From 98cdf231e3d85d7303e897c5d6b7cfe568e0d397 Mon Sep 17 00:00:00 2001
From: Bert Tenjy <bert.tenjy@gmail.com>
Date: Fri, 3 May 2019 12:45:45 -0500
Subject: [PATCH v1 7/12] PPC64: Add libmvec SIMD double-precision logarithm
function.
[BZ #24208]
Implements double-precision vector logarithm function. The algorithm is
an adaptation of the one in sysdeps/ieee754/dbl-64, modified to exploit
PPC64 VSX hardware. The version of ieee754/dbl-64 is commit #f41b0a43e4.
The patch has been tested on both Little-Endian and Big-Endian. It
passes all the tests for double-precision logarithm run by make check.
Integration into the make check infrastructure closely follows corres-
ponding changes done for x86_64 in commit #6af25acc7b.
2019-05-03 Bert Tenjy <bert.tenjy@gmail.com>
* NEWS: Noted the addition of PPC64 vector log function.
* sysdeps/powerpc/bits/math-vector.h: Added log function's entry.
* sysdeps/powerpc/powerpc64/fpu/Makefile:( CFLAGS-vec_finite_alias.c)
added -mabi=altivec -maltivec flags.
(CFLAGS-vec_d_log2_vsx.c, CFLAGS-vec_d_log_data.c): Added build of VSX
SIMD log function and tests.
* sysdeps/powerpc/powerpc64/fpu/Versions: Added log function's entry.
* sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile: (libmvec-sysdep_routines)
(CFLAGS-vec_d_log2_vsx.c, CFLAGS-vec_d_log_data.c): Added build of VSX
SIMD log function and tests.
* sysdeps/powerpc/powerpc64/fpu/multiarch/math_config.h: New file.
* sysdeps/powerpc/powerpc64/fpu/multiarch/test-double-vlen2-wrappers.c: Added
entry for log function.
* sysdeps/powerpc/powerpc64/fpu/multiarch/vec_d_log2_vsx.c: New file.
* sysdeps/powerpc/powerpc64/fpu/multiarch/vec_d_log_data.c: Likewise.
* sysdeps/unix/sysv/linux/powerpc/powerpc64/libmvec.abilist: SIMD log function added.
---
NEWS | 1 +
sysdeps/powerpc/bits/math-vector.h | 2 +
sysdeps/powerpc/powerpc64/fpu/Makefile | 2 +-
sysdeps/powerpc/powerpc64/fpu/Versions | 2 +-
.../powerpc/powerpc64/fpu/multiarch/Makefile | 5 +-
.../powerpc64/fpu/multiarch/math_config.h | 189 ++++++++++
.../multiarch/test-double-vlen2-wrappers.c | 2 +-
.../powerpc64/fpu/multiarch/vec_d_log2_vsx.c | 266 ++++++++++++++
.../powerpc64/fpu/multiarch/vec_d_log_data.c | 347 ++++++++++++++++++
.../linux/powerpc/powerpc64/libmvec.abilist | 1 +
10 files changed, 813 insertions(+), 4 deletions(-)
create mode 100644 sysdeps/powerpc/powerpc64/fpu/multiarch/math_config.h
create mode 100644 sysdeps/powerpc/powerpc64/fpu/multiarch/vec_d_log2_vsx.c
create mode 100644 sysdeps/powerpc/powerpc64/fpu/multiarch/vec_d_log_data.c
@@ -14,6 +14,7 @@ Major new features:
The following functions now have vector versions.
- double-precision cosine: cos
- single-precision cosine: cosf
+ - double-precision logarithm: log
- double-precision sine: sin
- single-precision sine: sinf
- double-precision sincos: sincos
@@ -36,6 +36,8 @@
# ifdef __DECL_SIMD_PPC64
# undef __DECL_SIMD_cos
# define __DECL_SIMD_cos __DECL_SIMD_PPC64
+# undef __DECL_SIMD_log
+# define __DECL_SIMD_log __DECL_SIMD_PPC64
# undef __DECL_SIMD_sincos
# define __DECL_SIMD_sincos __DECL_SIMD_PPC64
# undef __DECL_SIMD_sincosf
@@ -1,7 +1,7 @@
ifeq ($(subdir),mathvec)
libmvec-support += vec_finite_alias
-CFLAGS-vec_finite_alias.c += -mvsx
+CFLAGS-vec_finite_alias.c += -mabi=altivec -maltivec -mvsx
libmvec-static-only-routines = vec_finite_alias
endif
@@ -1,6 +1,6 @@
libmvec {
GLIBC_2.30 {
_ZGVbN2v_cos; _ZGVbN4v_cosf; _ZGVbN2v_sin; _ZGVbN4v_sinf;
- _ZGVbN2vvv_sincos; _ZGVbN4vvv_sincosf;
+ _ZGVbN2v_log; _ZGVbN2vvv_sincos; _ZGVbN4vvv_sincosf;
}
}
@@ -46,8 +46,11 @@ endif
ifeq ($(subdir),mathvec)
libmvec-sysdep_routines += vec_d_cos2_vsx vec_s_cosf4_vsx \
vec_d_sin2_vsx vec_s_sinf4_vsx \
+ vec_d_log2_vsx vec_d_log_data \
vec_d_sincos2_vsx vec_s_sincosf4_vsx
CFLAGS-vec_d_cos2_vsx.c += -mabi=altivec -maltivec -mvsx -mpower8-vector
+CFLAGS-vec_d_log2_vsx.c += -mabi=altivec -maltivec -mvsx -mpower8-vector
+CFLAGS-vec_d_log_data.c += -mabi=altivec -maltivec -mvsx -mpower8-vector
CFLAGS-vec_s_cosf4_vsx.c += -mabi=altivec -maltivec -mvsx
CFLAGS-vec_d_sin2_vsx.c += -mabi=altivec -maltivec -mvsx -mpower8-vector
CFLAGS-vec_s_sinf4_vsx.c += -mabi=altivec -maltivec -mvsx
@@ -60,7 +63,7 @@ ifeq ($(subdir),math)
ifeq ($(build-mathvec),yes)
libmvec-tests += double-vlen2 float-vlen4
-double-vlen2-funcs = cos sin sincos
+double-vlen2-funcs = cos sin sincos log
float-vlen4-funcs = cos sin sincos
double-vlen2-arch-ext-cflags = -mabi=altivec -maltivec -mvsx -DREQUIRE_VSX
new file mode 100644
@@ -0,0 +1,189 @@
+/* Configuration for double precision math routines.
