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 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 k = 1799; /* constant for reduction */ 39 40 static const double 41 kln2 = 1246.97177782734161156; /* k * ln2 */ 42 43 double complex 44 cexp(double complex z) 45 { 46 double x, y, exp_x; 47 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 */ 57 if ((hy | ly) == 0) 58 return (cpack(exp(x), y)); 59 if (hy >= 0x7ff00000) { 60 EXTRACT_WORDS(hx, lx, x); 61 if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) { 62 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ 63 return (cpack(y - y, y - y)); 64 } else if (hx & 0x80000000) { 65 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ 66 return (cpack(0.0, 0.0)); 67 } else { 68 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ 69 return (cpack(x, y - y)); 70 } 71 } 72 73 GET_HIGH_WORD(hx, x); 74 if (hx >= exp_ovfl && hx <= cexp_ovfl) { 75 /* 76 * x is between 709.7 and 1454.3, so we must scale to avoid 77 * overflow in exp(x). We use exp(x) = exp(x - kln2) * 2**k, 78 * carefully chosen to minimize |exp(kln2) - 2**k|. We also 79 * scale the exponent of exp(x) to MANT_DIG to avoid loss of 80 * accuracy due to underflow if sin(y) is tiny. 81 */ 82 exp_x = exp(x - kln2); 83 GET_HIGH_WORD(hx, exp_x); 84 SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 52) << 20)); 85 scale = (hx >> 20) - (0x3ff + 52) + k; 86 return (cpack(scalbn(cos(y) * exp_x, scale), 87 scalbn(sin(y) * exp_x, scale))); 88 } else { 89 /* 90 * Cases covered here: 91 * - x < exp_ovfl and exp(x) won't overflow (common case) 92 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 93 * - x = +-Inf (generated by exp()) 94 * - x = NaN (spurious inexact exception from y) 95 */ 96 exp_x = exp(x); 97 return (cpack(exp_x * cos(y), exp_x * sin(y))); 98 } 99 } 100