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/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* vim: set ts=8 sts=2 et sw=2 tw=80: */
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
/* mfbt maths algorithms. */
#ifndef mozilla_MathAlgorithms_h
#define mozilla_MathAlgorithms_h
#include "mozilla/Assertions.h"
#include <cmath>
#include <algorithm>
#include <limits.h>
#include <stdint.h>
#include <type_traits>
namespace mozilla {
namespace detail {
template <typename T>
struct AllowDeprecatedAbsFixed : std::false_type {};
template <>
struct AllowDeprecatedAbsFixed<int32_t> : std::true_type {};
template <>
struct AllowDeprecatedAbsFixed<int64_t> : std::true_type {};
template <typename T>
struct AllowDeprecatedAbs : AllowDeprecatedAbsFixed<T> {};
template <>
struct AllowDeprecatedAbs<int> : std::true_type {};
template <>
struct AllowDeprecatedAbs<long> : std::true_type {};
} // namespace detail
// DO NOT USE DeprecatedAbs. It exists only until its callers can be converted
// to Abs below, and it will be removed when all callers have been changed.
template <typename T>
inline std::enable_if_t<detail::AllowDeprecatedAbs<T>::value, T> DeprecatedAbs(
const T aValue) {
// The absolute value of the smallest possible value of a signed-integer type
// won't fit in that type (on twos-complement systems -- and we're blithely
// assuming we're on such systems, for the non-<stdint.h> types listed above),
// so assert that the input isn't that value.
//
// This is the case if: the value is non-negative; or if adding one (giving a
// value in the range [-maxvalue, 0]), then negating (giving a value in the
// range [0, maxvalue]), doesn't produce maxvalue (because in twos-complement,
// (minvalue + 1) == -maxvalue).
MOZ_ASSERT(aValue >= 0 ||
-(aValue + 1) != T((1ULL << (CHAR_BIT * sizeof(T) - 1)) - 1),
"You can't negate the smallest possible negative integer!");
return aValue >= 0 ? aValue : -aValue;
}
namespace detail {
template <typename T, typename = void>
struct AbsReturnType;
template <typename T>
struct AbsReturnType<
T, std::enable_if_t<std::is_integral_v<T> && std::is_signed_v<T>>> {
using Type = std::make_unsigned_t<T>;
};
template <typename T>
struct AbsReturnType<T, std::enable_if_t<std::is_floating_point_v<T>>> {
using Type = T;
};
} // namespace detail
template <typename T>
inline constexpr typename detail::AbsReturnType<T>::Type Abs(const T aValue) {
using ReturnType = typename detail::AbsReturnType<T>::Type;
return aValue >= 0 ? ReturnType(aValue) : ~ReturnType(aValue) + 1;
}
template <>
inline float Abs<float>(const float aFloat) {
return std::fabs(aFloat);
}
template <>
inline double Abs<double>(const double aDouble) {
return std::fabs(aDouble);
}
template <>
inline long double Abs<long double>(const long double aLongDouble) {
return std::fabs(aLongDouble);
}
} // namespace mozilla
#if defined(_MSC_VER) && (defined(_M_IX86) || defined(_M_AMD64) || \
defined(_M_X64) || defined(_M_ARM64))
# define MOZ_BITSCAN_WINDOWS
# include <intrin.h>
# pragma intrinsic(_BitScanForward, _BitScanReverse)
# if defined(_M_AMD64) || defined(_M_X64) || defined(_M_ARM64)
# define MOZ_BITSCAN_WINDOWS64
# pragma intrinsic(_BitScanForward64, _BitScanReverse64)
# endif
#endif
namespace mozilla {
namespace detail {
#if defined(MOZ_BITSCAN_WINDOWS)
inline uint_fast8_t CountLeadingZeroes32(uint32_t aValue) {
unsigned long index;
if (!_BitScanReverse(&index, static_cast<unsigned long>(aValue))) return 32;
return uint_fast8_t(31 - index);
