diff mbox

[1/9,v3] Optimized generic expf and exp2f with wrappers

Message ID 59C11310.5000004@arm.com
State New, archived
Headers show

Commit Message

Szabolcs Nagy Sept. 19, 2017, 12:52 p.m. UTC
Based on new expf and exp2f code from
https://github.com/ARM-software/optimized-routines/

with the new expf benchmark (with wrapper, aarch64):
reciprocal-throughput: 2.3x faster
latency: 1.7x faster
with the new expf benchmark (without wrapper, aarch64):
reciprocal-throughput: 3.3x faster
latency: 1.7x faster
with naive ubenchmark (without wrapper, aarch64):
reciprocal-throughput: 3.7x faster
latency: 1.3x faster
libm.so size on aarch64:
.text size: -152 bytes
.rodata size: -1740 bytes
expf/exp2f worst case nearest rounding error: 0.502 ulp
worst case non-nearest rounding error: 1 ulp

Error checks are inline and errno setting is in separate
tail called functions, but the wrappers are kept in this
patch to handle the _LIB_VERSION==_SVID_ case.  (So e.g.
errno is set twice for expf calls and once __expf_finite
calls now on targets where the new code is used.)

Double precision arithmetics is used which is expected
to be faster on most targets (including soft-float) than
using single precision and it is easier to get good
precision result with it.

Const data is kept in a separate translation unit which
complicates maintenance a bit, but is expected to give
good code for literal loads on most targets and allows
sharing data across expf, exp2f and powf. (This data is
disabled on i386 and ia64 which have their own expf, exp2f
and powf code.)

Some configuration is in a new math_config.h the settings
may need further discussion.

Some details may need target specific tweaks:
- best convert and round to int operation in the arg
reduction may be different across targets.
- code was optimized on fma target, optimal polynomial
eval may be different without fma.
- gcc does not always generate good code for fp bit
representation access via unions or it may be inherently
slow on some target.

The libm-test-ulps will need adjustment because..
- The argument reduction ideally uses nearest rounded rint,
but that is not efficient on most targets, so the polynomial
can get evaluated on a wider interval in non-nearest
rounding mode making 1 ulp errors common in that case.
- The polynomial is evaluated such that it has 1 ulp error
on negative tiny inputs with upward rounding, but in
exchange the evaluation is better pipelined.

v3:
- Add sysdeps/m68k/m680x0/fpu/{math_errf/e_exp2f_data}.c

2017-09-19  Szabolcs Nagy  <szabolcs.nagy@arm.com>

	* math/Makefile (type-float-routines): Add math_errf and e_exp2f_data.
	* sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define.
	(roundtoint, converttoint): Likewise.
	* sysdeps/ieee754/flt-32/e_expf.c: New implementation.
	* sysdeps/ieee754/flt-32/e_exp2f.c: New implementation.
	* sysdeps/ieee754/flt-32/e_exp2f_data.c: New file.
	* sysdeps/ieee754/flt-32/math_config.h: New file.
	* sysdeps/ieee754/flt-32/math_errf.c: New file.
	* sysdeps/ieee754/flt-32/t_exp2f.h: Remove.
	* sysdeps/i386/fpu/e_exp2f_data.c: New file.
	* sysdeps/i386/fpu/math_errf.c: New file.
	* sysdeps/ia64/fpu/e_exp2f_data.c: New file.
	* sysdeps/ia64/fpu/math_errf.c: New file.
	* sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file.
	* sysdeps/m68k/m680x0/fpu/math_errf.c: New file.

Comments

Szabolcs Nagy Sept. 20, 2017, 1:22 p.m. UTC | #1
On 19/09/17 13:52, Szabolcs Nagy wrote:
> Based on new expf and exp2f code from
> https://github.com/ARM-software/optimized-routines/
> 
> with the new expf benchmark (with wrapper, aarch64):
> reciprocal-throughput: 2.3x faster
> latency: 1.7x faster
> with the new expf benchmark (without wrapper, aarch64):
> reciprocal-throughput: 3.3x faster
> latency: 1.7x faster
> with naive ubenchmark (without wrapper, aarch64):
> reciprocal-throughput: 3.7x faster
> latency: 1.3x faster

with the committed exp2f benchmark it's

reciprocal-throughput: 2.8x faster
latency: 1.3x faster

> libm.so size on aarch64:
> .text size: -152 bytes
> .rodata size: -1740 bytes
> expf/exp2f worst case nearest rounding error: 0.502 ulp
> worst case non-nearest rounding error: 1 ulp
> 
> Error checks are inline and errno setting is in separate
> tail called functions, but the wrappers are kept in this
> patch to handle the _LIB_VERSION==_SVID_ case.  (So e.g.
> errno is set twice for expf calls and once __expf_finite
> calls now on targets where the new code is used.)
> 
> Double precision arithmetics is used which is expected
> to be faster on most targets (including soft-float) than
> using single precision and it is easier to get good
> precision result with it.
> 
> Const data is kept in a separate translation unit which
> complicates maintenance a bit, but is expected to give
> good code for literal loads on most targets and allows
> sharing data across expf, exp2f and powf. (This data is
> disabled on i386 and ia64 which have their own expf, exp2f
> and powf code.)
> 
> Some configuration is in a new math_config.h the settings
> may need further discussion.
> 
> Some details may need target specific tweaks:
> - best convert and round to int operation in the arg
> reduction may be different across targets.
> - code was optimized on fma target, optimal polynomial
> eval may be different without fma.
> - gcc does not always generate good code for fp bit
> representation access via unions or it may be inherently
> slow on some target.
> 
> The libm-test-ulps will need adjustment because..
> - The argument reduction ideally uses nearest rounded rint,
> but that is not efficient on most targets, so the polynomial
> can get evaluated on a wider interval in non-nearest
> rounding mode making 1 ulp errors common in that case.
> - The polynomial is evaluated such that it has 1 ulp error
> on negative tiny inputs with upward rounding, but in
> exchange the evaluation is better pipelined.
> 
> v3:
> - Add sysdeps/m68k/m680x0/fpu/{math_errf/e_exp2f_data}.c
> 
> 2017-09-19  Szabolcs Nagy  <szabolcs.nagy@arm.com>
> 
> 	* math/Makefile (type-float-routines): Add math_errf and e_exp2f_data.
> 	* sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define.
> 	(roundtoint, converttoint): Likewise.
> 	* sysdeps/ieee754/flt-32/e_expf.c: New implementation.
> 	* sysdeps/ieee754/flt-32/e_exp2f.c: New implementation.
> 	* sysdeps/ieee754/flt-32/e_exp2f_data.c: New file.
> 	* sysdeps/ieee754/flt-32/math_config.h: New file.
> 	* sysdeps/ieee754/flt-32/math_errf.c: New file.
> 	* sysdeps/ieee754/flt-32/t_exp2f.h: Remove.
> 	* sysdeps/i386/fpu/e_exp2f_data.c: New file.
> 	* sysdeps/i386/fpu/math_errf.c: New file.
> 	* sysdeps/ia64/fpu/e_exp2f_data.c: New file.
> 	* sysdeps/ia64/fpu/math_errf.c: New file.
> 	* sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file.
> 	* sysdeps/m68k/m680x0/fpu/math_errf.c: New file.
> 
>
Joseph Myers Sept. 21, 2017, 11:44 p.m. UTC | #2
On Tue, 19 Sep 2017, Szabolcs Nagy wrote:

