FM / util

/usr/local/lib64/python3.6/site-packages/torch/include/c10/util/

/usr/local/lib64/python3.6/site-packages/torch/include/c10/util

Name	Size	Mode	Actions
accumulate.h	4205	0644	edit dl rm
AlignOf.h	4835	0644	edit dl rm
Array.h	11354	0644	edit dl rm
ArrayRef.h	9058	0644	edit dl rm
Backtrace.h	364	0644	edit dl rm
BFloat16-inl.h	9222	0644	edit dl rm
BFloat16-math.h	5217	0644	edit dl rm
BFloat16.h	2372	0644	edit dl rm
Bitset.h	3414	0644	edit dl rm
C++17.h	13329	0644	edit dl rm
complex.h	17542	0644	edit dl rm
complex_math.h	10902	0644	edit dl rm
complex_utils.h	958	0644	edit dl rm
ConstexprCrc.h	6633	0644	edit dl rm
copysign.h	866	0644	edit dl rm
DeadlockDetection.h	1920	0644	edit dl rm
Deprecated.h	3579	0644	edit dl rm
either.h	6423	0644	edit dl rm
env.h	835	0644	edit dl rm
Exception.h	24723	0644	edit dl rm
ExclusivelyOwned.h	4759	0644	edit dl rm
Flags.h	10056	0644	edit dl rm
flat_hash_map.h	61655	0644	edit dl rm
FunctionRef.h	2301	0644	edit dl rm
Half-inl.h	8674	0644	edit dl rm
Half.h	18965	0644	edit dl rm
hash.h	5084	0644	edit dl rm
IdWrapper.h	2348	0644	edit dl rm
intrusive_ptr.h	35563	0644	edit dl rm
in_place.h	350	0644	edit dl rm
irange.h	2679	0644	edit dl rm
LeftRight.h	6016	0644	edit dl rm
llvmMathExtras.h	29168	0644	edit dl rm
Logging.h	11256	0644	edit dl rm
logging_is_google_glog.h	2031	0644	edit dl rm
logging_is_not_google_glog.h	8271	0644	edit dl rm
MathConstants.h	858	0644	edit dl rm
math_compat.h	7296	0644	edit dl rm
MaybeOwned.h	6689	0644	edit dl rm
Metaprogramming.h	15288	0644	edit dl rm
numa.h	696	0644	edit dl rm
Optional.h	35592	0644	edit dl rm
order_preserving_flat_hash_map.h	65482	0644	edit dl rm
overloaded.h	709	0644	edit dl rm
python_stub.h	56	0644	edit dl rm
qint8.h	472	0644	edit dl rm
qint32.h	319	0644	edit dl rm
quint4x2.h	366	0644	edit dl rm
quint8.h	320	0644	edit dl rm
Registry.h	12242	0644	edit dl rm
reverse_iterator.h	8796	0644	edit dl rm
ScopeExit.h	1345	0644	edit dl rm
signal_handler.h	3154	0644	edit dl rm
SmallBuffer.h	1243	0644	edit dl rm
SmallVector.h	34456	0644	edit dl rm
sparse_bitset.h	26511	0644	edit dl rm
StringUtil.h	4538	0644	edit dl rm
string_utils.h	3989	0644	edit dl rm
string_view.h	20189	0644	edit dl rm
tempfile.h	6029	0644	edit dl rm
ThreadLocal.h	3883	0644	edit dl rm
ThreadLocalDebugInfo.h	2603	0644	edit dl rm
thread_name.h	148	0644	edit dl rm
Type.h	607	0644	edit dl rm
TypeCast.h	6972	0644	edit dl rm
typeid.h	18793	0644	edit dl rm
TypeIndex.h	5251	0644	edit dl rm
TypeList.h	16901	0644	edit dl rm
TypeTraits.h	5368	0644	edit dl rm
Unicode.h	295	0644	edit dl rm
UniqueVoidPtr.h	4117	0644	edit dl rm
Unroll.h	667	0644	edit dl rm
variant.h	95182	0644	edit dl rm
win32-headers.h	858	0644	edit dl rm

Edit: /usr/local/lib64/python3.6/site-packages/torch/include/c10/util/llvmMathExtras.h (29168B)

//===-- 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.
//
//===----------------------------------------------------------------------===//

