gecko-dev/mfbt/MathAlgorithms.h

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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
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
/* mfbt maths algorithms. */
#ifndef mozilla_MathAlgorithms_h
#define mozilla_MathAlgorithms_h
#include "mozilla/Assertions.h"
#include "mozilla/TypeTraits.h"
#include <cmath>
#include <limits.h>
#include <stdint.h>
namespace mozilla {
// Greatest Common Divisor
template<typename IntegerType>
MOZ_ALWAYS_INLINE IntegerType
EuclidGCD(IntegerType a, IntegerType b)
{
// Euclid's algorithm; O(N) in the worst case. (There are better
// ways, but we don't need them for the current use of this algo.)
MOZ_ASSERT(a > 0);
MOZ_ASSERT(b > 0);
while (a != b) {
if (a > b) {
a = a - b;
} else {
b = b - a;
}
}
return a;
}
// Least Common Multiple
template<typename IntegerType>
MOZ_ALWAYS_INLINE IntegerType
EuclidLCM(IntegerType a, IntegerType b)
{
// Divide first to reduce overflow risk.
return (a / EuclidGCD(a, b)) * b;
}
namespace detail {
template<typename T>
struct AllowDeprecatedAbsFixed : FalseType {};
template<> struct AllowDeprecatedAbsFixed<int32_t> : TrueType {};
template<> struct AllowDeprecatedAbsFixed<int64_t> : TrueType {};
template<typename T>
struct AllowDeprecatedAbs : AllowDeprecatedAbsFixed<T> {};
template<> struct AllowDeprecatedAbs<int> : TrueType {};
template<> struct AllowDeprecatedAbs<long> : TrueType {};
} // 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 typename mozilla::EnableIf<detail::AllowDeprecatedAbs<T>::value, T>::Type
DeprecatedAbs(const T t)
{
// 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(t >= 0 ||
-(t + 1) != T((1ULL << (CHAR_BIT * sizeof(T) - 1)) - 1),
"You can't negate the smallest possible negative integer!");
return t >= 0 ? t : -t;
}
namespace detail {
// For now mozilla::Abs only takes intN_T, the signed natural types, and
// float/double/long double. Feel free to add overloads for other standard,
// signed types if you need them.
template<typename T>
struct AbsReturnTypeFixed;
template<> struct AbsReturnTypeFixed<int8_t> { typedef uint8_t Type; };
template<> struct AbsReturnTypeFixed<int16_t> { typedef uint16_t Type; };
template<> struct AbsReturnTypeFixed<int32_t> { typedef uint32_t Type; };
template<> struct AbsReturnTypeFixed<int64_t> { typedef uint64_t Type; };
template<typename T>
struct AbsReturnType : AbsReturnTypeFixed<T> {};
template<> struct AbsReturnType<char> : EnableIf<char(-1) < char(0), unsigned char> {};
template<> struct AbsReturnType<signed char> { typedef unsigned char Type; };
template<> struct AbsReturnType<short> { typedef unsigned short Type; };
template<> struct AbsReturnType<int> { typedef unsigned int Type; };
template<> struct AbsReturnType<long> { typedef unsigned long Type; };
template<> struct AbsReturnType<long long> { typedef unsigned long long Type; };
template<> struct AbsReturnType<float> { typedef float Type; };
template<> struct AbsReturnType<double> { typedef double Type; };
template<> struct AbsReturnType<long double> { typedef long double Type; };
} // namespace detail
template<typename T>
inline typename detail::AbsReturnType<T>::Type
Abs(const T t)
{
typedef typename detail::AbsReturnType<T>::Type ReturnType;
return t >= 0 ? ReturnType(t) : ~ReturnType(t) + 1;
}
template<>
inline float
Abs<float>(const float f)
{
return std::fabs(f);
}
template<>
inline double
Abs<double>(const double d)
{
return std::fabs(d);
}
template<>
inline long double
Abs<long double>(const long double d)
{
return std::fabs(d);
}
} // namespace mozilla
#if defined(_WIN32) && (_MSC_VER >= 1300) && (defined(_M_IX86) || defined(_M_AMD64) || defined(_M_X64))
# define MOZ_BITSCAN_WINDOWS
extern "C" {
unsigned char _BitScanForward(unsigned long* Index, unsigned long mask);
unsigned char _BitScanReverse(unsigned long* Index, unsigned long mask);
# pragma intrinsic(_BitScanForward, _BitScanReverse)
# if defined(_M_AMD64) || defined(_M_X64)
# define MOZ_BITSCAN_WINDOWS64
unsigned char _BitScanForward64(unsigned long* index, unsigned __int64 mask);
unsigned char _BitScanReverse64(unsigned long* index, unsigned __int64 mask);
# pragma intrinsic(_BitScanForward64, _BitScanReverse64)
# endif
} // extern "C"
#endif
namespace mozilla {
namespace detail {
#if defined(MOZ_BITSCAN_WINDOWS)
inline uint_fast8_t
CountLeadingZeroes32(uint32_t u)
{
unsigned long index;
_BitScanReverse(&index, static_cast<unsigned long>(u));
return uint_fast8_t(31 - index);
}
inline uint_fast8_t
CountTrailingZeroes32(uint32_t u)
