1 /* $NetBSD: cephes_subrl.c,v 1.2 2014/10/10 14:06:40 christos Exp $ */ 2 3 /*- 4 * Copyright (c) 2007 The NetBSD Foundation, Inc. 5 * All rights reserved. 6 * 7 * This code is derived from software written by Stephen L. Moshier. 8 * It is redistributed by the NetBSD Foundation by permission of the author. 9 * 10 * Redistribution and use in source and binary forms, with or without 11 * modification, are permitted provided that the following conditions 12 * are met: 13 * 1. Redistributions of source code must retain the above copyright 14 * notice, this list of conditions and the following disclaimer. 15 * 2. Redistributions in binary form must reproduce the above copyright 16 * notice, this list of conditions and the following disclaimer in the 17 * documentation and/or other materials provided with the distribution. 18 * 19 * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS 20 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED 21 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 22 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS 23 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 24 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 25 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 26 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 27 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 28 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 29 * POSSIBILITY OF SUCH DAMAGE. 30 */ 31 32 #include "../src/namespace.h" 33 #include <complex.h> 34 #include <math.h> 35 #include "cephes_subrl.h" 36 37 /* calculate cosh and sinh */ 38 39 void 40 _cchshl(long double x, long double *c, long double *s) 41 { 42 long double e, ei; 43 44 if (fabsl(x) <= 0.5L) { 45 *c = coshl(x); 46 *s = sinhl(x); 47 } else { 48 e = expl(x); 49 ei = 0.5L / e; 50 e = 0.5L * e; 51 *s = e - ei; 52 *c = e + ei; 53 } 54 } 55 56 /* Program to subtract nearest integer multiple of PI */ 57 58 /* extended precision value of PI: */ 59 static const long double DP1 = 3.14159265358979323829596852490908531763125L; 60 static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L; 61 #ifndef __vax__ 62 static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L; 63 #define MACHEPL 1.1e-38L 64 #else 65 static const long double DP3 = 0L; 66 #define MACHEPL 1.1e-19L 67 #endif 68 69 long double 70 _redupil(long double x) 71 { 72 long double t; 73 long long i; 74 75 t = x / M_PIL; 76 if (t >= 0.0L) 77 t += 0.5L; 78 else 79 t -= 0.5L; 80 81 i = t; /* the multiple */ 82 t = i; 83 t = ((x - t * DP1) - t * DP2) - t * DP3; 84 return t; 85 } 86 87 /* Taylor series expansion for cosh(2y) - cos(2x) */ 88 89 long double 90 _ctansl(long double complex z) 91 { 92 long double f, x, x2, y, y2, rn, t; 93 long double d; 94 95 x = fabsl(2.0L * creall(z)); 96 y = fabsl(2.0L * cimagl(z)); 97 98 x = _redupil(x); 99 100 x = x * x; 101 y = y * y; 102 x2 = 1.0; 103 y2 = 1.0; 104 f = 1.0; 105 rn = 0.0; 106 d = 0.0; 107 do { 108 rn += 1.0L; 109 f *= rn; 110 rn += 1.0L; 111 f *= rn; 112 x2 *= x; 113 y2 *= y; 114 t = y2 + x2; 115 t /= f; 116 d += t; 117 118 rn += 1.0L; 119 f *= rn; 120 rn += 1.0L; 121 f *= rn; 122 x2 *= x; 123 y2 *= y; 124 t = y2 - x2; 125 t /= f; 126 d += t; 127 } while (fabsl(t/d) > MACHEPL); 128 return d; 129 } 130
