michael@0: /* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
michael@0: /* vim: set ts=8 sts=2 et sw=2 tw=80: */
michael@0: /* This Source Code Form is subject to the terms of the Mozilla Public
michael@0:  * License, v. 2.0. If a copy of the MPL was not distributed with this
michael@0:  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
michael@0: 
michael@0: /* mfbt maths algorithms. */
michael@0: 
michael@0: #ifndef mozilla_MathAlgorithms_h
michael@0: #define mozilla_MathAlgorithms_h
michael@0: 
michael@0: #include "mozilla/Assertions.h"
michael@0: #include "mozilla/TypeTraits.h"
michael@0: 
michael@0: #include <cmath>
michael@0: #include <limits.h>
michael@0: #include <stdint.h>
michael@0: 
michael@0: namespace mozilla {
michael@0: 
michael@0: // Greatest Common Divisor
michael@0: template<typename IntegerType>
michael@0: MOZ_ALWAYS_INLINE IntegerType
michael@0: EuclidGCD(IntegerType a, IntegerType b)
michael@0: {
michael@0:   // Euclid's algorithm; O(N) in the worst case.  (There are better
michael@0:   // ways, but we don't need them for the current use of this algo.)
michael@0:   MOZ_ASSERT(a > 0);
michael@0:   MOZ_ASSERT(b > 0);
michael@0: 
michael@0:   while (a != b) {
michael@0:     if (a > b) {
michael@0:       a = a - b;
michael@0:     } else {
michael@0:       b = b - a;
michael@0:     }
michael@0:   }
michael@0: 
michael@0:   return a;
michael@0: }
michael@0: 
michael@0: // Least Common Multiple
michael@0: template<typename IntegerType>
michael@0: MOZ_ALWAYS_INLINE IntegerType
michael@0: EuclidLCM(IntegerType a, IntegerType b)
michael@0: {
michael@0:   // Divide first to reduce overflow risk.
michael@0:   return (a / EuclidGCD(a, b)) * b;
michael@0: }
michael@0: 
michael@0: namespace detail {
michael@0: 
michael@0: template<typename T>
michael@0: struct AllowDeprecatedAbsFixed : FalseType {};
michael@0: 
michael@0: template<> struct AllowDeprecatedAbsFixed<int32_t> : TrueType {};
michael@0: template<> struct AllowDeprecatedAbsFixed<int64_t> : TrueType {};
michael@0: 
michael@0: template<typename T>
michael@0: struct AllowDeprecatedAbs : AllowDeprecatedAbsFixed<T> {};
michael@0: 
michael@0: template<> struct AllowDeprecatedAbs<int> : TrueType {};
michael@0: template<> struct AllowDeprecatedAbs<long> : TrueType {};
michael@0: 
michael@0: } // namespace detail
michael@0: 
michael@0: // DO NOT USE DeprecatedAbs.  It exists only until its callers can be converted
michael@0: // to Abs below, and it will be removed when all callers have been changed.
michael@0: template<typename T>
michael@0: inline typename mozilla::EnableIf<detail::AllowDeprecatedAbs<T>::value, T>::Type
michael@0: DeprecatedAbs(const T t)
michael@0: {
michael@0:   // The absolute value of the smallest possible value of a signed-integer type
michael@0:   // won't fit in that type (on twos-complement systems -- and we're blithely
michael@0:   // assuming we're on such systems, for the non-<stdint.h> types listed above),
michael@0:   // so assert that the input isn't that value.
michael@0:   //
michael@0:   // This is the case if: the value is non-negative; or if adding one (giving a
michael@0:   // value in the range [-maxvalue, 0]), then negating (giving a value in the
michael@0:   // range [0, maxvalue]), doesn't produce maxvalue (because in twos-complement,
michael@0:   // (minvalue + 1) == -maxvalue).
michael@0:   MOZ_ASSERT(t >= 0 ||
michael@0:              -(t + 1) != T((1ULL << (CHAR_BIT * sizeof(T) - 1)) - 1),
michael@0:              "You can't negate the smallest possible negative integer!");
michael@0:   return t >= 0 ? t : -t;
michael@0: }
michael@0: 
michael@0: namespace detail {
michael@0: 
michael@0: // For now mozilla::Abs only takes intN_T, the signed natural types, and
michael@0: // float/double/long double.  Feel free to add overloads for other standard,
michael@0: // signed types if you need them.
