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Implementations of cexpl()

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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
This commit is contained in:
Steve Kargl 2021-11-05 04:04:01 +02:00 committed by Konstantin Belousov
parent 8b57ee7e01
commit 046e2d5db1
11 changed files with 265 additions and 31 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
include/complex.h
View File

@ -98,6 +98,8 @@ double complex ccosh(double complex);
float complex ccoshf(float complex);
double complex cexp(double complex);
float complex cexpf(float complex);
long double complex
cexpl(long double complex);
double cimag(double complex) __pure2;
float cimagf(float complex) __pure2;
long double cimagl(long double complex) __pure2;

4
lib/msun/Makefile
View File

@ -117,7 +117,7 @@ COMMON_SRCS+= catrigl.c \
e_lgammal.c e_lgammal_r.c e_powl.c \
e_remainderl.c e_sinhl.c e_sqrtl.c \
invtrig.c k_cosl.c k_sinl.c k_tanl.c \
s_asinhl.c s_atanl.c s_cbrtl.c s_ceill.c \
s_asinhl.c s_atanl.c s_cbrtl.c s_ceill.c s_cexpl.c \
s_clogl.c s_cosl.c s_cospil.c s_cprojl.c \
s_csqrtl.c s_erfl.c s_exp2l.c s_expl.c s_floorl.c s_fmal.c \
s_fmaxl.c s_fminl.c s_frexpl.c s_logbl.c s_logl.c s_nanl.c \
@ -189,7 +189,7 @@ MLINKS+=ccos.3 ccosf.3 ccos.3 csin.3 ccos.3 csinf.3 ccos.3 ctan.3 ccos.3 ctanf.3
MLINKS+=ccosh.3 ccoshf.3 ccosh.3 csinh.3 ccosh.3 csinhf.3 \
ccosh.3 ctanh.3 ccosh.3 ctanhf.3
MLINKS+=ceil.3 ceilf.3 ceil.3 ceill.3
MLINKS+=cexp.3 cexpf.3
MLINKS+=cexp.3 cexpf.3 cexp.3 cexpl.3
MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.3 \
cimag.3 conj.3 cimag.3 conjf.3 cimag.3 conjl.3 \
cimag.3 cproj.3 cimag.3 cprojf.3 cimag.3 cprojl.3 \

1
lib/msun/Symbol.map
View File

@ -307,6 +307,7 @@ FBSD_1.5 {
/* First added in 14.0-CURRENT */
FBSD_1.7 {
cexpl;
cospi;
cospif;
cospil;

94
lib/msun/ld128/s_cexpl.c Normal file
View File

@ -0,0 +1,94 @@
/*-
* SPDX-License-Identifier: BSD-2-Clause-FreeBSD
*
* Copyright (c) 2019 Steven G. Kargl <kargl@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.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <float.h>
#include <math.h>
#include "fpmath.h"
#include "math_private.h"
#include "k_expl.h"
/* XXX cexpl() should be converted to use bits likeo src/s_cexp.c. */
static const long double
cexp_ovfl = 2.27892930024498818830197576893019292e+04L,
exp_ovfl = 1.13565234062941439494919310779707649e+04L;
long double complex
cexpl(long double complex z)
{
long double c, exp_x, s, x, y;
x = creall(z);
y = cimagl(z);
/* cexp(x + I 0) = exp(x) + I 0 */
if (y == 0)
return (CMPLXL(expl(x), y));
/* cexp(0 + I y) = cos(y) + I sin(y) */
if (x == 0) {
sincosl(y, &s, &c);
return (CMPLXL(c, s));
}
if (!isfinite(y)) {
if (isfinite(x) || isnan(x)) {
/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
return (CMPLXL(y - y, y - y));
} else if (isinf(x) && copysignl(1.L, x) < 0) {
/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
return (CMPLXL(0.0, 0.0));
} else {
/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
return (CMPLXL(x, y - y));
}
}
if (x > exp_ovfl && x < cexp_ovfl) {
/*
* x is between exp_ovfl and cexp_ovfl, so we must scale to
* avoid overflow in exp(x).
*/
return (__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);
return (CMPLXL(exp_x * c, exp_x * s));
}
}

