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authorJoseph Myers <joseph@codesourcery.com>2017-12-19 18:11:37 +0000
committerJoseph Myers <joseph@codesourcery.com>2017-12-19 18:11:37 +0000
commitf1e005022ebd246e1541386cd2f3286f008d2d98 (patch)
treedc80cd25916cd4cb63da26f9a6e32036157977af /sysdeps/ieee754/dbl-64
parente184ac3a105a4a45b920bf2cdaa701a683c781a2 (diff)
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Revert exp reimplementation (causes test failures).
	Revert:

	2017-12-19  Joseph Myers  <joseph@codesourcery.com>

	* sysdeps/x86_64/fpu/libm-test-ulps: Update.

	2017-12-19  Patrick McGehearty  <patrick.mcgehearty@oracle.com>

	* sysdeps/ieee754/dbl-64/e_exp.c: Include <math-svid-compat.h> and
	<errno.h>.  Include "eexp.tbl".
	(half): New constant.
	(one): Likewise.
	(__ieee754_exp): Rewrite.
	(__slowexp): Remove prototype.
	* sysdeps/ieee754/dbl-64/eexp.tbl: New file.
	* sysdeps/ieee754/dbl-64/slowexp.c: Remove file.
	* sysdeps/i386/fpu/slowexp.c: Likewise.
	* sysdeps/ia64/fpu/slowexp.c: Likewise.
	* sysdeps/m68k/m680x0/fpu/slowexp.c: Likewise.
	* sysdeps/x86_64/fpu/multiarch/slowexp-avx.c: Likewise.
	* sysdeps/x86_64/fpu/multiarch/slowexp-fma.c: Likewise.
	* sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c: Likewise.
	* sysdeps/generic/math_private.h (__slowexp): Remove prototype.
	* sysdeps/ieee754/dbl-64/e_pow.c: Remove mention of slowexp.c in
	comment.
	* sysdeps/powerpc/power4/fpu/Makefile [$(subdir) = math]
	(CPPFLAGS-slowexp.c): Remove variable.
	* sysdeps/x86_64/fpu/multiarch/Makefile (libm-sysdep_routines):
	Remove slowexp-fma, slowexp-fma4 and slowexp-avx.
	(CFLAGS-slowexp-fma.c): Remove variable.
	(CFLAGS-slowexp-fma4.c): Likewise.
	(CFLAGS-slowexp-avx.c): Likewise.
	* sysdeps/x86_64/fpu/multiarch/e_exp-avx.c (__slowexp): Do not
	define as macro.
	* sysdeps/x86_64/fpu/multiarch/e_exp-fma.c (__slowexp): Likewise.
	* sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c (__slowexp): Likewise.
	* math/Makefile (type-double-routines): Remove slowexp.
	* manual/probes.texi (slowexp_p6): Remove.
	(slowexp_p32): Likewise.
Diffstat (limited to 'sysdeps/ieee754/dbl-64')
-rw-r--r--sysdeps/ieee754/dbl-64/e_exp.c398
-rw-r--r--sysdeps/ieee754/dbl-64/e_pow.c2
-rw-r--r--sysdeps/ieee754/dbl-64/eexp.tbl255
-rw-r--r--sysdeps/ieee754/dbl-64/slowexp.c86
4 files changed, 270 insertions, 471 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_exp.c b/sysdeps/ieee754/dbl-64/e_exp.c
index 6a7122f585..6757a14ce1 100644
--- a/sysdeps/ieee754/dbl-64/e_exp.c
+++ b/sysdeps/ieee754/dbl-64/e_exp.c
@@ -1,4 +1,3 @@
-/* EXP function - Compute double precision exponential */
 /*
  * IBM Accurate Mathematical Library
  * written by International Business Machines Corp.
@@ -24,7 +23,7 @@
 /*           exp1                                                          */
 /*                                                                         */
 /* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h                       */
-/*              mpa.c mpexp.x                                              */
+/*              mpa.c mpexp.x slowexp.c                                    */
 /*                                                                         */
 /* An ultimate exp routine. Given an IEEE double machine number x          */
 /* it computes the correctly rounded (to nearest) value of e^x             */
@@ -33,238 +32,207 @@
 /*                                                                         */
 /***************************************************************************/
 
-/*  IBM exp(x) replaced by following exp(x) in 2017. IBM exp1(x,xx) remains.  */
-/* exp(x)
-   Hybrid algorithm of Peter Tang's Table driven method (for large
-   arguments) and an accurate table (for small arguments).
-   Written by K.C. Ng, November 1988.
-   Revised by Patrick McGehearty, Nov 2017 to use j/64 instead of j/32
-   Method (large arguments):
-	1. Argument Reduction: given the input x, find r and integer k
-	   and j such that
-	             x = (k+j/64)*(ln2) + r,  |r| <= (1/128)*ln2
-
-	2. exp(x) = 2^k * (2^(j/64) + 2^(j/64)*expm1(r))
-	   a. expm1(r) is approximated by a polynomial:
-	      expm1(r) ~ r + t1*r^2 + t2*r^3 + ... + t5*r^6
-	      Here t1 = 1/2 exactly.
