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-rw-r--r--sysdeps/ieee754/dbl-64/e_exp.c62
-rw-r--r--sysdeps/ieee754/dbl-64/slowexp.c86
-rw-r--r--sysdeps/ieee754/dbl-64/uexp.h3
3 files changed, 18 insertions, 133 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_exp.c b/sysdeps/ieee754/dbl-64/e_exp.c
index 7a9daa5858..1bcb382c77 100644
--- a/sysdeps/ieee754/dbl-64/e_exp.c
+++ b/sysdeps/ieee754/dbl-64/e_exp.c
@@ -23,10 +23,10 @@
/* exp1 */
/* */
/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h */
-/* mpa.c mpexp.x slowexp.c */
+/* mpa.c mpexp.x */
/* */
/* An ultimate exp routine. Given an IEEE double machine number x */
-/* it computes the correctly rounded (to nearest) value of e^x */
+/* it computes an almost correctly rounded (to nearest) value of e^x */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
@@ -46,10 +46,6 @@
# define SECTION
#endif
-double __slowexp (double);
-
-/* An ultimate exp routine. Given an IEEE double machine number x it computes
- the correctly rounded (to nearest) value of e^x. */
double
SECTION
__ieee754_exp (double x)
@@ -93,17 +89,10 @@ __ieee754_exp (double x)
rem = (bet + bet * eps) + al * eps;
res = al + rem;
- cor = (al - res) + rem;
- if (res == (res + cor * err_0))
- {
- retval = res * binexp.x;
- goto ret;
- }
- else
- {
- retval = __slowexp (x);
- goto ret;
- } /*if error is over bound */
+ /* Maximum relative error is 7.8e-22 (70.1 bits).
+ Maximum ULP error is 0.500007. */
+ retval = res * binexp.x;
+ goto ret;
}
if (n <= smallint)
@@ -166,38 +155,22 @@ __ieee754_exp (double x)
if (ex >= -1022)
{
binexp.i[HIGH_HALF] = (1023 + ex) << 20;
- if (res == (res + cor * err_0))
- {
- retval = res * binexp.x;
- goto ret;
- }
- else
- {
- retval = __slowexp (x);
- goto check_uflow_ret;
- } /*if error is over bound */
+ /* Does not underflow: res >= 1.0, binexp >= 0x1p-1022
+ Maximum relative error is 7.8e-22 (70.1 bits).
+ Maximum ULP error is 0.500007. */
+ retval = res * binexp.x;
+ goto ret;
}
ex = -(1022 + ex);
binexp.i[HIGH_HALF] = (1023 - ex) << 20;
res *= binexp.x;
cor *= binexp.x;
- eps = 1.0000000001 + err_0 * binexp.x;
t = 1.0 + res;
y = ((1.0 - t) + res) + cor;
res = t + y;
- cor = (t - res) + y;
- if (res == (res + eps * cor))
- {
- binexp.i[HIGH_HALF] = 0x00100000;
- retval = (res - 1.0) * binexp.x;
- goto check_uflow_ret;
- }
- else
- {
- retval = __slowexp (x);
- goto check_uflow_ret;
- } /* if error is over bound */
- check_uflow_ret:
+ /* Maximum ULP error is 0.5000035. */
+ binexp.i[HIGH_HALF] = 0x00100000;
+ retval = (res - 1.0) * binexp.x;
if (retval < DBL_MIN)
{
double force_underflow = tiny * tiny;
@@ -210,10 +183,9 @@ __ieee754_exp (double x)
else
{
binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 767) << 20;
- if (res == (res + cor * err_0))
- retval = res * binexp.x * t256.x;
- else
- retval = __slowexp (x);
+ /* Maximum relative error is 7.8e-22 (70.1 bits).
+ Maximum ULP error is 0.500007. */
+ retval = res * binexp.x * t256.x;
if (isinf (retval))
goto ret_huge;
else
diff --git a/sysdeps/ieee754/dbl-64/slowexp.c b/sysdeps/ieee754/dbl-64/slowexp.c
deleted file mode 100644
index ba5617466c..0000000000
--- a/sysdeps/ieee754/dbl-64/slowexp.c
+++ /dev/null
@@ -1,86 +0,0 @@
-/*
- * IBM Accurate Mathematical Library
- * written by International Business Machines Corp.
- * Copyright (C) 2001-2018 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:slowexp.c */
-/* */
-/* FUNCTION:slowexp */
-/* */
-/* FILES NEEDED:mpa.h */
-/* mpa.c mpexp.c */
-/* */
-/*Converting from double precision to Multi-precision and calculating */
-/* e^x */
-/**************************************************************************/
-#include <math_private.h>
-
-#include <stap-probe.h>
-
-#ifndef USE_LONG_DOUBLE_FOR_MP
-# include "mpa.h"
-void __mpexp (mp_no *x, mp_no *y, int p);
-#endif
-
-#ifndef SECTION
-# define SECTION
-#endif
-
-/*Converting from double precision to Multi-precision and calculating e^x */
-double
-SECTION
-__slowexp (double x)
-{
-#ifndef USE_LONG_DOUBLE_FOR_MP
- double w, z, res, eps = 3.0e-26;
- int p;
- mp_no mpx, mpy, mpz, mpw, mpeps, mpcor;
-
- /* Use the multiple precision __MPEXP function to compute the exponential
- First at 144 bits and if it is not accurate enough, at 768 bits. */
- p = 6;
- __dbl_mp (x, &mpx, p);
- __mpexp (&mpx, &mpy, p);
- __dbl_mp (eps, &mpeps, p);
- __mul (&mpeps, &mpy, &mpcor, p);
- __add (&mpy, &mpcor, &mpw, p);
- __sub (&mpy, &mpcor, &mpz, p);
- __mp_dbl (&mpw, &w, p);
- __mp_dbl (&mpz, &z, p);
- if (w == z)
- {
- /* Track how often we get to the slow exp code plus
- its input/output values. */
- LIBC_PROBE (slowexp_p6, 2, &x, &w);
- return w;
- }
- else
- {
- p = 32;
- __dbl_mp (x, &mpx, p);
- __mpexp (&mpx, &mpy, p);
- __mp_dbl (&mpy, &res, p);
-
- /* Track how often we get to the uber-slow exp code plus
- its input/output values. */
- LIBC_PROBE (slowexp_p32, 2, &x, &res);
- return res;
- }
-#else
- return (double) __ieee754_expl((long double)x);
-#endif
-}
diff --git a/sysdeps/ieee754/dbl-64/uexp.h b/sysdeps/ieee754/dbl-64/uexp.h
index 2edf530b69..64ab2c8fca 100644
--- a/sysdeps/ieee754/dbl-64/uexp.h
+++ b/sysdeps/ieee754/dbl-64/uexp.h
@@ -29,8 +29,7 @@
#include "mydefs.h"
-const static double zero = 0.0, hhuge = 1.0e300, tiny = 1.0e-300,
-err_0 = 1.000014;
+const static double zero = 0.0, hhuge = 1.0e300, tiny = 1.0e-300;
const static int4 bigint = 0x40862002,
badint = 0x40876000,smallint = 0x3C8fffff;
const static int4 hugeint = 0x7FFFFFFF, infint = 0x7ff00000;
generated by cgit v1.2.3 (git 2.39.1) at 2024-09-25 07:14:21 +0000