text: //===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
  //
  //                     The LLVM Compiler Infrastructure
  //
  // This file is distributed under the University of Illinois Open Source
  // License. See LICENSE.TXT for details.
  //
  //===----------------------------------------------------------------------===//
  //
  // This file contains some functions that are useful for math stuff.
  //
  //===----------------------------------------------------------------------===//
  
  #ifndef LLVM_SUPPORT_MATHEXTRAS_H
  #define LLVM_SUPPORT_MATHEXTRAS_H
  
  #include "llvm/System/DataTypes.h"
  
  namespace llvm {
  
  // 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.
  
  /// Hi_32 - This function returns the high 32 bits of a 64 bit value.
  inline uint32_t Hi_32(uint64_t Value) {
    return static_cast<uint32_t>(Value >> 32);
  }
  
  /// Lo_32 - This function returns the low 32 bits of a 64 bit value.
  inline uint32_t Lo_32(uint64_t Value) {
    return static_cast<uint32_t>(Value);
  }
  
  /// isInt - Checks if an integer fits into the given bit width.
  template<unsigned N>
  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<>
  inline bool isInt<8>(int64_t x) {
    return static_cast<int8_t>(x) == x;
  }
  template<>
  inline bool isInt<16>(int64_t x) {
    return static_cast<int16_t>(x) == x;
  }
  template<>
  inline bool isInt<32>(int64_t x) {
    return static_cast<int32_t>(x) == x;
  }
  
  /// isUInt - Checks if an unsigned integer fits into the given bit width.
  template<unsigned N>
  inline bool isUInt(uint64_t x) {
    return N >= 64 || x < (UINT64_C(1)<<N);
  }
  // Template specializations to get better code for common cases.
  template<>
  inline bool isUInt<8>(uint64_t x) {
    return static_cast<uint8_t>(x) == x;
  }
  template<>
  inline bool isUInt<16>(uint64_t x) {
    return static_cast<uint16_t>(x) == x;
  }
  template<>
  inline bool isUInt<32>(uint64_t x) {
    return static_cast<uint32_t>(x) == x;
  }
  
  /// isMask_32 - This function returns true if the argument is a sequence of ones
  /// starting at the least significant bit with the remainder zero (32 bit
  /// version).   Ex. isMask_32(0x0000FFFFU) == true.
  inline bool isMask_32(uint32_t Value) {
    return Value && ((Value + 1) & Value) == 0;
  }
  
  /// isMask_64 - This function returns true if the argument is a sequence of ones
  /// starting at the least significant bit with the remainder zero (64 bit
  /// version).
  inline bool isMask_64(uint64_t Value) {
    return Value && ((Value + 1) & Value) == 0;
  }
  
  /// isShiftedMask_32 - This function returns true if the argument contains a
  /// sequence of ones with the remainder zero (32 bit version.)
  /// Ex. isShiftedMask_32(0x0000FF00U) == true.
  inline bool isShiftedMask_32(uint32_t Value) {
    return isMask_32((Value - 1) | Value);
  }
  
  /// isShiftedMask_64 - This function returns true if the argument contains a
  /// sequence of ones with the remainder zero (64 bit version.)
  inline bool isShiftedMask_64(uint64_t Value) {
    return isMask_64((Value - 1) | Value);
  }
  
  /// isPowerOf2_32 - This function returns true if the argument is a power of
  /// two > 0. Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
  inline bool isPowerOf2_32(uint32_t Value) {
    return Value && !(Value & (Value - 1));
  }
  
  /// isPowerOf2_64 - This function returns true if the argument is a power of two
  /// > 0 (64 bit edition.)
  inline bool isPowerOf2_64(uint64_t Value) {
    return Value && !(Value & (Value - int64_t(1L)));
  }
  
  /// ByteSwap_16 - This function returns a byte-swapped representation of the
  /// 16-bit argument, Value.
  inline uint16_t ByteSwap_16(uint16_t Value) {
  #if defined(_MSC_VER) && !defined(_DEBUG)
    // The DLL version of the runtime lacks these functions (bug!?), but in a
    // release build they're replaced with BSWAP instructions anyway.
    return _byteswap_ushort(Value);
  #else
    uint16_t Hi = Value << 8;
    uint16_t Lo = Value >> 8;
    return Hi | Lo;
  #endif
  }
  
