1 /* Double-precision log(x) function.
2 Copyright (C) 2018-2023 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 <math-svid-compat.h>
22 #include <libm-alias-finite.h>
23 #include <libm-alias-double.h>
24 #include "math_config.h"
26 #define T __log_data.tab
27 #define T2 __log_data.tab2
28 #define B __log_data.poly1
29 #define A __log_data.poly
30 #define Ln2hi __log_data.ln2hi
31 #define Ln2lo __log_data.ln2lo
32 #define N (1 << LOG_TABLE_BITS)
33 #define OFF 0x3fe6000000000000
35 /* Top 16 bits of a double. */
36 static inline uint32_t
39 return asuint64 (x
) >> 48;
50 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
51 double_t w
, z
, r
, r2
, r3
, y
, invc
, logc
, kd
, hi
, lo
;
59 #define LO asuint64 (1.0 - 0x1p-4)
60 #define HI asuint64 (1.0 + 0x1.09p-4)
61 if (__glibc_unlikely (ix
- LO
< HI
- LO
))
63 /* Handle close to 1.0 inputs separately. */
64 /* Fix sign of zero with downward rounding when x==1. */
65 if (WANT_ROUNDING
&& __glibc_unlikely (ix
== asuint64 (1.0)))
70 y
= r3
* (B
[1] + r
* B
[2] + r2
* B
[3]
71 + r3
* (B
[4] + r
* B
[5] + r2
* B
[6]
72 + r3
* (B
[7] + r
* B
[8] + r2
* B
[9] + r3
* B
[10])));
73 /* Worst-case error is around 0.507 ULP. */
75 double_t rhi
= r
+ w
- w
;
76 double_t rlo
= r
- rhi
;
77 w
= rhi
* rhi
* B
[0]; /* B[0] == -0.5. */
80 lo
+= B
[0] * rlo
* (rhi
+ r
);
85 if (__glibc_unlikely (top
- 0x0010 >= 0x7ff0 - 0x0010))
87 /* x < 0x1p-1022 or inf or nan. */
89 return __math_divzero (1);
90 if (ix
== asuint64 (INFINITY
)) /* log(inf) == inf. */
92 if ((top
& 0x8000) || (top
& 0x7ff0) == 0x7ff0)
93 return __math_invalid (x
);
94 /* x is subnormal, normalize it. */
95 ix
= asuint64 (x
* 0x1p
52);
99 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
100 The range is split into N subintervals.
101 The ith subinterval contains z and c is near its center. */
103 i
= (tmp
>> (52 - LOG_TABLE_BITS
)) % N
;
104 k
= (int64_t) tmp
>> 52; /* arithmetic shift */
105 iz
= ix
- (tmp
& 0xfffULL
<< 52);
110 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
111 /* r ~= z/c - 1, |r| < 1/(2*N). */
113 /* rounding error: 0x1p-55/N. */
114 r
= __builtin_fma (z
, invc
, -1.0);
116 /* rounding error: 0x1p-55/N + 0x1p-66. */
117 r
= (z
- T2
[i
].chi
- T2
[i
].clo
) * invc
;
121 /* hi + lo = r + log(c) + k*Ln2. */
122 w
= kd
* Ln2hi
+ logc
;
124 lo
= w
- hi
+ r
+ kd
* Ln2lo
;
126 /* log(x) = lo + (log1p(r) - r) + hi. */
127 r2
= r
* r
; /* rounding error: 0x1p-54/N^2. */
128 /* Worst case error if |y| > 0x1p-4: 0.519 ULP (0.520 ULP without fma).
129 0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma). */
130 y
= lo
+ r2
* A
[0] + r
* r2
* (A
[1] + r
* A
[2] + r2
* (A
[3] + r
* A
[4])) + hi
;
134 strong_alias (__log
, __ieee754_log
)
135 libm_alias_finite (__ieee754_log
, __log
)
136 # if LIBM_SVID_COMPAT
137 versioned_symbol (libm
, __log
, log
, GLIBC_2_29
);
138 libm_alias_double_other (__log
, log
)
140 libm_alias_double (__log
, log
)