text: //===-- llvm/ADT/APInt.h - For Arbitrary Precision Integer -----*- C++ -*--===//
  //
  //                     The LLVM Compiler Infrastructure
  //
  // This file is distributed under the University of Illinois Open Source
  // License. See LICENSE.TXT for details.
  //
  //===----------------------------------------------------------------------===//
  //
  // This file implements a class to represent arbitrary precision integral
  // constant values and operations on them.
  //
  //===----------------------------------------------------------------------===//
  
  #ifndef LLVM_APINT_H
  #define LLVM_APINT_H
  
  #include "llvm/Support/MathExtras.h"
  #include <cassert>
  #include <climits>
  #include <cstring>
  #include <string>
  
  namespace llvm {
    class Serializer;
    class Deserializer;
    class FoldingSetNodeID;
    class raw_ostream;
    class StringRef;
  
    template<typename T>
    class SmallVectorImpl;
  
    // An unsigned host type used as a single part of a multi-part
    // bignum.
    typedef uint64_t integerPart;
  
    const unsigned int host_char_bit = 8;
    const unsigned int integerPartWidth = host_char_bit *
      static_cast<unsigned int>(sizeof(integerPart));
  
  //===----------------------------------------------------------------------===//
  //                              APInt Class
  //===----------------------------------------------------------------------===//
  
  /// APInt - This class represents arbitrary precision constant integral values.
  /// It is a functional replacement for common case unsigned integer type like
  /// "unsigned", "unsigned long" or "uint64_t", but also allows non-byte-width
  /// integer sizes and large integer value types such as 3-bits, 15-bits, or more
  /// than 64-bits of precision. APInt provides a variety of arithmetic operators
  /// and methods to manipulate integer values of any bit-width. It supports both
  /// the typical integer arithmetic and comparison operations as well as bitwise
  /// manipulation.
  ///
  /// The class has several invariants worth noting:
  ///   * All bit, byte, and word positions are zero-based.
  ///   * Once the bit width is set, it doesn't change except by the Truncate,
  ///     SignExtend, or ZeroExtend operations.
  ///   * All binary operators must be on APInt instances of the same bit width.
  ///     Attempting to use these operators on instances with different bit
  ///     widths will yield an assertion.
  ///   * The value is stored canonically as an unsigned value. For operations
  ///     where it makes a difference, there are both signed and unsigned variants
  ///     of the operation. For example, sdiv and udiv. However, because the bit
  ///     widths must be the same, operations such as Mul and Add produce the same
  ///     results regardless of whether the values are interpreted as signed or
  ///     not.
  ///   * In general, the class tries to follow the style of computation that LLVM
  ///     uses in its IR. This simplifies its use for LLVM.
  ///
  /// @brief Class for arbitrary precision integers.
  class APInt {
    unsigned BitWidth;      ///< The number of bits in this APInt.
  
    /// This union is used to store the integer value. When the
    /// integer bit-width <= 64, it uses VAL, otherwise it uses pVal.
    union {
      uint64_t VAL;    ///< Used to store the <= 64 bits integer value.
      uint64_t *pVal;  ///< Used to store the >64 bits integer value.
    };
  
    /// This enum is used to hold the constants we needed for APInt.
    enum {
      /// Bits in a word
      APINT_BITS_PER_WORD = static_cast<unsigned int>(sizeof(uint64_t)) *
                            CHAR_BIT,
      /// Byte size of a word
      APINT_WORD_SIZE = static_cast<unsigned int>(sizeof(uint64_t))
    };
  
    /// This constructor is used only internally for speed of construction of
    /// temporaries. It is unsafe for general use so it is not public.
    /// @brief Fast internal constructor
    APInt(uint64_t* val, unsigned bits) : BitWidth(bits), pVal(val) { }
  
    /// @returns true if the number of bits <= 64, false otherwise.
    /// @brief Determine if this APInt just has one word to store value.
    bool isSingleWord() const {
      return BitWidth <= APINT_BITS_PER_WORD;
    }
  
    /// @returns the word position for the specified bit position.
    /// @brief Determine which word a bit is in.
    static unsigned whichWord(unsigned bitPosition) {
      return bitPosition / APINT_BITS_PER_WORD;
    }
  
    /// @returns the bit position in a word for the specified bit position
    /// in the APInt.
    /// @brief Determine which bit in a word a bit is in.
    static unsigned whichBit(unsigned bitPosition) {
      return bitPosition % APINT_BITS_PER_WORD;
    }
  
    /// This method generates and returns a uint64_t (word) mask for a single
    /// bit at a specific bit position. This is used to mask the bit in the
    /// corresponding word.
    /// @returns a uint64_t with only bit at "whichBit(bitPosition)" set
    /// @brief Get a single bit mask.
    static uint64_t maskBit(unsigned bitPosition) {
      return 1ULL << whichBit(bitPosition);
    }
  
    /// This method is used internally to clear the to "N" bits in the high order
    /// word that are not used by the APInt. This is needed after the most
    /// significant word is assigned a value to ensure that those bits are
    /// zero'd out.
    /// @brief Clear unused high order bits
    APInt& clearUnusedBits() {
      // Compute how many bits are used in the final word
      unsigned wordBits = BitWidth % APINT_BITS_PER_WORD;
      if (wordBits == 0)
        // If all bits are used, we want to leave the value alone. This also
        // avoids the undefined behavior of >> when the shift is the same size as
        // the word size (64).
        return *this;
  
      // Mask out the high bits.
      uint64_t mask = ~uint64_t(0ULL) >> (APINT_BITS_PER_WORD - wordBits);
      if (isSingleWord())
        VAL &= mask;
      else
        pVal[getNumWords() - 1] &= mask;
      return *this;
    }
  
    /// @returns the corresponding word for the specified bit position.
    /// @brief Get the word corresponding to a bit position
    uint64_t getWord(unsigned bitPosition) const {
      return isSingleWord() ? VAL : pVal[whichWord(bitPosition)];
    }
  
    /// Converts a string into a number.  The string must be non-empty
    /// and well-formed as a number of the given base. The bit-width
    /// must be sufficient to hold the result.
    ///
    /// This is used by the constructors that take string arguments.
    ///
    /// StringRef::getAsInteger is superficially similar but (1) does
    /// not assume that the string is well-formed and (2) grows the
    /// result to hold the input.
    ///
    /// @param radix 2, 8, 10, or 16
    /// @brief Convert a char array into an APInt
    void fromString(unsigned numBits, StringRef str, uint8_t radix);
  
    /// This is used by the toString method to divide by the radix. It simply
    /// provides a more convenient form of divide for internal use since KnuthDiv
    /// has specific constraints on its inputs. If those constraints are not met
    /// then it provides a simpler form of divide.
    /// @brief An internal division function for dividing APInts.
    static void divide(const APInt LHS, unsigned lhsWords,
                       const APInt &RHS, unsigned rhsWords,
                       APInt *Quotient, APInt *Remainder);
  
    /// out-of-line slow case for inline constructor
    void initSlowCase(unsigned numBits, uint64_t val, bool isSigned);
  
    /// out-of-line slow case for inline copy constructor
    void initSlowCase(const APInt& that);
  
    /// out-of-line slow case for shl
    APInt shlSlowCase(unsigned shiftAmt) const;
  
    /// out-of-line slow case for operator&
    APInt AndSlowCase(const APInt& RHS) const;
  
    /// out-of-line slow case for operator|
    APInt OrSlowCase(const APInt& RHS) const;
  
    /// out-of-line slow case for operator^
    APInt XorSlowCase(const APInt& RHS) const;
  
    /// out-of-line slow case for operator=
    APInt& AssignSlowCase(const APInt& RHS);
  
    /// out-of-line slow case for operator==
    bool EqualSlowCase(const APInt& RHS) const;
  
    /// out-of-line slow case for operator==
    bool EqualSlowCase(uint64_t Val) const;
  
    /// out-of-line slow case for countLeadingZeros
    unsigned countLeadingZerosSlowCase() const;
  
    /// out-of-line slow case for countTrailingOnes
    unsigned countTrailingOnesSlowCase() const;
  
