forked from OSchip/llvm-project
143 lines
4.0 KiB
C
143 lines
4.0 KiB
C
/*
|
|
* Double-precision log2(x) function.
|
|
*
|
|
* Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
|
|
* See https://llvm.org/LICENSE.txt for license information.
|
|
* SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
|
|
*/
|
|
|
|
#include <float.h>
|
|
#include <math.h>
|
|
#include <stdint.h>
|
|
#include "math_config.h"
|
|
|
|
#define T __log2_data.tab
|
|
#define T2 __log2_data.tab2
|
|
#define B __log2_data.poly1
|
|
#define A __log2_data.poly
|
|
#define InvLn2hi __log2_data.invln2hi
|
|
#define InvLn2lo __log2_data.invln2lo
|
|
#define N (1 << LOG2_TABLE_BITS)
|
|
#define OFF 0x3fe6000000000000
|
|
|
|
/* Top 16 bits of a double. */
|
|
static inline uint32_t
|
|
top16 (double x)
|
|
{
|
|
return asuint64 (x) >> 48;
|
|
}
|
|
|
|
double
|
|
log2 (double x)
|
|
{
|
|
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
|
|
double_t z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p;
|
|
uint64_t ix, iz, tmp;
|
|
uint32_t top;
|
|
int k, i;
|
|
|
|
ix = asuint64 (x);
|
|
top = top16 (x);
|
|
|
|
#if LOG2_POLY1_ORDER == 11
|
|
# define LO asuint64 (1.0 - 0x1.5b51p-5)
|
|
# define HI asuint64 (1.0 + 0x1.6ab2p-5)
|
|
#endif
|
|
if (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 && unlikely (ix == asuint64 (1.0)))
|
|
return 0;
|
|
r = x - 1.0;
|
|
#if HAVE_FAST_FMA
|
|
hi = r * InvLn2hi;
|
|
lo = r * InvLn2lo + fma (r, InvLn2hi, -hi);
|
|
#else
|
|
double_t rhi, rlo;
|
|
rhi = asdouble (asuint64 (r) & -1ULL << 32);
|
|
rlo = r - rhi;
|
|
hi = rhi * InvLn2hi;
|
|
lo = rlo * InvLn2hi + r * InvLn2lo;
|
|
#endif
|
|
r2 = r * r; /* rounding error: 0x1p-62. */
|
|
r4 = r2 * r2;
|
|
#if LOG2_POLY1_ORDER == 11
|
|
/* Worst-case error is less than 0.54 ULP (0.55 ULP without fma). */
|
|
p = r2 * (B[0] + r * B[1]);
|
|
y = hi + p;
|
|
lo += hi - y + p;
|
|
lo += r4 * (B[2] + r * B[3] + r2 * (B[4] + r * B[5])
|
|
+ r4 * (B[6] + r * B[7] + r2 * (B[8] + r * B[9])));
|
|
y += lo;
|
|
#endif
|
|
return eval_as_double (y);
|
|
}
|
|
if (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 - LOG2_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);
|
|
kd = (double_t) k;
|
|
|
|
/* log2(x) = log2(z/c) + log2(c) + k. */
|
|
/* r ~= z/c - 1, |r| < 1/(2*N). */
|
|
#if HAVE_FAST_FMA
|
|
/* rounding error: 0x1p-55/N. */
|
|
r = fma (z, invc, -1.0);
|
|
t1 = r * InvLn2hi;
|
|
t2 = r * InvLn2lo + fma (r, InvLn2hi, -t1);
|
|
#else
|
|
double_t rhi, rlo;
|
|
/* rounding error: 0x1p-55/N + 0x1p-65. */
|
|
r = (z - T2[i].chi - T2[i].clo) * invc;
|
|
rhi = asdouble (asuint64 (r) & -1ULL << 32);
|
|
rlo = r - rhi;
|
|
t1 = rhi * InvLn2hi;
|
|
t2 = rlo * InvLn2hi + r * InvLn2lo;
|
|
#endif
|
|
|
|
/* hi + lo = r/ln2 + log2(c) + k. */
|
|
t3 = kd + logc;
|
|
hi = t3 + t1;
|
|
lo = t3 - hi + t1 + t2;
|
|
|
|
/* log2(r+1) = r/ln2 + r^2*poly(r). */
|
|
/* Evaluation is optimized assuming superscalar pipelined execution. */
|
|
r2 = r * r; /* rounding error: 0x1p-54/N^2. */
|
|
r4 = r2 * r2;
|
|
#if LOG2_POLY_ORDER == 7
|
|
/* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma).
|
|
~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma). */
|
|
p = A[0] + r * A[1] + r2 * (A[2] + r * A[3]) + r4 * (A[4] + r * A[5]);
|
|
y = lo + r2 * p + hi;
|
|
#endif
|
|
return eval_as_double (y);
|
|
}
|
|
#if USE_GLIBC_ABI
|
|
strong_alias (log2, __log2_finite)
|
|
hidden_alias (log2, __ieee754_log2)
|
|
# if LDBL_MANT_DIG == 53
|
|
long double log2l (long double x) { return log2 (x); }
|
|
# endif
|
|
#endif
|