}
inline uint_fast8_t CountTrailingZeroes32(uint32_t aValue) {
unsigned long index;
if (!_BitScanForward(&index, static_cast<unsigned long>(aValue))) return 32;
return uint_fast8_t(index);
}
inline uint_fast8_t CountPopulation32(uint32_t aValue) {
uint32_t x = aValue - ((aValue >> 1) & 0x55555555);
x = (x & 0x33333333) + ((x >> 2) & 0x33333333);
return (((x + (x >> 4)) & 0xf0f0f0f) * 0x1010101) >> 24;
}
inline uint_fast8_t CountPopulation64(uint64_t aValue) {
return uint_fast8_t(CountPopulation32(aValue & 0xffffffff) +
CountPopulation32(aValue >> 32));
}
inline uint_fast8_t CountLeadingZeroes64(uint64_t aValue) {
# if defined(MOZ_BITSCAN_WINDOWS64)
unsigned long index;
if (!_BitScanReverse64(&index, static_cast<unsigned __int64>(aValue)))
return 64;
return uint_fast8_t(63 - index);
# else
uint32_t hi = uint32_t(aValue >> 32);
if (hi != 0) {
return CountLeadingZeroes32(hi);
}
return 32u + CountLeadingZeroes32(uint32_t(aValue));
# endif
}
inline uint_fast8_t CountTrailingZeroes64(uint64_t aValue) {
# if defined(MOZ_BITSCAN_WINDOWS64)
unsigned long index;
if (!_BitScanForward64(&index, static_cast<unsigned __int64>(aValue)))
return 64;
return uint_fast8_t(index);
# else
uint32_t lo = uint32_t(aValue);
if (lo != 0) {
return CountTrailingZeroes32(lo);
}
return 32u + CountTrailingZeroes32(uint32_t(aValue >> 32));
# endif
}
#elif defined(__clang__) || defined(__GNUC__)
# if defined(__clang__)
# if !__has_builtin(__builtin_ctz) || !__has_builtin(__builtin_clz)
# error "A clang providing __builtin_c[lt]z is required to build"
# endif
# else
// gcc has had __builtin_clz and friends since 3.4: no need to check.
# endif
inline uint_fast8_t CountLeadingZeroes32(uint32_t aValue) {
return static_cast<uint_fast8_t>(__builtin_clz(aValue));
}
inline uint_fast8_t CountTrailingZeroes32(uint32_t aValue) {
return static_cast<uint_fast8_t>(__builtin_ctz(aValue));
}
inline uint_fast8_t CountPopulation32(uint32_t aValue) {
return static_cast<uint_fast8_t>(__builtin_popcount(aValue));
}
inline uint_fast8_t CountPopulation64(uint64_t aValue) {
return static_cast<uint_fast8_t>(__builtin_popcountll(aValue));
}
inline uint_fast8_t CountLeadingZeroes64(uint64_t aValue) {
return static_cast<uint_fast8_t>(__builtin_clzll(aValue));
}
inline uint_fast8_t CountTrailingZeroes64(uint64_t aValue) {
return static_cast<uint_fast8_t>(__builtin_ctzll(aValue));
}
#else
# error "Implement these!"
inline uint_fast8_t CountLeadingZeroes32(uint32_t aValue) = delete;
inline uint_fast8_t CountTrailingZeroes32(uint32_t aValue) = delete;
inline uint_fast8_t CountPopulation32(uint32_t aValue) = delete;
inline uint_fast8_t CountPopulation64(uint64_t aValue) = delete;
inline uint_fast8_t CountLeadingZeroes64(uint64_t aValue) = delete;
inline uint_fast8_t CountTrailingZeroes64(uint64_t aValue) = delete;
#endif
} // namespace detail
/**
* Compute the number of high-order zero bits in the NON-ZERO number |aValue|.
* That is, looking at the bitwise representation of the number, with the
* highest- valued bits at the start, return the number of zeroes before the
* first one is observed.
*
* CountLeadingZeroes32(0xF0FF1000) is 0;
* CountLeadingZeroes32(0x7F8F0001) is 1;
* CountLeadingZeroes32(0x3FFF0100) is 2;
* CountLeadingZeroes32(0x1FF50010) is 3; and so on.
*/
inline uint_fast8_t CountLeadingZeroes32(uint32_t aValue) {
MOZ_ASSERT(aValue != 0);
return detail::CountLeadingZeroes32(aValue);
}
/**
* Compute the number of low-order zero bits in the NON-ZERO number |aValue|.
