mirror of https://gitlab.com/rnger/amath
120 lines
3.2 KiB
C
120 lines
3.2 KiB
C
/*-
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* Copyright (c) 2014-2018 Carsten Sonne Larsen <cs@innolan.net>
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* Copyright (c) 2007 The NetBSD Foundation, Inc.
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* All rights reserved.
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*
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* This code is derived from software written by Stephen L. Moshier.
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* It is redistributed by the NetBSD Foundation by permission of the author.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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* The original source code can be obtained from:
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* http://cvsweb.netbsd.org/bsdweb.cgi/src/lib/libm/complex/csqrt.c?rev=1.1
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*
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* Project homepage:
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* https://amath.innolan.net
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*
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*/
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#include "prim.h"
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/**
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* @brief Square root of complex number
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*/
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complex csqrt(complex z)
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{
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complex w;
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double x, y, r, t, scale;
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x = creal(z);
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y = cimag(z);
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if (y == 0.0)
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{
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if (x == 0.0)
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{
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w = cpack(0.0, y);
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}
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else
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{
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r = fabs(x);
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r = sqrt(r);
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if (x < 0.0)
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{
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w = cpack(0.0, r);
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}
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else
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{
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w = cpack(r, y);
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}
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}
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return w;
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}
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if (x == 0.0)
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{
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r = fabs(y);
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r = sqrt(0.5 * r);
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if (y > 0)
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w = cpack(r, r);
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else
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w = cpack(r, -r);
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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 ((fabs(x) > 4.0) || (fabs(y) > 4.0))
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{
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x *= 0.25;
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y *= 0.25;
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scale = 2.0;
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}
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else
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{
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#if 1
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x *= 1.8014398509481984e16; /* 2^54 */
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y *= 1.8014398509481984e16;
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scale = 7.450580596923828125e-9; /* 2^-27 */
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#else
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x *= 4.0;
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y *= 4.0;
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scale = 0.5;
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#endif
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}
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w = cpack(x, y);
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r = cabs(w);
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if (x > 0)
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{
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t = sqrt(0.5 * r + 0.5 * x);
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r = scale * fabs((0.5 * y) / t);
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t *= scale;
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}
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else
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{
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r = sqrt(0.5 * r - 0.5 * x);
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t = scale * fabs((0.5 * y) / r);
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r *= scale;
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}
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if (y < 0)
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w = cpack(t, -r);
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else
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w = cpack(t, r);
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return w;
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}
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