#pragma once

#include <algorithm>
#include <cassert>
#include <climits>
#include <cmath>
#include <cstdint>
#include <cstring>
#include <limits>
#include <type_traits>

#ifdef __ANDROID_NDK__
#include <android/api-level.h>
#endif

#ifndef __has_builtin
#define __has_builtin(x) 0
#endif

#ifndef LLVM_GNUC_PREREQ
#if defined(__GNUC__) && defined(__GNUC_MINOR__) && defined(__GNUC_PATCHLEVEL__)
#define LLVM_GNUC_PREREQ(maj, min, patch)                             \
  ((__GNUC__ << 20) + (__GNUC_MINOR__ << 10) + __GNUC_PATCHLEVEL__ >= \
   ((maj) << 20) + ((min) << 10) + (patch))
#elif defined(__GNUC__) && defined(__GNUC_MINOR__)
#define LLVM_GNUC_PREREQ(maj, min, patch) \
  ((__GNUC__ << 20) + (__GNUC_MINOR__ << 10) >= ((maj) << 20) + ((min) << 10))
#else
#define LLVM_GNUC_PREREQ(maj, min, patch) 0
#endif
#endif

#ifdef _MSC_VER
// Declare these intrinsics manually rather including intrin.h. It's very
// expensive, and MathExtras.h is popular.
// #include <intrin.h>
extern "C" {
unsigned char _BitScanForward(unsigned long* _Index, unsigned long _Mask);
unsigned char _BitScanForward64(unsigned long* _Index, unsigned __int64 _Mask);
unsigned char _BitScanReverse(unsigned long* _Index, unsigned long _Mask);
unsigned char _BitScanReverse64(unsigned long* _Index, unsigned __int64 _Mask);
}
#endif

namespace c10 {
namespace llvm {
/// The behavior an operation has on an input of 0.
enum ZeroBehavior {
  /// The returned value is undefined.
  ZB_Undefined,
  /// The returned value is numeric_limits<T>::max()
  ZB_Max,
  /// The returned value is numeric_limits<T>::digits
  ZB_Width
};

namespace detail {
template <typename T, std::size_t SizeOfT>
struct TrailingZerosCounter {
  static std::size_t count(T Val, ZeroBehavior) {
    if (!Val)
      return std::numeric_limits<T>::digits;
    if (Val & 0x1)
      return 0;

// Bisection method.
    std::size_t ZeroBits = 0;
    T Shift = std::numeric_limits<T>::digits >> 1;
    T Mask = std::numeric_limits<T>::max() >> Shift;
    while (Shift) {
      if ((Val & Mask) == 0) {
        Val >>= Shift;
        ZeroBits |= Shift;
      }
      Shift >>= 1;
      Mask >>= Shift;
    }
    return ZeroBits;
  }
};

#if (defined(__GNUC__) && __GNUC__ >= 4) || defined(_MSC_VER)
template <typename T>
struct TrailingZerosCounter<T, 4> {
  static std::size_t count(T Val, ZeroBehavior ZB) {
    if (ZB != ZB_Undefined && Val == 0)
      return 32;

#if __has_builtin(__builtin_ctz) || LLVM_GNUC_PREREQ(4, 0, 0)
    return __builtin_ctz(Val);
#elif defined(_MSC_VER)
    unsigned long Index;
    _BitScanForward(&Index, Val);
    return Index;
#endif
  }
};

#if !defined(_MSC_VER) || defined(_M_X64)
template <typename T>
struct TrailingZerosCounter<T, 8> {
  static std::size_t count(T Val, ZeroBehavior ZB) {
    if (ZB != ZB_Undefined && Val == 0)
      return 64;

#if __has_builtin(__builtin_ctzll) || LLVM_GNUC_PREREQ(4, 0, 0)
    return __builtin_ctzll(Val);
#elif defined(_MSC_VER)
    unsigned long Index;
    _BitScanForward64(&Index, Val);
    return Index;
#endif
  }
};
#endif
#endif
} // namespace detail

/// Count number of 0's from the least significant bit to the most
///   stopping at the first 1.
///
/// Only unsigned integral types are allowed.
///
/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
///   valid arguments.
template <typename T>
std::size_t countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
  static_assert(
      std::numeric_limits<T>::is_integer && !std::numeric_limits<T>::is_signed,
      "Only unsigned integral types are allowed.");
  return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB);
}

namespace detail {
template <typename T, std::size_t SizeOfT>
struct LeadingZerosCounter {
  static std::size_t count(T Val, ZeroBehavior) {
    if (!Val)
      return std::numeric_limits<T>::digits;