michael@0: 
michael@0: template<typename T>
michael@0: struct AbsReturnTypeFixed;
michael@0: 
michael@0: template<> struct AbsReturnTypeFixed<int8_t> { typedef uint8_t Type; };
michael@0: template<> struct AbsReturnTypeFixed<int16_t> { typedef uint16_t Type; };
michael@0: template<> struct AbsReturnTypeFixed<int32_t> { typedef uint32_t Type; };
michael@0: template<> struct AbsReturnTypeFixed<int64_t> { typedef uint64_t Type; };
michael@0: 
michael@0: template<typename T>
michael@0: struct AbsReturnType : AbsReturnTypeFixed<T> {};
michael@0: 
michael@0: template<> struct AbsReturnType<char> : EnableIf<char(-1) < char(0), unsigned char> {};
michael@0: template<> struct AbsReturnType<signed char> { typedef unsigned char Type; };
michael@0: template<> struct AbsReturnType<short> { typedef unsigned short Type; };
michael@0: template<> struct AbsReturnType<int> { typedef unsigned int Type; };
michael@0: template<> struct AbsReturnType<long> { typedef unsigned long Type; };
michael@0: template<> struct AbsReturnType<long long> { typedef unsigned long long Type; };
michael@0: template<> struct AbsReturnType<float> { typedef float Type; };
michael@0: template<> struct AbsReturnType<double> { typedef double Type; };
michael@0: template<> struct AbsReturnType<long double> { typedef long double Type; };
michael@0: 
michael@0: } // namespace detail
michael@0: 
michael@0: template<typename T>
michael@0: inline typename detail::AbsReturnType<T>::Type
michael@0: Abs(const T t)
michael@0: {
michael@0:   typedef typename detail::AbsReturnType<T>::Type ReturnType;
michael@0:   return t >= 0 ? ReturnType(t) : ~ReturnType(t) + 1;
michael@0: }
michael@0: 
michael@0: template<>
michael@0: inline float
michael@0: Abs<float>(const float f)
michael@0: {
michael@0:   return std::fabs(f);
michael@0: }
michael@0: 
michael@0: template<>
michael@0: inline double
michael@0: Abs<double>(const double d)
michael@0: {
michael@0:   return std::fabs(d);
michael@0: }
michael@0: 
michael@0: template<>
michael@0: inline long double
michael@0: Abs<long double>(const long double d)
michael@0: {
michael@0:   return std::fabs(d);
michael@0: }
michael@0: 
michael@0: } // namespace mozilla
michael@0: 
michael@0: #if defined(_WIN32) && (_MSC_VER >= 1300) && (defined(_M_IX86) || defined(_M_AMD64) || defined(_M_X64))
michael@0: #  define MOZ_BITSCAN_WINDOWS
michael@0: 
michael@0:   extern "C" {
michael@0:     unsigned char _BitScanForward(unsigned long* Index, unsigned long mask);
michael@0:     unsigned char _BitScanReverse(unsigned long* Index, unsigned long mask);
michael@0: #  pragma intrinsic(_BitScanForward, _BitScanReverse)
michael@0: 
michael@0: #  if defined(_M_AMD64) || defined(_M_X64)
michael@0: #    define MOZ_BITSCAN_WINDOWS64
michael@0:     unsigned char _BitScanForward64(unsigned long* index, unsigned __int64 mask);
michael@0:     unsigned char _BitScanReverse64(unsigned long* index, unsigned __int64 mask);
michael@0: #   pragma intrinsic(_BitScanForward64, _BitScanReverse64)
michael@0: #  endif
michael@0:   } // extern "C"
michael@0: 
michael@0: #endif
michael@0: 
michael@0: namespace mozilla {
michael@0: 
michael@0: namespace detail {
michael@0: 
michael@0: #if defined(MOZ_BITSCAN_WINDOWS)
michael@0: 
michael@0:   inline uint_fast8_t
michael@0:   CountLeadingZeroes32(uint32_t u)
michael@0:   {
michael@0:     unsigned long index;
michael@0:     _BitScanReverse(&index, static_cast<unsigned long>(u));
michael@0:     return uint_fast8_t(31 - index);
michael@0:   }
michael@0: 
michael@0: 
michael@0:   inline uint_fast8_t
michael@0:   CountTrailingZeroes32(uint32_t u)
michael@0:   {
michael@0:     unsigned long index;
michael@0:     _BitScanForward(&index, static_cast<unsigned long>(u));