> diff --git a/sysdeps/aarch64/fpu/math_private.h b/sysdeps/aarch64/fpu/math_private.h
> index 807111ea5a..775237ffb2 100644
> --- a/sysdeps/aarch64/fpu/math_private.h
> +++ b/sysdeps/aarch64/fpu/math_private.h
> @@ -319,6 +319,26 @@ libc_feresetround_noex_aarch64_ctx (struct rm_ctx *ctx)
>  #define libc_feresetround_noexf_ctx	libc_feresetround_noex_aarch64_ctx
>  #define libc_feresetround_noexl_ctx	libc_feresetround_noex_aarch64_ctx
>  
> +/* Hack: only include the large arm_neon.h when needed.  */
> +#ifdef _MATH_CONFIG_H
> +#include <arm_neon.h>
> +
> +/* ACLE intrinsics for frintn and fcvtns instructions.  */
> +#define TOINT_INTRINSICS 1

I'd expect preprocessor indentation here, "# include" and "# define", 
inside #ifdef (I think it's only the toplevel multiple-include conditional 
around a whole file that doesn't get such indentation used).

> +  /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k.  */
> +  kd = (double) (xd + SHIFT); /* Rounding to double precision is required.  */

Remark (not an issue while this code isn't used for 32-bit x86): a cast 
may not achieve that rounding with the default -fexcess-precision=fast so 
using this code for 32-bit x86 might require math_narrow_eval here.

> +extern const struct exp2f_data
> +{
> +  uint64_t tab[1 << EXP2F_TABLE_BITS];
> +  double shift_scaled;
> +  double poly[EXP2F_POLY_ORDER];
> +  double shift;
> +  double invln2_scaled;
> +  double poly_scaled[EXP2F_POLY_ORDER];
> +} __exp2f_data;

This ought to be attribute_hidden as well.

OK with the preprocessor indentation and attribute_hidden fixes.
Joseph Myers Sept. 21, 2017, 11:50 p.m. UTC | #3
Note that I'd expect each addition of an optimized function to add / 
update a NEWS entry.
Szabolcs Nagy Sept. 22, 2017, 4:26 p.m. UTC | #4
On 22/09/17 00:44, Joseph Myers wrote:
> On Tue, 19 Sep 2017, Szabolcs Nagy wrote:
>> +  /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k.  */
>> +  kd = (double) (xd + SHIFT); /* Rounding to double precision is required.  */
> 
> Remark (not an issue while this code isn't used for 32-bit x86): a cast 
> may not achieve that rounding with the default -fexcess-precision=fast so 
> using this code for 32-bit x86 might require math_narrow_eval here.
> 

it seems the generated code for i686 happens to be correct
with gcc-7, but i will add math_narrow_eval if that is
needed for guaranteed rounding here (in case it later gets
enabled for i686).
Joseph Myers Sept. 22, 2017, 4:33 p.m. UTC | #5
On Fri, 22 Sep 2017, Szabolcs Nagy wrote:

> On 22/09/17 00:44, Joseph Myers wrote:
> > On Tue, 19 Sep 2017, Szabolcs Nagy wrote:
> >> +  /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k.  */
> >> +  kd = (double) (xd + SHIFT); /* Rounding to double precision is required.  */
> > 
> > Remark (not an issue while this code isn't used for 32-bit x86): a cast 
> > may not achieve that rounding with the default -fexcess-precision=fast so 
> > using this code for 32-bit x86 might require math_narrow_eval here.
> 
> it seems the generated code for i686 happens to be correct
> with gcc-7, but i will add math_narrow_eval if that is
> needed for guaranteed rounding here (in case it later gets
> enabled for i686).

Note that code like this appears in both expf and exp2f, though I only 
mentioned it once in my review.
diff mbox

Patch

diff --git a/math/Makefile b/math/Makefile
index 0601f3ac43..04586156f8 100644
--- a/math/Makefile
+++ b/math/Makefile
@@ -115,7 +115,7 @@  type-double-routines := branred doasin dosincos halfulp mpa mpatan2	\
 
 # float support
 type-float-suffix := f
-type-float-routines := k_rem_pio2f
+type-float-routines := k_rem_pio2f math_errf e_exp2f_data
 
 # _Float128 support
 type-float128-suffix := f128
diff --git a/sysdeps/aarch64/fpu/math_private.h b/sysdeps/aarch64/fpu/math_private.h
index 807111ea5a..775237ffb2 100644
--- a/sysdeps/aarch64/fpu/math_private.h
+++ b/sysdeps/aarch64/fpu/math_private.h
@@ -319,6 +319,26 @@  libc_feresetround_noex_aarch64_ctx (struct rm_ctx *ctx)
 #define libc_feresetround_noexf_ctx	libc_feresetround_noex_aarch64_ctx
 #define libc_feresetround_noexl_ctx	libc_feresetround_noex_aarch64_ctx
 
+/* Hack: only include the large arm_neon.h when needed.  */
+#ifdef _MATH_CONFIG_H
+#include <arm_neon.h>
+
+/* ACLE intrinsics for frintn and fcvtns instructions.  */
+#define TOINT_INTRINSICS 1
+
+static inline double_t
+roundtoint (double_t x)
+{
+  return vget_lane_f64 (vrndn_f64 (vld1_f64 (&x)), 0);
+}
+
+static inline uint64_t
+converttoint (double_t x)
+{
+  return vcvtnd_s64_f64 (x);
+}
+#endif
+
 #include_next <math_private.h>
 
 #endif
diff --git a/sysdeps/i386/fpu/e_exp2f_data.c b/sysdeps/i386/fpu/e_exp2f_data.c
new file mode 100644
index 0000000000..1cc8931700
--- /dev/null
+++ b/sysdeps/i386/fpu/e_exp2f_data.c
@@ -0,0 +1 @@ 
+/* Not needed.  */
diff --git a/sysdeps/i386/fpu/math_errf.c b/sysdeps/i386/fpu/math_errf.c
new file mode 100644
index 0000000000..1cc8931700
--- /dev/null
+++ b/sysdeps/i386/fpu/math_errf.c
@@ -0,0 +1 @@ 
+/* Not needed.  */
diff --git a/sysdeps/ia64/fpu/e_exp2f_data.c b/sysdeps/ia64/fpu/e_exp2f_data.c
new file mode 100644
index 0000000000..1cc8931700
--- /dev/null
+++ b/sysdeps/ia64/fpu/e_exp2f_data.c
@@ -0,0 +1 @@ 
+/* Not needed.  */
diff --git a/sysdeps/ia64/fpu/math_errf.c b/sysdeps/ia64/fpu/math_errf.c
new file mode 100644
index 0000000000..1cc8931700
--- /dev/null
+++ b/sysdeps/ia64/fpu/math_errf.c
@@ -0,0 +1 @@ 
+/* Not needed.  */
diff --git a/sysdeps/ieee754/flt-32/e_exp2f.c b/sysdeps/ieee754/flt-32/e_exp2f.c
index 567d3ff6d0..be53e5c699 100644
--- a/sysdeps/ieee754/flt-32/e_exp2f.c
+++ b/sysdeps/ieee754/flt-32/e_exp2f.c
@@ -1,7 +1,6 @@ 
-/* Single-precision floating point 2^x.
-   Copyright (C) 1997-2017 Free Software Foundation, Inc.
+/* Single-precision 2^x function.
+   Copyright (C) 2017 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
-   Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
 
