1/* origin: OpenBSD /usr/src/lib/libm/src/s_catanl.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 * long double complex catanl(); 24 * long double complex z, w; 25 * 26 * w = catanl( 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 * 49 * ACCURACY: 50 * 51 * Relative error: 52 * arithmetic domain # trials peak rms 53 * DEC -10,+10 5900 1.3e-16 7.8e-18 54 * IEEE -10,+10 30000 2.3e-15 8.5e-17 55 * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2, 56 * had peak relative error 1.5e-16, rms relative error 57 * 2.9e-17. See also clog(). 58 */ 59 60#include <complex.h> 61#include <float.h> 62#include "libm.h" 63 64#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 65long double complex catanl(long double complex z) 66{ 67 return catan(z); 68} 69#else 70static const long double PIL = 3.141592653589793238462643383279502884197169L; 71static const long double DP1 = 3.14159265358979323829596852490908531763125L; 72static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L; 73static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L; 74 75static long double redupil(long double x) 76{ 77 long double t; 78 long i; 79 80 t = x / PIL; 81 if (t >= 0.0L) 82 t += 0.5L; 83 else 84 t -= 0.5L; 85 86 i = t; /* the multiple */ 87 t = i; 88 t = ((x - t * DP1) - t * DP2) - t * DP3; 89 return t; 90} 91 92long double complex catanl(long double complex z) 93{ 94 long double complex w; 95 long double a, t, x, x2, y; 96 97 x = creall(z); 98 y = cimagl(z); 99 100 if ((x == 0.0L) && (y > 1.0L)) 101 goto ovrf; 102 103 x2 = x * x; 104 a = 1.0L - x2 - (y * y); 105 if (a == 0.0L) 106 goto ovrf; 107 108 t = atan2l(2.0L * x, a) * 0.5L; 109 w = redupil(t); 110 111 t = y - 1.0L; 112 a = x2 + (t * t); 113 if (a == 0.0L) 114 goto ovrf; 115 116 t = y + 1.0L; 117 a = (x2 + (t * t)) / a; 118 w = w + (0.25L * logl(a)) * I; 119 return w; 120 121ovrf: 122 // FIXME 123 w = LDBL_MAX + LDBL_MAX * I; 124 return w; 125} 126#endif 127