110 lines
3.3 KiB
C
110 lines
3.3 KiB
C
/*-
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* Copyright (c) 2007-2008 David Schultz <das@FreeBSD.ORG>
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* All rights reserved.
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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 AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#include "cdefs-compat.h"
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#include <float.h>
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#include <openlibm_complex.h>
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#include <openlibm_math.h>
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#include "math_private.h"
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/*
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* gcc doesn't implement complex multiplication or division correctly,
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* so we need to handle infinities specially. We turn on this pragma to
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* notify conforming c99 compilers that the fast-but-incorrect code that
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* gcc generates is acceptable, since the special cases have already been
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* handled.
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*/
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#ifndef __GNUC__
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#pragma STDC CX_LIMITED_RANGE ON
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#endif
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/* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */
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#define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L)
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OLM_DLLEXPORT long double complex
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csqrtl(long double complex z)
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{
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long double complex result;
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long double a, b;
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long double t;
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int scale;
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a = creall(z);
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b = cimagl(z);
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/* Handle special cases. */
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if (z == 0)
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return (CMPLXL(0, b));
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if (isinf(b))
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return (CMPLXL(INFINITY, b));
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if (isnan(a)) {
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t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
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return (CMPLXL(a, t)); /* return NaN + NaN i */
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}
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if (isinf(a)) {
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/*
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* csqrt(inf + NaN i) = inf + NaN i
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* csqrt(inf + y i) = inf + 0 i
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* csqrt(-inf + NaN i) = NaN +- inf i
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* csqrt(-inf + y i) = 0 + inf i
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*/
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if (signbit(a))
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return (CMPLXL(fabsl(b - b), copysignl(a, b)));
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else
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return (CMPLXL(a, copysignl(b - b, b)));
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}
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/*
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* The remaining special case (b is NaN) is handled just fine by
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* the normal code path below.
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*/
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/* Scale to avoid overflow. */
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if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
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a *= 0.25;
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b *= 0.25;
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scale = 1;
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} else {
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scale = 0;
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}
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/* Algorithm 312, CACM vol 10, Oct 1967. */
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if (a >= 0) {
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t = sqrtl((a + hypotl(a, b)) * 0.5);
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result = CMPLXL(t, b / (2 * t));
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} else {
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t = sqrtl((-a + hypotl(a, b)) * 0.5);
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result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b));
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}
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/* Rescale. */
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if (scale)
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return (result * 2);
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else
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return (result);
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}
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