| 1 | /* $NetBSD: csqrt.c,v 1.1 2007/08/20 16:01:37 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 | /* |
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| 36 | FUNCTION |
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| 37 | <<csqrt>>, <<csqrtf>>---complex square root |
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| 38 | |
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| 39 | INDEX |
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| 40 | csqrt |
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| 41 | INDEX |
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| 42 | csqrtf |
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| 43 | |
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| 44 | SYNOPSIS |
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| 45 | #include <complex.h> |
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| 46 | double complex csqrt(double complex <[z]>); |
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| 47 | float complex csqrtf(float complex <[z]>); |
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| 48 | |
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| 49 | |
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| 50 | DESCRIPTION |
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| 51 | These functions compute the complex square root of <[z]>, with |
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| 52 | a branch cut along the negative real axis. |
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| 53 | |
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| 54 | <<csqrtf>> is identical to <<csqrt>>, except that it performs |
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| 55 | its calculations on <<floats complex>>. |
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| 56 | |
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| 57 | RETURNS |
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| 58 | The csqrt functions return the complex square root value, in |
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| 59 | the range of the right halfplane (including the imaginary axis). |
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| 60 | |
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| 61 | PORTABILITY |
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| 62 | <<csqrt>> and <<csqrtf>> are ISO C99 |
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| 63 | |
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| 64 | QUICKREF |
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| 65 | <<csqrt>> and <<csqrtf>> are ISO C99 |
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| 66 | |
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| 67 | */ |
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| 68 | |
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| 69 | |
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| 70 | #include <complex.h> |
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| 71 | #include <math.h> |
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| 72 | |
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| 73 | double complex |
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| 74 | csqrt(double complex z) |
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| 75 | { |
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| 76 | double complex w; |
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| 77 | double x, y, r, t, scale; |
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| 78 | |
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| 79 | x = creal (z); |
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| 80 | y = cimag (z); |
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| 81 | |
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| 82 | if (y == 0.0) { |
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| 83 | if (x == 0.0) { |
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| 84 | w = 0.0 + y * I; |
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| 85 | } else { |
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| 86 | r = fabs(x); |
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| 87 | r = sqrt(r); |
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| 88 | if (x < 0.0) { |
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| 89 | w = 0.0 + r * I; |
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| 90 | } else { |
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| 91 | w = r + y * I; |
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| 92 | } |
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| 93 | } |
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| 94 | return w; |
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| 95 | } |
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| 96 | if (x == 0.0) { |
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| 97 | r = fabs(y); |
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| 98 | r = sqrt(0.5 * r); |
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| 99 | if (y > 0) |
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| 100 | w = r + r * I; |
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| 101 | else |
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| 102 | w = r - r * I; |
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| 103 | return w; |
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| 104 | } |
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| 105 | /* Rescale to avoid internal overflow or underflow. */ |
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| 106 | if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) { |
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| 107 | x *= 0.25; |
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| 108 | y *= 0.25; |
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| 109 | scale = 2.0; |
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| 110 | } else { |
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| 111 | #if 1 |
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| 112 | x *= 1.8014398509481984e16; /* 2^54 */ |
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| 113 | y *= 1.8014398509481984e16; |
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| 114 | scale = 7.450580596923828125e-9; /* 2^-27 */ |
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| 115 | #else |
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| 116 | x *= 4.0; |
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| 117 | y *= 4.0; |
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| 118 | scale = 0.5; |
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| 119 | #endif |
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| 120 | } |
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| 121 | w = x + y * I; |
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| 122 | r = cabs(w); |
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| 123 | if (x > 0) { |
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| 124 | t = sqrt(0.5 * r + 0.5 * x); |
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| 125 | r = scale * fabs((0.5 * y) / t ); |
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| 126 | t *= scale; |
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| 127 | } else { |
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| 128 | r = sqrt(0.5 * r - 0.5 * x); |
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| 129 | t = scale * fabs((0.5 * y) / r); |
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| 130 | r *= scale; |
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| 131 | } |
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| 132 | if (y < 0) |
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| 133 | w = t - r * I; |
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| 134 | else |
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| 135 | w = t + r * I; |
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| 136 | return w; |
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| 137 | } |
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