| //===-- APInt.cpp - Implement APInt class ---------------------------------===// |
| // |
| // 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 integer |
| // constant values and provide a variety of arithmetic operations on them. |
| // |
| //===----------------------------------------------------------------------===// |
| |
| #define DEBUG_TYPE "apint" |
| #include "llvm/ADT/APInt.h" |
| #include "llvm/ADT/StringRef.h" |
| #include "llvm/ADT/FoldingSet.h" |
| #include "llvm/ADT/SmallString.h" |
| #include "llvm/Support/Debug.h" |
| #include "llvm/Support/ErrorHandling.h" |
| #include "llvm/Support/MathExtras.h" |
| #include "llvm/Support/raw_ostream.h" |
| #include <cmath> |
| #include <limits> |
| #include <cstring> |
| #include <cstdlib> |
| using namespace llvm; |
| |
| /// A utility function for allocating memory, checking for allocation failures, |
| /// and ensuring the contents are zeroed. |
| inline static uint64_t* getClearedMemory(unsigned numWords) { |
| uint64_t * result = new uint64_t[numWords]; |
| assert(result && "APInt memory allocation fails!"); |
| memset(result, 0, numWords * sizeof(uint64_t)); |
| return result; |
| } |
| |
| /// A utility function for allocating memory and checking for allocation |
| /// failure. The content is not zeroed. |
| inline static uint64_t* getMemory(unsigned numWords) { |
| uint64_t * result = new uint64_t[numWords]; |
| assert(result && "APInt memory allocation fails!"); |
| return result; |
| } |
| |
| /// A utility function that converts a character to a digit. |
| inline static unsigned getDigit(char cdigit, uint8_t radix) { |
| unsigned r; |
| |
| if (radix == 16) { |
| r = cdigit - '0'; |
| if (r <= 9) |
| return r; |
| |
| r = cdigit - 'A'; |
| if (r <= 5) |
| return r + 10; |
| |
| r = cdigit - 'a'; |
| if (r <= 5) |
| return r + 10; |
| } |
| |
| r = cdigit - '0'; |
| if (r < radix) |
| return r; |
| |
| return -1U; |
| } |
| |
| |
| void APInt::initSlowCase(unsigned numBits, uint64_t val, bool isSigned) { |
| pVal = getClearedMemory(getNumWords()); |
| pVal[0] = val; |
| if (isSigned && int64_t(val) < 0) |
| for (unsigned i = 1; i < getNumWords(); ++i) |
| pVal[i] = -1ULL; |
| } |
| |
| void APInt::initSlowCase(const APInt& that) { |
| pVal = getMemory(getNumWords()); |
| memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE); |
| } |
| |
| |
| APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[]) |
| : BitWidth(numBits), VAL(0) { |
| assert(BitWidth && "Bitwidth too small"); |
| assert(bigVal && "Null pointer detected!"); |
| if (isSingleWord()) |
| VAL = bigVal[0]; |
| else { |
| // Get memory, cleared to 0 |
| pVal = getClearedMemory(getNumWords()); |
| // Calculate the number of words to copy |
| unsigned words = std::min<unsigned>(numWords, getNumWords()); |
| // Copy the words from bigVal to pVal |
| memcpy(pVal, bigVal, words * APINT_WORD_SIZE); |
| } |
| // Make sure unused high bits are cleared |
| clearUnusedBits(); |
| } |
| |
| APInt::APInt(unsigned numbits, const StringRef& Str, uint8_t radix) |
| : BitWidth(numbits), VAL(0) { |
| assert(BitWidth && "Bitwidth too small"); |
| fromString(numbits, Str, radix); |
| } |
| |
| APInt& APInt::AssignSlowCase(const APInt& RHS) { |
| // Don't do anything for X = X |
| if (this == &RHS) |
| return *this; |
| |
| if (BitWidth == RHS.getBitWidth()) { |
| // assume same bit-width single-word case is already handled |
| assert(!isSingleWord()); |
| memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE); |
| return *this; |
| } |
| |
| if (isSingleWord()) { |
| // assume case where both are single words is already handled |
| assert(!RHS.isSingleWord()); |
| VAL = 0; |
| pVal = getMemory(RHS.getNumWords()); |
| memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); |
| } else if (getNumWords() == RHS.getNumWords()) |
| memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); |
