1 /* Single-precision log2 function.
2 Copyright (C) 2017-2023 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
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.
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.
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/>. */
21 #include <libm-alias-finite.h>
22 #include <libm-alias-float.h>
23 #include "math_config.h"
29 ULP error: 0.752 (nearest rounding.)
30 Relative error: 1.9 * 2^-26 (before rounding.)
33 #define N (1 << LOG2F_TABLE_BITS)
34 #define T __log2f_data.tab
35 #define A __log2f_data.poly
36 #define OFF 0x3f330000
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
;
48 /* Fix sign of zero with downward rounding when x==1. */
49 if (__glibc_unlikely (ix
== 0x3f800000))
52 if (__glibc_unlikely (ix
- 0x00800000 >= 0x7f800000 - 0x00800000))
54 /* x < 0x1p-126 or inf or nan. */
56 return __math_divzerof (1);
57 if (ix
== 0x7f800000) /* log2(inf) == inf. */
59 if ((ix
& 0x80000000) || ix
* 2 >= 0xff000000)
60 return __math_invalidf (x
);
61 /* x is subnormal, normalize it. */
62 ix
= asuint (x
* 0x1p
23f
);
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. */
70 i
= (tmp
>> (23 - LOG2F_TABLE_BITS
)) % N
;
71 top
= tmp
& 0xff800000;
73 k
= (int32_t) tmp
>> 23; /* arithmetic shift */
76 z
= (double_t
) asfloat (iz
);
78 /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
80 y0
= logc
+ (double_t
) k
;
82 /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
91 strong_alias (__log2f
, __ieee754_log2f
)
92 libm_alias_finite (__ieee754_log2f
, __log2f
)
93 versioned_symbol (libm
, __log2f
, log2f
, GLIBC_2_27
);
94 libm_alias_float_other (__log2
, log2
)