-	   b. 2^(j/64) is represented to twice double precision
-	      as TBL[2j]+TBL[2j+1].
-
-   Note: If divide were fast enough, we could use another approximation
-	 in 2.a:
-	      expm1(r) ~ (2r)/(2-R), R = r - r^2*(t1 + t2*r^2)
-	      (for the same t1 and t2 as above)
-
-   Special cases:
-	exp(INF) is INF, exp(NaN) is NaN;
-	exp(-INF)=  0;
-	for finite argument, only exp(0)=1 is exact.
-
-   Accuracy:
-	According to an error analysis, the error is always less than
-	an ulp (unit in the last place).  The largest errors observed
-	are less than 0.55 ulp for normal results and less than 0.75 ulp
-	for subnormal results.
-
-   Misc. info.
-	For IEEE double
-		if x >  7.09782712893383973096e+02 then exp(x) overflow
-		if x < -7.45133219101941108420e+02 then exp(x) underflow.  */
-
 #include <math.h>
-#include <math-svid-compat.h>
-#include <math_private.h>
-#include <errno.h>
 #include "endian.h"
 #include "uexp.h"
-#include "uexp.tbl"
 #include "mydefs.h"
 #include "MathLib.h"
+#include "uexp.tbl"
+#include <math_private.h>
 #include <fenv.h>
 #include <float.h>
 
-extern double __ieee754_exp (double);
-
-#include "eexp.tbl"
-
-static const double
-  half = 0.5,
-  one = 1.0;
+#ifndef SECTION
+# 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
-__ieee754_exp (double x_arg)
+SECTION
+__ieee754_exp (double x)
 {
-  double z, t;
+  double bexp, t, eps, del, base, y, al, bet, res, rem, cor;
+  mynumber junk1, junk2, binexp = {{0, 0}};
+  int4 i, j, m, n, ex;
   double retval;
-  int hx, ix, k, j, m;
-  int fe_val;
-  union
-  {
-    int i_part[2];
-    double x;
-  } xx;
-  union
-  {
-    int y_part[2];
-    double y;
-  } yy;
-  xx.x = x_arg;
-
-  ix = xx.i_part[HIGH_HALF];
-  hx = ix & ~0x80000000;
-
-  if (hx < 0x3ff0a2b2)
-    {				/* |x| < 3/2 ln 2 */
-      if (hx < 0x3f862e42)
-	{			/* |x| < 1/64 ln 2 */
-	  if (hx < 0x3ed00000)
-	    {			/* |x| < 2^-18 */
-	      if (hx < 0x3e300000)
-		{
-		  retval = one + xx.x;
-		  return retval;
-		}
-	      retval = one + xx.x * (one + half * xx.x);
-	      return retval;
-	    }
-	  /* Use FE_TONEAREST rounding mode for computing yy.y.
-	     Avoid set/reset of rounding mode if in FE_TONEAREST mode.  */
-	  fe_val = get_rounding_mode ();
-	  if (fe_val == FE_TONEAREST)
-	    {
-	      t = xx.x * xx.x;
-	      yy.y = xx.x + (t * (half + xx.x * t2)
-			     + (t * t) * (t3 + xx.x * t4 + t * t5));
-	      retval = one + yy.y;
-	    }
-	  else
-	    {
-	      libc_fesetround (FE_TONEAREST);
-	      t = xx.x * xx.x;
-	      yy.y = xx.x + (t * (half + xx.x * t2)
-			     + (t * t) * (t3 + xx.x * t4 + t * t5));
-	      retval = one + yy.y;
-	      libc_fesetround (fe_val);
-	    }
-	  return retval;
-	}
-
-      /* Find the multiple of 2^-6 nearest x.  */
-      k = hx >> 20;
-      j = (0x00100000 | (hx & 0x000fffff)) >> (0x40c - k);
-      j = (j - 1) & ~1;
-      if (ix < 0)
-	j += 134;
-      /* Use FE_TONEAREST rounding mode for computing yy.y.