    /// out-of-line slow case for countPopulation
    unsigned countPopulationSlowCase() const;
  
  public:
    /// @name Constructors
    /// @{
    /// If isSigned is true then val is treated as if it were a signed value
    /// (i.e. as an int64_t) and the appropriate sign extension to the bit width
    /// will be done. Otherwise, no sign extension occurs (high order bits beyond
    /// the range of val are zero filled).
    /// @param numBits the bit width of the constructed APInt
    /// @param val the initial value of the APInt
    /// @param isSigned how to treat signedness of val
    /// @brief Create a new APInt of numBits width, initialized as val.
    APInt(unsigned numBits, uint64_t val, bool isSigned = false)
      : BitWidth(numBits), VAL(0) {
      assert(BitWidth && "bitwidth too small");
      if (isSingleWord())
        VAL = val;
      else
        initSlowCase(numBits, val, isSigned);
      clearUnusedBits();
    }
  
    /// Note that numWords can be smaller or larger than the corresponding bit
    /// width but any extraneous bits will be dropped.
    /// @param numBits the bit width of the constructed APInt
    /// @param numWords the number of words in bigVal
    /// @param bigVal a sequence of words to form the initial value of the APInt
    /// @brief Construct an APInt of numBits width, initialized as bigVal[].
    APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[]);
  
    /// This constructor interprets the string \arg str in the given radix. The
    /// interpretation stops when the first character that is not suitable for the
    /// radix is encountered, or the end of the string. Acceptable radix values
    /// are 2, 8, 10 and 16. It is an error for the value implied by the string to
    /// require more bits than numBits.
    ///
    /// @param numBits the bit width of the constructed APInt
    /// @param str the string to be interpreted
    /// @param radix the radix to use for the conversion 
    /// @brief Construct an APInt from a string representation.
    APInt(unsigned numBits, StringRef str, uint8_t radix);
  
    /// Simply makes *this a copy of that.
    /// @brief Copy Constructor.
    APInt(const APInt& that)
      : BitWidth(that.BitWidth), VAL(0) {
      assert(BitWidth && "bitwidth too small");
      if (isSingleWord())
        VAL = that.VAL;
      else
        initSlowCase(that);
    }
  
    /// @brief Destructor.
    ~APInt() {
      if (!isSingleWord())
        delete [] pVal;
    }
  
    /// Default constructor that creates an uninitialized APInt.  This is useful
    ///  for object deserialization (pair this with the static method Read).
    explicit APInt() : BitWidth(1) {}
  
    /// Profile - Used to insert APInt objects, or objects that contain APInt
    ///  objects, into FoldingSets.
    void Profile(FoldingSetNodeID& id) const;
  
    /// @}
    /// @name Value Tests
    /// @{
    /// This tests the high bit of this APInt to determine if it is set.
    /// @returns true if this APInt is negative, false otherwise
    /// @brief Determine sign of this APInt.
    bool isNegative() const {
      return (*this)[BitWidth - 1];
    }
  
    /// This tests the high bit of the APInt to determine if it is unset.
    /// @brief Determine if this APInt Value is non-negative (>= 0)
    bool isNonNegative() const {
      return !isNegative();
    }
  
    /// This tests if the value of this APInt is positive (> 0). Note
    /// that 0 is not a positive value.
    /// @returns true if this APInt is positive.
    /// @brief Determine if this APInt Value is positive.
    bool isStrictlyPositive() const {
      return isNonNegative() && !!*this;
    }
  
    /// This checks to see if the value has all bits of the APInt are set or not.
    /// @brief Determine if all bits are set
    bool isAllOnesValue() const {
      return countPopulation() == BitWidth;
    }
  
    /// This checks to see if the value of this APInt is the maximum unsigned
    /// value for the APInt's bit width.
    /// @brief Determine if this is the largest unsigned value.
    bool isMaxValue() const {
      return countPopulation() == BitWidth;
    }
  
    /// This checks to see if the value of this APInt is the maximum signed
    /// value for the APInt's bit width.
    /// @brief Determine if this is the largest signed value.
    bool isMaxSignedValue() const {
      return BitWidth == 1 ? VAL == 0 :
                            !isNegative() && countPopulation() == BitWidth - 1;
    }
  
    /// This checks to see if the value of this APInt is the minimum unsigned
    /// value for the APInt's bit width.
    /// @brief Determine if this is the smallest unsigned value.
    bool isMinValue() const {
      return !*this;
    }
  
    /// This checks to see if the value of this APInt is the minimum signed
    /// value for the APInt's bit width.
    /// @brief Determine if this is the smallest signed value.
    bool isMinSignedValue() const {
      return BitWidth == 1 ? VAL == 1 : isNegative() && isPowerOf2();
    }
  
    /// @brief Check if this APInt has an N-bits unsigned integer value.
    bool isIntN(unsigned N) const {
      assert(N && "N == 0 ???");
      if (N >= getBitWidth())
        return true;
  
      if (isSingleWord())
        return isUIntN(N, VAL);
      return APInt(N, getNumWords(), pVal).zext(getBitWidth()) == (*this);
    }
  
    /// @brief Check if this APInt has an N-bits signed integer value.
    bool isSignedIntN(unsigned N) const {
      assert(N && "N == 0 ???");
      return getMinSignedBits() <= N;
    }
  
    /// @returns true if the argument APInt value is a power of two > 0.
    bool isPowerOf2() const {
      if (isSingleWord())
        return isPowerOf2_64(VAL);
      return countPopulationSlowCase() == 1;
    }
  
    /// isSignBit - Return true if this is the value returned by getSignBit.
    bool isSignBit() const { return isMinSignedValue(); }
  
    /// This converts the APInt to a boolean value as a test against zero.
    /// @brief Boolean conversion function.
    bool getBoolValue() const {
      return !!*this;
    }
  
    /// getLimitedValue - If this value is smaller than the specified limit,
    /// return it, otherwise return the limit value.  This causes the value
    /// to saturate to the limit.
    uint64_t getLimitedValue(uint64_t Limit = ~0ULL) const {
      return (getActiveBits() > 64 || getZExtValue() > Limit) ?
        Limit :  getZExtValue();
    }
  
    /// @}
    /// @name Value Generators
    /// @{
    /// @brief Gets maximum unsigned value of APInt for specific bit width.
    static APInt getMaxValue(unsigned numBits) {
      return getAllOnesValue(numBits);
    }
  
    /// @brief Gets maximum signed value of APInt for a specific bit width.
    static APInt getSignedMaxValue(unsigned numBits) {
      APInt API = getAllOnesValue(numBits);
      API.clearBit(numBits - 1);
      return API;
    }
  
    /// @brief Gets minimum unsigned value of APInt for a specific bit width.
    static APInt getMinValue(unsigned numBits) {
      return APInt(numBits, 0);
    }
  
    /// @brief Gets minimum signed value of APInt for a specific bit width.
    static APInt getSignedMinValue(unsigned numBits) {
      APInt API(numBits, 0);
      API.setBit(numBits - 1);
      return API;
    }
  
    /// getSignBit - This is just a wrapper function of getSignedMinValue(), and
    /// it helps code readability when we want to get a SignBit.
    /// @brief Get the SignBit for a specific bit width.
    static APInt getSignBit(unsigned BitWidth) {
      return getSignedMinValue(BitWidth);
    }
  
    /// @returns the all-ones value for an APInt of the specified bit-width.
    /// @brief Get the all-ones value.
    static APInt getAllOnesValue(unsigned numBits) {
      return APInt(numBits, -1ULL, true);
    }
  
    /// @returns the '0' value for an APInt of the specified bit-width.
    /// @brief Get the '0' value.
    static APInt getNullValue(unsigned numBits) {
      return APInt(numBits, 0);
    }
  
    /// Get an APInt with the same BitWidth as this APInt, just zero mask
    /// the low bits and right shift to the least significant bit.
    /// @returns the high "numBits" bits of this APInt.
    APInt getHiBits(unsigned numBits) const;
  
