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 sine of a complex argument z = x + i y. 31 * 32 * sinh(z) = sinh(x+iy) 33 * = sinh(x) cos(y) + i cosh(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 sinh(conj(z)) == conj(sinh(z)) and sinh(-z) == -sinh(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 csinh(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(sinh(x), y)); 67 68 sincos(y, &s, &c); 69 if (ix < 0x40360000) /* |x| < 22: normal case */ 70 return (CMPLX(sinh(x) * c, cosh(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(copysign(h, x) * c, h * 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) * copysign(1, x), cimag(z))); 81 } else { 82 /* x >= 1455: the result always overflows */ 83 h = huge * x; 84 return (CMPLX(h * c, h * h * s)); 85 } 86 } 87 88 /* 89 * sinh(+-0 +- I Inf) = +-0 + I dNaN. 90 * The sign of 0 in the result is unspecified. Choice = same sign 91 * as the argument. Raise the invalid floating-point exception. 92 * 93 * sinh(+-0 +- I NaN) = +-0 + I d(NaN). 94 * The sign of 0 in the result is unspecified. Choice = same sign 95 * as the argument. 96 */ 97 if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */ 98 return (CMPLX(x, y - y)); 99 100 /* 101 * sinh(+-Inf +- I 0) = +-Inf + I +-0. 102 * 103 * sinh(NaN +- I 0) = d(NaN) + I +-0. 104 */ 105 if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */ 106 return (CMPLX(x + x, y)); 107 108 /* 109 * sinh(x +- I Inf) = dNaN + I dNaN. 110 * Raise the invalid floating-point exception for finite nonzero x. 111 * 112 * sinh(x + I NaN) = d(NaN) + I d(NaN). 113 * Optionally raises the invalid floating-point exception for finite 114 * nonzero x. Choice = don't raise (except for signaling NaNs). 115 */ 116 if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */ 117 return (CMPLX(y - y, y - y)); 118 119 /* 120 * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). 121 * The sign of Inf in the result is unspecified. Choice = same sign 122 * as the argument. 123 * 124 * sinh(+-Inf +- I Inf) = +-Inf + I dNaN. 125 * The sign of Inf in the result is unspecified. Choice = same sign 126 * as the argument. Raise the invalid floating-point exception. 127 * 128 * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) 129 */ 130 if (ix == 0x7ff00000 && lx == 0) { 131 if (iy >= 0x7ff00000) 132 return (CMPLX(x, y - y)); 133 134 sincos(y, &s, &c); 135 return (CMPLX(x * c, INFINITY * s)); 136 } 137 138 /* 139 * sinh(NaN1 + I NaN2) = d(NaN1, NaN2) + I d(NaN1, NaN2). 140 * 141 * sinh(NaN +- I Inf) = d(NaN, dNaN) + I d(NaN, dNaN). 142 * Optionally raises the invalid floating-point exception. 143 * Choice = raise. 144 * 145 * sinh(NaN + I y) = d(NaN) + I d(NaN). 146 * Optionally raises the invalid floating-point exception for finite 147 * nonzero y. Choice = don't raise (except for signaling NaNs). 148 */ 149 return (CMPLX(((long double)x + x) * (y - y), 150 ((long double)x * x) * (y - y))); 151 } 152 153 double complex 154 csin(double complex z) 155 { 156 157 /* csin(z) = -I * csinh(I * z) = I * conj(csinh(I * conj(z))). */ 158 z = csinh(CMPLX(cimag(z), creal(z))); 159 return (CMPLX(cimag(z), creal(z))); 160 } 161 162 #if (LDBL_MANT_DIG == 53) 163 __weak_reference(csinh, csinhl); 164 __weak_reference(csin, csinl); 165 #endif 166