mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-29 08:11:08 +00:00
143 lines
4.1 KiB
C
143 lines
4.1 KiB
C
/* Double-precision log(x) function.
|
|
Copyright (C) 2018-2024 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
|
|
<https://www.gnu.org/licenses/>. */
|
|
|
|
#include <math.h>
|
|
#include <stdint.h>
|
|
#include <math-svid-compat.h>
|
|
#include <libm-alias-finite.h>
|
|
#include <libm-alias-double.h>
|
|
#include "math_config.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
|
|
|
|
/* Top 16 bits of a double. */
|
|
static inline uint32_t
|
|
top16 (double x)
|
|
{
|
|
return asuint64 (x) >> 48;
|
|
}
|
|
|
|
#ifndef SECTION
|
|
# define SECTION
|
|
#endif
|
|
|
|
double
|
|
SECTION
|
|
__log (double x)
|
|
{
|
|
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
|
|
double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
|
|
uint64_t ix, iz, tmp;
|
|
uint32_t top;
|
|
int k, i;
|
|
|
|
ix = asuint64 (x);
|
|
top = top16 (x);
|
|
|
|
#define LO asuint64 (1.0 - 0x1p-4)
|
|
#define HI asuint64 (1.0 + 0x1.09p-4)
|
|
if (__glibc_unlikely (ix - 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 == asuint64 (1.0)))
|
|
return 0;
|
|
r = x - 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 * 0x1p27;
|
|
double_t rhi = r + w - w;
|
|
double_t 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;
|
|
}
|
|
if (__glibc_unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
|
|
{
|
|
/* x < 0x1p-1022 or inf or nan. */
|
|
if (ix * 2 == 0)
|
|
return __math_divzero (1);
|
|
if (ix == asuint64 (INFINITY)) /* log(inf) == inf. */
|
|
return x;
|
|
if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
|
|
return __math_invalid (x);
|
|
/* x is subnormal, normalize it. */
|
|
ix = asuint64 (x * 0x1p52);
|
|
ix -= 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 - OFF;
|
|
i = (tmp >> (52 - LOG_TABLE_BITS)) % N;
|
|
k = (int64_t) tmp >> 52; /* arithmetic shift */
|
|
iz = ix - (tmp & 0xfffULL << 52);
|
|
invc = T[i].invc;
|
|
logc = T[i].logc;
|
|
z = asdouble (iz);
|
|
|
|
/* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
|
|
/* r ~= z/c - 1, |r| < 1/(2*N). */
|
|
#ifdef __FP_FAST_FMA
|
|
/* rounding error: 0x1p-55/N. */
|
|
r = __builtin_fma (z, invc, -1.0);
|
|
#else
|
|
/* rounding error: 0x1p-55/N + 0x1p-66. */
|
|
r = (z - T2[i].chi - T2[i].clo) * invc;
|
|
#endif
|
|
kd = (double_t) 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;
|
|
}
|
|
#ifndef __log
|
|
strong_alias (__log, __ieee754_log)
|
|
libm_alias_finite (__ieee754_log, __log)
|
|
# if LIBM_SVID_COMPAT
|
|
versioned_symbol (libm, __log, log, GLIBC_2_29);
|
|
libm_alias_double_other (__log, log)
|
|
# else
|
|
libm_alias_double (__log, log)
|
|
# endif
|
|
#endif
|