2010-10-15 19:26:06 +00:00
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/* Compute x * y + z as ternary operation.
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2022-01-01 18:54:23 +00:00
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Copyright (C) 2010-2022 Free Software Foundation, Inc.
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2010-10-15 19:26:06 +00:00
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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2012-02-09 23:18:22 +00:00
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License along with the GNU C Library; if not, see
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Prefer https to http for gnu.org and fsf.org URLs
Also, change sources.redhat.com to sourceware.org.
This patch was automatically generated by running the following shell
script, which uses GNU sed, and which avoids modifying files imported
from upstream:
sed -ri '
s,(http|ftp)(://(.*\.)?(gnu|fsf|sourceware)\.org($|[^.]|\.[^a-z])),https\2,g
s,(http|ftp)(://(.*\.)?)sources\.redhat\.com($|[^.]|\.[^a-z]),https\2sourceware.org\4,g
' \
$(find $(git ls-files) -prune -type f \
! -name '*.po' \
! -name 'ChangeLog*' \
! -path COPYING ! -path COPYING.LIB \
! -path manual/fdl-1.3.texi ! -path manual/lgpl-2.1.texi \
! -path manual/texinfo.tex ! -path scripts/config.guess \
! -path scripts/config.sub ! -path scripts/install-sh \
! -path scripts/mkinstalldirs ! -path scripts/move-if-change \
! -path INSTALL ! -path locale/programs/charmap-kw.h \
! -path po/libc.pot ! -path sysdeps/gnu/errlist.c \
! '(' -name configure \
-execdir test -f configure.ac -o -f configure.in ';' ')' \
! '(' -name preconfigure \
-execdir test -f preconfigure.ac ';' ')' \
-print)
and then by running 'make dist-prepare' to regenerate files built
from the altered files, and then executing the following to cleanup:
chmod a+x sysdeps/unix/sysv/linux/riscv/configure
# Omit irrelevant whitespace and comment-only changes,
# perhaps from a slightly-different Autoconf version.
git checkout -f \
sysdeps/csky/configure \
sysdeps/hppa/configure \
sysdeps/riscv/configure \
sysdeps/unix/sysv/linux/csky/configure
# Omit changes that caused a pre-commit check to fail like this:
# remote: *** error: sysdeps/powerpc/powerpc64/ppc-mcount.S: trailing lines
git checkout -f \
sysdeps/powerpc/powerpc64/ppc-mcount.S \
sysdeps/unix/sysv/linux/s390/s390-64/syscall.S
# Omit change that caused a pre-commit check to fail like this:
# remote: *** error: sysdeps/sparc/sparc64/multiarch/memcpy-ultra3.S: last line does not end in newline
git checkout -f sysdeps/sparc/sparc64/multiarch/memcpy-ultra3.S
2019-09-07 05:40:42 +00:00
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<https://www.gnu.org/licenses/>. */
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2010-10-15 19:26:06 +00:00
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2021-09-15 22:57:35 +00:00
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#define NO_MATH_REDIRECT
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2010-10-15 19:26:06 +00:00
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#include <float.h>
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#include <math.h>
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#include <fenv.h>
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#include <ieee754.h>
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2018-05-11 15:11:38 +00:00
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#include <math-barriers.h>
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2017-10-05 21:13:40 +00:00
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#include <libm-alias-ldouble.h>
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2012-10-31 13:01:17 +00:00
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#include <tininess.h>
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2010-10-15 19:26:06 +00:00
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/* This implementation uses rounding to odd to avoid problems with
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double rounding. See a paper by Boldo and Melquiond:
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http://www.lri.fr/~melquion/doc/08-tc.pdf */
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long double
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__fmal (long double x, long double y, long double z)
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{
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union ieee854_long_double u, v, w;
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int adjust = 0;
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u.d = x;
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v.d = y;
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w.d = z;
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if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
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>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS
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- LDBL_MANT_DIG, 0)
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|| __builtin_expect (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
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|| __builtin_expect (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
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|| __builtin_expect (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
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|| __builtin_expect (u.ieee.exponent + v.ieee.exponent
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<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG, 0))
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{
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/* If z is Inf, but x and y are finite, the result should be
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z rather than NaN. */
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if (w.ieee.exponent == 0x7fff
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&& u.ieee.exponent != 0x7fff
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&& v.ieee.exponent != 0x7fff)
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return (z + x) + y;
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2012-10-01 08:30:06 +00:00
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/* If z is zero and x are y are nonzero, compute the result
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as x * y to avoid the wrong sign of a zero result if x * y
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underflows to 0. */
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if (z == 0 && x != 0 && y != 0)
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return x * y;
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2012-11-04 19:26:02 +00:00
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/* If x or y or z is Inf/NaN, or if x * y is zero, compute as
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x * y + z. */
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2010-10-15 19:26:06 +00:00
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if (u.ieee.exponent == 0x7fff
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|| v.ieee.exponent == 0x7fff
