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1//===-- Utilities for trigonometric 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-exception6//7//===----------------------------------------------------------------------===//8 9#ifndef LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_H10#define LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_H11 12#include "src/__support/FPUtil/FPBits.h"13#include "src/__support/FPUtil/multiply_add.h"14#include "src/__support/FPUtil/nearest_integer.h"15#include "src/__support/common.h"16#include "src/__support/macros/config.h"17 18namespace LIBC_NAMESPACE_DECL {19 20namespace generic {21 22static constexpr uint32_t FAST_PASS_BOUND = 0x4a80'0000U; // 2^2223 24static constexpr int N_ENTRIES = 8;25 26// We choose to split bits of 32/pi into 28-bit precision pieces, so that the27// product of x * THIRTYTWO_OVER_PI_28[i] is exact.28// These are generated by Sollya with:29// > a1 = D(round(32/pi, 28, RN)); a1;30// > a2 = D(round(32/pi - a1, 28, RN)); a2;31// > a3 = D(round(32/pi - a1 - a2, 28, RN)); a3;32// > a4 = D(round(32/pi - a1 - a2 - a3, 28, RN)); a4;33// ...34static constexpr double THIRTYTWO_OVER_PI_28[N_ENTRIES] = {35 0x1.45f306ep+3, -0x1.b1bbeaep-28, 0x1.3f84ebp-57, -0x1.7056592p-87,36 0x1.c0db62ap-116, -0x1.4cd8778p-145, -0x1.bef806cp-174, 0x1.63abdecp-204};37 38// Exponents of the least significant bits of the corresponding entries in39// THIRTYTWO_OVER_PI_28.40static constexpr int THIRTYTWO_OVER_PI_28_LSB_EXP[N_ENTRIES] = {41 -24, -55, -81, -114, -143, -170, -200, -230};42 43// Return k and y, where44// k = round(x * 16 / pi) and y = (x * 16 / pi) - k.45LIBC_INLINE int64_t small_range_reduction(double x, double &y) {46 double prod = x * THIRTYTWO_OVER_PI_28[0];47 double kd = fputil::nearest_integer(prod);48 y = prod - kd;49 y = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[1], y);50 y = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[2], y);51 return static_cast<int64_t>(kd);52}53 54// Return k and y, where55// k = round(x * 32 / pi) and y = (x * 32 / pi) - k.56// For large range, there are at most 2 parts of THIRTYTWO_OVER_PI_2857// contributing to the lowest 6 binary digits (k & 63). If the least58// significant bit of x * the least significant bit of THIRTYTWO_OVER_PI_28[i]59// >= 64, we can completely ignore THIRTYTWO_OVER_PI_28[i].60LIBC_INLINE int64_t large_range_reduction(double x, int x_exp, double &y) {61 int idx = 0;62 y = 0;63 int x_lsb_exp_m4 = x_exp - fputil::FPBits<float>::FRACTION_LEN;64 65 // Skipping the first parts of 32/pi such that:66 // LSB of x * LSB of THIRTYTWO_OVER_PI_28[i] >= 32.67 while (x_lsb_exp_m4 + THIRTYTWO_OVER_PI_28_LSB_EXP[idx] > 5)68 ++idx;69 70 double prod_hi = x * THIRTYTWO_OVER_PI_28[idx];71 // Get the integral part of x * THIRTYTWO_OVER_PI_28[idx]72 double k_hi = fputil::nearest_integer(prod_hi);73 // Get the fractional part of x * THIRTYTWO_OVER_PI_28[idx]74 double frac = prod_hi - k_hi;75 double prod_lo = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[idx + 1], frac);76 double k_lo = fputil::nearest_integer(prod_lo);77 78 // Now y is the fractional parts.79 y = prod_lo - k_lo;80 y = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[idx + 2], y);81 y = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[idx + 3], y);82 83 return static_cast<int64_t>(k_hi) + static_cast<int64_t>(k_lo);84}85 86} // namespace generic87 88} // namespace LIBC_NAMESPACE_DECL89 90#endif // LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_H91