1/* Single-precision log2 function.
2 Copyright (C) 2017-2023 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <https://www.gnu.org/licenses/>. */
18
19#include <math.h>
20#include <stdint.h>
21#include <libm-alias-finite.h>
22#include <libm-alias-float.h>
23#include "math_config.h"
24
25/*
26LOG2F_TABLE_BITS = 4
27LOG2F_POLY_ORDER = 4
28
29ULP error: 0.752 (nearest rounding.)
30Relative error: 1.9 * 2^-26 (before rounding.)
31*/
32
33#define N (1 << LOG2F_TABLE_BITS)
34#define T __log2f_data.tab
35#define A __log2f_data.poly
36#define OFF 0x3f330000
37
38float
39__log2f (float x)
40{
41 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
42 double_t z, r, r2, p, y, y0, invc, logc;
43 uint32_t ix, iz, top, tmp;
44 int k, i;
45
46 ix = asuint (x);
47#if WANT_ROUNDING
48 /* Fix sign of zero with downward rounding when x==1. */
49 if (__glibc_unlikely (ix == 0x3f800000))
50 return 0;
51#endif
52 if (__glibc_unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
53 {
54 /* x < 0x1p-126 or inf or nan. */
55 if (ix * 2 == 0)
56 return __math_divzerof (1);
57 if (ix == 0x7f800000) /* log2(inf) == inf. */
58 return x;
59 if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
60 return __math_invalidf (x);
61 /* x is subnormal, normalize it. */
62 ix = asuint (x * 0x1p23f);
63 ix -= 23 << 23;
64 }
65
66 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
67 The range is split into N subintervals.
68 The ith subinterval contains z and c is near its center. */
69 tmp = ix - OFF;
70 i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
71 top = tmp & 0xff800000;
72 iz = ix - top;
73 k = (int32_t) tmp >> 23; /* arithmetic shift */
74 invc = T[i].invc;
75 logc = T[i].logc;
76 z = (double_t) asfloat (iz);
77
78 /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
79 r = z * invc - 1;
80 y0 = logc + (double_t) k;
81
82 /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
83 r2 = r * r;
84 y = A[1] * r + A[2];
85 y = A[0] * r2 + y;
86 p = A[3] * r + y0;
87 y = y * r2 + p;
88 return (float) y;
89}
90#ifndef __log2f
91strong_alias (__log2f, __ieee754_log2f)
92libm_alias_finite (__ieee754_log2f, __log2f)
93versioned_symbol (libm, __log2f, log2f, GLIBC_2_27);
94libm_alias_float_other (__log2, log2)
95#endif
96