107
lib/msun/ld80/s_cexpl.c Normal file
View File

@ -0,0 +1,107 @@
/*-
* 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));
}
}

17
lib/msun/man/cexp.3
View File

@ -24,12 +24,13 @@
.\"
.\" $FreeBSD$
.\"
.Dd March 6, 2011
.Dd November 3, 2021
.Dt CEXP 3
.Os
.Sh NAME
.Nm cexp ,
.Nm cexpf
.Nm cexpf ,
.Nm cexpl
.Nd complex exponential functions
.Sh LIBRARY
.Lb libm
@ -39,11 +40,14 @@
.Fn cexp "double complex z"
.Ft float complex
.Fn cexpf "float complex z"
.Ft long double complex
.Fn cexpl "long double complex z"
.Sh DESCRIPTION
The
.Fn cexp
.Fn cexp ,
.Fn cexpf ,
and
.Fn cexpf
.Fn cexpl
functions compute the complex exponential of
.Fa z ,
also known as
@ -106,8 +110,9 @@ is not finite, the sign of the result is indeterminate.
.Xr math 3
.Sh STANDARDS
The
.Fn cexp
.Fn cexp ,
.Fn cexpf ,
and
.Fn cexpf
.Fn cexpl
functions conform to
.St -isoC-99 .

8
lib/msun/man/complex.3
View File

@ -24,7 +24,7 @@
.\"
.\" $FreeBSD$
.\"
.Dd June 19, 2018
.Dd November 3, 2021
.Dt COMPLEX 3
.Os
.Sh NAME
@ -121,3 +121,9 @@ The
.In complex.h
functions described here conform to
.St -isoC-99 .
.Sh BUGS
The power functions,
.Fn cpowf, cpow ,
and
.Fn cpowl ,
are implemented, but the code was neither reviewed nor tested.

29
lib/msun/src/k_sincosl.h
View File

@ -76,13 +76,6 @@ __kernel_sincosl(long double x, long double y, int iy, long double *sn,
#elif LDBL_MANT_DIG == 113 /* ld128 version of k_sincosl.c. */
static const long double
C1 = 0.04166666666666666666666666666666658424671L,
C2 = -0.001388888888888888888888888888863490893732L,
C3 = 0.00002480158730158730158730158600795304914210L,
C4 = -0.2755731922398589065255474947078934284324e-6L,
C5 = 0.2087675698786809897659225313136400793948e-8L,
C6 = -0.1147074559772972315817149986812031204775e-10L,
C7 = 0.4779477332386808976875457937252120293400e-13L,
S1 = -0.16666666666666666666666666666666666606732416116558L,
S2 = 0.0083333333333333333333333333333331135404851288270047L,
S3 = -0.00019841269841269841269841269839935785325638310428717L,
@ -93,15 +86,25 @@ S7 = -0.76471637318198151807063387954939213287488216303768e-12L,
S8 = 0.28114572543451292625024967174638477283187397621303e-14L;
static const double
C8 = -0.1561920696721507929516718307820958119868e-15,
C9 = 0.4110317413744594971475941557607804508039e-18,
C10 = -0.8896592467191938803288521958313920156409e-21,
C11 = 0.1601061435794535138244346256065192782581e-23,
S9 = -0.82206352458348947812512122163446202498005154296863e-17,
S10 = 0.19572940011906109418080609928334380560135358385256e-19,
S11 = -0.38680813379701966970673724299207480965452616911420e-22,
S12 = 0.64038150078671872796678569586315881020659912139412e-25;
static const long double
C1 = 4.16666666666666666666666666666666667e-02L,
C2 = -1.38888888888888888888888888888888834e-03L,
C3 = 2.48015873015873015873015873015446795e-05L,
C4 = -2.75573192239858906525573190949988493e-07L,
C5 = 2.08767569878680989792098886701451072e-09L,
C6 = -1.14707455977297247136657111139971865e-11L,
C7 = 4.77947733238738518870113294139830239e-14L,
C8 = -1.56192069685858079920640872925306403e-16L,
C9 = 4.11031762320473354032038893429515732e-19L,
C10= -8.89679121027589608738005163931958096e-22L,
C11= 1.61171797801314301767074036661901531e-24L,
C12= -2.46748624357670948912574279501044295e-27L;
static inline void
__kernel_sincosl(long double x, long double y, int iy, long double *sn,
long double *cs)
@ -120,12 +123,12 @@ __kernel_sincosl(long double x, long double y, int iy, long double *sn,
if (iy == 0)
*sn = x + v * (S1 + z * r);
else
*cs = x - ((z * (y / 2 - v * r) - y) - v * S1);
*sn = x - ((z * (y / 2 - v * r) - y) - v * S1);
hz = z / 2;
w = 1 - hz;
r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * C11))))))))));
z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * (C11+z*C12)))))))))));
*cs = w + (((1 - w) - hz) + (z * r - x * y));
}

