llvm/llvm/include/llvm/Support/MathExtras.h

//===-- llvm/Support/MathExtras.h - Useful math 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
//
//===----------------------------------------------------------------------===//
//
// This file contains some functions that are useful for math stuff.
//
//===----------------------------------------------------------------------===//

#ifndef LLVM_SUPPORT_MATHEXTRAS_H
#define LLVM_SUPPORT_MATHEXTRAS_H

#include "llvm/ADT/bit.h"
#include "llvm/Support/Compiler.h"
#include <cassert>
#include <climits>
#include <cstdint>
#include <cstring>
#include <limits>
#include <type_traits>

namespace llvm {
/// Some template parameter helpers to optimize for bitwidth, for functions that
/// take multiple arguments.

// We can't verify signedness, since callers rely on implicit coercions to
// signed/unsigned.
enableif_int;

// Use std::common_type_t to widen only up to the widest argument.
common_uint;
common_sint;

/// Mathematical constants.
namespace numbers {
// TODO: Track C++20 std::numbers.
// TODO: Favor using the hexadecimal FP constants (requires C++17).
constexpr double e          = …, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113
                 egamma     = …, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620
                 ln2        = …, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162
                 ln10       = …, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392
                 log2e      = …, // (0x1.71547652b82feP+0)
                 log10e     = …, // (0x1.bcb7b1526e50eP-2)
                 pi         = …, // (0x1.921fb54442d18P+1) https://oeis.org/A000796
                 inv_pi     = …, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541
                 sqrtpi     = …, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161
                 inv_sqrtpi = …, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197
                 sqrt2      = …, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219
                 inv_sqrt2  = …, // (0x1.6a09e667f3bcdP-1)
                 sqrt3      = …, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194
                 inv_sqrt3  = …, // (0x1.279a74590331cP-1)
                 phi        = …; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622
constexpr float ef          = …, // (0x1.5bf0a8P+1) https://oeis.org/A001113
                egammaf     = …, // (0x1.2788d0P-1) https://oeis.org/A001620
                ln2f        = …, // (0x1.62e430P-1) https://oeis.org/A002162
                ln10f       = …, // (0x1.26bb1cP+1) https://oeis.org/A002392
                log2ef      = …, // (0x1.715476P+0)
                log10ef     = …, // (0x1.bcb7b2P-2)
                pif         = …, // (0x1.921fb6P+1) https://oeis.org/A000796
                inv_pif     = …, // (0x1.45f306P-2) https://oeis.org/A049541
                sqrtpif     = …, // (0x1.c5bf8aP+0) https://oeis.org/A002161
                inv_sqrtpif = …, // (0x1.20dd76P-1) https://oeis.org/A087197
                sqrt2f      = …, // (0x1.6a09e6P+0) https://oeis.org/A002193
                inv_sqrt2f  = …, // (0x1.6a09e6P-1)
                sqrt3f      = …, // (0x1.bb67aeP+0) https://oeis.org/A002194
                inv_sqrt3f  = …, // (0x1.279a74P-1)
                phif        = …; // (0x1.9e377aP+0) https://oeis.org/A001622
} // namespace numbers

/// Create a bitmask with the N right-most bits set to 1, and all other
/// bits set to 0.  Only unsigned types are allowed.
template <typename T> T maskTrailingOnes(unsigned N) { … }

/// Create a bitmask with the N left-most bits set to 1, and all other
/// bits set to 0.  Only unsigned types are allowed.
template <typename T> T maskLeadingOnes(unsigned N) { … }

/// Create a bitmask with the N right-most bits set to 0, and all other
/// bits set to 1.  Only unsigned types are allowed.
template <typename T> T maskTrailingZeros(unsigned N) { … }

/// Create a bitmask with the N left-most bits set to 0, and all other
/// bits set to 1.  Only unsigned types are allowed.
template <typename T> T maskLeadingZeros(unsigned N) { … }

/// Macro compressed bit reversal table for 256 bits.
///
/// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
static const unsigned char BitReverseTable256[256] = …;

/// Reverse the bits in \p Val.
template <typename T> T reverseBits(T Val) { … }

// NOTE: The following support functions use the _32/_64 extensions instead of
// type overloading so that signed and unsigned integers can be used without
// ambiguity.

