1 /* $OpenBSD: s_csin.c,v 1.6 2013/07/03 04:46:36 espie 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 <float.h> 56 #include <math.h> 57 58 /* calculate cosh and sinh */ 59 60 static void 61 cchsh(double x, double *c, double *s) 62 { 63 double e, ei; 64 65 if (fabs(x) <= 0.5) { 66 *c = cosh(x); 67 *s = sinh(x); 68 } 69 else { 70 e = exp(x); 71 ei = 0.5/e; 72 e = 0.5 * e; 73 *s = e - ei; 74 *c = e + ei; 75 } 76 } 77 78 double complex 79 csin(double complex z) 80 { 81 double complex w; 82 double ch, sh; 83 84 cchsh( cimag (z), &ch, &sh ); 85 w = sin (creal(z)) * ch + (cos (creal(z)) * sh) * I; 86 return (w); 87 } 88 89 #if LDBL_MANT_DIG == DBL_MANT_DIG 90 __strong_alias(csinl, csin); 91 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 92