16
lib/msun/src/s_cexp.c
View File

@ -30,6 +30,7 @@
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <float.h>
#include <math.h>
#include "math_private.h"
@ -41,7 +42,7 @@ cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
double complex
cexp(double complex z)
{
double x, y, exp_x;
double c, exp_x, s, x, y;
uint32_t hx, hy, lx, ly;
x = creal(z);
@ -55,8 +56,10 @@ cexp(double complex z)
return (CMPLX(exp(x), y));
EXTRACT_WORDS(hx, lx, x);
/* cexp(0 + I y) = cos(y) + I sin(y) */
if (((hx & 0x7fffffff) | lx) == 0)
return (CMPLX(cos(y), sin(y)));
if (((hx & 0x7fffffff) | lx) == 0) {
sincos(y, &s, &c);
return (CMPLX(c, s));
}
if (hy >= 0x7ff00000) {
if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
@ -86,6 +89,11 @@ cexp(double complex z)
* - x = NaN (spurious inexact exception from y)
*/
exp_x = exp(x);
return (CMPLX(exp_x * cos(y), exp_x * sin(y)));
sincos(y, &s, &c);
return (CMPLX(exp_x * c, exp_x * s));
}
}
#if (LDBL_MANT_DIG == 53)
__weak_reference(cexp, cexpl);
#endif

11
lib/msun/src/s_cexpf.c
View File

@ -41,7 +41,7 @@ cexp_ovfl = 0x43400074; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
float complex
cexpf(float complex z)
{
float x, y, exp_x;
float c, exp_x, s, x, y;
uint32_t hx, hy;
x = crealf(z);
@ -55,8 +55,10 @@ cexpf(float complex z)
return (CMPLXF(expf(x), y));
GET_FLOAT_WORD(hx, x);
/* cexp(0 + I y) = cos(y) + I sin(y) */
if ((hx & 0x7fffffff) == 0)
return (CMPLXF(cosf(y), sinf(y)));
if ((hx & 0x7fffffff) == 0) {
sincosf(y, &s, &c);
return (CMPLXF(c, s));
}
if (hy >= 0x7f800000) {
if ((hx & 0x7fffffff) != 0x7f800000) {
@ -86,6 +88,7 @@ cexpf(float complex z)
* - x = NaN (spurious inexact exception from y)
*/
exp_x = expf(x);
return (CMPLXF(exp_x * cosf(y), exp_x * sinf(y)));
sincosf(y, &s, &c);
return (CMPLXF(exp_x * c, exp_x * s));
}
}

7
lib/msun/src/s_cosl.c
View File

@ -39,12 +39,17 @@ __FBSDID("$FreeBSD$");
#include <ieeefp.h>
#endif
#include "fpmath.h"
#include "math.h"
#include "math_private.h"
#if LDBL_MANT_DIG == 64
#include "../ld80/e_rem_pio2l.h"
static const union IEEEl2bits
pio4u = LD80C(0xc90fdaa22168c235, -00001, 7.85398163397448309628e-01L);
#define pio4 (pio4u.e)
#elif LDBL_MANT_DIG == 113
#include "../ld128/e_rem_pio2l.h"
long double pio4 = 7.85398163397448309615660845819875721e-1L;
#else
#error "Unsupported long double format"
#endif
@ -71,7 +76,7 @@ cosl(long double x)
ENTERI();
/* Optimize the case where x is already within range. */
if (z.e < M_PI_4)
if (z.e < pio4)
RETURNI(__kernel_cosl(z.e, 0));
e0 = __ieee754_rem_pio2l(x, y);