llvm/libc/src/math/generic/range_reduction.h

//===-- Utilities for trigonometric functions -------------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#ifndef LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_H
#define LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_H

#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/common.h"
#include "src/__support/macros/config.h"

namespace LIBC_NAMESPACE_DECL {

namespace generic {

static constexpr uint32_t FAST_PASS_BOUND = …; // 2^22

static constexpr int N_ENTRIES = …;

// We choose to split bits of 32/pi into 28-bit precision pieces, so that the
// product of x * THIRTYTWO_OVER_PI_28[i] is exact.
// These are generated by Sollya with:
// > a1 = D(round(32/pi, 28, RN)); a1;
// > a2 = D(round(32/pi - a1, 28, RN)); a2;
// > a3 = D(round(32/pi - a1 - a2, 28, RN)); a3;
// > a4 = D(round(32/pi - a1 - a2 - a3, 28, RN)); a4;
// ...
static constexpr double THIRTYTWO_OVER_PI_28[N_ENTRIES] = …;

// Exponents of the least significant bits of the corresponding entries in
// THIRTYTWO_OVER_PI_28.
static constexpr int THIRTYTWO_OVER_PI_28_LSB_EXP[N_ENTRIES] = …;

// Return k and y, where
//   k = round(x * 16 / pi) and y = (x * 16 / pi) - k.
LIBC_INLINE int64_t small_range_reduction(double x, double &y) { … }

// Return k and y, where
//   k = round(x * 32 / pi) and y = (x * 32 / pi) - k.
// For large range, there are at most 2 parts of THIRTYTWO_OVER_PI_28
// contributing to the lowest 6 binary digits (k & 63).  If the least
// significant bit of x * the least significant bit of THIRTYTWO_OVER_PI_28[i]
// >= 64, we can completely ignore THIRTYTWO_OVER_PI_28[i].
LIBC_INLINE int64_t large_range_reduction(double x, int x_exp, double &y) { … }

} // namespace generic

} // namespace LIBC_NAMESPACE_DECL

#endif // LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_H