  /// ByteSwap_32 - This function returns a byte-swapped representation of the
  /// 32-bit argument, Value.
  inline uint32_t ByteSwap_32(uint32_t Value) {
  #if defined(__llvm__) || \
      (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3)) && !defined(__ICC)
    return __builtin_bswap32(Value);
  #elif defined(_MSC_VER) && !defined(_DEBUG)
    return _byteswap_ulong(Value);
  #else
    uint32_t Byte0 = Value & 0x000000FF;
    uint32_t Byte1 = Value & 0x0000FF00;
    uint32_t Byte2 = Value & 0x00FF0000;
    uint32_t Byte3 = Value & 0xFF000000;
    return (Byte0 << 24) | (Byte1 << 8) | (Byte2 >> 8) | (Byte3 >> 24);
  #endif
  }
  
  /// ByteSwap_64 - This function returns a byte-swapped representation of the
  /// 64-bit argument, Value.
  inline uint64_t ByteSwap_64(uint64_t Value) {
  #if defined(__llvm__) || \
      (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3)) && !defined(__ICC)
    return __builtin_bswap64(Value);
  #elif defined(_MSC_VER) && !defined(_DEBUG)
    return _byteswap_uint64(Value);
  #else
    uint64_t Hi = ByteSwap_32(uint32_t(Value));
    uint32_t Lo = ByteSwap_32(uint32_t(Value >> 32));
    return (Hi << 32) | Lo;
  #endif
  }
  
  /// CountLeadingZeros_32 - this function performs the platform optimal form of
  /// counting the number of zeros from the most significant bit to the first one
  /// bit.  Ex. CountLeadingZeros_32(0x00F000FF) == 8.
  /// Returns 32 if the word is zero.
  inline unsigned CountLeadingZeros_32(uint32_t Value) {
    unsigned Count; // result
  #if __GNUC__ >= 4
    // PowerPC is defined for __builtin_clz(0)
  #if !defined(__ppc__) && !defined(__ppc64__)
    if (!Value) return 32;
  #endif
    Count = __builtin_clz(Value);
  #else
    if (!Value) return 32;
    Count = 0;
    // bisection method for count leading zeros
    for (unsigned Shift = 32 >> 1; Shift; Shift >>= 1) {
      uint32_t Tmp = Value >> Shift;
      if (Tmp) {
        Value = Tmp;
      } else {
        Count |= Shift;
      }
    }
  #endif
    return Count;
  }
  
  /// CountLeadingOnes_32 - this function performs the operation of
  /// counting the number of ones from the most significant bit to the first zero
  /// bit.  Ex. CountLeadingOnes_32(0xFF0FFF00) == 8.
  /// Returns 32 if the word is all ones.
  inline unsigned CountLeadingOnes_32(uint32_t Value) {
    return CountLeadingZeros_32(~Value);
  }
  
  /// CountLeadingZeros_64 - This function performs the platform optimal form
  /// of counting the number of zeros from the most significant bit to the first
  /// one bit (64 bit edition.)
  /// Returns 64 if the word is zero.
  inline unsigned CountLeadingZeros_64(uint64_t Value) {
    unsigned Count; // result
  #if __GNUC__ >= 4
    // PowerPC is defined for __builtin_clzll(0)
  #if !defined(__ppc__) && !defined(__ppc64__)
    if (!Value) return 64;
  #endif
    Count = __builtin_clzll(Value);
  #else
    if (sizeof(long) == sizeof(int64_t)) {
      if (!Value) return 64;
      Count = 0;
      // bisection method for count leading zeros
      for (unsigned Shift = 64 >> 1; Shift; Shift >>= 1) {
        uint64_t Tmp = Value >> Shift;
        if (Tmp) {
          Value = Tmp;
        } else {
          Count |= Shift;
        }
      }
    } else {
      // get hi portion
      uint32_t Hi = Hi_32(Value);
  
