glibc/sysdeps/powerpc/w_sqrt.c
Ulrich Drepper 39e16978c3 Update.
1997-08-29 02:36  Ulrich Drepper  <drepper@cygnus.com>

	* Makefile (version-info.h): Use ISO form for the date.

	* catgets/catgetsinfo.h: Include <bits/libc-lock.h>.
	(struct catalog_obj): Add lock field.
	(__open_catalog): Remove second parameter from prototype.
	* catgets/catgets.c (catopen): Initialize lock field.
	(catgets): Don't pass second parameter to __open_catalog.
	* catgets/gencat.c: Initialize lock field and don't pass second
	parameter to __open_catalog.
	* catgets/open_catalog.c (__open_catalog): Decide about use of
	path by examining path in struct, not based on extra argument.
	Acquire a the lock before trying to load the catalog and release
	it before returning.

	* csu/Makefile (abi-tag.h): Make sure target directory exists.

	* io/Makefile (headers): Add bits/poll.h.
	* io/sys/poll.h: Remove definitions of POLL* constants.
	Include <bits/poll.h>.
	* sysdeps/generic/bits/poll.h: New file.
	* sysdeps/unix/sysv/linux/bits/poll.h: New file.
	* sysdeps/unix/sysv/linux/m68k/bits/poll.h: New file.
	* sysdeps/unix/sysv/linux/mips/bits/poll.h: New file.
	* sysdeps/unix/sysv/linux/sparc/bits/poll.h: New file.

	* libio/fileops.c (_IO_file_read, _IO_file_write): Remove dead code.

	* malloc/obstack.c: Add casts to keep very verbose compilers on
	64bit machine quiet.

	* nss/Makefile (libnss_db.so): Find libdb.so in db2 directory.

1997-08-28 17:30  Ulrich Drepper  <drepper@cygnus.com>

	* catgets/catgets.c (catopen): Correctly determine length of string
	in NLSPATH evironment variable.  Patch by HJ Lu <hjl@gnu.ai.mit.edu>.

1997-08-27 23:19  Richard Henderson  <rth@cygnus.com>

	* sysdeps/generic/dl-sysdep.c (DL_FIND_ARG_COMPONENTS): Provide
	default macro to track down arguments from stack start.
	(_dl_sysdep_start): Use it.
	* sysdeps/unix/sysv/linux/powerpc/dl-sysdep.c: Truncate to simply
	providing a special DL_FIND_ARG_COMPONENTS and including the next
	file up the line.

	* sysdeps/powerpc/e_sqrt.c: Move contents to w_sqrt.c and provide stub.
	* sysdeps/powerpc/e_sqrtf.c: Likewise.
	* sysdeps/powerpc/s_copysignf.S: Provide empty file; symbol is with
	the double precision version.
	* sysdeps/powerpc/s_fabsf.S: Likewise.
	* sysdeps/powerpc/s_isnanf.S: Likewise.
1997-08-29 01:19:12 +00:00

