046e2d5db1
The change implements cexpl() for both ld80 and ld128 architectures.
Testing was done on x86_64 and aarch64 systems.
Along the way sincos[fl]() use an optimization that reduces the argument
to being done one rather than twice. This optimization actually pointed
to a bug in the ld128 version of sincosl(), which is now fixed. In
addition, the minmax polynomial coefficients for sincosl() have been
updated.
A concise log of the file-by-file changes follows.
* include/complex.h:
. Add a prototype for cexpl().
* lib/msun/Makefile:
. Add s_cexpl.c to the build.
. Setup a link for cexpl.3 to cexp.3.
* lib/msun/Symbol.map:
. Expose cexpl symbol in libm shared library.
* lib/msun/ld128/s_cexpl.c:
* Implementation of cexpl() for 128-bit long double architectures.
Tested on an aarch64 system.
* lib/msun/ld80/s_cexpl.c:
* Implementation of cexpl() for Intel 80-bit long double.
* lib/msun/man/cexp.3:
. Document cexpl().
* lib/msun/man/complex.3:
. Add a BUGS section about cpow[fl].
* lib/msun/src/s_cexp.c:
. Include float.h for weak references on 53-bit long double targets.
. Use sincos() to reduce argument reduction cost.
* lib/msun/src/s_cexpf.c:
. Use sincosf() to reduce argument reduction cost.
* lib/msun/src/k_sincosl.h:
. Catch up with the new minmax polynomial coefficients for the kernel for
the 128-bit cosl() implementation.
. BUG FIX: *cs was used where *sn should have been. This means that sinl()
was no computed correctly when iy != 0.
* lib/msun/src/s_cosl.c:
. Include fpmath.h to get access to IEEEl2bits.
. Replace M_PI_4 with pio4, a 64-bit or 113-bit approximation for pi / 4.
PR: 216862
MFC after: 1 week
95 lines
2.9 KiB
C
95 lines
2.9 KiB
C
/*-
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* SPDX-License-Identifier: BSD-2-Clause-FreeBSD
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*
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* Copyright (c) 2019 Steven G. Kargl <kargl@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 "fpmath.h"
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#include "math_private.h"
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#include "k_expl.h"
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/* XXX cexpl() should be converted to use bits likeo src/s_cexp.c. */
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static const long double
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cexp_ovfl = 2.27892930024498818830197576893019292e+04L,
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exp_ovfl = 1.13565234062941439494919310779707649e+04L;
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long double complex
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cexpl(long double complex z)
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{
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long double c, exp_x, s, x, y;
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x = creall(z);
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y = cimagl(z);
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/* cexp(x + I 0) = exp(x) + I 0 */
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if (y == 0)
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return (CMPLXL(expl(x), y));
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/* cexp(0 + I y) = cos(y) + I sin(y) */
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if (x == 0) {
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sincosl(y, &s, &c);
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return (CMPLXL(c, s));
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}
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if (!isfinite(y)) {
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if (isfinite(x) || isnan(x)) {
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/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
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return (CMPLXL(y - y, y - y));
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} else if (isinf(x) && copysignl(1.L, x) < 0) {
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/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
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return (CMPLXL(0.0, 0.0));
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} else {
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/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
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return (CMPLXL(x, y - y));
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}
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}
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if (x > exp_ovfl && x < cexp_ovfl) {
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/*
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* x is between exp_ovfl and cexp_ovfl, so we must scale to
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* avoid overflow in exp(x).
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*/
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return (__ldexp_cexpl(z, 0));
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} else {
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/*
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* Cases covered here:
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* - x < exp_ovfl and exp(x) won't overflow (common case)
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* - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
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* - x = +-Inf (generated by exp())
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* - x = NaN (spurious inexact exception from y)
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*/
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exp_x = expl(x);
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sincosl(y, &s, &c);
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return (CMPLXL(exp_x * c, exp_x * s));
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}
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}
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