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 */ 36 37 #include <sys/cdefs.h> 38 __FBSDID("$FreeBSD$"); 39 40 #include <complex.h> 41 #include <math.h> 42 43 #include "math_private.h" 44 45 static const double huge = 0x1p1023; 46 47 double complex 48 csinh(double complex z) 49 { 50 double x, y, h; 51 int32_t hx, hy, ix, iy, lx, ly; 52 53 x = creal(z); 54 y = cimag(z); 55 56 EXTRACT_WORDS(hx, lx, x); 57 EXTRACT_WORDS(hy, ly, y); 58 59 ix = 0x7fffffff & hx; 60 iy = 0x7fffffff & hy; 61 62 /* Handle the nearly-non-exceptional cases where x and y are finite. */ 63 if (ix < 0x7ff00000 && iy < 0x7ff00000) { 64 if ((iy | ly) == 0) 65 return (cpack(sinh(x), y)); 66 if (ix < 0x40360000) /* small x: normal case */ 67 return (cpack(sinh(x) * cos(y), cosh(x) * sin(y))); 68 69 /* |x| >= 22, so cosh(x) ~= exp(|x|) */ 70 if (ix < 0x40862e42) { 71 /* x < 710: exp(|x|) won't overflow */ 72 h = exp(fabs(x)) * 0.5; 73 return (cpack(copysign(h, x) * cos(y), h * sin(y))); 74 } else if (ix < 0x4096bbaa) { 75 /* x < 1455: scale to avoid overflow */ 76 z = __ldexp_cexp(cpack(fabs(x), y), -1); 77 return (cpack(creal(z) * copysign(1, x), cimag(z))); 78 } else { 79 /* x >= 1455: the result always overflows */ 80 h = huge * x; 81 return (cpack(h * cos(y), h * h * sin(y))); 82 } 83 } 84 85 /* 86 * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN. 87 * The sign of 0 in the result is unspecified. Choice = normally 88 * the same as dNaN. Raise the invalid floating-point exception. 89 * 90 * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN). 91 * The sign of 0 in the result is unspecified. Choice = normally 92 * the same as d(NaN). 93 */ 94 if ((ix | lx) == 0 && iy >= 0x7ff00000) 95 return (cpack(copysign(0, x * (y - y)), y - y)); 96 97 /* 98 * sinh(+-Inf +- I 0) = +-Inf + I +-0. 99 * 100 * sinh(NaN +- I 0) = d(NaN) + I +-0. 101 */ 102 if ((iy | ly) == 0 && ix >= 0x7ff00000) { 103 if (((hx & 0xfffff) | lx) == 0) 104 return (cpack(x, y)); 105 return (cpack(x, copysign(0, y))); 106 } 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 (cpack(y - y, x * (y - y))); 118 119 /* 120 * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). 121 * The sign of Inf in the result is unspecified. Choice = normally 122 * the same as d(NaN). 123 * 124 * sinh(+-Inf +- I Inf) = +Inf + I dNaN. 125 * The sign of Inf in the result is unspecified. Choice = always +. 126 * Raise the invalid floating-point exception. 127 * 128 * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) 129 */ 130 if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { 131 if (iy >= 0x7ff00000) 132 return (cpack(x * x, x * (y - y))); 133 return (cpack(x * cos(y), INFINITY * sin(y))); 134 } 135 136 /* 137 * sinh(NaN + I NaN) = d(NaN) + I d(NaN). 138 * 139 * sinh(NaN +- I Inf) = d(NaN) + I d(NaN). 140 * Optionally raises the invalid floating-point exception. 141 * Choice = raise. 142 * 143 * sinh(NaN + I y) = d(NaN) + I d(NaN). 144 * Optionally raises the invalid floating-point exception for finite 145 * nonzero y. Choice = don't raise (except for signaling NaNs). 146 */ 147 return (cpack((x * x) * (y - y), (x + x) * (y - y))); 148 } 149 150 double complex 151 csin(double complex z) 152 { 153 154 /* csin(z) = -I * csinh(I * z) */ 155 z = csinh(cpack(-cimag(z), creal(z))); 156 return (cpack(cimag(z), -creal(z))); 157 } 158