Author: kib
Date: Tue Jun 5 13:46:18 2018
New Revision: 334654
URL: https://svnweb.freebsd.org/changeset/base/334654
Log:
MFC r333577:
Add implementations for clog(3), clogf(3), and clogl(3).
PR: 216863
Added:
stable/11/lib/msun/man/clog.3
- copied unchanged from r333577, head/lib/msun/man/clog.3
stable/11/lib/msun/src/s_clog.c
- copied unchanged from r333577, head/lib/msun/src/s_clog.c
stable/11/lib/msun/src/s_clogf.c
- copied unchanged from r333577, head/lib/msun/src/s_clogf.c
stable/11/lib/msun/src/s_clogl.c
- copied unchanged from r333577, head/lib/msun/src/s_clogl.c
Modified:
stable/11/include/complex.h
stable/11/lib/libc/softfloat/bits64/softfloat-macros
stable/11/lib/msun/Makefile
stable/11/lib/msun/Symbol.map
stable/11/lib/msun/man/complex.3
stable/11/lib/msun/src/math_private.h
Directory Properties:
stable/11/ (props changed)
Modified: stable/11/include/complex.h
==============================================================================
--- stable/11/include/complex.h Tue Jun 5 13:06:06 2018 (r334653)
+++ stable/11/include/complex.h Tue Jun 5 13:46:18 2018 (r334654)
@@ -87,6 +87,10 @@ float complex cexpf(float complex);
double cimag(double complex) __pure2;
float cimagf(float complex) __pure2;
long double cimagl(long double complex) __pure2;
+double complex clog(double complex);
+float complex clogf(float complex);
+long double complex
+ clogl(long double complex);
double complex conj(double complex) __pure2;
float complex conjf(float complex) __pure2;
long double complex
Modified: stable/11/lib/libc/softfloat/bits64/softfloat-macros
==============================================================================
--- stable/11/lib/libc/softfloat/bits64/softfloat-macros Tue Jun 5
13:06:06 2018 (r334653)
+++ stable/11/lib/libc/softfloat/bits64/softfloat-macros Tue Jun 5
13:46:18 2018 (r334654)
@@ -157,7 +157,7 @@ INLINE void
z0 = a0>>count;
}
else {
- z1 = ( count < 64 ) ? ( a0>>( count & 63 ) ) : 0;
+ z1 = ( count < 128 ) ? ( a0>>( count & 63 ) ) : 0;
z0 = 0;
}
*z1Ptr = z1;
Modified: stable/11/lib/msun/Makefile
==============================================================================
--- stable/11/lib/msun/Makefile Tue Jun 5 13:06:06 2018 (r334653)
+++ stable/11/lib/msun/Makefile Tue Jun 5 13:46:18 2018 (r334654)
@@ -57,7 +57,7 @@ COMMON_SRCS= b_exp.c b_log.c b_tgamma.c \
k_cos.c k_cosf.c k_exp.c k_expf.c k_rem_pio2.c k_sin.c k_sinf.c \
k_tan.c k_tanf.c \
s_asinh.c s_asinhf.c s_atan.c s_atanf.c s_carg.c s_cargf.c s_cargl.c \
- s_cbrt.c s_cbrtf.c s_ceil.c s_ceilf.c \
+ s_cbrt.c s_cbrtf.c s_ceil.c s_ceilf.c s_clog.c s_clogf.c \
s_copysign.c s_copysignf.c s_cos.c s_cosf.c \
s_csqrt.c s_csqrtf.c s_erf.c s_erff.c \
s_exp2.c s_exp2f.c s_expm1.c s_expm1f.c s_fabsf.c s_fdim.c \
@@ -101,7 +101,8 @@ COMMON_SRCS+= catrigl.c \
e_lgammal.c e_lgammal_r.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_cosl.c s_cprojl.c \
+ s_asinhl.c s_atanl.c s_cbrtl.c s_ceill.c \
+ s_clogl.c s_cosl.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 \
s_nextafterl.c s_nexttoward.c s_remquol.c s_rintl.c s_roundl.c \
@@ -133,7 +134,8 @@ INCS+= fenv.h math.h
MAN= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 \
ceil.3 cacos.3 ccos.3 ccosh.3 cexp.3 \
- cimag.3 copysign.3 cos.3 cosh.3 csqrt.3 erf.3 exp.3 fabs.3 fdim.3 \
+ cimag.3 clog.3 copysign.3 cos.3 cosh.3 csqrt.3 erf.3 \
