mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-23 13:30:06 +00:00
4da6db5188
This patch fixes bug 16315, bad pow handling of overflow/underflow in non-default rounding modes. Tests of pow are duly converted to ALL_RM_TEST to run all tests in all rounding modes. There are two main issues here. First, various implementations compute a negative result by negating a positive result, but this yields inappropriate overflow / underflow values for directed rounding, so either overflow / underflow results need recomputing in the correct sign, or the relevant overflowing / underflowing operation needs to be made to have a result of the correct sign. Second, the dbl-64 implementation sets FE_TONEAREST internally; in the overflow / underflow case, the result needs recomputing in the original rounding mode. Tested x86_64 and x86 and ulps updated accordingly. [BZ #16315] * sysdeps/i386/fpu/e_pow.S (__ieee754_pow): Ensure possibly overflowing or underflowing operations take place with sign of result. * sysdeps/i386/fpu/e_powf.S (__ieee754_powf): Likewise. * sysdeps/i386/fpu/e_powl.S (__ieee754_powl): Likewise. * sysdeps/ieee754/dbl-64/e_pow.c: Include <math.h>. (__ieee754_pow): Recompute overflowing and underflowing results in original rounding mode. * sysdeps/x86/fpu/powl_helper.c: Include <stdbool.h>. (__powl_helper): Allow negative argument X and scale negated value as needed. Avoid passing value outside [-1, 1] to f2xm1. * sysdeps/x86_64/fpu/e_powl.S (__ieee754_powl): Ensure possibly overflowing or underflowing operations take place with sign of result. * sysdeps/x86_64/fpu/multiarch/e_pow.c [HAVE_FMA4_SUPPORT]: Include <math.h>. * math/auto-libm-test-in: Add more tests of pow. * math/auto-libm-test-out: Regenerated. * math/libm-test.inc (pow_test): Use ALL_RM_TEST. (pow_tonearest_test_data): Remove. (pow_test_tonearest): Likewise. (pow_towardzero_test_data): Likewise. (pow_test_towardzero): Likewise. (pow_downward_test_data): Likewise. (pow_test_downward): Likewise. (pow_upward_test_data): Likewise. (pow_test_upward): Likewise. (main): Don't call removed functions. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
477 lines
13 KiB
C
477 lines
13 KiB
C
/*
|
|
* IBM Accurate Mathematical Library
|
|
* written by International Business Machines Corp.
|
|
* Copyright (C) 2001-2014 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: upow.c */
|
|
/* */
|
|
/* FUNCTIONS: upow */
|
|
/* power1 */
|
|
/* my_log2 */
|
|
/* log1 */
|
|
/* checkint */
|
|
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h */
|
|
/* halfulp.c mpexp.c mplog.c slowexp.c slowpow.c mpa.c */
|
|
/* uexp.c upow.c */
|
|
/* root.tbl uexp.tbl upow.tbl */
|
|
/* An ultimate power routine. Given two IEEE double machine numbers y,x */
|
|
/* it computes the correctly rounded (to nearest) value of x^y. */
|
|
/* Assumption: Machine arithmetic operations are performed in */
|
|
