1/*
2 * Single-precision log2 function.
3 *
4 * Copyright (c) 2017-2018, Arm Limited.
5 * SPDX-License-Identifier: MIT
6 */
7
8#include <math.h>
9#include <stdint.h>
10#include "libm.h"
11#include "log2f_data.h"
12
13/*
14LOG2F_TABLE_BITS = 4
15LOG2F_POLY_ORDER = 4
16
17ULP error: 0.752 (nearest rounding.)
18Relative error: 1.9 * 2^-26 (before rounding.)
19*/
20
21#define N (1 << LOG2F_TABLE_BITS)
22#define T __log2f_data.tab
23#define A __log2f_data.poly
24#define OFF 0x3f330000
25
26float log2f(float x)
27{
28	double_t z, r, r2, p, y, y0, invc, logc;
29	uint32_t ix, iz, top, tmp;
30	int k, i;
31
32	ix = asuint(x);
33	/* Fix sign of zero with downward rounding when x==1.  */
34	if (WANT_ROUNDING && predict_false(ix == 0x3f800000))
35		return 0;
36	if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
37		/* x < 0x1p-126 or inf or nan.  */
38		if (ix * 2 == 0)
39			return __math_divzerof(1);
40		if (ix == 0x7f800000) /* log2(inf) == inf.  */
41			return x;
42		if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
43			return __math_invalidf(x);
44		/* x is subnormal, normalize it.  */
45		ix = asuint(x * 0x1p23f);
46		ix -= 23 << 23;
47	}
48
49	/* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
50	   The range is split into N subintervals.
51	   The ith subinterval contains z and c is near its center.  */
52	tmp = ix - OFF;
53	i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
54	top = tmp & 0xff800000;
55	iz = ix - top;
56	k = (int32_t)tmp >> 23; /* arithmetic shift */
57	invc = T[i].invc;
58	logc = T[i].logc;
59	z = (double_t)asfloat(iz);
60
61	/* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
62	r = z * invc - 1;
63	y0 = logc + (double_t)k;
64
65	/* Pipelined polynomial evaluation to approximate log1p(r)/ln2.  */
66	r2 = r * r;
67	y = A[1] * r + A[2];
68	y = A[0] * r2 + y;
69	p = A[3] * r + y0;
70	y = y * r2 + p;
71	return eval_as_float(y);
72}
73