+ exp.3 fabs.3 fdim.3 \
feclearexcept.3 feenableexcept.3 fegetenv.3 \
fegetround.3 fenv.3 floor.3 \
fma.3 fmax.3 fmod.3 hypot.3 ieee.3 ieee_test.3 ilogb.3 j0.3 \
@@ -166,6 +168,7 @@ 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 \
cimag.3 creal.3 cimag.3 crealf.3 cimag.3 creall.3
+MLINKS+=clog.3 clogf.3 clog.3 clogl.3
MLINKS+=copysign.3 copysignf.3 copysign.3 copysignl.3
MLINKS+=cos.3 cosf.3 cos.3 cosl.3
MLINKS+=cosh.3 coshf.3 cosh.3 coshl.3
Modified: stable/11/lib/msun/Symbol.map
==============================================================================
--- stable/11/lib/msun/Symbol.map Tue Jun 5 13:06:06 2018
(r334653)
+++ stable/11/lib/msun/Symbol.map Tue Jun 5 13:46:18 2018
(r334654)
@@ -294,6 +294,9 @@ FBSD_1.5 {
casinl;
catanl;
catanhl;
+ clog;
+ clogf;
+ clogl;
sincos;
sincosf;
sincosl;
Copied: stable/11/lib/msun/man/clog.3 (from r333577, head/lib/msun/man/clog.3)
==============================================================================
--- /dev/null 00:00:00 1970 (empty, because file is newly added)
+++ stable/11/lib/msun/man/clog.3 Tue Jun 5 13:46:18 2018
(r334654, copy of r333577, head/lib/msun/man/clog.3)
@@ -0,0 +1,103 @@
+.\" Copyright (c) 2017 Steven G. Kargl <ka...@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.
+.\"
+.\" $FreeBSD$
+.\"
+.Dd February 13, 2017
+.Dt CLOG 3
+.Os
+.Sh NAME
+.Nm clog ,
+.Nm clogf ,
+and
+.Nm clogl
+.Nd complex natural logrithm functions
+.Sh LIBRARY
+.Lb libm
+.Sh SYNOPSIS
+.In complex.h
+.Ft double complex
+.Fn clog "double complex z"
+.Ft float complex
+.Fn clogf "float complex z"
+.Ft long double complex
+.Fn clogl "long double complex z"
+.Sh DESCRIPTION
+The
+.Fn clog ,
+.Fn clogf ,
+and
+.Fn clogl
+functions compute the complex natural logrithm of
+.Fa z .
+with a branch cut along the negative real axis .
+.Sh RETURN VALUES
+The
+.Fn clog
+function returns the complex natural logarithm value, in the
+range of a strip mathematically unbounded along the real axis and in
+the interval [-I* \*(Pi , +I* \*(Pi ] along the imaginary axis.
+The function satisfies the relationship:
+.Fo clog
+.Fn conj "z" Fc
+=
+.Fo conj
+.Fn clog "z" Fc .
+.Pp
+
+.\" Table is formatted for an 80-column xterm.
+.Bl -column ".Sy +\*(If + I*\*(Na" ".Sy Return value" ".Sy Divide-by-zero
exception"
+.It Sy Argument Ta Sy Return value Ta Sy Comment
+.It -0 + I*0 Ta -\*(If + I*\*(Pi Ta Divide-by-zero exception
+.It Ta Ta raised
+.It +0 + I*0 Ta -\*(If + I*0 Ta Divide by zero exception
+.It Ta Ta raised
+.It x + I*\*(If Ta +\*(If + I*\*(Pi/2 Ta For finite x
+.It x + I*\*(Na Ta \*(Na + I*\*(Na Ta Optionally raises invalid
+.It Ta Ta floating-point exception
+.It Ta Ta for finite x
+.It -\*(If + I*y Ta +\*(If + I*\*(Pi Ta For finite positive-signed y
+.It +\*(If + I*y Ta +\*(If + I*0 Ta For finite positive-signed y
+.It -\*(If + I*\*(If Ta +\*(If + I*3\*(Pi/4
+.It +\*(If + I*\*(If Ta +\*(If + I*\*(Pi/4
+.It \*(Pm\*(If + I*\*(Na Ta +\*(If + I*\*(Na
+.It \*(Na + I*y Ta \*(Na + I*\*(Na Ta Optionally raises invalid
+.It Ta Ta floating-point exception
+.It Ta Ta for finite y
+.It \*(Na + I*\*(If Ta +\*(If + I*\*(Na
+.It \*(Na + I*\*(Na Ta \*(Na + I*\*(Na
+.El
+
+.Sh SEE ALSO
+.Xr complex 3 ,
+.Xr log 3 ,
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn clog ,
+.Fn cexpf ,
+and
+.Fn clogl
+functions conform to
+.St -isoC-99 .