-	 Avoid set/reset of rounding mode if in FE_TONEAREST mode.  */
-      fe_val = get_rounding_mode ();
-      if (fe_val == FE_TONEAREST)
-	{
-	  z = xx.x - TBL2[j];
-	  t = z * z;
-	  yy.y = z + (t * (half + (z * t2))
-		      + (t * t) * (t3 + z * t4 + t * t5));
-	  retval = TBL2[j + 1] + TBL2[j + 1] * yy.y;
-	}
-      else
-	{
-	  libc_fesetround (FE_TONEAREST);
-	  z = xx.x - TBL2[j];
-	  t = z * z;
-	  yy.y = z + (t * (half + (z * t2))
-		      + (t * t) * (t3 + z * t4 + t * t5));
-	  retval = TBL2[j + 1] + TBL2[j + 1] * yy.y;
-	  libc_fesetround (fe_val);
-	}
-      return retval;
-    }
-
-  if (hx >= 0x40862e42)
-    {				/* x is large, infinite, or nan.  */
-      if (hx >= 0x7ff00000)
-	{
-	  if (ix == 0xfff00000 && xx.i_part[LOW_HALF] == 0)
-	    return zero;	/* exp(-inf) = 0.  */
-	  return (xx.x * xx.x);	/* exp(nan/inf) is nan or inf.  */
-	}
-      if (xx.x > threshold1)
-	{			/* Set overflow error condition.  */
-	  retval = hhuge * hhuge;
-	  return retval;
-	}
-      if (-xx.x > threshold2)
-	{			/* Set underflow error condition.  */
-	  double force_underflow = tiny * tiny;
-	  math_force_eval (force_underflow);
-	  retval = force_underflow;
-	  return retval;
-	}
-    }
-
-  /* Use FE_TONEAREST rounding mode for computing yy.y.
-     Avoid set/reset of rounding mode if already in FE_TONEAREST mode.  */
-  fe_val = get_rounding_mode ();
-  if (fe_val == FE_TONEAREST)
-    {
-      t = invln2_64 * xx.x;
-      if (ix < 0)
-	t -= half;
-      else
-	t += half;
-      k = (int) t;
-      j = (k & 0x3f) << 1;
-      m = k >> 6;
-      z = (xx.x - k * ln2_64hi) - k * ln2_64lo;
-
-      /* z is now in primary range.  */
-      t = z * z;
-      yy.y = z + (t * (half + z * t2) + (t * t) * (t3 + z * t4 + t * t5));
-      yy.y = TBL[j] + (TBL[j + 1] + TBL[j] * yy.y);
-    }
-  else
-    {
-      libc_fesetround (FE_TONEAREST);
-      t = invln2_64 * xx.x;
-      if (ix < 0)
-	t -= half;
-      else
-	t += half;
-      k = (int) t;
-      j = (k & 0x3f) << 1;
-      m = k >> 6;
-      z = (xx.x - k * ln2_64hi) - k * ln2_64lo;
-
-      /* z is now in primary range.  */
-      t = z * z;
-      yy.y = z + (t * (half + z * t2) + (t * t) * (t3 + z * t4 + t * t5));
-      yy.y = TBL[j] + (TBL[j + 1] + TBL[j] * yy.y);
-      libc_fesetround (fe_val);
-    }
 
-  if (m < -1021)
-    {
-      yy.y_part[HIGH_HALF] += (m + 54) << 20;
-      retval = twom54 * yy.y;
-      if (retval < DBL_MIN)
-	{
-	  double force_underflow = tiny * tiny;
-	  math_force_eval (force_underflow);
-	}
-      return retval;
-    }
-  yy.y_part[HIGH_HALF] += m << 20;
-  return yy.y;
+  {
+    SET_RESTORE_ROUND (FE_TONEAREST);
+
+    junk1.x = x;
+    m = junk1.i[HIGH_HALF];
+    n = m & hugeint;
+
+    if (n > smallint && n < bigint)
+      {
+	y = x * log2e.x + three51.x;
+	bexp = y - three51.x;	/*  multiply the result by 2**bexp        */
+
+	junk1.x = y;
+
+	eps = bexp * ln_two2.x;	/* x = bexp*ln(2) + t - eps               */
+	t = x - bexp * ln_two1.x;
+
+	y = t + three33.x;
+	base = y - three33.x;	/* t rounded to a multiple of 2**-18      */
+	junk2.x = y;
+	del = (t - base) - eps;	/*  x = bexp*ln(2) + base + del           */
+	eps = del + del * del * (p3.x * del + p2.x);
+
+	binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 1023) << 20;
+
+	i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356;
+	j = (junk2.i[LOW_HALF] & 511) << 1;
+
+	al = coar.x[i] * fine.x[j];
+	bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j])
+	       + coar.x[i + 1] * fine.x[j + 1]);
+
+	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 */
+      }
+
