72 lines
1.7 KiB
C
72 lines
1.7 KiB
C
|
/*
|
||
|
|
* Single-precision log2 function.
|
||
|
|
*
|
||
|
|
* Copyright (c) 2017-2018, Arm Limited.
|
||
|
|
* SPDX-License-Identifier: MIT
|
||
|
|
*/
|
||
|
|
|
||
|
|
#include "libc/math/math.h"
|
||
|
|
#include "libc/math/libm.h"
|
||
|
|
#include "libc/math/log2f_data.h"
|
||
|
|
|
||
|
|
/*
|
||
|
|
LOG2F_TABLE_BITS = 4
|
||
|
|
LOG2F_POLY_ORDER = 4
|
||
|
|
|
||
|
|
ULP error: 0.752 (nearest rounding.)
|
||
|
|
Relative error: 1.9 * 2^-26 (before rounding.)
|
||
|
|
*/
|
||
|
|
|
||
|
|
#define N (1 << LOG2F_TABLE_BITS)
|
||
|
|
#define T __log2f_data.tab
|
||
|
|
#define A __log2f_data.poly
|
||
|
|
#define OFF 0x3f330000
|
||
|
|
|
||
|
|
float log2f(float x)
|
||
|
|
{
|
||
|
|
double_t z, r, r2, p, y, y0, invc, logc;
|
||
|
|
uint32_t ix, iz, top, tmp;
|
||
|
|
int k, i;
|
||
|
|
|
||
|
|
ix = asuint(x);
|
||
|
|
/* Fix sign of zero with downward rounding when x==1. */
|
||
|
|
if (WANT_ROUNDING && predict_false(ix == 0x3f800000))
|
||
|
|
return 0;
|
||
|
|
if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
|
||
|
|
/* x < 0x1p-126 or inf or nan. */
|
||
|
|
if (ix * 2 == 0)
|
||
|
|
return __math_divzerof(1);
|
||
|
|
if (ix == 0x7f800000) /* log2(inf) == inf. */
|
||
|
|
return x;
|
||
|
|
if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
|
||
|
|
return __math_invalidf(x);
|
||
|
|
/* x is subnormal, normalize it. */
|
||
|
|
ix = asuint(x * 0x1p23f);
|
||
|
|
ix -= 23 << 23;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* 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 >> (23 - LOG2F_TABLE_BITS)) % N;
|
||
|
|
top = tmp & 0xff800000;
|
||
|
|
iz = ix - top;
|
||
|
|
k = (int32_t)tmp >> 23; /* arithmetic shift */
|
||
|
|
invc = T[i].invc;
|
||
|
|
logc = T[i].logc;
|
||
|
|
z = (double_t)asfloat(iz);
|
||
|
|
|
||
|
|
/* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
|
||
|
|
r = z * invc - 1;
|
||
|
|
y0 = logc + (double_t)k;
|
||
|
|
|
||
|
|
/* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
|
||
|
|
r2 = r * r;
|
||
|
|
y = A[1] * r + A[2];
|
||
|
|
y = A[0] * r2 + y;
|
||
|
|
p = A[3] * r + y0;
|
||
|
|
y = y * r2 + p;
|
||
|
|
return eval_as_float(y);
|
||
|
|
}
|