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

 #ifndef LLVM_SUPPORT_MATHEXTRAS_H
 #define LLVM_SUPPORT_MATHEXTRAS_H

 #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 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.