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/* Single-precision log2 function.
Copyright (C) 2017 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_config.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
__ieee754_log2f (float x)
{
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
double_t z, r, r2, p, y, y0, invc, logc;
uint32_t ix, iz, top, tmp;
int k, i;
ix = asuint (x);
#if WANT_ROUNDING
/* Fix sign of zero with downward rounding when x==1. */
if (__glibc_unlikely (ix == 0x3f800000))
return 0;
#endif
if (__glibc_unlikely (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 (float) y;
}
strong_alias (__ieee754_log2f, __log2f_finite)
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