| else if (RHS.isSingleWord()) { |
| delete [] pVal; |
| VAL = RHS.VAL; |
| } else { |
| delete [] pVal; |
| pVal = getMemory(RHS.getNumWords()); |
| memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); |
| } |
| BitWidth = RHS.BitWidth; |
| return clearUnusedBits(); |
| } |
| |
| APInt& APInt::operator=(uint64_t RHS) { |
| if (isSingleWord()) |
| VAL = RHS; |
| else { |
| pVal[0] = RHS; |
| memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE); |
| } |
| return clearUnusedBits(); |
| } |
| |
| /// Profile - This method 'profiles' an APInt for use with FoldingSet. |
| void APInt::Profile(FoldingSetNodeID& ID) const { |
| ID.AddInteger(BitWidth); |
| |
| if (isSingleWord()) { |
| ID.AddInteger(VAL); |
| return; |
| } |
| |
| unsigned NumWords = getNumWords(); |
| for (unsigned i = 0; i < NumWords; ++i) |
| ID.AddInteger(pVal[i]); |
| } |
| |
| /// add_1 - This function adds a single "digit" integer, y, to the multiple |
| /// "digit" integer array, x[]. x[] is modified to reflect the addition and |
| /// 1 is returned if there is a carry out, otherwise 0 is returned. |
| /// @returns the carry of the addition. |
| static bool add_1(uint64_t dest[], uint64_t x[], unsigned len, uint64_t y) { |
| for (unsigned i = 0; i < len; ++i) { |
| dest[i] = y + x[i]; |
| if (dest[i] < y) |
| y = 1; // Carry one to next digit. |
| else { |
| y = 0; // No need to carry so exit early |
| break; |
| } |
| } |
| return y; |
| } |
| |
| /// @brief Prefix increment operator. Increments the APInt by one. |
| APInt& APInt::operator++() { |
| if (isSingleWord()) |
| ++VAL; |
| else |
| add_1(pVal, pVal, getNumWords(), 1); |
| return clearUnusedBits(); |
| } |
| |
| /// sub_1 - This function subtracts a single "digit" (64-bit word), y, from |
| /// the multi-digit integer array, x[], propagating the borrowed 1 value until |
| /// no further borrowing is neeeded or it runs out of "digits" in x. The result |
| /// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted. |
| /// In other words, if y > x then this function returns 1, otherwise 0. |
| /// @returns the borrow out of the subtraction |
| static bool sub_1(uint64_t x[], unsigned len, uint64_t y) { |
| for (unsigned i = 0; i < len; ++i) { |
| uint64_t X = x[i]; |
| x[i] -= y; |
| if (y > X) |
| y = 1; // We have to "borrow 1" from next "digit" |
| else { |
| y = 0; // No need to borrow |
| break; // Remaining digits are unchanged so exit early |
| } |
| } |
| return bool(y); |
| } |
| |
| /// @brief Prefix decrement operator. Decrements the APInt by one. |
| APInt& APInt::operator--() { |
| if (isSingleWord()) |
| --VAL; |
| else |
| sub_1(pVal, getNumWords(), 1); |
| return clearUnusedBits(); |
| } |
| |
| /// add - This function adds the integer array x to the integer array Y and |
| /// places the result in dest. |
| /// @returns the carry out from the addition |
| /// @brief General addition of 64-bit integer arrays |
| static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y, |
| unsigned len) { |
| bool carry = false; |
| for (unsigned i = 0; i< len; ++i) { |
| uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x |
| dest[i] = x[i] + y[i] + carry; |
| carry = dest[i] < limit || (carry && dest[i] == limit); |
| } |
| return carry; |
| } |
| |
| /// Adds the RHS APint to this APInt. |
| /// @returns this, after addition of RHS. |
| /// @brief Addition assignment operator. |
| APInt& APInt::operator+=(const APInt& RHS) { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) |
| VAL += RHS.VAL; |
| else { |
| add(pVal, pVal, RHS.pVal, getNumWords()); |
| } |
| return clearUnusedBits(); |
| } |
| |
| /// Subtracts the integer array y from the integer array x |
| /// @returns returns the borrow out. |
| /// @brief Generalized subtraction of 64-bit integer arrays. |
| static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y, |
| unsigned len) { |
