[444] | 1 | /* $NetBSD: cephes_subr.c,v 1.1 2007/08/20 16:01:33 drochner Exp $ */ |
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| 2 | |
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| 3 | /*- |
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| 4 | * Copyright (c) 2007 The NetBSD Foundation, Inc. |
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| 5 | * All rights reserved. |
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| 6 | * |
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| 7 | * This code is derived from software written by Stephen L. Moshier. |
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| 8 | * It is redistributed by the NetBSD Foundation by permission of the author. |
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| 9 | * |
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| 10 | * Redistribution and use in source and binary forms, with or without |
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| 11 | * modification, are permitted provided that the following conditions |
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| 12 | * are met: |
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| 13 | * 1. Redistributions of source code must retain the above copyright |
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| 14 | * notice, this list of conditions and the following disclaimer. |
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| 15 | * 2. Redistributions in binary form must reproduce the above copyright |
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| 16 | * notice, this list of conditions and the following disclaimer in the |
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| 17 | * documentation and/or other materials provided with the distribution. |
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| 18 | * |
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| 19 | * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS |
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| 20 | * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED |
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| 21 | * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
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| 22 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS |
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| 23 | * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
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| 24 | * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
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| 25 | * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
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| 26 | * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
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| 27 | * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
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| 28 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
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| 29 | * POSSIBILITY OF SUCH DAMAGE. |
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| 30 | * |
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| 31 | * imported and modified include for newlib 2010/10/03 |
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| 32 | * Marco Atzeri <marco_atzeri@yahoo.it> |
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| 33 | */ |
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| 34 | |
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| 35 | #include <complex.h> |
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| 36 | #include <math.h> |
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| 37 | #include "cephes_subr.h" |
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| 38 | |
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| 39 | /* calculate cosh and sinh */ |
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| 40 | |
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| 41 | void |
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| 42 | _cchsh(double x, double *c, double *s) |
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| 43 | { |
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| 44 | double e, ei; |
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| 45 | |
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| 46 | if (fabs(x) <= 0.5) { |
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| 47 | *c = cosh(x); |
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| 48 | *s = sinh(x); |
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| 49 | } else { |
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| 50 | e = exp(x); |
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| 51 | ei = 0.5 / e; |
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| 52 | e = 0.5 * e; |
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| 53 | *s = e - ei; |
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| 54 | *c = e + ei; |
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| 55 | } |
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| 56 | } |
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| 57 | |
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| 58 | /* Program to subtract nearest integer multiple of PI */ |
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| 59 | |
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| 60 | /* extended precision value of PI: */ |
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| 61 | static const double DP1 = 3.14159265160560607910E0; |
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| 62 | static const double DP2 = 1.98418714791870343106E-9; |
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| 63 | static const double DP3 = 1.14423774522196636802E-17; |
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| 64 | #define MACHEP 1.1e-16 |
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| 65 | |
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| 66 | double |
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| 67 | _redupi(double x) |
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| 68 | { |
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| 69 | double t; |
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| 70 | long i; |
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| 71 | |
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| 72 | t = x / M_PI; |
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| 73 | if (t >= 0.0) |
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| 74 | t += 0.5; |
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| 75 | else |
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| 76 | t -= 0.5; |
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| 77 | |
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| 78 | i = t; /* the multiple */ |
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| 79 | t = i; |
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| 80 | t = ((x - t * DP1) - t * DP2) - t * DP3; |
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| 81 | return t; |
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| 82 | } |
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| 83 | |
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| 84 | /* Taylor series expansion for cosh(2y) - cos(2x) */ |
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| 85 | |
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| 86 | double |
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| 87 | _ctans(double complex z) |
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| 88 | { |
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| 89 | double f, x, x2, y, y2, rn, t; |
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| 90 | double d; |
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| 91 | |
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| 92 | x = fabs(2.0 * creal(z)); |
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| 93 | y = fabs(2.0 * cimag(z)); |
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| 94 | |
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| 95 | x = _redupi(x); |
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| 96 | |
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| 97 | x = x * x; |
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| 98 | y = y * y; |
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| 99 | x2 = 1.0; |
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| 100 | y2 = 1.0; |
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| 101 | f = 1.0; |
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| 102 | rn = 0.0; |
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| 103 | d = 0.0; |
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| 104 | do { |
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| 105 | rn += 1.0; |
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| 106 | f *= rn; |
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| 107 | rn += 1.0; |
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| 108 | f *= rn; |
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| 109 | x2 *= x; |
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| 110 | y2 *= y; |
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| 111 | t = y2 + x2; |
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| 112 | t /= f; |
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| 113 | d += t; |
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| 114 | |
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| 115 | rn += 1.0; |
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| 116 | f *= rn; |
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| 117 | rn += 1.0; |
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| 118 | f *= rn; |
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| 119 | x2 *= x; |
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| 120 | y2 *= y; |
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| 121 | t = y2 - x2; |
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| 122 | t /= f; |
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| 123 | d += t; |
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| 124 | } while (fabs(t/d) > MACHEP); |
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| 125 | return d; |
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| 126 | } |
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