1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD 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 <sys/cdefs.h> 42 __FBSDID("$FreeBSD$"); 43 44 #include <complex.h> 45 #include <math.h> 46 47 #include "math_private.h" 48 49 static const double huge = 0x1p1023; 50 51 double complex 52 csinh(double complex z) 53 { 54 double x, y, h; 55 int32_t hx, hy, ix, iy, lx, ly; 56 57 x = creal(z); 58 y = cimag(z); 59 60 EXTRACT_WORDS(hx, lx, x); 61 EXTRACT_WORDS(hy, ly, y); 62 63 ix = 0x7fffffff & hx; 64 iy = 0x7fffffff & hy; 65 66 /* Handle the nearly-non-exceptional cases where x and y are finite. */ 67 if (ix < 0x7ff00000 && iy < 0x7ff00000) { 68 if ((iy | ly) == 0) 69 return (CMPLX(sinh(x), y)); 70 if (ix < 0x40360000) /* |x| < 22: normal case */ 71 return (CMPLX(sinh(x) * cos(y), cosh(x) * sin(y))); 72 73 /* |x| >= 22, so cosh(x) ~= exp(|x|) */ 74 if (ix < 0x40862e42) { 75 /* x < 710: exp(|x|) won't overflow */ 76 h = exp(fabs(x)) * 0.5; 77 return (CMPLX(copysign(h, x) * cos(y), h * sin(y))); 78 } else if (ix < 0x4096bbaa) { 79 /* x < 1455: scale to avoid overflow */ 80 z = __ldexp_cexp(CMPLX(fabs(x), y), -1); 81 return (CMPLX(creal(z) * copysign(1, x), cimag(z))); 82 } else { 83 /* x >= 1455: the result always overflows */ 84 h = huge * x; 85 return (CMPLX(h * cos(y), h * h * sin(y))); 86 } 87 } 88 89 /* 90 * sinh(+-0 +- I Inf) = +-0 + I dNaN. 91 * The sign of 0 in the result is unspecified. Choice = same sign 92 * as the argument. Raise the invalid floating-point exception. 93 * 94 * sinh(+-0 +- I NaN) = +-0 + I d(NaN). 95 * The sign of 0 in the result is unspecified. Choice = same sign 96 * as the argument. 97 */ 98 if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */ 99 return (CMPLX(x, y - y)); 100 101 /* 102 * sinh(+-Inf +- I 0) = +-Inf + I +-0. 103 * 104 * sinh(NaN +- I 0) = d(NaN) + I +-0. 105 */ 106 if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */ 107 return (CMPLX(x + x, y)); 108 109 /* 110 * sinh(x +- I Inf) = dNaN + I dNaN. 111 * Raise the invalid floating-point exception for finite nonzero x. 112 * 113 * sinh(x + I NaN) = d(NaN) + I d(NaN). 114 * Optionally raises the invalid floating-point exception for finite 115 * nonzero x. Choice = don't raise (except for signaling NaNs). 116 */ 117 if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */ 118 return (CMPLX(y - y, y - y)); 119 120 /* 121 * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). 122 * The sign of Inf in the result is unspecified. Choice = same sign 123 * as the argument. 124 * 125 * sinh(+-Inf +- I Inf) = +-Inf + I dNaN. 126 * The sign of Inf in the result is unspecified. Choice = same sign 127 * as the argument. Raise the invalid floating-point exception. 128 * 129 * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) 130 */ 131 if (ix == 0x7ff00000 && lx == 0) { 132 if (iy >= 0x7ff00000) 133 return (CMPLX(x, y - y)); 134 return (CMPLX(x * cos(y), INFINITY * sin(y))); 135 } 136 137 /* 138 * sinh(NaN1 + I NaN2) = d(NaN1, NaN2) + I d(NaN1, NaN2). 139 * 140 * sinh(NaN +- I Inf) = d(NaN, dNaN) + I d(NaN, dNaN). 141 * Optionally raises the invalid floating-point exception. 142 * Choice = raise. 143 * 144 * sinh(NaN + I y) = d(NaN) + I d(NaN). 145 * Optionally raises the invalid floating-point exception for finite 146 * nonzero y. Choice = don't raise (except for signaling NaNs). 147 */ 148 return (CMPLX((x + x) * (y - y), (x * x) * (y - y))); 149 } 150 151 double complex 152 csin(double complex z) 153 { 154 155 /* csin(z) = -I * csinh(I * z) = I * conj(csinh(I * conj(z))). */ 156 z = csinh(CMPLX(cimag(z), creal(z))); 157 return (CMPLX(cimag(z), creal(z))); 158 } 159