1 /* $NetBSD: cephes_subr.c,v 1.1 2007/08/20 16:01:33 drochner 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_subr.h" 36 37 /* calculate cosh and sinh */ 38 39 void 40 _cchsh(double x, double *c, double *s) 41 { 42 double e, ei; 43 44 if (fabs(x) <= 0.5) { 45 *c = cosh(x); 46 *s = sinh(x); 47 } else { 48 e = exp(x); 49 ei = 0.5 / e; 50 e = 0.5 * 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 double DP1 = 3.14159265160560607910E0; 60 static const double DP2 = 1.98418714791870343106E-9; 61 static const double DP3 = 1.14423774522196636802E-17; 62 #define MACHEP 1.1e-16 63 64 double 65 _redupi(double x) 66 { 67 double t; 68 long i; 69 70 t = x / M_PI; 71 if (t >= 0.0) 72 t += 0.5; 73 else 74 t -= 0.5; 75 76 i = t; /* the multiple */ 77 t = i; 78 t = ((x - t * DP1) - t * DP2) - t * DP3; 79 return t; 80 } 81 82 /* Taylor series expansion for cosh(2y) - cos(2x) */ 83 84 double 85 _ctans(double complex z) 86 { 87 double f, x, x2, y, y2, rn, t; 88 double d; 89 90 x = fabs(2.0 * creal(z)); 91 y = fabs(2.0 * cimag(z)); 92 93 x = _redupi(x); 94 95 x = x * x; 96 y = y * y; 97 x2 = 1.0; 98 y2 = 1.0; 99 f = 1.0; 100 rn = 0.0; 101 d = 0.0; 102 do { 103 rn += 1.0; 104 f *= rn; 105 rn += 1.0; 106 f *= rn; 107 x2 *= x; 108 y2 *= y; 109 t = y2 + x2; 110 t /= f; 111 d += t; 112 113 rn += 1.0; 114 f *= rn; 115 rn += 1.0; 116 f *= rn; 117 x2 *= x; 118 y2 *= y; 119 t = y2 - x2; 120 t /= f; 121 d += t; 122 } while (fabs(t/d) > MACHEP); 123 return d; 124 } 125