rocksdb/util/math128.h

//  Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
//  This source code is licensed under both the GPLv2 (found in the
//  COPYING file in the root directory) and Apache 2.0 License
//  (found in the LICENSE.Apache file in the root directory).

#pragma once

#include "util/coding_lean.h"
#include "util/math.h"

#ifdef TEST_UINT128_COMPAT
#undef HAVE_UINT128_EXTENSION
#endif

namespace ROCKSDB_NAMESPACE {

// Unsigned128 is a 128 bit value supporting (at least) bitwise operators,
// shifts, and comparisons. __uint128_t is not always available.

#ifdef HAVE_UINT128_EXTENSION
using Unsigned128 = __uint128_t;
#else
struct Unsigned128 {
  uint64_t lo;
  uint64_t hi;

  inline Unsigned128() {
    static_assert(sizeof(Unsigned128) == 2 * sizeof(uint64_t),
                  "unexpected overhead in representation");
    lo = 0;
    hi = 0;
  }

  inline Unsigned128(uint64_t lower) {
    lo = lower;
    hi = 0;
  }

  inline Unsigned128(uint64_t lower, uint64_t upper) {
    lo = lower;
    hi = upper;
  }

  // Convert to any integer 64 bits or less.
  template <typename T,
            typename = std::enable_if_t<std::is_integral_v<T> &&
                                        sizeof(T) <= sizeof(uint64_t)> >
  explicit operator T() {
    return static_cast<T>(lo);
  }
};

inline Unsigned128 operator<<(const Unsigned128& lhs, unsigned shift) {
  shift &= 127;
  Unsigned128 rv;
  if (shift >= 64) {
    rv.lo = 0;
    rv.hi = lhs.lo << (shift & 63);
  } else {
    uint64_t tmp = lhs.lo;
    rv.lo = tmp << shift;
    // Ensure shift==0 shifts away everything. (This avoids another
    // conditional branch on shift == 0.)
    tmp = tmp >> 1 >> (63 - shift);
    rv.hi = tmp | (lhs.hi << shift);
  }
  return rv;
}

inline Unsigned128& operator<<=(Unsigned128& lhs, unsigned shift) {
  lhs = lhs << shift;
  return lhs;
}

inline Unsigned128 operator>>(const Unsigned128& lhs, unsigned shift) {
  shift &= 127;
  Unsigned128 rv;
  if (shift >= 64) {
    rv.hi = 0;
    rv.lo = lhs.hi >> (shift & 63);
  } else {
    uint64_t tmp = lhs.hi;
    rv.hi = tmp >> shift;
    // Ensure shift==0 shifts away everything
    tmp = tmp << 1 << (63 - shift);
    rv.lo = tmp | (lhs.lo >> shift);
  }
  return rv;
}

inline Unsigned128& operator>>=(Unsigned128& lhs, unsigned shift) {
  lhs = lhs >> shift;
  return lhs;
}

inline Unsigned128 operator&(const Unsigned128& lhs, const Unsigned128& rhs) {
  return Unsigned128(lhs.lo & rhs.lo, lhs.hi & rhs.hi);
}

inline Unsigned128& operator&=(Unsigned128& lhs, const Unsigned128& rhs) {
  lhs = lhs & rhs;
  return lhs;
}

inline Unsigned128 operator|(const Unsigned128& lhs, const Unsigned128& rhs) {
  return Unsigned128(lhs.lo | rhs.lo, lhs.hi | rhs.hi);
}

inline Unsigned128& operator|=(Unsigned128& lhs, const Unsigned128& rhs) {
  lhs = lhs | rhs;
  return lhs;
}

inline Unsigned128 operator^(const Unsigned128& lhs, const Unsigned128& rhs) {
  return Unsigned128(lhs.lo ^ rhs.lo, lhs.hi ^ rhs.hi);
}

inline Unsigned128& operator^=(Unsigned128& lhs, const Unsigned128& rhs) {
  lhs = lhs ^ rhs;
  return lhs;
}