michael@0:     return uint_fast8_t(index);
michael@0:   }
michael@0: 
michael@0:   inline uint_fast8_t
michael@0:   CountPopulation32(uint32_t u)
michael@0:   {
michael@0:     uint32_t x = u - ((u >> 1) & 0x55555555);
michael@0:     x = (x & 0x33333333) + ((x >> 2) & 0x33333333);
michael@0:     return (((x + (x >> 4)) & 0xf0f0f0f) * 0x1010101) >> 24;
michael@0:   }
michael@0: 
michael@0:   inline uint_fast8_t
michael@0:   CountLeadingZeroes64(uint64_t u)
michael@0:   {
michael@0: #  if defined(MOZ_BITSCAN_WINDOWS64)
michael@0:     unsigned long index;
michael@0:     _BitScanReverse64(&index, static_cast<unsigned __int64>(u));
michael@0:     return uint_fast8_t(63 - index);
michael@0: #  else
michael@0:     uint32_t hi = uint32_t(u >> 32);
michael@0:     if (hi != 0)
michael@0:       return CountLeadingZeroes32(hi);
michael@0:     return 32 + CountLeadingZeroes32(uint32_t(u));
michael@0: #  endif
michael@0:   }
michael@0: 
michael@0:   inline uint_fast8_t
michael@0:   CountTrailingZeroes64(uint64_t u)
michael@0:   {
michael@0: #  if defined(MOZ_BITSCAN_WINDOWS64)
michael@0:     unsigned long index;
michael@0:     _BitScanForward64(&index, static_cast<unsigned __int64>(u));
michael@0:     return uint_fast8_t(index);
michael@0: #  else
michael@0:     uint32_t lo = uint32_t(u);
michael@0:     if (lo != 0)
michael@0:       return CountTrailingZeroes32(lo);
michael@0:     return 32 + CountTrailingZeroes32(uint32_t(u >> 32));
michael@0: #  endif
michael@0:   }
michael@0: 
michael@0: #  ifdef MOZ_HAVE_BITSCAN64
michael@0: #    undef MOZ_HAVE_BITSCAN64
michael@0: #  endif
michael@0: 
michael@0: #elif defined(__clang__) || defined(__GNUC__)
michael@0: 
michael@0: #  if defined(__clang__)
michael@0: #    if !__has_builtin(__builtin_ctz) || !__has_builtin(__builtin_clz)
michael@0: #      error "A clang providing __builtin_c[lt]z is required to build"
michael@0: #    endif
michael@0: #  else
michael@0:      // gcc has had __builtin_clz and friends since 3.4: no need to check.
michael@0: #  endif
michael@0: 
michael@0:   inline uint_fast8_t
michael@0:   CountLeadingZeroes32(uint32_t u)
michael@0:   {
michael@0:     return __builtin_clz(u);
michael@0:   }
michael@0: 
michael@0:   inline uint_fast8_t
michael@0:   CountTrailingZeroes32(uint32_t u)
michael@0:   {
michael@0:     return __builtin_ctz(u);
michael@0:   }
michael@0: 
michael@0:   inline uint_fast8_t
michael@0:   CountPopulation32(uint32_t u)
michael@0:   {
michael@0:     return __builtin_popcount(u);
michael@0:   }
michael@0: 
michael@0:   inline uint_fast8_t
michael@0:   CountLeadingZeroes64(uint64_t u)
michael@0:   {
michael@0:     return __builtin_clzll(u);
michael@0:   }
michael@0: 
michael@0:   inline uint_fast8_t
michael@0:   CountTrailingZeroes64(uint64_t u)
michael@0:   {
michael@0:     return __builtin_ctzll(u);
michael@0:   }
michael@0: 
michael@0: #else
michael@0: #  error "Implement these!"
michael@0:   inline uint_fast8_t CountLeadingZeroes32(uint32_t u) MOZ_DELETE;
michael@0:   inline uint_fast8_t CountTrailingZeroes32(uint32_t u) MOZ_DELETE;
michael@0:   inline uint_fast8_t CountPopulation32(uint32_t u) MOZ_DELETE;
michael@0:   inline uint_fast8_t CountLeadingZeroes64(uint64_t u) MOZ_DELETE;
michael@0:   inline uint_fast8_t CountTrailingZeroes64(uint64_t u) MOZ_DELETE;
michael@0: #endif
michael@0: 
michael@0: } // namespace detail
michael@0: 
michael@0: /**
michael@0:  * Compute the number of high-order zero bits in the NON-ZERO number |u|.  That
michael@0:  * is, looking at the bitwise representation of the number, with the highest-
michael@0:  * valued bits at the start, return the number of zeroes before the first one
michael@0:  * is observed.
