[llvm-commits] CVS: llvm/lib/Support/APInt.cpp

Zhou Sheng zhousheng00 at gmail.com
Mon Feb 5 19:00:37 PST 2007



Changes in directory llvm/lib/Support:

APInt.cpp added (r1.1)
---
Log message:

Add a class APInt to represent arbitrary precision constant integral values.
It is a functional replacement for common case integer type like "unsigned",
"uint64_t", but also allows non-byte-width integer type and large integer
value types such as 3-bits, 15-bits, or more than 64-bits of precision. For
more details, see pr1043: http://llvm.org/PR1043 .


---
Diffs of the changes:  (+1113 -0)

 APInt.cpp | 1113 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 files changed, 1113 insertions(+)


Index: llvm/lib/Support/APInt.cpp
diff -c /dev/null llvm/lib/Support/APInt.cpp:1.1
*** /dev/null	Mon Feb  5 21:00:27 2007
--- llvm/lib/Support/APInt.cpp	Mon Feb  5 21:00:16 2007
***************
*** 0 ****
--- 1,1113 ----
+ //===-- APInt.cpp - Implement APInt class ---------------------------------===//
+ //
+ //                     The LLVM Compiler Infrastructure
+ //
+ // This file was developed by Sheng Zhou and 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.
+ //
+ //===----------------------------------------------------------------------===//
+ 
+ #include "llvm/ADT/APInt.h"
+ #include "llvm/DerivedTypes.h"
+ #include "llvm/Support/MathExtras.h"
+ #include <strings.h>
+ #include <iostream>
+ #include <sstream>
+ #include <iomanip>
+ #include <cstdlib>
+ using namespace llvm;
+ 
+ APInt::APInt(uint64_t val, unsigned numBits, bool sign)
+   : bitsnum(numBits), isSigned(sign) {
+   assert(bitsnum >= IntegerType::MIN_INT_BITS && "bitwidth too small");
+   assert(bitsnum <= IntegerType::MAX_INT_BITS && "bitwidth too large");
+   if (isSingleWord()) 
+     VAL = val & (~uint64_t(0ULL) >> (APINT_BITS_PER_WORD - bitsnum));
+   else {
+     // Memory allocation and check if successful.
+     assert((pVal = new uint64_t[numWords()]) && 
+             "APInt memory allocation fails!");
+     bzero(pVal, numWords() * 8);
+     pVal[0] = val;
+   }
+ }
+ 
+ APInt::APInt(unsigned numBits, uint64_t bigVal[], bool sign)
+   : bitsnum(numBits), isSigned(sign) {
+   assert(bitsnum >= IntegerType::MIN_INT_BITS && "bitwidth too small");
+   assert(bitsnum <= IntegerType::MAX_INT_BITS && "bitwidth too large");
+   assert(bigVal && "Null pointer detected!");
+   if (isSingleWord())
+     VAL = bigVal[0] & (~uint64_t(0ULL) >> (APINT_BITS_PER_WORD - bitsnum));
+   else {
+     // Memory allocation and check if successful.
+     assert((pVal = new uint64_t[numWords()]) && 
+            "APInt memory allocation fails!");
+     // Calculate the actual length of bigVal[].
+     unsigned n = sizeof(*bigVal) / sizeof(bigVal[0]);
+     unsigned maxN = std::max<unsigned>(n, numWords());
+     unsigned minN = std::min<unsigned>(n, numWords());
+     memcpy(pVal, bigVal, (minN - 1) * 8);
+     pVal[minN-1] = bigVal[minN-1] & (~uint64_t(0ULL) >> (64 - bitsnum % 64));
+     if (maxN == numWords())
+       bzero(pVal+n, (numWords() - n) * 8);
+   }
+ }
+ 
+ APInt::APInt(std::string& Val, uint8_t radix, bool sign)
+   : isSigned(sign) {
+   assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
+          "Radix should be 2, 8, 10, or 16!");
+   assert(!Val.empty() && "String empty?");
+   unsigned slen = Val.size();
+   unsigned size = 0;
+   // If the radix is a power of 2, read the input
+   // from most significant to least significant.
+   if ((radix & (radix - 1)) == 0) {
+     unsigned nextBitPos = 0, bits_per_digit = radix / 8 + 2;
+     uint64_t resDigit = 0;
+     bitsnum = slen * bits_per_digit;
+     if (numWords() > 1)
+       assert((pVal = new uint64_t[numWords()]) && 
+              "APInt memory allocation fails!");
+     for (int i = slen - 1; i >= 0; --i) {
+       uint64_t digit = Val[i] - 48;             // '0' == 48.
+       resDigit |= digit << nextBitPos;
+       nextBitPos += bits_per_digit;
+       if (nextBitPos >= 64) {
+         if (isSingleWord()) {
+           VAL = resDigit;
+            break;
+         }
+         pVal[size++] = resDigit;
+         nextBitPos -= 64;
+         resDigit = digit >> (bits_per_digit - nextBitPos);
+       }
+     }
+     if (!isSingleWord() && size <= numWords()) 
+       pVal[size] = resDigit;
+   } else {   // General case.  The radix is not a power of 2.
+     // For 10-radix, the max value of 64-bit integer is 18446744073709551615,
+     // and its digits number is 14.
+     const unsigned chars_per_word = 20;
+     if (slen < chars_per_word || 
+         (Val <= "18446744073709551615" && 
+          slen == chars_per_word)) { // In case Val <= 2^64 - 1
+       bitsnum = 64;
+       VAL = strtoull(Val.c_str(), 0, 10);
+     } else { // In case Val > 2^64 - 1
+       bitsnum = (slen / chars_per_word + 1) * 64;
+       assert((pVal = new uint64_t[numWords()]) && 
+              "APInt memory allocation fails!");
+       bzero(pVal, numWords() * 8);
+       unsigned str_pos = 0;
+       while (str_pos < slen) {
+         unsigned chunk = slen - str_pos;
+         if (chunk > chars_per_word - 1)
+           chunk = chars_per_word - 1;
+         uint64_t resDigit = Val[str_pos++] - 48;  // 48 == '0'.