+ Copyright (C) 2018-2019 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 <nan-high-order-bit.h>
+#include <stdint.h>
+#include <altivec.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
+/* When set, the roundtoint and converttoint functions are provided with
+ the semantics documented below. */
+# define TOINT_INTRINSICS 0
+#endif
+
+#if TOINT_INTRINSICS
+/* Round x to nearest int in all rounding modes, ties have to be rounded
+ consistently with converttoint so the results match. If the result
+ would be outside of [-2^31, 2^31-1] then the semantics is unspecified. */
+static inline double_t
+roundtoint (double_t x);
+
+/* Convert x to nearest int in all rounding modes, ties have to be rounded
+ consistently with roundtoint. If the result is not representible in an
+ int32_t then the semantics is unspecified. */
+static inline int32_t
+converttoint (double_t x);
+#endif
+
+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;
+}
+
+static inline int
+issignaling_inline (double x)
+{
+ uint64_t ix = asuint64 (x);
+ if (HIGH_ORDER_BIT_IS_SET_FOR_SNAN)
+ return (ix & 0x7ff8000000000000) == 0x7ff8000000000000;
+ return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL;
+}
+
+#define NOINLINE __attribute__ ((noinline))
+
+/* Error handling tail calls for special cases, with a sign argument.
+ The sign of the return value is set if the argument is non-zero. */
+
+/* The result overflows. */
+attribute_hidden double __math_oflow (uint32_t);
+/* The result underflows to 0 in nearest rounding mode. */
+attribute_hidden double __math_uflow (uint32_t);
+/* The result underflows to 0 in some directed rounding mode only. */
+attribute_hidden double __math_may_uflow (uint32_t);
+/* Division by zero. */
+attribute_hidden double __math_divzero (uint32_t);
+
+/* Error handling using input checking. */
+
+/* Invalid input unless it is a quiet NaN. */
+attribute_hidden double __math_invalid (double);
+
+/* Error handling using output checking, only for errno setting. */
+
+/* Check if the result overflowed to infinity. */
+attribute_hidden double __math_check_oflow (double);
+/* Check if the result underflowed to 0. */
+attribute_hidden double __math_check_uflow (double);
+
+/* Check if the result overflowed to infinity. */
+static inline double
+check_oflow (double x)
+{
+ return WANT_ERRNO ? __math_check_oflow (x) : x;
+}
+
+/* Check if the result underflowed to 0. */
+static inline double
+check_uflow (double x)
+{
+ return WANT_ERRNO ? __math_check_uflow (x) : x;
+}
+
+#define EXP_TABLE_BITS 7
+#define EXP_POLY_ORDER 5
+#define EXP2_POLY_ORDER 5
+extern const struct exp_data
+{
+ double invln2N;
+ double shift;
+ double negln2hiN;
+ double negln2loN;
+ double poly[4]; /* Last four coefficients. */
+ double exp2_shift;
+ double exp2_poly[EXP2_POLY_ORDER];
+ uint64_t tab[2*(1 << EXP_TABLE_BITS)];
+} __exp_data attribute_hidden;
+
+#define LOG_TABLE_BITS 7
+#define LOG_POLY_ORDER 6
+#define LOG_POLY1_ORDER 12
+extern const struct log_data
+{
+ vector double ln2hi;
+ vector double ln2lo;
+ vector double poly[LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
+ vector double poly1[LOG_POLY1_ORDER - 1];
+ /* See e_log_data.c for details. */
+ struct {double invc, logc;} tab[1 << LOG_TABLE_BITS];
+ struct {double chi, clo;} tab2[1 << LOG_TABLE_BITS];
+} __log_data attribute_hidden;
+
+#define LOG2_TABLE_BITS 6
+#define LOG2_POLY_ORDER 7
+#define LOG2_POLY1_ORDER 11
+extern const struct log2_data
+{
+ double invln2hi;
+ double invln2lo;
+ double poly[LOG2_POLY_ORDER - 1];
+ double poly1[LOG2_POLY1_ORDER - 1];
+ /* See e_log2_data.c for details. */
+ struct {double invc, logc;} tab[1 << LOG2_TABLE_BITS];
+#ifndef __FP_FAST_FMA
+ struct {double chi, clo;} tab2[1 << LOG2_TABLE_BITS];
+#endif
+} __log2_data attribute_hidden;
+
+#define POW_LOG_TABLE_BITS 7
+#define POW_LOG_POLY_ORDER 8
+extern const struct pow_log_data
+{
+ double ln2hi;
+ double ln2lo;
+ double poly[POW_LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
+ /* Note: the pad field is unused, but allows slightly faster indexing. */
+ /* See e_pow_log_data.c for details. */
+ struct {double invc, pad, logc, logctail;} tab[1 << POW_LOG_TABLE_BITS];
+} __pow_log_data attribute_hidden;
+
+#endif
@@ -23,5 +23,5 @@
VECTOR_WRAPPER (WRAPPER_NAME (cos), _ZGVbN2v_cos)
VECTOR_WRAPPER (WRAPPER_NAME (sin), _ZGVbN2v_sin)
-
+VECTOR_WRAPPER (WRAPPER_NAME (log), _ZGVbN2v_log)
VECTOR_WRAPPER_fFF (WRAPPER_NAME (sincos), _ZGVbN2vvv_sincos)
new file mode 100644
@@ -0,0 +1,266 @@
+/* Double-precision vector log(x) function.