    /// Get an APInt with the same BitWidth as this APInt, just zero mask
    /// the high bits.
    /// @returns the low "numBits" bits of this APInt.
    APInt getLoBits(unsigned numBits) const;
  
    /// getOneBitSet - Return an APInt with exactly one bit set in the result.
    static APInt getOneBitSet(unsigned numBits, unsigned BitNo) {
      APInt Res(numBits, 0);
      Res.setBit(BitNo);
      return Res;
    }
    
    /// Constructs an APInt value that has a contiguous range of bits set. The
    /// bits from loBit (inclusive) to hiBit (exclusive) will be set. All other
    /// bits will be zero. For example, with parameters(32, 0, 16) you would get
    /// 0x0000FFFF. If hiBit is less than loBit then the set bits "wrap". For
    /// example, with parameters (32, 28, 4), you would get 0xF000000F.
    /// @param numBits the intended bit width of the result
    /// @param loBit the index of the lowest bit set.
    /// @param hiBit the index of the highest bit set.
    /// @returns An APInt value with the requested bits set.
    /// @brief Get a value with a block of bits set.
    static APInt getBitsSet(unsigned numBits, unsigned loBit, unsigned hiBit) {
      assert(hiBit <= numBits && "hiBit out of range");
      assert(loBit < numBits && "loBit out of range");
      if (hiBit < loBit)
        return getLowBitsSet(numBits, hiBit) |
               getHighBitsSet(numBits, numBits-loBit);
      return getLowBitsSet(numBits, hiBit-loBit).shl(loBit);
    }
  
    /// Constructs an APInt value that has the top hiBitsSet bits set.
    /// @param numBits the bitwidth of the result
    /// @param hiBitsSet the number of high-order bits set in the result.
    /// @brief Get a value with high bits set
    static APInt getHighBitsSet(unsigned numBits, unsigned hiBitsSet) {
      assert(hiBitsSet <= numBits && "Too many bits to set!");
      // Handle a degenerate case, to avoid shifting by word size
      if (hiBitsSet == 0)
        return APInt(numBits, 0);
      unsigned shiftAmt = numBits - hiBitsSet;
      // For small values, return quickly
      if (numBits <= APINT_BITS_PER_WORD)
        return APInt(numBits, ~0ULL << shiftAmt);
      return getAllOnesValue(numBits).shl(shiftAmt);
    }
  
    /// Constructs an APInt value that has the bottom loBitsSet bits set.
    /// @param numBits the bitwidth of the result
    /// @param loBitsSet the number of low-order bits set in the result.
    /// @brief Get a value with low bits set
    static APInt getLowBitsSet(unsigned numBits, unsigned loBitsSet) {
      assert(loBitsSet <= numBits && "Too many bits to set!");
      // Handle a degenerate case, to avoid shifting by word size
      if (loBitsSet == 0)
        return APInt(numBits, 0);
      if (loBitsSet == APINT_BITS_PER_WORD)
        return APInt(numBits, -1ULL);
      // For small values, return quickly.
      if (numBits < APINT_BITS_PER_WORD)
        return APInt(numBits, (1ULL << loBitsSet) - 1);
      return getAllOnesValue(numBits).lshr(numBits - loBitsSet);
    }
  
    /// The hash value is computed as the sum of the words and the bit width.
    /// @returns A hash value computed from the sum of the APInt words.
    /// @brief Get a hash value based on this APInt
    uint64_t getHashValue() const;
  
    /// This function returns a pointer to the internal storage of the APInt.
    /// This is useful for writing out the APInt in binary form without any
    /// conversions.
    const uint64_t* getRawData() const {
      if (isSingleWord())
        return &VAL;
      return &pVal[0];
    }
  
    /// @}
    /// @name Unary Operators
    /// @{
    /// @returns a new APInt value representing *this incremented by one
    /// @brief Postfix increment operator.
    const APInt operator++(int) {
      APInt API(*this);
      ++(*this);
      return API;
    }
  
    /// @returns *this incremented by one
    /// @brief Prefix increment operator.
    APInt& operator++();
  
    /// @returns a new APInt representing *this decremented by one.
    /// @brief Postfix decrement operator.
    const APInt operator--(int) {
      APInt API(*this);
      --(*this);
      return API;
    }
  
    /// @returns *this decremented by one.
    /// @brief Prefix decrement operator.
    APInt& operator--();
  
    /// Performs a bitwise complement operation on this APInt.
    /// @returns an APInt that is the bitwise complement of *this
    /// @brief Unary bitwise complement operator.
    APInt operator~() const {
      APInt Result(*this);
      Result.flipAllBits();
      return Result;
    }
  
    /// Negates *this using two's complement logic.
    /// @returns An APInt value representing the negation of *this.
    /// @brief Unary negation operator
    APInt operator-() const {
      return APInt(BitWidth, 0) - (*this);
    }
  
    /// Performs logical negation operation on this APInt.
    /// @returns true if *this is zero, false otherwise.
    /// @brief Logical negation operator.
    bool operator!() const;
  
    /// @}
    /// @name Assignment Operators
    /// @{
    /// @returns *this after assignment of RHS.
    /// @brief Copy assignment operator.
    APInt& operator=(const APInt& RHS) {
      // If the bitwidths are the same, we can avoid mucking with memory
      if (isSingleWord() && RHS.isSingleWord()) {
        VAL = RHS.VAL;
        BitWidth = RHS.BitWidth;
        return clearUnusedBits();
      }
  
      return AssignSlowCase(RHS);
    }
  
    /// The RHS value is assigned to *this. If the significant bits in RHS exceed
    /// the bit width, the excess bits are truncated. If the bit width is larger
    /// than 64, the value is zero filled in the unspecified high order bits.
    /// @returns *this after assignment of RHS value.
    /// @brief Assignment operator.
    APInt& operator=(uint64_t RHS);
  
    /// Performs a bitwise AND operation on this APInt and RHS. The result is
    /// assigned to *this.
    /// @returns *this after ANDing with RHS.
    /// @brief Bitwise AND assignment operator.
    APInt& operator&=(const APInt& RHS);
  
    /// Performs a bitwise OR operation on this APInt and RHS. The result is
    /// assigned *this;
    /// @returns *this after ORing with RHS.
    /// @brief Bitwise OR assignment operator.
    APInt& operator|=(const APInt& RHS);
  
    /// Performs a bitwise OR operation on this APInt and RHS. RHS is
    /// logically zero-extended or truncated to match the bit-width of
    /// the LHS.
    /// 
    /// @brief Bitwise OR assignment operator.
    APInt& operator|=(uint64_t RHS) {
      if (isSingleWord()) {
        VAL |= RHS;
        clearUnusedBits();
      } else {
        pVal[0] |= RHS;
      }
      return *this;
    }
  
    /// Performs a bitwise XOR operation on this APInt and RHS. The result is
    /// assigned to *this.
    /// @returns *this after XORing with RHS.
    /// @brief Bitwise XOR assignment operator.
    APInt& operator^=(const APInt& RHS);
  
    /// Multiplies this APInt by RHS and assigns the result to *this.
    /// @returns *this
    /// @brief Multiplication assignment operator.
    APInt& operator*=(const APInt& RHS);
  
    /// Adds RHS to *this and assigns the result to *this.
    /// @returns *this
    /// @brief Addition assignment operator.
    APInt& operator+=(const APInt& RHS);
  
    /// Subtracts RHS from *this and assigns the result to *this.
    /// @returns *this
    /// @brief Subtraction assignment operator.
    APInt& operator-=(const APInt& RHS);
  
    /// Shifts *this left by shiftAmt and assigns the result to *this.
    /// @returns *this after shifting left by shiftAmt
    /// @brief Left-shift assignment function.
    APInt& operator<<=(unsigned shiftAmt) {
      *this = shl(shiftAmt);
      return *this;
    }
  
    /// @}
    /// @name Binary Operators
    /// @{
    /// Performs a bitwise AND operation on *this and RHS.
    /// @returns An APInt value representing the bitwise AND of *this and RHS.
    /// @brief Bitwise AND operator.
    APInt operator&(const APInt& RHS) const {
      assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
      if (isSingleWord())
        return APInt(getBitWidth(), VAL & RHS.VAL);
      return AndSlowCase(RHS);
    }
    APInt And(const APInt& RHS) const {
      return this->operator&(RHS);
    }
  