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|| w.ieee.exponent == 0x7fff
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2012-11-01 16:47:26 +00:00
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|| x == 0
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|| y == 0)
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2010-10-15 19:26:06 +00:00
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return x * y + z;
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2012-11-04 19:26:02 +00:00
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/* If fma will certainly overflow, compute as x * y. */
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if (u.ieee.exponent + v.ieee.exponent
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> 0x7fff + IEEE854_LONG_DOUBLE_BIAS)
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return x * y;
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2015-10-28 21:42:52 +00:00
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/* If x * y is less than 1/4 of LDBL_TRUE_MIN, neither the
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2012-11-01 16:47:26 +00:00
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result nor whether there is underflow depends on its exact
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value, only on its sign. */
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if (u.ieee.exponent + v.ieee.exponent
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< IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2)
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{
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int neg = u.ieee.negative ^ v.ieee.negative;
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long double tiny = neg ? -0x1p-16445L : 0x1p-16445L;
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if (w.ieee.exponent >= 3)
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return tiny + z;
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/* Scaling up, adding TINY and scaling down produces the
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correct result, because in round-to-nearest mode adding
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TINY has no effect and in other modes double rounding is
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harmless. But it may not produce required underflow
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exceptions. */
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v.d = z * 0x1p65L + tiny;
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if (TININESS_AFTER_ROUNDING
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? v.ieee.exponent < 66
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: (w.ieee.exponent == 0
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|| (w.ieee.exponent == 1
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&& w.ieee.negative != neg
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&& w.ieee.mantissa1 == 0
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&& w.ieee.mantissa0 == 0x80000000)))
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{
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2015-09-23 22:42:30 +00:00
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long double force_underflow = x * y;
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math_force_eval (force_underflow);
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2012-11-01 16:47:26 +00:00
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}
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return v.d * 0x1p-65L;
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}
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2010-10-15 19:26:06 +00:00
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if (u.ieee.exponent + v.ieee.exponent
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>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG)
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{
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/* Compute 1p-64 times smaller result and multiply
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at the end. */
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if (u.ieee.exponent > v.ieee.exponent)
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u.ieee.exponent -= LDBL_MANT_DIG;
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else
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v.ieee.exponent -= LDBL_MANT_DIG;
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/* If x + y exponent is very large and z exponent is very small,
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it doesn't matter if we don't adjust it. */
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if (w.ieee.exponent > LDBL_MANT_DIG)
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w.ieee.exponent -= LDBL_MANT_DIG;
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adjust = 1;
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}
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else if (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
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{
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/* Similarly.
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If z exponent is very large and x and y exponents are
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2012-11-06 14:12:54 +00:00
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very small, adjust them up to avoid spurious underflows,
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rather than down. */
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if (u.ieee.exponent + v.ieee.exponent
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Fix fma spurious underflows (bug 18824).
Various fma implementations have logic that, when computing fma (x, y,
z) where z is large (so care needs taking to avoid internal overflow)
but x * y is small, scale x * y up instead of down to avoid internal
underflows resulting from scaling down. (In these cases, x * y is
small enough that only its sign actually matters rather than the exact
value.)
The threshold for scaling up instead of down was correct for "if the
unscaled values were multiplied, the low part of the multiplication
could underflow", and the scaling was sufficient to ensure that the
low part of the multiplication did not underflow (given that cases of
very small x * y - less than half the least subnormal - were
previously dealt with). However, the choice in the functions wasn't
between scaling up or no scaling, but between scaling up and scaling
down (scaling down actually being needed when x * y isn't so small
compared to z and so the exact value does matter). Thus a larger
threshold is needed to ensure that scaling down doesn't produce values
the multiplication of whose low parts underflows. This patch
increases the thresholds accordingly.
Tested for x86_64, x86 and mips64 (with the MIPS version of s_fmal.c
removed so that the ldbl-128 version gets tested instead of the
soft-fp one).
[BZ #18824]
* sysdeps/ieee754/dbl-64/s_fma.c (__fma): Increase threshold for
scaling x * y up instead of down.
* sysdeps/ieee754/ldbl-128/s_fmal.c (__fmal): Likewise.