+ Copyright (C) 2019 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.h>
+#include <stdint.h>
+#include <math/math-svid-compat.h>
+#include <shlib-compat.h>
+#include <libm-alias-double.h>
+#include "math_config.h"
+#include <altivec.h>
+
+#define T __log_data.tab
+#define T2 __log_data.tab2
+#define B __log_data.poly1
+#define A __log_data.poly
+#define Ln2hi __log_data.ln2hi
+#define Ln2lo __log_data.ln2lo
+#define N (1 << LOG_TABLE_BITS)
+#define OFF 0x3fe6000000000000
+#define LO asuint64 (1.0 - 0x1p-4)
+#define HI asuint64 (1.0 + 0x1.09p-4)
+
+/* Top 16 bits of a double. */
+static inline uint32_t
+top16 (double x)
+{
+ return asuint64 (x) >> 48;
+}
+
+vector double
+_ZGVbN2v_log (vector double x)
+{
+ vector double w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
+ vector double rhi, rlo;
+ vector unsigned long long ix, iz, tmp, top;
+ vector signed long long k, i;
+
+ ix[0] = asuint64 (x[0]);
+ ix[1] = asuint64 (x[1]);
+ top[0] = top16 (x[0]);
+ top[1] = top16 (x[1]);
+
+ if (__glibc_unlikely ((ix[0] - LO < HI - LO) && (ix[1] - LO < HI - LO)))
+ {
+ /* Handle close to 1.0 inputs separately. */
+ /* Fix sign of zero with downward rounding when x==1. */
+ if (WANT_ROUNDING && __glibc_unlikely ((ix[0] == asuint64 (1.0))
+ && (ix[1] == asuint64 (1.0))))
+ {
+ y[0] = 0.0;
+ y[1] = 0.0;
+ return y;
+ }
+ else if (WANT_ROUNDING && __glibc_unlikely (ix[0] == asuint64 (1.0)))
+ {
+ y[0] = 0.0;
+ y[1] = log (x[1]);
+ return y;
+ }
+ else if (WANT_ROUNDING && __glibc_unlikely (ix[1] == asuint64 (1.0)))
+ {
+ y[0] = log (x[0]);
+ y[1] = 0.0;
+ return y;
+ }
+ r = x - (vector double) {1.0, 1.0};
+ r2 = r * r;
+ r3 = r * r2;
+ y = r3 * (B[1] + r * B[2] + r2 * B[3]
+ + r3 * (B[4] + r * B[5] + r2 * B[6]
+ + r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10])));
+ /* Worst-case error is around 0.507 ULP. */
+ w = r * (vector double) {0x1p27, 0x1p27};
+ rhi = r + w - w;
+ rlo = r - rhi;
+ w = rhi * rhi * B[0]; /* B[0] == -0.5. */
+ hi = r + w;
+ lo = r - hi + w;
+ lo += B[0] * rlo * (rhi + r);
+ y += lo;
+ y += hi;
+ return y;
+ }
+ else if (__glibc_unlikely ((ix[0] - LO < HI - LO)))
+ {
+ /* Handle close to 1.0 inputs separately. */
+ /* Fix sign of zero with downward rounding when x==1. */
+ if (WANT_ROUNDING && __glibc_unlikely (ix[0] == asuint64 (1.0)))
+ {
+ y[0] = 0.0;
+ y[1] = log (x[1]);
+ return y;
+ }
+ y[0] = log (x[0]);
+ y[1] = log (x[1]);
+ return y;
+ }
+ else if (__glibc_unlikely ((ix[1] - LO < HI - LO)))
+ {
+ /* Handle close to 1.0 inputs separately. */
+ /* Fix sign of zero with downward rounding when x==1. */
+ if (WANT_ROUNDING && __glibc_unlikely (ix[1] == asuint64 (1.0)))
+ {
+ y[0] = log (x[0]);
+ y[1] = 0.0;
+ return y;
+ }
+ y[0] = log (x[0]);
+ y[1] = log (x[1]);
+ return y;
+ }
+
+ if (__glibc_unlikely ((top[0] - 0x0010 >= 0x7ff0 - 0x0010)
+ && (top[1] - 0x0010 >= 0x7ff0 - 0x0010)))
+ {
+ /* x < 0x1p-1022 or inf or nan. */
+ if ((ix[0] * 2 == 0) || (ix[1] * 2 == 0))
+ {
+ y[0] = log (x[0]);
+ y[1] = log (x[1]);
+ return y;
+ }
+
+ /* log(inf) == inf. */
+ if ((ix[0] == asuint64 (INFINITY)) && (ix[1] == asuint64 (INFINITY)))
+ {
+ y[0] = x[0];
+ y[1] = x[1];
+ return y;
+ }
+ else if (ix[0] == asuint64 (INFINITY))
+ {
+ y[0] = x[0];
+ y[1] = log (x[1]);
+ return y;
+ }
+ else if (ix[1] == asuint64 (INFINITY))
+ {
+ y[0] = log (x[0]);
+ y[1] = x[1];
+ return y;
+ }
+
+ if (((top[0] & 0x8000) || (top[0] & 0x7ff0) == 0x7ff0)
+ || ((top[1] & 0x8000) || (top[1] & 0x7ff0) == 0x7ff0))
+ {
+ y[0] = log (x[0]);
+ y[1] = log (x[1]);
+ return y;
+ }
+
+ /* x is subnormal, normalize it. */
+ ix[0] = asuint64 (x[0] * 0x1p52);
+ ix[0] -= 52ULL << 52;
+ ix[1] = asuint64 (x[1] * 0x1p52);
+ ix[1] -= 52ULL << 52;
+ }
+ else if (__glibc_unlikely (top[0] - 0x0010 >= 0x7ff0 - 0x0010))
+ {
+ /* x < 0x1p-1022 or inf or nan. */
+ if (ix[0] * 2 == 0)
+ {
+ y[0] = log (x[0]);
+ y[1] = log (x[1]);
+ return y;
+ }
+
+ /* log(inf) == inf. */
+ if (ix[0] == asuint64 (INFINITY))
+ {
+ y[0] = x[0];
+ y[1] = log (x[1]);
+ return y;
+ }
+
+ if (((top[0] & 0x8000) || (top[0] & 0x7ff0) == 0x7ff0))
+ {
+ y[0] = log (x[0]);
+ y[1] = log (x[1]);
+ return y;
+ }
+
+ /* x is subnormal, normalize it. */
+ ix[0] = asuint64 (x[0] * 0x1p52);
+ ix[0] -= 52ULL << 52;
+ }
+ else if (__glibc_unlikely (top[1] - 0x0010 >= 0x7ff0 - 0x0010))
+ {
+ /* x < 0x1p-1022 or inf or nan. */
+ if (ix[1] * 2 == 0)
+ {
+ y[0] = log (x[0]);
+ y[1] = log (x[1]);
+ return y;
+ }
+
+ /* log(inf) == inf. */
+ if (ix[1] == asuint64 (INFINITY))
+ {
+ y[0] = log (x[0]);
+ y[1] = x[1];
+ return y;
+ }
+
+ if (((top[1] & 0x8000) || (top[1] & 0x7ff0) == 0x7ff0))
+ {
+ y[0] = log (x[0]);
+ y[1] = log (x[1]);
+ return y;
+ }
+
+ /* x is subnormal, normalize it. */
+ ix[1] = asuint64 (x[1] * 0x1p52);
+ ix[1] -= 52ULL << 52;
+ }
+
+ /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
+ The range is split into N subintervals.