    /// Performs a bitwise OR operation on *this and RHS.
    /// @returns An APInt value representing the bitwise OR of *this and RHS.
    /// @brief Bitwise OR operator.
    APInt operator|(const APInt& RHS) const {
      assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
      if (isSingleWord())
        return APInt(getBitWidth(), VAL | RHS.VAL);
      return OrSlowCase(RHS);
    }
    APInt Or(const APInt& RHS) const {
      return this->operator|(RHS);
    }
  
    /// Performs a bitwise XOR operation on *this and RHS.
    /// @returns An APInt value representing the bitwise XOR of *this and RHS.
    /// @brief Bitwise XOR operator.
    APInt operator^(const APInt& RHS) const {
      assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
      if (isSingleWord())
        return APInt(BitWidth, VAL ^ RHS.VAL);
      return XorSlowCase(RHS);
    }
    APInt Xor(const APInt& RHS) const {
      return this->operator^(RHS);
    }
  
    /// Multiplies this APInt by RHS and returns the result.
    /// @brief Multiplication operator.
    APInt operator*(const APInt& RHS) const;
  
    /// Adds RHS to this APInt and returns the result.
    /// @brief Addition operator.
    APInt operator+(const APInt& RHS) const;
    APInt operator+(uint64_t RHS) const {
      return (*this) + APInt(BitWidth, RHS);
    }
  
    /// Subtracts RHS from this APInt and returns the result.
    /// @brief Subtraction operator.
    APInt operator-(const APInt& RHS) const;
    APInt operator-(uint64_t RHS) const {
      return (*this) - APInt(BitWidth, RHS);
    }
  
    APInt operator<<(unsigned Bits) const {
      return shl(Bits);
    }
  
    APInt operator<<(const APInt &Bits) const {
      return shl(Bits);
    }
  
    /// Arithmetic right-shift this APInt by shiftAmt.
    /// @brief Arithmetic right-shift function.
    APInt ashr(unsigned shiftAmt) const;
  
    /// Logical right-shift this APInt by shiftAmt.
    /// @brief Logical right-shift function.
    APInt lshr(unsigned shiftAmt) const;
  
    /// Left-shift this APInt by shiftAmt.
    /// @brief Left-shift function.
    APInt shl(unsigned shiftAmt) const {
      assert(shiftAmt <= BitWidth && "Invalid shift amount");
      if (isSingleWord()) {
        if (shiftAmt == BitWidth)
          return APInt(BitWidth, 0); // avoid undefined shift results
        return APInt(BitWidth, VAL << shiftAmt);
      }
      return shlSlowCase(shiftAmt);
    }
  
    /// @brief Rotate left by rotateAmt.
    APInt rotl(unsigned rotateAmt) const;
  
    /// @brief Rotate right by rotateAmt.
    APInt rotr(unsigned rotateAmt) const;
  
    /// Arithmetic right-shift this APInt by shiftAmt.
    /// @brief Arithmetic right-shift function.
    APInt ashr(const APInt &shiftAmt) const;
  
    /// Logical right-shift this APInt by shiftAmt.
    /// @brief Logical right-shift function.
    APInt lshr(const APInt &shiftAmt) const;
  
    /// Left-shift this APInt by shiftAmt.
    /// @brief Left-shift function.
    APInt shl(const APInt &shiftAmt) const;
  
    /// @brief Rotate left by rotateAmt.
    APInt rotl(const APInt &rotateAmt) const;
  
    /// @brief Rotate right by rotateAmt.
    APInt rotr(const APInt &rotateAmt) const;
  
    /// Perform an unsigned divide operation on this APInt by RHS. Both this and
    /// RHS are treated as unsigned quantities for purposes of this division.
    /// @returns a new APInt value containing the division result
    /// @brief Unsigned division operation.
    APInt udiv(const APInt &RHS) const;
  
    /// Signed divide this APInt by APInt RHS.
    /// @brief Signed division function for APInt.
    APInt sdiv(const APInt &RHS) const {
      if (isNegative())
        if (RHS.isNegative())
          return (-(*this)).udiv(-RHS);
        else
          return -((-(*this)).udiv(RHS));
      else if (RHS.isNegative())
        return -(this->udiv(-RHS));
      return this->udiv(RHS);
    }
  
    /// Perform an unsigned remainder operation on this APInt with RHS being the
    /// divisor. Both this and RHS are treated as unsigned quantities for purposes
    /// of this operation. Note that this is a true remainder operation and not
    /// a modulo operation because the sign follows the sign of the dividend
    /// which is *this.
    /// @returns a new APInt value containing the remainder result
    /// @brief Unsigned remainder operation.
    APInt urem(const APInt &RHS) const;
  
    /// Signed remainder operation on APInt.
    /// @brief Function for signed remainder operation.
    APInt srem(const APInt &RHS) const {
      if (isNegative())
        if (RHS.isNegative())
          return -((-(*this)).urem(-RHS));
        else
          return -((-(*this)).urem(RHS));
      else if (RHS.isNegative())
        return this->urem(-RHS);
      return this->urem(RHS);
    }
  
    /// Sometimes it is convenient to divide two APInt values and obtain both the
    /// quotient and remainder. This function does both operations in the same
    /// computation making it a little more efficient. The pair of input arguments
    /// may overlap with the pair of output arguments. It is safe to call
    /// udivrem(X, Y, X, Y), for example.
    /// @brief Dual division/remainder interface.
    static void udivrem(const APInt &LHS, const APInt &RHS,
                        APInt &Quotient, APInt &Remainder);
  
    static void sdivrem(const APInt &LHS, const APInt &RHS,
                        APInt &Quotient, APInt &Remainder) {
      if (LHS.isNegative()) {
        if (RHS.isNegative())
          APInt::udivrem(-LHS, -RHS, Quotient, Remainder);
        else
          APInt::udivrem(-LHS, RHS, Quotient, Remainder);
        Quotient = -Quotient;
        Remainder = -Remainder;
      } else if (RHS.isNegative()) {
        APInt::udivrem(LHS, -RHS, Quotient, Remainder);
        Quotient = -Quotient;
      } else {
        APInt::udivrem(LHS, RHS, Quotient, Remainder);
      }
    }
    
    
    // Operations that return overflow indicators.
    APInt sadd_ov(const APInt &RHS, bool &Overflow) const;
    APInt uadd_ov(const APInt &RHS, bool &Overflow) const;
    APInt ssub_ov(const APInt &RHS, bool &Overflow) const;
    APInt usub_ov(const APInt &RHS, bool &Overflow) const;
    APInt sdiv_ov(const APInt &RHS, bool &Overflow) const;
    APInt smul_ov(const APInt &RHS, bool &Overflow) const;
    APInt sshl_ov(unsigned Amt, bool &Overflow) const;
  
    /// @returns the bit value at bitPosition
    /// @brief Array-indexing support.
    bool operator[](unsigned bitPosition) const;
  
    /// @}
    /// @name Comparison Operators
    /// @{
    /// Compares this APInt with RHS for the validity of the equality
    /// relationship.
    /// @brief Equality operator.
    bool operator==(const APInt& RHS) const {
      assert(BitWidth == RHS.BitWidth && "Comparison requires equal bit widths");
      if (isSingleWord())
        return VAL == RHS.VAL;
      return EqualSlowCase(RHS);
    }
  
    /// Compares this APInt with a uint64_t for the validity of the equality
    /// relationship.
    /// @returns true if *this == Val
    /// @brief Equality operator.
    bool operator==(uint64_t Val) const {
      if (isSingleWord())
        return VAL == Val;
      return EqualSlowCase(Val);
    }
  
    /// Compares this APInt with RHS for the validity of the equality
    /// relationship.
    /// @returns true if *this == Val
    /// @brief Equality comparison.
    bool eq(const APInt &RHS) const {
      return (*this) == RHS;
    }
  
