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git.ipfire.org Git - thirdparty/glibc.git/blob - sysdeps/ieee754/dbl-64/e_log2.c
1 /* Double-precision log2(x) function.
2 Copyright (C) 2018 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 <http://www.gnu.org/licenses/>. */
21 #include <math-svid-compat.h>
22 #include <shlib-compat.h>
23 #include <libm-alias-double.h>
24 #include "math_config.h"
26 #define T __log2_data.tab
27 #define T2 __log2_data.tab2
28 #define B __log2_data.poly1
29 #define A __log2_data.poly
30 #define InvLn2hi __log2_data.invln2hi
31 #define InvLn2lo __log2_data.invln2lo
32 #define N (1 << LOG2_TABLE_BITS)
33 #define OFF 0x3fe6000000000000
35 /* Top 16 bits of a double. */
36 static inline uint32_t
39 return asuint64 (x
) >> 48;
45 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
46 double_t z
, r
, r2
, r4
, y
, invc
, logc
, kd
, hi
, lo
, t1
, t2
, t3
, p
;
54 #define LO asuint64 (1.0 - 0x1.5b51p-5)
55 #define HI asuint64 (1.0 + 0x1.6ab2p-5)
56 if (__glibc_unlikely (ix
- LO
< HI
- LO
))
58 /* Handle close to 1.0 inputs separately. */
59 /* Fix sign of zero with downward rounding when x==1. */
60 if (WANT_ROUNDING
&& __glibc_unlikely (ix
== asuint64 (1.0)))
65 lo
= r
* InvLn2lo
+ __builtin_fma (r
, InvLn2hi
, -hi
);
68 rhi
= asdouble (asuint64 (r
) & -1ULL << 32);
71 lo
= rlo
* InvLn2hi
+ r
* InvLn2lo
;
73 r2
= r
* r
; /* rounding error: 0x1p-62. */
75 /* Worst-case error is less than 0.54 ULP (0.55 ULP without fma). */
76 p
= r2
* (B
[0] + r
* B
[1]);
79 lo
+= r4
* (B
[2] + r
* B
[3] + r2
* (B
[4] + r
* B
[5])
80 + r4
* (B
[6] + r
* B
[7] + r2
* (B
[8] + r
* B
[9])));
84 if (__glibc_unlikely (top
- 0x0010 >= 0x7ff0 - 0x0010))
86 /* x < 0x1p-1022 or inf or nan. */
88 return __math_divzero (1);
89 if (ix
== asuint64 (INFINITY
)) /* log(inf) == inf. */
91 if ((top
& 0x8000) || (top
& 0x7ff0) == 0x7ff0)
92 return __math_invalid (x
);
93 /* x is subnormal, normalize it. */
94 ix
= asuint64 (x
* 0x1p
52);
98 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
99 The range is split into N subintervals.
100 The ith subinterval contains z and c is near its center. */
102 i
= (tmp
>> (52 - LOG2_TABLE_BITS
)) % N
;
103 k
= (int64_t) tmp
>> 52; /* arithmetic shift */
104 iz
= ix
- (tmp
& 0xfffULL
<< 52);
110 /* log2(x) = log2(z/c) + log2(c) + k. */
111 /* r ~= z/c - 1, |r| < 1/(2*N). */
113 /* rounding error: 0x1p-55/N. */
114 r
= __builtin_fma (z
, invc
, -1.0);
116 t2
= r
* InvLn2lo
+ __builtin_fma (r
, InvLn2hi
, -t1
);
119 /* rounding error: 0x1p-55/N + 0x1p-65. */
120 r
= (z
- T2
[i
].chi
- T2
[i
].clo
) * invc
;
121 rhi
= asdouble (asuint64 (r
) & -1ULL << 32);
124 t2
= rlo
* InvLn2hi
+ r
* InvLn2lo
;
127 /* hi + lo = r/ln2 + log2(c) + k. */
130 lo
= t3
- hi
+ t1
+ t2
;
132 /* log2(r+1) = r/ln2 + r^2*poly(r). */
133 /* Evaluation is optimized assuming superscalar pipelined execution. */
134 r2
= r
* r
; /* rounding error: 0x1p-54/N^2. */
136 /* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma).
137 ~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma). */
138 p
= A
[0] + r
* A
[1] + r2
* (A
[2] + r
* A
[3]) + r4
* (A
[4] + r
* A
[5]);
139 y
= lo
+ r2
* p
+ hi
;
143 strong_alias (__log2
, __ieee754_log2
)
144 strong_alias (__log2
, __log2_finite
)
145 # if LIBM_SVID_COMPAT
146 versioned_symbol (libm
, __log2
, log2
, GLIBC_2_29
);
147 libm_alias_double_other (__log2
, log2
)
149 libm_alias_double (__log2
, log2
)