Add new log implementation
Optimized log using carefully generated lookup table with 1/c and log(c) values for small intervalls around 1. The log(c) is very near a double precision value, it has about 62 bits precision. The algorithm is log(2^k x) = k log(2) + log(c) + log(x/c), where the last term is approximated by a polynomial of x/c - 1. Near 1 a single polynomial of x - 1 is used. There is separate code path when fma instruction is not available for computing x/c - 1 precisely, in which case the table size is doubled. The code uses __builtin_fma under __FP_FAST_FMA to ensure it is inlined as an instruction. With the default configuration settings the worst case error is 0.519 ULP (and 0.520 without fma), the rodata size is 2192 bytes (4240 without fma). The non-nearest rounding error is less than 1 ULP. Improvements on Cortex-A72 compared to current glibc master: log thruput: 3.28x in [0.01 11.1] log latency: 2.23x in [0.01 11.1] log thruput: 1.56x in [0.999 1.001] log latency: 1.57x in [0.999 1.001] Tested on aarch64-linux-gnu (defined __FP_FAST_FMA) arm-linux-gnueabihf (!defined __FP_FAST_FMA) x86_64-linux-gnu (!defined __FP_FAST_FMA) powerpc64le-linux-gnu (defined __FP_FAST_FMA) targets. * NEWS: Mention log improvement. * math/Makefile (type-double-routines): Add e_log_data. * sysdeps/i386/fpu/e_log_data.c: New file. * sysdeps/ia64/fpu/e_log_data.c: New file. * sysdeps/ieee754/dbl-64/e_log.c: Rewrite. * sysdeps/ieee754/dbl-64/e_log_data.c: New file. * sysdeps/ieee754/dbl-64/math_config.h (__log_data): Add. * sysdeps/ieee754/dbl-64/ulog.h: Remove. * sysdeps/ieee754/dbl-64/ulog.tbl: Remove. * sysdeps/m68k/m680x0/fpu/e_log_data.c: New file.
This commit is contained in:
Szabolcs Nagy
parent
5a274db4ea
commit
f41b0a43e4
13
ChangeLog
13
ChangeLog
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@ -1,3 +1,16 @@
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2018-09-12 Szabolcs Nagy <szabolcs.nagy@arm.com>
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* NEWS: Mention log improvement.
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* math/Makefile (type-double-routines): Add e_log_data.
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* sysdeps/i386/fpu/e_log_data.c: New file.
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* sysdeps/ia64/fpu/e_log_data.c: New file.
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* sysdeps/ieee754/dbl-64/e_log.c: Rewrite.
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* sysdeps/ieee754/dbl-64/e_log_data.c: New file.
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* sysdeps/ieee754/dbl-64/math_config.h (__log_data): Add.
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* sysdeps/ieee754/dbl-64/ulog.h: Remove.
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* sysdeps/ieee754/dbl-64/ulog.tbl: Remove.
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* sysdeps/m68k/m680x0/fpu/e_log_data.c: New file.
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2018-09-12 H.J. Lu <hongjiu.lu@intel.com>
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Xuepeng Guo <xuepeng.guo@intel.com>
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2
NEWS
2
NEWS
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@ -16,7 +16,7 @@ Major new features:
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to set the install root if you wish to install into a non-default
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configured location.
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* Optimized generic exp, exp2, sinf, cosf, sincosf and tanf.
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* Optimized generic exp, exp2, log, sinf, cosf, sincosf and tanf.
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* The reallocarray function is now declared under _DEFAULT_SOURCE, not just
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for _GNU_SOURCE, to match BSD environments.
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@ -127,7 +127,7 @@ type-ldouble-yes := ldouble
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type-double-suffix :=
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type-double-routines := branred doasin dosincos mpa mpatan2 \
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k_rem_pio2 mpatan mpsqrt mptan sincos32 \
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sincostab math_err e_exp_data
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sincostab math_err e_exp_data e_log_data
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# float support
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type-float-suffix := f
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1
sysdeps/i386/fpu/e_log_data.c
Normal file
1
sysdeps/i386/fpu/e_log_data.c
Normal file
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@ -0,0 +1 @@
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/* Not needed. */
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1
sysdeps/ia64/fpu/e_log_data.c
Normal file
1
sysdeps/ia64/fpu/e_log_data.c
Normal file
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@ -0,0 +1 @@
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/* Not needed. */
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@ -1,167 +1,132 @@
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/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001-2018 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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/*********************************************************************/
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/* */
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/* MODULE_NAME:ulog.c */
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/* */
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/* FUNCTION:ulog */
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/* */
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/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h ulog.h */
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/* ulog.tbl */
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/* */
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/* An ultimate log routine. Given an IEEE double machine number x */
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/* it computes the rounded (to nearest) value of log(x). */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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/*********************************************************************/
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/* Double-precision log(x) function.