+         uint64_t big_base = radix;
+         while (--chunk > 0) {
+           resDigit = resDigit * radix + Val[str_pos++] - 48;
+           big_base *= radix;
+         }
+        
+         uint64_t carry;
+         if (!size)
+           carry = resDigit;
+         else {
+           carry = mul_1(pVal, pVal, size, big_base);
+           carry += add_1(pVal, pVal, size, resDigit);
+         }
+         
+         if (carry) pVal[size++] = carry;
+       }
+     }
+   }
+ }
+ 
+ APInt::APInt(const APInt& APIVal)
+   : bitsnum(APIVal.bitsnum), isSigned(APIVal.isSigned) {
+   if (isSingleWord()) VAL = APIVal.VAL;
+   else {
+     // Memory allocation and check if successful.
+     assert((pVal = new uint64_t[numWords()]) && 
+            "APInt memory allocation fails!");
+     memcpy(pVal, APIVal.pVal, numWords() * 8);
+   }
+ }
+ 
+ APInt::~APInt() {
+   if (!isSingleWord() && pVal) delete[] pVal;
+ }
+ 
+ /// whichByte - This function returns the word position 
+ /// for the specified bit position.
+ inline unsigned APInt::whichByte(unsigned bitPosition)
+ { return (bitPosition % APINT_BITS_PER_WORD) / 8; }
+ 
+ /// getWord - returns the corresponding word for the specified bit position.
+ inline uint64_t& APInt::getWord(unsigned bitPosition)
+ { return isSingleWord() ? VAL : pVal[whichWord(bitPosition)]; }
+ 
+ /// getWord - returns the corresponding word for the specified bit position.
+ /// This is a constant version.
+ inline uint64_t APInt::getWord(unsigned bitPosition) const
+ { return isSingleWord() ? VAL : pVal[whichWord(bitPosition)]; }
+ 
+ /// mul_1 - This function multiplies the integer array x[] by a integer y and 
+ /// returns the carry.
+ uint64_t APInt::mul_1(uint64_t dest[], uint64_t x[],
+                      unsigned len, uint64_t y) {
+   // Split y into high 32-bit part and low 32-bit part.
+   uint64_t ly = y & 0xffffffffULL, hy = y >> 32;
+   uint64_t carry = 0, lx, hx;
+   for (unsigned i = 0; i < len; ++i) {
+     lx = x[i] & 0xffffffffULL;
+     hx = x[i] >> 32;
+     // hasCarry - A flag to indicate if has carry.
+     // hasCarry == 0, no carry
+     // hasCarry == 1, has carry
+     // hasCarry == 2, no carry and the calculation result == 0.
+     uint8_t hasCarry = 0;
+     dest[i] = carry + lx * ly;
+     // Determine if the add above introduces carry.
+     hasCarry = (dest[i] < carry) ? 1 : 0;
+     carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0);
+     // The upper limit of carry can be (2^32 - 1)(2^32 - 1) + 
+     // (2^32 - 1) + 2^32 = 2^64.
+     hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
+ 
+     carry += (lx * hy) & 0xffffffffULL;
+     dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL);
+     carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) + 
+             (carry >> 32) + ((lx * hy) >> 32) + hx * hy;
+   }
+ 
+   return carry;
+ }
+ 
+ /// mul - This function multiplies integer array x[] by integer array y[] and
+ /// stores the result into integer array dest[].
+ /// Note the array dest[]'s size should no less than xlen + ylen.
+ void APInt::mul(uint64_t dest[], uint64_t x[], unsigned xlen,
+                uint64_t y[], unsigned ylen) {
+   dest[xlen] = mul_1(dest, x, xlen, y[0]);
+ 
+   for (unsigned i = 1; i < ylen; ++i) {
+     uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32;
+     uint64_t carry = 0, lx, hx;
+     for (unsigned j = 0; j < xlen; ++j) {
+       lx = x[j] & 0xffffffffULL;
+       hx = x[j] >> 32;
+       // hasCarry - A flag to indicate if has carry.
+       // hasCarry == 0, no carry
+       // hasCarry == 1, has carry
+       // hasCarry == 2, no carry and the calculation result == 0.
+       uint8_t hasCarry = 0;
+       uint64_t resul = carry + lx * ly;
+       hasCarry = (resul < carry) ? 1 : 0;
+       carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32);
+       hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
+ 
+       carry += (lx * hy) & 0xffffffffULL;
+       resul = (carry << 32) | (resul & 0xffffffffULL);
+       dest[i+j] += resul;
+       carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+
+               (carry >> 32) + (dest[i+j] < resul ? 1 : 0) + 
+               ((lx * hy) >> 32) + hx * hy;
+     }
+     dest[i+xlen] = carry;
+   }
+ }
+ 
+ /// add_1 - This function adds the integer array x[] by integer y and
+ /// returns the carry.
+ uint64_t APInt::add_1(uint64_t dest[], uint64_t x[],
+                       unsigned len, uint64_t y) {
+   uint64_t carry = y;
+ 
+   for (unsigned i = 0; i < len; ++i) {
+     dest[i] = carry + x[i];
+     carry = (dest[i] < carry) ? 1 : 0;
+   }
+   return carry;
+ }
+ 
+ /// add - This function adds the integer array x[] by integer array
+ /// y[] and returns the carry.
+ uint64_t APInt::add(uint64_t dest[], uint64_t x[],
+                     uint64_t y[], unsigned len) {
+   unsigned carry = 0;
+   
+   for (unsigned i = 0; i< len; ++i) {
+     carry += x[i];
+     dest[i] = carry + y[i];
+     carry = carry < x[i] ? 1 : (dest[i] < carry ? 1 : 0);
+   }
+   return carry;
+ }
+ 
+ /// sub_1 - This function subtracts the integer array x[] by
+ /// integer y and returns the borrow-out carry.
