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 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 x, y, h; 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 if (ix < 0x40360000) /* |x| < 22: normal case */ 68 return (CMPLX(sinh(x) * cos(y), cosh(x) * sin(y))); 69 70 /* |x| >= 22, so cosh(x) ~= exp(|x|) */ 71 if (ix < 0x40862e42) { 72 /* x < 710: exp(|x|) won't overflow */ 73 h = exp(fabs(x)) * 0.5; 74 return (CMPLX(copysign(h, x) * cos(y), h * sin(y))); 75 } else if (ix < 0x4096bbaa) { 76 /* x < 1455: scale to avoid overflow */ 77 z = __ldexp_cexp(CMPLX(fabs(x), y), -1); 78 return (CMPLX(creal(z) * copysign(1, x), cimag(z))); 79 } else { 80 /* x >= 1455: the result always overflows */ 81 h = huge * x; 82 return (CMPLX(h * cos(y), h * h * sin(y))); 83 } 84 } 85 86 /* 87 * sinh(+-0 +- I Inf) = +-0 + I dNaN. 88 * The sign of 0 in the result is unspecified. Choice = same sign 89 * as the argument. Raise the invalid floating-point exception. 90 * 91 * sinh(+-0 +- I NaN) = +-0 + I d(NaN). 92 * The sign of 0 in the result is unspecified. Choice = same sign 93 * as the argument. 94 */ 95 if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */ 96 return (CMPLX(x, y - y)); 97 98 /* 99 * sinh(+-Inf +- I 0) = +-Inf + I +-0. 100 * 101 * sinh(NaN +- I 0) = d(NaN) + I +-0. 102 */ 103 if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */ 104 return (CMPLX(x + x, y)); 105 106 /* 107 * sinh(x +- I Inf) = dNaN + I dNaN. 108 * Raise the invalid floating-point exception for finite nonzero x. 109 * 110 * sinh(x + I NaN) = d(NaN) + I d(NaN). 111 * Optionally raises the invalid floating-point exception for finite 112 * nonzero x. Choice = don't raise (except for signaling NaNs). 113 */ 114 if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */ 115 return (CMPLX(y - y, y - y)); 116 117 /* 118 * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). 119 * The sign of Inf in the result is unspecified. Choice = same sign 120 * as the argument. 121 * 122 * sinh(+-Inf +- I Inf) = +-Inf + I dNaN. 123 * The sign of Inf in the result is unspecified. Choice = same sign 124 * as the argument. Raise the invalid floating-point exception. 125 * 126 * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) 127 */ 128 if (ix == 0x7ff00000 && lx == 0) { 129 if (iy >= 0x7ff00000) 130 return (CMPLX(x, y - y)); 131 return (CMPLX(x * cos(y), INFINITY * sin(y))); 132 } 133 134 /* 135 * sinh(NaN1 + I NaN2) = d(NaN1, NaN2) + I d(NaN1, NaN2). 136 * 137 * sinh(NaN +- I Inf) = d(NaN, dNaN) + I d(NaN, dNaN). 138 * Optionally raises the invalid floating-point exception. 139 * Choice = raise. 140 * 141 * sinh(NaN + I y) = d(NaN) + I d(NaN). 142 * Optionally raises the invalid floating-point exception for finite 143 * nonzero y. Choice = don't raise (except for signaling NaNs). 144 */ 145 return (CMPLX(((long double)x + x) * (y - y), 146 ((long double)x * x) * (y - y))); 147 } 148 149 double complex 150 csin(double complex z) 151 { 152 153 /* csin(z) = -I * csinh(I * z) = I * conj(csinh(I * conj(z))). */ 154 z = csinh(CMPLX(cimag(z), creal(z))); 155 return (CMPLX(cimag(z), creal(z))); 156 } 157