    The GNU C Library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
@@ -17,116 +16,73 @@ 
    License along with the GNU C Library; if not, see
    <http://www.gnu.org/licenses/>.  */
 
-/* The basic design here is from
-   Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical
-   Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft.,
-   17 (1), March 1991, pp. 26-45.
-   It has been slightly modified to compute 2^x instead of e^x, and for
-   single-precision.
-   */
-#ifndef _GNU_SOURCE
-# define _GNU_SOURCE
-#endif
-#include <stdlib.h>
-#include <float.h>
-#include <ieee754.h>
 #include <math.h>
-#include <fenv.h>
-#include <inttypes.h>
-#include <math_private.h>
-
-#include "t_exp2f.h"
-
-static const float TWOM100 = 7.88860905e-31;
-static const float TWO127 = 1.7014118346e+38;
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+EXP2F_TABLE_BITS = 5
+EXP2F_POLY_ORDER = 3
+
+ULP error: 0.502 (nearest rounding.)
+Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
+Wrong count: 168353 (all nearest rounding wrong results with fma.)
+Non-nearest ULP error: 1 (rounded ULP error)
+*/
+
+#define N (1 << EXP2F_TABLE_BITS)
+#define T __exp2f_data.tab
+#define C __exp2f_data.poly
+#define SHIFT __exp2f_data.shift_scaled
+
+static inline uint32_t
+top12 (float x)
+{
+  return asuint (x) >> 20;
+}
 
 float
 __ieee754_exp2f (float x)
 {
-  static const float himark = (float) FLT_MAX_EXP;
-  static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1);
-
-  /* Check for usual case.  */
-  if (isless (x, himark) && isgreaterequal (x, lomark))
+  uint32_t abstop;
+  uint64_t ki, t;
+  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
+  double_t kd, xd, z, r, r2, y, s;
+
+  xd = (double_t) x;
+  abstop = top12 (x) & 0x7ff;
+  if (__glibc_unlikely (abstop >= top12 (128.0f)))
     {
-      static const float THREEp14 = 49152.0;
-      int tval, unsafe;
-      float rx, x22, result;
-      union ieee754_float ex2_u, scale_u;
-
-      if (fabsf (x) < FLT_EPSILON / 4.0f)
-	return 1.0f + x;
-
-      {
-	SET_RESTORE_ROUND_NOEXF (FE_TONEAREST);
-
-	/* 1. Argument reduction.
-	   Choose integers ex, -128 <= t < 128, and some real
-	   -1/512 <= x1 <= 1/512 so that
-	   x = ex + t/512 + x1.
-
-	   First, calculate rx = ex + t/256.  */
-	rx = x + THREEp14;
-	rx -= THREEp14;
-	x -= rx;  /* Compute x=x1. */
-	/* Compute tval = (ex*256 + t)+128.
-	   Now, t = (tval mod 256)-128 and ex=tval/256  [that's mod, NOT %;
-	   and /-round-to-nearest not the usual c integer /].  */
-	tval = (int) (rx * 256.0f + 128.0f);
-
-	/* 2. Adjust for accurate table entry.
-	   Find e so that
-	   x = ex + t/256 + e + x2
-	   where -7e-4 < e < 7e-4, and
-	   (float)(2^(t/256+e))
-	   is accurate to one part in 2^-64.  */
-
-	/* 'tval & 255' is the same as 'tval%256' except that it's always
-	   positive.
-	   Compute x = x2.  */
-	x -= __exp2f_deltatable[tval & 255];
-
-	/* 3. Compute ex2 = 2^(t/255+e+ex).  */
-	ex2_u.f = __exp2f_atable[tval & 255];
-	tval >>= 8;
-	/* x2 is an integer multiple of 2^-30; avoid intermediate
-	   underflow from the calculation of x22 * x.  */
-	unsafe = abs(tval) >= -FLT_MIN_EXP - 32;
-	ex2_u.ieee.exponent += tval >> unsafe;
-	scale_u.f = 1.0;
-	scale_u.ieee.exponent += tval - (tval >> unsafe);
-
-	/* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
-	   with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14]
-	   less than 1.3e-10.  */
-
-	x22 = (.24022656679f * x + .69314736128f) * ex2_u.f;
-      }
-
-      /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex).  */
-      result = x22 * x + ex2_u.f;
-
-      if (!unsafe)
-	return result;
-      else
-	{
-	  result *= scale_u.f;
-	  math_check_force_underflow_nonneg (result);
-	  return result;
-	}
-    }
-  /* Exceptional cases:  */
-  else if (isless (x, himark))
-    {
-      if (isinf (x))
-	/* e^-inf == 0, with no error.  */
-	return 0;
-      else
-	/* Underflow */
-	return TWOM100 * TWOM100;
+      /* |x| >= 128 or x is nan.  */
+      if (asuint (x) == asuint (-INFINITY))
+	return 0.0f;
+      if (abstop >= top12 (INFINITY))
+	return x + x;
+      if (x > 0.0f)
+	return __math_oflowf (0);
+      if (x <= -150.0f)
+	return __math_uflowf (0);
+#if WANT_ERRNO_UFLOW
+      if (x < -149.0f)
+	return __math_may_uflowf (0);
+#endif
     }
-  else
-    /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
-    return TWO127*x;
+
+  /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k.  */
+  kd = (double) (xd + SHIFT); /* Rounding to double precision is required.  */
+  ki = asuint64 (kd);
+  kd -= SHIFT; /* k/N for int k.  */
+  r = xd - kd;
+
+  /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+  t = T[ki % N];
+  t += ki << (52 - EXP2F_TABLE_BITS);
+  s = asdouble (t);
+  z = C[0] * r + C[1];
+  r2 = r * r;
+  y = C[2] * r + 1;
+  y = z * r2 + y;
+  y = y * s;
+  return (float) y;
 }
 strong_alias (__ieee754_exp2f, __exp2f_finite)
diff --git a/sysdeps/ieee754/flt-32/e_exp2f_data.c b/sysdeps/ieee754/flt-32/e_exp2f_data.c
new file mode 100644
index 0000000000..390dcae333
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/e_exp2f_data.c
@@ -0,0 +1,44 @@ 
+/* Shared data between expf, exp2f and powf.
+   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/>.  */
+
+#include "math_config.h"
+
+#define N (1 << EXP2F_TABLE_BITS)
+
+const struct exp2f_data __exp2f_data = {
+  /* tab[i] = uint(2^(i/N)) - (i << 52-BITS)
+     used for computing 2^(k/N) for an int |k| < 150 N as
+     double(tab[k%N] + (k << 52-BITS)) */
+  .tab = {
+0x3ff0000000000000, 0x3fefd9b0d3158574, 0x3fefb5586cf9890f, 0x3fef9301d0125b51,
+0x3fef72b83c7d517b, 0x3fef54873168b9aa, 0x3fef387a6e756238, 0x3fef1e9df51fdee1,
+0x3fef06fe0a31b715, 0x3feef1a7373aa9cb, 0x3feedea64c123422, 0x3feece086061892d,
+0x3feebfdad5362a27, 0x3feeb42b569d4f82, 0x3feeab07dd485429, 0x3feea47eb03a5585,
+0x3feea09e667f3bcd, 0x3fee9f75e8ec5f74, 0x3feea11473eb0187, 0x3feea589994cce13,
+0x3feeace5422aa0db, 0x3feeb737b0cdc5e5, 0x3feec49182a3f090, 0x3feed503b23e255d,
+0x3feee89f995ad3ad, 0x3feeff76f2fb5e47, 0x3fef199bdd85529c, 0x3fef3720dcef9069,
+0x3fef5818dcfba487, 0x3fef7c97337b9b5f, 0x3fefa4afa2a490da, 0x3fefd0765b6e4540,
+  },
+  .shift_scaled = 0x1.8p+52 / N,
+  .poly = { 0x1.c6af84b912394p-5, 0x1.ebfce50fac4f3p-3, 0x1.62e42ff0c52d6p-1 },
+  .shift = 0x1.8p+52,
+  .invln2_scaled = 0x1.71547652b82fep+0 * N,
+  .poly_scaled = {
+0x1.c6af84b912394p-5/N/N/N, 0x1.ebfce50fac4f3p-3/N/N, 0x1.62e42ff0c52d6p-1/N
+  },
+};
diff --git a/sysdeps/ieee754/flt-32/e_expf.c b/sysdeps/ieee754/flt-32/e_expf.c
index 782072f213..b8244a82cf 100644
--- a/sysdeps/ieee754/flt-32/e_expf.c
+++ b/sysdeps/ieee754/flt-32/e_expf.c
@@ -1,7 +1,6 @@ 
-/* Single-precision floating point e^x.
-   Copyright (C) 1997-2017 Free Software Foundation, Inc.
+/* Single-precision e^x function.
+   Copyright (C) 2017 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
-   Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
 
