ 42 double x, y, exp_x; 43 uint32_t hx, hy, lx, ly; |
| 48 int scale; | |
| 49 50 x = creal(z); 51 y = cimag(z); 52 53 EXTRACT_WORDS(hy, ly, y); 54 hy &= 0x7fffffff; 55 56 /* cexp(x + I 0) = exp(x) + I 0 */ --- 15 unchanged lines hidden (view full) --- 72 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ 73 return (cpack(x, y - y)); 74 } 75 } 76 77 if (hx >= exp_ovfl && hx <= cexp_ovfl) { 78 /* 79 * x is between 709.7 and 1454.3, so we must scale to avoid | 44 45 x = creal(z); 46 y = cimag(z); 47 48 EXTRACT_WORDS(hy, ly, y); 49 hy &= 0x7fffffff; 50 51 /* cexp(x + I 0) = exp(x) + I 0 */ --- 15 unchanged lines hidden (view full) --- 67 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ 68 return (cpack(x, y - y)); 69 } 70 } 71 72 if (hx >= exp_ovfl && hx <= cexp_ovfl) { 73 /* 74 * x is between 709.7 and 1454.3, so we must scale to avoid |
| 80 * overflow in exp(x). We use exp(x) = exp(x - kln2) * 2**k, 81 * carefully chosen to minimize |exp(kln2) - 2**k|. We also 82 * scale the exponent of exp(x) to MANT_DIG to avoid loss of 83 * accuracy due to underflow if sin(y) is tiny. | 75 * overflow in exp(x). |
| 84 */ | 76 */ |
| 85 exp_x = exp(x - kln2); 86 GET_HIGH_WORD(hx, exp_x); 87 SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 52) << 20)); 88 scale = (hx >> 20) - (0x3ff + 52) + k; 89 return (cpack(scalbn(cos(y) * exp_x, scale), 90 scalbn(sin(y) * exp_x, scale))); | 77 return (__ldexp_cexp(z, 0)); |
| 91 } else { 92 /* 93 * Cases covered here: 94 * - x < exp_ovfl and exp(x) won't overflow (common case) 95 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 96 * - x = +-Inf (generated by exp()) 97 * - x = NaN (spurious inexact exception from y) 98 */ 99 exp_x = exp(x); 100 return (cpack(exp_x * cos(y), exp_x * sin(y))); 101 } 102} | 78 } else { 79 /* 80 * Cases covered here: 81 * - x < exp_ovfl and exp(x) won't overflow (common case) 82 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 83 * - x = +-Inf (generated by exp()) 84 * - x = NaN (spurious inexact exception from y) 85 */ 86 exp_x = exp(x); 87 return (cpack(exp_x * cos(y), exp_x * sin(y))); 88 } 89} |