* sysdeps/ieee754/ldbl-96/s_fmal.c (__fmal): Likewise.
* math/auto-libm-test-in: Add more tests of fma.
* math/auto-libm-test-out: Regenerated.
2015-08-14 17:15:06 +00:00
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<= IEEE854_LONG_DOUBLE_BIAS + 2 * LDBL_MANT_DIG)
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2012-11-06 14:12:54 +00:00
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{
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if (u.ieee.exponent > v.ieee.exponent)
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u.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
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else
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v.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
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}
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else if (u.ieee.exponent > v.ieee.exponent)
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2010-10-15 19:26:06 +00:00
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{
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if (u.ieee.exponent > LDBL_MANT_DIG)
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u.ieee.exponent -= LDBL_MANT_DIG;
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}
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else if (v.ieee.exponent > LDBL_MANT_DIG)
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v.ieee.exponent -= LDBL_MANT_DIG;
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w.ieee.exponent -= LDBL_MANT_DIG;
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adjust = 1;
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}
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else if (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
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{
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u.ieee.exponent -= LDBL_MANT_DIG;
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if (v.ieee.exponent)
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v.ieee.exponent += LDBL_MANT_DIG;
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else
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v.d *= 0x1p64L;
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}
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else if (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
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{
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v.ieee.exponent -= LDBL_MANT_DIG;
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if (u.ieee.exponent)
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u.ieee.exponent += LDBL_MANT_DIG;
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else
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u.d *= 0x1p64L;
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}
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else /* if (u.ieee.exponent + v.ieee.exponent
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<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */
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{
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if (u.ieee.exponent > v.ieee.exponent)
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2012-11-06 14:12:54 +00:00
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u.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
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2010-10-15 19:26:06 +00:00
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else
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2012-11-06 14:12:54 +00:00
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v.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
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if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 6)
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2010-10-15 19:26:06 +00:00
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{
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if (w.ieee.exponent)
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2012-11-06 14:12:54 +00:00
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w.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
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2010-10-15 19:26:06 +00:00
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else
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2012-11-06 14:12:54 +00:00
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w.d *= 0x1p130L;
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2010-10-15 19:26:06 +00:00
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adjust = -1;
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}
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/* Otherwise x * y should just affect inexact
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and nothing else. */
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}
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x = u.d;
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y = v.d;
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z = w.d;
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}
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2012-09-29 18:31:54 +00:00
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/* Ensure correct sign of exact 0 + 0. */
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2014-02-10 13:45:42 +00:00
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if (__glibc_unlikely ((x == 0 || y == 0) && z == 0))
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2016-01-15 13:22:59 +00:00
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{
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x = math_opt_barrier (x);
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return x * y + z;
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}
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2012-09-29 18:31:54 +00:00
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2012-11-03 19:48:53 +00:00
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fenv_t env;
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feholdexcept (&env);
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fesetround (FE_TONEAREST);
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2010-10-15 19:26:06 +00:00
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/* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
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#define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
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long double x1 = x * C;
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long double y1 = y * C;
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long double m1 = x * y;
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x1 = (x - x1) + x1;
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y1 = (y - y1) + y1;
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long double x2 = x - x1;
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long double y2 = y - y1;
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long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