inline Unsigned128 operator~(const Unsigned128& v) {
  return Unsigned128(~v.lo, ~v.hi);
}

inline bool operator==(const Unsigned128& lhs, const Unsigned128& rhs) {
  return lhs.lo == rhs.lo && lhs.hi == rhs.hi;
}

inline bool operator!=(const Unsigned128& lhs, const Unsigned128& rhs) {
  return lhs.lo != rhs.lo || lhs.hi != rhs.hi;
}

inline bool operator>(const Unsigned128& lhs, const Unsigned128& rhs) {
  return lhs.hi > rhs.hi || (lhs.hi == rhs.hi && lhs.lo > rhs.lo);
}

inline bool operator<(const Unsigned128& lhs, const Unsigned128& rhs) {
  return lhs.hi < rhs.hi || (lhs.hi == rhs.hi && lhs.lo < rhs.lo);
}

inline bool operator>=(const Unsigned128& lhs, const Unsigned128& rhs) {
  return lhs.hi > rhs.hi || (lhs.hi == rhs.hi && lhs.lo >= rhs.lo);
}

inline bool operator<=(const Unsigned128& lhs, const Unsigned128& rhs) {
  return lhs.hi < rhs.hi || (lhs.hi == rhs.hi && lhs.lo <= rhs.lo);
}
#endif

inline uint64_t Lower64of128(Unsigned128 v) {
#ifdef HAVE_UINT128_EXTENSION
  return static_cast<uint64_t>(v);
#else
  return v.lo;
#endif
}

inline uint64_t Upper64of128(Unsigned128 v) {
#ifdef HAVE_UINT128_EXTENSION
  return static_cast<uint64_t>(v >> 64);
#else
  return v.hi;
#endif
}

// This generally compiles down to a single fast instruction on 64-bit.
// This doesn't really make sense as operator* because it's not a
// general 128x128 multiply and provides more output than 64x64 multiply.
inline Unsigned128 Multiply64to128(uint64_t a, uint64_t b) {
#ifdef HAVE_UINT128_EXTENSION
  return Unsigned128{a} * Unsigned128{b};
#else
  // Full decomposition
  // NOTE: GCC seems to fully understand this code as 64-bit x 64-bit
  // -> 128-bit multiplication and optimize it appropriately.
  uint64_t tmp = uint64_t{b & 0xffffFFFF} * uint64_t{a & 0xffffFFFF};
  uint64_t lower = tmp & 0xffffFFFF;
  tmp >>= 32;
  tmp += uint64_t{b & 0xffffFFFF} * uint64_t{a >> 32};
  // Avoid overflow: first add lower 32 of tmp2, and later upper 32
  uint64_t tmp2 = uint64_t{b >> 32} * uint64_t{a & 0xffffFFFF};
  tmp += tmp2 & 0xffffFFFF;
  lower |= tmp << 32;
  tmp >>= 32;
  tmp += tmp2 >> 32;
  tmp += uint64_t{b >> 32} * uint64_t{a >> 32};
  return Unsigned128(lower, tmp);
#endif
}

template <>
inline Unsigned128 BottomNBits(Unsigned128 v, int nbits) {
  if (nbits < 64) {
    return BottomNBits(Lower64of128(v), nbits);
  } else {
    return (Unsigned128{BottomNBits(Upper64of128(v), nbits - 64)} << 64) |
           Lower64of128(v);
  }
}

template <>
inline int FloorLog2(Unsigned128 v) {
  if (Upper64of128(v) == 0) {
    return FloorLog2(Lower64of128(v));
  } else {
    return FloorLog2(Upper64of128(v)) + 64;
  }
}

template <>
inline int CountTrailingZeroBits(Unsigned128 v) {
  if (Lower64of128(v) != 0) {
    return CountTrailingZeroBits(Lower64of128(v));
  } else {
    return CountTrailingZeroBits(Upper64of128(v)) + 64;
  }
}

template <>
inline int BitsSetToOne(Unsigned128 v) {
  return BitsSetToOne(Lower64of128(v)) + BitsSetToOne(Upper64of128(v));
}