| bool borrow = false; |
| for (unsigned i = 0; i < len; ++i) { |
| uint64_t x_tmp = borrow ? x[i] - 1 : x[i]; |
| borrow = y[i] > x_tmp || (borrow && x[i] == 0); |
| dest[i] = x_tmp - y[i]; |
| } |
| return borrow; |
| } |
| |
| /// Subtracts the RHS APInt from this APInt |
| /// @returns this, after subtraction |
| /// @brief Subtraction assignment operator. |
| APInt& APInt::operator-=(const APInt& RHS) { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) |
| VAL -= RHS.VAL; |
| else |
| sub(pVal, pVal, RHS.pVal, getNumWords()); |
| return clearUnusedBits(); |
| } |
| |
| /// Multiplies an integer array, x by a a uint64_t integer and places the result |
| /// into dest. |
| /// @returns the carry out of the multiplication. |
| /// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer. |
| static uint64_t mul_1(uint64_t dest[], uint64_t x[], unsigned len, uint64_t y) { |
| // Split y into high 32-bit part (hy) and low 32-bit part (ly) |
| uint64_t ly = y & 0xffffffffULL, hy = y >> 32; |
| uint64_t carry = 0; |
| |
| // For each digit of x. |
| for (unsigned i = 0; i < len; ++i) { |
| // Split x into high and low words |
| uint64_t lx = x[i] & 0xffffffffULL; |
| uint64_t hx = x[i] >> 32; |
| // hasCarry - A flag to indicate if there is a carry to the next digit. |
| // 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; |
| } |
| |
| /// Multiplies integer array x by integer array y and stores the result into |
| /// the integer array dest. Note that dest's size must be >= xlen + ylen. |
| /// @brief Generalized multiplicate of integer arrays. |
| static void 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 = 0, hx = 0; |
| 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; |
| } |
| } |
| |
| APInt& APInt::operator*=(const APInt& RHS) { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) { |
| VAL *= RHS.VAL; |
| clearUnusedBits(); |
| return *this; |
| } |
| |
| // Get some bit facts about LHS and check for zero |
| unsigned lhsBits = getActiveBits(); |
| unsigned lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1; |
| if (!lhsWords) |
| // 0 * X ===> 0 |
| return *this; |
| |
| // Get some bit facts about RHS and check for zero |
| unsigned rhsBits = RHS.getActiveBits(); |
| unsigned rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1; |
| if (!rhsWords) { |
| // X * 0 ===> 0 |
| clear(); |
| return *this; |
| } |
| |
| // Allocate space for the result |
| unsigned destWords = rhsWords + lhsWords; |
| uint64_t *dest = getMemory(destWords); |
| |
| // Perform the long multiply |
| mul(dest, pVal, lhsWords, RHS.pVal, rhsWords); |
| |
| // Copy result back into *this |
| clear(); |
| unsigned wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords; |
| memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE); |
| |
| // delete dest array and return |
| delete[] dest; |
| return *this; |
| } |
| |
| APInt& APInt::operator&=(const APInt& RHS) { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) { |
| VAL &= RHS.VAL; |
| return *this; |
| } |
| unsigned numWords = getNumWords(); |
| for (unsigned i = 0; i < numWords; ++i) |
| pVal[i] &= RHS.pVal[i]; |
| return *this; |
| } |
| |
| APInt& APInt::operator|=(const APInt& RHS) { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) { |
| VAL |= RHS.VAL; |
| return *this; |
| } |
| unsigned numWords = getNumWords(); |
| for (unsigned i = 0; i < numWords; ++i) |
| pVal[i] |= RHS.pVal[i]; |
| return *this; |
| } |
| |
| APInt& APInt::operator^=(const APInt& RHS) { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) { |
| VAL ^= RHS.VAL; |
| this->clearUnusedBits(); |
| return *this; |
| } |
| unsigned numWords = getNumWords(); |
| for (unsigned i = 0; i < numWords; ++i) |
| pVal[i] ^= RHS.pVal[i]; |
| return clearUnusedBits(); |
| } |
| |
| APInt APInt::AndSlowCase(const APInt& RHS) const { |
| unsigned numWords = getNumWords(); |