    /// Compares this APInt with RHS for the validity of the inequality
    /// relationship.
    /// @returns true if *this != Val
    /// @brief Inequality operator.
    bool operator!=(const APInt& RHS) const {
      return !((*this) == RHS);
    }
  
    /// Compares this APInt with a uint64_t for the validity of the inequality
    /// relationship.
    /// @returns true if *this != Val
    /// @brief Inequality operator.
    bool operator!=(uint64_t Val) const {
      return !((*this) == Val);
    }
  
    /// Compares this APInt with RHS for the validity of the inequality
    /// relationship.
    /// @returns true if *this != Val
    /// @brief Inequality comparison
    bool ne(const APInt &RHS) const {
      return !((*this) == RHS);
    }
  
    /// Regards both *this and RHS as unsigned quantities and compares them for
    /// the validity of the less-than relationship.
    /// @returns true if *this < RHS when both are considered unsigned.
    /// @brief Unsigned less than comparison
    bool ult(const APInt &RHS) const;
  
    /// Regards both *this as an unsigned quantity and compares it with RHS for
    /// the validity of the less-than relationship.
    /// @returns true if *this < RHS when considered unsigned.
    /// @brief Unsigned less than comparison
    bool ult(uint64_t RHS) const {
      return ult(APInt(getBitWidth(), RHS));
    }
  
    /// Regards both *this and RHS as signed quantities and compares them for
    /// validity of the less-than relationship.
    /// @returns true if *this < RHS when both are considered signed.
    /// @brief Signed less than comparison
    bool slt(const APInt& RHS) const;
  
    /// Regards both *this as a signed quantity and compares it with RHS for
    /// the validity of the less-than relationship.
    /// @returns true if *this < RHS when considered signed.
    /// @brief Signed less than comparison
    bool slt(uint64_t RHS) const {
      return slt(APInt(getBitWidth(), RHS));
    }
  
    /// Regards both *this and RHS as unsigned quantities and compares them for
    /// validity of the less-or-equal relationship.
    /// @returns true if *this <= RHS when both are considered unsigned.
    /// @brief Unsigned less or equal comparison
    bool ule(const APInt& RHS) const {
      return ult(RHS) || eq(RHS);
    }
  
    /// Regards both *this as an unsigned quantity and compares it with RHS for
    /// the validity of the less-or-equal relationship.
    /// @returns true if *this <= RHS when considered unsigned.
    /// @brief Unsigned less or equal comparison
    bool ule(uint64_t RHS) const {
      return ule(APInt(getBitWidth(), RHS));
    }
  
    /// Regards both *this and RHS as signed quantities and compares them for
    /// validity of the less-or-equal relationship.
    /// @returns true if *this <= RHS when both are considered signed.
    /// @brief Signed less or equal comparison
    bool sle(const APInt& RHS) const {
      return slt(RHS) || eq(RHS);
    }
  
    /// Regards both *this as a signed quantity and compares it with RHS for
    /// the validity of the less-or-equal relationship.
    /// @returns true if *this <= RHS when considered signed.
    /// @brief Signed less or equal comparison
    bool sle(uint64_t RHS) const {
      return sle(APInt(getBitWidth(), RHS));
    }
  
    /// Regards both *this and RHS as unsigned quantities and compares them for
    /// the validity of the greater-than relationship.
    /// @returns true if *this > RHS when both are considered unsigned.
    /// @brief Unsigned greather than comparison
    bool ugt(const APInt& RHS) const {
      return !ult(RHS) && !eq(RHS);
    }
  
    /// Regards both *this as an unsigned quantity and compares it with RHS for
    /// the validity of the greater-than relationship.
    /// @returns true if *this > RHS when considered unsigned.
    /// @brief Unsigned greater than comparison
    bool ugt(uint64_t RHS) const {
      return ugt(APInt(getBitWidth(), RHS));
    }
  
    /// Regards both *this and RHS as signed quantities and compares them for
    /// the validity of the greater-than relationship.
    /// @returns true if *this > RHS when both are considered signed.
    /// @brief Signed greather than comparison
    bool sgt(const APInt& RHS) const {
      return !slt(RHS) && !eq(RHS);
    }
  
    /// Regards both *this as a signed quantity and compares it with RHS for
    /// the validity of the greater-than relationship.
    /// @returns true if *this > RHS when considered signed.
    /// @brief Signed greater than comparison
    bool sgt(uint64_t RHS) const {
      return sgt(APInt(getBitWidth(), RHS));
    }
  
    /// Regards both *this and RHS as unsigned quantities and compares them for
    /// validity of the greater-or-equal relationship.
    /// @returns true if *this >= RHS when both are considered unsigned.
    /// @brief Unsigned greater or equal comparison
    bool uge(const APInt& RHS) const {
      return !ult(RHS);
    }
  
    /// Regards both *this as an unsigned quantity and compares it with RHS for
    /// the validity of the greater-or-equal relationship.
    /// @returns true if *this >= RHS when considered unsigned.
    /// @brief Unsigned greater or equal comparison
    bool uge(uint64_t RHS) const {
      return uge(APInt(getBitWidth(), RHS));
    }
  
    /// Regards both *this and RHS as signed quantities and compares them for
    /// validity of the greater-or-equal relationship.
    /// @returns true if *this >= RHS when both are considered signed.
    /// @brief Signed greather or equal comparison
    bool sge(const APInt& RHS) const {
      return !slt(RHS);
    }
  
    /// Regards both *this as a signed quantity and compares it with RHS for
    /// the validity of the greater-or-equal relationship.
    /// @returns true if *this >= RHS when considered signed.
    /// @brief Signed greater or equal comparison
    bool sge(uint64_t RHS) const {
      return sge(APInt(getBitWidth(), RHS));
    }
  
    
    
    
    /// This operation tests if there are any pairs of corresponding bits
    /// between this APInt and RHS that are both set.
    bool intersects(const APInt &RHS) const {
      return (*this & RHS) != 0;
    }
  
    /// @}
    /// @name Resizing Operators
    /// @{
    /// Truncate the APInt to a specified width. It is an error to specify a width
    /// that is greater than or equal to the current width.
    /// @brief Truncate to new width.
    APInt trunc(unsigned width) const;
  
    /// This operation sign extends the APInt to a new width. If the high order
    /// bit is set, the fill on the left will be done with 1 bits, otherwise zero.
    /// It is an error to specify a width that is less than or equal to the
    /// current width.
    /// @brief Sign extend to a new width.
    APInt sext(unsigned width) const;
  
    /// This operation zero extends the APInt to a new width. The high order bits
    /// are filled with 0 bits.  It is an error to specify a width that is less
    /// than or equal to the current width.
    /// @brief Zero extend to a new width.
    APInt zext(unsigned width) const;
  
    /// Make this APInt have the bit width given by \p width. The value is sign
    /// extended, truncated, or left alone to make it that width.
    /// @brief Sign extend or truncate to width
    APInt sextOrTrunc(unsigned width) const;
  
    /// Make this APInt have the bit width given by \p width. The value is zero
    /// extended, truncated, or left alone to make it that width.
    /// @brief Zero extend or truncate to width
    APInt zextOrTrunc(unsigned width) const;
  
    /// @}
    /// @name Bit Manipulation Operators
    /// @{
    /// @brief Set every bit to 1.
    void setAllBits() {
      if (isSingleWord())
        VAL = -1ULL;
      else {
        // Set all the bits in all the words.
        for (unsigned i = 0; i < getNumWords(); ++i)
  	pVal[i] = -1ULL;
      }
      // Clear the unused ones
      clearUnusedBits();
    }
  
    /// Set the given bit to 1 whose position is given as "bitPosition".
    /// @brief Set a given bit to 1.
    void setBit(unsigned bitPosition);
  
    /// @brief Set every bit to 0.
    void clearAllBits() {
      if (isSingleWord())
        VAL = 0;
      else
        memset(pVal, 0, getNumWords() * APINT_WORD_SIZE);
    }
  