/// Return the high 32 bits of a 64 bit value.
constexpr uint32_t Hi_32(uint64_t Value) { … }

/// Return the low 32 bits of a 64 bit value.
constexpr uint32_t Lo_32(uint64_t Value) { … }

/// Make a 64-bit integer from a high / low pair of 32-bit integers.
constexpr uint64_t Make_64(uint32_t High, uint32_t Low) { … }

/// Checks if an integer fits into the given bit width.
template <unsigned N> constexpr bool isInt(int64_t x) { … }

/// Checks if a signed integer is an N bit number shifted left by S.
template <unsigned N, unsigned S>
constexpr bool isShiftedInt(int64_t x) { … }

/// Checks if an unsigned integer fits into the given bit width.
template <unsigned N> constexpr bool isUInt(uint64_t x) { … }

/// Checks if a unsigned integer is an N bit number shifted left by S.
template <unsigned N, unsigned S>
constexpr bool isShiftedUInt(uint64_t x) { … }

/// Gets the maximum value for a N-bit unsigned integer.
inline uint64_t maxUIntN(uint64_t N) { … }

/// Gets the minimum value for a N-bit signed integer.
inline int64_t minIntN(int64_t N) { … }

/// Gets the maximum value for a N-bit signed integer.
inline int64_t maxIntN(int64_t N) { … }

/// Checks if an unsigned integer fits into the given (dynamic) bit width.
inline bool isUIntN(unsigned N, uint64_t x) { … }

/// Checks if an signed integer fits into the given (dynamic) bit width.
inline bool isIntN(unsigned N, int64_t x) { … }

/// Return true if the argument is a non-empty sequence of ones starting at the
/// least significant bit with the remainder zero (32 bit version).
/// Ex. isMask_32(0x0000FFFFU) == true.
constexpr bool isMask_32(uint32_t Value) { … }

/// Return true if the argument is a non-empty sequence of ones starting at the
/// least significant bit with the remainder zero (64 bit version).
constexpr bool isMask_64(uint64_t Value) { … }

/// Return true if the argument contains a non-empty sequence of ones with the
/// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
constexpr bool isShiftedMask_32(uint32_t Value) { … }

/// Return true if the argument contains a non-empty sequence of ones with the
/// remainder zero (64 bit version.)
constexpr bool isShiftedMask_64(uint64_t Value) { … }

/// Return true if the argument is a power of two > 0.
/// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
constexpr bool isPowerOf2_32(uint32_t Value) { … }

/// Return true if the argument is a power of two > 0 (64 bit edition.)
constexpr bool isPowerOf2_64(uint64_t Value) { … }

/// Return true if the argument contains a non-empty sequence of ones with the
/// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
/// If true, \p MaskIdx will specify the index of the lowest set bit and \p
/// MaskLen is updated to specify the length of the mask, else neither are
/// updated.
inline bool isShiftedMask_32(uint32_t Value, unsigned &MaskIdx,
                             unsigned &MaskLen) { … }

/// Return true if the argument contains a non-empty sequence of ones with the
/// remainder zero (64 bit version.) If true, \p MaskIdx will specify the index
/// of the lowest set bit and \p MaskLen is updated to specify the length of the
/// mask, else neither are updated.
inline bool isShiftedMask_64(uint64_t Value, unsigned &MaskIdx,
                             unsigned &MaskLen) { … }

/// Compile time Log2.
/// Valid only for positive powers of two.
template <size_t kValue> constexpr size_t CTLog2() { … }

template <> constexpr size_t CTLog2<1>() { … }

/// Return the floor log base 2 of the specified value, -1 if the value is zero.
/// (32 bit edition.)
/// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
inline unsigned Log2_32(uint32_t Value) { … }