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/* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
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long double a1 = z + m1;
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long double t1 = a1 - z;
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long double t2 = a1 - t1;
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t1 = m1 - t1;
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t2 = z - t2;
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long double a2 = t1 + t2;
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2014-08-01 22:13:50 +00:00
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/* Ensure the arithmetic is not scheduled after feclearexcept call. */
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math_force_eval (m2);
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math_force_eval (a2);
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2012-11-03 19:48:53 +00:00
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feclearexcept (FE_INEXACT);
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2014-08-01 22:13:50 +00:00
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/* If the result is an exact zero, ensure it has the correct sign. */
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2012-11-03 19:48:53 +00:00
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if (a1 == 0 && m2 == 0)
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{
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feupdateenv (&env);
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2014-08-01 22:13:50 +00:00
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/* Ensure that round-to-nearest value of z + m1 is not reused. */
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z = math_opt_barrier (z);
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2012-11-03 19:48:53 +00:00
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return z + m1;
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}
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2010-10-15 19:26:06 +00:00
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fesetround (FE_TOWARDZERO);
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/* Perform m2 + a2 addition with round to odd. */
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u.d = a2 + m2;
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2014-02-10 13:45:42 +00:00
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if (__glibc_likely (adjust == 0))
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2010-10-15 19:26:06 +00:00
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{
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if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
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u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
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feupdateenv (&env);
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/* Result is a1 + u.d. */
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return a1 + u.d;
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}
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2014-02-10 13:45:42 +00:00
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else if (__glibc_likely (adjust > 0))
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2010-10-15 19:26:06 +00:00
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{
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if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
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u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
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feupdateenv (&env);
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/* Result is a1 + u.d, scaled up. */
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return (a1 + u.d) * 0x1p64L;
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}
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else
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{
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if ((u.ieee.mantissa1 & 1) == 0)
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u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
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v.d = a1 + u.d;
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2012-06-01 19:02:21 +00:00
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/* Ensure the addition is not scheduled after fetestexcept call. */
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|
|
|
math_force_eval (v.d);
|
2010-10-15 19:26:06 +00:00
|
|
|
int j = fetestexcept (FE_INEXACT) != 0;
|
|
|
|
feupdateenv (&env);
|
|
|
|
/* Ensure the following computations are performed in default rounding
|
|
|
|
mode instead of just reusing the round to zero computation. */
|
|
|
|
asm volatile ("" : "=m" (u) : "m" (u));
|
|
|
|
/* If a1 + u.d is exact, the only rounding happens during
|
|
|
|
scaling down. */
|
|
|
|
if (j == 0)
|
2012-11-06 14:12:54 +00:00
|
|
|
return v.d * 0x1p-130L;
|
2010-10-15 19:26:06 +00:00
|
|
|
/* If result rounded to zero is not subnormal, no double
|
|
|
|
rounding will occur. */
|
2012-11-06 14:12:54 +00:00
|
|
|
if (v.ieee.exponent > 130)
|
|
|
|
return (a1 + u.d) * 0x1p-130L;
|
|
|
|
/* If v.d * 0x1p-130L with round to zero is a subnormal above
|
|
|
|
or equal to LDBL_MIN / 2, then v.d * 0x1p-130L shifts mantissa
|
2010-10-15 19:26:06 +00:00
|
|
|
down just by 1 bit, which means v.ieee.mantissa1 |= j would
|
|
|
|
change the round bit, not sticky or guard bit.
|
2012-11-06 14:12:54 +00:00
|
|
|
v.d * 0x1p-130L never normalizes by shifting up,
|
2010-10-15 19:26:06 +00:00
|
|
|
so round bit plus sticky bit should be already enough
|
|
|
|
for proper rounding. */
|
2012-11-06 14:12:54 +00:00
|
|
|
if (v.ieee.exponent == 130)
|
2010-10-15 19:26:06 +00:00
|
|
|
{
|
2012-10-31 13:01:17 +00:00
|
|
|
/* If the exponent would be in the normal range when
|
|
|
|
rounding to normal precision with unbounded exponent
|
|
|
|
range, the exact result is known and spurious underflows
|
|
|
|
must be avoided on systems detecting tininess after
|
|
|
|
rounding. */
|
|
|
|
if (TININESS_AFTER_ROUNDING)
|
|
|
|
{
|
|
|
|
w.d = a1 + u.d;
|
2012-11-06 14:12:54 +00:00
|
|
|
if (w.ieee.exponent == 131)
|
|
|
|
return w.d * 0x1p-130L;
|
2012-10-31 13:01:17 +00:00
|
|
|
}
|
2010-10-15 19:26:06 +00:00
|
|
|
/* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding,
|
|
|
|
v.ieee.mantissa1 & 1 is the round bit and j is our sticky
|
2012-10-30 13:54:50 +00:00
|
|
|
bit. */
|
|
|
|
w.d = 0.0L;
|
|
|
|
w.ieee.mantissa1 = ((v.ieee.mantissa1 & 3) << 1) | j;
|
|
|
|
w.ieee.negative = v.ieee.negative;
|
|
|
|
v.ieee.mantissa1 &= ~3U;
|
2012-11-06 14:12:54 +00:00
|
|
|
v.d *= 0x1p-130L;
|
2012-10-30 13:54:50 +00:00
|
|
|
w.d *= 0x1p-2L;
|
|
|
|
return v.d + w.d;
|
2010-10-15 19:26:06 +00:00
|
|
|
}
|
|
|
|
v.ieee.mantissa1 |= j;
|
2012-11-06 14:12:54 +00:00
|
|
|
return v.d * 0x1p-130L;
|
2010-10-15 19:26:06 +00:00
|
|
|
}
|
|
|
|
}
|
2017-10-05 21:13:40 +00:00
|
|
|
libm_alias_ldouble (__fma, fma)
|