Modified: stable/11/lib/msun/man/complex.3
==============================================================================
--- stable/11/lib/msun/man/complex.3 Tue Jun 5 13:06:06 2018
(r334653)
+++ stable/11/lib/msun/man/complex.3 Tue Jun 5 13:46:18 2018
(r334654)
@@ -24,7 +24,7 @@
.\"
.\" $FreeBSD$
.\"
-.Dd October 17, 2011
+.Dd May 13, 2018
.Dt COMPLEX 3
.Os
.Sh NAME
@@ -77,6 +77,10 @@ csqrt complex square root
.Cl
cexp exponential base e
.El
+.Ss Natural logrithm Function
+.Cl
+clog natural logrithm
+.El
.\" Section 7.3.9 of ISO C99 standard
.Ss Manipulation Functions
.Cl
@@ -117,8 +121,6 @@ The
functions described here conform to
.St -isoC-99 .
.Sh BUGS
-The logarithmic functions
-.Fn clog
-and the power functions
+The power functions
.Fn cpow
are not implemented.
Modified: stable/11/lib/msun/src/math_private.h
==============================================================================
--- stable/11/lib/msun/src/math_private.h Tue Jun 5 13:06:06 2018
(r334653)
+++ stable/11/lib/msun/src/math_private.h Tue Jun 5 13:46:18 2018
(r334654)
@@ -294,8 +294,9 @@ do {
\
/* Support switching the mode to FP_PE if necessary. */
#if defined(__i386__) && !defined(NO_FPSETPREC)
-#define ENTERI() \
- long double __retval; \
+#define ENTERI() ENTERIT(long double)
+#define ENTERIT(returntype) \
+ returntype __retval; \
fp_prec_t __oprec; \
\
if ((__oprec = fpgetprec()) != FP_PE) \
@@ -318,6 +319,7 @@ do {
\
} while (0)
#else
#define ENTERI()
+#define ENTERIT(x)
#define RETURNI(x) RETURNF(x)
#define ENTERV()
#define RETURNV() return
Copied: stable/11/lib/msun/src/s_clog.c (from r333577,
head/lib/msun/src/s_clog.c)
==============================================================================
--- /dev/null 00:00:00 1970 (empty, because file is newly added)
+++ stable/11/lib/msun/src/s_clog.c Tue Jun 5 13:46:18 2018
(r334654, copy of r333577, head/lib/msun/src/s_clog.c)
@@ -0,0 +1,155 @@
+/*-
+ * Copyright (c) 2013 Bruce D. Evans
+ * 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 unmodified, 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 ``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 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 "fpmath.h"
+#include "math.h"
+#include "math_private.h"
+
+#define MANT_DIG DBL_MANT_DIG
+#define MAX_EXP DBL_MAX_EXP
+#define MIN_EXP DBL_MIN_EXP
+
+static const double
+ln2_hi = 6.9314718055829871e-1, /* 0x162e42fefa0000.0p-53 */
+ln2_lo = 1.6465949582897082e-12; /* 0x1cf79abc9e3b3a.0p-92 */
+
+double complex
+clog(double complex z)
+{
+ double_t ax, ax2h, ax2l, axh, axl, ay, ay2h, ay2l, ayh, ayl, sh, sl, t;
+ double x, y, v;
+ uint32_t hax, hay;
+ int kx, ky;
+
+ x = creal(z);
+ y = cimag(z);
+ v = atan2(y, x);
+
+ ax = fabs(x);
+ ay = fabs(y);
+ if (ax < ay) {
+ t = ax;
+ ax = ay;
