1 /* $NetBSD: cephes_subrf.c,v 1.1 2007/08/20 16:01:34 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_subrf.h" 36 37 /* calculate cosh and sinh */ 38 39 void 40 _cchshf(float x, float *c, float *s) 41 { 42 float e, ei; 43 44 if (fabsf(x) <= 0.5f) { 45 *c = coshf(x); 46 *s = sinhf(x); 47 } else { 48 e = expf(x); 49 ei = 0.5f / e; 50 e = 0.5f * 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 = 3.140625; 60 static const double DP2 = 9.67502593994140625E-4; 61 static const double DP3 = 1.509957990978376432E-7; 62 #define MACHEPF 3.0e-8 63 64 float 65 _redupif(float x) 66 { 67 float t; 68 long i; 69 70 t = x / (float)M_PI; 71 if (t >= 0.0f) 72 t += 0.5f; 73 else 74 t -= 0.5f; 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 float 85 _ctansf(float complex z) 86 { 87 float f, x, x2, y, y2, rn, t, d; 88 89 x = fabsf(2.0f * crealf(z)); 90 y = fabsf(2.0f * cimagf(z)); 91 92 x = _redupif(x); 93 94 x = x * x; 95 y = y * y; 96 x2 = 1.0f; 97 y2 = 1.0f; 98 f = 1.0f; 99 rn = 0.0f; 100 d = 0.0f; 101 do { 102 rn += 1.0f; 103 f *= rn; 104 rn += 1.0f; 105 f *= rn; 106 x2 *= x; 107 y2 *= y; 108 t = y2 + x2; 109 t /= f; 110 d += t; 111 112 rn += 1.0f; 113 f *= rn; 114 rn += 1.0f; 115 f *= rn; 116 x2 *= x; 117 y2 *= y; 118 t = y2 - x2; 119 t /= f; 120 d += t; 121 } while (fabsf(t/d) > MACHEPF); 122 return d; 123 } 124