+    if (n <= smallint)
+      {
+	retval = 1.0;
+	goto ret;
+      }
+
+    if (n >= badint)
+      {
+	if (n > infint)
+	  {
+	    retval = x + x;
+	    goto ret;
+	  }			/* x is NaN */
+	if (n < infint)
+	  {
+	    if (x > 0)
+	      goto ret_huge;
+	    else
+	      goto ret_tiny;
+	  }
+	/* x is finite,  cause either overflow or underflow  */
+	if (junk1.i[LOW_HALF] != 0)
+	  {
+	    retval = x + x;
+	    goto ret;
+	  }			/*  x is NaN  */
+	retval = (x > 0) ? inf.x : zero;	/* |x| = inf;  return either inf or 0 */
+	goto ret;
+      }
+
+    y = x * log2e.x + three51.x;
+    bexp = y - three51.x;
+    junk1.x = y;
+    eps = bexp * ln_two2.x;
+    t = x - bexp * ln_two1.x;
+    y = t + three33.x;
+    base = y - three33.x;
+    junk2.x = y;
+    del = (t - base) - eps;
+    eps = del + del * del * (p3.x * del + p2.x);
+    i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356;
+    j = (junk2.i[LOW_HALF] & 511) << 1;
+    al = coar.x[i] * fine.x[j];
+    bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j])
+	   + coar.x[i + 1] * fine.x[j + 1]);
+    rem = (bet + bet * eps) + al * eps;
+    res = al + rem;
+    cor = (al - res) + rem;
+    if (m >> 31)
+      {
+	ex = junk1.i[LOW_HALF];
+	if (res < 1.0)
+	  {
+	    res += res;
+	    cor += cor;
+	    ex -= 1;
+	  }
+	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 */
+	  }
+	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:
+	if (retval < DBL_MIN)
+	  {
+	    double force_underflow = tiny * tiny;
+	    math_force_eval (force_underflow);
+	  }
+	if (retval == 0)
+	  goto ret_tiny;
+	goto ret;
+      }
+    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);
+	if (isinf (retval))
+	  goto ret_huge;
+	else
+	  goto ret;
+      }
+  }
+ret:
+  return retval;
+
+ ret_huge:
+  return hhuge * hhuge;
+
+ ret_tiny:
+  return tiny * tiny;
 }
 #ifndef __ieee754_exp
 strong_alias (__ieee754_exp, __exp_finite)
 #endif
 
-#ifndef SECTION
-# define SECTION
-#endif
-
 /* Compute e^(x+xx).  The routine also receives bound of error of previous
    calculation.  If after computing exp the error exceeds the allowed bounds,
    the routine returns a non-positive number.  Otherwise it returns the
diff --git a/sysdeps/ieee754/dbl-64/e_pow.c b/sysdeps/ieee754/dbl-64/e_pow.c
index 2eb8dbfd5f..9f6439ee42 100644
--- a/sysdeps/ieee754/dbl-64/e_pow.c
+++ b/sysdeps/ieee754/dbl-64/e_pow.c
@@ -25,7 +25,7 @@
 /*             log1                                                        */
 /*             checkint                                                    */
 /* FILES NEEDED: dla.h endian.h mpa.h mydefs.h                             */
-/*               halfulp.c mpexp.c mplog.c slowpow.c mpa.c                 */
+/*               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    */
diff --git a/sysdeps/ieee754/dbl-64/eexp.tbl b/sysdeps/ieee754/dbl-64/eexp.tbl
deleted file mode 100644
index 5941b9522b..0000000000
--- a/sysdeps/ieee754/dbl-64/eexp.tbl
+++ /dev/null
@@ -1,255 +0,0 @@
-/* EXP function tables - for use in computing double precision exponential
-   Copyright (C) 2017 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 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.
-
-   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
-   Lesser General Public License for more details.
-
-   You should have received a copy of the GNU Lesser General Public
-   License along with the GNU C Library; if not, see
-   <http://www.gnu.org/licenses/>.  */
-
-
-/*
-   TBL[2*j] is 2**(j/64), rounded to nearest.
-   TBL[2*j+1] is 2**(j/64) - TBL[2*j], rounded to nearest.
