1 /*- 2 * Copyright (c) 2011 David Schultz <das (at) 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 9 * notice, this list of conditions and the following disclaimer. 10 * 2. Redistributions in binary form must reproduce the above copyright 11 * notice, this list of conditions and the following disclaimer in the 12 * documentation and/or other materials provided with the distribution. 13 * 14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 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("$FreeBSD$"); 29 30 #include <complex.h> 31 #include <math.h> 32 33 #include "math_private.h" 34 35 static const uint32_t 36 exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */ 37 cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ 38 39 double complex 40 cexp(double complex z) 41 { 42 double x, y, exp_x; 43 uint32_t hx, hy, lx, ly; 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 */ 52 if ((hy | ly) == 0) 53 return (cpack(exp(x), y)); 54 EXTRACT_WORDS(hx, lx, x); 55 /* cexp(0 + I y) = cos(y) + I sin(y) */ 56 if (((hx & 0x7fffffff) | lx) == 0) 57 return (cpack(cos(y), sin(y))); 58 59 if (hy >= 0x7ff00000) { 60 if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) { 61 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ 62 return (cpack(y - y, y - y)); 63 } else if (hx & 0x80000000) { 64 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ 65 return (cpack(0.0, 0.0)); 66 } else { 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 75 * overflow in exp(x). 76 */ 77 return (__ldexp_cexp(z, 0)); 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 } 90