+ The ith subinterval contains z and c is near its center. */
+ tmp = ix - (vector unsigned long long) {OFF, OFF};
+ i = (vector signed long)
+ (tmp >> vec_splats ((unsigned long) (52 - LOG_TABLE_BITS)))
+ % vec_splats ((unsigned long) N);
+ k = ((vector signed long long) tmp) >> vec_splats (52ULL);
+ iz = ix - (tmp & vec_splats (0xfffULL) << vec_splats (52ULL));
+ invc[0] = T[i[0]].invc;
+ logc[0] = T[i[0]].logc;
+ invc[1] = T[i[1]].invc;
+ logc[1] = T[i[1]].logc;
+ z[0] = asdouble (iz[0]);
+ z[1] = asdouble (iz[1]);
+
+ /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
+ /* r ~= z/c - 1, |r| < 1/(2*N). */
+ /* rounding error: 0x1p-55/N + 0x1p-66. */
+ r = z * invc - (vector double) {1.0, 1.0};
+ kd = vec_double (k);
+
+ /* hi + lo = r + log(c) + k*Ln2. */
+ w = kd * Ln2hi + logc;
+ hi = w + r;
+ lo = w - hi + r + kd * Ln2lo;
+
+ /* log(x) = lo + (log1p(r) - r) + hi. */
+ r2 = r * r; /* rounding error: 0x1p-54/N^2. */
+ /* Worst case error if |y| > 0x1p-4: 0.519 ULP (0.520 ULP without fma).
+ 0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma). */
+ y = lo + r2 * A[0]
+ + r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi;
+ return y;
+}
new file mode 100644
@@ -0,0 +1,347 @@
+/* Data for double-precision log.
+ Copyright (C) 2019 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 << LOG_TABLE_BITS)
+
+const struct log_data __log_data = {
+.ln2hi = {0x1.62e42fefa3800p-1, 0x1.62e42fefa3800p-1},
+.ln2lo = {0x1.ef35793c76730p-45, 0x1.ef35793c76730p-45},
+.poly1 = {
+#if LOG_POLY1_ORDER == 12
+// relative error: 0x1.c04d76cp-63
+// in -0x1p-4 0x1.09p-4 (|log(1+x)| > 0x1p-4 outside the interval)
+{-0x1p-1, -0x1p-1},
+{0x1.5555555555577p-2, 0x1.5555555555577p-2},
+{-0x1.ffffffffffdcbp-3, -0x1.ffffffffffdcbp-3},
+{0x1.999999995dd0cp-3, 0x1.999999995dd0cp-3},
+{-0x1.55555556745a7p-3, -0x1.55555556745a7p-3},
+{0x1.24924a344de3p-3, 0x1.24924a344de3p-3},
+{-0x1.fffffa4423d65p-4, -0x1.fffffa4423d65p-4},
+{0x1.c7184282ad6cap-4, 0x1.c7184282ad6cap-4},
+{-0x1.999eb43b068ffp-4, -0x1.999eb43b068ffp-4},
+{0x1.78182f7afd085p-4, 0x1.78182f7afd085p-4},
+{-0x1.5521375d145cdp-4, -0x1.5521375d145cdp-4},
+#endif
+},
+.poly = {
+#if N == 128 && LOG_POLY_ORDER == 6
+// relative error: 0x1.926199e8p-56
+// abs error: 0x1.882ff33p-65
+// in -0x1.fp-9 0x1.fp-9
+{-0x1.0000000000001p-1, -0x1.0000000000001p-1},
+{0x1.555555551305bp-2, 0x1.555555551305bp-2},
+{-0x1.fffffffeb459p-3, -0x1.fffffffeb459p-3},
+{0x1.999b324f10111p-3, 0x1.999b324f10111p-3},
+{-0x1.55575e506c89fp-3, -0x1.55575e506c89fp-3},
+#endif
+},
+/* Algorithm:
+
+ x = 2^k z
+ log(x) = k ln2 + log(c) + log(z/c)
+ log(z/c) = poly(z/c - 1)
+
+where z is in [1.6p-1; 1.6p0] which is split into N subintervals and z falls
+into the ith one, then table entries are computed as
+
+ tab[i].invc = 1/c
+ tab[i].logc = (double)log(c)
+ tab2[i].chi = (double)c
+ tab2[i].clo = (double)(c - (double)c)
+
+where c is near the center of the subinterval and is chosen by trying +-2^29
+floating point invc candidates around 1/center and selecting one for which
+
+ 1) the rounding error in 0x1.8p9 + logc is 0,
+ 2) the rounding error in z - chi - clo is < 0x1p-66 and
+ 3) the rounding error in (double)log(c) is minimized (< 0x1p-66).