| uint64_t* val = getMemory(numWords); |
| for (unsigned i = 0; i < numWords; ++i) |
| val[i] = pVal[i] & RHS.pVal[i]; |
| return APInt(val, getBitWidth()); |
| } |
| |
| APInt APInt::OrSlowCase(const APInt& RHS) const { |
| unsigned numWords = getNumWords(); |
| uint64_t *val = getMemory(numWords); |
| for (unsigned i = 0; i < numWords; ++i) |
| val[i] = pVal[i] | RHS.pVal[i]; |
| return APInt(val, getBitWidth()); |
| } |
| |
| APInt APInt::XorSlowCase(const APInt& RHS) const { |
| unsigned numWords = getNumWords(); |
| uint64_t *val = getMemory(numWords); |
| for (unsigned i = 0; i < numWords; ++i) |
| val[i] = pVal[i] ^ RHS.pVal[i]; |
| |
| // 0^0==1 so clear the high bits in case they got set. |
| return APInt(val, getBitWidth()).clearUnusedBits(); |
| } |
| |
| bool APInt::operator !() const { |
| if (isSingleWord()) |
| return !VAL; |
| |
| for (unsigned i = 0; i < getNumWords(); ++i) |
| if (pVal[i]) |
| return false; |
| return true; |
| } |
| |
| APInt APInt::operator*(const APInt& RHS) const { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) |
| return APInt(BitWidth, VAL * RHS.VAL); |
| APInt Result(*this); |
| Result *= RHS; |
| return Result.clearUnusedBits(); |
| } |
| |
| APInt APInt::operator+(const APInt& RHS) const { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) |
| return APInt(BitWidth, VAL + RHS.VAL); |
| APInt Result(BitWidth, 0); |
| add(Result.pVal, this->pVal, RHS.pVal, getNumWords()); |
| return Result.clearUnusedBits(); |
| } |
| |
| APInt APInt::operator-(const APInt& RHS) const { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) |
| return APInt(BitWidth, VAL - RHS.VAL); |
| APInt Result(BitWidth, 0); |
| sub(Result.pVal, this->pVal, RHS.pVal, getNumWords()); |
| return Result.clearUnusedBits(); |
| } |
| |
| bool APInt::operator[](unsigned bitPosition) const { |
| return (maskBit(bitPosition) & |
| (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0; |
| } |
| |
| bool APInt::EqualSlowCase(const APInt& RHS) const { |
| // Get some facts about the number of bits used in the two operands. |
| unsigned n1 = getActiveBits(); |
| unsigned n2 = RHS.getActiveBits(); |
| |
| // If the number of bits isn't the same, they aren't equal |
| if (n1 != n2) |
| return false; |
| |
| // If the number of bits fits in a word, we only need to compare the low word. |
| if (n1 <= APINT_BITS_PER_WORD) |
| return pVal[0] == RHS.pVal[0]; |
| |
| // Otherwise, compare everything |
| for (int i = whichWord(n1 - 1); i >= 0; --i) |
| if (pVal[i] != RHS.pVal[i]) |
| return false; |
| return true; |
| } |
| |
| bool APInt::EqualSlowCase(uint64_t Val) const { |
| unsigned n = getActiveBits(); |
| if (n <= APINT_BITS_PER_WORD) |
| return pVal[0] == Val; |
| else |
| return false; |
| } |
| |
| bool APInt::ult(const APInt& RHS) const { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); |
| if (isSingleWord()) |
| return VAL < RHS.VAL; |
| |
| // Get active bit length of both operands |
| unsigned n1 = getActiveBits(); |
| unsigned n2 = RHS.getActiveBits(); |
| |
| // If magnitude of LHS is less than RHS, return true. |
| if (n1 < n2) |
| return true; |
| |
| // If magnitude of RHS is greather than LHS, return false. |
| if (n2 < n1) |
| return false; |
| |
| // If they bot fit in a word, just compare the low order word |
| if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD) |
| return pVal[0] < RHS.pVal[0]; |
| |
| // Otherwise, compare all words |
| unsigned topWord = whichWord(std::max(n1,n2)-1); |
| for (int i = topWord; i >= 0; --i) { |
| if (pVal[i] > RHS.pVal[i]) |
| return false; |
| if (pVal[i] < RHS.pVal[i]) |
| return true; |
| } |
| return false; |
| } |
| |
| bool APInt::slt(const APInt& RHS) const { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); |
| if (isSingleWord()) { |
| int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth); |