    The GNU C Library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
@@ -17,117 +16,87 @@ 
    License along with the GNU C Library; if not, see
    <http://www.gnu.org/licenses/>.  */
 
-/* How this works:
-
-   The input value, x, is written as
-
-   x = n * ln(2) + t/512 + delta[t] + x;
-
-   where:
-   - n is an integer, 127 >= n >= -150;
-   - t is an integer, 177 >= t >= -177
-   - delta is based on a table entry, delta[t] < 2^-28
-   - x is whatever is left, |x| < 2^-10
-
-   Then e^x is approximated as
-
-   e^x = 2^n ( e^(t/512 + delta[t])
-	       + ( e^(t/512 + delta[t])
-		   * ( p(x + delta[t] + n * ln(2)) - delta ) ) )
-
-   where
-   - p(x) is a polynomial approximating e(x)-1;
-   - e^(t/512 + delta[t]) is obtained from a table.
-
-   The table used is the same one as for the double precision version;
-   since we have the table, we might as well use it.
-
-   It turns out to be faster to do calculations in double precision than
-   to perform an 'accurate table method' expf, because of the range reduction
-   overhead (compare exp2f).
-   */
-#include <float.h>
-#include <ieee754.h>
 #include <math.h>
-#include <fenv.h>
-#include <inttypes.h>
-#include <math_private.h>
-
-extern const float __exp_deltatable[178];
-extern const double __exp_atable[355] /* __attribute__((mode(DF))) */;
-
-static const float TWOM100 = 7.88860905e-31;
-static const float TWO127 = 1.7014118346e+38;
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+EXP2F_TABLE_BITS = 5
+EXP2F_POLY_ORDER = 3
+
+ULP error: 0.502 (nearest rounding.)
+Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
+Wrong count: 170635 (all nearest rounding wrong results with fma.)
+Non-nearest ULP error: 1 (rounded ULP error)
+*/
+
+#define N (1 << EXP2F_TABLE_BITS)
+#define InvLn2N __exp2f_data.invln2_scaled
+#define T __exp2f_data.tab
+#define C __exp2f_data.poly_scaled
+
+static inline uint32_t
+top12 (float x)
+{
+  return asuint (x) >> 20;
+}
 