+ uint64_t APInt::sub_1(uint64_t x[], unsigned len, uint64_t y) {
+   uint64_t cy = y;
+ 
+   for (unsigned i = 0; i < len; ++i) {
+     uint64_t X = x[i];
+     x[i] -= cy;
+     if (cy > X) 
+       cy = 1;
+     else {
+       cy = 0;
+       break;
+     }
+   }
+ 
+   return cy;
+ }
+ 
+ /// sub - This function subtracts the integer array x[] by
+ /// integer array y[], and returns the borrow-out carry.
+ uint64_t APInt::sub(uint64_t dest[], uint64_t x[],
+                     uint64_t y[], unsigned len) {
+   // Carry indicator.
+   uint64_t cy = 0;
+   
+   for (unsigned i = 0; i < len; ++i) {
+     uint64_t Y = y[i], X = x[i];
+     Y += cy;
+ 
+     cy = Y < cy ? 1 : 0;
+     Y = X - Y;
+     cy += Y > X ? 1 : 0;
+     dest[i] = Y;
+   }
+   return cy;
+ }
+ 
+ /// UnitDiv - This function divides N by D, 
+ /// and returns (remainder << 32) | quotient.
+ /// Assumes (N >> 32) < D.
+ uint64_t APInt::unitDiv(uint64_t N, unsigned D) {
+   uint64_t q, r;                   // q: quotient, r: remainder.
+   uint64_t a1 = N >> 32;           // a1: high 32-bit part of N.
+   uint64_t a0 = N & 0xffffffffL;   // a0: low 32-bit part of N
+   if (a1 < ((D - a1 - (a0 >> 31)) & 0xffffffffL)) {
+       q = N / D;
+       r = N % D;
+   }
+   else {
+     // Compute c1*2^32 + c0 = a1*2^32 + a0 - 2^31*d
+     uint64_t c = N - ((uint64_t) D << 31);
+     // Divide (c1*2^32 + c0) by d
+     q = c / D;
+     r = c % D;
+     // Add 2^31 to quotient 
+     q += 1 << 31;
+   }
+ 
+   return (r << 32) | (q & 0xFFFFFFFFl);
+ }
+ 
+ /// subMul - This function substracts x[len-1:0] * y from 
+ /// dest[offset+len-1:offset], and returns the most significant 
+ /// word of the product, minus the borrow-out from the subtraction.
+ unsigned APInt::subMul(unsigned dest[], unsigned offset, 
+                         unsigned x[], unsigned len, unsigned y) {
+   uint64_t yl = (uint64_t) y & 0xffffffffL;
+   unsigned carry = 0;
+   unsigned j = 0;
+   do {
+     uint64_t prod = ((uint64_t) x[j] & 0xffffffffL) * yl;
+     unsigned prod_low = (unsigned) prod;
+     unsigned prod_high = (unsigned) (prod >> 32);
+     prod_low += carry;
+     carry = (prod_low < carry ? 1 : 0) + prod_high;
+     unsigned x_j = dest[offset+j];
+     prod_low = x_j - prod_low;
+     if (prod_low > x_j) ++carry;
+     dest[offset+j] = prod_low;
+   } while (++j < len);
+   return carry;
+ }
+ 
+ /// div - This is basically Knuth's formulation of the classical algorithm.
+ /// Correspondance with Knuth's notation:
+ /// Knuth's u[0:m+n] == zds[nx:0].
+ /// Knuth's v[1:n] == y[ny-1:0]
+ /// Knuth's n == ny.
+ /// Knuth's m == nx-ny.
+ /// Our nx == Knuth's m+n.
+ /// Could be re-implemented using gmp's mpn_divrem:
+ /// zds[nx] = mpn_divrem (&zds[ny], 0, zds, nx, y, ny).
+ void APInt::div(unsigned zds[], unsigned nx, unsigned y[], unsigned ny) {
+   unsigned j = nx;
+   do {                          // loop over digits of quotient
+     // Knuth's j == our nx-j.
+     // Knuth's u[j:j+n] == our zds[j:j-ny].
+     unsigned qhat;  // treated as unsigned
+     if (zds[j] == y[ny-1]) qhat = -1U;  // 0xffffffff
+     else {
+       uint64_t w = (((uint64_t)(zds[j])) << 32) + 
+                    ((uint64_t)zds[j-1] & 0xffffffffL);
+       qhat = (unsigned) unitDiv(w, y[ny-1]);
+     }
+     if (qhat) {
+       unsigned borrow = subMul(zds, j - ny, y, ny, qhat);
+       unsigned save = zds[j];
+       uint64_t num = ((uint64_t)save&0xffffffffL) - 
+                      ((uint64_t)borrow&0xffffffffL);
+       while (num) {
+         qhat--;
+         uint64_t carry = 0;
+         for (unsigned i = 0;  i < ny; i++) {
+           carry += ((uint64_t) zds[j-ny+i] & 0xffffffffL)
+             + ((uint64_t) y[i] & 0xffffffffL);
+           zds[j-ny+i] = (unsigned) carry;
+           carry >>= 32;
+         }
+         zds[j] += carry;
+         num = carry - 1;
+       }
+     }
+     zds[j] = qhat;
+   } while (--j >= ny);
+ }
+ 
+ /// lshift - This function shift x[0:len-1] left by shiftAmt bits, and 
+ /// store the len least significant words of the result in 
+ /// dest[d_offset:d_offset+len-1]. It returns the bits shifted out from 
+ /// the most significant digit.
+ uint64_t APInt::lshift(uint64_t dest[], unsigned d_offset,
+                        uint64_t x[], unsigned len, unsigned shiftAmt) {
+   unsigned count = 64 - shiftAmt;
+   int i = len - 1;
+   uint64_t high_word = x[i], retVal = high_word >> count;
+   ++d_offset;
+   while (--i >= 0) {
+     uint64_t low_word = x[i];
+     dest[d_offset+i] = (high_word << shiftAmt) | (low_word >> count);
+     high_word = low_word;
+   }
+   dest[d_offset+i] = high_word << shiftAmt;
+   return retVal;
+ }
+ 
+ /// @brief Copy assignment operator. Create a new object from the given
+ /// APInt one by initialization.
