1 /* $OpenBSD: s_csinl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ 2 3 /* 4 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> 5 * 6 * Permission to use, copy, modify, and distribute this software for any 7 * purpose with or without fee is hereby granted, provided that the above 8 * copyright notice and this permission notice appear in all copies. 9 * 10 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 11 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 12 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 13 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 14 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 15 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 16 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 17 */ 18 19 /* csinl() 20 * 21 * Complex circular sine 22 * 23 * 24 * 25 * SYNOPSIS: 26 * 27 * long double complex csinl(); 28 * long double complex z, w; 29 * 30 * w = csinl( z ); 31 * 32 * 33 * 34 * DESCRIPTION: 35 * 36 * If 37 * z = x + iy, 38 * 39 * then 40 * 41 * w = sin x cosh y + i cos x sinh y. 42 * 43 * 44 * 45 * ACCURACY: 46 * 47 * Relative error: 48 * arithmetic domain # trials peak rms 49 * DEC -10,+10 8400 5.3e-17 1.3e-17 50 * IEEE -10,+10 30000 3.8e-16 1.0e-16 51 * Also tested by csin(casin(z)) = z. 52 * 53 */ 54 55 #include <complex.h> 56 #include <math.h> 57 58 static void 59 cchshl(long double x, long double *c, long double *s) 60 { 61 long double e, ei; 62 63 if(fabsl(x) <= 0.5L) { 64 *c = coshl(x); 65 *s = sinhl(x); 66 } else { 67 e = expl(x); 68 ei = 0.5L/e; 69 e = 0.5L * e; 70 *s = e - ei; 71 *c = e + ei; 72 } 73 } 74 75 long double complex 76 csinl(long double complex z) 77 { 78 long double complex w; 79 long double ch, sh; 80 81 cchshl(cimagl(z), &ch, &sh); 82 w = sinl(creall(z)) * ch + (cosl(creall(z)) * sh) * I; 83 return (w); 84 } 85