/* round to nearest mode of IEEE 754 standard. */
|
|
/* */
|
|
/***************************************************************************/
|
|
#include <math.h>
|
|
#include "endian.h"
|
|
#include "upow.h"
|
|
#include <dla.h>
|
|
#include "mydefs.h"
|
|
#include "MathLib.h"
|
|
#include "upow.tbl"
|
|
#include <math_private.h>
|
|
#include <fenv.h>
|
|
|
|
#ifndef SECTION
|
|
# define SECTION
|
|
#endif
|
|
|
|
static const double huge = 1.0e300, tiny = 1.0e-300;
|
|
|
|
double __exp1 (double x, double xx, double error);
|
|
static double log1 (double x, double *delta, double *error);
|
|
static double my_log2 (double x, double *delta, double *error);
|
|
double __slowpow (double x, double y, double z);
|
|
static double power1 (double x, double y);
|
|
static int checkint (double x);
|
|
|
|
/* An ultimate power routine. Given two IEEE double machine numbers y, x it
|
|
computes the correctly rounded (to nearest) value of X^y. */
|
|
double
|
|
SECTION
|
|
__ieee754_pow (double x, double y)
|
|
{
|
|
double z, a, aa, error, t, a1, a2, y1, y2;
|
|
mynumber u, v;
|
|
int k;
|
|
int4 qx, qy;
|
|
v.x = y;
|
|
u.x = x;
|
|
if (v.i[LOW_HALF] == 0)
|
|
{ /* of y */
|
|
qx = u.i[HIGH_HALF] & 0x7fffffff;
|
|
/* Is x a NaN? */
|
|
if (((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000))
|
|
return x;
|
|
if (y == 1.0)
|
|
return x;
|
|
if (y == 2.0)
|
|
return x * x;
|
|
if (y == -1.0)
|
|
return 1.0 / x;
|
|
if (y == 0)
|
|
return 1.0;
|
|
}
|
|
/* else */
|
|
if (((u.i[HIGH_HALF] > 0 && u.i[HIGH_HALF] < 0x7ff00000) || /* x>0 and not x->0 */
|
|
(u.i[HIGH_HALF] == 0 && u.i[LOW_HALF] != 0)) &&
|
|
/* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
|
|
(v.i[HIGH_HALF] & 0x7fffffff) < 0x4ff00000)
|
|
{ /* if y<-1 or y>1 */
|
|
double retval;
|
|
|
|
{
|
|
SET_RESTORE_ROUND (FE_TONEAREST);
|
|
|
|
/* Avoid internal underflow for tiny y. The exact value of y does
|
|
not matter if |y| <= 2**-64. */
|
|
if (ABS (y) < 0x1p-64)
|
|
y = y < 0 ? -0x1p-64 : 0x1p-64;
|
|
z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */
|
|
t = y * CN;
|
|
y1 = t - (t - y);
|
|
y2 = y - y1;
|
|
t = z * CN;
|
|
a1 = t - (t - z);
|
|
a2 = (z - a1) + aa;
|
|
a = y1 * a1;
|
|
aa = y2 * a1 + y * a2;
|
|
a1 = a + aa;
|
|
a2 = (a - a1) + aa;
|
|
error = error * ABS (y);
|
|
t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */
|
|
retval = (t > 0) ? t : power1 (x, y);
|
|
}
|
|
|
|
if (__isinf (retval))
|
|
retval = huge * huge;
|
|
else if (retval == 0)
|
|
retval = tiny * tiny;
|
|
return retval;
|
|
}
|
|
|
|
if (x == 0)
|
|
{
|
|
if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0)
|
|
|| (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */
|
|
return y;
|
|
if (ABS (y) > 1.0e20)
|
|
return (y > 0) ? 0 : 1.0 / 0.0;
|
|
k = checkint (y);
|
|
if (k == -1)
|
|
return y < 0 ? 1.0 / x : x;
|
|
else
|
|
return y < 0 ? 1.0 / 0.0 : 0.0; /* return 0 */
|
|
}
|
|
|
|
