1 /* $OpenBSD: s_catanf.c,v 1.3 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 /* catanf() 19 * 20 * Complex circular arc tangent 21 * 22 * 23 * 24 * SYNOPSIS: 25 * 26 * float complex catanf(); 27 * float complex z, w; 28 * 29 * w = catanf( z ); 30 * 31 * 32 * 33 * DESCRIPTION: 34 * 35 * If 36 * z = x + iy, 37 * 38 * then 39 * 1 ( 2x ) 40 * Re w = - arctan(-----------) + k PI 41 * 2 ( 2 2) 42 * (1 - x - y ) 43 * 44 * ( 2 2) 45 * 1 (x + (y+1) ) 46 * Im w = - log(------------) 47 * 4 ( 2 2) 48 * (x + (y-1) ) 49 * 50 * Where k is an arbitrary integer. 51 * 52 * 53 * 54 * ACCURACY: 55 * 56 * Relative error: 57 * arithmetic domain # trials peak rms 58 * IEEE -10,+10 30000 2.3e-6 5.2e-8 59 * 60 */ 61 62 #include <complex.h> 63 #include <math.h> 64 65 #define MAXNUMF 1.0e38F 66 67 static const double DP1 = 3.140625; 68 static const double DP2 = 9.67502593994140625E-4; 69 static const double DP3 = 1.509957990978376432E-7; 70 71 static float 72 _redupif(float xx) 73 { 74 float x, t; 75 long i; 76 77 x = xx; 78 t = x/(float)M_PI; 79 if(t >= 0.0) 80 t += 0.5; 81 else 82 t -= 0.5; 83 84 i = t; /* the multiple */ 85 t = i; 86 t = ((x - t * DP1) - t * DP2) - t * DP3; 87 return(t); 88 } 89 90 float complex 91 catanf(float complex z) 92 { 93 float complex w; 94 float a, t, x, x2, y; 95 96 x = crealf(z); 97 y = cimagf(z); 98 99 if((x == 0.0f) && (y > 1.0f)) 100 goto ovrf; 101 102 x2 = x * x; 103 a = 1.0f - x2 - (y * y); 104 if (a == 0.0f) 105 goto ovrf; 106 107 t = 0.5f * atan2f(2.0f * x, a); 108 w = _redupif(t); 109 110 t = y - 1.0f; 111 a = x2 + (t * t); 112 if(a == 0.0f) 113 goto ovrf; 114 115 t = y + 1.0f; 116 a = (x2 + (t * t))/a; 117 w = w + (0.25f * logf (a)) * I; 118 return (w); 119 120 ovrf: 121 /*mtherr( "catanf", OVERFLOW );*/ 122 w = MAXNUMF + MAXNUMF * I; 123 return (w); 124 } 125 DEF_STD(catanf); 126