Warning: This file is not a C or C++ file. It does not have highlighting.
| 1 | //===-- Utilities for trigonometric functions with FMA ----------*- 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_RANGE_REDUCTION_FMA_H |
| 10 | #define LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_FMA_H |
| 11 | |
| 12 | #include "src/__support/FPUtil/FMA.h" |
| 13 | #include "src/__support/FPUtil/FPBits.h" |
| 14 | #include "src/__support/FPUtil/nearest_integer.h" |
| 15 | #include "src/__support/macros/config.h" |
| 16 | |
| 17 | namespace LIBC_NAMESPACE_DECL { |
| 18 | |
| 19 | namespace fma { |
| 20 | |
| 21 | static constexpr uint32_t FAST_PASS_BOUND = 0x5600'0000U; // 2^45 |
| 22 | |
| 23 | // Digits of 32/pi, generated by Sollya with: |
| 24 | // > a0 = D(32/pi); |
| 25 | // > a1 = D(32/pi - a0); |
| 26 | // > a2 = D(32/pi - a0 - a1); |
| 27 | // > a3 = D(32/pi - a0 - a1 - a2); |
| 28 | static constexpr double THIRTYTWO_OVER_PI[5] = { |
| 29 | 0x1.45f306dc9c883p+3, -0x1.6b01ec5417056p-51, -0x1.6447e493ad4cep-105, |
| 30 | 0x1.e21c820ff28b2p-159, -0x1.508510ea79237p-214}; |
| 31 | |
| 32 | // Return k and y, where |
| 33 | // k = round(x * 32 / pi) and y = (x * 32 / pi) - k. |
| 34 | LIBC_INLINE int64_t small_range_reduction(double x, double &y) { |
| 35 | double kd = fputil::nearest_integer(x * THIRTYTWO_OVER_PI[0]); |
| 36 | y = fputil::fma<double>(x, THIRTYTWO_OVER_PI[0], -kd); |
| 37 | y = fputil::fma<double>(x, THIRTYTWO_OVER_PI[1], y); |
| 38 | return static_cast<int64_t>(kd); |
| 39 | } |
| 40 | |
| 41 | // Return k and y, where |
| 42 | // k = round(x * 32 / pi) and y = (x * 32 / pi) - k. |
| 43 | // This is used for sinf, cosf, sincosf. |
| 44 | LIBC_INLINE int64_t large_range_reduction(double x, int x_exp, double &y) { |
| 45 | // 2^45 <= |x| < 2^99 |
| 46 | if (x_exp < 99) { |
| 47 | // - When x < 2^99, the full exact product of x * THIRTYTWO_OVER_PI[0] |
| 48 | // contains at least one integral bit <= 2^5. |
| 49 | // - When 2^45 <= |x| < 2^55, the lowest 6 unit bits are contained |
| 50 | // in the last 12 bits of double(x * THIRTYTWO_OVER_PI[0]). |
| 51 | // - When |x| >= 2^55, the LSB of double(x * THIRTYTWO_OVER_PI[0]) is at |
| 52 | // least 2^6. |
| 53 | fputil::FPBits<double> prod_hi(x * THIRTYTWO_OVER_PI[0]); |
| 54 | prod_hi.set_uintval(prod_hi.uintval() & |
| 55 | ((x_exp < 55) ? (~0xfffULL) : (~0ULL))); // |x| < 2^55 |
| 56 | double k_hi = fputil::nearest_integer(prod_hi.get_val()); |
| 57 | double truncated_prod = fputil::fma<double>(x, THIRTYTWO_OVER_PI[0], -k_hi); |
| 58 | double prod_lo = |
| 59 | fputil::fma<double>(x, THIRTYTWO_OVER_PI[1], truncated_prod); |
| 60 | double k_lo = fputil::nearest_integer(prod_lo); |
| 61 | y = fputil::fma<double>(x, THIRTYTWO_OVER_PI[1], truncated_prod - k_lo); |
| 62 | y = fputil::fma<double>(x, THIRTYTWO_OVER_PI[2], y); |
| 63 | y = fputil::fma<double>(x, THIRTYTWO_OVER_PI[3], y); |
| 64 | |
| 65 | return static_cast<int64_t>(k_lo); |
| 66 | } |
| 67 | |
| 68 | // - When x >= 2^110, the full exact product of x * THIRTYTWO_OVER_PI[0] does |
| 69 | // not contain any of the lowest 6 unit bits, so we can ignore it completely. |
| 70 | // - When 2^99 <= |x| < 2^110, the lowest 6 unit bits are contained |
| 71 | // in the last 12 bits of double(x * THIRTYTWO_OVER_PI[1]). |
| 72 | // - When |x| >= 2^110, the LSB of double(x * THIRTYTWO_OVER_PI[1]) is at |
| 73 | // least 64. |
| 74 | fputil::FPBits<double> prod_hi(x * THIRTYTWO_OVER_PI[1]); |
| 75 | prod_hi.set_uintval(prod_hi.uintval() & |
| 76 | ((x_exp < 110) ? (~0xfffULL) : (~0ULL))); // |x| < 2^110 |
| 77 | double k_hi = fputil::nearest_integer(prod_hi.get_val()); |
| 78 | double truncated_prod = fputil::fma<double>(x, THIRTYTWO_OVER_PI[1], -k_hi); |
| 79 | double prod_lo = fputil::fma<double>(x, THIRTYTWO_OVER_PI[2], truncated_prod); |
| 80 | double k_lo = fputil::nearest_integer(prod_lo); |
| 81 | y = fputil::fma<double>(x, THIRTYTWO_OVER_PI[2], truncated_prod - k_lo); |
| 82 | y = fputil::fma<double>(x, THIRTYTWO_OVER_PI[3], y); |
| 83 | y = fputil::fma<double>(x, THIRTYTWO_OVER_PI[4], y); |
| 84 | |
| 85 | return static_cast<int64_t>(k_lo); |
| 86 | } |
| 87 | |
| 88 | } // namespace fma |
| 89 | |
| 90 | } // namespace LIBC_NAMESPACE_DECL |
| 91 | |
| 92 | #endif // LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_FMA_H |
| 93 |
Warning: This file is not a C or C++ file. It does not have highlighting.