2004-05-26 04:47:00 +00:00
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/* Single-precision floating point square root.
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2022-01-01 18:54:23 +00:00
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Copyright (C) 1997-2022 Free Software Foundation, Inc.
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2004-05-26 04:47:00 +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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2004-05-26 04:47:00 +00:00
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#include <math.h>
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#include <math_private.h>
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#include <fenv_libc.h>
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2019-07-16 15:17:22 +00:00
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#include <libm-alias-finite.h>
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2020-06-04 19:47:16 +00:00
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#include <math-use-builtins.h>
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2004-05-26 04:47:00 +00:00
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2020-06-04 19:47:16 +00:00
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float
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__ieee754_sqrtf (float x)
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{
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#if USE_SQRTF_BUILTIN
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return __builtin_sqrtf (x);
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#else
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2004-05-26 04:47:00 +00:00
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/* The method is based on a description in
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Computation of elementary functions on the IBM RISC System/6000 processor,
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P. W. Markstein, IBM J. Res. Develop, 34(1) 1990.
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2009-11-06 17:33:27 +00:00
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Basically, it consists of two interleaved Newton-Raphson approximations,
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2004-05-26 04:47:00 +00:00
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one to find the actual square root, and one to find its reciprocal
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without the expense of a division operation. The tricky bit here
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is the use of the POWER/PowerPC multiply-add operation to get the
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required accuracy with high speed.
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The argument reduction works by a combination of table lookup to
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obtain the initial guesses, and some careful modification of the
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generated guesses (which mostly runs on the integer unit, while the
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2009-11-06 17:33:27 +00:00
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Newton-Raphson is running on the FPU). */
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2004-05-26 04:47:00 +00:00
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2020-06-04 19:47:16 +00:00
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extern const float __t_sqrt[1024];
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2004-05-26 04:47:00 +00:00
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if (x > 0)
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{
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2020-06-04 19:47:16 +00:00
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if (x != INFINITY)
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2004-05-26 04:47:00 +00:00
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{
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/* Variables named starting with 's' exist in the
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argument-reduced space, so that 2 > sx >= 0.5,
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1.41... > sg >= 0.70.., 0.70.. >= sy > 0.35... .
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Variables named ending with 'i' are integer versions of
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floating-point values. */
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float sx; /* The value of which we're trying to find the square
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root. */
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float sg, g; /* Guess of the square root of x. */
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float sd, d; /* Difference between the square of the guess and x. */
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float sy; /* Estimate of 1/2g (overestimated by 1ulp). */
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float sy2; /* 2*sy */
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float e; /* Difference between y*g and 1/2 (note that e==se). */
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float shx; /* == sx * fsg */
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float fsg; /* sg*fsg == g. */
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fenv_t fe; /* Saved floating-point environment (stores rounding
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mode and whether the inexact exception is
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enabled). */
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uint32_t xi, sxi, fsgi;
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const float *t_sqrt;
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GET_FLOAT_WORD (xi, x);
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fe = fegetenv_register ();
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relax_fenv_state ();
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sxi = (xi & 0x3fffffff) | 0x3f000000;
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SET_FLOAT_WORD (sx, sxi);
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t_sqrt = __t_sqrt + (xi >> (23 - 8 - 1) & 0x3fe);
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sg = t_sqrt[0];
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sy = t_sqrt[1];
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2009-11-06 17:33:27 +00:00
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/* Here we have three Newton-Raphson iterations each of a
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2004-05-26 04:47:00 +00:00
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division and a square root and the remainder of the
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argument reduction, all interleaved. */
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2015-02-13 16:20:36 +00:00
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sd = -__builtin_fmaf (sg, sg, -sx);
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2004-05-26 04:47:00 +00:00
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fsgi = (xi + 0x40000000) >> 1 & 0x7f800000;
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sy2 = sy + sy;
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2015-02-13 16:20:36 +00:00
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sg = __builtin_fmaf (sy, sd, sg); /* 16-bit approximation to
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sqrt(sx). */
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2020-06-04 19:47:16 +00:00
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e = -__builtin_fmaf (sy, sg, -0x1.0000020365653p-1);
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2004-05-26 04:47:00 +00:00
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SET_FLOAT_WORD (fsg, fsgi);
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2015-02-13 16:20:36 +00:00
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sd = -__builtin_fmaf (sg, sg, -sx);
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sy = __builtin_fmaf (e, sy2, sy);
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2004-05-26 04:47:00 +00:00
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if ((xi & 0x7f800000) == 0)
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goto denorm;
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shx = sx * fsg;
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2015-02-13 16:20:36 +00:00
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sg = __builtin_fmaf (sy, sd, sg); /* 32-bit approximation to
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sqrt(sx), but perhaps
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rounded incorrectly. */
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2004-05-26 04:47:00 +00:00
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sy2 = sy + sy;
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g = sg * fsg;
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2020-06-04 19:47:16 +00:00
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e = -__builtin_fmaf (sy, sg, -0x1.0000020365653p-1);
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2015-02-13 16:20:36 +00:00
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d = -__builtin_fmaf (g, sg, -shx);
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sy = __builtin_fmaf (e, sy2, sy);
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2004-05-26 04:47:00 +00:00
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fesetenv_register (fe);
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2015-02-13 16:20:36 +00:00
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return __builtin_fmaf (sy, d, g);
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2004-05-26 04:47:00 +00:00
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denorm:
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/* For denormalised numbers, we normalise, calculate the
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square root, and return an adjusted result. */
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fesetenv_register (fe);
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2020-06-04 19:47:16 +00:00
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return __ieee754_sqrtf (x * 0x1p+48) * 0x1p-24;
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2004-05-26 04:47:00 +00:00
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}
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}
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else if (x < 0)
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{
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/* For some reason, some PowerPC32 processors don't implement
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2011-10-12 15:27:51 +00:00
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FE_INVALID_SQRT. */
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2020-06-04 19:47:16 +00:00
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# ifdef FE_INVALID_SQRT
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2004-05-26 04:47:00 +00:00
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feraiseexcept (FE_INVALID_SQRT);
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2008-04-12 03:39:30 +00:00
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fenv_union_t u = { .fenv = fegetenv_register () };
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2013-08-17 08:58:55 +00:00
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if ((u.l & FE_INVALID) == 0)
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2020-06-04 19:47:16 +00:00
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# endif
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2004-05-26 04:47:00 +00:00
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feraiseexcept (FE_INVALID);
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2020-06-04 19:47:16 +00:00
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x = NAN;
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2004-05-26 04:47:00 +00:00
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}
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return f_washf (x);
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2020-06-04 19:47:16 +00:00
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#endif /* USE_SQRTF_BUILTIN */
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2004-05-26 04:47:00 +00:00
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}
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2019-07-16 15:17:22 +00:00
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libm_alias_finite (__ieee754_sqrtf, __sqrtf)
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