+ APInt& APInt::operator=(const APInt& RHS) {
+   if (isSingleWord()) VAL = RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0];
+   else {
+     unsigned minN = std::min(numWords(), RHS.numWords());
+     memcpy(pVal, RHS.isSingleWord() ? &RHS.VAL : RHS.pVal, minN * 8);
+     if (numWords() != minN)
+       bzero(pVal + minN, (numWords() - minN) * 8);
+   }
+   return *this;
+ }
+ 
+ /// @brief Assignment operator. Assigns a common case integer value to 
+ /// the APInt.
+ APInt& APInt::operator=(uint64_t RHS) {
+   if (isSingleWord()) VAL = RHS;
+   else {
+     pVal[0] = RHS;
+     bzero(pVal, (numWords() - 1) * 8);
+   }
+   return *this;
+ }
+ 
+ /// @brief Postfix increment operator. Increments the APInt by one.
+ const APInt APInt::operator++(int) {
+   APInt API(*this);
+   if (isSingleWord()) ++VAL;
+   else
+     add_1(pVal, pVal, numWords(), 1);
+   API.TruncToBits();
+   return API;
+ }
+ 
+ /// @brief Prefix increment operator. Increments the APInt by one.
+ APInt& APInt::operator++() {
+   if (isSingleWord()) ++VAL;
+   else
+     add_1(pVal, pVal, numWords(), 1);
+   TruncToBits();
+   return *this;
+ }
+ 
+ /// @brief Postfix decrement operator. Decrements the APInt by one.
+ const APInt APInt::operator--(int) {
+   APInt API(*this);
+   if (isSingleWord()) --VAL;
+   else
+     sub_1(API.pVal, API.numWords(), 1);
+   API.TruncToBits();
+   return API;
+ }
+ 
+ /// @brief Prefix decrement operator. Decrements the APInt by one.
+ APInt& APInt::operator--() {
+   if (isSingleWord()) --VAL;
+   else
+     sub_1(pVal, numWords(), 1);
+   TruncToBits();
+   return *this;
+ }
+ 
+ /// @brief Addition assignment operator. Adds this APInt by the given APInt&
+ /// RHS and assigns the result to this APInt.
+ APInt& APInt::operator+=(const APInt& RHS) {
+   if (isSingleWord()) VAL += RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0];
+   else {
+     if (RHS.isSingleWord()) add_1(pVal, pVal, numWords(), RHS.VAL);
+     else {
+       if (numWords() <= RHS.numWords()) 
+         add(pVal, pVal, RHS.pVal, numWords());
+       else {
+         uint64_t carry = add(pVal, pVal, RHS.pVal, RHS.numWords());
+         add_1(pVal + RHS.numWords(), pVal + RHS.numWords(), 
+               numWords() - RHS.numWords(), carry);
+       }
+     }
+   }
+   TruncToBits();
+   return *this;
+ }
+ 
+ /// @brief Subtraction assignment operator. Subtracts this APInt by the given
+ /// APInt &RHS and assigns the result to this APInt.
+ APInt& APInt::operator-=(const APInt& RHS) {
+   if (isSingleWord()) 
+     VAL -= RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0];
+   else {
+     if (RHS.isSingleWord())
+       sub_1(pVal, numWords(), RHS.VAL);
+     else {
+       if (RHS.numWords() < numWords()) { 
+         uint64_t carry = sub(pVal, pVal, RHS.pVal, RHS.numWords());
+         sub_1(pVal + RHS.numWords(), numWords() - RHS.numWords(), carry); 
+       }
+       else
+         sub(pVal, pVal, RHS.pVal, numWords());
+     }
+   }
+   TruncToBits();
+   return *this;
+ }
+ 
+ /// @brief Multiplication assignment operator. Multiplies this APInt by the 
+ /// given APInt& RHS and assigns the result to this APInt.
+ APInt& APInt::operator*=(const APInt& RHS) {
+   if (isSingleWord()) VAL *= RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0];
+   else {
+     // one-based first non-zero bit position.
+     unsigned first = numWords() * APINT_BITS_PER_WORD - CountLeadingZeros();
+     unsigned xlen = !first ? 0 : whichWord(first - 1) + 1;
+     if (!xlen) 
+       return *this;
+     else if (RHS.isSingleWord()) 
+       mul_1(pVal, pVal, xlen, RHS.VAL);
+     else {
+       first = RHS.numWords() * APINT_BITS_PER_WORD - RHS.CountLeadingZeros();
+       unsigned ylen = !first ? 0 : whichWord(first - 1) + 1;
+       if (!ylen) {
+         bzero(pVal, numWords() * 8);
+         return *this;
+       }
+       uint64_t *dest = new uint64_t[xlen+ylen];
+       assert(dest && "Memory Allocation Failed!");
+       mul(dest, pVal, xlen, RHS.pVal, ylen);
+       memcpy(pVal, dest, ((xlen + ylen >= numWords()) ? numWords() : xlen + ylen) * 8);
+       delete[] dest;
+     }
+   }
+   TruncToBits();
+   return *this;
+ }
+ 
+ /// @brief Division assignment operator. Divides this APInt by the given APInt
+ /// &RHS and assigns the result to this APInt.