| int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth); |
| return lhsSext < rhsSext; |
| } |
| |
| APInt lhs(*this); |
| APInt rhs(RHS); |
| bool lhsNeg = isNegative(); |
| bool rhsNeg = rhs.isNegative(); |
| if (lhsNeg) { |
| // Sign bit is set so perform two's complement to make it positive |
| lhs.flip(); |
| lhs++; |
| } |
| if (rhsNeg) { |
| // Sign bit is set so perform two's complement to make it positive |
| rhs.flip(); |
| rhs++; |
| } |
| |
| // Now we have unsigned values to compare so do the comparison if necessary |
| // based on the negativeness of the values. |
| if (lhsNeg) |
| if (rhsNeg) |
| return lhs.ugt(rhs); |
| else |
| return true; |
| else if (rhsNeg) |
| return false; |
| else |
| return lhs.ult(rhs); |
| } |
| |
| APInt& APInt::set(unsigned bitPosition) { |
| if (isSingleWord()) |
| VAL |= maskBit(bitPosition); |
| else |
| pVal[whichWord(bitPosition)] |= maskBit(bitPosition); |
| 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 Toggle every bit to its opposite value. |
| |
| /// 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 < BitWidth && "Out of the bit-width range!"); |
| if ((*this)[bitPosition]) clear(bitPosition); |
| else set(bitPosition); |
| return *this; |
| } |
| |
| unsigned APInt::getBitsNeeded(const StringRef& str, uint8_t radix) { |
| assert(!str.empty() && "Invalid string length"); |
| assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) && |
| "Radix should be 2, 8, 10, or 16!"); |
| |
| size_t slen = str.size(); |
| |
| // Each computation below needs to know if it's negative. |
| StringRef::iterator p = str.begin(); |
| unsigned isNegative = *p == '-'; |
| if (*p == '-' || *p == '+') { |
| p++; |
| slen--; |
| assert(slen && "String is only a sign, needs a value."); |
| } |
| |
| // For radixes of power-of-two values, the bits required is accurately and |
| // easily computed |
| if (radix == 2) |
| return slen + isNegative; |
| if (radix == 8) |
| return slen * 3 + isNegative; |
| if (radix == 16) |
| return slen * 4 + isNegative; |
| |
| // This is grossly inefficient but accurate. We could probably do something |
| // with a computation of roughly slen*64/20 and then adjust by the value of |
| // the first few digits. But, I'm not sure how accurate that could be. |
| |
| // Compute a sufficient number of bits that is always large enough but might |
| // be too large. This avoids the assertion in the constructor. This |
| // calculation doesn't work appropriately for the numbers 0-9, so just use 4 |
| // bits in that case. |
| unsigned sufficient = slen == 1 ? 4 : slen * 64/18; |
| |
| // Convert to the actual binary value. |
| APInt tmp(sufficient, StringRef(p, slen), radix); |
| |
| // Compute how many bits are required. If the log is infinite, assume we need |
| // just bit. |
| unsigned log = tmp.logBase2(); |
| if (log == (unsigned)-1) { |
| return isNegative + 1; |
| } else { |
| return isNegative + log + 1; |
| } |
| } |
| |
| // From http://www.burtleburtle.net, byBob Jenkins. |
| // When targeting x86, both GCC and LLVM seem to recognize this as a |
| // rotate instruction. |
| #define rot(x,k) (((x)<<(k)) | ((x)>>(32-(k)))) |
| |
| // From http://www.burtleburtle.net, by Bob Jenkins. |
| #define mix(a,b,c) \ |
| { \ |
| a -= c; a ^= rot(c, 4); c += b; \ |
| b -= a; b ^= rot(a, 6); a += c; \ |
| c -= b; c ^= rot(b, 8); b += a; \ |
| a -= c; a ^= rot(c,16); c += b; \ |
| b -= a; b ^= rot(a,19); a += c; \ |
| c -= b; c ^= rot(b, 4); b += a; \ |
| } |
| |
| // From http://www.burtleburtle.net, by Bob Jenkins. |
| #define final(a,b,c) \ |
| { \ |
| c ^= b; c -= rot(b,14); \ |
| a ^= c; a -= rot(c,11); \ |
| b ^= a; b -= rot(a,25); \ |
| c ^= b; c -= rot(b,16); \ |
| a ^= c; a -= rot(c,4); \ |
| b ^= a; b -= rot(a,14); \ |
| c ^= b; c -= rot(b,24); \ |
| } |
| |
| // hashword() was adapted from http://www.burtleburtle.net, by Bob |
