From 9feaa15d988bcd48a399b8616eb234de805e7b5e Mon Sep 17 00:00:00 2001
From: Szabolcs Nagy <szabolcs.nagy@arm.com>
Date: Wed, 6 Sep 2017 17:42:00 +0100
Subject: [PATCH 1/4] expf

---
 math/Makefile                         |   2 +-
 sysdeps/aarch64/fpu/math_private.h    |  20 ++
 sysdeps/i386/fpu/e_exp2f_data.c       |   1 +
 sysdeps/i386/fpu/math_errf.c          |   1 +
 sysdeps/ia64/fpu/e_exp2f_data.c       |   1 +
 sysdeps/ia64/fpu/math_errf.c          |   1 +
 sysdeps/ieee754/flt-32/e_exp2f.c      | 170 ++++++----------
 sysdeps/ieee754/flt-32/e_exp2f_data.c |  44 +++++
 sysdeps/ieee754/flt-32/e_expf.c       | 185 ++++++++----------
 sysdeps/ieee754/flt-32/math_config.h  | 114 +++++++++++
 sysdeps/ieee754/flt-32/math_errf.c    |  76 ++++++++
 sysdeps/ieee754/flt-32/t_exp2f.h      | 351 ----------------------------------
 12 files changed, 399 insertions(+), 567 deletions(-)
 create mode 100644 sysdeps/i386/fpu/e_exp2f_data.c
 create mode 100644 sysdeps/i386/fpu/math_errf.c
 create mode 100644 sysdeps/ia64/fpu/e_exp2f_data.c
 create mode 100644 sysdeps/ia64/fpu/math_errf.c
 create mode 100644 sysdeps/ieee754/flt-32/e_exp2f_data.c
 create mode 100644 sysdeps/ieee754/flt-32/math_config.h
 create mode 100644 sysdeps/ieee754/flt-32/math_errf.c
 delete mode 100644 sysdeps/ieee754/flt-32/t_exp2f.h

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 */
-};
-- 
2.11.0