    /// Set the given bit to 0 whose position is given as "bitPosition".
    /// @brief Set a given bit to 0.
    void clearBit(unsigned bitPosition);
  
    /// @brief Toggle every bit to its opposite value.
    void flipAllBits() {
      if (isSingleWord())
        VAL ^= -1ULL;
      else {
        for (unsigned i = 0; i < getNumWords(); ++i)
          pVal[i] ^= -1ULL;
      }
      clearUnusedBits();
    }
  
    /// Toggle a given bit to its opposite value whose position is given
    /// as "bitPosition".
    /// @brief Toggles a given bit to its opposite value.
    void flipBit(unsigned bitPosition);
  
    /// @}
    /// @name Value Characterization Functions
    /// @{
  
    /// @returns the total number of bits.
    unsigned getBitWidth() const {
      return BitWidth;
    }
  
    /// Here one word's bitwidth equals to that of uint64_t.
    /// @returns the number of words to hold the integer value of this APInt.
    /// @brief Get the number of words.
    unsigned getNumWords() const {
      return getNumWords(BitWidth);
    }
  
    /// Here one word's bitwidth equals to that of uint64_t.
    /// @returns the number of words to hold the integer value with a
    /// given bit width.
    /// @brief Get the number of words.
    static unsigned getNumWords(unsigned BitWidth) {
      return (BitWidth + APINT_BITS_PER_WORD - 1) / APINT_BITS_PER_WORD;
    }
  
    /// This function returns the number of active bits which is defined as the
    /// bit width minus the number of leading zeros. This is used in several
    /// computations to see how "wide" the value is.
    /// @brief Compute the number of active bits in the value
    unsigned getActiveBits() const {
      return BitWidth - countLeadingZeros();
    }
  
    /// This function returns the number of active words in the value of this
    /// APInt. This is used in conjunction with getActiveData to extract the raw
    /// value of the APInt.
    unsigned getActiveWords() const {
      return whichWord(getActiveBits()-1) + 1;
    }
  
    /// Computes the minimum bit width for this APInt while considering it to be
    /// a signed (and probably negative) value. If the value is not negative,
    /// this function returns the same value as getActiveBits()+1. Otherwise, it
    /// returns the smallest bit width that will retain the negative value. For
    /// example, -1 can be written as 0b1 or 0xFFFFFFFFFF. 0b1 is shorter and so
    /// for -1, this function will always return 1.
    /// @brief Get the minimum bit size for this signed APInt
    unsigned getMinSignedBits() const {
      if (isNegative())
        return BitWidth - countLeadingOnes() + 1;
      return getActiveBits()+1;
    }
  
    /// This method attempts to return the value of this APInt as a zero extended
    /// uint64_t. The bitwidth must be <= 64 or the value must fit within a
    /// uint64_t. Otherwise an assertion will result.
    /// @brief Get zero extended value
    uint64_t getZExtValue() const {
      if (isSingleWord())
        return VAL;
      assert(getActiveBits() <= 64 && "Too many bits for uint64_t");
      return pVal[0];
    }
  
    /// This method attempts to return the value of this APInt as a sign extended
    /// int64_t. The bit width must be <= 64 or the value must fit within an
    /// int64_t. Otherwise an assertion will result.
    /// @brief Get sign extended value
    int64_t getSExtValue() const {
      if (isSingleWord())
        return int64_t(VAL << (APINT_BITS_PER_WORD - BitWidth)) >>
                       (APINT_BITS_PER_WORD - BitWidth);
      assert(getMinSignedBits() <= 64 && "Too many bits for int64_t");
      return int64_t(pVal[0]);
    }
  
    /// This method determines how many bits are required to hold the APInt
    /// equivalent of the string given by \arg str.
    /// @brief Get bits required for string value.
    static unsigned getBitsNeeded(StringRef str, uint8_t radix);
  
    /// countLeadingZeros - This function is an APInt version of the
    /// countLeadingZeros_{32,64} functions in MathExtras.h. It counts the number
    /// of zeros from the most significant bit to the first one bit.
    /// @returns BitWidth if the value is zero.
    /// @returns the number of zeros from the most significant bit to the first
    /// one bits.
    unsigned countLeadingZeros() const {
      if (isSingleWord()) {
        unsigned unusedBits = APINT_BITS_PER_WORD - BitWidth;
        return CountLeadingZeros_64(VAL) - unusedBits;
      }
      return countLeadingZerosSlowCase();
    }
  
    /// countLeadingOnes - This function is an APInt version of the
    /// countLeadingOnes_{32,64} functions in MathExtras.h. It counts the number
    /// of ones from the most significant bit to the first zero bit.
    /// @returns 0 if the high order bit is not set
    /// @returns the number of 1 bits from the most significant to the least
    /// @brief Count the number of leading one bits.
    unsigned countLeadingOnes() const;
  
    /// Computes the number of leading bits of this APInt that are equal to its
    /// sign bit.
    unsigned getNumSignBits() const {
      return isNegative() ? countLeadingOnes() : countLeadingZeros();
    }
  
    /// countTrailingZeros - This function is an APInt version of the
    /// countTrailingZeros_{32,64} functions in MathExtras.h. It counts
    /// the number of zeros from the least significant bit to the first set bit.
    /// @returns BitWidth if the value is zero.
    /// @returns the number of zeros from the least significant bit to the first
    /// one bit.
    /// @brief Count the number of trailing zero bits.
    unsigned countTrailingZeros() const;
  
    /// countTrailingOnes - This function is an APInt version of the
    /// countTrailingOnes_{32,64} functions in MathExtras.h. It counts
    /// the number of ones from the least significant bit to the first zero bit.
    /// @returns BitWidth if the value is all ones.
    /// @returns the number of ones from the least significant bit to the first
    /// zero bit.
    /// @brief Count the number of trailing one bits.
    unsigned countTrailingOnes() const {
      if (isSingleWord())
        return CountTrailingOnes_64(VAL);
      return countTrailingOnesSlowCase();
    }
  
    /// countPopulation - This function is an APInt version of the
    /// countPopulation_{32,64} functions in MathExtras.h. It counts the number
    /// of 1 bits in the APInt value.
    /// @returns 0 if the value is zero.
    /// @returns the number of set bits.
    /// @brief Count the number of bits set.
    unsigned countPopulation() const {
      if (isSingleWord())
        return CountPopulation_64(VAL);
      return countPopulationSlowCase();
    }
  
    /// @}
    /// @name Conversion Functions
    /// @{
    void print(raw_ostream &OS, bool isSigned) const;
  
    /// toString - Converts an APInt to a string and append it to Str.  Str is
    /// commonly a SmallString.
    void toString(SmallVectorImpl<char> &Str, unsigned Radix, bool Signed) const;
  
    /// Considers the APInt to be unsigned and converts it into a string in the
    /// radix given. The radix can be 2, 8, 10 or 16.
    void toStringUnsigned(SmallVectorImpl<char> &Str, unsigned Radix = 10) const {
      toString(Str, Radix, false);
    }
  
    /// Considers the APInt to be signed and converts it into a string in the
    /// radix given. The radix can be 2, 8, 10 or 16.
    void toStringSigned(SmallVectorImpl<char> &Str, unsigned Radix = 10) const {
      toString(Str, Radix, true);
    }
  
    /// toString - This returns the APInt as a std::string.  Note that this is an
    /// inefficient method.  It is better to pass in a SmallVector/SmallString
    /// to the methods above to avoid thrashing the heap for the string.
    std::string toString(unsigned Radix, bool Signed) const;
  
  
    /// @returns a byte-swapped representation of this APInt Value.
    APInt byteSwap() const;
  
    /// @brief Converts this APInt to a double value.
    double roundToDouble(bool isSigned) const;
  
    /// @brief Converts this unsigned APInt to a double value.
    double roundToDouble() const {
      return roundToDouble(false);
    }
  
    /// @brief Converts this signed APInt to a double value.
    double signedRoundToDouble() const {
      return roundToDouble(true);
    }
  