+
+Note: 1) ensures that k*ln2hi + logc can be computed without rounding error,
+2) ensures that z/c - 1 can be computed as (z - chi - clo)*invc with close to
+a single rounding error when there is no fast fma for z*invc - 1, 3) ensures
+that logc + poly(z/c - 1) has small error, however near x == 1 when
+|log(x)| < 0x1p-4, this is not enough so that is special cased. */
+.tab = {
+#if N == 128
+{0x1.734f0c3e0de9fp+0, -0x1.7cc7f79e69000p-2},
+{0x1.713786a2ce91fp+0, -0x1.76feec20d0000p-2},
+{0x1.6f26008fab5a0p+0, -0x1.713e31351e000p-2},
+{0x1.6d1a61f138c7dp+0, -0x1.6b85b38287800p-2},
+{0x1.6b1490bc5b4d1p+0, -0x1.65d5590807800p-2},
+{0x1.69147332f0cbap+0, -0x1.602d076180000p-2},
+{0x1.6719f18224223p+0, -0x1.5a8ca86909000p-2},
+{0x1.6524f99a51ed9p+0, -0x1.54f4356035000p-2},
+{0x1.63356aa8f24c4p+0, -0x1.4f637c36b4000p-2},
+{0x1.614b36b9ddc14p+0, -0x1.49da7fda85000p-2},
+{0x1.5f66452c65c4cp+0, -0x1.445923989a800p-2},
+{0x1.5d867b5912c4fp+0, -0x1.3edf439b0b800p-2},
+{0x1.5babccb5b90dep+0, -0x1.396ce448f7000p-2},
+{0x1.59d61f2d91a78p+0, -0x1.3401e17bda000p-2},
+{0x1.5805612465687p+0, -0x1.2e9e2ef468000p-2},
+{0x1.56397cee76bd3p+0, -0x1.2941b3830e000p-2},
+{0x1.54725e2a77f93p+0, -0x1.23ec58cda8800p-2},
+{0x1.52aff42064583p+0, -0x1.1e9e129279000p-2},
+{0x1.50f22dbb2bddfp+0, -0x1.1956d2b48f800p-2},
+{0x1.4f38f4734ded7p+0, -0x1.141679ab9f800p-2},
+{0x1.4d843cfde2840p+0, -0x1.0edd094ef9800p-2},
+{0x1.4bd3ec078a3c8p+0, -0x1.09aa518db1000p-2},
+{0x1.4a27fc3e0258ap+0, -0x1.047e65263b800p-2},
+{0x1.4880524d48434p+0, -0x1.feb224586f000p-3},
+{0x1.46dce1b192d0bp+0, -0x1.f474a7517b000p-3},
+{0x1.453d9d3391854p+0, -0x1.ea4443d103000p-3},
+{0x1.43a2744b4845ap+0, -0x1.e020d44e9b000p-3},
+{0x1.420b54115f8fbp+0, -0x1.d60a22977f000p-3},
+{0x1.40782da3ef4b1p+0, -0x1.cc00104959000p-3},
+{0x1.3ee8f5d57fe8fp+0, -0x1.c202956891000p-3},
+{0x1.3d5d9a00b4ce9p+0, -0x1.b81178d811000p-3},
+{0x1.3bd60c010c12bp+0, -0x1.ae2c9ccd3d000p-3},
+{0x1.3a5242b75dab8p+0, -0x1.a45402e129000p-3},
+{0x1.38d22cd9fd002p+0, -0x1.9a877681df000p-3},
+{0x1.3755bc5847a1cp+0, -0x1.90c6d69483000p-3},
+{0x1.35dce49ad36e2p+0, -0x1.87120a645c000p-3},
+{0x1.34679984dd440p+0, -0x1.7d68fb4143000p-3},
+{0x1.32f5cceffcb24p+0, -0x1.73cb83c627000p-3},
+{0x1.3187775a10d49p+0, -0x1.6a39a9b376000p-3},
+{0x1.301c8373e3990p+0, -0x1.60b3154b7a000p-3},
+{0x1.2eb4ebb95f841p+0, -0x1.5737d76243000p-3},
+{0x1.2d50a0219a9d1p+0, -0x1.4dc7b8fc23000p-3},
+{0x1.2bef9a8b7fd2ap+0, -0x1.4462c51d20000p-3},
+{0x1.2a91c7a0c1babp+0, -0x1.3b08abc830000p-3},
+{0x1.293726014b530p+0, -0x1.31b996b490000p-3},
+{0x1.27dfa5757a1f5p+0, -0x1.2875490a44000p-3},
+{0x1.268b39b1d3bbfp+0, -0x1.1f3b9f879a000p-3},
+{0x1.2539d838ff5bdp+0, -0x1.160c8252ca000p-3},
+{0x1.23eb7aac9083bp+0, -0x1.0ce7f57f72000p-3},
+{0x1.22a012ba940b6p+0, -0x1.03cdc49fea000p-3},
+{0x1.2157996cc4132p+0, -0x1.f57bdbc4b8000p-4},
+{0x1.201201dd2fc9bp+0, -0x1.e370896404000p-4},
+{0x1.1ecf4494d480bp+0, -0x1.d17983ef94000p-4},
+{0x1.1d8f5528f6569p+0, -0x1.bf9674ed8a000p-4},
+{0x1.1c52311577e7cp+0, -0x1.adc79202f6000p-4},
+{0x1.1b17c74cb26e9p+0, -0x1.9c0c3e7288000p-4},
+{0x1.19e010c2c1ab6p+0, -0x1.8a646b372c000p-4},
+{0x1.18ab07bb670bdp+0, -0x1.78d01b3ac0000p-4},
+{0x1.1778a25efbcb6p+0, -0x1.674f145380000p-4},