+ ay = t;
+ }
+
+ GET_HIGH_WORD(hax, ax);
+ kx = (hax >> 20) - 1023;
+ GET_HIGH_WORD(hay, ay);
+ ky = (hay >> 20) - 1023;
+
+ /* Handle NaNs and Infs using the general formula. */
+ if (kx == MAX_EXP || ky == MAX_EXP)
+ return (CMPLX(log(hypot(x, y)), v));
+
+ /* Avoid spurious underflow, and reduce inaccuracies when ax is 1. */
+ if (ax == 1) {
+ if (ky < (MIN_EXP - 1) / 2)
+ return (CMPLX((ay / 2) * ay, v));
+ return (CMPLX(log1p(ay * ay) / 2, v));
+ }
+
+ /* Avoid underflow when ax is not small. Also handle zero args. */
+ if (kx - ky > MANT_DIG || ay == 0)
+ return (CMPLX(log(ax), v));
+
+ /* Avoid overflow. */
+ if (kx >= MAX_EXP - 1)
+ return (CMPLX(log(hypot(x * 0x1p-1022, y * 0x1p-1022)) +
+ (MAX_EXP - 2) * ln2_lo + (MAX_EXP - 2) * ln2_hi, v));
+ if (kx >= (MAX_EXP - 1) / 2)
+ return (CMPLX(log(hypot(x, y)), v));
+
+ /* Reduce inaccuracies and avoid underflow when ax is denormal. */
+ if (kx <= MIN_EXP - 2)
+ return (CMPLX(log(hypot(x * 0x1p1023, y * 0x1p1023)) +
+ (MIN_EXP - 2) * ln2_lo + (MIN_EXP - 2) * ln2_hi, v));
+
+ /* Avoid remaining underflows (when ax is small but not denormal). */
+ if (ky < (MIN_EXP - 1) / 2 + MANT_DIG)
+ return (CMPLX(log(hypot(x, y)), v));
+
+ /* Calculate ax*ax and ay*ay exactly using Dekker's algorithm. */
+ t = (double)(ax * (0x1p27 + 1));
+ axh = (double)(ax - t) + t;
+ axl = ax - axh;
+ ax2h = ax * ax;
+ ax2l = axh * axh - ax2h + 2 * axh * axl + axl * axl;
+ t = (double)(ay * (0x1p27 + 1));
+ ayh = (double)(ay - t) + t;
+ ayl = ay - ayh;
+ ay2h = ay * ay;
+ ay2l = ayh * ayh - ay2h + 2 * ayh * ayl + ayl * ayl;
+
+ /*
+ * When log(|z|) is far from 1, accuracy in calculating the sum
+ * of the squares is not very important since log() reduces
+ * inaccuracies. We depended on this to use the general
+ * formula when log(|z|) is very far from 1. When log(|z|) is
+ * moderately far from 1, we go through the extra-precision
+ * calculations to reduce branches and gain a little accuracy.
+ *
+ * When |z| is near 1, we subtract 1 and use log1p() and don't
+ * leave it to log() to subtract 1, since we gain at least 1 bit
+ * of accuracy in this way.
+ *
+ * When |z| is very near 1, subtracting 1 can cancel almost
+ * 3*MANT_DIG bits. We arrange that subtracting 1 is exact in
+ * doubled precision, and then do the rest of the calculation
+ * in sloppy doubled precision. Although large cancellations
+ * often lose lots of accuracy, here the final result is exact
+ * in doubled precision if the large calculation occurs (because
+ * then it is exact in tripled precision and the cancellation
+ * removes enough bits to fit in doubled precision). Thus the
+ * result is accurate in sloppy doubled precision, and the only
+ * significant loss of accuracy is when it is summed and passed
+ * to log1p().