michael@0:  *
michael@0:  * CountLeadingZeroes32(0xF0FF1000) is 0;
michael@0:  * CountLeadingZeroes32(0x7F8F0001) is 1;
michael@0:  * CountLeadingZeroes32(0x3FFF0100) is 2;
michael@0:  * CountLeadingZeroes32(0x1FF50010) is 3; and so on.
michael@0:  */
michael@0: inline uint_fast8_t
michael@0: CountLeadingZeroes32(uint32_t u)
michael@0: {
michael@0:   MOZ_ASSERT(u != 0);
michael@0:   return detail::CountLeadingZeroes32(u);
michael@0: }
michael@0: 
michael@0: /**
michael@0:  * Compute the number of low-order zero bits in the NON-ZERO number |u|.  That
michael@0:  * is, looking at the bitwise representation of the number, with the lowest-
michael@0:  * valued bits at the start, return the number of zeroes before the first one
michael@0:  * is observed.
michael@0:  *
michael@0:  * CountTrailingZeroes32(0x0100FFFF) is 0;
michael@0:  * CountTrailingZeroes32(0x7000FFFE) is 1;
michael@0:  * CountTrailingZeroes32(0x0080FFFC) is 2;
michael@0:  * CountTrailingZeroes32(0x0080FFF8) is 3; and so on.
michael@0:  */
michael@0: inline uint_fast8_t
michael@0: CountTrailingZeroes32(uint32_t u)
michael@0: {
michael@0:   MOZ_ASSERT(u != 0);
michael@0:   return detail::CountTrailingZeroes32(u);
michael@0: }
michael@0: 
michael@0: /**
michael@0:  * Compute the number of one bits in the number |u|,
michael@0:  */
michael@0: inline uint_fast8_t
michael@0: CountPopulation32(uint32_t u)
michael@0: {
michael@0:   return detail::CountPopulation32(u);
michael@0: }
michael@0: 
michael@0: /** Analogous to CountLeadingZeroes32, but for 64-bit numbers. */
michael@0: inline uint_fast8_t
michael@0: CountLeadingZeroes64(uint64_t u)
michael@0: {
michael@0:   MOZ_ASSERT(u != 0);
michael@0:   return detail::CountLeadingZeroes64(u);
michael@0: }
michael@0: 
michael@0: /** Analogous to CountTrailingZeroes32, but for 64-bit numbers. */
michael@0: inline uint_fast8_t
michael@0: CountTrailingZeroes64(uint64_t u)
michael@0: {
michael@0:   MOZ_ASSERT(u != 0);
michael@0:   return detail::CountTrailingZeroes64(u);
michael@0: }
michael@0: 
michael@0: namespace detail {
michael@0: 
michael@0: template<typename T, size_t Size = sizeof(T)>
michael@0: class CeilingLog2;
michael@0: 
michael@0: template<typename T>
michael@0: class CeilingLog2<T, 4>
michael@0: {
michael@0:   public:
michael@0:     static uint_fast8_t compute(const T t) {
michael@0:       // Check for <= 1 to avoid the == 0 undefined case.
michael@0:       return t <= 1 ? 0 : 32 - CountLeadingZeroes32(t - 1);
michael@0:     }
michael@0: };
michael@0: 
michael@0: template<typename T>
michael@0: class CeilingLog2<T, 8>
michael@0: {
michael@0:   public:
michael@0:     static uint_fast8_t compute(const T t) {
michael@0:       // Check for <= 1 to avoid the == 0 undefined case.
michael@0:       return t <= 1 ? 0 : 64 - CountLeadingZeroes64(t - 1);
michael@0:     }
michael@0: };
michael@0: 
michael@0: } // namespace detail
michael@0: 
michael@0: /**
michael@0:  * Compute the log of the least power of 2 greater than or equal to |t|.