+{0x1.1648d354c31dap+0, -0x1.55e0e6d878000p-4},
+{0x1.151b990275fddp+0, -0x1.4485cdea1e000p-4},
+{0x1.13f0ea432d24cp+0, -0x1.333d94d6aa000p-4},
+{0x1.12c8b7210f9dap+0, -0x1.22079f8c56000p-4},
+{0x1.11a3028ecb531p+0, -0x1.10e4698622000p-4},
+{0x1.107fbda8434afp+0, -0x1.ffa6c6ad20000p-5},
+{0x1.0f5ee0f4e6bb3p+0, -0x1.dda8d4a774000p-5},
+{0x1.0e4065d2a9fcep+0, -0x1.bbcece4850000p-5},
+{0x1.0d244632ca521p+0, -0x1.9a1894012c000p-5},
+{0x1.0c0a77ce2981ap+0, -0x1.788583302c000p-5},
+{0x1.0af2f83c636d1p+0, -0x1.5715e67d68000p-5},
+{0x1.09ddb98a01339p+0, -0x1.35c8a49658000p-5},
+{0x1.08cabaf52e7dfp+0, -0x1.149e364154000p-5},
+{0x1.07b9f2f4e28fbp+0, -0x1.e72c082eb8000p-6},
+{0x1.06ab58c358f19p+0, -0x1.a55f152528000p-6},
+{0x1.059eea5ecf92cp+0, -0x1.63d62cf818000p-6},
+{0x1.04949cdd12c90p+0, -0x1.228fb8caa0000p-6},
+{0x1.038c6c6f0ada9p+0, -0x1.c317b20f90000p-7},
+{0x1.02865137932a9p+0, -0x1.419355daa0000p-7},
+{0x1.0182427ea7348p+0, -0x1.81203c2ec0000p-8},
+{0x1.008040614b195p+0, -0x1.0040979240000p-9},
+{0x1.fe01ff726fa1ap-1, 0x1.feff384900000p-9},
+{0x1.fa11cc261ea74p-1, 0x1.7dc41353d0000p-7},
+{0x1.f6310b081992ep-1, 0x1.3cea3c4c28000p-6},
+{0x1.f25f63ceeadcdp-1, 0x1.b9fc114890000p-6},
+{0x1.ee9c8039113e7p-1, 0x1.1b0d8ce110000p-5},
+{0x1.eae8078cbb1abp-1, 0x1.58a5bd001c000p-5},
+{0x1.e741aa29d0c9bp-1, 0x1.95c8340d88000p-5},
+{0x1.e3a91830a99b5p-1, 0x1.d276aef578000p-5},
+{0x1.e01e009609a56p-1, 0x1.07598e598c000p-4},
+{0x1.dca01e577bb98p-1, 0x1.253f5e30d2000p-4},
+{0x1.d92f20b7c9103p-1, 0x1.42edd8b380000p-4},
+{0x1.d5cac66fb5ccep-1, 0x1.606598757c000p-4},
+{0x1.d272caa5ede9dp-1, 0x1.7da76356a0000p-4},
+{0x1.cf26e3e6b2ccdp-1, 0x1.9ab434e1c6000p-4},
+{0x1.cbe6da2a77902p-1, 0x1.b78c7bb0d6000p-4},
+{0x1.c8b266d37086dp-1, 0x1.d431332e72000p-4},
+{0x1.c5894bd5d5804p-1, 0x1.f0a3171de6000p-4},
+{0x1.c26b533bb9f8cp-1, 0x1.067152b914000p-3},
+{0x1.bf583eeece73fp-1, 0x1.147858292b000p-3},
+{0x1.bc4fd75db96c1p-1, 0x1.2266ecdca3000p-3},
+{0x1.b951e0c864a28p-1, 0x1.303d7a6c55000p-3},
+{0x1.b65e2c5ef3e2cp-1, 0x1.3dfc33c331000p-3},
+{0x1.b374867c9888bp-1, 0x1.4ba366b7a8000p-3},
+{0x1.b094b211d304ap-1, 0x1.5933928d1f000p-3},
+{0x1.adbe885f2ef7ep-1, 0x1.66acd2418f000p-3},
+{0x1.aaf1d31603da2p-1, 0x1.740f8ec669000p-3},
+{0x1.a82e63fd358a7p-1, 0x1.815c0f51af000p-3},
+{0x1.a5740ef09738bp-1, 0x1.8e92954f68000p-3},
+{0x1.a2c2a90ab4b27p-1, 0x1.9bb3602f84000p-3},
+{0x1.a01a01393f2d1p-1, 0x1.a8bed1c2c0000p-3},
+{0x1.9d79f24db3c1bp-1, 0x1.b5b515c01d000p-3},
+{0x1.9ae2505c7b190p-1, 0x1.c2967ccbcc000p-3},
+{0x1.9852ef297ce2fp-1, 0x1.cf635d5486000p-3},
+{0x1.95cbaeea44b75p-1, 0x1.dc1bd3446c000p-3},
+{0x1.934c69de74838p-1, 0x1.e8c01b8cfe000p-3},
+{0x1.90d4f2f6752e6p-1, 0x1.f5509c0179000p-3},
+{0x1.8e6528effd79dp-1, 0x1.00e6c121fb800p-2},
+{0x1.8bfce9fcc007cp-1, 0x1.071b80e93d000p-2},
+{0x1.899c0dabec30ep-1, 0x1.0d46b9e867000p-2},
+{0x1.87427aa2317fbp-1, 0x1.13687334bd000p-2},
+{0x1.84f00acb39a08p-1, 0x1.1980d67234800p-2},
+{0x1.82a49e8653e55p-1, 0x1.1f8ffe0cc8000p-2},
+{0x1.8060195f40260p-1, 0x1.2595fd7636800p-2},
+{0x1.7e22563e0a329p-1, 0x1.2b9300914a800p-2},
+{0x1.7beb377dcb5adp-1, 0x1.3187210436000p-2},
+{0x1.79baa679725c2p-1, 0x1.377266dec1800p-2},
+{0x1.77907f2170657p-1, 0x1.3d54ffbaf3000p-2},
+{0x1.756cadbd6130cp-1, 0x1.432eee32fe000p-2},
