133 lines
2.7 KiB
C
133 lines
2.7 KiB
C
/* $OpenBSD: s_csqrtf.c,v 1.4 2016/09/12 19:47:02 guenther 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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/* csqrtf()
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*
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* Complex square root
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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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* float complex csqrtf();
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* float complex z, w;
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*
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* w = csqrtf( 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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*
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* If z = x + iy, r = |z|, then
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*
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* 1/2
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* Re w = [ (r + x)/2 ] ,
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*
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* 1/2
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* Im w = [ (r - x)/2 ] .
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*
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* Cancellation error in r-x or r+x is avoided by using the
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* identity 2 Re w Im w = y.
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*
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* Note that -w is also a square root of z. The root chosen
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* is always in the right half plane and Im w has the same sign as y.
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*
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*
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*
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* ACCURACY:
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*
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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 1,000,000 1.8e-7 3.5e-8
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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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float complex
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csqrtf(float complex z)
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{
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float complex w;
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float x, y, r, t, scale;
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x = crealf(z);
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y = cimagf(z);
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if(y == 0.0f) {
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if (x < 0.0f) {
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w = 0.0f + copysign(sqrtf(-x), y) * I;
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return (w);
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}
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else if (x == 0.0f) {
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return (0.0f + y * I);
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}
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else {
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w = sqrtf(x) + y * I;
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return (w);
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}
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}
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if (x == 0.0f) {
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r = fabsf(y);
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r = sqrtf(0.5f*r);
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if(y > 0)
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w = r + r * I;
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else
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w = r - r * I;
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return (w);
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}
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/* Rescale to avoid internal overflow or underflow. */
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if ((fabsf(x) > 4.0f) || (fabsf(y) > 4.0f)) {
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x *= 0.25f;
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y *= 0.25f;
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scale = 2.0f;
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}
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else {
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x *= 6.7108864e7f; /* 2^26 */
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y *= 6.7108864e7f;
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scale = 1.220703125e-4f; /* 2^-13 */
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#if 0
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x *= 4.0f;
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y *= 4.0f;
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scale = 0.5f;
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#endif
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}
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w = x + y * I;
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r = cabsf(w);
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if (x > 0) {
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t = sqrtf( 0.5f * r + 0.5f * x );
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r = scale * fabsf((0.5f * y) / t);
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t *= scale;
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}
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else {
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r = sqrtf(0.5f * r - 0.5f * x);
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t = scale * fabsf((0.5f * y) / r);
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r *= scale;
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}
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if (y < 0)
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w = t - r * I;
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else
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w = t + r * I;
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return (w);
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}
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DEF_STD(csqrtf);
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