1//===-- Common constants for math functions ---------------------*- C++ -*-===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8
9#ifndef LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H
10#define LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H
11
12#include "src/__support/FPUtil/triple_double.h"
13#include "src/__support/macros/config.h"
14#include "src/__support/number_pair.h"
15
16namespace LIBC_NAMESPACE_DECL {
17
18// Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127,
19// computed and stored as float precision constants.
20extern const float ONE_OVER_F_FLOAT[128];
21
22// Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127.
23extern const double ONE_OVER_F[128];
24
25// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127,
26// computed and stored as float precision constants.
27extern const float LOG_F_FLOAT[128];
28
29// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127.
30extern const double LOG_F[128];
31
32// Lookup table for range reduction constants r for logarithms.
33extern const float R[128];
34
35// Lookup table for range reduction constants r for logarithms.
36extern const double RD[128];
37
38// Lookup table for compensated constants for exact range reduction when FMA
39// instructions are not available.
40extern const double CD[128];
41
42// Lookup table for -log(r)
43extern const double LOG_R[128];
44extern const NumberPair<double> LOG_R_DD[128];
45
46// Lookup table for -log2(r)
47extern const double LOG2_R[128];
48
49// Minimax polynomial for (log(1 + x) - x)/x^2, generated by sollya with:
50// > P = fpminimax((log(1 + x) - x)/x^2, 5, [|D...|], [-2^-8, 2^-7]);
51constexpr double LOG_COEFFS[6] = {-0x1.fffffffffffffp-2, 0x1.5555555554a9bp-2,
52 -0x1.0000000094567p-2, 0x1.99999dcc9823cp-3,
53 -0x1.55550ac2e537ap-3, 0x1.21a02c4e624d7p-3};
54
55// Logarithm Range Reduction - Step 2, 3, and 4.
56extern const int S2[193];
57extern const int S3[161];
58extern const int S4[130];
59
60extern const double R2[193];
61
62// log(2) generated by Sollya with:
63// > a = 2^-43 * nearestint(2^43*log(2));
64// LSB = 2^-43 is chosen so that e_x * LOG_2_HI is exact for -1075 < e_x < 1024.
65constexpr double LOG_2_HI = 0x1.62e42fefa38p-1; // LSB = 2^-43
66// > b = round(log10(2) - a, D, RN);
67constexpr double LOG_2_LO = 0x1.ef35793c7673p-45; // LSB = 2^-97
68
69// Lookup table for exp(m) with m = -104, ..., 89.
70// -104 = floor(log(single precision's min denormal))
71// 89 = ceil(log(single precision's max normal))
72// Table is generated with Sollya as follow:
73// > display = hexadecimal;
74// > for i from -104 to 89 do { D(exp(i)); };
75extern const double EXP_M1[195];
76
77// Lookup table for exp(m * 2^(-7)) with m = 0, ..., 127.
78// Table is generated with Sollya as follow:
79// > display = hexadecimal;
80// > for i from 0 to 127 do { D(exp(i / 128)); };
81extern const double EXP_M2[128];
82
83// Lookup table for 2^(k * 2^-6) with k = 0..63.
84extern const fputil::TripleDouble EXP2_MID1[64];
85
86// Lookup table for 2^(k * 2^-12) with k = 0..63.
87extern const fputil::TripleDouble EXP2_MID2[64];
88
89} // namespace LIBC_NAMESPACE_DECL
90
91#endif // LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H
92

source code of libc/src/math/generic/common_constants.h