qx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */
|
|
qy = v.i[HIGH_HALF] & 0x7fffffff; /* no sign */
|
|
|
|
if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */
|
|
return x;
|
|
if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */
|
|
return x == 1.0 ? 1.0 : y;
|
|
|
|
/* if x<0 */
|
|
if (u.i[HIGH_HALF] < 0)
|
|
{
|
|
k = checkint (y);
|
|
if (k == 0)
|
|
{
|
|
if (qy == 0x7ff00000)
|
|
{
|
|
if (x == -1.0)
|
|
return 1.0;
|
|
else if (x > -1.0)
|
|
return v.i[HIGH_HALF] < 0 ? INF.x : 0.0;
|
|
else
|
|
return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x;
|
|
}
|
|
else if (qx == 0x7ff00000)
|
|
return y < 0 ? 0.0 : INF.x;
|
|
return (x - x) / (x - x); /* y not integer and x<0 */
|
|
}
|
|
else if (qx == 0x7ff00000)
|
|
{
|
|
if (k < 0)
|
|
return y < 0 ? nZERO.x : nINF.x;
|
|
else
|
|
return y < 0 ? 0.0 : INF.x;
|
|
}
|
|
/* if y even or odd */
|
|
if (k == 1)
|
|
return __ieee754_pow (-x, y);
|
|
else
|
|
{
|
|
double retval;
|
|
{
|
|
SET_RESTORE_ROUND (FE_TONEAREST);
|
|
retval = -__ieee754_pow (-x, y);
|
|
}
|
|
if (__isinf (retval))
|
|
retval = -huge * huge;
|
|
else if (retval == 0)
|
|
retval = -tiny * tiny;
|
|
return retval;
|
|
}
|
|
}
|
|
/* x>0 */
|
|
|
|
if (qx == 0x7ff00000) /* x= 2^-0x3ff */
|
|
return y > 0 ? x : 0;
|
|
|
|
if (qy > 0x45f00000 && qy < 0x7ff00000)
|
|
{
|
|
if (x == 1.0)
|
|
return 1.0;
|
|
if (y > 0)
|
|
return (x > 1.0) ? huge * huge : tiny * tiny;
|
|
if (y < 0)
|
|
return (x < 1.0) ? huge * huge : tiny * tiny;
|
|
}
|
|
|
|
if (x == 1.0)
|
|
return 1.0;
|
|
if (y > 0)
|
|
return (x > 1.0) ? INF.x : 0;
|
|
if (y < 0)
|
|
return (x < 1.0) ? INF.x : 0;
|
|
return 0; /* unreachable, to make the compiler happy */
|
|
}
|
|
|
|
#ifndef __ieee754_pow
|
|
strong_alias (__ieee754_pow, __pow_finite)
|
|
#endif
|
|
|
|
/* Compute x^y using more accurate but more slow log routine. */
|
|
static double
|
|
SECTION
|
|
power1 (double x, double y)
|
|
{
|
|
double z, a, aa, error, t, a1, a2, y1, y2;
|
|
z = my_log2 (x, &aa, &error);
|
|
t = y * CN;
|
|
y1 = t - (t - y);
|
|
y2 = y - y1;
|
|
t = z * CN;
|
|
a1 = t - (t - z);
|
|
a2 = z - a1;
|
|
a = y * z;
|
|
aa = ((y1 * a1 - a) + y1 * a2 + y2 * a1) + y2 * a2 + aa * y;
|
|
a1 = a + aa;
|
|
a2 = (a - a1) + aa;
|
|
error = error * ABS (y);
|
|
t = __exp1 (a1, a2, 1.9e16 * error);
|
|
return (t >= 0) ? t : __slowpow (x, y, z);
|
|
}
|
|
|
|
/* Compute log(x) (x is left argument). The result is the returned double + the
|
|
parameter DELTA. The result is bounded by ERROR. */
|
|
static double
|
|
SECTION
|
|
log1 (double x, double *delta, double *error)
|
|
{
|
|
int i, j, m;
|
|
double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0;
|
|
mynumber u, v;
|
|
#ifdef BIG_ENDI
|
|
mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */
|
|
#else
|
|
# ifdef LITTLE_ENDI
|
|
mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */
|
|
# endif
|
|
#endif
|
