1 /* $OpenBSD: s_casinf.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 /* casinf() 19 * 20 * Complex circular arc sine 21 * 22 * 23 * 24 * SYNOPSIS: 25 * 26 * void casinf(); 27 * cmplxf z, w; 28 * 29 * casinf( &z, &w ); 30 * 31 * 32 * 33 * DESCRIPTION: 34 * 35 * Inverse complex sine: 36 * 37 * 2 38 * w = -i clog( iz + csqrt( 1 - z ) ). 39 * 40 * 41 * ACCURACY: 42 * 43 * Relative error: 44 * arithmetic domain # trials peak rms 45 * IEEE -10,+10 30000 1.1e-5 1.5e-6 46 * Larger relative error can be observed for z near zero. 47 * 48 */ 49 50 #include <complex.h> 51 #include <math.h> 52 53 float complex 54 casinf(float complex z) 55 { 56 float complex w; 57 float x, y; 58 static float complex ca, ct, zz, z2; 59 /* 60 float cn, n; 61 static float a, b, s, t, u, v, y2; 62 static cmplxf sum; 63 */ 64 65 x = creal(z); 66 y = cimag(z); 67 68 if(y == 0.0f) { 69 if(fabsf(x) > 1.0f) { 70 w = M_PI_2 + 0.0f * I; 71 /*mtherr( "casinf", DOMAIN );*/ 72 } 73 else { 74 w = asinf (x) + 0.0f * I; 75 } 76 return (w); 77 } 78 79 /* Power series expansion */ 80 /* 81 b = cabsf(z); 82 if(b < 0.125) { 83 z2.r = (x - y) * (x + y); 84 z2.i = 2.0 * x * y; 85 86 cn = 1.0; 87 n = 1.0; 88 ca.r = x; 89 ca.i = y; 90 sum.r = x; 91 sum.i = y; 92 do { 93 ct.r = z2.r * ca.r - z2.i * ca.i; 94 ct.i = z2.r * ca.i + z2.i * ca.r; 95 ca.r = ct.r; 96 ca.i = ct.i; 97 98 cn *= n; 99 n += 1.0; 100 cn /= n; 101 n += 1.0; 102 b = cn/n; 103 104 ct.r *= b; 105 ct.i *= b; 106 sum.r += ct.r; 107 sum.i += ct.i; 108 b = fabsf(ct.r) + fabsf(ct.i); 109 } 110 while(b > MACHEPF); 111 w->r = sum.r; 112 w->i = sum.i; 113 return; 114 } 115 */ 116 117 118 ca = x + y * I; 119 ct = ca * I; /* iz */ 120 /* sqrt( 1 - z*z) */ 121 /* cmul( &ca, &ca, &zz ) */ 122 /*x * x - y * y */ 123 zz = (x - y) * (x + y) + (2.0f * x * y) * I; 124 zz = 1.0f - creal(zz) - cimag(zz) * I; 125 z2 = csqrtf (zz); 126 127 zz = ct + z2; 128 zz = clogf (zz); 129 /* multiply by 1/i = -i */ 130 w = zz * (-1.0f * I); 131 return (w); 132 } 133