michael@0:  *
michael@0:  * CeilingLog2(0..1) is 0;
michael@0:  * CeilingLog2(2) is 1;
michael@0:  * CeilingLog2(3..4) is 2;
michael@0:  * CeilingLog2(5..8) is 3;
michael@0:  * CeilingLog2(9..16) is 4; and so on.
michael@0:  */
michael@0: template<typename T>
michael@0: inline uint_fast8_t
michael@0: CeilingLog2(const T t)
michael@0: {
michael@0:   return detail::CeilingLog2<T>::compute(t);
michael@0: }
michael@0: 
michael@0: /** A CeilingLog2 variant that accepts only size_t. */
michael@0: inline uint_fast8_t
michael@0: CeilingLog2Size(size_t n)
michael@0: {
michael@0:   return CeilingLog2(n);
michael@0: }
michael@0: 
michael@0: namespace detail {
michael@0: 
michael@0: template<typename T, size_t Size = sizeof(T)>
michael@0: class FloorLog2;
michael@0: 
michael@0: template<typename T>
michael@0: class FloorLog2<T, 4>
michael@0: {
michael@0:   public:
michael@0:     static uint_fast8_t compute(const T t) {
michael@0:       return 31 - CountLeadingZeroes32(t | 1);
michael@0:     }
michael@0: };
michael@0: 
michael@0: template<typename T>
michael@0: class FloorLog2<T, 8>
michael@0: {
michael@0:   public:
michael@0:     static uint_fast8_t compute(const T t) {
michael@0:       return 63 - CountLeadingZeroes64(t | 1);
michael@0:     }
michael@0: };
michael@0: 
michael@0: } // namespace detail
michael@0: 
michael@0: /**
michael@0:  * Compute the log of the greatest power of 2 less than or equal to |t|.
michael@0:  *
michael@0:  * FloorLog2(0..1) is 0;
michael@0:  * FloorLog2(2..3) is 1;
michael@0:  * FloorLog2(4..7) is 2;
michael@0:  * FloorLog2(8..15) is 3; and so on.
michael@0:  */
michael@0: template<typename T>
michael@0: inline uint_fast8_t
michael@0: FloorLog2(const T t)
michael@0: {
michael@0:   return detail::FloorLog2<T>::compute(t);
michael@0: }
michael@0: 
michael@0: /** A FloorLog2 variant that accepts only size_t. */
michael@0: inline uint_fast8_t
michael@0: FloorLog2Size(size_t n)
michael@0: {
michael@0:   return FloorLog2(n);
michael@0: }
michael@0: 
michael@0: /*
michael@0:  * Compute the smallest power of 2 greater than or equal to |x|.  |x| must not
michael@0:  * be so great that the computed value would overflow |size_t|.
michael@0:  */
michael@0: inline size_t
michael@0: RoundUpPow2(size_t x)
michael@0: {
michael@0:   MOZ_ASSERT(x <= (size_t(1) << (sizeof(size_t) * CHAR_BIT - 1)),
michael@0:              "can't round up -- will overflow!");
michael@0:   return size_t(1) << CeilingLog2(x);
michael@0: }
michael@0: 
michael@0: /**
michael@0:  * Rotates the bits of the given value left by the amount of the shift width.
michael@0:  */
michael@0: template<typename T>
michael@0: inline T
michael@0: RotateLeft(const T t, uint_fast8_t shift)
michael@0: {
michael@0:   MOZ_ASSERT(shift < sizeof(T) * CHAR_BIT, "Shift value is too large!");
michael@0:   static_assert(IsUnsigned<T>::value, "Rotates require unsigned values");
michael@0:   return (t << shift) | (t >> (sizeof(T) * CHAR_BIT - shift));
michael@0: }
michael@0: 
michael@0: /**
michael@0:  * Rotates the bits of the given value right by the amount of the shift width.
michael@0:  */
michael@0: template<typename T>
michael@0: inline T
michael@0: RotateRight(const T t, uint_fast8_t shift)
michael@0: {
michael@0:   MOZ_ASSERT(shift < sizeof(T) * CHAR_BIT, "Shift value is too large!");
michael@0:   static_assert(IsUnsigned<T>::value, "Rotates require unsigned values");
michael@0:   return (t >> shift) | (t << (sizeof(T) * CHAR_BIT - shift));
michael@0: }
michael@0: 
michael@0: } /* namespace mozilla */
michael@0: 
michael@0: #endif /* mozilla_MathAlgorithms_h */