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