1 /* $OpenBSD: s_catan.c,v 1.7 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 /* catan() 19 * 20 * Complex circular arc tangent 21 * 22 * 23 * 24 * SYNOPSIS: 25 * 26 * double complex catan(); 27 * double complex z, w; 28 * 29 * w = catan (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 * catan(z) = -i catanh(iz). 53 * 54 * ACCURACY: 55 * 56 * Relative error: 57 * arithmetic domain # trials peak rms 58 * DEC -10,+10 5900 1.3e-16 7.8e-18 59 * IEEE -10,+10 30000 2.3e-15 8.5e-17 60 * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2, 61 * had peak relative error 1.5e-16, rms relative error 62 * 2.9e-17. See also clog(). 63 */ 64 65 #include <complex.h> 66 #include <float.h> 67 #include <math.h> 68 69 #define MAXNUM 1.0e308 70 71 static const double DP1 = 3.14159265160560607910E0; 72 static const double DP2 = 1.98418714791870343106E-9; 73 static const double DP3 = 1.14423774522196636802E-17; 74 75 static double 76 _redupi(double x) 77 { 78 double t; 79 long i; 80 81 t = x/M_PI; 82 if(t >= 0.0) 83 t += 0.5; 84 else 85 t -= 0.5; 86 87 i = t; /* the multiple */ 88 t = i; 89 t = ((x - t * DP1) - t * DP2) - t * DP3; 90 return (t); 91 } 92 93 double complex 94 catan(double complex z) 95 { 96 double complex w; 97 double a, t, x, x2, y; 98 99 x = creal (z); 100 y = cimag (z); 101 102 if ((x == 0.0) && (y > 1.0)) 103 goto ovrf; 104 105 x2 = x * x; 106 a = 1.0 - x2 - (y * y); 107 if (a == 0.0) 108 goto ovrf; 109 110 t = 0.5 * atan2 (2.0 * x, a); 111 w = _redupi (t); 112 113 t = y - 1.0; 114 a = x2 + (t * t); 115 if (a == 0.0) 116 goto ovrf; 117 118 t = y + 1.0; 119 a = (x2 + (t * t))/a; 120 w = w + (0.25 * log (a)) * I; 121 return (w); 122 123 ovrf: 124 /*mtherr ("catan", OVERFLOW);*/ 125 w = MAXNUM + MAXNUM * I; 126 return (w); 127 } 128 DEF_STD(catan); 129 LDBL_MAYBE_CLONE(catan); 130