* That is, looking at the bitwise representation of the number, with the
* lowest- valued bits at the start, return the number of zeroes before the
* first one is observed.
*
* CountTrailingZeroes32(0x0100FFFF) is 0;
* CountTrailingZeroes32(0x7000FFFE) is 1;
* CountTrailingZeroes32(0x0080FFFC) is 2;
* CountTrailingZeroes32(0x0080FFF8) is 3; and so on.
*/
inline uint_fast8_t CountTrailingZeroes32(uint32_t aValue) {
MOZ_ASSERT(aValue != 0);
return detail::CountTrailingZeroes32(aValue);
}
/**
* Compute the number of one bits in the number |aValue|,
*/
inline uint_fast8_t CountPopulation32(uint32_t aValue) {
return detail::CountPopulation32(aValue);
}
/** Analogous to CountPopulation32, but for 64-bit numbers */
inline uint_fast8_t CountPopulation64(uint64_t aValue) {
return detail::CountPopulation64(aValue);
}
/** Analogous to CountLeadingZeroes32, but for 64-bit numbers. */
inline uint_fast8_t CountLeadingZeroes64(uint64_t aValue) {
MOZ_ASSERT(aValue != 0);
return detail::CountLeadingZeroes64(aValue);
}
/** Analogous to CountTrailingZeroes32, but for 64-bit numbers. */
inline uint_fast8_t CountTrailingZeroes64(uint64_t aValue) {
MOZ_ASSERT(aValue != 0);
return detail::CountTrailingZeroes64(aValue);
}
namespace detail {
template <typename T, size_t Size = sizeof(T)>
class CeilingLog2;
template <typename T>
class CeilingLog2<T, 4> {
public:
static uint_fast8_t compute(const T aValue) {
// Check for <= 1 to avoid the == 0 undefined case.
return aValue <= 1 ? 0u : 32u - CountLeadingZeroes32(aValue - 1);
}
};
template <typename T>
class CeilingLog2<T, 8> {
public:
static uint_fast8_t compute(const T aValue) {
// Check for <= 1 to avoid the == 0 undefined case.
return aValue <= 1 ? 0u : 64u - CountLeadingZeroes64(aValue - 1);
}
};
} // namespace detail
/**
* Compute the log of the least power of 2 greater than or equal to |aValue|.
*
* CeilingLog2(0..1) is 0;
* CeilingLog2(2) is 1;
* CeilingLog2(3..4) is 2;
* CeilingLog2(5..8) is 3;
* CeilingLog2(9..16) is 4; and so on.
*/
template <typename T>
inline uint_fast8_t CeilingLog2(const T aValue) {
return detail::CeilingLog2<T>::compute(aValue);
}
/** A CeilingLog2 variant that accepts only size_t. */
inline uint_fast8_t CeilingLog2Size(size_t aValue) {
return CeilingLog2(aValue);
}
namespace detail {
template <typename T, size_t Size = sizeof(T)>
class FloorLog2;
template <typename T>
class FloorLog2<T, 4> {
public:
static uint_fast8_t compute(const T aValue) {
return 31u - CountLeadingZeroes32(aValue | 1);
}
};
template <typename T>
class FloorLog2<T, 8> {
public:
static uint_fast8_t compute(const T aValue) {
return 63u - CountLeadingZeroes64(aValue | 1);
}
};
} // namespace detail
/**
* Compute the log of the greatest power of 2 less than or equal to |aValue|.
*
* FloorLog2(0..1) is 0;
* FloorLog2(2..3) is 1;
* FloorLog2(4..7) is 2;
* FloorLog2(8..15) is 3; and so on.
*/
template <typename T>
inline constexpr uint_fast8_t FloorLog2(const T aValue) {
return detail::FloorLog2<T>::compute(aValue);
}
/** A FloorLog2 variant that accepts only size_t. */
inline uint_fast8_t FloorLog2Size(size_t aValue) { return FloorLog2(aValue); }
/*
* Compute the smallest power of 2 greater than or equal to |x|. |x| must not
* be so great that the computed value would overflow |size_t|.
