163d2df00STue Ly //===-- Common constants for math functions ---------------------*- C++ -*-===// 263d2df00STue Ly // 363d2df00STue Ly // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 463d2df00STue Ly // See https://llvm.org/LICENSE.txt for license information. 563d2df00STue Ly // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 663d2df00STue Ly // 763d2df00STue Ly //===----------------------------------------------------------------------===// 863d2df00STue Ly 963d2df00STue Ly #ifndef LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H 1063d2df00STue Ly #define LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H 1163d2df00STue Ly 128ca614aaSTue Ly #include "src/__support/FPUtil/triple_double.h" 13*5ff3ff33SPetr Hosek #include "src/__support/macros/config.h" 14a0c92a38STue Ly #include "src/__support/number_pair.h" 15a0c92a38STue Ly 16*5ff3ff33SPetr Hosek namespace LIBC_NAMESPACE_DECL { 1763d2df00STue Ly 1863d2df00STue Ly // Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127. 1963d2df00STue Ly extern const double ONE_OVER_F[128]; 2063d2df00STue Ly 219e7688c7STue Ly // Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127. 229e7688c7STue Ly extern const double LOG_F[128]; 239e7688c7STue Ly 249af8dca7STue Ly // Lookup table for range reduction constants r for logarithms. 259af8dca7STue Ly extern const float R[128]; 269af8dca7STue Ly 27bc8e87efSTue Ly // Lookup table for range reduction constants r for logarithms. 28bc8e87efSTue Ly extern const double RD[128]; 29bc8e87efSTue Ly 30a0c92a38STue Ly // Lookup table for compensated constants for exact range reduction when FMA 31a0c92a38STue Ly // instructions are not available. 32a0c92a38STue Ly extern const double CD[128]; 33a0c92a38STue Ly 34bc8e87efSTue Ly // Lookup table for -log(r) 35bc8e87efSTue Ly extern const double LOG_R[128]; 36a0c92a38STue Ly extern const NumberPair<double> LOG_R_DD[128]; 37a0c92a38STue Ly 38bc7a3bd8Slntue // Lookup table for -log2(r) 39bc7a3bd8Slntue extern const double LOG2_R[128]; 40bc7a3bd8Slntue 41a0c92a38STue Ly // Minimax polynomial for (log(1 + x) - x)/x^2, generated by sollya with: 42a0c92a38STue Ly // > P = fpminimax((log(1 + x) - x)/x^2, 5, [|D...|], [-2^-8, 2^-7]); 43a0c92a38STue Ly constexpr double LOG_COEFFS[6] = {-0x1.fffffffffffffp-2, 0x1.5555555554a9bp-2, 44a0c92a38STue Ly -0x1.0000000094567p-2, 0x1.99999dcc9823cp-3, 45a0c92a38STue Ly -0x1.55550ac2e537ap-3, 0x1.21a02c4e624d7p-3}; 46a0c92a38STue Ly 47a68bbf42STue Ly // Logarithm Range Reduction - Step 2, 3, and 4. 48a68bbf42STue Ly extern const int S2[193]; 49a68bbf42STue Ly extern const int S3[161]; 50a68bbf42STue Ly extern const int S4[130]; 51a68bbf42STue Ly 52bc7a3bd8Slntue extern const double R2[193]; 53bc7a3bd8Slntue 54a0c92a38STue Ly // log(2) generated by Sollya with: 55a0c92a38STue Ly // > a = 2^-43 * nearestint(2^43*log(2)); 56a0c92a38STue Ly // LSB = 2^-43 is chosen so that e_x * LOG_2_HI is exact for -1075 < e_x < 1024. 57a0c92a38STue Ly constexpr double LOG_2_HI = 0x1.62e42fefa38p-1; // LSB = 2^-43 58a0c92a38STue Ly // > b = round(log10(2) - a, D, RN); 59a0c92a38STue Ly constexpr double LOG_2_LO = 0x1.ef35793c7673p-45; // LSB = 2^-97 60bc8e87efSTue Ly 6164af346bSTue Ly // Lookup table for exp(m) with m = -104, ..., 89. 6264af346bSTue Ly // -104 = floor(log(single precision's min denormal)) 6364af346bSTue Ly // 89 = ceil(log(single precision's max normal)) 6464af346bSTue Ly // Table is generated with Sollya as follow: 6564af346bSTue Ly // > display = hexadecimal; 6664af346bSTue Ly // > for i from -104 to 89 do { D(exp(i)); }; 6764af346bSTue Ly extern const double EXP_M1[195]; 6864af346bSTue Ly 6964af346bSTue Ly // Lookup table for exp(m * 2^(-7)) with m = 0, ..., 127. 7064af346bSTue Ly // Table is generated with Sollya as follow: 7164af346bSTue Ly // > display = hexadecimal; 7264af346bSTue Ly // > for i from 0 to 127 do { D(exp(i / 128)); }; 7364af346bSTue Ly extern const double EXP_M2[128]; 7464af346bSTue Ly 758ca614aaSTue Ly // Lookup table for 2^(k * 2^-6) with k = 0..63. 768ca614aaSTue Ly extern const fputil::TripleDouble EXP2_MID1[64]; 778ca614aaSTue Ly 788ca614aaSTue Ly // Lookup table for 2^(k * 2^-12) with k = 0..63. 798ca614aaSTue Ly extern const fputil::TripleDouble EXP2_MID2[64]; 808ca614aaSTue Ly 81*5ff3ff33SPetr Hosek } // namespace LIBC_NAMESPACE_DECL 8263d2df00STue Ly 8363d2df00STue Ly #endif // LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H 84