+ APInt& APInt::operator/=(const APInt& RHS) {
+   unsigned first = RHS.numWords() * APINT_BITS_PER_WORD - 
+                    RHS.CountLeadingZeros();
+   unsigned ylen = !first ? 0 : whichWord(first - 1) + 1;
+   assert(ylen && "Divided by zero???");
+   if (isSingleWord()) {
+     if (isSigned && RHS.isSigned)
+       VAL = RHS.isSingleWord() ? (int64_t(VAL) / int64_t(RHS.VAL)) :
+             (ylen > 1 ? 0 : int64_t(VAL) / int64_t(RHS.pVal[0]));
+     else
+       VAL = RHS.isSingleWord() ? (VAL / RHS.VAL) : 
+           (ylen > 1 ? 0 : VAL / RHS.pVal[0]);
+   } else {
+     unsigned first2 = numWords() * APINT_BITS_PER_WORD - CountLeadingZeros();
+     unsigned xlen = !first2 ? 0 : whichWord(first2 - 1) + 1;
+     if (!xlen)
+       return *this;
+     else if ((*this) < RHS)
+       bzero(pVal, numWords() * 8);
+     else if ((*this) == RHS) {
+       bzero(pVal, numWords() * 8);
+       pVal[0] = 1;
+     } else if (xlen == 1)
+       pVal[0] /= RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0];
+     else {
+       uint64_t *xwords = new uint64_t[xlen+1], *ywords = new uint64_t[ylen];
+       assert(xwords && ywords && "Memory Allocation Failed!");
+       memcpy(xwords, pVal, xlen * 8);
+       xwords[xlen] = 0;
+       memcpy(ywords, RHS.isSingleWord() ? &RHS.VAL : RHS.pVal, ylen * 8);
+       if (unsigned nshift = 63 - (first - 1) % 64) {
+         lshift(ywords, 0, ywords, ylen, nshift);
+         unsigned xlentmp = xlen;
+         xwords[xlen++] = lshift(xwords, 0, xwords, xlentmp, nshift);
+       }
+       div((unsigned*)xwords, xlen*2-1, (unsigned*)ywords, ylen*2);
+       bzero(pVal, numWords() * 8);
+       memcpy(pVal, xwords + ylen, (xlen - ylen) * 8);
+       delete[] xwords;
+       delete[] ywords;
+     }
+   }
+   return *this;
+ }
+ 
+ /// @brief Remainder assignment operator. Yields the remainder from the 
+ /// division of this APInt by the given APInt& RHS and assigns the remainder 
+ /// to this APInt.
+ APInt& APInt::operator%=(const APInt& RHS) {
+   unsigned first = RHS.numWords() * APINT_BITS_PER_WORD -
+                    RHS.CountLeadingZeros();
+   unsigned ylen = !first ? 0 : whichWord(first - 1) + 1;
+   assert(ylen && "Performing remainder operation by zero ???");
+   if (isSingleWord()) {
+     if (isSigned && RHS.isSigned)
+       VAL = RHS.isSingleWord() ? (int64_t(VAL) % int64_t(RHS.VAL)) :
+             (ylen > 1 ? VAL : int64_t(VAL) % int64_t(RHS.pVal[0]));
+     else
+       VAL = RHS.isSingleWord() ? (VAL % RHS.VAL) : 
+           (ylen > 1 ? VAL : VAL % RHS.pVal[0]);
+   } else {
+     unsigned first2 = numWords() * APINT_BITS_PER_WORD - CountLeadingZeros();
+     unsigned xlen = !first2 ? 0 : whichWord(first2 - 1) + 1;
+     if (!xlen || (*this) < RHS)
+       return *this;
+     else if ((*this) == RHS) 
+       bzero(pVal, numWords() * 8);
+     else if (xlen == 1) 
+       pVal[0] %= RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0];
+     else {
+       uint64_t *xwords = new uint64_t[xlen+1], *ywords = new uint64_t[ylen];
+       assert(xwords && ywords && "Memory Allocation Failed!");
+       memcpy(xwords, pVal, xlen * 8);
+       xwords[xlen] = 0;
+       memcpy(ywords, RHS.isSingleWord() ? &RHS.VAL : RHS.pVal, ylen * 8);
+       unsigned nshift = 63 - (first - 1) % 64;
+       if (nshift) {
+         lshift(ywords, 0, ywords, ylen, nshift);
+         unsigned xlentmp = xlen;
+         xwords[xlen++] = lshift(xwords, 0, xwords, xlentmp, nshift);
+       }
+       div((unsigned*)xwords, xlen*2-1, (unsigned*)ywords, ylen*2);
+       bzero(pVal, numWords() * 8);
+       for (unsigned i = 0; i < ylen-1; ++i)
+         pVal[i] = (xwords[i] >> nshift) | (xwords[i+1] << (64 - nshift));
+       pVal[ylen-1] = xwords[ylen-1] >> nshift;
+       delete[] xwords;
+       delete[] ywords;
+     }
+   }
+   return *this;
+ }
+ 
+ /// @brief Bitwise AND assignment operator. Performs bitwise AND operation on
+ /// this APInt and the given APInt& RHS, assigns the result to this APInt.
+ APInt& APInt::operator&=(const APInt& RHS) {
+   if (isSingleWord()) {
+     if (RHS.isSingleWord()) VAL &= RHS.VAL;
+     else VAL &= RHS.pVal[0];
+   } else {
+     if (RHS.isSingleWord()) {
+       bzero(pVal, (numWords() - 1) * 8);
+       pVal[0] &= RHS.VAL;
+     } else {
+       unsigned minwords = numWords() < RHS.numWords() ? numWords() : RHS.numWords();
+       for (unsigned i = 0; i < minwords; ++i)
+         pVal[i] &= RHS.pVal[i];
+       if (numWords() > minwords) bzero(pVal+minwords, (numWords() - minwords) * 8);
+     }
+   }
+   return *this;
+ }
+ 
+ /// @brief Bitwise OR assignment operator. Performs bitwise OR operation on 
+ /// this APInt and the given APInt& RHS, assigns the result to this APInt.
+ APInt& APInt::operator|=(const APInt& RHS) {
+   if (isSingleWord()) {
+     if (RHS.isSingleWord()) VAL |= RHS.VAL;
+     else VAL |= RHS.pVal[0];
+   } else {
+     if (RHS.isSingleWord()) {
+       pVal[0] |= RHS.VAL;
+     } else {
+       unsigned minwords = numWords() < RHS.numWords() ? numWords() : RHS.numWords();
+       for (unsigned i = 0; i < minwords; ++i)
+         pVal[i] |= RHS.pVal[i];
+     }
+   }
+   TruncToBits();
+   return *this;
+ }
+ 
+ /// @brief Bitwise XOR assignment operator. Performs bitwise XOR operation on
+ /// this APInt and the given APInt& RHS, assigns the result to this APInt.