      // if some bits in hi portion
      if (Hi) {
          // leading zeros in hi portion plus all bits in lo portion
          Count = CountLeadingZeros_32(Hi);
      } else {
          // get lo portion
          uint32_t Lo = Lo_32(Value);
          // same as 32 bit value
          Count = CountLeadingZeros_32(Lo)+32;
      }
    }
  #endif
    return Count;
  }
  
  /// CountLeadingOnes_64 - This function performs the operation
  /// of counting the number of ones from the most significant bit to the first
  /// zero bit (64 bit edition.)
  /// Returns 64 if the word is all ones.
  inline unsigned CountLeadingOnes_64(uint64_t Value) {
    return CountLeadingZeros_64(~Value);
  }
  
  /// CountTrailingZeros_32 - this function performs the platform optimal form of
  /// counting the number of zeros from the least significant bit to the first one
  /// bit.  Ex. CountTrailingZeros_32(0xFF00FF00) == 8.
  /// Returns 32 if the word is zero.
  inline unsigned CountTrailingZeros_32(uint32_t Value) {
  #if __GNUC__ >= 4
    return Value ? __builtin_ctz(Value) : 32;
  #else
    static const unsigned Mod37BitPosition[] = {
      32, 0, 1, 26, 2, 23, 27, 0, 3, 16, 24, 30, 28, 11, 0, 13,
      4, 7, 17, 0, 25, 22, 31, 15, 29, 10, 12, 6, 0, 21, 14, 9,
      5, 20, 8, 19, 18
    };
    return Mod37BitPosition[(-Value & Value) % 37];
  #endif
  }
  
  /// CountTrailingOnes_32 - this function performs the operation of
  /// counting the number of ones from the least significant bit to the first zero
  /// bit.  Ex. CountTrailingOnes_32(0x00FF00FF) == 8.
  /// Returns 32 if the word is all ones.
  inline unsigned CountTrailingOnes_32(uint32_t Value) {
    return CountTrailingZeros_32(~Value);
  }
  
  /// CountTrailingZeros_64 - This function performs the platform optimal form
  /// of counting the number of zeros from the least significant bit to the first
  /// one bit (64 bit edition.)
  /// Returns 64 if the word is zero.
  inline unsigned CountTrailingZeros_64(uint64_t Value) {
  #if __GNUC__ >= 4
    return Value ? __builtin_ctzll(Value) : 64;
  #else
    static const unsigned Mod67Position[] = {
      64, 0, 1, 39, 2, 15, 40, 23, 3, 12, 16, 59, 41, 19, 24, 54,
      4, 64, 13, 10, 17, 62, 60, 28, 42, 30, 20, 51, 25, 44, 55,
      47, 5, 32, 65, 38, 14, 22, 11, 58, 18, 53, 63, 9, 61, 27,
      29, 50, 43, 46, 31, 37, 21, 57, 52, 8, 26, 49, 45, 36, 56,
      7, 48, 35, 6, 34, 33, 0
    };
    return Mod67Position[(-Value & Value) % 67];
  #endif
  }
  
  /// CountTrailingOnes_64 - This function performs the operation
  /// of counting the number of ones from the least significant bit to the first
  /// zero bit (64 bit edition.)
  /// Returns 64 if the word is all ones.
  inline unsigned CountTrailingOnes_64(uint64_t Value) {
    return CountTrailingZeros_64(~Value);
  }
  
  /// CountPopulation_32 - this function counts the number of set bits in a value.
  /// Ex. CountPopulation(0xF000F000) = 8
  /// Returns 0 if the word is zero.
  inline unsigned CountPopulation_32(uint32_t Value) {
  #if __GNUC__ >= 4
    return __builtin_popcount(Value);
  #else
    uint32_t v = Value - ((Value >> 1) & 0x55555555);
    v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
    return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
  #endif
  }
  
  /// CountPopulation_64 - this function counts the number of set bits in a value,
  /// (64 bit edition.)
  inline unsigned CountPopulation_64(uint64_t Value) {
  #if __GNUC__ >= 4
    return __builtin_popcountll(Value);
  #else
    uint64_t v = Value - ((Value >> 1) & 0x5555555555555555ULL);
    v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
    v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
    return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
  #endif
  }
  
