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/* $OpenBSD: s_cpowl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ |
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/* |
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* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> |
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* |
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* Permission to use, copy, modify, and distribute this software for any |
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* purpose with or without fee is hereby granted, provided that the above |
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* copyright notice and this permission notice appear in all copies. |
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* |
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR |
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN |
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF |
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. |
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*/ |
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/* cpowl |
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* |
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* Complex power function |
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* |
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* |
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* |
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* SYNOPSIS: |
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* |
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* long double complex cpowl(); |
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* long double complex a, z, w; |
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* |
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* w = cpowl (a, z); |
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* |
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* |
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* |
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* DESCRIPTION: |
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* |
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* Raises complex A to the complex Zth power. |
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* Definition is per AMS55 # 4.2.8, |
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* analytically equivalent to cpow(a,z) = cexp(z clog(a)). |
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* |
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* ACCURACY: |
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* |
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* Relative error: |
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* arithmetic domain # trials peak rms |
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* IEEE -10,+10 30000 9.4e-15 1.5e-15 |
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* |
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*/ |
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#include <complex.h> |
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#include <math.h> |
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long double complex |
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cpowl(long double complex a, long double complex z) |
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{ |
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long double complex w; |
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long double x, y, r, theta, absa, arga; |
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x = creall(z); |
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y = cimagl(z); |
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absa = cabsl(a); |
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if (absa == 0.0L) { |
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return (0.0L + 0.0L * I); |
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} |
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arga = cargl(a); |
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r = powl(absa, x); |
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theta = x * arga; |
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if (y != 0.0L) { |
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r = r * expl(-y * arga); |
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theta = theta + y * logl(absa); |
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} |
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w = r * cosl(theta) + (r * sinl(theta)) * I; |
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return (w); |
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} |