-   These values are used to approximate exp(x) using the formula
-   given in the comments for e_exp.c.  */
-
-static const double TBL[128] = {
-    0x1.0000000000000p+0,  0x0.0000000000000p+0,
-    0x1.02c9a3e778061p+0, -0x1.19083535b085dp-56,
-    0x1.059b0d3158574p+0,  0x1.d73e2a475b465p-55,
-    0x1.0874518759bc8p+0,  0x1.186be4bb284ffp-57,
-    0x1.0b5586cf9890fp+0,  0x1.8a62e4adc610bp-54,
-    0x1.0e3ec32d3d1a2p+0,  0x1.03a1727c57b52p-59,
-    0x1.11301d0125b51p+0, -0x1.6c51039449b3ap-54,
-    0x1.1429aaea92de0p+0, -0x1.32fbf9af1369ep-54,
-    0x1.172b83c7d517bp+0, -0x1.19041b9d78a76p-55,
-    0x1.1a35beb6fcb75p+0,  0x1.e5b4c7b4968e4p-55,
-    0x1.1d4873168b9aap+0,  0x1.e016e00a2643cp-54,
-    0x1.2063b88628cd6p+0,  0x1.dc775814a8495p-55,
-    0x1.2387a6e756238p+0,  0x1.9b07eb6c70573p-54,
-    0x1.26b4565e27cddp+0,  0x1.2bd339940e9d9p-55,
-    0x1.29e9df51fdee1p+0,  0x1.612e8afad1255p-55,
-    0x1.2d285a6e4030bp+0,  0x1.0024754db41d5p-54,
-    0x1.306fe0a31b715p+0,  0x1.6f46ad23182e4p-55,
-    0x1.33c08b26416ffp+0,  0x1.32721843659a6p-54,
-    0x1.371a7373aa9cbp+0, -0x1.63aeabf42eae2p-54,
-    0x1.3a7db34e59ff7p+0, -0x1.5e436d661f5e3p-56,
-    0x1.3dea64c123422p+0,  0x1.ada0911f09ebcp-55,
-    0x1.4160a21f72e2ap+0, -0x1.ef3691c309278p-58,
-    0x1.44e086061892dp+0,  0x1.89b7a04ef80d0p-59,
-    0x1.486a2b5c13cd0p+0,  0x1.3c1a3b69062f0p-56,
-    0x1.4bfdad5362a27p+0,  0x1.d4397afec42e2p-56,
-    0x1.4f9b2769d2ca7p+0, -0x1.4b309d25957e3p-54,
-    0x1.5342b569d4f82p+0, -0x1.07abe1db13cadp-55,
-    0x1.56f4736b527dap+0,  0x1.9bb2c011d93adp-54,
-    0x1.5ab07dd485429p+0,  0x1.6324c054647adp-54,
-    0x1.5e76f15ad2148p+0,  0x1.ba6f93080e65ep-54,
-    0x1.6247eb03a5585p+0, -0x1.383c17e40b497p-54,
-    0x1.6623882552225p+0, -0x1.bb60987591c34p-54,
-    0x1.6a09e667f3bcdp+0, -0x1.bdd3413b26456p-54,
-    0x1.6dfb23c651a2fp+0, -0x1.bbe3a683c88abp-57,
-    0x1.71f75e8ec5f74p+0, -0x1.16e4786887a99p-55,
-    0x1.75feb564267c9p+0, -0x1.0245957316dd3p-54,
-    0x1.7a11473eb0187p+0, -0x1.41577ee04992fp-55,
-    0x1.7e2f336cf4e62p+0,  0x1.05d02ba15797ep-56,
-    0x1.82589994cce13p+0, -0x1.d4c1dd41532d8p-54,
-    0x1.868d99b4492edp+0, -0x1.fc6f89bd4f6bap-54,
-    0x1.8ace5422aa0dbp+0,  0x1.6e9f156864b27p-54,
-    0x1.8f1ae99157736p+0,  0x1.5cc13a2e3976cp-55,
-    0x1.93737b0cdc5e5p+0, -0x1.75fc781b57ebcp-57,
-    0x1.97d829fde4e50p+0, -0x1.d185b7c1b85d1p-54,
-    0x1.9c49182a3f090p+0,  0x1.c7c46b071f2bep-56,
-    0x1.a0c667b5de565p+0, -0x1.359495d1cd533p-54,
-    0x1.a5503b23e255dp+0, -0x1.d2f6edb8d41e1p-54,
-    0x1.a9e6b5579fdbfp+0,  0x1.0fac90ef7fd31p-54,
-    0x1.ae89f995ad3adp+0,  0x1.7a1cd345dcc81p-54,
-    0x1.b33a2b84f15fbp+0, -0x1.2805e3084d708p-57,
-    0x1.b7f76f2fb5e47p+0, -0x1.5584f7e54ac3bp-56,
-    0x1.bcc1e904bc1d2p+0,  0x1.23dd07a2d9e84p-55,
-    0x1.c199bdd85529cp+0,  0x1.11065895048ddp-55,
-    0x1.c67f12e57d14bp+0,  0x1.2884dff483cadp-54,
-    0x1.cb720dcef9069p+0,  0x1.503cbd1e949dbp-56,
-    0x1.d072d4a07897cp+0, -0x1.cbc3743797a9cp-54,
-    0x1.d5818dcfba487p+0,  0x1.2ed02d75b3707p-55,
-    0x1.da9e603db3285p+0,  0x1.c2300696db532p-54,
-    0x1.dfc97337b9b5fp+0, -0x1.1a5cd4f184b5cp-54,
-    0x1.e502ee78b3ff6p+0,  0x1.39e8980a9cc8fp-55,
-    0x1.ea4afa2a490dap+0, -0x1.e9c23179c2893p-54,
-    0x1.efa1bee615a27p+0,  0x1.dc7f486a4b6b0p-54,
-    0x1.f50765b6e4540p+0,  0x1.9d3e12dd8a18bp-54,
-    0x1.fa7c1819e90d8p+0,  0x1.74853f3a5931ep-55};
-
-/* For i = 0, ..., 66,
-     TBL2[2*i] is a double precision number near (i+1)*2^-6, and
-     TBL2[2*i+1] = exp(TBL2[2*i]) to within a relative error less
-     than 2^-60.