 float
 __ieee754_expf (float x)
 {
-  static const float himark = 88.72283935546875;
-  static const float lomark = -103.972084045410;
-  /* Check for usual case.  */
-  if (isless (x, himark) && isgreater (x, lomark))
+  uint32_t abstop;
+  uint64_t ki, t;
+  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
+  double_t kd, xd, z, r, r2, y, s;
+
+  xd = (double_t) x;
+  abstop = top12 (x) & 0x7ff;
+  if (__glibc_unlikely (abstop >= top12 (88.0f)))
     {
-      static const float THREEp42 = 13194139533312.0;
-      static const float THREEp22 = 12582912.0;
-      /* 1/ln(2).  */
-#undef M_1_LN2
-      static const float M_1_LN2 = 1.44269502163f;
-      /* ln(2) */
-#undef M_LN2
-      static const double M_LN2 = .6931471805599452862;
-
-      int tval;
-      double x22, t, result, dx;
-      float n, delta;
-      union ieee754_double ex2_u;
-
-      {
-	SET_RESTORE_ROUND_NOEXF (FE_TONEAREST);
-
-	/* Calculate n.  */
-	n = x * M_1_LN2 + THREEp22;
-	n -= THREEp22;
-	dx = x - n*M_LN2;
-
-	/* Calculate t/512.  */
-	t = dx + THREEp42;
-	t -= THREEp42;
-	dx -= t;
-
-	/* Compute tval = t.  */
-	tval = (int) (t * 512.0);
-
-	if (t >= 0)
-	  delta = - __exp_deltatable[tval];
-	else
-	  delta = __exp_deltatable[-tval];
-
-	/* Compute ex2 = 2^n e^(t/512+delta[t]).  */
-	ex2_u.d = __exp_atable[tval+177];
-	ex2_u.ieee.exponent += (int) n;
-
-	/* Approximate e^(dx+delta) - 1, using a second-degree polynomial,
-	   with maximum error in [-2^-10-2^-28,2^-10+2^-28]
-	   less than 5e-11.  */
-	x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta;
-      }
-
-      /* Return result.  */
-      result = x22 * ex2_u.d + ex2_u.d;
-      return (float) result;
+      /* |x| >= 88 or x is nan.  */
+      if (asuint (x) == asuint (-INFINITY))
+	return 0.0f;
+      if (abstop >= top12 (INFINITY))
+	return x + x;
+      if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
+	return __math_oflowf (0);
+      if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
+	return __math_uflowf (0);
+#if WANT_ERRNO_UFLOW
+      if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */
+	return __math_may_uflowf (0);
+#endif
     }
-  /* Exceptional cases:  */
-  else if (isless (x, himark))
-    {
-      if (isinf (x))
-	/* e^-inf == 0, with no error.  */
-	return 0;
-      else
-	/* Underflow */
-	return TWOM100 * TWOM100;
-    }
-  else
-    /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
-    return TWO127*x;
+
+  /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k.  */
+  z = InvLn2N * xd;
+
+  /* Round and convert z to int, the result is in [-150*N, 128*N] and
+     ideally ties-to-even rule is used, otherwise the magnitude of r
+     can be bigger which gives larger approximation error.  */
+#if TOINT_INTRINSICS
+  kd = roundtoint (z);
+  ki = converttoint (z);
+#elif TOINT_RINT
+  kd = rint (z);
+  ki = (long) kd;
+#elif TOINT_SHIFT
+# define SHIFT __exp2f_data.shift
+  kd = (double) (z + SHIFT); /* Rounding to double precision is required.  */
+  ki = asuint64 (kd);
+  kd -= SHIFT;
+#endif
+  r = z - kd;
+
+  /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+  t = T[ki % N];
+  t += ki << (52 - EXP2F_TABLE_BITS);
+  s = asdouble (t);
+  z = C[0] * r + C[1];
+  r2 = r * r;
+  y = C[2] * r + 1;
+  y = z * r2 + y;
+  y = y * s;
+  return (float) y;
 }
 strong_alias (__ieee754_expf, __expf_finite)
diff --git a/sysdeps/ieee754/flt-32/math_config.h b/sysdeps/ieee754/flt-32/math_config.h
new file mode 100644
index 0000000000..1759c447c8
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/math_config.h
@@ -0,0 +1,114 @@ 
+/* Configuration for math routines.
+   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/>.  */
+
+#ifndef _MATH_CONFIG_H
+#define _MATH_CONFIG_H
+
+#include <math.h>
+#include <math_private.h>
+#include <stdint.h>
+
+#ifndef WANT_ROUNDING
+/* Correct special case results in non-nearest rounding modes.  */
+# define WANT_ROUNDING 1
+#endif
+#ifndef WANT_ERRNO
+/* Set errno according to ISO C with (math_errhandling & MATH_ERRNO) != 0.  */
+# define WANT_ERRNO 1
+#endif
+#ifndef WANT_ERRNO_UFLOW
+/* Set errno to ERANGE if result underflows to 0 (in all rounding modes).  */
+# define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO)
+#endif
+
+#ifndef TOINT_INTRINSICS
+# define TOINT_INTRINSICS 0
+#endif
+#ifndef TOINT_RINT
+# define TOINT_RINT 0
+#endif
+#ifndef TOINT_SHIFT
+# define TOINT_SHIFT 1
+#endif
+
+static inline uint32_t
+asuint (float f)
+{
+  union
+  {
+    float f;
+    uint32_t i;
+  } u = {f};
+  return u.i;
+}
+
+static inline float
+asfloat (uint32_t i)
+{
+  union
+  {
+    uint32_t i;
+    float f;
+  } u = {i};
+  return u.f;
+}
+
+static inline uint64_t
+asuint64 (double f)
+{
+  union
+  {
+    double f;
+    uint64_t i;
+  } u = {f};
+  return u.i;
+}
+
+static inline double
+asdouble (uint64_t i)
+{
+  union
+  {
+    uint64_t i;
+    double f;
+  } u = {i};
+  return u.f;
+}
+
+#define NOINLINE __attribute__ ((noinline))
+
+attribute_hidden float __math_oflowf (unsigned long);
+attribute_hidden float __math_uflowf (unsigned long);
+attribute_hidden float __math_may_uflowf (unsigned long);
+attribute_hidden float __math_divzerof (unsigned long);
+attribute_hidden float __math_invalidf (float);
+
+/* Shared between expf, exp2f and powf.  */
+#define EXP2F_TABLE_BITS 5
+#define EXP2F_POLY_ORDER 3
+extern const struct exp2f_data
+{
+  uint64_t tab[1 << EXP2F_TABLE_BITS];
+  double shift_scaled;
+  double poly[EXP2F_POLY_ORDER];
+  double shift;
+  double invln2_scaled;
+  double poly_scaled[EXP2F_POLY_ORDER];
