glibc/sysdeps/ieee754/dbl-64/e_sqrt.c
Joseph Myers 60f435bb0c Use hex float constants in sysdeps/ieee754/dbl-64/e_sqrt.c.
Various sysdeps/ieee754/dbl-64 functions use double constants defined
using a union between a double and two ints, with separate big-endian
and little-endian definitions of the constants.

With modern C, this is unnecessary complication; hex float constants
(or __builtin_inf etc.) suffice to specify the exact value desired,
and so can avoid separate versions for each endianness.  Having this
complication also complicates cleanups such as removing slow paths
from these library functions, as they need to make sure to remove both
copies of variables that are no longer used after such a cleanup (and
in at least one case, proper removal of a slow path will also involve
removing slow-path-only values from the middle of an array - an array
with both big-endian and little-endian copies - and adjusting other
references to that array).

So it makes sense to clean up the code to define these constants using
hex floats and so eliminate the endianness conditional.  This patch
does so in the case of sqrt, where the two constants are such that it
makes sense just to put them directly in the code using them and
eliminate the names for them altogether.

Tested for arm (the code generated for sqrt does change, though not in
any significant way).

	* sysdeps/ieee754/dbl-64/e_sqrt.c: Do not include uroot.h.
	(__ieee754_sqrt): Use hex float constants instead of tm256.x and
	t512.x.
	* sysdeps/ieee754/dbl-64/uroot.h: Remove file.
2015-12-01 01:01:36 +00:00

140 lines
4.8 KiB
C

/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2015 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or
* (at your option) any later version.
*
* This program 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, see <http://www.gnu.org/licenses/>.
*/
/*********************************************************************/
/* MODULE_NAME: uroot.c */
/* */
/* FUNCTION: usqrt */
/* */
/* FILES NEEDED: dla.h endian.h mydefs.h */
/* uroot.tbl */
/* */
/* An ultimate sqrt routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of square */
/* root of x. */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/*********************************************************************/
#include "endian.h"
#include "mydefs.h"
#include <dla.h>
#include "MathLib.h"
#include "root.tbl"
#include <math_private.h>
/*********************************************************************/
/* An ultimate sqrt routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of square */
/* root of x. */
/*********************************************************************/
double
__ieee754_sqrt (double x)
{
static const double
rt0 = 9.99999999859990725855365213134618E-01,
rt1 = 4.99999999495955425917856814202739E-01,
rt2 = 3.75017500867345182581453026130850E-01,
rt3 = 3.12523626554518656309172508769531E-01;
static const double big = 134217728.0;
double y, t, del, res, res1, hy, z, zz, p, hx, tx, ty, s;
mynumber a, c = { { 0, 0 } };
int4 k;
a.x = x;
k = a.i[HIGH_HALF];
a.i[HIGH_HALF] = (k & 0x001fffff) | 0x3fe00000;
t = inroot[(k & 0x001fffff) >> 14];
s = a.x;
/*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
if (k > 0x000fffff && k < 0x7ff00000)
{
int rm = __fegetround ();
fenv_t env;
libc_feholdexcept_setround (&env, FE_TONEAREST);
double ret;
y = 1.0 - t * (t * s);
t = t * (rt0 + y * (rt1 + y * (rt2 + y * rt3)));
c.i[HIGH_HALF] = 0x20000000 + ((k & 0x7fe00000) >> 1);
y = t * s;
hy = (y + big) - big;
del = 0.5 * t * ((s - hy * hy) - (y - hy) * (y + hy));
res = y + del;
if (res == (res + 1.002 * ((y - res) + del)))
ret = res * c.x;
else
{
res1 = res + 1.5 * ((y - res) + del);
EMULV (res, res1, z, zz, p, hx, tx, hy, ty); /* (z+zz)=res*res1 */
res = ((((z - s) + zz) < 0) ? max (res, res1) :
min (res, res1));
ret = res * c.x;
}
math_force_eval (ret);
libc_fesetenv (&env);
double dret = x / ret;
if (dret != ret)
{
double force_inexact = 1.0 / 3.0;
math_force_eval (force_inexact);
/* The square root is inexact, ret is the round-to-nearest
value which may need adjusting for other rounding
modes. */
switch (rm)
{
#ifdef FE_UPWARD
case FE_UPWARD:
if (dret > ret)
ret = (res + 0x1p-1022) * c.x;
break;
#endif
#ifdef FE_DOWNWARD
case FE_DOWNWARD:
#endif
#ifdef FE_TOWARDZERO
case FE_TOWARDZERO:
#endif
#if defined FE_DOWNWARD || defined FE_TOWARDZERO
if (dret < ret)
ret = (res - 0x1p-1022) * c.x;
break;
#endif
default:
break;
}
}
/* Otherwise (x / ret == ret), either the square root was exact or
the division was inexact. */
return ret;
}
else
{
if ((k & 0x7ff00000) == 0x7ff00000)
return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
if (x == 0)
return x; /* sqrt(+0)=+0, sqrt(-0)=-0 */
if (k < 0)
return (x - x) / (x - x); /* sqrt(-ve)=sNaN */
return 0x1p-256 * __ieee754_sqrt (x * 0x1p512);
}
}
strong_alias (__ieee754_sqrt, __sqrt_finite)