1 /* $OpenBSD: s_casinf.c,v 1.5 2016/09/12 19:47:02 guenther 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 = crealf(z); 66 y = cimagf(z); 67 68 #if 0 69 if(y == 0.0f) { 70 if(fabsf(x) > 1.0f) { 71 w = (float)M_PI_2 + 0.0f * I; 72 /*mtherr( "casinf", DOMAIN );*/ 73 } 74 else { 75 w = asinf (x) + 0.0f * I; 76 } 77 return (w); 78 } 79 #endif 80 81 /* Power series expansion */ 82 /* 83 b = cabsf(z); 84 if(b < 0.125) { 85 z2.r = (x - y) * (x + y); 86 z2.i = 2.0 * x * y; 87 88 cn = 1.0; 89 n = 1.0; 90 ca.r = x; 91 ca.i = y; 92 sum.r = x; 93 sum.i = y; 94 do { 95 ct.r = z2.r * ca.r - z2.i * ca.i; 96 ct.i = z2.r * ca.i + z2.i * ca.r; 97 ca.r = ct.r; 98 ca.i = ct.i; 99 100 cn *= n; 101 n += 1.0; 102 cn /= n; 103 n += 1.0; 104 b = cn/n; 105 106 ct.r *= b; 107 ct.i *= b; 108 sum.r += ct.r; 109 sum.i += ct.i; 110 b = fabsf(ct.r) + fabsf(ct.i); 111 } 112 while(b > MACHEPF); 113 w->r = sum.r; 114 w->i = sum.i; 115 return; 116 } 117 */ 118 119 120 ca = x + y * I; 121 ct = ca * I; /* iz */ 122 /* sqrt( 1 - z*z) */ 123 /* cmul( &ca, &ca, &zz ) */ 124 /*x * x - y * y */ 125 zz = (x - y) * (x + y) + (2.0f * x * y) * I; 126 zz = 1.0f - crealf(zz) - cimagf(zz) * I; 127 z2 = csqrtf (zz); 128 129 zz = ct + z2; 130 zz = clogf (zz); 131 /* multiply by 1/i = -i */ 132 w = zz * (-1.0f * I); 133 return (w); 134 } 135 DEF_STD(casinf); 136