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Copyright (C) 2018 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include "endian.h"
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#include <dla.h>
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#include "mpa.h"
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#include "MathLib.h"
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#include <math.h>
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#include <math_private.h>
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#include <stdint.h>
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#include "math_config.h"
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#define T __log_data.tab
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#define T2 __log_data.tab2
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#define B __log_data.poly1
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#define A __log_data.poly
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#define Ln2hi __log_data.ln2hi
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#define Ln2lo __log_data.ln2lo
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#define N (1 << LOG_TABLE_BITS)
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#define OFF 0x3fe6000000000000
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/* Top 16 bits of a double. */
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static inline uint32_t
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top16 (double x)
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{
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return asuint64 (x) >> 48;
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}
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#ifndef SECTION
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# define SECTION
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#endif
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/*********************************************************************/
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/* An ultimate log routine. Given an IEEE double machine number x */
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/* it computes the rounded (to nearest) value of log(x). */
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/*********************************************************************/
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double
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SECTION
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__ieee754_log (double x)
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{
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int i, j, n, ux, dx;
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double dbl_n, u, p0, q, r0, w, nln2a, luai, lubi, lvaj, lvbj,
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sij, ssij, ttij, A, B, B0, polI, polII, t8, a, aa, b, bb, c;
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#ifndef DLA_FMS
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double t1, t2, t3, t4, t5;
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/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
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double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
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uint64_t ix, iz, tmp;
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uint32_t top;
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int k, i;
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ix = asuint64 (x);
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top = top16 (x);
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#define LO asuint64 (1.0 - 0x1p-4)
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#define HI asuint64 (1.0 + 0x1.09p-4)
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if (__glibc_unlikely (ix - LO < HI - LO))
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{
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/* Handle close to 1.0 inputs separately. */
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/* Fix sign of zero with downward rounding when x==1. */
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if (WANT_ROUNDING && __glibc_unlikely (ix == asuint64 (1.0)))
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return 0;
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r = x - 1.0;
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r2 = r * r;
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r3 = r * r2;
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y = r3 * (B[1] + r * B[2] + r2 * B[3]
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+ r3 * (B[4] + r * B[5] + r2 * B[6]
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+ r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10])));
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/* Worst-case error is around 0.507 ULP. */
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w = r * 0x1p27;
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double_t rhi = r + w - w;
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double_t rlo = r - rhi;
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w = rhi * rhi * B[0]; /* B[0] == -0.5. */
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hi = r + w;
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lo = r - hi + w;
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lo += B[0] * rlo * (rhi + r);
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y += lo;
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y += hi;
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return y;
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}
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if (__glibc_unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
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{
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/* x < 0x1p-1022 or inf or nan. */
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if (ix * 2 == 0)
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return __math_divzero (1);
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if (ix == asuint64 (INFINITY)) /* log(inf) == inf. */
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return x;
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if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
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return __math_invalid (x);
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/* x is subnormal, normalize it. */
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ix = asuint64 (x * 0x1p52);
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ix -= 52ULL << 52;
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}
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/* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
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The range is split into N subintervals.
