1 /* $OpenBSD: s_csin.c,v 1.1 2008/09/07 20:36:09 martynas Exp $ */ 2 /* 3 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> 4 * 5 * Permission to use, copy, modify, and distribute this software for any 6 * purpose with or without fee is hereby granted, provided that the above 7 * copyright notice and this permission notice appear in all copies. 8 * 9 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 10 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 11 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 12 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 13 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 14 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 15 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 16 */ 17 18 /* csin() 19 * 20 * Complex circular sine 21 * 22 * 23 * 24 * SYNOPSIS: 25 * 26 * double complex csin(); 27 * double complex z, w; 28 * 29 * w = csin (z); 30 * 31 * 32 * 33 * DESCRIPTION: 34 * 35 * If 36 * z = x + iy, 37 * 38 * then 39 * 40 * w = sin x cosh y + i cos x sinh y. 41 * 42 * csin(z) = -i csinh(iz). 43 * 44 * ACCURACY: 45 * 46 * Relative error: 47 * arithmetic domain # trials peak rms 48 * DEC -10,+10 8400 5.3e-17 1.3e-17 49 * IEEE -10,+10 30000 3.8e-16 1.0e-16 50 * Also tested by csin(casin(z)) = z. 51 * 52 */ 53 54 #include <complex.h> 55 #include <math.h> 56 57 /* calculate cosh and sinh */ 58 59 static void 60 cchsh(double x, double *c, double *s) 61 { 62 double e, ei; 63 64 if (fabs(x) <= 0.5) { 65 *c = cosh(x); 66 *s = sinh(x); 67 } 68 else { 69 e = exp(x); 70 ei = 0.5/e; 71 e = 0.5 * e; 72 *s = e - ei; 73 *c = e + ei; 74 } 75 } 76 77 double complex 78 csin(double complex z) 79 { 80 double complex w; 81 double ch, sh; 82 83 cchsh( cimag (z), &ch, &sh ); 84 w = sin (creal(z)) * ch + (cos (creal(z)) * sh) * I; 85 return (w); 86 } 87