+} __exp2f_data;
+
+#endif
diff --git a/sysdeps/ieee754/flt-32/math_errf.c b/sysdeps/ieee754/flt-32/math_errf.c
new file mode 100644
index 0000000000..ab546e24cf
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/math_errf.c
@@ -0,0 +1,76 @@ 
+/* Single-precision math error handling.
+   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/>.  */
+
+#include "math_config.h"
+
+#if WANT_ERRNO
+# include <errno.h>
+/* NOINLINE reduces code size.  */
+NOINLINE static float
+with_errnof (float y, int e)
+{
+  errno = e;
+  return y;
+}
+#else
+# define with_errnof(x, e) (x)
+#endif
+
+/* NOINLINE prevents fenv semantics breaking optimizations.  */
+NOINLINE static float
+xflowf (unsigned long sign, float y)
+{
+  y = (sign ? -y : y) * y;
+  return with_errnof (y, ERANGE);
+}
+
+attribute_hidden float
+__math_uflowf (unsigned long sign)
+{
+  return xflowf (sign, 0x1p-95f);
+}
+
+#if WANT_ERRNO_UFLOW
+/* Underflows to zero in some non-nearest rounding mode, setting errno
+   is valid even if the result is non-zero, but in the subnormal range.  */
+attribute_hidden float
+__math_may_uflowf (unsigned long sign)
+{
+  return xflowf (sign, 0x1.4p-75f);
+}
+#endif
+
+attribute_hidden float
+__math_oflowf (unsigned long sign)
+{
+  return xflowf (sign, 0x1p97f);
+}
+
+attribute_hidden float
+__math_divzerof (unsigned long sign)
+{
+  float y = 0;
+  return with_errnof ((sign ? -1 : 1) / y, ERANGE);
+}
+
+attribute_hidden float
+__math_invalidf (float x)
+{
+  float y = (x - x) / (x - x);
+  return isnan (x) ? y : with_errnof (y, EDOM);
+}
diff --git a/sysdeps/ieee754/flt-32/t_exp2f.h b/sysdeps/ieee754/flt-32/t_exp2f.h
deleted file mode 100644
index aecabcc372..0000000000
--- a/sysdeps/ieee754/flt-32/t_exp2f.h
+++ /dev/null
@@ -1,351 +0,0 @@ 
-/* Accurate tables for exp2f().
-   Copyright (C) 1998-2017 Free Software Foundation, Inc.
-   This file is part of the GNU C Library.
-   Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
-
-   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/>.  */
-
-/* This table has the property that, for all integers -128 <= i <= 127,
-   exp(i/256.0 + __exp2f_deltatable[i-128]) == __exp2f_atable[i+128] + r
-   for some -2^-35 < r < 2^-35 (abs(r) < 2^-36 if i <= 0); and that
-   __exp2f_deltatable[i+128] == t * 2^-30
-   for integer t so that abs(t) <= 43447 * 2^0.  */
-
-#define W30 (9.31322575e-10)
-static const float __exp2f_deltatable[256] = {
-      -810*W30,       283*W30,     -1514*W30,      1304*W30,
-     -1148*W30,       -98*W30,      -744*W30,      -156*W30,
-      -419*W30,      -155*W30,       474*W30,       167*W30,
-     -1984*W30,      -826*W30,       692*W30,       781*W30,
-      -578*W30,      -411*W30,      -129*W30,     -1500*W30,
-       654*W30,      -141*W30,      -816*W30,       -53*W30,
-       148*W30,       493*W30,     -2214*W30,       760*W30,
-       260*W30,       750*W30,     -1300*W30,      1424*W30,
-     -1445*W30,      -339*W30,      -680*W30,      -349*W30,
-      -922*W30,       531*W30,       193*W30,     -2892*W30,
-       290*W30,     -2145*W30,      -276*W30,       485*W30,
-      -695*W30,       215*W30,     -7093*W30,       412*W30,
-     -4596*W30,       367*W30,       592*W30,      -615*W30,
-       -97*W30,     -1066*W30,       972*W30,      -226*W30,
-      -625*W30,      -374*W30,     -5647*W30,      -180*W30,
-     20349*W30,      -447*W30,       111*W30,     -4164*W30,
-       -87*W30,       -21*W30,      -251*W30,        66*W30,
-      -517*W30,      2093*W30,      -263*W30,       182*W30,
-      -601*W30,       475*W30,      -483*W30,     -1251*W30,
-      -373*W30,      1471*W30,       -92*W30,      -215*W30,
-       -97*W30,      -190*W30,         0*W30,      -290*W30,
-     -2647*W30,      1940*W30,      -582*W30,        28*W30,
-       833*W30,      1493*W30,        34*W30,       321*W30,
-      3327*W30,       -35*W30,       177*W30,      -135*W30,
-      -796*W30,      -428*W30,       129*W30,      9332*W30,
-       -12*W30,       -69*W30,     -1743*W30,      6508*W30,
-       -60*W30,       359*W30,     43447*W30,        15*W30,
-       -23*W30,      -305*W30,      -375*W30,      -652*W30,
-       667*W30,       269*W30,     -1575*W30,       185*W30,
-      -329*W30,       200*W30,      6002*W30,       163*W30,
-      -647*W30,        19*W30,      -603*W30,      -755*W30,
-       742*W30,      -438*W30,      3587*W30,      2560*W30,
-         0*W30,      -520*W30,      -241*W30,      -299*W30,
-     -1270*W30,      -991*W30,     -1138*W30,       255*W30,
-     -1192*W30,      1722*W30,      1023*W30,      3700*W30,
-     -1388*W30,     -1551*W30,     -2549*W30,        27*W30,
-       282*W30,       673*W30,       113*W30,      1561*W30,
-        72*W30,       873*W30,        87*W30,      -395*W30,
-      -433*W30,       629*W30,      3440*W30,      -284*W30,
-      -592*W30,      -103*W30,       -46*W30,     -3844*W30,
-      1712*W30,       303*W30,      1555*W30,      -631*W30,
-     -1400*W30,      -961*W30,      -854*W30,      -276*W30,
-       407*W30,       833*W30,      -345*W30,     -1501*W30,
-       121*W30,     -1581*W30,       400*W30,       150*W30,
-      1224*W30,      -139*W30,      -563*W30,       879*W30,
-       933*W30,      2939*W30,       788*W30,       211*W30,
-       530*W30,      -192*W30,       706*W30,    -13347*W30,
-      1065*W30,         3*W30,       111*W30,      -208*W30,
-      -360*W30,      -532*W30,      -291*W30,       483*W30,
-       987*W30,       -33*W30,     -1373*W30,      -166*W30,
-     -1174*W30,     -3955*W30,      1601*W30,      -280*W30,