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The ith subinterval contains z and c is near its center. */
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tmp = ix - OFF;
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i = (tmp >> (52 - LOG_TABLE_BITS)) % N;
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k = (int64_t) tmp >> 52; /* arithmetic shift */
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iz = ix - (tmp & 0xfffULL << 52);
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invc = T[i].invc;
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logc = T[i].logc;
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z = asdouble (iz);
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/* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
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/* r ~= z/c - 1, |r| < 1/(2*N). */
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#ifdef __FP_FAST_FMA
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/* rounding error: 0x1p-55/N. */
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r = __builtin_fma (z, invc, -1.0);
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#else
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/* rounding error: 0x1p-55/N + 0x1p-66. */
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r = (z - T2[i].chi - T2[i].clo) * invc;
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#endif
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number num;
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kd = (double_t) k;
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#include "ulog.tbl"
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#include "ulog.h"
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/* hi + lo = r + log(c) + k*Ln2. */
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w = kd * Ln2hi + logc;
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hi = w + r;
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lo = w - hi + r + kd * Ln2lo;
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/* Treating special values of x ( x<=0, x=INF, x=NaN etc.). */
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num.d = x;
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ux = num.i[HIGH_HALF];
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dx = num.i[LOW_HALF];
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n = 0;
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if (__glibc_unlikely (ux < 0x00100000))
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{
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if (__glibc_unlikely (((ux & 0x7fffffff) | dx) == 0))
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return MHALF / 0.0; /* return -INF */
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if (__glibc_unlikely (ux < 0))
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return (x - x) / 0.0; /* return NaN */
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n -= 54;
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x *= two54.d; /* scale x */
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num.d = x;
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}
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if (__glibc_unlikely (ux >= 0x7ff00000))
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return x + x; /* INF or NaN */
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/* Regular values of x */
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w = x - 1;
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if (__glibc_likely (fabs (w) > U03))
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goto case_03;
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/* log (1) is +0 in all rounding modes. */
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if (w == 0.0)
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return 0.0;
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/*--- The case abs(x-1) < 0.03 */
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t8 = MHALF * w;
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EMULV (t8, w, a, aa, t1, t2, t3, t4, t5);
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EADD (w, a, b, bb);
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/* Evaluate polynomial II */
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polII = b7.d + w * b8.d;
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polII = b6.d + w * polII;
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polII = b5.d + w * polII;
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polII = b4.d + w * polII;
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polII = b3.d + w * polII;
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polII = b2.d + w * polII;
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polII = b1.d + w * polII;
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polII = b0.d + w * polII;
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polII *= w * w * w;
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c = (aa + bb) + polII;
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/* Here b contains the high part of the result, and c the low part.
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Maximum error is b * 2.334e-19, so accuracy is >61 bits.
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Therefore max ULP error of b + c is ~0.502. */
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return b + c;
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/*--- The case abs(x-1) > 0.03 */
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case_03:
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/* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */
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n += (num.i[HIGH_HALF] >> 20) - 1023;
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num.i[HIGH_HALF] = (num.i[HIGH_HALF] & 0x000fffff) | 0x3ff00000;
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if (num.d > SQRT_2)
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{
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num.d *= HALF;
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n++;
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}
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u = num.d;
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dbl_n = (double) n;
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/* Find i such that ui=1+(i-75)/2**8 is closest to u (i= 0,1,2,...,181) */
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num.d += h1.d;
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i = (num.i[HIGH_HALF] & 0x000fffff) >> 12;
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/* Find j such that vj=1+(j-180)/2**16 is closest to v=u/ui (j= 0,...,361) */
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num.d = u * Iu[i].d + h2.d;
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j = (num.i[HIGH_HALF] & 0x000fffff) >> 4;
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/* Compute w=(u-ui*vj)/(ui*vj) */
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p0 = (1 + (i - 75) * DEL_U) * (1 + (j - 180) * DEL_V);
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q = u - p0;
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r0 = Iu[i].d * Iv[j].d;
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w = q * r0;
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/* Evaluate polynomial I */
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polI = w + (a2.d + a3.d * w) * w * w;
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/* Add up everything */
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nln2a = dbl_n * LN2A;
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luai = Lu[i][0].d;
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lubi = Lu[i][1].d;
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lvaj = Lv[j][0].d;
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lvbj = Lv[j][1].d;
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EADD (luai, lvaj, sij, ssij);
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EADD (nln2a, sij, A, ttij);
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B0 = (((lubi + lvbj) + ssij) + ttij) + dbl_n * LN2B;
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B = polI + B0;
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/* Here A contains the high part of the result, and B the low part.
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Maximum abs error is 6.095e-21 and min log (x) is 0.0295 since x > 1.03.
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Therefore max ULP error of A + B is ~0.502. */
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return A + B;
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/* log(x) = lo + (log1p(r) - r) + hi. */
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r2 = r * r; /* rounding error: 0x1p-54/N^2. */
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/* Worst case error if |y| > 0x1p-4: 0.519 ULP (0.520 ULP without fma).
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0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma). */
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y = lo + r2 * A[0] + r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi;
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return y;
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}
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#ifndef __ieee754_log
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strong_alias (__ieee754_log, __log_finite)
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#endif
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|
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347
sysdeps/ieee754/dbl-64/e_log_data.c
Normal file
347
sysdeps/ieee754/dbl-64/e_log_data.c
Normal file
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@ -0,0 +1,347 @@
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/* Data for log.