142 lines
5.0 KiB
C

/* Single-precision floating point square root.
Copyright (C) 1997 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If not,
write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
#include <math.h>
#include <math_private.h>
#include <fenv_libc.h>
#include <inttypes.h>
static const double almost_half = 0.5000000000000001; /* 0.5 + 2^-53 */
static const uint32_t a_nan = 0x7fc00000;
static const uint32_t a_inf = 0x7f800000;
static const float two108 = 3.245185536584267269e+32;
static const float twom54 = 5.551115123125782702e-17;
extern const float __t_sqrt[1024];
/* The method is based on a description in
Computation of elementary functions on the IBM RISC System/6000 processor,
P. W. Markstein, IBM J. Res. Develop, 34(1) 1990.
Basically, it consists of two interleaved Newton-Rhapson approximations,
one to find the actual square root, and one to find its reciprocal
without the expense of a division operation. The tricky bit here
is the use of the POWER/PowerPC multiply-add operation to get the
required accuracy with high speed.
The argument reduction works by a combination of table lookup to
obtain the initial guesses, and some careful modification of the
generated guesses (which mostly runs on the integer unit, while the
Newton-Rhapson is running on the FPU). */
double
__sqrt(double x)
{
const float inf = *(const float *)&a_inf;
/* x = f_wash(x); *//* This ensures only one exception for SNaN. */
if (x > 0)
{
if (x != inf)
{
/* Variables named starting with 's' exist in the
argument-reduced space, so that 2 > sx >= 0.5,
1.41... > sg >= 0.70.., 0.70.. >= sy > 0.35... .
Variables named ending with 'i' are integer versions of
floating-point values. */
double sx; /* The value of which we're trying to find the
square root. */
double sg,g; /* Guess of the square root of x. */
double sd,d; /* Difference between the square of the guess and x. */
double sy; /* Estimate of 1/2g (overestimated by 1ulp). */
double sy2; /* 2*sy */
double e; /* Difference between y*g and 1/2 (se = e * fsy). */
double shx; /* == sx * fsg */
double fsg; /* sg*fsg == g. */
fenv_t fe; /* Saved floating-point environment (stores rounding
mode and whether the inexact exception is
enabled). */
uint32_t xi0, xi1, sxi, fsgi;
const float *t_sqrt;
fe = fegetenv_register();
EXTRACT_WORDS (xi0,xi1,x);
relax_fenv_state();
sxi = xi0 & 0x3fffffff | 0x3fe00000;
INSERT_WORDS (sx, sxi, xi1);
t_sqrt = __t_sqrt + (xi0 >> 52-32-8-1 & 0x3fe);
sg = t_sqrt[0];
sy = t_sqrt[1];
/* Here we have three Newton-Rhapson iterations each of a
division and a square root and the remainder of the
argument reduction, all interleaved. */
sd = -(sg*sg - sx);
fsgi = xi0 + 0x40000000 >> 1 & 0x7ff00000;
sy2 = sy + sy;
sg = sy*sd + sg; /* 16-bit approximation to sqrt(sx). */
INSERT_WORDS (fsg, fsgi, 0);
e = -(sy*sg - almost_half);
sd = -(sg*sg - sx);
if ((xi0 & 0x7ff00000) == 0)
goto denorm;
sy = sy + e*sy2;
sg = sg + sy*sd; /* 32-bit approximation to sqrt(sx). */
sy2 = sy + sy;
e = -(sy*sg - almost_half);
sd = -(sg*sg - sx);
sy = sy + e*sy2;
shx = sx * fsg;
sg = sg + sy*sd; /* 64-bit approximation to sqrt(sx),
but perhaps rounded incorrectly. */
sy2 = sy + sy;
g = sg * fsg;
e = -(sy*sg - almost_half);
d = -(g*sg - shx);
sy = sy + e*sy2;
fesetenv_register (fe);
return g + sy*d;
denorm:
/* For denormalised numbers, we normalise, calculate the
square root, and return an adjusted result. */
fesetenv_register (fe);
return __sqrt(x * two108) * twom54;
}
}
else if (x < 0)
{
#ifdef FE_INVALID_SQRT
feraiseexcept (FE_INVALID_SQRT);
/* For some reason, some PowerPC processors don't implement
FE_INVALID_SQRT. I guess no-one ever thought they'd be
used for square roots... :-) */
if (!fetestexcept (FE_INVALID))
#endif
feraiseexcept (FE_INVALID);
#ifndef _IEEE_LIBM
if (_LIB_VERSION != _IEEE_)
x = __kernel_standard(x,x,26);
else
#endif
x = *(const float*)&a_nan;
}
return f_wash(x);
}
weak_alias (__sqrt, sqrt)
/* Strictly, this is wrong, but the only places where _ieee754_sqrt is
used will not pass in a negative result. */
strong_alias(__sqrt,__ieee754_sqrt)