1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause 3 * 4 * Copyright (c) 2005-2025 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 <complex.h> 42 #include <math.h> 43 44 #include "math_private.h" 45 46 static const double huge = 0x1p1023; 47 48 double complex 49 ccosh(double complex z) 50 { 51 double c, h, s, x, y; 52 int32_t hx, hy, ix, iy, lx, ly; 53 54 x = creal(z); 55 y = cimag(z); 56 57 EXTRACT_WORDS(hx, lx, x); 58 EXTRACT_WORDS(hy, ly, y); 59 60 ix = 0x7fffffff & hx; 61 iy = 0x7fffffff & hy; 62 63 /* Handle the nearly-non-exceptional cases where x and y are finite. */ 64 if (ix < 0x7ff00000 && iy < 0x7ff00000) { 65 if ((iy | ly) == 0) 66 return (CMPLX(cosh(x), x * y)); 67 68 sincos(y, &s, &c); 69 if (ix < 0x40360000) /* |x| < 22: normal case */ 70 return (CMPLX(cosh(x) * c, sinh(x) * s)); 71 72 /* |x| >= 22, so cosh(x) ~= exp(|x|) */ 73 if (ix < 0x40862e42) { 74 /* x < 710: exp(|x|) won't overflow */ 75 h = exp(fabs(x)) / 2; 76 return (CMPLX(h * c, copysign(h, x) * s)); 77 } else if (ix < 0x4096bbaa) { 78 /* x < 1455: scale to avoid overflow */ 79 z = __ldexp_cexp(CMPLX(fabs(x), y), -1); 80 return (CMPLX(creal(z), cimag(z) * copysign(1, x))); 81 } else { 82 /* x >= 1455: the result always overflows */ 83 h = huge * x; 84 return (CMPLX(h * h * c, h * s)); 85 } 86 } 87 88 /* 89 * cosh(+-0 +- I Inf) = dNaN + I (+-)(+-)0. 90 * The sign of 0 in the result is unspecified. Choice = product 91 * of the signs of the argument. Raise the invalid floating-point 92 * exception. 93 * 94 * cosh(+-0 +- I NaN) = d(NaN) + I (+-)(+-)0. 95 * The sign of 0 in the result is unspecified. Choice = product 96 * of the signs of the argument. 97 */ 98 if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */ 99 return (CMPLX(y - y, x * copysign(0, y))); 100 101 /* 102 * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0. 103 * 104 * cosh(NaN +- I 0) = d(NaN) + I (+-)(+-)0. 105 * The sign of 0 in the result is unspecified. Choice = product 106 * of the signs of the argument. 107 */ 108 if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */ 109 return (CMPLX(x * x, copysign(0, x) * y)); 110 111 /* 112 * cosh(x +- I Inf) = dNaN + I dNaN. 113 * Raise the invalid floating-point exception for finite nonzero x. 114 * 115 * cosh(x + I NaN) = d(NaN) + I d(NaN). 116 * Optionally raises the invalid floating-point exception for finite 117 * nonzero x. Choice = don't raise (except for signaling NaNs). 118 */ 119 if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */ 120 return (CMPLX(y - y, x * (y - y))); 121 122 /* 123 * cosh(+-Inf + I NaN) = +Inf + I d(NaN). 124 * 125 * cosh(+-Inf +- I Inf) = +Inf + I dNaN. 126 * The sign of Inf in the result is unspecified. Choice = always +. 127 * Raise the invalid floating-point exception. 128 * 129 * cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y) 130 */ 131 if (ix == 0x7ff00000 && lx == 0) { 132 if (iy >= 0x7ff00000) 133 return (CMPLX(INFINITY, x * (y - y))); 134 135 sincos(y, &s, &c); 136 return (CMPLX(INFINITY * c, x * s)); 137 } 138 139 /* 140 * cosh(NaN + I NaN) = d(NaN) + I d(NaN). 141 * 142 * cosh(NaN +- I Inf) = d(NaN) + I d(NaN). 143 * Optionally raises the invalid floating-point exception. 144 * Choice = raise. 145 * 146 * cosh(NaN + I y) = d(NaN) + I d(NaN). 147 * Optionally raises the invalid floating-point exception for finite 148 * nonzero y. Choice = don't raise (except for signaling NaNs). 149 */ 150 return (CMPLX(((long double)x * x) * (y - y), 151 ((long double)x + x) * (y - y))); 152 } 153 154 double complex 155 ccos(double complex z) 156 { 157 158 /* ccos(z) = ccosh(I * z) */ 159 return (ccosh(CMPLX(-cimag(z), creal(z)))); 160 } 161 162 #if (LDBL_MANT_DIG == 53) 163 __weak_reference(ccosh, ccoshl); 164 __weak_reference(ccos, ccosl); 165 #endif 166