-
-   For i = 67, ..., 133,
-     TBL2[2*i] is a double precision number near -(i+1)*2^-6, and
-     TBL2[2*i+1] = exp(TBL2[2*i]) to within a relative error less
-     than 2^-60.  */
-
-static const double TBL2[268] = {
-    0x1.ffffffffffc82p-7,   0x1.04080ab55de32p+0,
-    0x1.fffffffffffdbp-6,   0x1.08205601127ecp+0,
-    0x1.80000000000a0p-5,   0x1.0c49236829e91p+0,
-    0x1.fffffffffff79p-5,   0x1.1082b577d34e9p+0,
-    0x1.3fffffffffffcp-4,   0x1.14cd4fc989cd6p+0,
-    0x1.8000000000060p-4,   0x1.192937074e0d4p+0,
-    0x1.c000000000061p-4,   0x1.1d96b0eff0e80p+0,
-    0x1.fffffffffffd6p-4,   0x1.2216045b6f5cap+0,
-    0x1.1ffffffffff58p-3,   0x1.26a7793f6014cp+0,
-    0x1.3ffffffffff75p-3,   0x1.2b4b58b372c65p+0,
-    0x1.5ffffffffff00p-3,   0x1.3001ecf601ad1p+0,
-    0x1.8000000000020p-3,   0x1.34cb8170b583ap+0,
-    0x1.9ffffffffa629p-3,   0x1.39a862bd3b344p+0,
-    0x1.c00000000000fp-3,   0x1.3e98deaa11dcep+0,
-    0x1.e00000000007fp-3,   0x1.439d443f5f16dp+0,
-    0x1.0000000000072p-2,   0x1.48b5e3c3e81abp+0,
-    0x1.0fffffffffecap-2,   0x1.4de30ec211dfbp+0,
-    0x1.1ffffffffff8fp-2,   0x1.5325180cfacd2p+0,
-    0x1.300000000003bp-2,   0x1.587c53c5a7b04p+0,
-    0x1.4000000000034p-2,   0x1.5de9176046007p+0,
-    0x1.4ffffffffff89p-2,   0x1.636bb9a98322fp+0,
-    0x1.5ffffffffffe7p-2,   0x1.690492cbf942ap+0,
-    0x1.6ffffffffff78p-2,   0x1.6eb3fc55b1e45p+0,
-    0x1.7ffffffffff65p-2,   0x1.747a513dbef32p+0,
-    0x1.8ffffffffffd5p-2,   0x1.7a57ede9ea22ep+0,
-    0x1.9ffffffffff6ep-2,   0x1.804d30347b50fp+0,
-    0x1.affffffffffc3p-2,   0x1.865a7772164aep+0,
-    0x1.c000000000053p-2,   0x1.8c802477b0030p+0,
-    0x1.d00000000004dp-2,   0x1.92be99a09bf1ep+0,
-    0x1.e000000000096p-2,   0x1.99163ad4b1e08p+0,
-    0x1.efffffffffefap-2,   0x1.9f876d8e8c4fcp+0,
-    0x1.fffffffffffd0p-2,   0x1.a61298e1e0688p+0,
-    0x1.0800000000002p-1,   0x1.acb82581eee56p+0,
-    0x1.100000000001fp-1,   0x1.b3787dc80f979p+0,
-    0x1.17ffffffffff8p-1,   0x1.ba540dba56e4fp+0,
-    0x1.1fffffffffffap-1,   0x1.c14b431256441p+0,
-    0x1.27fffffffffc4p-1,   0x1.c85e8d43f7c9bp+0,
-    0x1.2fffffffffffdp-1,   0x1.cf8e5d84758a6p+0,
-    0x1.380000000001fp-1,   0x1.d6db26d16cd84p+0,
-    0x1.3ffffffffffd8p-1,   0x1.de455df80e39bp+0,
-    0x1.4800000000052p-1,   0x1.e5cd799c6a59cp+0,
-    0x1.4ffffffffffc8p-1,   0x1.ed73f240dc10cp+0,
-    0x1.5800000000013p-1,   0x1.f539424d90f71p+0,
-    0x1.5ffffffffffbcp-1,   0x1.fd1de6182f885p+0,
-    0x1.680000000002dp-1,   0x1.02912df5ce741p+1,
-    0x1.7000000000040p-1,   0x1.06a39207f0a2ap+1,
-    0x1.780000000004fp-1,   0x1.0ac660691652ap+1,
-    0x1.7ffffffffff6fp-1,   0x1.0ef9db467dcabp+1,
-    0x1.87fffffffffe5p-1,   0x1.133e45d82e943p+1,
-    0x1.9000000000035p-1,   0x1.1793e4652cc6dp+1,
-    0x1.97fffffffffb3p-1,   0x1.1bfafc47bda48p+1,