template <>
inline int BitParity(Unsigned128 v) {
  return BitParity(Lower64of128(v) ^ Upper64of128(v));
}

template <>
inline Unsigned128 EndianSwapValue(Unsigned128 v) {
  return (Unsigned128{EndianSwapValue(Lower64of128(v))} << 64) |
         EndianSwapValue(Upper64of128(v));
}

template <>
inline Unsigned128 ReverseBits(Unsigned128 v) {
  return (Unsigned128{ReverseBits(Lower64of128(v))} << 64) |
         ReverseBits(Upper64of128(v));
}

template <>
inline Unsigned128 DownwardInvolution(Unsigned128 v) {
  return (Unsigned128{DownwardInvolution(Upper64of128(v))} << 64) |
         DownwardInvolution(Upper64of128(v) ^ Lower64of128(v));
}

template <typename A>
inline std::remove_reference_t<A> BitwiseAnd(A a, Unsigned128 b) {
  static_assert(sizeof(A) <= sizeof(Unsigned128));
  return static_cast<A>(a & b);
}

template <typename B>
inline std::remove_reference_t<B> BitwiseAnd(Unsigned128 a, B b) {
  static_assert(sizeof(B) <= sizeof(Unsigned128));
  return static_cast<B>(a & b);
}

template <typename T>
struct IsUnsignedUpTo128
    : std::integral_constant<bool, std::is_unsigned<T>::value ||
                                       std::is_same<T, Unsigned128>::value> {};

inline void EncodeFixed128(char* dst, Unsigned128 value) {
  EncodeFixed64(dst, Lower64of128(value));
  EncodeFixed64(dst + 8, Upper64of128(value));
}

inline Unsigned128 DecodeFixed128(const char* ptr) {
  Unsigned128 rv = DecodeFixed64(ptr + 8);
  return (rv << 64) | DecodeFixed64(ptr);
}

// A version of EncodeFixed* for generic algorithms. Likely to be used
// with Unsigned128, so lives here for now.
template <typename T>
inline void EncodeFixedGeneric(char* /*dst*/, T /*value*/) {
  // Unfortunately, GCC does not appear to optimize this simple code down
  // to a trivial load on Intel:
  //
  // T ret_val = 0;
  // for (size_t i = 0; i < sizeof(T); ++i) {
  //   ret_val |= (static_cast<T>(static_cast<unsigned char>(ptr[i])) << (8 *
  //   i));
  // }
  // return ret_val;
  //
  // But does unroll the loop, and does optimize manually unrolled version
  // for specific sizes down to a trivial load. I have no idea why it doesn't
  // do both on this code.

  // So instead, we rely on specializations
  static_assert(sizeof(T) == 0, "No specialization provided for this type");
}

template <>
inline void EncodeFixedGeneric(char* dst, uint16_t value) {
  return EncodeFixed16(dst, value);
}
template <>
inline void EncodeFixedGeneric(char* dst, uint32_t value) {
  return EncodeFixed32(dst, value);
}
template <>
inline void EncodeFixedGeneric(char* dst, uint64_t value) {
  return EncodeFixed64(dst, value);
}
template <>
inline void EncodeFixedGeneric(char* dst, Unsigned128 value) {
  return EncodeFixed128(dst, value);
}

// A version of EncodeFixed* for generic algorithms.
template <typename T>
inline T DecodeFixedGeneric(const char* /*dst*/) {
  static_assert(sizeof(T) == 0, "No specialization provided for this type");
}

template <>
inline uint16_t DecodeFixedGeneric(const char* dst) {
  return DecodeFixed16(dst);
}
template <>
inline uint32_t DecodeFixedGeneric(const char* dst) {
  return DecodeFixed32(dst);
}
template <>
inline uint64_t DecodeFixedGeneric(const char* dst) {
  return DecodeFixed64(dst);
}
template <>
inline Unsigned128 DecodeFixedGeneric(const char* dst) {
  return DecodeFixed128(dst);
}

}  // namespace ROCKSDB_NAMESPACE