  /// Log2_32 - This function returns 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 31 - CountLeadingZeros_32(Value);
  }
  
  /// Log2_64 - This function returns 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 63 - CountLeadingZeros_64(Value);
  }
  
  /// Log2_32_Ceil - This function returns 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 32-CountLeadingZeros_32(Value-1);
  }
  
  /// Log2_64_Ceil - This function returns 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 64-CountLeadingZeros_64(Value-1);
  }
  
  /// GreatestCommonDivisor64 - Return the greatest common divisor of the two
  /// 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;
  }
  
  /// BitsToDouble - This function takes a 64-bit integer and returns the bit
  /// equivalent double.
  inline double BitsToDouble(uint64_t Bits) {
    union {
      uint64_t L;
      double D;
    } T;
    T.L = Bits;
    return T.D;
  }
  
  /// BitsToFloat - This function takes a 32-bit integer and returns the bit
  /// equivalent float.
  inline float BitsToFloat(uint32_t Bits) {
    union {
      uint32_t I;
      float F;
    } T;
    T.I = Bits;
    return T.F;
  }
  
  /// DoubleToBits - 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) {
    union {
      uint64_t L;
      double D;
    } T;
    T.D = Double;
    return T.L;
  }
  
  /// FloatToBits - 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) {
    union {
      uint32_t I;
      float F;
    } T;
    T.F = Float;
    return T.I;
  }
  
  /// Platform-independent wrappers for the C99 isnan() function.
  int IsNAN(float f);
  int IsNAN(double d);
  
  /// Platform-independent wrappers for the C99 isinf() function.
  int IsInf(float f);
  int IsInf(double d);
  
  /// MinAlign - A and B are either alignments or offsets.  Return the minimum
  /// alignment that may be assumed after adding the two together.
  static inline uint64_t MinAlign(uint64_t A, uint64_t B) {
    // The largest power of 2 that divides both A and B.
    return (A | B) & -(A | B);
  }
  
  /// NextPowerOf2 - Returns the next power of two (in 64-bits)
  /// that is strictly greater than A.  Returns zero on overflow.
  static 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;
  }
  
  /// RoundUpToAlignment - Returns the next integer (mod 2**64) that is
  /// greater than or equal to \arg Value and is a multiple of \arg
  /// Align. Align must be non-zero.
  ///
  /// Examples:
  /// RoundUpToAlignment(5, 8) = 8
  /// RoundUpToAlignment(17, 8) = 24
  /// RoundUpToAlignment(~0LL, 8) = 0
  inline uint64_t RoundUpToAlignment(uint64_t Value, uint64_t Align) {
    return ((Value + Align - 1) / Align) * Align;
  }
  
  /// OffsetToAlignment - Return the offset to the next integer (mod 2**64) that
  /// is greater than or equal to \arg Value and is a multiple of \arg
  /// Align. Align must be non-zero.
  inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
    return RoundUpToAlignment(Value, Align) - Value;
  }
  
  /// abs64 - absolute value of a 64-bit int.  Not all environments support
  /// "abs" on whatever their name for the 64-bit int type is.  The absolute
  /// value of the largest negative number is undefined, as with "abs".
  inline int64_t abs64(int64_t x) {
    return (x < 0) ? -x : x;
  }
  
  /// SignExtend32 - Sign extend B-bit number x to 32-bit int.
  /// Usage int32_t r = SignExtend32<5>(x);
  template <unsigned B> inline int32_t SignExtend32(uint32_t x) {
    return int32_t(x << (32 - B)) >> (32 - B);
  }
  
  /// SignExtend64 - Sign extend B-bit number x to 64-bit int.
  /// Usage int64_t r = SignExtend64<5>(x);
  template <unsigned B> inline int64_t SignExtend64(uint64_t x) {
    return int64_t(x << (64 - B)) >> (64 - B);
  }
  
  } // End llvm namespace
  
  #endif
  