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f41b0a43 | 1 | /* Double-precision log(x) function. |
6d7e8eda | 2 | Copyright (C) 2018-2023 Free Software Foundation, Inc. |
f41b0a43 | 3 | This file is part of the GNU C Library. |
e4d82761 | 4 | |
f41b0a43 SN |
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 | |
5a82c748 | 17 | <https://www.gnu.org/licenses/>. */ |
e4d82761 | 18 | |
0e9be4db | 19 | #include <math.h> |
f41b0a43 | 20 | #include <stdint.h> |
f29b7c49 | 21 | #include <math-svid-compat.h> |
220622dd | 22 | #include <libm-alias-finite.h> |
f29b7c49 | 23 | #include <libm-alias-double.h> |
f41b0a43 SN |
24 | #include "math_config.h" |
25 | ||
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 | |
34 | ||
35 | /* Top 16 bits of a double. */ | |
36 | static inline uint32_t | |
37 | top16 (double x) | |
38 | { | |
39 | return asuint64 (x) >> 48; | |
40 | } | |
e859d1d9 | 41 | |
31d3cc00 UD |
42 | #ifndef SECTION |
43 | # define SECTION | |
44 | #endif | |
45 | ||
31d3cc00 UD |
46 | double |
47 | SECTION | |
f29b7c49 | 48 | __log (double x) |
0f6a8d4b | 49 | { |
f41b0a43 SN |
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; | |
52 | uint64_t ix, iz, tmp; | |
53 | uint32_t top; | |
54 | int k, i; | |
55 | ||
56 | ix = asuint64 (x); | |
57 | top = top16 (x); | |
58 | ||
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)) | |
0f6a8d4b | 62 | { |
f41b0a43 SN |
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))) | |
66 | return 0; | |
67 | r = x - 1.0; | |
68 | r2 = r * r; | |
69 | r3 = r * r2; | |
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. */ | |
74 | w = r * 0x1p27; | |
75 | double_t rhi = r + w - w; | |
76 | double_t rlo = r - rhi; | |
77 | w = rhi * rhi * B[0]; /* B[0] == -0.5. */ | |
78 | hi = r + w; | |
79 | lo = r - hi + w; | |
80 | lo += B[0] * rlo * (rhi + r); | |
81 | y += lo; | |
82 | y += hi; | |
83 | return y; | |
0f6a8d4b | 84 | } |
f41b0a43 | 85 | if (__glibc_unlikely (top - 0x0010 >= 0x7ff0 - 0x0010)) |
0f6a8d4b | 86 | { |
f41b0a43 SN |
87 | /* x < 0x1p-1022 or inf or nan. */ |
88 | if (ix * 2 == 0) | |
89 | return __math_divzero (1); | |
90 | if (ix == asuint64 (INFINITY)) /* log(inf) == inf. */ | |
91 | return x; | |
92 | if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0) | |
93 | return __math_invalid (x); | |
94 | /* x is subnormal, normalize it. */ | |
95 | ix = asuint64 (x * 0x1p52); | |
96 | ix -= 52ULL << 52; | |
0f6a8d4b | 97 | } |
e4d82761 | 98 | |
f41b0a43 SN |
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. */ | |
102 | tmp = ix - OFF; | |
103 | i = (tmp >> (52 - LOG_TABLE_BITS)) % N; | |
104 | k = (int64_t) tmp >> 52; /* arithmetic shift */ | |
105 | iz = ix - (tmp & 0xfffULL << 52); | |
106 | invc = T[i].invc; | |
107 | logc = T[i].logc; | |
108 | z = asdouble (iz); | |
109 | ||
110 | /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ | |
111 | /* r ~= z/c - 1, |r| < 1/(2*N). */ | |
112 | #ifdef __FP_FAST_FMA | |
113 | /* rounding error: 0x1p-55/N. */ | |
114 | r = __builtin_fma (z, invc, -1.0); | |
115 | #else | |
116 | /* rounding error: 0x1p-55/N + 0x1p-66. */ | |
117 | r = (z - T2[i].chi - T2[i].clo) * invc; | |
118 | #endif | |
119 | kd = (double_t) k; | |
120 | ||
121 | /* hi + lo = r + log(c) + k*Ln2. */ | |
122 | w = kd * Ln2hi + logc; | |
123 | hi = w + r; | |
124 | lo = w - hi + r + kd * Ln2lo; | |
125 | ||
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; | |
131 | return y; | |
f7eac6eb | 132 | } |
f29b7c49 SN |
133 | #ifndef __log |
134 | strong_alias (__log, __ieee754_log) | |
220622dd | 135 | libm_alias_finite (__ieee754_log, __log) |
f29b7c49 SN |
136 | # if LIBM_SVID_COMPAT |
137 | versioned_symbol (libm, __log, log, GLIBC_2_29); | |
138 | libm_alias_double_other (__log, log) | |
139 | # else | |
140 | libm_alias_double (__log, log) | |
141 | # endif | |
af968f62 | 142 | #endif |