// Bisection method.
    std::size_t ZeroBits = 0;
    for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
      T Tmp = Val >> Shift;
      if (Tmp)
        Val = Tmp;
      else
        ZeroBits |= Shift;
    }
    return ZeroBits;
  }
};

#if (defined(__GNUC__) && __GNUC__ >= 4) || defined(_MSC_VER)
template <typename T>
struct LeadingZerosCounter<T, 4> {
  static std::size_t count(T Val, ZeroBehavior ZB) {
    if (ZB != ZB_Undefined && Val == 0)
      return 32;

#if __has_builtin(__builtin_clz) || LLVM_GNUC_PREREQ(4, 0, 0)
    return __builtin_clz(Val);
#elif defined(_MSC_VER)
    unsigned long Index;
    _BitScanReverse(&Index, Val);
    return Index ^ 31;
#endif
  }
};

#if !defined(_MSC_VER) || defined(_M_X64)
template <typename T>
struct LeadingZerosCounter<T, 8> {
  static std::size_t count(T Val, ZeroBehavior ZB) {
    if (ZB != ZB_Undefined && Val == 0)
      return 64;

#if __has_builtin(__builtin_clzll) || LLVM_GNUC_PREREQ(4, 0, 0)
    return __builtin_clzll(Val);
#elif defined(_MSC_VER)
    unsigned long Index;
    _BitScanReverse64(&Index, Val);
    return Index ^ 63;
#endif
  }
};
#endif
#endif
} // namespace detail

/// Count number of 0's from the most significant bit to the least
///   stopping at the first 1.
///
/// Only unsigned integral types are allowed.
///
/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
///   valid arguments.
template <typename T>
std::size_t countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
  static_assert(
      std::numeric_limits<T>::is_integer && !std::numeric_limits<T>::is_signed,
      "Only unsigned integral types are allowed.");
  return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
}

/// Get the index of the first set bit starting from the least
///   significant bit.
///
/// Only unsigned integral types are allowed.
///
/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
///   valid arguments.
template <typename T>
T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
  if (ZB == ZB_Max && Val == 0)
    return std::numeric_limits<T>::max();

return countTrailingZeros(Val, ZB_Undefined);
}

/// 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) {
  static_assert(std::is_unsigned<T>::value, "Invalid type!");
  const unsigned Bits = CHAR_BIT * sizeof(T);
  assert(N <= Bits && "Invalid bit index");
  return N == 0 ? 0 : (T(-1) >> (Bits - 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) {
  return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - 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) {
  return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - 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) {
  return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
}

/// Get the index of the last set bit starting from the least
///   significant bit.
///
/// Only unsigned integral types are allowed.
///
/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
///   valid arguments.
template <typename T>
T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
  if (ZB == ZB_Max && Val == 0)
    return std::numeric_limits<T>::max();

// Use ^ instead of - because both gcc and llvm can remove the associated ^
  // in the __builtin_clz intrinsic on x86.
  return countLeadingZeros(Val, ZB_Undefined) ^
      (std::numeric_limits<T>::digits - 1);
}

/// Macro compressed bit reversal table for 256 bits.
///
/// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
static const unsigned char BitReverseTable256[256] = {
#define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
#define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
#define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
    R6(0),
    R6(2),
    R6(1),
    R6(3)
#undef R2
#undef R4
#undef R6
};

/// Reverse the bits in \p Val.
template <typename T>
T reverseBits(T Val) {
  unsigned char in[sizeof(Val)];
  unsigned char out[sizeof(Val)];
  std::memcpy(in, &Val, sizeof(Val));
  for (unsigned i = 0; i < sizeof(Val); ++i)
    out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
  std::memcpy(&Val, out, sizeof(Val));
  return 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 inline uint32_t Hi_32(uint64_t Value) {
  return static_cast<uint32_t>(Value >> 32);
}

/// Return the low 32 bits of a 64 bit value.
constexpr inline uint32_t Lo_32(uint64_t Value) {
  return static_cast<uint32_t>(Value);
}