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Copyright (C) 2018 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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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
|
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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/>. */
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#include "math_config.h"
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#define N (1 << LOG_TABLE_BITS)
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const struct log_data __log_data = {
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.ln2hi = 0x1.62e42fefa3800p-1,
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.ln2lo = 0x1.ef35793c76730p-45,
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.poly1 = {
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#if LOG_POLY1_ORDER == 12
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// relative error: 0x1.c04d76cp-63
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// in -0x1p-4 0x1.09p-4 (|log(1+x)| > 0x1p-4 outside the interval)
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-0x1p-1,
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0x1.5555555555577p-2,
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-0x1.ffffffffffdcbp-3,
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0x1.999999995dd0cp-3,
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-0x1.55555556745a7p-3,
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0x1.24924a344de3p-3,
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-0x1.fffffa4423d65p-4,
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0x1.c7184282ad6cap-4,
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-0x1.999eb43b068ffp-4,
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0x1.78182f7afd085p-4,
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-0x1.5521375d145cdp-4,
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#endif
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},
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.poly = {
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#if N == 128 && LOG_POLY_ORDER == 6
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// relative error: 0x1.926199e8p-56
|
||||
// abs error: 0x1.882ff33p-65
|
||||
// in -0x1.fp-9 0x1.fp-9
|
||||
-0x1.0000000000001p-1,
|
||||
0x1.555555551305bp-2,
|
||||
-0x1.fffffffeb459p-3,
|
||||
0x1.999b324f10111p-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 */
|
||||
};
|
||||
|
|
@ -133,4 +133,20 @@ extern const struct exp_data
|
|||
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
|
||||
{
|
||||
double ln2hi;
|
||||
double ln2lo;
|
||||
double poly[LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
|
||||
double poly1[LOG_POLY1_ORDER - 1];
|
||||
/* See e_log_data.c for details. */
|
||||
struct {double invc, logc;} tab[1 << LOG_TABLE_BITS];
|
||||
#ifndef __FP_FAST_FMA
|
||||
struct {double chi, clo;} tab2[1 << LOG_TABLE_BITS];
|
||||
#endif
|
||||
} __log_data attribute_hidden;
|
||||
|
||||
#endif
|
||||
|
|
|
|||
|
|
@ -1,93 +0,0 @@
|
|||
/*
|
||||
* IBM Accurate Mathematical Library
|
||||
* Written by International Business Machines Corp.
|
||||
* Copyright (C) 2001-2018 Free Software Foundation, Inc.
|
||||
*
|
||||
* This program is free software; you can redistribute it and/or modify
|
||||
* it under the terms of the GNU Lesser General Public License as published by
|
||||
* the Free Software Foundation; either version 2.1 of the License, or
|
||||
* (at your option) any later version.
|
||||
*
|
||||
* This program is distributed in the hope that it will be useful,
|
||||
* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
