1 /* $OpenBSD: s_catanl.c,v 1.4 2016/09/12 19:47:02 guenther Exp $ */ 2 3 /* 4 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> 5 * 6 * Permission to use, copy, modify, and distribute this software for any 7 * purpose with or without fee is hereby granted, provided that the above 8 * copyright notice and this permission notice appear in all copies. 9 * 10 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 11 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 12 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 13 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 14 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 15 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 16 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 17 */ 18 19 /* catanl() 20 * 21 * Complex circular arc tangent 22 * 23 * 24 * 25 * SYNOPSIS: 26 * 27 * long double complex catanl(); 28 * long double complex z, w; 29 * 30 * w = catanl( z ); 31 * 32 * 33 * 34 * DESCRIPTION: 35 * 36 * If 37 * z = x + iy, 38 * 39 * then 40 * 1 ( 2x ) 41 * Re w = - arctan(-----------) + k PI 42 * 2 ( 2 2) 43 * (1 - x - y ) 44 * 45 * ( 2 2) 46 * 1 (x + (y+1) ) 47 * Im w = - log(------------) 48 * 4 ( 2 2) 49 * (x + (y-1) ) 50 * 51 * Where k is an arbitrary integer. 52 * 53 * 54 * 55 * ACCURACY: 56 * 57 * Relative error: 58 * arithmetic domain # trials peak rms 59 * DEC -10,+10 5900 1.3e-16 7.8e-18 60 * IEEE -10,+10 30000 2.3e-15 8.5e-17 61 * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2, 62 * had peak relative error 1.5e-16, rms relative error 63 * 2.9e-17. See also clog(). 64 */ 65 66 #include <complex.h> 67 #include <float.h> 68 #include <math.h> 69 70 static const long double PIL = 3.141592653589793238462643383279502884197169L; 71 static const long double DP1 = 3.14159265358979323829596852490908531763125L; 72 static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L; 73 static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L; 74 75 static long double 76 redupil(long double x) 77 { 78 long double t; 79 long i; 80 81 t = x / PIL; 82 if (t >= 0.0L) 83 t += 0.5L; 84 else 85 t -= 0.5L; 86 87 i = t; /* the multiple */ 88 t = i; 89 t = ((x - t * DP1) - t * DP2) - t * DP3; 90 return (t); 91 } 92 93 long double complex 94 catanl(long double complex z) 95 { 96 long double complex w; 97 long double a, t, x, x2, y; 98 99 x = creall(z); 100 y = cimagl(z); 101 102 if ((x == 0.0L) && (y > 1.0L)) 103 goto ovrf; 104 105 x2 = x * x; 106 a = 1.0L - x2 - (y * y); 107 if (a == 0.0L) 108 goto ovrf; 109 110 t = atan2l(2.0L * x, a) * 0.5L; 111 w = redupil(t); 112 113 t = y - 1.0L; 114 a = x2 + (t * t); 115 if (a == 0.0L) 116 goto ovrf; 117 118 t = y + 1.0L; 119 a = (x2 + (t * t)) / a; 120 w = w + (0.25L * logl(a)) * I; 121 return (w); 122 123 ovrf: 124 /*mtherr( "catanl", OVERFLOW );*/ 125 w = LDBL_MAX + LDBL_MAX * I; 126 return (w); 127 } 128 DEF_STD(catanl); 129