+ */
+ sh = ax2h;
+ sl = ay2h;
+ _2sumF(sh, sl);
+ if (sh < 0.5 || sh >= 3)
+ return (CMPLX(log(ay2l + ax2l + sl + sh) / 2, v));
+ sh -= 1;
+ _2sum(sh, sl);
+ _2sum(ax2l, ay2l);
+ /* Briggs-Kahan algorithm (except we discard the final low term): */
+ _2sum(sh, ax2l);
+ _2sum(sl, ay2l);
+ t = ax2l + sl;
+ _2sumF(sh, t);
+ return (CMPLX(log1p(ay2l + t + sh) / 2, v));
+}
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(clog, clogl);
+#endif
Copied: stable/11/lib/msun/src/s_clogf.c (from r333577,
head/lib/msun/src/s_clogf.c)
==============================================================================
--- /dev/null 00:00:00 1970 (empty, because file is newly added)
+++ stable/11/lib/msun/src/s_clogf.c Tue Jun 5 13:46:18 2018
(r334654, copy of r333577, head/lib/msun/src/s_clogf.c)
@@ -0,0 +1,151 @@
+/*-
+ * Copyright (c) 2013 Bruce D. Evans
+ * 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 unmodified, 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 ``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 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 "fpmath.h"
+#include "math.h"
+#include "math_private.h"
+
+#define MANT_DIG FLT_MANT_DIG
+#define MAX_EXP FLT_MAX_EXP
+#define MIN_EXP FLT_MIN_EXP
+
+static const float
+ln2f_hi = 6.9314575195e-1, /* 0xb17200.0p-24 */
+ln2f_lo = 1.4286067653e-6; /* 0xbfbe8e.0p-43 */
+
+float complex
+clogf(float complex z)
+{
+ float_t ax, ax2h, ax2l, axh, axl, ay, ay2h, ay2l, ayh, ayl, sh, sl, t;
+ float x, y, v;
+ uint32_t hax, hay;
+ int kx, ky;
+
+ x = crealf(z);
+ y = cimagf(z);
+ v = atan2f(y, x);
+
+ ax = fabsf(x);
+ ay = fabsf(y);
+ if (ax < ay) {
+ t = ax;
+ ax = ay;
+ ay = t;
+ }
+
+ GET_FLOAT_WORD(hax, ax);
+ kx = (hax >> 23) - 127;
+ GET_FLOAT_WORD(hay, ay);
+ ky = (hay >> 23) - 127;
+
+ /* Handle NaNs and Infs using the general formula. */
+ if (kx == MAX_EXP || ky == MAX_EXP)
+ return (CMPLXF(logf(hypotf(x, y)), v));
+
+ /* Avoid spurious underflow, and reduce inaccuracies when ax is 1. */
+ if (hax == 0x3f800000) {
+ if (ky < (MIN_EXP - 1) / 2)
+ return (CMPLXF((ay / 2) * ay, v));
+ return (CMPLXF(log1pf(ay * ay) / 2, v));
+ }
+
+ /* Avoid underflow when ax is not small. Also handle zero args. */
+ if (kx - ky > MANT_DIG || hay == 0)
+ return (CMPLXF(logf(ax), v));
+
+ /* Avoid overflow. */
+ if (kx >= MAX_EXP - 1)
+ return (CMPLXF(logf(hypotf(x * 0x1p-126F, y * 0x1p-126F)) +
+ (MAX_EXP - 2) * ln2f_lo + (MAX_EXP - 2) * ln2f_hi, v));
+ if (kx >= (MAX_EXP - 1) / 2)
+ return (CMPLXF(logf(hypotf(x, y)), v));
+
+ /* Reduce inaccuracies and avoid underflow when ax is denormal. */
+ if (kx <= MIN_EXP - 2)
+ return (CMPLXF(logf(hypotf(x * 0x1p127F, y * 0x1p127F)) +
+ (MIN_EXP - 2) * ln2f_lo + (MIN_EXP - 2) * ln2f_hi, v));
+
+ /* Avoid remaining underflows (when ax is small but not denormal). */
+ if (ky < (MIN_EXP - 1) / 2 + MANT_DIG)
+ return (CMPLXF(logf(hypotf(x, y)), v));
+
+ /* Calculate ax*ax and ay*ay exactly using Dekker's algorithm. */
+ t = (float)(ax * (0x1p12F + 1));
+ axh = (float)(ax - t) + t;
+ axl = ax - axh;
+ ax2h = ax * ax;
+ ax2l = axh * axh - ax2h + 2 * axh * axl + axl * axl;
+ t = (float)(ay * (0x1p12F + 1));
+ ayh = (float)(ay - t) + t;
+ ayl = ay - ayh;
+ ay2h = ay * ay;
+ ay2l = ayh * ayh - ay2h + 2 * ayh * ayl + ayl * ayl;
+
+ /*
+ * When log(|z|) is far from 1, accuracy in calculating the sum
+ * of the squares is not very important since log() reduces
+ * inaccuracies. We depended on this to use the general
+ * formula when log(|z|) is very far from 1. When log(|z|) is
+ * moderately far from 1, we go through the extra-precision
+ * calculations to reduce branches and gain a little accuracy.