    /// The conversion does not do a translation from integer to double, it just
    /// re-interprets the bits as a double. Note that it is valid to do this on
    /// any bit width. Exactly 64 bits will be translated.
    /// @brief Converts APInt bits to a double
    double bitsToDouble() const {
      union {
        uint64_t I;
        double D;
      } T;
      T.I = (isSingleWord() ? VAL : pVal[0]);
      return T.D;
    }
  
    /// The conversion does not do a translation from integer to float, it just
    /// re-interprets the bits as a float. Note that it is valid to do this on
    /// any bit width. Exactly 32 bits will be translated.
    /// @brief Converts APInt bits to a double
    float bitsToFloat() const {
      union {
        unsigned I;
        float F;
      } T;
      T.I = unsigned((isSingleWord() ? VAL : pVal[0]));
      return T.F;
    }
  
    /// The conversion does not do a translation from double to integer, it just
    /// re-interprets the bits of the double.
    /// @brief Converts a double to APInt bits.
    static APInt doubleToBits(double V) {
      union {
        uint64_t I;
        double D;
      } T;
      T.D = V;
      return APInt(sizeof T * CHAR_BIT, T.I);
    }
  
    /// The conversion does not do a translation from float to integer, it just
    /// re-interprets the bits of the float.
    /// @brief Converts a float to APInt bits.
    static APInt floatToBits(float V) {
      union {
        unsigned I;
        float F;
      } T;
      T.F = V;
      return APInt(sizeof T * CHAR_BIT, T.I);
    }
  
    /// @}
    /// @name Mathematics Operations
    /// @{
  
    /// @returns the floor log base 2 of this APInt.
    unsigned logBase2() const {
      return BitWidth - 1 - countLeadingZeros();
    }
  
    /// @returns the ceil log base 2 of this APInt.
    unsigned ceilLogBase2() const {
      return BitWidth - (*this - 1).countLeadingZeros();
    }
  
    /// @returns the log base 2 of this APInt if its an exact power of two, -1
    /// otherwise
    int32_t exactLogBase2() const {
      if (!isPowerOf2())
        return -1;
      return logBase2();
    }
  
    /// @brief Compute the square root
    APInt sqrt() const;
  
    /// If *this is < 0 then return -(*this), otherwise *this;
    /// @brief Get the absolute value;
    APInt abs() const {
      if (isNegative())
        return -(*this);
      return *this;
    }
  
    /// @returns the multiplicative inverse for a given modulo.
    APInt multiplicativeInverse(const APInt& modulo) const;
  
    /// @}
    /// @name Support for division by constant
    /// @{
  
    /// Calculate the magic number for signed division by a constant.
    struct ms;
    ms magic() const;
  
    /// Calculate the magic number for unsigned division by a constant.
    struct mu;
    mu magicu() const;
  
    /// @}
    /// @name Building-block Operations for APInt and APFloat
    /// @{
  
    // These building block operations operate on a representation of
    // arbitrary precision, two's-complement, bignum integer values.
    // They should be sufficient to implement APInt and APFloat bignum
    // requirements.  Inputs are generally a pointer to the base of an
    // array of integer parts, representing an unsigned bignum, and a
    // count of how many parts there are.
  
    /// Sets the least significant part of a bignum to the input value,
    /// and zeroes out higher parts.  */
    static void tcSet(integerPart *, integerPart, unsigned int);
  
    /// Assign one bignum to another.
    static void tcAssign(integerPart *, const integerPart *, unsigned int);
  
    /// Returns true if a bignum is zero, false otherwise.
    static bool tcIsZero(const integerPart *, unsigned int);
  
    /// Extract the given bit of a bignum; returns 0 or 1.  Zero-based.
    static int tcExtractBit(const integerPart *, unsigned int bit);
  
    /// Copy the bit vector of width srcBITS from SRC, starting at bit
    /// srcLSB, to DST, of dstCOUNT parts, such that the bit srcLSB
    /// becomes the least significant bit of DST.  All high bits above
    /// srcBITS in DST are zero-filled.
    static void tcExtract(integerPart *, unsigned int dstCount,
                          const integerPart *,
                          unsigned int srcBits, unsigned int srcLSB);
  
    /// Set the given bit of a bignum.  Zero-based.
    static void tcSetBit(integerPart *, unsigned int bit);
  
    /// Clear the given bit of a bignum.  Zero-based.
    static void tcClearBit(integerPart *, unsigned int bit);
  
    /// Returns the bit number of the least or most significant set bit
    /// of a number.  If the input number has no bits set -1U is
    /// returned.
    static unsigned int tcLSB(const integerPart *, unsigned int);
    static unsigned int tcMSB(const integerPart *parts, unsigned int n);
  
    /// Negate a bignum in-place.
    static void tcNegate(integerPart *, unsigned int);
  
    /// DST += RHS + CARRY where CARRY is zero or one.  Returns the
    /// carry flag.
    static integerPart tcAdd(integerPart *, const integerPart *,
                             integerPart carry, unsigned);
  
    /// DST -= RHS + CARRY where CARRY is zero or one.  Returns the
    /// carry flag.
    static integerPart tcSubtract(integerPart *, const integerPart *,
                                  integerPart carry, unsigned);
  
    ///  DST += SRC * MULTIPLIER + PART   if add is true
    ///  DST  = SRC * MULTIPLIER + PART   if add is false
    ///
    ///  Requires 0 <= DSTPARTS <= SRCPARTS + 1.  If DST overlaps SRC
    ///  they must start at the same point, i.e. DST == SRC.
    ///
    ///  If DSTPARTS == SRC_PARTS + 1 no overflow occurs and zero is
    ///  returned.  Otherwise DST is filled with the least significant
    ///  DSTPARTS parts of the result, and if all of the omitted higher
    ///  parts were zero return zero, otherwise overflow occurred and
    ///  return one.
    static int tcMultiplyPart(integerPart *dst, const integerPart *src,
                              integerPart multiplier, integerPart carry,
                              unsigned int srcParts, unsigned int dstParts,
                              bool add);
  
    /// DST = LHS * RHS, where DST has the same width as the operands
    /// and is filled with the least significant parts of the result.
    /// Returns one if overflow occurred, otherwise zero.  DST must be
    /// disjoint from both operands.
    static int tcMultiply(integerPart *, const integerPart *,
                          const integerPart *, unsigned);
  
    /// DST = LHS * RHS, where DST has width the sum of the widths of
    /// the operands.  No overflow occurs.  DST must be disjoint from
    /// both operands. Returns the number of parts required to hold the
    /// result.
    static unsigned int tcFullMultiply(integerPart *, const integerPart *,
                                       const integerPart *, unsigned, unsigned);
  
    /// If RHS is zero LHS and REMAINDER are left unchanged, return one.
    /// Otherwise set LHS to LHS / RHS with the fractional part
    /// discarded, set REMAINDER to the remainder, return zero.  i.e.
    ///
    ///  OLD_LHS = RHS * LHS + REMAINDER
    ///
    ///  SCRATCH is a bignum of the same size as the operands and result
    ///  for use by the routine; its contents need not be initialized
    ///  and are destroyed.  LHS, REMAINDER and SCRATCH must be
    ///  distinct.
    static int tcDivide(integerPart *lhs, const integerPart *rhs,
                        integerPart *remainder, integerPart *scratch,
                        unsigned int parts);
  
    /// Shift a bignum left COUNT bits.  Shifted in bits are zero.
    /// There are no restrictions on COUNT.
    static void tcShiftLeft(integerPart *, unsigned int parts,
                            unsigned int count);
  
    /// Shift a bignum right COUNT bits.  Shifted in bits are zero.
    /// There are no restrictions on COUNT.
    static void tcShiftRight(integerPart *, unsigned int parts,
                             unsigned int count);
  
    /// The obvious AND, OR and XOR and complement operations.
    static void tcAnd(integerPart *, const integerPart *, unsigned int);
    static void tcOr(integerPart *, const integerPart *, unsigned int);
    static void tcXor(integerPart *, const integerPart *, unsigned int);
    static void tcComplement(integerPart *, unsigned int);
  
    /// Comparison (unsigned) of two bignums.
    static int tcCompare(const integerPart *, const integerPart *,
                         unsigned int);
  