* GNU Lesser General Public License for more details.
|
||||
*
|
||||
* You should have received a copy of the GNU Lesser General Public License
|
||||
* along with this program; if not, see <http://www.gnu.org/licenses/>.
|
||||
*/
|
||||
|
||||
/******************************************************************/
|
||||
/* */
|
||||
/* MODULE_NAME:ulog.h */
|
||||
/* */
|
||||
/* common data and variables prototype and definition */
|
||||
/******************************************************************/
|
||||
|
||||
#ifndef ULOG_H
|
||||
#define ULOG_H
|
||||
|
||||
#ifdef BIG_ENDI
|
||||
static const number
|
||||
/* polynomial I */
|
||||
/**/ a2 = {{0xbfe00000, 0x0001aa8f} }, /* -0.500... */
|
||||
/**/ a3 = {{0x3fd55555, 0x55588d2e} }, /* 0.333... */
|
||||
/* polynomial II */
|
||||
/**/ b0 = {{0x3fd55555, 0x55555555} }, /* 0.333... */
|
||||
/**/ b1 = {{0xbfcfffff, 0xffffffbb} }, /* -0.249... */
|
||||
/**/ b2 = {{0x3fc99999, 0x9999992f} }, /* 0.199... */
|
||||
/**/ b3 = {{0xbfc55555, 0x556503fd} }, /* -0.166... */
|
||||
/**/ b4 = {{0x3fc24924, 0x925b3d62} }, /* 0.142... */
|
||||
/**/ b5 = {{0xbfbffffe, 0x160472fc} }, /* -0.124... */
|
||||
/**/ b6 = {{0x3fbc71c5, 0x25db58ac} }, /* 0.111... */
|
||||
/**/ b7 = {{0xbfb9a4ac, 0x11a2a61c} }, /* -0.100... */
|
||||
/**/ b8 = {{0x3fb75077, 0x0df2b591} }, /* 0.091... */
|
||||
/* constants */
|
||||
/**/ sqrt_2 = {{0x3ff6a09e, 0x667f3bcc} }, /* sqrt(2) */
|
||||
/**/ h1 = {{0x3fd2e000, 0x00000000} }, /* 151/2**9 */
|
||||
/**/ h2 = {{0x3f669000, 0x00000000} }, /* 361/2**17 */
|
||||
/**/ delu = {{0x3f700000, 0x00000000} }, /* 1/2**8 */
|
||||
/**/ delv = {{0x3ef00000, 0x00000000} }, /* 1/2**16 */
|
||||
/**/ ln2a = {{0x3fe62e42, 0xfefa3800} }, /* ln(2) 43 bits */
|
||||
/**/ ln2b = {{0x3d2ef357, 0x93c76730} }, /* ln(2)-ln2a */
|
||||
/**/ two54 = {{0x43500000, 0x00000000} }, /* 2**54 */
|
||||
/**/ u03 = {{0x3f9eb851, 0xeb851eb8} }; /* 0.03 */
|
||||
|
||||
#else
|
||||
#ifdef LITTLE_ENDI
|
||||
static const number
|
||||
/* polynomial I */
|
||||
/**/ a2 = {{0x0001aa8f, 0xbfe00000} }, /* -0.500... */
|
||||
/**/ a3 = {{0x55588d2e, 0x3fd55555} }, /* 0.333... */
|
||||
/* polynomial II */
|
||||
/**/ b0 = {{0x55555555, 0x3fd55555} }, /* 0.333... */
|
||||
/**/ b1 = {{0xffffffbb, 0xbfcfffff} }, /* -0.249... */
|
||||
/**/ b2 = {{0x9999992f, 0x3fc99999} }, /* 0.199... */
|
||||
/**/ b3 = {{0x556503fd, 0xbfc55555} }, /* -0.166... */
|
||||
/**/ b4 = {{0x925b3d62, 0x3fc24924} }, /* 0.142... */
|
||||
/**/ b5 = {{0x160472fc, 0xbfbffffe} }, /* -0.124... */
|
||||
/**/ b6 = {{0x25db58ac, 0x3fbc71c5} }, /* 0.111... */
|
||||
/**/ b7 = {{0x11a2a61c, 0xbfb9a4ac} }, /* -0.100... */
|
||||
/**/ b8 = {{0x0df2b591, 0x3fb75077} }, /* 0.091... */
|
||||
/* constants */
|
||||
/**/ sqrt_2 = {{0x667f3bcc, 0x3ff6a09e} }, /* sqrt(2) */
|
||||
/**/ h1 = {{0x00000000, 0x3fd2e000} }, /* 151/2**9 */
|
||||
/**/ h2 = {{0x00000000, 0x3f669000} }, /* 361/2**17 */
|
||||
/**/ delu = {{0x00000000, 0x3f700000} }, /* 1/2**8 */
|
||||
/**/ delv = {{0x00000000, 0x3ef00000} }, /* 1/2**16 */
|
||||
/**/ ln2a = {{0xfefa3800, 0x3fe62e42} }, /* ln(2) 43 bits */
|
||||
/**/ ln2b = {{0x93c76730, 0x3d2ef357} }, /* ln(2)-ln2a */
|
||||
/**/ two54 = {{0x00000000, 0x43500000} }, /* 2**54 */
|
||||
/**/ u03 = {{0xeb851eb8, 0x3f9eb851} }; /* 0.03 */
|
||||
|
||||
#endif
|
||||
#endif
|
||||
|
||||
#define SQRT_2 sqrt_2.d
|
||||
#define DEL_U delu.d
|
||||
#define DEL_V delv.d
|
||||
#define LN2A ln2a.d
|
||||
#define LN2B ln2b.d
|
||||
#define U03 u03.d
|
||||
|
||||
#endif
|
||||
File diff suppressed because it is too large
Load diff
1
sysdeps/m68k/m680x0/fpu/e_log_data.c
Normal file
1
sysdeps/m68k/m680x0/fpu/e_log_data.c
Normal file
|
|
@ -0,0 +1 @@
|
|||
/* Not needed. */
|
||||
Loading…
Reference in a new issue