*/
inline size_t RoundUpPow2(size_t aValue) {
MOZ_ASSERT(aValue <= (size_t(1) << (sizeof(size_t) * CHAR_BIT - 1)),
"can't round up -- will overflow!");
return size_t(1) << CeilingLog2(aValue);
}
/**
* Rotates the bits of the given value left by the amount of the shift width.
*/
template <typename T>
MOZ_NO_SANITIZE_UNSIGNED_OVERFLOW inline T RotateLeft(const T aValue,
uint_fast8_t aShift) {
static_assert(std::is_unsigned_v<T>, "Rotates require unsigned values");
MOZ_ASSERT(aShift < sizeof(T) * CHAR_BIT, "Shift value is too large!");
MOZ_ASSERT(aShift > 0,
"Rotation by value length is undefined behavior, but compilers "
"do not currently fold a test into the rotate instruction. "
"Please remove this restriction when compilers optimize the "
return (aValue << aShift) | (aValue >> (sizeof(T) * CHAR_BIT - aShift));
}
/**
* Rotates the bits of the given value right by the amount of the shift width.
*/
template <typename T>
MOZ_NO_SANITIZE_UNSIGNED_OVERFLOW inline T RotateRight(const T aValue,
uint_fast8_t aShift) {
static_assert(std::is_unsigned_v<T>, "Rotates require unsigned values");
MOZ_ASSERT(aShift < sizeof(T) * CHAR_BIT, "Shift value is too large!");
MOZ_ASSERT(aShift > 0,
"Rotation by value length is undefined behavior, but compilers "
"do not currently fold a test into the rotate instruction. "
"Please remove this restriction when compilers optimize the "
return (aValue >> aShift) | (aValue << (sizeof(T) * CHAR_BIT - aShift));
}
/**
* Returns true if |x| is a power of two.
* Zero is not an integer power of two. (-Inf is not an integer)
*/
template <typename T>
constexpr bool IsPowerOfTwo(T x) {
static_assert(std::is_unsigned_v<T>, "IsPowerOfTwo requires unsigned values");
return x && (x & (x - 1)) == 0;
}
template <typename T>
inline T Clamp(const T aValue, const T aMin, const T aMax) {
static_assert(std::is_integral_v<T>,
"Clamp accepts only integral types, so that it doesn't have"
" to distinguish differently-signed zeroes (which users may"
" or may not care to distinguish, likely at a perf cost) or"
" to decide how to clamp NaN or a range with a NaN"
" endpoint.");
MOZ_ASSERT(aMin <= aMax);
if (aValue <= aMin) return aMin;
if (aValue >= aMax) return aMax;
return aValue;
}
template <typename T>
inline uint_fast8_t CountTrailingZeroes(T aValue) {
static_assert(sizeof(T) <= 8);
static_assert(std::is_integral_v<T>);
// This casts to 32-bits
if constexpr (sizeof(T) <= 4) {
return CountTrailingZeroes32(aValue);
}
// This doesn't
if constexpr (sizeof(T) == 8) {
return CountTrailingZeroes64(aValue);
}
}
// Greatest Common Divisor, from
template <typename T>
MOZ_ALWAYS_INLINE T GCD(T aA, T aB) {
static_assert(std::is_integral_v<T>);
MOZ_ASSERT(aA >= 0);
MOZ_ASSERT(aB >= 0);
if (aA == 0) {
return aB;
}
if (aB == 0) {
return aA;
}
T az = CountTrailingZeroes(aA);
T bz = CountTrailingZeroes(aB);
T shift = std::min<T>(az, bz);
aA >>= az;
aB >>= bz;
while (aA != 0) {
if constexpr (!std::is_signed_v<T>) {
if (aA < aB) {
std::swap(aA, aB);
}
}
T diff = aA - aB;
if constexpr (std::is_signed_v<T>) {
aB = std::min<T>(aA, aB);
}
if constexpr (std::is_signed_v<T>) {
aA = std::abs(diff);
} else {
aA = diff;
}
if (aA) {
aA >>= CountTrailingZeroes(aA);
}
}
return aB << shift;
}
} /* namespace mozilla */
#endif /* mozilla_MathAlgorithms_h */