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