1 /* $OpenBSD: s_ccos.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 /* ccos() 19 * 20 * Complex circular cosine 21 * 22 * 23 * 24 * SYNOPSIS: 25 * 26 * double complex ccos(); 27 * double complex z, w; 28 * 29 * w = ccos (z); 30 * 31 * 32 * 33 * DESCRIPTION: 34 * 35 * If 36 * z = x + iy, 37 * 38 * then 39 * 40 * w = cos x cosh y - i sin x sinh y. 41 * 42 * 43 * 44 * ACCURACY: 45 * 46 * Relative error: 47 * arithmetic domain # trials peak rms 48 * DEC -10,+10 8400 4.5e-17 1.3e-17 49 * IEEE -10,+10 30000 3.8e-16 1.0e-16 50 */ 51 52 #include <complex.h> 53 #include <float.h> 54 #include <math.h> 55 56 /* calculate cosh and sinh */ 57 58 static void 59 _cchsh(double x, double *c, double *s) 60 { 61 double e, ei; 62 63 if (fabs(x) <= 0.5) { 64 *c = cosh(x); 65 *s = sinh(x); 66 } 67 else { 68 e = exp(x); 69 ei = 0.5/e; 70 e = 0.5 * e; 71 *s = e - ei; 72 *c = e + ei; 73 } 74 } 75 76 double complex 77 ccos(double complex z) 78 { 79 double complex w; 80 double ch, sh; 81 82 _cchsh( cimag(z), &ch, &sh ); 83 w = cos(creal (z)) * ch - (sin (creal (z)) * sh) * I; 84 return (w); 85 } 86 87 #if LDBL_MANT_DIG == DBL_MANT_DIG 88 __strong_alias(ccosl, ccos); 89 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 90