-    0x1.a000000000000p-1,   0x1.2073d3f1bd518p+1,
-    0x1.a80000000004ap-1,   0x1.24feb2f105ce2p+1,
-    0x1.affffffffffedp-1,   0x1.299be1f3e7f11p+1,
-    0x1.b7ffffffffffbp-1,   0x1.2e4baacdb6611p+1,
-    0x1.c00000000001dp-1,   0x1.330e587b62b39p+1,
-    0x1.c800000000079p-1,   0x1.37e437282d538p+1,
-    0x1.cffffffffff51p-1,   0x1.3ccd943268248p+1,
-    0x1.d7fffffffff74p-1,   0x1.41cabe304cadcp+1,
-    0x1.e000000000011p-1,   0x1.46dc04f4e5343p+1,
-    0x1.e80000000001ep-1,   0x1.4c01b9950a124p+1,
-    0x1.effffffffff9ep-1,   0x1.513c2e6c73196p+1,
-    0x1.f7fffffffffedp-1,   0x1.568bb722dd586p+1,
-    0x1.0000000000034p+0,   0x1.5bf0a8b1457b0p+1,
-    0x1.03fffffffffe2p+0,   0x1.616b5967376dfp+1,
-    0x1.07fffffffff4bp+0,   0x1.66fc20f0337a9p+1,
-    0x1.0bffffffffffdp+0,   0x1.6ca35859290f5p+1,
-   -0x1.fffffffffffe4p-7,   0x1.f80feabfeefa5p-1,
-   -0x1.ffffffffffb0bp-6,   0x1.f03f56a88b5fep-1,
-   -0x1.7ffffffffffa7p-5,   0x1.e88dc6afecfc5p-1,
-   -0x1.ffffffffffea8p-5,   0x1.e0fabfbc702b8p-1,
-   -0x1.3ffffffffffb3p-4,   0x1.d985c89d041acp-1,
-   -0x1.7ffffffffffe3p-4,   0x1.d22e6a0197c06p-1,
-   -0x1.bffffffffff9ap-4,   0x1.caf42e73a4c89p-1,
-   -0x1.fffffffffff98p-4,   0x1.c3d6a24ed822dp-1,
-   -0x1.1ffffffffffe9p-3,   0x1.bcd553b9d7b67p-1,
-   -0x1.3ffffffffffe0p-3,   0x1.b5efd29f24c2dp-1,
-   -0x1.5fffffffff553p-3,   0x1.af25b0a61a9f4p-1,
-   -0x1.7ffffffffff8bp-3,   0x1.a876812c08794p-1,
-   -0x1.9fffffffffe51p-3,   0x1.a1e1d93d68828p-1,
-   -0x1.bffffffffff6ep-3,   0x1.9b674f8f2f3f5p-1,
-   -0x1.dffffffffff7fp-3,   0x1.95067c7837a0cp-1,
-   -0x1.fffffffffff7ap-3,   0x1.8ebef9eac8225p-1,
-   -0x1.0fffffffffffep-2,   0x1.8890636e31f55p-1,
-   -0x1.1ffffffffff41p-2,   0x1.827a56188975ep-1,
-   -0x1.2ffffffffffbap-2,   0x1.7c7c708877656p-1,
-   -0x1.3fffffffffff8p-2,   0x1.769652df22f81p-1,
-   -0x1.4ffffffffff90p-2,   0x1.70c79eba33c2fp-1,
-   -0x1.5ffffffffffdbp-2,   0x1.6b0ff72deb8aap-1,
-   -0x1.6ffffffffff9ap-2,   0x1.656f00bf5798ep-1,
-   -0x1.7ffffffffff9fp-2,   0x1.5fe4615e98eb0p-1,
-   -0x1.8ffffffffffeep-2,   0x1.5a6fc061433cep-1,
-   -0x1.9fffffffffc4ap-2,   0x1.5510c67cd26cdp-1,
-   -0x1.affffffffff30p-2,   0x1.4fc71dc13566bp-1,
-   -0x1.bfffffffffff0p-2,   0x1.4a9271936fd0ep-1,
-   -0x1.cfffffffffff3p-2,   0x1.45726ea84fb8cp-1,
-   -0x1.dfffffffffff3p-2,   0x1.4066c2ff3912bp-1,
-   -0x1.effffffffff80p-2,   0x1.3b6f1ddd05ab9p-1,
-   -0x1.fffffffffffdfp-2,   0x1.368b2fc6f9614p-1,
-   -0x1.0800000000000p-1,   0x1.31baaa7dca843p-1,
-   -0x1.0ffffffffffa4p-1,   0x1.2cfd40f8bdce4p-1,
-   -0x1.17fffffffff0ap-1,   0x1.2852a760d5ce7p-1,
-   -0x1.2000000000000p-1,   0x1.23ba930c1568bp-1,
-   -0x1.27fffffffffbbp-1,   0x1.1f34ba78d568dp-1,
-   -0x1.2fffffffffe32p-1,   0x1.1ac0d5492c1dbp-1,
-   -0x1.37ffffffff042p-1,   0x1.165e9c3e67ef2p-1,