    /// Increment a bignum in-place.  Return the carry flag.
    static integerPart tcIncrement(integerPart *, unsigned int);
  
    /// Set the least significant BITS and clear the rest.
    static void tcSetLeastSignificantBits(integerPart *, unsigned int,
                                          unsigned int bits);
  
    /// @brief debug method
    void dump() const;
  
    /// @}
  };
  
  /// Magic data for optimising signed division by a constant.
  struct APInt::ms {
    APInt m;  ///< magic number
    unsigned s;  ///< shift amount
  };
  
  /// Magic data for optimising unsigned division by a constant.
  struct APInt::mu {
    APInt m;     ///< magic number
    bool a;      ///< add indicator
    unsigned s;  ///< shift amount
  };
  
  inline bool operator==(uint64_t V1, const APInt& V2) {
    return V2 == V1;
  }
  
  inline bool operator!=(uint64_t V1, const APInt& V2) {
    return V2 != V1;
  }
  
  inline raw_ostream &operator<<(raw_ostream &OS, const APInt &I) {
    I.print(OS, true);
    return OS;
  }
  
  namespace APIntOps {
  
  /// @brief Determine the smaller of two APInts considered to be signed.
  inline APInt smin(const APInt &A, const APInt &B) {
    return A.slt(B) ? A : B;
  }
  
  /// @brief Determine the larger of two APInts considered to be signed.
  inline APInt smax(const APInt &A, const APInt &B) {
    return A.sgt(B) ? A : B;
  }
  
  /// @brief Determine the smaller of two APInts considered to be signed.
  inline APInt umin(const APInt &A, const APInt &B) {
    return A.ult(B) ? A : B;
  }
  
  /// @brief Determine the larger of two APInts considered to be unsigned.
  inline APInt umax(const APInt &A, const APInt &B) {
    return A.ugt(B) ? A : B;
  }
  
  /// @brief Check if the specified APInt has a N-bits unsigned integer value.
  inline bool isIntN(unsigned N, const APInt& APIVal) {
    return APIVal.isIntN(N);
  }
  
  /// @brief Check if the specified APInt has a N-bits signed integer value.
  inline bool isSignedIntN(unsigned N, const APInt& APIVal) {
    return APIVal.isSignedIntN(N);
  }
  
  /// @returns true if the argument APInt value is a sequence of ones
  /// starting at the least significant bit with the remainder zero.
  inline bool isMask(unsigned numBits, const APInt& APIVal) {
    return numBits <= APIVal.getBitWidth() &&
      APIVal == APInt::getLowBitsSet(APIVal.getBitWidth(), numBits);
  }
  
  /// @returns true if the argument APInt value contains a sequence of ones
  /// with the remainder zero.
  inline bool isShiftedMask(unsigned numBits, const APInt& APIVal) {
    return isMask(numBits, (APIVal - APInt(numBits,1)) | APIVal);
  }
  
  /// @returns a byte-swapped representation of the specified APInt Value.
  inline APInt byteSwap(const APInt& APIVal) {
    return APIVal.byteSwap();
  }
  
  /// @returns the floor log base 2 of the specified APInt value.
  inline unsigned logBase2(const APInt& APIVal) {
    return APIVal.logBase2();
  }
  
  /// GreatestCommonDivisor - This function returns the greatest common
  /// divisor of the two APInt values using Euclid's algorithm.
  /// @returns the greatest common divisor of Val1 and Val2
  /// @brief Compute GCD of two APInt values.
  APInt GreatestCommonDivisor(const APInt& Val1, const APInt& Val2);
  
  /// Treats the APInt as an unsigned value for conversion purposes.
  /// @brief Converts the given APInt to a double value.
  inline double RoundAPIntToDouble(const APInt& APIVal) {
    return APIVal.roundToDouble();
  }
  
  /// Treats the APInt as a signed value for conversion purposes.
  /// @brief Converts the given APInt to a double value.
  inline double RoundSignedAPIntToDouble(const APInt& APIVal) {
    return APIVal.signedRoundToDouble();
  }
  
  /// @brief Converts the given APInt to a float vlalue.
  inline float RoundAPIntToFloat(const APInt& APIVal) {
    return float(RoundAPIntToDouble(APIVal));
  }
  
  /// Treast the APInt as a signed value for conversion purposes.
  /// @brief Converts the given APInt to a float value.
  inline float RoundSignedAPIntToFloat(const APInt& APIVal) {
    return float(APIVal.signedRoundToDouble());
  }
  
  /// RoundDoubleToAPInt - This function convert a double value to an APInt value.
  /// @brief Converts the given double value into a APInt.
  APInt RoundDoubleToAPInt(double Double, unsigned width);
  
  /// RoundFloatToAPInt - Converts a float value into an APInt value.
  /// @brief Converts a float value into a APInt.
  inline APInt RoundFloatToAPInt(float Float, unsigned width) {
    return RoundDoubleToAPInt(double(Float), width);
  }
  
  /// Arithmetic right-shift the APInt by shiftAmt.
  /// @brief Arithmetic right-shift function.
  inline APInt ashr(const APInt& LHS, unsigned shiftAmt) {
    return LHS.ashr(shiftAmt);
  }
  
  /// Logical right-shift the APInt by shiftAmt.
  /// @brief Logical right-shift function.
  inline APInt lshr(const APInt& LHS, unsigned shiftAmt) {
    return LHS.lshr(shiftAmt);
  }
  
  /// Left-shift the APInt by shiftAmt.
  /// @brief Left-shift function.
  inline APInt shl(const APInt& LHS, unsigned shiftAmt) {
    return LHS.shl(shiftAmt);
  }
  
  /// Signed divide APInt LHS by APInt RHS.
  /// @brief Signed division function for APInt.
  inline APInt sdiv(const APInt& LHS, const APInt& RHS) {
    return LHS.sdiv(RHS);
  }
  
  /// Unsigned divide APInt LHS by APInt RHS.
  /// @brief Unsigned division function for APInt.
  inline APInt udiv(const APInt& LHS, const APInt& RHS) {
    return LHS.udiv(RHS);
  }
  
  /// Signed remainder operation on APInt.
  /// @brief Function for signed remainder operation.
  inline APInt srem(const APInt& LHS, const APInt& RHS) {
    return LHS.srem(RHS);
  }
  
  /// Unsigned remainder operation on APInt.
  /// @brief Function for unsigned remainder operation.
  inline APInt urem(const APInt& LHS, const APInt& RHS) {
    return LHS.urem(RHS);
  }
  
  /// Performs multiplication on APInt values.
  /// @brief Function for multiplication operation.
  inline APInt mul(const APInt& LHS, const APInt& RHS) {
    return LHS * RHS;
  }
  
  /// Performs addition on APInt values.
  /// @brief Function for addition operation.
  inline APInt add(const APInt& LHS, const APInt& RHS) {
    return LHS + RHS;
  }
  
  /// Performs subtraction on APInt values.
  /// @brief Function for subtraction operation.
  inline APInt sub(const APInt& LHS, const APInt& RHS) {
    return LHS - RHS;
  }
  
  /// Performs bitwise AND operation on APInt LHS and
  /// APInt RHS.
  /// @brief Bitwise AND function for APInt.
  inline APInt And(const APInt& LHS, const APInt& RHS) {
    return LHS & RHS;
  }
  
  /// Performs bitwise OR operation on APInt LHS and APInt RHS.
  /// @brief Bitwise OR function for APInt.
  inline APInt Or(const APInt& LHS, const APInt& RHS) {
    return LHS | RHS;
  }
  
  /// Performs bitwise XOR operation on APInt.
  /// @brief Bitwise XOR function for APInt.
  inline APInt Xor(const APInt& LHS, const APInt& RHS) {
    return LHS ^ RHS;
  }
  
  /// Performs a bitwise complement operation on APInt.
  /// @brief Bitwise complement function.
  inline APInt Not(const APInt& APIVal) {
    return ~APIVal;
  }
  
  } // End of APIntOps namespace
  
  } // End of llvm namespace
  
  #endif
  