1 /* $OpenBSD: s_catan.c,v 1.2 2011/07/08 19:25:31 martynas 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 /* LINTLIBRARY */ 19 20 /* catan() 21 * 22 * Complex circular arc tangent 23 * 24 * 25 * 26 * SYNOPSIS: 27 * 28 * double complex catan(); 29 * double complex z, w; 30 * 31 * w = catan (z); 32 * 33 * 34 * 35 * DESCRIPTION: 36 * 37 * If 38 * z = x + iy, 39 * 40 * then 41 * 1 ( 2x ) 42 * Re w = - arctan(-----------) + k PI 43 * 2 ( 2 2) 44 * (1 - x - y ) 45 * 46 * ( 2 2) 47 * 1 (x + (y+1) ) 48 * Im w = - log(------------) 49 * 4 ( 2 2) 50 * (x + (y-1) ) 51 * 52 * Where k is an arbitrary integer. 53 * 54 * catan(z) = -i catanh(iz). 55 * 56 * ACCURACY: 57 * 58 * Relative error: 59 * arithmetic domain # trials peak rms 60 * DEC -10,+10 5900 1.3e-16 7.8e-18 61 * IEEE -10,+10 30000 2.3e-15 8.5e-17 62 * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2, 63 * had peak relative error 1.5e-16, rms relative error 64 * 2.9e-17. See also clog(). 65 */ 66 67 #include <sys/cdefs.h> 68 #include <complex.h> 69 #include <float.h> 70 #include <math.h> 71 72 #define MAXNUM 1.0e308 73 74 static const double DP1 = 3.14159265160560607910E0; 75 static const double DP2 = 1.98418714791870343106E-9; 76 static const double DP3 = 1.14423774522196636802E-17; 77 78 static double 79 _redupi(double x) 80 { 81 double t; 82 long i; 83 84 t = x/M_PI; 85 if(t >= 0.0) 86 t += 0.5; 87 else 88 t -= 0.5; 89 90 i = t; /* the multiple */ 91 t = i; 92 t = ((x - t * DP1) - t * DP2) - t * DP3; 93 return (t); 94 } 95 96 double complex 97 catan(double complex z) 98 { 99 double complex w; 100 double a, t, x, x2, y; 101 102 x = creal (z); 103 y = cimag (z); 104 105 if ((x == 0.0) && (y > 1.0)) 106 goto ovrf; 107 108 x2 = x * x; 109 a = 1.0 - x2 - (y * y); 110 if (a == 0.0) 111 goto ovrf; 112 113 t = 0.5 * atan2 (2.0 * x, a); 114 w = _redupi (t); 115 116 t = y - 1.0; 117 a = x2 + (t * t); 118 if (a == 0.0) 119 goto ovrf; 120 121 t = y + 1.0; 122 a = (x2 + (t * t))/a; 123 w = w + (0.25 * log (a)) * I; 124 return (w); 125 126 ovrf: 127 /*mtherr ("catan", OVERFLOW);*/ 128 w = MAXNUM + MAXNUM * I; 129 return (w); 130 } 131 132 #if LDBL_MANT_DIG == 53 133 #ifdef lint 134 /* PROTOLIB1 */ 135 long double complex catanl(long double complex); 136 #else /* lint */ 137 __weak_alias(catanl, catan); 138 #endif /* lint */ 139 #endif /* LDBL_MANT_DIG == 53 */ 140