+ *
+ * When |z| is near 1, we subtract 1 and use log1p() and don't
+ * leave it to log() to subtract 1, since we gain at least 1 bit
+ * of accuracy in this way.
+ *
+ * When |z| is very near 1, subtracting 1 can cancel almost
+ * 3*MANT_DIG bits. We arrange that subtracting 1 is exact in
+ * doubled precision, and then do the rest of the calculation
+ * in sloppy doubled precision. Although large cancellations
+ * often lose lots of accuracy, here the final result is exact
+ * in doubled precision if the large calculation occurs (because
+ * then it is exact in tripled precision and the cancellation
+ * removes enough bits to fit in doubled precision). Thus the
+ * result is accurate in sloppy doubled precision, and the only
+ * significant loss of accuracy is when it is summed and passed
+ * to log1p().
+ */
+ sh = ax2h;
+ sl = ay2h;
+ _2sumF(sh, sl);
+ if (sh < 0.5F || sh >= 3)
+ return (CMPLXF(logf(ay2l + ax2l + sl + sh) / 2, v));
+ sh -= 1;
+ _2sum(sh, sl);
+ _2sum(ax2l, ay2l);
+ /* Briggs-Kahan algorithm (except we discard the final low term): */
+ _2sum(sh, ax2l);
+ _2sum(sl, ay2l);
+ t = ax2l + sl;
+ _2sumF(sh, t);
+ return (CMPLXF(log1pf(ay2l + t + sh) / 2, v));
+}
Copied: stable/11/lib/msun/src/s_clogl.c (from r333577,
head/lib/msun/src/s_clogl.c)
==============================================================================
--- /dev/null 00:00:00 1970 (empty, because file is newly added)
+++ stable/11/lib/msun/src/s_clogl.c Tue Jun 5 13:46:18 2018
(r334654, copy of r333577, head/lib/msun/src/s_clogl.c)
@@ -0,0 +1,168 @@
+/*-
+ * Copyright (c) 2013 Bruce D. Evans
+ * 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 unmodified, 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 ``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 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>
+#ifdef __i386__
+#include <ieeefp.h>
+#endif
+
+#include "fpmath.h"
+#include "math.h"
+#include "math_private.h"
+
+#define MANT_DIG LDBL_MANT_DIG
+#define MAX_EXP LDBL_MAX_EXP
+#define MIN_EXP LDBL_MIN_EXP
+
+static const double
+ln2_hi = 6.9314718055829871e-1; /* 0x162e42fefa0000.0p-53 */
+
+#if LDBL_MANT_DIG == 64
+#define MULT_REDUX 0x1p32 /* exponent MANT_DIG / 2
rounded up */
+static const double
+ln2l_lo = 1.6465949582897082e-12; /* 0x1cf79abc9e3b3a.0p-92 */
+#elif LDBL_MANT_DIG == 113
+#define MULT_REDUX 0x1p57
+static const long double
+ln2l_lo = 1.64659495828970812809844307550013433e-12L; /*
0x1cf79abc9e3b39803f2f6af40f343.0p-152L */
+#else
+#error "Unsupported long double format"
+#endif
+
+long double complex
+clogl(long double complex z)
+{
+ long double ax, ax2h, ax2l, axh, axl, ay, ay2h, ay2l, ayh, ayl;
+ long double sh, sl, t;
+ long double x, y, v;
+ uint16_t hax, hay;
+ int kx, ky;
+
+ ENTERIT(long double complex);
+
+ x = creall(z);
+ y = cimagl(z);
+ v = atan2l(y, x);
+
+ ax = fabsl(x);
+ ay = fabsl(y);
+ if (ax < ay) {
+ t = ax;
+ ax = ay;
+ ay = t;
+ }
+
+ GET_LDBL_EXPSIGN(hax, ax);
+ kx = hax - 16383;
+ GET_LDBL_EXPSIGN(hay, ay);
+ ky = hay - 16383;
+
+ /* Handle NaNs and Infs using the general formula. */