-   -0x1.3ffffffffff77p-1,   0x1.120dc93499431p-1,
-   -0x1.47fffffffff6bp-1,   0x1.0dce171e34ecep-1,
-   -0x1.4fffffffffff1p-1,   0x1.099f41ffbe588p-1,
-   -0x1.57ffffffffe02p-1,   0x1.058106eb8a7aep-1,
-   -0x1.5ffffffffffe5p-1,   0x1.017323fd9002ep-1,
-   -0x1.67fffffffffb0p-1,   0x1.faeab0ae9386cp-2,
-   -0x1.6ffffffffffb2p-1,   0x1.f30ec837503d7p-2,
-   -0x1.77fffffffff7fp-1,   0x1.eb5210d627133p-2,
-   -0x1.7ffffffffffe8p-1,   0x1.e3b40ebefcd95p-2,
-   -0x1.87fffffffffc8p-1,   0x1.dc3448110dae2p-2,
-   -0x1.8fffffffffb30p-1,   0x1.d4d244cf4ef06p-2,
-   -0x1.97fffffffffefp-1,   0x1.cd8d8ed8ee395p-2,
-   -0x1.9ffffffffffa7p-1,   0x1.c665b1e1f1e5cp-2,
-   -0x1.a7fffffffffdcp-1,   0x1.bf5a3b6bf18d6p-2,
-   -0x1.affffffffff95p-1,   0x1.b86ababeef93bp-2,
-   -0x1.b7fffffffffcbp-1,   0x1.b196c0e24d256p-2,
-   -0x1.bffffffffff32p-1,   0x1.aadde095dadf7p-2,
-   -0x1.c7fffffffff6ap-1,   0x1.a43fae4b047c9p-2,
-   -0x1.cffffffffffb6p-1,   0x1.9dbbc01e182a4p-2,
-   -0x1.d7fffffffffcap-1,   0x1.9751adcfa81ecp-2,
-   -0x1.dffffffffffcdp-1,   0x1.910110be0699ep-2,
-   -0x1.e7ffffffffffbp-1,   0x1.8ac983dedbc69p-2,
-   -0x1.effffffffff88p-1,   0x1.84aaa3b8d51a9p-2,
-   -0x1.f7fffffffffbbp-1,   0x1.7ea40e5d6d92ep-2,
-   -0x1.fffffffffffdbp-1,   0x1.78b56362cef53p-2,
-   -0x1.03fffffffff00p+0,   0x1.72de43ddcb1f2p-2,
-   -0x1.07ffffffffe6fp+0,   0x1.6d1e525bed085p-2,
-   -0x1.0bfffffffffd6p+0,   0x1.677532dda1c57p-2};
-
-static const double
-/* invln2_64 = 64/ln2 - used to scale x to primary range. */
-  invln2_64 = 0x1.71547652b82fep+6,
-/* ln2_64hi = high 32 bits of log(2.)/64. */
-  ln2_64hi = 0x1.62e42fee00000p-7,
-/* ln2_64lo = remainder bits for log(2.)/64 - ln2_64hi. */
-  ln2_64lo = 0x1.a39ef35793c76p-39,
-/* t2-t5 terms used for polynomial computation.  */
-  t2 = 0x1.5555555555555p-3, /* 1.6666666666666665741e-1 */
-  t3 = 0x1.5555555555555p-5, /* 4.1666666666666664354e-2 */
-  t4 = 0x1.1111111111111p-7, /* 8.3333333333333332177e-3 */
-  t5 = 0x1.6c16c16c16c17p-10, /* 1.3888888888888719040e-3 */
-/* Maximum value for x to not overflow.  */
-  threshold1 = 0x1.62e42fefa39efp+9, /* 7.09782712893383973096e+02 */
-/* Maximum value for -x to not underflow to zero in FE_TONEAREST mode.  */
-  threshold2 = 0x1.74910d52d3051p+9, /* 7.45133219101941108420e+02 */
-/* Scaling factor used when result near zero.  */
-  twom54 = 0x1.0000000000000p-54; /* 5.55111512312578270212e-17 */
diff --git a/sysdeps/ieee754/dbl-64/slowexp.c b/sysdeps/ieee754/dbl-64/slowexp.c
new file mode 100644
index 0000000000..e8fa2e263b
--- /dev/null
+++ b/sysdeps/ieee754/dbl-64/slowexp.c
@@ -0,0 +1,86 @@
+/*
+ * IBM Accurate Mathematical Library
+ * written by International Business Machines Corp.
+ * Copyright (C) 2001-2017 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
+}