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

/// Checks if an integer fits into the given bit width.
template <unsigned N>
constexpr inline bool isInt(int64_t x) {
  return N >= 64 ||
      (-(INT64_C(1) << (N - 1)) <= x && x < (INT64_C(1) << (N - 1)));
}
// Template specializations to get better code for common cases.
template <>
constexpr inline bool isInt<8>(int64_t x) {
  return static_cast<int8_t>(x) == x;
}
template <>
constexpr inline bool isInt<16>(int64_t x) {
  return static_cast<int16_t>(x) == x;
}
template <>
constexpr inline bool isInt<32>(int64_t x) {
  return static_cast<int32_t>(x) == x;
}

/// Checks if a signed integer is an N bit number shifted left by S.
template <unsigned N, unsigned S>
constexpr inline bool isShiftedInt(int64_t x) {
  static_assert(
      N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
  static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
  return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
}

/// Checks if an unsigned integer fits into the given bit width.
///
/// This is written as two functions rather than as simply
///
///   return N >= 64 || X < (UINT64_C(1) << N);
///
/// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
/// left too many places.
template <unsigned N>
constexpr inline typename std::enable_if<(N < 64), bool>::type isUInt(
    uint64_t X) {
  static_assert(N > 0, "isUInt<0> doesn't make sense");
  return X < (UINT64_C(1) << (N));
}
template <unsigned N>
constexpr inline typename std::enable_if<N >= 64, bool>::type isUInt(
    uint64_t X) {
  return true;
}

// Template specializations to get better code for common cases.
template <>
constexpr inline bool isUInt<8>(uint64_t x) {
  return static_cast<uint8_t>(x) == x;
}
template <>
constexpr inline bool isUInt<16>(uint64_t x) {
  return static_cast<uint16_t>(x) == x;
}
template <>
constexpr inline bool isUInt<32>(uint64_t x) {
  return static_cast<uint32_t>(x) == x;
}

/// Checks if a unsigned integer is an N bit number shifted left by S.
template <unsigned N, unsigned S>
constexpr inline bool isShiftedUInt(uint64_t x) {
  static_assert(
      N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
  static_assert(
      N + S <= 64, "isShiftedUInt<N, S> with N + S > 64 is too wide.");
  // Per the two static_asserts above, S must be strictly less than 64.  So
  // 1 << S is not undefined behavior.
  return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
}

/// Gets the maximum value for a N-bit unsigned integer.
inline uint64_t maxUIntN(uint64_t N) {
  assert(N > 0 && N <= 64 && "integer width out of range");

// uint64_t(1) << 64 is undefined behavior, so we can't do
  //   (uint64_t(1) << N) - 1
  // without checking first that N != 64.  But this works and doesn't have a
  // branch.
  return UINT64_MAX >> (64 - N);
}

// Ignore the false warning "Arithmetic overflow" for MSVC
#ifdef _MSC_VER
#pragma warning(push)
#pragma warning(disable : 4146)
#endif

/// Gets the minimum value for a N-bit signed integer.
inline int64_t minIntN(int64_t N) {
  assert(N > 0 && N <= 64 && "integer width out of range");

return -(UINT64_C(1) << (N - 1));
}

#ifdef _MSC_VER
#pragma warning(pop)
#endif

/// Gets the maximum value for a N-bit signed integer.
inline int64_t maxIntN(int64_t N) {
  assert(N > 0 && N <= 64 && "integer width out of range");

// This relies on two's complement wraparound when N == 64, so we convert to
  // int64_t only at the very end to avoid UB.
  return (UINT64_C(1) << (N - 1)) - 1;
}

/// Checks if an unsigned integer fits into the given (dynamic) bit width.
inline bool isUIntN(unsigned N, uint64_t x) {
  return N >= 64 || x <= maxUIntN(N);
}

/// Checks if an signed integer fits into the given (dynamic) bit width.
inline bool isIntN(unsigned N, int64_t x) {
  return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
}

/// 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 inline bool isMask_32(uint32_t Value) {
  return Value && ((Value + 1) & Value) == 0;
}

/// 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 inline bool isMask_64(uint64_t Value) {
  return Value && ((Value + 1) & Value) == 0;
}

/// 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 inline bool isShiftedMask_32(uint32_t Value) {
  return Value && isMask_32((Value - 1) | Value);
}

/// Return true if the argument contains a non-empty sequence of ones with the
/// remainder zero (64 bit version.)
constexpr inline bool isShiftedMask_64(uint64_t Value) {
  return Value && isMask_64((Value - 1) | Value);
}