+ if (kx == MAX_EXP || ky == MAX_EXP)
+ RETURNI(CMPLXL(logl(hypotl(x, y)), v));
+
+ /* Avoid spurious underflow, and reduce inaccuracies when ax is 1. */
+ if (ax == 1) {
+ if (ky < (MIN_EXP - 1) / 2)
+ RETURNI(CMPLXL((ay / 2) * ay, v));
+ RETURNI(CMPLXL(log1pl(ay * ay) / 2, v));
+ }
+
+ /* Avoid underflow when ax is not small. Also handle zero args. */
+ if (kx - ky > MANT_DIG || ay == 0)
+ RETURNI(CMPLXL(logl(ax), v));
+
+ /* Avoid overflow. */
+ if (kx >= MAX_EXP - 1)
+ RETURNI(CMPLXL(logl(hypotl(x * 0x1p-16382L, y * 0x1p-16382L)) +
+ (MAX_EXP - 2) * ln2l_lo + (MAX_EXP - 2) * ln2_hi, v));
+ if (kx >= (MAX_EXP - 1) / 2)
+ RETURNI(CMPLXL(logl(hypotl(x, y)), v));
+
+ /* Reduce inaccuracies and avoid underflow when ax is denormal. */
+ if (kx <= MIN_EXP - 2)
+ RETURNI(CMPLXL(logl(hypotl(x * 0x1p16383L, y * 0x1p16383L)) +
+ (MIN_EXP - 2) * ln2l_lo + (MIN_EXP - 2) * ln2_hi, v));
+
+ /* Avoid remaining underflows (when ax is small but not denormal). */
+ if (ky < (MIN_EXP - 1) / 2 + MANT_DIG)
+ RETURNI(CMPLXL(logl(hypotl(x, y)), v));
+
+ /* Calculate ax*ax and ay*ay exactly using Dekker's algorithm. */
+ t = (long double)(ax * (MULT_REDUX + 1));
+ axh = (long double)(ax - t) + t;
+ axl = ax - axh;
+ ax2h = ax * ax;
+ ax2l = axh * axh - ax2h + 2 * axh * axl + axl * axl;
+ t = (long double)(ay * (MULT_REDUX + 1));
+ ayh = (long double)(ay - t) + t;
+ ayl = ay - ayh;
+ ay2h = ay * ay;
+ ay2l = ayh * ayh - ay2h + 2 * ayh * ayl + ayl * ayl;
+
+ /*
+ * When log(|z|) is far from 1, accuracy in calculating the sum
+ * of the squares is not very important since log() reduces
+ * inaccuracies. We depended on this to use the general
+ * formula when log(|z|) is very far from 1. When log(|z|) is
+ * moderately far from 1, we go through the extra-precision
+ * calculations to reduce branches and gain a little accuracy.
+ *
+ * When |z| is near 1, we subtract 1 and use log1p() and don't
+ * leave it to log() to subtract 1, since we gain at least 1 bit
+ * of accuracy in this way.
+ *
+ * When |z| is very near 1, subtracting 1 can cancel almost
+ * 3*MANT_DIG bits. We arrange that subtracting 1 is exact in
+ * doubled precision, and then do the rest of the calculation
+ * in sloppy doubled precision. Although large cancellations
+ * often lose lots of accuracy, here the final result is exact
+ * in doubled precision if the large calculation occurs (because
+ * then it is exact in tripled precision and the cancellation
+ * removes enough bits to fit in doubled precision). Thus the
+ * result is accurate in sloppy doubled precision, and the only
+ * significant loss of accuracy is when it is summed and passed
+ * to log1p().
+ */
+ sh = ax2h;
+ sl = ay2h;
+ _2sumF(sh, sl);
+ if (sh < 0.5 || sh >= 3)
+ RETURNI(CMPLXL(logl(ay2l + ax2l + sl + sh) / 2, v));
+ sh -= 1;
+ _2sum(sh, sl);
+ _2sum(ax2l, ay2l);
+ /* Briggs-Kahan algorithm (except we discard the final low term): */
+ _2sum(sh, ax2l);
+ _2sum(sl, ay2l);
+ t = ax2l + sl;
+ _2sumF(sh, t);
+ RETURNI(CMPLXL(log1pl(ay2l + t + sh) / 2, v));
+}
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