-      1405*W30,       600*W30,     -1659*W30,       -23*W30,
-       390*W30,       449*W30,       570*W30,    -13143*W30,
-        -9*W30,     -1646*W30,      1201*W30,       294*W30,
-      2181*W30,     -1173*W30,      1388*W30,     -4504*W30,
-       190*W30,     -2304*W30,       211*W30,       239*W30,
-        48*W30,      -817*W30,      1018*W30,      1828*W30,
-      -663*W30,      1408*W30,       408*W30,       -36*W30,
-      1295*W30,      -230*W30,      1341*W30,         9*W30,
-        40*W30,       705*W30,       186*W30,       376*W30,
-       557*W30,      5866*W30,       363*W30,     -1558*W30,
-       718*W30,       669*W30,      1369*W30,     -2972*W30,
-      -468*W30,      -121*W30,      -219*W30,       667*W30,
-     29954*W30,       366*W30,        48*W30,      -203*W30
-};
-
-static const float __exp2f_atable[256] /* __attribute__((mode(SF))) */ = {
- 0.707106411447, /* 0x0.b504ecfff */
- 0.709024071690, /* 0x0.b58299fff */
- 0.710945606239, /* 0x0.b60088000 */
- 0.712874472142, /* 0x0.b67ef1000 */
- 0.714806139464, /* 0x0.b6fd88fff */
- 0.716744661340, /* 0x0.b77c94000 */
- 0.718687653549, /* 0x0.b7fbea000 */
- 0.720636486992, /* 0x0.b87ba1fff */
- 0.722590208040, /* 0x0.b8fbabfff */
- 0.724549472323, /* 0x0.b97c12fff */
- 0.726514220228, /* 0x0.b9fcd5fff */
- 0.728483855735, /* 0x0.ba7deb000 */
- 0.730457961549, /* 0x0.baff4afff */
- 0.732438981522, /* 0x0.bb811efff */
- 0.734425544748, /* 0x0.bc0350000 */
- 0.736416816713, /* 0x0.bc85d0000 */
- 0.738412797450, /* 0x0.bd089efff */
- 0.740414917465, /* 0x0.bd8bd4fff */
- 0.742422521111, /* 0x0.be0f66fff */
- 0.744434773914, /* 0x0.be9346fff */
- 0.746454179287, /* 0x0.bf179f000 */
- 0.748477637755, /* 0x0.bf9c3afff */
- 0.750506639473, /* 0x0.c02133fff */
- 0.752541840064, /* 0x0.c0a694fff */
- 0.754582285889, /* 0x0.c12c4e000 */
- 0.756628334525, /* 0x0.c1b265000 */
- 0.758678436269, /* 0x0.c238bffff */
- 0.760736882681, /* 0x0.c2bfa6fff */
- 0.762799203401, /* 0x0.c346cf000 */
- 0.764867603790, /* 0x0.c3ce5d000 */
- 0.766940355298, /* 0x0.c45633fff */
- 0.769021093841, /* 0x0.c4de90fff */
- 0.771104693409, /* 0x0.c5671dfff */
- 0.773195922364, /* 0x0.c5f02afff */
- 0.775292098512, /* 0x0.c6798afff */
- 0.777394294745, /* 0x0.c70350000 */
- 0.779501736166, /* 0x0.c78d6d000 */
- 0.781615912910, /* 0x0.c817fafff */
- 0.783734917628, /* 0x0.c8a2d9fff */
- 0.785858273516, /* 0x0.c92e02000 */
- 0.787990570071, /* 0x0.c9b9c0000 */
- 0.790125787245, /* 0x0.ca45aefff */
- 0.792268991467, /* 0x0.cad223fff */
- 0.794417440881, /* 0x0.cb5ef0fff */
- 0.796570718287, /* 0x0.cbec0efff */
- 0.798730909811, /* 0x0.cc79a0fff */
- 0.800892710672, /* 0x0.cd074dfff */
- 0.803068041795, /* 0x0.cd95ddfff */
- 0.805242776881, /* 0x0.ce2464000 */
- 0.807428598393, /* 0x0.ceb3a3fff */
- 0.809617877002, /* 0x0.cf431dfff */
- 0.811812341211, /* 0x0.cfd2eefff */
- 0.814013659956, /* 0x0.d06333000 */
- 0.816220164311, /* 0x0.d0f3ce000 */
- 0.818434238424, /* 0x0.d184e7fff */
- 0.820652604094, /* 0x0.d21649fff */
- 0.822877407074, /* 0x0.d2a818000 */
- 0.825108587751, /* 0x0.d33a51000 */
- 0.827342867839, /* 0x0.d3ccbdfff */
- 0.829588949684, /* 0x0.d45ff1000 */
- 0.831849217401, /* 0x0.d4f411fff */
- 0.834093391880, /* 0x0.d58724fff */
- 0.836355149750, /* 0x0.d61b5f000 */
- 0.838620424257, /* 0x0.d6afd3fff */
- 0.840896368027, /* 0x0.d744fc000 */
- 0.843176305293, /* 0x0.d7da66fff */
- 0.845462262643, /* 0x0.d87037000 */
- 0.847754716864, /* 0x0.d90673fff */
- 0.850052893157, /* 0x0.d99d10fff */
- 0.852359056469, /* 0x0.da3433fff */
- 0.854668736446, /* 0x0.dacb91fff */
- 0.856986224651, /* 0x0.db6373000 */
- 0.859309315673, /* 0x0.dbfbb1fff */
- 0.861639738080, /* 0x0.dc946bfff */
- 0.863975346095, /* 0x0.dd2d7d000 */
- 0.866317391394, /* 0x0.ddc6f9fff */
- 0.868666708472, /* 0x0.de60f1000 */
- 0.871022939695, /* 0x0.defb5c000 */
- 0.873383641229, /* 0x0.df9611fff */
- 0.875751554968, /* 0x0.e03141000 */
- 0.878126025200, /* 0x0.e0ccde000 */
- 0.880506813521, /* 0x0.e168e4fff */
- 0.882894217966, /* 0x0.e2055afff */
- 0.885287821299, /* 0x0.e2a239000 */
- 0.887686729423, /* 0x0.e33f6ffff */
- 0.890096127973, /* 0x0.e3dd56fff */
- 0.892507970338, /* 0x0.e47b67000 */
- 0.894928157336, /* 0x0.e51a03000 */
- 0.897355020043, /* 0x0.e5b90efff */
- 0.899788379682, /* 0x0.e65888000 */
- 0.902227103705, /* 0x0.e6f85afff */
- 0.904673457151, /* 0x0.e798ae000 */
- 0.907128036008, /* 0x0.e8398afff */
- 0.909585535528, /* 0x0.e8da99000 */
- 0.912051796915, /* 0x0.e97c3a000 */
- 0.914524436003, /* 0x0.ea1e46000 */
- 0.917003571999, /* 0x0.eac0bf000 */
- 0.919490039339, /* 0x0.eb63b2fff */
- 0.921983361257, /* 0x0.ec071a000 */
- 0.924488604054, /* 0x0.ecab48fff */
- 0.926989555360, /* 0x0.ed4f30000 */
- 0.929502844812, /* 0x0.edf3e6000 */
- 0.932021975503, /* 0x0.ee98fdfff */
- 0.934553921208, /* 0x0.ef3eecfff */
- 0.937083780759, /* 0x0.efe4b8fff */
- 0.939624726786, /* 0x0.f08b3f000 */
- 0.942198514924, /* 0x0.f133ebfff */
- 0.944726586343, /* 0x0.f1d99a000 */
- 0.947287976728, /* 0x0.f28176fff */
- 0.949856162070, /* 0x0.f329c5fff */
- 0.952431440345, /* 0x0.f3d28bfff */
- 0.955013573175, /* 0x0.f47bc5000 */
- 0.957603693021, /* 0x0.f52584000 */
- 0.960199773321, /* 0x0.f5cfa7000 */
- 0.962801992906, /* 0x0.f67a31000 */
- 0.965413510788, /* 0x0.f72556fff */
- 0.968030691152, /* 0x0.f7d0dc000 */
- 0.970655620084, /* 0x0.f87ce2fff */
- 0.973290979849, /* 0x0.f92998fff */
- 0.975926160805, /* 0x0.f9d64bfff */
- 0.978571653370, /* 0x0.fa83ac000 */
- 0.981225252139, /* 0x0.fb3193fff */