/// Return true if the argument is a power of two > 0.
/// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
constexpr inline bool isPowerOf2_32(uint32_t Value) {
  return Value && !(Value & (Value - 1));
}

/// Return true if the argument is a power of two > 0 (64 bit edition.)
constexpr inline bool isPowerOf2_64(uint64_t Value) {
  return Value && !(Value & (Value - 1));
}

/// Count the number of ones from the most significant bit to the first
/// zero bit.
///
/// Ex. countLeadingOnes(0xFF0FFF00) == 8.
/// Only unsigned integral types are allowed.
///
/// \param ZB the behavior on an input of all ones. Only ZB_Width and
/// ZB_Undefined are valid arguments.
template <typename T>
std::size_t countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
  static_assert(
      std::numeric_limits<T>::is_integer && !std::numeric_limits<T>::is_signed,
      "Only unsigned integral types are allowed.");
  return countLeadingZeros<T>(~Value, ZB);
}

/// Count the number of ones from the least significant bit to the first
/// zero bit.
///
/// Ex. countTrailingOnes(0x00FF00FF) == 8.
/// Only unsigned integral types are allowed.
///
/// \param ZB the behavior on an input of all ones. Only ZB_Width and
/// ZB_Undefined are valid arguments.
template <typename T>
std::size_t countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
  static_assert(
      std::numeric_limits<T>::is_integer && !std::numeric_limits<T>::is_signed,
      "Only unsigned integral types are allowed.");
  return countTrailingZeros<T>(~Value, ZB);
}

namespace detail {
template <typename T, std::size_t SizeOfT>
struct PopulationCounter {
  static unsigned count(T Value) {
    // Generic version, forward to 32 bits.
    static_assert(SizeOfT <= 4, "Not implemented!");
#if defined(__GNUC__) && __GNUC__ >= 4
    return __builtin_popcount(Value);
#else
    uint32_t v = Value;
    v = v - ((v >> 1) & 0x55555555);
    v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
    return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
#endif
  }
};

template <typename T>
struct PopulationCounter<T, 8> {
  static unsigned count(T Value) {
#if defined(__GNUC__) && __GNUC__ >= 4
    return __builtin_popcountll(Value);
#else
    uint64_t v = Value;
    v = v - ((v >> 1) & 0x5555555555555555ULL);
    v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
    v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
    return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
#endif
  }
};
} // namespace detail

/// Count the number of set bits in a value.
/// Ex. countPopulation(0xF000F000) = 8
/// Returns 0 if the word is zero.
template <typename T>
inline unsigned countPopulation(T Value) {
  static_assert(
      std::numeric_limits<T>::is_integer && !std::numeric_limits<T>::is_signed,
      "Only unsigned integral types are allowed.");
  return detail::PopulationCounter<T, sizeof(T)>::count(Value);
}

/// Return the log base 2 of the specified value.
inline double Log2(double Value) {
#if defined(__ANDROID_API__) && __ANDROID_API__ < 18
  return __builtin_log(Value) / __builtin_log(2.0);
#else
  return log2(Value);
#endif
}

/// 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 static_cast<unsigned>(31 - countLeadingZeros(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 static_cast<unsigned>(63 - countLeadingZeros(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 static_cast<unsigned>(32 - countLeadingZeros(Value - 1));
}

/// 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) {
  return static_cast<unsigned>(64 - countLeadingZeros(Value - 1));
}

/// Return the greatest common divisor of the values using Euclid's algorithm.
inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
  while (B) {
    uint64_t T = B;
    B = A % B;
    A = T;
  }
  return A;
}

/// This function takes a 64-bit integer and returns the bit equivalent double.
inline double BitsToDouble(uint64_t Bits) {
  double D;
  static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
  memcpy(&D, &Bits, sizeof(Bits));
  return D;
}

/// This function takes a 32-bit integer and returns the bit equivalent float.
inline float BitsToFloat(uint32_t Bits) {
  // TODO: Use bit_cast once C++20 becomes available.
  float F;
  static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
  memcpy(&F, &Bits, sizeof(Bits));
  return F;
}

