3f8c0a6661
The C11 standard introduced a set of macros (CMPLX, CMPLXF, CMPLXL) that can be used to construct complex numbers from a pair of real and imaginary numbers. Unfortunately, they require some compiler support, which is why we only define them for Clang and GCC>=4.7. The cpack() function in libm performs the same task as CMPLX(), but cannot be used to generate compile-time constants. This means that all invocations of cpack() can safely be replaced by C11's CMPLX(). To keep the code building with GCC 4.2, provide copies of CMPLX() that can at least be used to generate run-time complex numbers. This makes it easier to build some of the functions outside of libm.
109 lines
3.2 KiB
C
109 lines
3.2 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 <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#include <complex.h>
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#include <float.h>
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#include <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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#pragma STDC CX_LIMITED_RANGE ON
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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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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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