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
108 lines
3.2 KiB
C
108 lines
3.2 KiB
C
/*-
|
|
* SPDX-License-Identifier: BSD-2-Clause-FreeBSD
|
|
*
|
|
* Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
|
|
* All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
* documentation and/or other materials provided with the distribution.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
|
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
|
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
|
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
|
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
|
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
|
* SUCH DAMAGE.
|
|
*
|
|
* src/s_cexp.c converted to long double complex by Steven G. Kargl
|
|
*/
|
|
|
|
#include <sys/cdefs.h>
|
|
__FBSDID("$FreeBSD$");
|
|
|
|
#include <complex.h>
|
|
#include <float.h>
|
|
#ifdef __i386__
|
|
#include <ieeefp.h>
|
|
#endif
|
|
|
|
#include "fpmath.h"
|
|
#include "math.h"
|
|
#include "math_private.h"
|
|
#include "k_expl.h"
|
|
|
|
long double complex
|
|
cexpl (long double complex z)
|
|
{
|
|
long double c, exp_x, s, x, y;
|
|
uint64_t lx, ly;
|
|
uint16_t hx, hy;
|
|
|
|
ENTERI();
|
|
|
|
x = creall(z);
|
|
y = cimagl(z);
|
|
|
|
EXTRACT_LDBL80_WORDS(hy, ly, y);
|
|
hy &= 0x7fff;
|
|
|
|
/* cexp(x + I 0) = exp(x) + I 0 */
|
|
if ((hy | ly) == 0)
|
|
RETURNI(CMPLXL(expl(x), y));
|
|
EXTRACT_LDBL80_WORDS(hx, lx, x);
|
|
/* cexp(0 + I y) = cos(y) + I sin(y) */
|
|
if (((hx & 0x7fff) | lx) == 0) {
|
|
sincosl(y, &s, &c);
|
|
RETURNI(CMPLXL(c, s));
|
|
}
|
|
|
|
if (hy >= 0x7fff) {
|
|
if ((hx & 0x7fff) < 0x7fff || ((hx & 0x7fff) == 0x7fff &&
|
|
(lx & 0x7fffffffffffffffULL) != 0)) {
|
|
/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
|
|
RETURNI(CMPLXL(y - y, y - y));
|
|
} else if (hx & 0x8000) {
|
|
/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
|
|
RETURNI(CMPLXL(0.0, 0.0));
|
|
} else {
|
|
/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
|
|
RETURNI(CMPLXL(x, y - y));
|
|
}
|
|
}
|
|
|
|
/*
|
|
* exp_ovfl = 11356.5234062941439497
|
|
* cexp_ovfl = 22755.3287906024445633
|
|
*/
|
|
if ((hx == 0x400c && lx > 0xb17217f7d1cf79acULL) ||
|
|
(hx == 0x400d && lx < 0xb1c6a8573de9768cULL)) {
|
|
/*
|
|
* x is between exp_ovfl and cexp_ovfl, so we must scale to
|
|
* avoid overflow in exp(x).
|
|
*/
|
|
RETURNI(__ldexp_cexpl(z, 0));
|
|
} else {
|
|
/*
|
|
* Cases covered here:
|
|
* - x < exp_ovfl and exp(x) won't overflow (common case)
|
|
* - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
|
|
* - x = +-Inf (generated by exp())
|
|
* - x = NaN (spurious inexact exception from y)
|
|
*/
|
|
exp_x = expl(x);
|
|
sincosl(y, &s, &c);
|
|
RETURNI(CMPLXL(exp_x * c, exp_x * s));
|
|
}
|
|
}
|