1a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes/*- 2a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> 3a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * All rights reserved. 4a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 5a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Redistribution and use in source and binary forms, with or without 6a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * modification, are permitted provided that the following conditions 7a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * are met: 8a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 1. Redistributions of source code must retain the above copyright 9a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * notice, this list of conditions and the following disclaimer. 10a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 2. Redistributions in binary form must reproduce the above copyright 11a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * notice, this list of conditions and the following disclaimer in the 12a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * documentation and/or other materials provided with the distribution. 13a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 14a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 15a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 16a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 17a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 18a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 19a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 20a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 21a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 22a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 23a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 24a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * SUCH DAMAGE. 25a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes */ 26a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 27a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <sys/cdefs.h> 28a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes__FBSDID("$FreeBSD$"); 29a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 30a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <complex.h> 31a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <math.h> 32a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 33a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include "math_private.h" 34a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 35a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesstatic const uint32_t 36a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesexp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */ 37a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughescexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ 38a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 39a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesdouble complex 40a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughescexp(double complex z) 41a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes{ 42a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes double x, y, exp_x; 43a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes uint32_t hx, hy, lx, ly; 44a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 45a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes x = creal(z); 46a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes y = cimag(z); 47a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 48a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes EXTRACT_WORDS(hy, ly, y); 49a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes hy &= 0x7fffffff; 50a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 51a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* cexp(x + I 0) = exp(x) + I 0 */ 52a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if ((hy | ly) == 0) 53a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return (cpack(exp(x), y)); 54a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes EXTRACT_WORDS(hx, lx, x); 55a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* cexp(0 + I y) = cos(y) + I sin(y) */ 56a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (((hx & 0x7fffffff) | lx) == 0) 57a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return (cpack(cos(y), sin(y))); 58a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 59a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (hy >= 0x7ff00000) { 60a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) { 61a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ 62a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return (cpack(y - y, y - y)); 63a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } else if (hx & 0x80000000) { 64a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ 65a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return (cpack(0.0, 0.0)); 66a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } else { 67a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ 68a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return (cpack(x, y - y)); 69a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } 70a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } 71a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 72a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (hx >= exp_ovfl && hx <= cexp_ovfl) { 73a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* 74a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * x is between 709.7 and 1454.3, so we must scale to avoid 75a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * overflow in exp(x). 76a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes */ 77a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return (__ldexp_cexp(z, 0)); 78a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } else { 79a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* 80a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Cases covered here: 81a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * - x < exp_ovfl and exp(x) won't overflow (common case) 82a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 83a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * - x = +-Inf (generated by exp()) 84a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * - x = NaN (spurious inexact exception from y) 85a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes */ 86a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes exp_x = exp(x); 87a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return (cpack(exp_x * cos(y), exp_x * sin(y))); 88a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } 89a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes} 90