1/* origin: OpenBSD /usr/src/lib/libm/src/s_catan.c */ 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 * Complex circular arc tangent 19 * 20 * 21 * SYNOPSIS: 22 * 23 * double complex catan(); 24 * double complex z, w; 25 * 26 * w = catan (z); 27 * 28 * 29 * DESCRIPTION: 30 * 31 * If 32 * z = x + iy, 33 * 34 * then 35 * 1 ( 2x ) 36 * Re w = - arctan(-----------) + k PI 37 * 2 ( 2 2) 38 * (1 - x - y ) 39 * 40 * ( 2 2) 41 * 1 (x + (y+1) ) 42 * Im w = - log(------------) 43 * 4 ( 2 2) 44 * (x + (y-1) ) 45 * 46 * Where k is an arbitrary integer. 47 * 48 * catan(z) = -i catanh(iz). 49 * 50 * ACCURACY: 51 * 52 * Relative error: 53 * arithmetic domain # trials peak rms 54 * DEC -10,+10 5900 1.3e-16 7.8e-18 55 * IEEE -10,+10 30000 2.3e-15 8.5e-17 56 * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2, 57 * had peak relative error 1.5e-16, rms relative error 58 * 2.9e-17. See also clog(). 59 */ 60 61#include "libm.h" 62 63#define MAXNUM 1.0e308 64 65static const double DP1 = 3.14159265160560607910E0; 66static const double DP2 = 1.98418714791870343106E-9; 67static const double DP3 = 1.14423774522196636802E-17; 68 69static double _redupi(double x) 70{ 71 double t; 72 long i; 73 74 t = x/M_PI; 75 if (t >= 0.0) 76 t += 0.5; 77 else 78 t -= 0.5; 79 80 i = t; /* the multiple */ 81 t = i; 82 t = ((x - t * DP1) - t * DP2) - t * DP3; 83 return t; 84} 85 86double complex catan(double complex z) 87{ 88 double complex w; 89 double a, t, x, x2, y; 90 91 x = creal(z); 92 y = cimag(z); 93 94 if (x == 0.0 && y > 1.0) 95 goto ovrf; 96 97 x2 = x * x; 98 a = 1.0 - x2 - (y * y); 99 if (a == 0.0) 100 goto ovrf; 101 102 t = 0.5 * atan2(2.0 * x, a); 103 w = _redupi(t); 104 105 t = y - 1.0; 106 a = x2 + (t * t); 107 if (a == 0.0) 108 goto ovrf; 109 110 t = y + 1.0; 111 a = (x2 + t * t)/a; 112 w = w + (0.25 * log(a)) * I; 113 return w; 114 115ovrf: 116 // FIXME 117 w = MAXNUM + MAXNUM * I; 118 return w; 119} 120