1226458Sdas/*- 2226458Sdas * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl 3226458Sdas * All rights reserved. 4226458Sdas * 5226458Sdas * Redistribution and use in source and binary forms, with or without 6226458Sdas * modification, are permitted provided that the following conditions 7226458Sdas * are met: 8226458Sdas * 1. Redistributions of source code must retain the above copyright 9226458Sdas * notice unmodified, this list of conditions, and the following 10226458Sdas * disclaimer. 11226458Sdas * 2. Redistributions in binary form must reproduce the above copyright 12226458Sdas * notice, this list of conditions and the following disclaimer in the 13226458Sdas * documentation and/or other materials provided with the distribution. 14226458Sdas * 15226458Sdas * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 16226458Sdas * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 17226458Sdas * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 18226458Sdas * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 19226458Sdas * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 20226458Sdas * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 21226458Sdas * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 22226458Sdas * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 23226458Sdas * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 24226458Sdas * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 25226458Sdas */ 26226458Sdas 27226458Sdas/* 28226458Sdas * Hyperbolic cosine of a complex argument z = x + i y. 29226458Sdas * 30226458Sdas * cosh(z) = cosh(x+iy) 31226458Sdas * = cosh(x) cos(y) + i sinh(x) sin(y). 32226458Sdas * 33226458Sdas * Exceptional values are noted in the comments within the source code. 34226458Sdas * These values and the return value were taken from n1124.pdf. 35226458Sdas */ 36226458Sdas 37226458Sdas#include <sys/cdefs.h> 38226458Sdas__FBSDID("$FreeBSD$"); 39226458Sdas 40226458Sdas#include <complex.h> 41226458Sdas#include <math.h> 42226458Sdas 43226458Sdas#include "math_private.h" 44226458Sdas 45226599Sdasstatic const double huge = 0x1p1023; 46226599Sdas 47226458Sdasdouble complex 48226458Sdasccosh(double complex z) 49226458Sdas{ 50226599Sdas double x, y, h; 51226458Sdas int32_t hx, hy, ix, iy, lx, ly; 52226458Sdas 53226458Sdas x = creal(z); 54226458Sdas y = cimag(z); 55226458Sdas 56226458Sdas EXTRACT_WORDS(hx, lx, x); 57226458Sdas EXTRACT_WORDS(hy, ly, y); 58226458Sdas 59226458Sdas ix = 0x7fffffff & hx; 60226458Sdas iy = 0x7fffffff & hy; 61226458Sdas 62226458Sdas /* Handle the nearly-non-exceptional cases where x and y are finite. */ 63226458Sdas if (ix < 0x7ff00000 && iy < 0x7ff00000) { 64226458Sdas if ((iy | ly) == 0) 65226458Sdas return (cpack(cosh(x), x * y)); 66226599Sdas if (ix < 0x40360000) /* small x: normal case */ 67226599Sdas return (cpack(cosh(x) * cos(y), sinh(x) * sin(y))); 68226599Sdas 69226599Sdas /* |x| >= 22, so cosh(x) ~= exp(|x|) */ 70226599Sdas if (ix < 0x40862e42) { 71226599Sdas /* x < 710: exp(|x|) won't overflow */ 72226599Sdas h = exp(fabs(x)) * 0.5; 73226599Sdas return (cpack(h * cos(y), copysign(h, x) * sin(y))); 74226599Sdas } else if (ix < 0x4096bbaa) { 75226599Sdas /* x < 1455: scale to avoid overflow */ 76226599Sdas z = __ldexp_cexp(cpack(fabs(x), y), -1); 77226599Sdas return (cpack(creal(z), cimag(z) * copysign(1, x))); 78226599Sdas } else { 79226599Sdas /* x >= 1455: the result always overflows */ 80226599Sdas h = huge * x; 81226599Sdas return (cpack(h * h * cos(y), h * sin(y))); 82226599Sdas } 83226458Sdas } 84226458Sdas 85226458Sdas /* 86226458Sdas * cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0. 87226458Sdas * The sign of 0 in the result is unspecified. Choice = normally 88226458Sdas * the same as dNaN. Raise the invalid floating-point exception. 89226458Sdas * 90226458Sdas * cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0. 91226458Sdas * The sign of 0 in the result is unspecified. Choice = normally 92226458Sdas * the same as d(NaN). 93226458Sdas */ 94226458Sdas if ((ix | lx) == 0 && iy >= 0x7ff00000) 95226458Sdas return (cpack(y - y, copysign(0, x * (y - y)))); 96226458Sdas 97226458Sdas /* 98226458Sdas * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0. 99226458Sdas * 100226458Sdas * cosh(NaN +- I 0) = d(NaN) + I sign(d(NaN, +-0))0. 101226458Sdas * The sign of 0 in the result is unspecified. 102226458Sdas */ 103226458Sdas if ((iy | ly) == 0 && ix >= 0x7ff00000) { 104226458Sdas if (((hx & 0xfffff) | lx) == 0) 105226458Sdas return (cpack(x * x, copysign(0, x) * y)); 106226458Sdas return (cpack(x * x, copysign(0, (x + x) * y))); 107226458Sdas } 108226458Sdas 109226458Sdas /* 110226458Sdas * cosh(x +- I Inf) = dNaN + I dNaN. 111226458Sdas * Raise the invalid floating-point exception for finite nonzero x. 112226458Sdas * 113226458Sdas * cosh(x + I NaN) = d(NaN) + I d(NaN). 114226458Sdas * Optionally raises the invalid floating-point exception for finite 115226458Sdas * nonzero x. Choice = don't raise (except for signaling NaNs). 116226458Sdas */ 117226458Sdas if (ix < 0x7ff00000 && iy >= 0x7ff00000) 118226458Sdas return (cpack(y - y, x * (y - y))); 119226458Sdas 120226458Sdas /* 121226458Sdas * cosh(+-Inf + I NaN) = +Inf + I d(NaN). 122226458Sdas * 123226458Sdas * cosh(+-Inf +- I Inf) = +Inf + I dNaN. 124226458Sdas * The sign of Inf in the result is unspecified. Choice = always +. 125226458Sdas * Raise the invalid floating-point exception. 126226458Sdas * 127226458Sdas * cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y) 128226458Sdas */ 129226458Sdas if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { 130226458Sdas if (iy >= 0x7ff00000) 131226458Sdas return (cpack(x * x, x * (y - y))); 132226458Sdas return (cpack((x * x) * cos(y), x * sin(y))); 133226458Sdas } 134226458Sdas 135226458Sdas /* 136226458Sdas * cosh(NaN + I NaN) = d(NaN) + I d(NaN). 137226458Sdas * 138226458Sdas * cosh(NaN +- I Inf) = d(NaN) + I d(NaN). 139226458Sdas * Optionally raises the invalid floating-point exception. 140226458Sdas * Choice = raise. 141226458Sdas * 142226458Sdas * cosh(NaN + I y) = d(NaN) + I d(NaN). 143226458Sdas * Optionally raises the invalid floating-point exception for finite 144226458Sdas * nonzero y. Choice = don't raise (except for signaling NaNs). 145226458Sdas */ 146226458Sdas return (cpack((x * x) * (y - y), (x + x) * (y - y))); 147226458Sdas} 148226458Sdas 149226458Sdasdouble complex 150226458Sdasccos(double complex z) 151226458Sdas{ 152226458Sdas 153226458Sdas /* ccos(z) = ccosh(I * z) */ 154226458Sdas return (ccosh(cpack(-cimag(z), creal(z)))); 155226458Sdas} 156