/// This function takes a double and returns the bit equivalent 64-bit integer.
/// Note that copying doubles around changes the bits of NaNs on some hosts,
/// notably x86, so this routine cannot be used if these bits are needed.
inline uint64_t DoubleToBits(double Double) {
  uint64_t Bits;
  static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
  memcpy(&Bits, &Double, sizeof(Double));
  return Bits;
}

/// This function takes a float and returns the bit equivalent 32-bit integer.
/// Note that copying floats around changes the bits of NaNs on some hosts,
/// notably x86, so this routine cannot be used if these bits are needed.
inline uint32_t FloatToBits(float Float) {
  uint32_t Bits;
  static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
  memcpy(&Bits, &Float, sizeof(Float));
  return Bits;
}

/// A and B are either alignments or offsets. Return the minimum alignment that
/// may be assumed after adding the two together.
constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
  // The largest power of 2 that divides both A and B.
  //
  // Replace "-Value" by "1+~Value" in the following commented code to avoid
  // MSVC warning C4146
  //    return (A | B) & -(A | B);
  return (A | B) & (1 + ~(A | B));
}

/// Aligns \c Addr to \c Alignment bytes, rounding up.
///
/// Alignment should be a power of two.  This method rounds up, so
/// alignAddr(7, 4) == 8 and alignAddr(8, 4) == 8.
inline uintptr_t alignAddr(const void* Addr, size_t Alignment) {
  assert(
      Alignment && isPowerOf2_64((uint64_t)Alignment) &&
      "Alignment is not a power of two!");

assert((uintptr_t)Addr + Alignment - 1 >= (uintptr_t)Addr);

return (((uintptr_t)Addr + Alignment - 1) & ~(uintptr_t)(Alignment - 1));
}

/// Returns the necessary adjustment for aligning \c Ptr to \c Alignment
/// bytes, rounding up.
inline size_t alignmentAdjustment(const void* Ptr, size_t Alignment) {
  return alignAddr(Ptr, Alignment) - (uintptr_t)Ptr;
}

/// Returns the next power of two (in 64-bits) that is strictly greater than A.
/// Returns zero on overflow.
inline uint64_t NextPowerOf2(uint64_t A) {
  A |= (A >> 1);
  A |= (A >> 2);
  A |= (A >> 4);
  A |= (A >> 8);
  A |= (A >> 16);
  A |= (A >> 32);
  return A + 1;
}

/// Returns the power of two which is less than or equal to the given value.
/// Essentially, it is a floor operation across the domain of powers of two.
inline uint64_t PowerOf2Floor(uint64_t A) {
  if (!A)
    return 0;
  return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
}

/// 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) {
  if (!A)
    return 0;
  return NextPowerOf2(A - 1);
}

/// Returns the next integer (mod 2**64) that is greater than or equal to
/// \p Value and is a multiple of \p Align. \p Align must be non-zero.
///
/// If non-zero \p Skew is specified, the return value will be a minimal
/// integer that is greater than or equal to \p Value and equal to
/// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
/// \p Align, its value is adjusted to '\p Skew mod \p Align'.
///
/// Examples:
/// \code
///   alignTo(5, 8) = 8
///   alignTo(17, 8) = 24
///   alignTo(~0LL, 8) = 0
///   alignTo(321, 255) = 510
///
///   alignTo(5, 8, 7) = 7
///   alignTo(17, 8, 1) = 17
///   alignTo(~0LL, 8, 3) = 3
///   alignTo(321, 255, 42) = 552
/// \endcode
inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
  assert(Align != 0u && "Align can't be 0.");
  Skew %= Align;
  return (Value + Align - 1 - Skew) / Align * Align + Skew;
}

/// Returns the next integer (mod 2**64) that is greater than or equal to
/// \p Value and is a multiple of \c Align. \c Align must be non-zero.
template <uint64_t Align>
constexpr inline uint64_t alignTo(uint64_t Value) {
  static_assert(Align != 0u, "Align must be non-zero");
  return (Value + Align - 1) / Align * Align;
}

/// Returns the integer ceil(Numerator / Denominator).
inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
  return alignTo(Numerator, Denominator) / Denominator;
}

/// \c alignTo for contexts where a constant expression is required.
/// \sa alignTo
///
/// \todo FIXME: remove when \c constexpr becomes really \c constexpr
template <uint64_t Align>
struct AlignTo {
  static_assert(Align != 0u, "Align must be non-zero");
  template <uint64_t Value>
  struct from_value {
    static const uint64_t value = (Value + Align - 1) / Align * Align;
  };
};