/// Return the floor log base 2 of the specified value, -1 if the value is zero.
/// (64 bit edition.)
inline unsigned Log2_64(uint64_t Value) { … }

/// Return the ceil log base 2 of the specified value, 32 if the value is zero.
/// (32 bit edition).
/// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
inline unsigned Log2_32_Ceil(uint32_t Value) { … }

/// Return the ceil log base 2 of the specified value, 64 if the value is zero.
/// (64 bit edition.)
inline unsigned Log2_64_Ceil(uint64_t Value) { … }

/// A and B are either alignments or offsets. Return the minimum alignment that
/// may be assumed after adding the two together.
template <typename U, typename V, typename T = common_uint<U, V>>
constexpr T MinAlign(U A, V B) { … }

/// Fallback when arguments aren't integral.
constexpr uint64_t MinAlign(uint64_t A, uint64_t B) { … }

/// Returns the next power of two (in 64-bits) that is strictly greater than A.
/// Returns zero on overflow.
constexpr uint64_t NextPowerOf2(uint64_t A) { … }

/// Returns the power of two which is greater than or equal to the given value.
/// Essentially, it is a ceil operation across the domain of powers of two.
inline uint64_t PowerOf2Ceil(uint64_t A) { … }

/// Returns the integer ceil(Numerator / Denominator). Unsigned version.
/// Guaranteed to never overflow.
template <typename U, typename V, typename T = common_uint<U, V>>
constexpr T divideCeil(U Numerator, V Denominator) { … }

/// Fallback when arguments aren't integral.
constexpr uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) { … }

// Check whether divideCeilSigned or divideFloorSigned would overflow. This
// happens only when Numerator = INT_MIN and Denominator = -1.
template <typename U, typename V>
constexpr bool divideSignedWouldOverflow(U Numerator, V Denominator) { … }

/// Returns the integer ceil(Numerator / Denominator). Signed version.
/// Overflow is explicitly forbidden with an assert.
template <typename U, typename V, typename T = common_sint<U, V>>
constexpr T divideCeilSigned(U Numerator, V Denominator) { … }

/// Returns the integer floor(Numerator / Denominator). Signed version.
/// Overflow is explicitly forbidden with an assert.
template <typename U, typename V, typename T = common_sint<U, V>>
constexpr T divideFloorSigned(U Numerator, V Denominator) { … }

/// Returns the remainder of the Euclidean division of LHS by RHS. Result is
/// always non-negative.
template <typename U, typename V, typename T = common_sint<U, V>>
constexpr T mod(U Numerator, V Denominator) { … }

/// Returns (Numerator / Denominator) rounded by round-half-up. Guaranteed to
/// never overflow.
template <typename U, typename V, typename T = common_uint<U, V>>
constexpr T divideNearest(U Numerator, V Denominator) { … }

/// Returns the next integer (mod 2**nbits) that is greater than or equal to
/// \p Value and is a multiple of \p Align. \p Align must be non-zero.
///
/// Examples:
/// \code
///   alignTo(5, 8) = 8
///   alignTo(17, 8) = 24
///   alignTo(~0LL, 8) = 0
///   alignTo(321, 255) = 510
/// \endcode
///
/// Will overflow only if result is not representable in T.
template <typename U, typename V, typename T = common_uint<U, V>>
constexpr T alignTo(U Value, V Align) { … }

/// Fallback when arguments aren't integral.
constexpr uint64_t alignTo(uint64_t Value, uint64_t Align) { … }

/// Will overflow only if result is not representable in T.
template <typename U, typename V, typename T = common_uint<U, V>>
constexpr T alignToPowerOf2(U Value, V Align) { … }

/// Fallback when arguments aren't integral.
constexpr uint64_t alignToPowerOf2(uint64_t Value, uint64_t Align) { … }