+ APInt& APInt::operator^=(const APInt& RHS) {
+   if (isSingleWord()) {
+     if (RHS.isSingleWord()) VAL ^= RHS.VAL;
+     else VAL ^= RHS.pVal[0];
+   } else {
+     if (RHS.isSingleWord()) {
+       for (unsigned i = 0; i < numWords(); ++i)
+         pVal[i] ^= RHS.VAL;
+     } else {
+       unsigned minwords = numWords() < RHS.numWords() ? numWords() : RHS.numWords();
+       for (unsigned i = 0; i < minwords; ++i)
+         pVal[i] ^= RHS.pVal[i];
+       if (numWords() > minwords)
+         for (unsigned i = minwords; i < numWords(); ++i)
+           pVal[i] ^= 0;
+     }
+   }
+   TruncToBits();
+   return *this;
+ }
+ 
+ /// @brief Bitwise AND operator. Performs bitwise AND operation on this APInt
+ /// and the given APInt& RHS.
+ APInt APInt::operator&(const APInt& RHS) const {
+   APInt API(RHS);
+   return API &= *this;
+ }
+ 
+ /// @brief Bitwise OR operator. Performs bitwise OR operation on this APInt 
+ /// and the given APInt& RHS.
+ APInt APInt::operator|(const APInt& RHS) const {
+   APInt API(RHS);
+   API |= *this;
+   API.TruncToBits();
+   return API;
+ }
+ 
+ /// @brief Bitwise XOR operator. Performs bitwise XOR operation on this APInt
+ /// and the given APInt& RHS.
+ APInt APInt::operator^(const APInt& RHS) const {
+   APInt API(RHS);
+   API ^= *this;
+   API.TruncToBits();
+   return API;
+ }
+ 
+ /// @brief Logical AND operator. Performs logical AND operation on this APInt
+ /// and the given APInt& RHS.
+ bool APInt::operator&&(const APInt& RHS) const {
+   if (isSingleWord()) 
+     return RHS.isSingleWord() ? VAL && RHS.VAL : VAL && RHS.pVal[0];
+   else if (RHS.isSingleWord())
+     return RHS.VAL && pVal[0];
+   else {
+     unsigned minN = std::min(numWords(), RHS.numWords());
+     for (unsigned i = 0; i < minN; ++i)
+       if (pVal[i] && RHS.pVal[i])
+         return true;
+   }
+   return false;
+ }
+ 
+ /// @brief Logical OR operator. Performs logical OR operation on this APInt 
+ /// and the given APInt& RHS.
+ bool APInt::operator||(const APInt& RHS) const {
+   if (isSingleWord()) 
+     return RHS.isSingleWord() ? VAL || RHS.VAL : VAL || RHS.pVal[0];
+   else if (RHS.isSingleWord())
+     return RHS.VAL || pVal[0];
+   else {
+     unsigned minN = std::min(numWords(), RHS.numWords());
+     for (unsigned i = 0; i < minN; ++i)
+       if (pVal[i] || RHS.pVal[i])
+         return true;
+   }
+   return false;
+ }
+ 
+ /// @brief Logical negation operator. Performs logical negation operation on
+ /// this APInt.
+ bool APInt::operator !() const {
+   if (isSingleWord())
+     return !VAL;
+   else
+     for (unsigned i = 0; i < numWords(); ++i)
+        if (pVal[i]) 
+          return false;
+   return true;
+ }
+ 
+ /// @brief Multiplication operator. Multiplies this APInt by the given APInt& 
+ /// RHS.
+ APInt APInt::operator*(const APInt& RHS) const {
+   APInt API(RHS);
+   API *= *this;
+   API.TruncToBits();
+   return API;
+ }
+ 
+ /// @brief Division operator. Divides this APInt by the given APInt& RHS.
+ APInt APInt::operator/(const APInt& RHS) const {
+   APInt API(*this);
+   return API /= RHS;
+ }
+ 
+ /// @brief Remainder operator. Yields the remainder from the division of this
+ /// APInt and the given APInt& RHS.
+ APInt APInt::operator%(const APInt& RHS) const {
+   APInt API(*this);
+   return API %= RHS;
+ }
+ 
+ /// @brief Addition operator. Adds this APInt by the given APInt& RHS.
+ APInt APInt::operator+(const APInt& RHS) const {
+   APInt API(*this);
+   API += RHS;
+   API.TruncToBits();
+   return API;
+ }
+ 
+ /// @brief Subtraction operator. Subtracts this APInt by the given APInt& RHS
+ APInt APInt::operator-(const APInt& RHS) const {
+   APInt API(*this);
+   API -= RHS;
+   API.TruncToBits();
+   return API;
+ }
+ 
+ /// @brief Array-indexing support.
+ bool APInt::operator[](unsigned bitPosition) const {
+   return maskBit(bitPosition) & (isSingleWord() ? 
+          VAL : pVal[whichWord(bitPosition)]) != 0;
+ }
+ 
+ /// @brief Equality operator. Compare this APInt with the given APInt& RHS 
+ /// for the validity of the equality relationship.
+ bool APInt::operator==(const APInt& RHS) const {
+   unsigned n1 = numWords() * APINT_BITS_PER_WORD - CountLeadingZeros(), 
+            n2 = RHS.numWords() * APINT_BITS_PER_WORD - RHS.CountLeadingZeros();
+   if (n1 != n2) return false;
+   else if (isSingleWord()) 
+     return VAL == (RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0]);
+   else {
+     if (n1 <= 64)
+       return pVal[0] == (RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0]);
+     for (int i = whichWord(n1 - 1); i >= 0; --i)
+       if (pVal[i] != RHS.pVal[i]) return false;
+   }
+   return true;
+ }
+ 
+ /// @brief Inequality operator. Compare this APInt with the given APInt& RHS
+ /// for the validity of the inequality relationship.
