1 /*- 2 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright 9 * notice unmodified, this list of conditions, and the following 10 * disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 16 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 17 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 18 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 19 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 25 */ 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 * The sign of the result for some exceptional values is unspecified but 36 * must satisfy both sinh(conj(z)) == conj(sinh(z)) and sinh(-z) == -sinh(z). 37 */ 38 39 #include <sys/cdefs.h> 40 __FBSDID("$FreeBSD$"); 41 42 #include <complex.h> 43 #include <math.h> 44 45 #include "math_private.h" 46 47 static const double huge = 0x1p1023; 48 49 double complex 50 csinh(double complex z) 51 { 52 double x, y, h; 53 int32_t hx, hy, ix, iy, lx, ly; 54 55 x = creal(z); 56 y = cimag(z); 57 58 EXTRACT_WORDS(hx, lx, x); 59 EXTRACT_WORDS(hy, ly, y); 60 61 ix = 0x7fffffff & hx; 62 iy = 0x7fffffff & hy; 63 64 /* Handle the nearly-non-exceptional cases where x and y are finite. */ 65 if (ix < 0x7ff00000 && iy < 0x7ff00000) { 66 if ((iy | ly) == 0) 67 return (CMPLX(sinh(x), y)); 68 if (ix < 0x40360000) /* |x| < 22: normal case */ 69 return (CMPLX(sinh(x) * cos(y), cosh(x) * sin(y))); 70 71 /* |x| >= 22, so cosh(x) ~= exp(|x|) */ 72 if (ix < 0x40862e42) { 73 /* x < 710: exp(|x|) won't overflow */ 74 h = exp(fabs(x)) * 0.5; 75 return (CMPLX(copysign(h, x) * cos(y), h * sin(y))); 76 } else if (ix < 0x4096bbaa) { 77 /* x < 1455: scale to avoid overflow */ 78 z = __ldexp_cexp(CMPLX(fabs(x), y), -1); 79 return (CMPLX(creal(z) * copysign(1, x), cimag(z))); 80 } else { 81 /* x >= 1455: the result always overflows */ 82 h = huge * x; 83 return (CMPLX(h * cos(y), h * h * sin(y))); 84 } 85 } 86 87 /* 88 * sinh(+-0 +- I Inf) = +-0 + I dNaN. 89 * The sign of 0 in the result is unspecified. Choice = same sign 90 * as the argument. Raise the invalid floating-point exception. 91 * 92 * sinh(+-0 +- I NaN) = +-0 + I d(NaN). 93 * The sign of 0 in the result is unspecified. Choice = same sign 94 * as the argument. 95 */ 96 if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */ 97 return (CMPLX(x, y - y)); 98 99 /* 100 * sinh(+-Inf +- I 0) = +-Inf + I +-0. 101 * 102 * sinh(NaN +- I 0) = d(NaN) + I +-0. 103 */ 104 if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */ 105 return (CMPLX(x + x, y)); 106 107 /* 108 * sinh(x +- I Inf) = dNaN + I dNaN. 109 * Raise the invalid floating-point exception for finite nonzero x. 110 * 111 * sinh(x + I NaN) = d(NaN) + I d(NaN). 112 * Optionally raises the invalid floating-point exception for finite 113 * nonzero x. Choice = don't raise (except for signaling NaNs). 114 */ 115 if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */ 116 return (CMPLX(y - y, y - y)); 117 118 /* 119 * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). 120 * The sign of Inf in the result is unspecified. Choice = same sign 121 * as the argument. 122 * 123 * sinh(+-Inf +- I Inf) = +-Inf + I dNaN. 124 * The sign of Inf in the result is unspecified. Choice = same sign 125 * as the argument. Raise the invalid floating-point exception. 126 * 127 * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) 128 */ 129 if (ix == 0x7ff00000 && lx == 0) { 130 if (iy >= 0x7ff00000) 131 return (CMPLX(x, y - y)); 132 return (CMPLX(x * cos(y), INFINITY * sin(y))); 133 } 134 135 /* 136 * sinh(NaN1 + I NaN2) = d(NaN1, NaN2) + I d(NaN1, NaN2). 137 * 138 * sinh(NaN +- I Inf) = d(NaN, dNaN) + I d(NaN, dNaN). 139 * Optionally raises the invalid floating-point exception. 140 * Choice = raise. 141 * 142 * sinh(NaN + I y) = d(NaN) + I d(NaN). 143 * Optionally raises the invalid floating-point exception for finite 144 * nonzero y. Choice = don't raise (except for signaling NaNs). 145 */ 146 return (CMPLX((x + x) * (y - y), (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