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 "math_config.h"
11
12/*
13LOG2F_TABLE_BITS = 4
14LOG2F_POLY_ORDER = 4
15
16ULP error: 0.752 (nearest rounding.)
17Relative error: 1.9 * 2^-26 (before rounding.)
18*/
19
20#define N (1 << LOG2F_TABLE_BITS)
21#define T __log2f_data.tab
22#define A __log2f_data.poly
23#define OFF 0x3f330000
24
25float
26log2f (float x)
27{
28  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
29  double_t z, r, r2, p, y, y0, invc, logc;
30  uint32_t ix, iz, top, tmp;
31  int k, i;
32
33  ix = asuint (x);
34#if WANT_ROUNDING
35  /* Fix sign of zero with downward rounding when x==1.  */
36  if (unlikely (ix == 0x3f800000))
37    return 0;
38#endif
39  if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
40    {
41      /* x < 0x1p-126 or inf or nan.  */
42      if (ix * 2 == 0)
43	return __math_divzerof (1);
44      if (ix == 0x7f800000) /* log2(inf) == inf.  */
45	return x;
46      if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
47	return __math_invalidf (x);
48      /* x is subnormal, normalize it.  */
49      ix = asuint (x * 0x1p23f);
50      ix -= 23 << 23;
51    }
52
53  /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
54     The range is split into N subintervals.
55     The ith subinterval contains z and c is near its center.  */
56  tmp = ix - OFF;
57  i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
58  top = tmp & 0xff800000;
59  iz = ix - top;
60  k = (int32_t) tmp >> 23; /* arithmetic shift */
61  invc = T[i].invc;
62  logc = T[i].logc;
63  z = (double_t) asfloat (iz);
64
65  /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
66  r = z * invc - 1;
67  y0 = logc + (double_t) k;
68
69  /* Pipelined polynomial evaluation to approximate log1p(r)/ln2.  */
70  r2 = r * r;
71  y = A[1] * r + A[2];
72  y = A[0] * r2 + y;
73  p = A[3] * r + y0;
74  y = y * r2 + p;
75  return eval_as_float (y);
76}
77#if USE_GLIBC_ABI
78strong_alias (log2f, __log2f_finite)
79hidden_alias (log2f, __ieee754_log2f)
80#endif
81