+ bool APInt::operator!=(const APInt& RHS) const {
+   return !((*this) == RHS);
+ }
+ 
+ /// @brief Less-than operator. Compare this APInt with the given APInt& RHS
+ /// for the validity of the less-than relationship.
+ bool APInt::operator <(const APInt& RHS) const {
+   if (isSigned && RHS.isSigned) {
+     if ((*this)[bitsnum-1] > RHS[RHS.bitsnum-1])
+       return false;
+     else if ((*this)[bitsnum-1] < RHS[RHS.bitsnum-1])
+       return true;
+   }
+   unsigned n1 = numWords() * 64 - CountLeadingZeros(), 
+            n2 = RHS.numWords() * 64 - RHS.CountLeadingZeros();
+   if (n1 < n2) return true;
+   else if (n1 > n2) return false;
+   else if (isSingleWord())
+     return VAL < (RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0]);
+   else {
+     if (n1 <= 64)
+       return pVal[0] < (RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0]);
+     for (int i = whichWord(n1 - 1); i >= 0; --i) {
+       if (pVal[i] > RHS.pVal[i]) return false;
+       else if (pVal[i] < RHS.pVal[i]) return true;
+     }
+   }
+   return false;
+ }
+ 
+ /// @brief Less-than-or-equal operator. Compare this APInt with the given 
+ /// APInt& RHS for the validity of the less-than-or-equal relationship.
+ bool APInt::operator<=(const APInt& RHS) const {
+   return (*this) == RHS || (*this) < RHS;
+ }
+ 
+ /// @brief Greater-than operator. Compare this APInt with the given APInt& RHS
+ /// for the validity of the greater-than relationship.
+ bool APInt::operator >(const APInt& RHS) const {
+   return !((*this) <= RHS);
+ }
+ 
+ /// @brief Greater-than-or-equal operator. Compare this APInt with the given 
+ /// APInt& RHS for the validity of the greater-than-or-equal relationship.
+ bool APInt::operator>=(const APInt& RHS) const {
+   return !((*this) < RHS);
+ }  
+ 
+ /// Set the given bit to 1 whose poition is given as "bitPosition".
+ /// @brief Set a given bit to 1.
+ APInt& APInt::set(unsigned bitPosition) {
+   if (isSingleWord()) VAL |= maskBit(bitPosition);
+   else pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
+   return *this;
+ }
+ 
+ /// @brief Set every bit to 1.
+ APInt& APInt::set() {
+   if (isSingleWord()) VAL = -1ULL;
+   else
+     for (unsigned i = 0; i < numWords(); ++i)
+       pVal[i] = -1ULL;
+   return *this;
+ }
+ 
+ /// Set the given bit to 0 whose position is given as "bitPosition".
+ /// @brief Set a given bit to 0.
+ APInt& APInt::clear(unsigned bitPosition) {
+   if (isSingleWord()) VAL &= ~maskBit(bitPosition);
+   else pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
+   return *this;
+ }
+ 
+ /// @brief Set every bit to 0.
+ APInt& APInt::clear() {
+   if (isSingleWord()) VAL = 0;
+   else bzero(pVal, numWords() * 8);
+   return *this;
+ }
+ 
+ /// @brief Left-shift assignment operator. Left-shift the APInt by shiftAmt
+ /// and assigns the result to this APInt.
+ APInt& APInt::operator<<=(unsigned shiftAmt) {
+   if (shiftAmt >= bitsnum) {
+     if (isSingleWord()) VAL = 0;
+     else bzero(pVal, numWords() * 8);
+   } else {
+     for (unsigned i = 0; i < shiftAmt; ++i) clear(i);
+     for (unsigned i = shiftAmt; i < bitsnum; ++i) {
+       if ((*this)[i-shiftAmt]) set(i);
+       else clear(i);
+     }
+   }
+   return *this;
+ }
+ 
+ /// @brief Left-shift operator. Left-shift the APInt by shiftAmt.
+ APInt APInt::operator<<(unsigned shiftAmt) const {
+   APInt API(*this);
+   API <<= shiftAmt;
+   return API;
+ }
+ 
+ /// @brief Right-shift assignment operator. Right-shift the APInt by shiftAmt
+ /// and assigns the result to this APInt.
+ APInt& APInt::operator>>=(unsigned shiftAmt) {
+   bool isAShr = isSigned && (*this)[bitsnum-1];
+   if (isSingleWord())
+     VAL = isAShr ? (int64_t(VAL) >> shiftAmt) : (VAL >> shiftAmt);
+   else {
+     unsigned i = 0;
+     for (i = 0; i < bitsnum - shiftAmt; ++i)
+       if ((*this)[i+shiftAmt]) set(i);
+       else clear(i);
+     for (; i < bitsnum; ++i)
+       isAShr ? set(i) : clear(i);
+   }
+   return *this;
+ }
+ 
+ /// @brief Right-shift operator. Right-shift the APInt by shiftAmt.
+ APInt APInt::operator>>(unsigned shiftAmt) const {
+   APInt API(*this);
+   API >>= shiftAmt;
+   return API;
+ }
+ 
+ /// @brief Bitwise NOT operator. Performs a bitwise logical NOT operation on
+ /// this APInt.
+ APInt APInt::operator~() const {
+   APInt API(*this);
+   API.flip();
+   return API;
+ }
+ 
+ /// @brief Toggle every bit to its opposite value.
+ APInt& APInt::flip() {
+   if (isSingleWord()) VAL = (~(VAL << (64 - bitsnum))) >> (64 - bitsnum);
+   else {
+     unsigned i = 0;
+     for (; i < numWords() - 1; ++i)
+       pVal[i] = ~pVal[i];
+     unsigned offset = 64 - (bitsnum - 64 * (i - 1));
+     pVal[i] = (~(pVal[i] << offset)) >> offset;
+   }
+   return *this;
+ }
+ 
+ /// Toggle a given bit to its opposite value whose position is given 
+ /// as "bitPosition".
