Remove slow paths from exp

Remove the __slowexp code, so exp is no longer correctly rounded.  The
result is computed to about 70 bits precision so the worst case ulp
error is about 0.500007 in nearest rounding mode.

	* manual/probes.texi: Remove slowexp probes.
	* math/Makefile: Remove slowexp.
	* sysdeps/generic/math_private.h (__slowexp): Remove.
	* sysdeps/ieee754/dbl-64/e_exp.c (__ieee754_exp): Remove __slowexp and
	document error bounds.
	* sysdeps/i386/fpu/slowexp.c: Remove.
	* sysdeps/ia64/fpu/slowexp.c: Remove.
	* sysdeps/ieee754/dbl-64/slowexp.c: Remove.
	* sysdeps/ieee754/dbl-64/uexp.h (err_0): Remove.
	* sysdeps/m68k/m680x0/fpu/slowexp.c: Remove.
	* sysdeps/powerpc/power4/fpu/Makefile (CPPFLAGS-slowexp.c): Remove.
	* sysdeps/x86_64/fpu/multiarch/Makefile: Remove slowexp-fma.
	* sysdeps/x86_64/fpu/multiarch/e_exp-avx.c (__slowexp): Remove.
	* sysdeps/x86_64/fpu/multiarch/e_exp-fma.c (__slowexp): Remove.
	* sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c (__slowexp): Remove.
	* sysdeps/x86_64/fpu/multiarch/slowexp-avx.c: Remove.
	* sysdeps/x86_64/fpu/multiarch/slowexp-fma.c: Remove.
	* sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c: Remove.

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 7a9daa5..1bcb382 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 ba56174..0000000
--- 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 2edf530..64ab2c8 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;