|
|
|
u.x = x;
|
|
m = u.i[HIGH_HALF];
|
|
*error = 0;
|
|
*delta = 0;
|
|
if (m < 0x00100000) /* 1<x<2^-1007 */
|
|
{
|
|
x = x * t52.x;
|
|
add = -52.0;
|
|
u.x = x;
|
|
m = u.i[HIGH_HALF];
|
|
}
|
|
|
|
if ((m & 0x000fffff) < 0x0006a09e)
|
|
{
|
|
u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000;
|
|
two52.i[LOW_HALF] = (m >> 20);
|
|
}
|
|
else
|
|
{
|
|
u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000;
|
|
two52.i[LOW_HALF] = (m >> 20) + 1;
|
|
}
|
|
|
|
v.x = u.x + bigu.x;
|
|
uu = v.x - bigu.x;
|
|
i = (v.i[LOW_HALF] & 0x000003ff) << 2;
|
|
if (two52.i[LOW_HALF] == 1023) /* nx = 0 */
|
|
{
|
|
if (i > 1192 && i < 1208) /* |x-1| < 1.5*2**-10 */
|
|
{
|
|
t = x - 1.0;
|
|
t1 = (t + 5.0e6) - 5.0e6;
|
|
t2 = t - t1;
|
|
e1 = t - 0.5 * t1 * t1;
|
|
e2 = (t * t * t * (r3 + t * (r4 + t * (r5 + t * (r6 + t
|
|
* (r7 + t * r8)))))
|
|
- 0.5 * t2 * (t + t1));
|
|
res = e1 + e2;
|
|
*error = 1.0e-21 * ABS (t);
|
|
*delta = (e1 - res) + e2;
|
|
return res;
|
|
} /* |x-1| < 1.5*2**-10 */
|
|
else
|
|
{
|
|
v.x = u.x * (ui.x[i] + ui.x[i + 1]) + bigv.x;
|
|
vv = v.x - bigv.x;
|
|
j = v.i[LOW_HALF] & 0x0007ffff;
|
|
j = j + j + j;
|
|
eps = u.x - uu * vv;
|
|
e1 = eps * ui.x[i];
|
|
e2 = eps * (ui.x[i + 1] + vj.x[j] * (ui.x[i] + ui.x[i + 1]));
|
|
e = e1 + e2;
|
|
e2 = ((e1 - e) + e2);
|
|
t = ui.x[i + 2] + vj.x[j + 1];
|
|
t1 = t + e;
|
|
t2 = ((((t - t1) + e) + (ui.x[i + 3] + vj.x[j + 2])) + e2 + e * e
|
|
* (p2 + e * (p3 + e * p4)));
|
|
res = t1 + t2;
|
|
*error = 1.0e-24;
|
|
*delta = (t1 - res) + t2;
|
|
return res;
|
|
}
|
|
} /* nx = 0 */
|
|
else /* nx != 0 */
|
|
{
|
|
eps = u.x - uu;
|
|
nx = (two52.x - two52e.x) + add;
|
|
e1 = eps * ui.x[i];
|
|
e2 = eps * ui.x[i + 1];
|
|
e = e1 + e2;
|
|
e2 = (e1 - e) + e2;
|
|
t = nx * ln2a.x + ui.x[i + 2];
|
|
t1 = t + e;
|
|
t2 = ((((t - t1) + e) + nx * ln2b.x + ui.x[i + 3] + e2) + e * e
|
|
* (q2 + e * (q3 + e * (q4 + e * (q5 + e * q6)))));
|
|
res = t1 + t2;
|
|
*error = 1.0e-21;
|
|
*delta = (t1 - res) + t2;
|
|
return res;
|
|
} /* nx != 0 */
|
|
}
|
|
|
|
/* Slower but more accurate routine of log. The returned result is double +
|
|
DELTA. The result is bounded by ERROR. */
|
|
static double
|
|
SECTION
|
|
my_log2 (double x, double *delta, double *error)
|
|
{
|
|
int i, j, m;
|
|
double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0;
|
|
double ou1, ou2, lu1, lu2, ov, lv1, lv2, a, a1, a2;
|
|
double y, yy, z, zz, j1, j2, j7, j8;
|
|
#ifndef DLA_FMS
|
|
double j3, j4, j5, j6;
|
|
#endif
|
|
mynumber u, v;
|
|
#ifdef BIG_ENDI
|
|
mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */
|
|
#else
|
|
# ifdef LITTLE_ENDI
|
|
mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */
|
|
# endif
|
|
#endif
|
|
|
|
u.x = x;
|
|
m = u.i[HIGH_HALF];
|
|
*error = 0;
|
|
*delta = 0;
|
|
add = 0;
|
|
if (m < 0x00100000)
|
|
{ /* x < 2^-1022 */
|
|
x = x * t52.x;
|
|
add = -52.0;
|
|
u.x = x;