/// Returns the largest uint64_t less than or equal to \p Value and is
/// \p Skew mod \p Align. \p Align must be non-zero
inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
  assert(Align != 0u && "Align can't be 0.");
  Skew %= Align;
  return (Value - Skew) / Align * Align + Skew;
}

/// Returns the offset to the next integer (mod 2**64) that is greater than
/// or equal to \p Value and is a multiple of \p Align. \p Align must be
/// non-zero.
inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
  return alignTo(Value, Align) - Value;
}

/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
/// Requires 0 < B <= 32.
template <unsigned B>
constexpr inline int32_t SignExtend32(uint32_t X) {
  static_assert(B > 0, "Bit width can't be 0.");
  static_assert(B <= 32, "Bit width out of range.");
  return int32_t(X << (32 - B)) >> (32 - B);
}

/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
/// Requires 0 < B < 32.
inline int32_t SignExtend32(uint32_t X, unsigned B) {
  assert(B > 0 && "Bit width can't be 0.");
  assert(B <= 32 && "Bit width out of range.");
  return int32_t(X << (32 - B)) >> (32 - B);
}

/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
/// Requires 0 < B < 64.
template <unsigned B>
constexpr inline int64_t SignExtend64(uint64_t x) {
  static_assert(B > 0, "Bit width can't be 0.");
  static_assert(B <= 64, "Bit width out of range.");
  return int64_t(x << (64 - B)) >> (64 - B);
}

/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
/// Requires 0 < B < 64.
inline int64_t SignExtend64(uint64_t X, unsigned B) {
  assert(B > 0 && "Bit width can't be 0.");
  assert(B <= 64 && "Bit width out of range.");
  return int64_t(X << (64 - B)) >> (64 - B);
}

/// Subtract two unsigned integers, X and Y, of type T and return the absolute
/// value of the result.
template <typename T>
typename std::enable_if<std::is_unsigned<T>::value, T>::type AbsoluteDifference(
    T X,
    T Y) {
  return std::max(X, Y) - std::min(X, 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>
typename std::enable_if<std::is_unsigned<T>::value, T>::type SaturatingAdd(
    T X,
    T Y,
    bool* ResultOverflowed = nullptr) {
  bool Dummy;
  bool& Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
  // Hacker's Delight, p. 29
  T Z = X + Y;
  Overflowed = (Z < X || Z < Y);
  if (Overflowed)
    return std::numeric_limits<T>::max();
  else
    return Z;
}

/// 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>
typename std::enable_if<std::is_unsigned<T>::value, T>::type SaturatingMultiply(
    T X,
    T Y,
    bool* ResultOverflowed = nullptr) {
  bool Dummy;
  bool& Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;

// Hacker's Delight, p. 30 has a different algorithm, but we don't use that
  // because it fails for uint16_t (where multiplication can have undefined
  // behavior due to promotion to int), and requires a division in addition
  // to the multiplication.

Overflowed = false;

// Log2(Z) would be either Log2Z or Log2Z + 1.
  // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
  // will necessarily be less than Log2Max as desired.
  int Log2Z = Log2_64(X) + Log2_64(Y);
  const T Max = std::numeric_limits<T>::max();
  int Log2Max = Log2_64(Max);
  if (Log2Z < Log2Max) {
    return X * Y;
  }
  if (Log2Z > Log2Max) {
    Overflowed = true;
    return Max;
  }

// We're going to use the top bit, and maybe overflow one
  // bit past it. Multiply all but the bottom bit then add
  // that on at the end.
  T Z = (X >> 1) * Y;
  if (Z & ~(Max >> 1)) {
    Overflowed = true;
    return Max;
  }
  Z <<= 1;
  if (X & 1)
    return SaturatingAdd(Z, Y, ResultOverflowed);

return Z;
}

/// 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>
typename std::enable_if<std::is_unsigned<T>::value, T>::type
SaturatingMultiplyAdd(T X, T Y, T A, bool* ResultOverflowed = nullptr) {
  bool Dummy;
  bool& Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;

T Product = SaturatingMultiply(X, Y, &Overflowed);
  if (Overflowed)
    return Product;

return SaturatingAdd(A, Product, &Overflowed);
}

/// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
extern const float huge_valf;
} // namespace llvm
} // namespace c10

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