1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause 3 * 4 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl 5 * All rights reserved. 6 * 7 * Redistribution and use in source and binary forms, with or without 8 * modification, are permitted provided that the following conditions 9 * are met: 10 * 1. Redistributions of source code must retain the above copyright 11 * notice unmodified, this list of conditions, and the following 12 * disclaimer. 13 * 2. Redistributions in binary form must reproduce the above copyright 14 * notice, this list of conditions and the following disclaimer in the 15 * documentation and/or other materials provided with the distribution. 16 * 17 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 18 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 19 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 20 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 21 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 22 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 23 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 24 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 25 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 26 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 27 */ 28 29 /* 30 * Hyperbolic cosine of a complex argument z = x + i y. 31 * 32 * cosh(z) = cosh(x+iy) 33 * = cosh(x) cos(y) + i sinh(x) sin(y). 34 * 35 * Exceptional values are noted in the comments within the source code. 36 * These values and the return value were taken from n1124.pdf. 37 * The sign of the result for some exceptional values is unspecified but 38 * must satisfy both cosh(conj(z)) == conj(cosh(z)) and cosh(-z) == cosh(z). 39 */ 40 41 #include <sys/cdefs.h> 42 #include <complex.h> 43 #include <math.h> 44 45 #include "math_private.h" 46 47 static const double huge = 0x1p1023; 48 49 double complex 50 ccosh(double complex z) 51 { 52 double x, y, h; 53 int32_t hx, hy, ix, iy, lx, ly; 54 55 x = creal(z); 56 y = cimag(z); 57 58 EXTRACT_WORDS(hx, lx, x); 59 EXTRACT_WORDS(hy, ly, y); 60 61 ix = 0x7fffffff & hx; 62 iy = 0x7fffffff & hy; 63 64 /* Handle the nearly-non-exceptional cases where x and y are finite. */ 65 if (ix < 0x7ff00000 && iy < 0x7ff00000) { 66 if ((iy | ly) == 0) 67 return (CMPLX(cosh(x), x * y)); 68 if (ix < 0x40360000) /* |x| < 22: normal case */ 69 return (CMPLX(cosh(x) * cos(y), sinh(x) * sin(y))); 70 71 /* |x| >= 22, so cosh(x) ~= exp(|x|) */ 72 if (ix < 0x40862e42) { 73 /* x < 710: exp(|x|) won't overflow */ 74 h = exp(fabs(x)) * 0.5; 75 return (CMPLX(h * cos(y), copysign(h, x) * sin(y))); 76 } else if (ix < 0x4096bbaa) { 77 /* x < 1455: scale to avoid overflow */ 78 z = __ldexp_cexp(CMPLX(fabs(x), y), -1); 79 return (CMPLX(creal(z), cimag(z) * copysign(1, x))); 80 } else { 81 /* x >= 1455: the result always overflows */ 82 h = huge * x; 83 return (CMPLX(h * h * cos(y), h * sin(y))); 84 } 85 } 86 87 /* 88 * cosh(+-0 +- I Inf) = dNaN + I (+-)(+-)0. 89 * The sign of 0 in the result is unspecified. Choice = product 90 * of the signs of the argument. Raise the invalid floating-point 91 * exception. 92 * 93 * cosh(+-0 +- I NaN) = d(NaN) + I (+-)(+-)0. 94 * The sign of 0 in the result is unspecified. Choice = product 95 * of the signs of the argument. 96 */ 97 if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */ 98 return (CMPLX(y - y, x * copysign(0, y))); 99 100 /* 101 * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0. 102 * 103 * cosh(NaN +- I 0) = d(NaN) + I (+-)(+-)0. 104 * The sign of 0 in the result is unspecified. Choice = product 105 * of the signs of the argument. 106 */ 107 if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */ 108 return (CMPLX(x * x, copysign(0, x) * y)); 109 110 /* 111 * cosh(x +- I Inf) = dNaN + I dNaN. 112 * Raise the invalid floating-point exception for finite nonzero x. 113 * 114 * cosh(x + I NaN) = d(NaN) + I d(NaN). 115 * Optionally raises the invalid floating-point exception for finite 116 * nonzero x. Choice = don't raise (except for signaling NaNs). 117 */ 118 if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */ 119 return (CMPLX(y - y, x * (y - y))); 120 121 /* 122 * cosh(+-Inf + I NaN) = +Inf + I d(NaN). 123 * 124 * cosh(+-Inf +- I Inf) = +Inf + I dNaN. 125 * The sign of Inf in the result is unspecified. Choice = always +. 126 * Raise the invalid floating-point exception. 127 * 128 * cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y) 129 */ 130 if (ix == 0x7ff00000 && lx == 0) { 131 if (iy >= 0x7ff00000) 132 return (CMPLX(INFINITY, x * (y - y))); 133 return (CMPLX(INFINITY * cos(y), x * sin(y))); 134 } 135 136 /* 137 * cosh(NaN + I NaN) = d(NaN) + I d(NaN). 138 * 139 * cosh(NaN +- I Inf) = d(NaN) + I d(NaN). 140 * Optionally raises the invalid floating-point exception. 141 * Choice = raise. 142 * 143 * cosh(NaN + I y) = d(NaN) + I d(NaN). 144 * Optionally raises the invalid floating-point exception for finite 145 * nonzero y. Choice = don't raise (except for signaling NaNs). 146 */ 147 return (CMPLX(((long double)x * x) * (y - y), 148 ((long double)x + x) * (y - y))); 149 } 150 151 double complex 152 ccos(double complex z) 153 { 154 155 /* ccos(z) = ccosh(I * z) */ 156 return (ccosh(CMPLX(-cimag(z), creal(z)))); 157 } 158