|
|
m = u.i[HIGH_HALF];
|
|
}
|
|
|
|
if ((m & 0x000fffff) < 0x0006a09e)
|
|
{
|
|
u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000;
|
|
two52.i[LOW_HALF] = (m >> 20);
|
|
}
|
|
else
|
|
{
|
|
u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000;
|
|
two52.i[LOW_HALF] = (m >> 20) + 1;
|
|
}
|
|
|
|
v.x = u.x + bigu.x;
|
|
uu = v.x - bigu.x;
|
|
i = (v.i[LOW_HALF] & 0x000003ff) << 2;
|
|
/*------------------------------------- |x-1| < 2**-11------------------------------- */
|
|
if ((two52.i[LOW_HALF] == 1023) && (i == 1200))
|
|
{
|
|
t = x - 1.0;
|
|
EMULV (t, s3, y, yy, j1, j2, j3, j4, j5);
|
|
ADD2 (-0.5, 0, y, yy, z, zz, j1, j2);
|
|
MUL2 (t, 0, z, zz, y, yy, j1, j2, j3, j4, j5, j6, j7, j8);
|
|
MUL2 (t, 0, y, yy, z, zz, j1, j2, j3, j4, j5, j6, j7, j8);
|
|
|
|
e1 = t + z;
|
|
e2 = ((((t - e1) + z) + zz) + t * t * t
|
|
* (ss3 + t * (s4 + t * (s5 + t * (s6 + t * (s7 + t * s8))))));
|
|
res = e1 + e2;
|
|
*error = 1.0e-25 * ABS (t);
|
|
*delta = (e1 - res) + e2;
|
|
return res;
|
|
}
|
|
/*----------------------------- |x-1| > 2**-11 -------------------------- */
|
|
else
|
|
{ /*Computing log(x) according to log table */
|
|
nx = (two52.x - two52e.x) + add;
|
|
ou1 = ui.x[i];
|
|
ou2 = ui.x[i + 1];
|
|
lu1 = ui.x[i + 2];
|
|
lu2 = ui.x[i + 3];
|
|
v.x = u.x * (ou1 + ou2) + bigv.x;
|
|
vv = v.x - bigv.x;
|
|
j = v.i[LOW_HALF] & 0x0007ffff;
|
|
j = j + j + j;
|
|
eps = u.x - uu * vv;
|
|
ov = vj.x[j];
|
|
lv1 = vj.x[j + 1];
|
|
lv2 = vj.x[j + 2];
|
|
a = (ou1 + ou2) * (1.0 + ov);
|
|
a1 = (a + 1.0e10) - 1.0e10;
|
|
a2 = a * (1.0 - a1 * uu * vv);
|
|
e1 = eps * a1;
|
|
e2 = eps * a2;
|
|
e = e1 + e2;
|
|
e2 = (e1 - e) + e2;
|
|
t = nx * ln2a.x + lu1 + lv1;
|
|
t1 = t + e;
|
|
t2 = ((((t - t1) + e) + (lu2 + lv2 + nx * ln2b.x + e2)) + e * e
|
|
* (p2 + e * (p3 + e * p4)));
|
|
res = t1 + t2;
|
|
*error = 1.0e-27;
|
|
*delta = (t1 - res) + t2;
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* This function receives a double x and checks if it is an integer. If not,
|
|
it returns 0, else it returns 1 if even or -1 if odd. */
|
|
static int
|
|
SECTION
|
|
checkint (double x)
|
|
{
|
|
union
|
|
{
|
|
int4 i[2];
|
|
double x;
|
|
} u;
|
|
int k, m, n;
|
|
u.x = x;
|
|
m = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */
|
|
if (m >= 0x7ff00000)
|
|
return 0; /* x is +/-inf or NaN */
|
|
if (m >= 0x43400000)
|
|
return 1; /* |x| >= 2**53 */
|
|
if (m < 0x40000000)
|
|
return 0; /* |x| < 2, can not be 0 or 1 */
|
|
n = u.i[LOW_HALF];
|
|
k = (m >> 20) - 1023; /* 1 <= k <= 52 */
|
|
if (k == 52)
|
|
return (n & 1) ? -1 : 1; /* odd or even */
|
|
if (k > 20)
|
|
{
|
|
if (n << (k - 20))
|
|
return 0; /* if not integer */
|
|
return (n << (k - 21)) ? -1 : 1;
|
|
}
|
|
if (n)
|
|
return 0; /*if not integer */
|
|
if (k == 20)
|
|
return (m & 1) ? -1 : 1;
|
|
if (m << (k + 12))
|
|
return 0;
|
|
return (m << (k + 11)) ? -1 : 1;
|
|
}
|