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 double complex 46 csinh(double complex z) 47 { 48 double x, y; 49 int32_t hx, hy, ix, iy, lx, ly; 50 51 x = creal(z); 52 y = cimag(z); 53 54 EXTRACT_WORDS(hx, lx, x); 55 EXTRACT_WORDS(hy, ly, y); 56 57 ix = 0x7fffffff & hx; 58 iy = 0x7fffffff & hy; 59 60 /* Handle the nearly-non-exceptional cases where x and y are finite. */ 61 if (ix < 0x7ff00000 && iy < 0x7ff00000) { 62 if ((iy | ly) == 0) 63 return (cpack(sinh(x), y)); 64 /* XXX We don't handle |x| > DBL_MAX ln(2) yet. */ 65 return (cpack(sinh(x) * cos(y), cosh(x) * sin(y))); 66 } 67 68 /* 69 * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN. 70 * The sign of 0 in the result is unspecified. Choice = normally 71 * the same as dNaN. Raise the invalid floating-point exception. 72 * 73 * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN). 74 * The sign of 0 in the result is unspecified. Choice = normally 75 * the same as d(NaN). 76 */ 77 if ((ix | lx) == 0 && iy >= 0x7ff00000) 78 return (cpack(copysign(0, x * (y - y)), y - y)); 79 80 /* 81 * sinh(+-Inf +- I 0) = +-Inf + I (+-)(+-)0. 82 * 83 * sinh(NaN +- I 0) = d(NaN) + I +-0. 84 */ 85 if ((iy | ly) == 0 && ix >= 0x7ff00000) { 86 if (((hx & 0xfffff) | lx) == 0) 87 return (cpack(x, copysign(0, x) * y)); 88 return (cpack(x, copysign(0, y))); 89 } 90 91 /* 92 * sinh(x +- I Inf) = dNaN + I dNaN. 93 * Raise the invalid floating-point exception for finite nonzero x. 94 * 95 * sinh(x + I NaN) = d(NaN) + I d(NaN). 96 * Optionally raises the invalid floating-point exception for finite 97 * nonzero x. Choice = don't raise (except for signaling NaNs). 98 */ 99 if (ix < 0x7ff00000 && iy >= 0x7ff00000) 100 return (cpack(y - y, x * (y - y))); 101 102 /* 103 * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). 104 * The sign of Inf in the result is unspecified. Choice = normally 105 * the same as d(NaN). 106 * 107 * sinh(+-Inf +- I Inf) = +Inf + I dNaN. 108 * The sign of Inf in the result is unspecified. Choice = always +. 109 * Raise the invalid floating-point exception. 110 * 111 * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) 112 */ 113 if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { 114 if (iy >= 0x7ff00000) 115 return (cpack(x * x, x * (y - y))); 116 return (cpack(x * cos(y), INFINITY * sin(y))); 117 } 118 119 /* 120 * sinh(NaN + I NaN) = d(NaN) + I d(NaN). 121 * 122 * sinh(NaN +- I Inf) = d(NaN) + I d(NaN). 123 * Optionally raises the invalid floating-point exception. 124 * Choice = raise. 125 * 126 * sinh(NaN + I y) = d(NaN) + I d(NaN). 127 * Optionally raises the invalid floating-point exception for finite 128 * nonzero y. Choice = don't raise (except for signaling NaNs). 129 */ 130 return (cpack((x * x) * (y - y), (x + x) * (y - y))); 131 } 132 133 double complex 134 csin(double complex z) 135 { 136 137 /* csin(z) = -I * csinh(I * z) */ 138 z = csinh(cpack(-cimag(z), creal(z))); 139 return (cpack(cimag(z), -creal(z))); 140 } 141