/// If non-zero \p Skew is specified, the return value will be a minimal integer
/// that is greater than or equal to \p Size and equal to \p A * N + \p Skew for
/// some integer N. If \p Skew is larger than \p A, its value is adjusted to '\p
/// Skew mod \p A'. \p Align must be non-zero.
///
/// Examples:
/// \code
///   alignTo(5, 8, 7) = 7
///   alignTo(17, 8, 1) = 17
///   alignTo(~0LL, 8, 3) = 3
///   alignTo(321, 255, 42) = 552
/// \endcode
///
/// May overflow.
template <typename U, typename V, typename W,
          typename T = common_uint<common_uint<U, V>, W>>
constexpr T alignTo(U Value, V Align, W Skew) { … }

/// Returns the next integer (mod 2**nbits) that is greater than or equal to
/// \p Value and is a multiple of \c Align. \c Align must be non-zero.
///
/// Will overflow only if result is not representable in T.
template <auto Align, typename V, typename T = common_uint<decltype(Align), V>>
constexpr T alignTo(V Value) { … }

/// Returns the largest unsigned integer less than or equal to \p Value and is
/// \p Skew mod \p Align. \p Align must be non-zero. Guaranteed to never
/// overflow.
template <typename U, typename V, typename W = uint8_t,
          typename T = common_uint<common_uint<U, V>, W>>
constexpr T alignDown(U Value, V Align, W Skew = 0) { … }

/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
/// Requires B <= 32.
template <unsigned B> constexpr int32_t SignExtend32(uint32_t X) { … }

/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
/// Requires B <= 32.
inline int32_t SignExtend32(uint32_t X, unsigned B) { … }

/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
/// Requires B <= 64.
template <unsigned B> constexpr int64_t SignExtend64(uint64_t x) { … }

/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
/// Requires B <= 64.
inline int64_t SignExtend64(uint64_t X, unsigned B) { … }

/// Subtract two unsigned integers, X and Y, of type T and return the absolute
/// value of the result.
template <typename U, typename V, typename T = common_uint<U, V>>
constexpr T AbsoluteDifference(U X, V Y) { … }

/// Add two unsigned integers, X and Y, of type T.  Clamp the result to the
/// maximum representable value of T on overflow.  ResultOverflowed indicates if
/// the result is larger than the maximum representable value of type T.
template <typename T>
std::enable_if_t<std::is_unsigned_v<T>, T>
SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) { … }

/// Add multiple unsigned integers of type T.  Clamp the result to the
/// maximum representable value of T on overflow.
template <class T, class... Ts>
std::enable_if_t<std::is_unsigned_v<T>, T> SaturatingAdd(T X, T Y, T Z,
                                                         Ts... Args) { … }

/// Multiply two unsigned integers, X and Y, of type T.  Clamp the result to the
/// maximum representable value of T on overflow.  ResultOverflowed indicates if
/// the result is larger than the maximum representable value of type T.
template <typename T>
std::enable_if_t<std::is_unsigned_v<T>, T>
SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) { … }

/// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
/// the product. Clamp the result to the maximum representable value of T on
/// overflow. ResultOverflowed indicates if the result is larger than the
/// maximum representable value of type T.
template <typename T>
std::enable_if_t<std::is_unsigned_v<T>, T>
SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) { … }

/// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
extern const float huge_valf;

/// Add two signed integers, computing the two's complement truncated result,
/// returning true if overflow occurred.
template <typename T>
std::enable_if_t<std::is_signed_v<T>, T> AddOverflow(T X, T Y, T &Result) { … }

/// Subtract two signed integers, computing the two's complement truncated
/// result, returning true if an overflow ocurred.
template <typename T>
std::enable_if_t<std::is_signed_v<T>, T> SubOverflow(T X, T Y, T &Result) { … }

/// Multiply two signed integers, computing the two's complement truncated
/// result, returning true if an overflow ocurred.
template <typename T>
std::enable_if_t<std::is_signed_v<T>, T> MulOverflow(T X, T Y, T &Result) { … }

/// Type to force float point values onto the stack, so that x86 doesn't add
/// hidden precision, avoiding rounding differences on various platforms.
#if defined(__i386__) || defined(_M_IX86)
using stack_float_t = volatile float;
#else
stack_float_t;
#endif

} // namespace llvm

#endif