+ /// @brief Toggles a given bit to its opposite value.
+ APInt& APInt::flip(unsigned bitPosition) {
+   assert(bitPosition < bitsnum && "Out of the bit-width range!");
+   if ((*this)[bitPosition]) clear(bitPosition);
+   else set(bitPosition);
+   return *this;
+ }
+ 
+ /// to_string - This function translates the APInt into a string.
+ std::string APInt::to_string(uint8_t radix) const {
+   assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
+          "Radix should be 2, 8, 10, or 16!");
+   std::ostringstream buf;
+   buf << std::setbase(radix);
+   // If the radix is a power of 2, set the format of ostringstream,
+   // and output the value into buf.
+   if ((radix & (radix - 1)) == 0) {
+     if (isSingleWord()) buf << VAL;
+     else {
+       buf << pVal[numWords()-1];
+       buf << std::setw(64 / (radix / 8 + 2)) << std::setfill('0');
+       for (int i = numWords() - 2; i >= 0; --i)
+         buf << pVal[i];
+     }
+   }
+   else {  // If the radix = 10, need to translate the value into a
+           // string.
+     if (isSingleWord()) buf << VAL;
+     else {
+       // FIXME: To be supported.
+     }
+   }
+   return buf.str();
+ }
+ 
+ /// getMaxValue - This function returns the largest value
+ /// for an APInt of the specified bit-width and if isSign == true,
+ /// it should be largest signed value, otherwise unsigned value.
+ APInt APInt::getMaxValue(unsigned numBits, bool isSign) {
+   APInt APIVal(numBits, 1);
+   APIVal.set();
+   return isSign ? APIVal.clear(numBits) : APIVal;
+ }
+ 
+ /// getMinValue - This function returns the smallest value for
+ /// an APInt of the given bit-width and if isSign == true,
+ /// it should be smallest signed value, otherwise zero.
+ APInt APInt::getMinValue(unsigned numBits, bool isSign) {
+   APInt APIVal(0, numBits);
+   return isSign ? APIVal : APIVal.set(numBits);
+ }
+ 
+ /// getAllOnesValue - This function returns an all-ones value for
+ /// an APInt of the specified bit-width.
+ APInt APInt::getAllOnesValue(unsigned numBits) {
+   return getMaxValue(numBits, false);
+ }
+ 
+ /// getNullValue - This function creates an '0' value for an
+ /// APInt of the specified bit-width.
+ APInt APInt::getNullValue(unsigned numBits) {
+   return getMinValue(numBits, true);
+ }
+ 
+ /// HiBits - This function returns the high "numBits" bits of this APInt.
+ APInt APInt::HiBits(unsigned numBits) const {
+   return (*this) >> (bitsnum - numBits); 
+ }
+ 
+ /// LoBits - This function returns the low "numBits" bits of this APInt.
+ APInt APInt::LoBits(unsigned numBits) const {
+   return ((*this) << (bitsnum - numBits)) >> (bitsnum - numBits);
+ }
+ 
+ /// CountLeadingZeros - This function is a APInt version corresponding to 
+ /// llvm/include/llvm/Support/MathExtras.h's function 
+ /// CountLeadingZeros_{32, 64}. It performs platform optimal form of counting 
+ /// the number of zeros from the most significant bit to the first one bit.
+ /// @returns numWord() * 64 if the value is zero.
+ unsigned APInt::CountLeadingZeros() const {
+   if (isSingleWord())
+     return CountLeadingZeros_64(VAL);
+   unsigned Count = 0;
+   for (int i = numWords() - 1; i >= 0; --i) {
+     unsigned tmp = CountLeadingZeros_64(pVal[i]);
+     Count += tmp;
+     if (tmp != 64)
+       break;
+   }
+   return Count;
+ }
+ 
+ /// CountTrailingZero - This function is a APInt version corresponding to
+ /// llvm/include/llvm/Support/MathExtras.h's function 
+ /// CountTrailingZeros_{32, 64}. It performs platform optimal form of counting 
+ /// the number of zeros from the least significant bit to the first one bit.
+ /// @returns numWord() * 64 if the value is zero.
+ unsigned APInt::CountTrailingZeros() const {
+   if (isSingleWord())
+     return CountTrailingZeros_64(~VAL & (VAL - 1));
+   APInt Tmp = ~(*this) & ((*this) - 1);
+   return numWords() * 64 - Tmp.CountLeadingZeros();
+ }
+ 
+ /// CountPopulation - This function is a APInt version corresponding to
+ /// llvm/include/llvm/Support/MathExtras.h's function
+ /// CountPopulation_{32, 64}. It counts the number of set bits in a value.
+ /// @returns 0 if the value is zero.
+ unsigned APInt::CountPopulation() const {
+   if (isSingleWord())
+     return CountPopulation_64(VAL);
+   unsigned Count = 0;
+   for (unsigned i = 0; i < numWords(); ++i)
+     Count += CountPopulation_64(pVal[i]);
+   return Count;
+ }
+ 
+ 
+ /// ByteSwap - This function returns a byte-swapped representation of the
+ /// APInt argument, APIVal.
+ APInt llvm::ByteSwap(const APInt& APIVal) {
+   if (APIVal.bitsnum <= 32)
+     return APInt(APIVal.bitsnum, ByteSwap_32(unsigned(APIVal.VAL)));
+   else if (APIVal.bitsnum <= 64)
+     return APInt(APIVal.bitsnum, ByteSwap_64(APIVal.VAL));
+   else
+     return APIVal;
+ }
+ 
+ /// GreatestCommonDivisor - This function returns the greatest common
+ /// divisor of the two APInt values using Enclid's algorithm.
+ APInt llvm::GreatestCommonDivisor(const APInt& API1, const APInt& API2) {
+   APInt A = API1, B = API2;
+   while (!!B) {
+     APInt T = B;
+     B = A % B;
+     A = T;
+   }
+   return A;
+ }






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