+#endif
+},
+#ifndef __FP_FAST_FMA
+.tab2 = {
+# if N == 128
+{0x1.61000014fb66bp-1, 0x1.e026c91425b3cp-56},
+{0x1.63000034db495p-1, 0x1.dbfea48005d41p-55},
+{0x1.650000d94d478p-1, 0x1.e7fa786d6a5b7p-55},
+{0x1.67000074e6fadp-1, 0x1.1fcea6b54254cp-57},
+{0x1.68ffffedf0faep-1, -0x1.c7e274c590efdp-56},
+{0x1.6b0000763c5bcp-1, -0x1.ac16848dcda01p-55},
+{0x1.6d0001e5cc1f6p-1, 0x1.33f1c9d499311p-55},
+{0x1.6efffeb05f63ep-1, -0x1.e80041ae22d53p-56},
+{0x1.710000e86978p-1, 0x1.bff6671097952p-56},
+{0x1.72ffffc67e912p-1, 0x1.c00e226bd8724p-55},
+{0x1.74fffdf81116ap-1, -0x1.e02916ef101d2p-57},
+{0x1.770000f679c9p-1, -0x1.7fc71cd549c74p-57},
+{0x1.78ffffa7ec835p-1, 0x1.1bec19ef50483p-55},
+{0x1.7affffe20c2e6p-1, -0x1.07e1729cc6465p-56},
+{0x1.7cfffed3fc9p-1, -0x1.08072087b8b1cp-55},
+{0x1.7efffe9261a76p-1, 0x1.dc0286d9df9aep-55},
+{0x1.81000049ca3e8p-1, 0x1.97fd251e54c33p-55},
+{0x1.8300017932c8fp-1, -0x1.afee9b630f381p-55},
+{0x1.850000633739cp-1, 0x1.9bfbf6b6535bcp-55},
+{0x1.87000204289c6p-1, -0x1.bbf65f3117b75p-55},
+{0x1.88fffebf57904p-1, -0x1.9006ea23dcb57p-55},
+{0x1.8b00022bc04dfp-1, -0x1.d00df38e04b0ap-56},
+{0x1.8cfffe50c1b8ap-1, -0x1.8007146ff9f05p-55},
+{0x1.8effffc918e43p-1, 0x1.3817bd07a7038p-55},
+{0x1.910001efa5fc7p-1, 0x1.93e9176dfb403p-55},
+{0x1.9300013467bb9p-1, 0x1.f804e4b980276p-56},
+{0x1.94fffe6ee076fp-1, -0x1.f7ef0d9ff622ep-55},
+{0x1.96fffde3c12d1p-1, -0x1.082aa962638bap-56},
+{0x1.98ffff4458a0dp-1, -0x1.7801b9164a8efp-55},
+{0x1.9afffdd982e3ep-1, -0x1.740e08a5a9337p-55},
+{0x1.9cfffed49fb66p-1, 0x1.fce08c19bep-60},
+{0x1.9f00020f19c51p-1, -0x1.a3faa27885b0ap-55},
+{0x1.a10001145b006p-1, 0x1.4ff489958da56p-56},
+{0x1.a300007bbf6fap-1, 0x1.cbeab8a2b6d18p-55},
+{0x1.a500010971d79p-1, 0x1.8fecadd78793p-55},
+{0x1.a70001df52e48p-1, -0x1.f41763dd8abdbp-55},
+{0x1.a90001c593352p-1, -0x1.ebf0284c27612p-55},
+{0x1.ab0002a4f3e4bp-1, -0x1.9fd043cff3f5fp-57},
+{0x1.acfffd7ae1ed1p-1, -0x1.23ee7129070b4p-55},
+{0x1.aefffee510478p-1, 0x1.a063ee00edea3p-57},
+{0x1.b0fffdb650d5bp-1, 0x1.a06c8381f0ab9p-58},
+{0x1.b2ffffeaaca57p-1, -0x1.9011e74233c1dp-56},
+{0x1.b4fffd995badcp-1, -0x1.9ff1068862a9fp-56},
+{0x1.b7000249e659cp-1, 0x1.aff45d0864f3ep-55},
+{0x1.b8ffff987164p-1, 0x1.cfe7796c2c3f9p-56},
+{0x1.bafffd204cb4fp-1, -0x1.3ff27eef22bc4p-57},
+{0x1.bcfffd2415c45p-1, -0x1.cffb7ee3bea21p-57},
+{0x1.beffff86309dfp-1, -0x1.14103972e0b5cp-55},
+{0x1.c0fffe1b57653p-1, 0x1.bc16494b76a19p-55},
+{0x1.c2ffff1fa57e3p-1, -0x1.4feef8d30c6edp-57},
+{0x1.c4fffdcbfe424p-1, -0x1.43f68bcec4775p-55},
+{0x1.c6fffed54b9f7p-1, 0x1.47ea3f053e0ecp-55},
+{0x1.c8fffeb998fd5p-1, 0x1.383068df992f1p-56},
+{0x1.cb0002125219ap-1, -0x1.8fd8e64180e04p-57},
+{0x1.ccfffdd94469cp-1, 0x1.e7ebe1cc7ea72p-55},
+{0x1.cefffeafdc476p-1, 0x1.ebe39ad9f88fep-55},
+{0x1.d1000169af82bp-1, 0x1.57d91a8b95a71p-56},
+{0x1.d30000d0ff71dp-1, 0x1.9c1906970c7dap-55},
+{0x1.d4fffea790fc4p-1, -0x1.80e37c558fe0cp-58},
+{0x1.d70002edc87e5p-1, -0x1.f80d64dc10f44p-56},
+{0x1.d900021dc82aap-1, -0x1.47c8f94fd5c5cp-56},
+{0x1.dafffd86b0283p-1, 0x1.c7f1dc521617ep-55},
+{0x1.dd000296c4739p-1, 0x1.8019eb2ffb153p-55},
+{0x1.defffe54490f5p-1, 0x1.e00d2c652cc89p-57},
+{0x1.e0fffcdabf694p-1, -0x1.f8340202d69d2p-56},