- 0.983885228626, /* 0x0.fbdfe6fff */
- 0.986552715296, /* 0x0.fc8eb7fff */
- 0.989228487027, /* 0x0.fd3e14000 */
- 0.991909801964, /* 0x0.fdedcd000 */
- 0.994601726545, /* 0x0.fe9e38000 */
- 0.997297704209, /* 0x0.ff4ee6fff */
- 1.000000000000, /* 0x1.000000000 */
- 1.002710938457, /* 0x1.00b1aa000 */
- 1.005429744692, /* 0x1.0163d7ffe */
- 1.008155703526, /* 0x1.02167dffe */
- 1.010888457284, /* 0x1.02c995fff */
- 1.013629436498, /* 0x1.037d38000 */
- 1.016377568250, /* 0x1.043152000 */
- 1.019134163841, /* 0x1.04e5f9ffe */
- 1.021896362316, /* 0x1.059b00000 */
- 1.024668931945, /* 0x1.0650b3ffe */
- 1.027446627635, /* 0x1.0706be001 */
- 1.030234098408, /* 0x1.07bd6bffe */
- 1.033023953416, /* 0x1.087441ffe */
- 1.035824656494, /* 0x1.092bce000 */
- 1.038632392900, /* 0x1.09e3d0001 */
- 1.041450142840, /* 0x1.0a9c79ffe */
- 1.044273972530, /* 0x1.0b558a001 */
- 1.047105550795, /* 0x1.0c0f1c001 */
- 1.049944162390, /* 0x1.0cc924001 */
- 1.052791833895, /* 0x1.0d83c4001 */
- 1.055645227426, /* 0x1.0e3ec3fff */
- 1.058507919326, /* 0x1.0efa60001 */
- 1.061377286898, /* 0x1.0fb66bfff */
- 1.064254641510, /* 0x1.1072fdffe */
- 1.067140102389, /* 0x1.113018000 */
- 1.070034146304, /* 0x1.11edc1fff */
- 1.072937250162, /* 0x1.12ac04001 */
- 1.075843691823, /* 0x1.136a7dfff */
- 1.078760385496, /* 0x1.1429a3ffe */
- 1.081685543070, /* 0x1.14e958000 */
- 1.084618330005, /* 0x1.15a98c000 */
- 1.087556362176, /* 0x1.166a18001 */
- 1.090508937863, /* 0x1.172b98001 */
- 1.093464612954, /* 0x1.17ed4bfff */
- 1.096430182434, /* 0x1.18afa5ffe */
- 1.099401354802, /* 0x1.19725e000 */
- 1.102381587017, /* 0x1.1a35adfff */
- 1.105370759965, /* 0x1.1af994000 */
- 1.108367800686, /* 0x1.1bbdfdffe */
- 1.111373305331, /* 0x1.1c82f6000 */
- 1.114387035385, /* 0x1.1d4878001 */
- 1.117408752440, /* 0x1.1e0e7ffff */
- 1.120437502874, /* 0x1.1ed4fe000 */
- 1.123474478729, /* 0x1.1f9c06000 */
- 1.126521706601, /* 0x1.2063ba001 */
- 1.129574775716, /* 0x1.212bd0001 */
- 1.132638812065, /* 0x1.21f49e000 */
- 1.135709524130, /* 0x1.22bddbffe */
- 1.138789534565, /* 0x1.2387b5fff */
- 1.141876101508, /* 0x1.2451fe000 */
- 1.144971728301, /* 0x1.251cddffe */
- 1.148077130296, /* 0x1.25e861ffe */
- 1.151189923305, /* 0x1.26b462001 */
- 1.154312610610, /* 0x1.278107ffe */
- 1.157440662410, /* 0x1.284e08001 */
- 1.160578370109, /* 0x1.291baa001 */
- 1.163725256932, /* 0x1.29e9e6000 */
- 1.166879892324, /* 0x1.2ab8a3ffe */
- 1.170044302935, /* 0x1.2b8805fff */
- 1.173205971694, /* 0x1.2c5739ffe */
- 1.176397800428, /* 0x1.2d2867ffe */
- 1.179586529747, /* 0x1.2df962001 */
- 1.182784795737, /* 0x1.2ecafbffe */
- 1.185991406414, /* 0x1.2f9d21ffe */
- 1.189206838636, /* 0x1.306fdc001 */
- 1.192430973067, /* 0x1.314328000 */
- 1.195664167430, /* 0x1.32170c001 */
- 1.198906540890, /* 0x1.32eb8a001 */
- 1.202157497408, /* 0x1.33c098000 */
- 1.205416083326, /* 0x1.349625fff */
- 1.208683252332, /* 0x1.356c43fff */
- 1.211961269402, /* 0x1.364318001 */
- 1.215246438983, /* 0x1.371a64000 */
- 1.218539118740, /* 0x1.37f22dffe */
- 1.221847295770, /* 0x1.38cafc000 */
- 1.225158572187, /* 0x1.39a3fdfff */
- 1.228481650325, /* 0x1.3a7dc5ffe */
- 1.231811761846, /* 0x1.3b5803fff */
- 1.235149741144, /* 0x1.3c32c5ffe */
- 1.238499879811, /* 0x1.3d0e53ffe */
- 1.241858124726, /* 0x1.3dea69fff */
- 1.245225191102, /* 0x1.3ec713fff */
- 1.248601436624, /* 0x1.3fa458000 */
- 1.251975655584, /* 0x1.40817a001 */
- 1.255380749731, /* 0x1.4160a2001 */
- 1.258783102010, /* 0x1.423f9bffe */
- 1.262198328973, /* 0x1.431f6e000 */
- 1.265619754780, /* 0x1.43ffa7fff */
- 1.269052743928, /* 0x1.44e0a4001 */
- 1.272490739830, /* 0x1.45c1f4000 */
- 1.275942921659, /* 0x1.46a432001 */
- 1.279397487615, /* 0x1.478697ffe */
- 1.282870173427, /* 0x1.486a2dffe */
- 1.286346316319, /* 0x1.494dfdffe */
- 1.289836049094, /* 0x1.4a32b2001 */
- 1.293333172770, /* 0x1.4b17e1ffe */
- 1.296839594835, /* 0x1.4bfdadfff */
- 1.300354957560, /* 0x1.4ce40fffe */
- 1.303882122055, /* 0x1.4dcb38001 */
- 1.307417988757, /* 0x1.4eb2f1ffe */
- 1.310960650439, /* 0x1.4f9b1dfff */
- 1.314516782746, /* 0x1.50842bfff */
- 1.318079948424, /* 0x1.516daffff */
- 1.321653246888, /* 0x1.5257de000 */
- 1.325237751030, /* 0x1.5342c8001 */
- 1.328829526907, /* 0x1.542e2c000 */
- 1.332433700535, /* 0x1.551a5fffe */
- 1.336045145966, /* 0x1.56070dffe */
- 1.339667558645, /* 0x1.56f473ffe */
- 1.343300342533, /* 0x1.57e287ffe */
- 1.346941947961, /* 0x1.58d130001 */
- 1.350594043714, /* 0x1.59c087ffe */
- 1.354256033883, /* 0x1.5ab085fff */
- 1.357932448365, /* 0x1.5ba175ffe */
- 1.361609339707, /* 0x1.5c926dfff */
- 1.365299344044, /* 0x1.5d8441ffe */
- 1.369003057507, /* 0x1.5e76fc001 */
- 1.372714757920, /* 0x1.5f6a3c000 */
- 1.376437187179, /* 0x1.605e2fffe */
- 1.380165219333, /* 0x1.615282001 */
- 1.383909463864, /* 0x1.6247e3ffe */
- 1.387661933907, /* 0x1.633dd0000 */
- 1.391424179060, /* 0x1.64345fffe */
- 1.395197510706, /* 0x1.652ba9fff */
- 1.399006724329, /* 0x1.66254dffe */
- 1.402773022651, /* 0x1.671c22000 */
- 1.406576037403, /* 0x1.68155dfff */
- 1.410389423392, /* 0x1.690f48001 */
-};
diff --git a/sysdeps/m68k/m680x0/fpu/e_exp2f_data.c b/sysdeps/m68k/m680x0/fpu/e_exp2f_data.c
new file mode 100644
index 0000000000..1cc8931700
--- /dev/null
+++ b/sysdeps/m68k/m680x0/fpu/e_exp2f_data.c
@@ -0,0 +1 @@ 
+/* Not needed.  */
diff --git a/sysdeps/m68k/m680x0/fpu/math_errf.c b/sysdeps/m68k/m680x0/fpu/math_errf.c
new file mode 100644
index 0000000000..1cc8931700
--- /dev/null
+++ b/sysdeps/m68k/m680x0/fpu/math_errf.c
@@ -0,0 +1 @@ 
+/* Not needed.  */