{
unsigned long index;
_BitScanForward(&index, static_cast<unsigned long>(u));
return uint_fast8_t(index);
}
inline uint_fast8_t
CountPopulation32(uint32_t u)
{
uint32_t sum2 = (u & 0x55555555) + ((u & 0xaaaaaaaa) >> 1);
uint32_t sum4 = (sum2 & 0x33333333) + ((sum2 & 0xcccccccc) >> 2);
uint32_t sum8 = (sum4 & 0x0f0f0f0f) + ((sum4 & 0xf0f0f0f0) >> 4);
uint32_t sum16 = (sum8 & 0x00ff00ff) + ((sum8 & 0xff00ff00) >> 8);
return sum16;
}
inline uint_fast8_t
CountLeadingZeroes64(uint64_t u)
{
# if defined(MOZ_BITSCAN_WINDOWS64)
unsigned long index;
_BitScanReverse64(&index, static_cast<unsigned __int64>(u));
return uint_fast8_t(63 - index);
# else
uint32_t hi = uint32_t(u >> 32);
if (hi != 0)
return CountLeadingZeroes32(hi);
return 32 + CountLeadingZeroes32(uint32_t(u));
# endif
}
inline uint_fast8_t
CountTrailingZeroes64(uint64_t u)
{
# if defined(MOZ_BITSCAN_WINDOWS64)
unsigned long index;
_BitScanForward64(&index, static_cast<unsigned __int64>(u));
return uint_fast8_t(index);
# else
uint32_t lo = uint32_t(u);
if (lo != 0)
return CountTrailingZeroes32(lo);
return 32 + CountTrailingZeroes32(uint32_t(u >> 32));
# endif
}
# ifdef MOZ_HAVE_BITSCAN64
# undef MOZ_HAVE_BITSCAN64
# 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 u)
{
return __builtin_clz(u);
}
inline uint_fast8_t
CountTrailingZeroes32(uint32_t u)
{
return __builtin_ctz(u);
}
inline uint_fast8_t
CountPopulation32(uint32_t u)
{
return __builtin_popcount(u);
}
inline uint_fast8_t
CountLeadingZeroes64(uint64_t u)
{
return __builtin_clzll(u);
}
inline uint_fast8_t
CountTrailingZeroes64(uint64_t u)
{
return __builtin_ctzll(u);
}
#else
# error "Implement these!"
inline uint_fast8_t CountLeadingZeroes32(uint32_t u) MOZ_DELETE;
inline uint_fast8_t CountTrailingZeroes32(uint32_t u) MOZ_DELETE;
inline uint_fast8_t CountPopulation32(uint32_t u) MOZ_DELETE;
inline uint_fast8_t CountLeadingZeroes64(uint64_t u) MOZ_DELETE;
inline uint_fast8_t CountTrailingZeroes64(uint64_t u) MOZ_DELETE;
#endif
} // namespace detail
/**
* Compute the number of high-order zero bits in the NON-ZERO number |u|. 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 u)
{
MOZ_ASSERT(u != 0);
return detail::CountLeadingZeroes32(u);
}
/**
* Compute the number of low-order zero bits in the NON-ZERO number |u|. 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 u)
{
MOZ_ASSERT(u != 0);
return detail::CountTrailingZeroes32(u);
}
/**
* Compute the number of one bits in the number |u|,
*/
inline uint_fast8_t
CountPopulation32(uint32_t u)
{
return detail::CountPopulation32(u);
}
/** Analogous to CountLeadingZeroes32, but for 64-bit numbers. */
inline uint_fast8_t
CountLeadingZeroes64(uint64_t u)
{
MOZ_ASSERT(u != 0);
return detail::CountLeadingZeroes64(u);
}
/** Analogous to CountTrailingZeroes32, but for 64-bit numbers. */
inline uint_fast8_t
CountTrailingZeroes64(uint64_t u)
{
MOZ_ASSERT(u != 0);
return detail::CountTrailingZeroes64(u);
}
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 t) {
// Check for <= 1 to avoid the == 0 undefined case.
return t <= 1 ? 0 : 32 - CountLeadingZeroes32(t - 1);
}
};
template<typename T>
class CeilingLog2<T, 8>
{
public:
static uint_fast8_t compute(const T t) {
// Check for <= 1 to avoid the == 0 undefined case.
return t <= 1 ? 0 : 64 - CountLeadingZeroes64(t - 1);
}
};
} // namespace detail
/**
* Compute the log of the least power of 2 greater than or equal to |t|.
*
* 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 t)
{
return detail::CeilingLog2<T>::compute(t);
}
/** A CeilingLog2 variant that accepts only size_t. */
inline uint_fast8_t
CeilingLog2Size(size_t n)
{
return CeilingLog2(n);
}
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 t) {
return 31 - CountLeadingZeroes32(t | 1);
}
};
template<typename T>
class FloorLog2<T, 8>
{
public:
static uint_fast8_t compute(const T t) {
return 63 - CountLeadingZeroes64(t | 1);
}
};
} // namespace detail
/**
* Compute the log of the greatest power of 2 less than or equal to |t|.
*
* 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 uint_fast8_t
FloorLog2(const T t)
{
return detail::FloorLog2<T>::compute(t);
}
/** A FloorLog2 variant that accepts only size_t. */
inline uint_fast8_t
FloorLog2Size(size_t n)
{
return FloorLog2(n);
}
/*
* 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 x)
{
MOZ_ASSERT(x <= (size_t(1) << (sizeof(size_t) * CHAR_BIT - 1)),
"can't round up -- will overflow!");
return size_t(1) << CeilingLog2(x);
}
} /* namespace mozilla */
#endif /* mozilla_MathAlgorithms_h */