1 /* $OpenBSD: s_csin.c,v 1.2 2011/07/08 19:25:31 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 /* LINTLIBRARY */ 19 20 /* csin() 21 * 22 * Complex circular sine 23 * 24 * 25 * 26 * SYNOPSIS: 27 * 28 * double complex csin(); 29 * double complex z, w; 30 * 31 * w = csin (z); 32 * 33 * 34 * 35 * DESCRIPTION: 36 * 37 * If 38 * z = x + iy, 39 * 40 * then 41 * 42 * w = sin x cosh y + i cos x sinh y. 43 * 44 * csin(z) = -i csinh(iz). 45 * 46 * ACCURACY: 47 * 48 * Relative error: 49 * arithmetic domain # trials peak rms 50 * DEC -10,+10 8400 5.3e-17 1.3e-17 51 * IEEE -10,+10 30000 3.8e-16 1.0e-16 52 * Also tested by csin(casin(z)) = z. 53 * 54 */ 55 56 #include <sys/cdefs.h> 57 #include <complex.h> 58 #include <float.h> 59 #include <math.h> 60 61 /* calculate cosh and sinh */ 62 63 static void 64 cchsh(double x, double *c, double *s) 65 { 66 double e, ei; 67 68 if (fabs(x) <= 0.5) { 69 *c = cosh(x); 70 *s = sinh(x); 71 } 72 else { 73 e = exp(x); 74 ei = 0.5/e; 75 e = 0.5 * e; 76 *s = e - ei; 77 *c = e + ei; 78 } 79 } 80 81 double complex 82 csin(double complex z) 83 { 84 double complex w; 85 double ch, sh; 86 87 cchsh( cimag (z), &ch, &sh ); 88 w = sin (creal(z)) * ch + (cos (creal(z)) * sh) * I; 89 return (w); 90 } 91 92 #if LDBL_MANT_DIG == 53 93 #ifdef lint 94 /* PROTOLIB1 */ 95 long double complex csinl(long double complex); 96 #else /* lint */ 97 __weak_alias(csinl, csin); 98 #endif /* lint */ 99 #endif /* LDBL_MANT_DIG == 53 */ 100