+{0x1.e2fffdb52c8ddp-1, 0x1.b00c1ca1b0864p-56},
+{0x1.e4ffff24216efp-1, 0x1.2ffa8b094ab51p-56},
+{0x1.e6fffe88a5e11p-1, -0x1.7f673b1efbe59p-58},
+{0x1.e9000119eff0dp-1, -0x1.4808d5e0bc801p-55},
+{0x1.eafffdfa51744p-1, 0x1.80006d54320b5p-56},
+{0x1.ed0001a127fa1p-1, -0x1.002f860565c92p-58},
+{0x1.ef00007babcc4p-1, -0x1.540445d35e611p-55},
+{0x1.f0ffff57a8d02p-1, -0x1.ffb3139ef9105p-59},
+{0x1.f30001ee58ac7p-1, 0x1.a81acf2731155p-55},
+{0x1.f4ffff5823494p-1, 0x1.a3f41d4d7c743p-55},
+{0x1.f6ffffca94c6bp-1, -0x1.202f41c987875p-57},
+{0x1.f8fffe1f9c441p-1, 0x1.77dd1f477e74bp-56},
+{0x1.fafffd2e0e37ep-1, -0x1.f01199a7ca331p-57},
+{0x1.fd0001c77e49ep-1, 0x1.181ee4bceacb1p-56},
+{0x1.feffff7e0c331p-1, -0x1.e05370170875ap-57},
+{0x1.00ffff465606ep+0, -0x1.a7ead491c0adap-55},
+{0x1.02ffff3867a58p+0, -0x1.77f69c3fcb2ep-54},
+{0x1.04ffffdfc0d17p+0, 0x1.7bffe34cb945bp-54},
+{0x1.0700003cd4d82p+0, 0x1.20083c0e456cbp-55},
+{0x1.08ffff9f2cbe8p+0, -0x1.dffdfbe37751ap-57},
+{0x1.0b000010cda65p+0, -0x1.13f7faee626ebp-54},
+{0x1.0d00001a4d338p+0, 0x1.07dfa79489ff7p-55},
+{0x1.0effffadafdfdp+0, -0x1.7040570d66bcp-56},
+{0x1.110000bbafd96p+0, 0x1.e80d4846d0b62p-55},
+{0x1.12ffffae5f45dp+0, 0x1.dbffa64fd36efp-54},
+{0x1.150000dd59ad9p+0, 0x1.a0077701250aep-54},
+{0x1.170000f21559ap+0, 0x1.dfdf9e2e3deeep-55},
+{0x1.18ffffc275426p+0, 0x1.10030dc3b7273p-54},
+{0x1.1b000123d3c59p+0, 0x1.97f7980030188p-54},
+{0x1.1cffff8299eb7p+0, -0x1.5f932ab9f8c67p-57},
+{0x1.1effff48ad4p+0, 0x1.37fbf9da75bebp-54},
+{0x1.210000c8b86a4p+0, 0x1.f806b91fd5b22p-54},
+{0x1.2300003854303p+0, 0x1.3ffc2eb9fbf33p-54},
+{0x1.24fffffbcf684p+0, 0x1.601e77e2e2e72p-56},
+{0x1.26ffff52921d9p+0, 0x1.ffcbb767f0c61p-56},
+{0x1.2900014933a3cp+0, -0x1.202ca3c02412bp-56},
+{0x1.2b00014556313p+0, -0x1.2808233f21f02p-54},
+{0x1.2cfffebfe523bp+0, -0x1.8ff7e384fdcf2p-55},
+{0x1.2f0000bb8ad96p+0, -0x1.5ff51503041c5p-55},
+{0x1.30ffffb7ae2afp+0, -0x1.10071885e289dp-55},
+{0x1.32ffffeac5f7fp+0, -0x1.1ff5d3fb7b715p-54},
+{0x1.350000ca66756p+0, 0x1.57f82228b82bdp-54},
+{0x1.3700011fbf721p+0, 0x1.000bac40dd5ccp-55},
+{0x1.38ffff9592fb9p+0, -0x1.43f9d2db2a751p-54},
+{0x1.3b00004ddd242p+0, 0x1.57f6b707638e1p-55},
+{0x1.3cffff5b2c957p+0, 0x1.a023a10bf1231p-56},
+{0x1.3efffeab0b418p+0, 0x1.87f6d66b152bp-54},
+{0x1.410001532aff4p+0, 0x1.7f8375f198524p-57},
+{0x1.4300017478b29p+0, 0x1.301e672dc5143p-55},
+{0x1.44fffe795b463p+0, 0x1.9ff69b8b2895ap-55},
+{0x1.46fffe80475ep+0, -0x1.5c0b19bc2f254p-54},
+{0x1.48fffef6fc1e7p+0, 0x1.b4009f23a2a72p-54},
+{0x1.4afffe5bea704p+0, -0x1.4ffb7bf0d7d45p-54},
+{0x1.4d000171027dep+0, -0x1.9c06471dc6a3dp-54},
+{0x1.4f0000ff03ee2p+0, 0x1.77f890b85531cp-54},
+{0x1.5100012dc4bd1p+0, 0x1.004657166a436p-57},
+{0x1.530001605277ap+0, -0x1.6bfcece233209p-54},
+{0x1.54fffecdb704cp+0, -0x1.902720505a1d7p-55},
+{0x1.56fffef5f54a9p+0, 0x1.bbfe60ec96412p-54},
+{0x1.5900017e61012p+0, 0x1.87ec581afef9p-55},
+{0x1.5b00003c93e92p+0, -0x1.f41080abf0ccp-54},
+{0x1.5d0001d4919bcp+0, -0x1.8812afb254729p-54},
+{0x1.5efffe7b87a89p+0, -0x1.47eb780ed6904p-54},
+#endif
+},
+#endif /* __FP_FAST_FMA */
+};
@@ -1,4 +1,5 @@
GLIBC_2.30 _ZGVbN2v_cos F
+GLIBC_2.30 _ZGVbN2v_log F
GLIBC_2.30 _ZGVbN2v_sin F
GLIBC_2.30 _ZGVbN2vvv_sincos F
GLIBC_2.30 _ZGVbN4v_cosf F
--
2.20.1