| // Jenkins. k is a pointer to an array of uint32_t values; length is |
| // the length of the key, in 32-bit chunks. This version only handles |
| // keys that are a multiple of 32 bits in size. |
| static inline uint32_t hashword(const uint64_t *k64, size_t length) |
| { |
| const uint32_t *k = reinterpret_cast<const uint32_t *>(k64); |
| uint32_t a,b,c; |
| |
| /* Set up the internal state */ |
| a = b = c = 0xdeadbeef + (((uint32_t)length)<<2); |
| |
| /*------------------------------------------------- handle most of the key */ |
| while (length > 3) |
| { |
| a += k[0]; |
| b += k[1]; |
| c += k[2]; |
| mix(a,b,c); |
| length -= 3; |
| k += 3; |
| } |
| |
| /*------------------------------------------- handle the last 3 uint32_t's */ |
| switch (length) { /* all the case statements fall through */ |
| case 3 : c+=k[2]; |
| case 2 : b+=k[1]; |
| case 1 : a+=k[0]; |
| final(a,b,c); |
| case 0: /* case 0: nothing left to add */ |
| break; |
| } |
| /*------------------------------------------------------ report the result */ |
| return c; |
| } |
| |
| // hashword8() was adapted from http://www.burtleburtle.net, by Bob |
| // Jenkins. This computes a 32-bit hash from one 64-bit word. When |
| // targeting x86 (32 or 64 bit), both LLVM and GCC compile this |
| // function into about 35 instructions when inlined. |
| static inline uint32_t hashword8(const uint64_t k64) |
| { |
| uint32_t a,b,c; |
| a = b = c = 0xdeadbeef + 4; |
| b += k64 >> 32; |
| a += k64 & 0xffffffff; |
| final(a,b,c); |
| return c; |
| } |
| #undef final |
| #undef mix |
| #undef rot |
| |
| uint64_t APInt::getHashValue() const { |
| uint64_t hash; |
| if (isSingleWord()) |
| hash = hashword8(VAL); |
| else |
| hash = hashword(pVal, getNumWords()*2); |
| return hash; |
| } |
| |
| /// HiBits - This function returns the high "numBits" bits of this APInt. |
| APInt APInt::getHiBits(unsigned numBits) const { |
| return APIntOps::lshr(*this, BitWidth - numBits); |
| } |
| |
| /// LoBits - This function returns the low "numBits" bits of this APInt. |
| APInt APInt::getLoBits(unsigned numBits) const { |
| return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits), |
| BitWidth - numBits); |
| } |
| |
| bool APInt::isPowerOf2() const { |
| return (!!*this) && !(*this & (*this - APInt(BitWidth,1))); |
| } |
| |
| unsigned APInt::countLeadingZerosSlowCase() const { |
| unsigned Count = 0; |
| for (unsigned i = getNumWords(); i > 0u; --i) { |
| if (pVal[i-1] == 0) |
| Count += APINT_BITS_PER_WORD; |
| else { |
| Count += CountLeadingZeros_64(pVal[i-1]); |
| break; |
| } |
| } |
| unsigned remainder = BitWidth % APINT_BITS_PER_WORD; |
| if (remainder) |
| Count -= APINT_BITS_PER_WORD - remainder; |
| return std::min(Count, BitWidth); |
| } |
| |
| static unsigned countLeadingOnes_64(uint64_t V, unsigned skip) { |
| unsigned Count = 0; |
| if (skip) |
| V <<= skip; |
| while (V && (V & (1ULL << 63))) { |
| Count++; |
| V <<= 1; |
| } |
| return Count; |
| } |
| |
| unsigned APInt::countLeadingOnes() const { |
| if (isSingleWord()) |
| return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth); |
| |
| unsigned highWordBits = BitWidth % APINT_BITS_PER_WORD; |
| unsigned shift; |
| if (!highWordBits) { |
| highWordBits = APINT_BITS_PER_WORD; |
| shift = 0; |
| } else { |
| shift = APINT_BITS_PER_WORD - highWordBits; |
| } |
| int i = getNumWords() - 1; |
| unsigned Count = countLeadingOnes_64(pVal[i], shift); |
| if (Count == highWordBits) { |
| for (i--; i >= 0; --i) { |
| if (pVal[i] == -1ULL) |
| Count += APINT_BITS_PER_WORD; |
| else { |
| Count += countLeadingOnes_64(pVal[i], 0); |
| break; |
| } |
| } |
| } |
| return Count; |
| } |
| |
| unsigned APInt::countTrailingZeros() const { |
| if (isSingleWord()) |
| return std::min(unsigned(CountTrailingZeros_64(VAL)), BitWidth); |
| unsigned Count = 0; |
| unsigned i = 0; |
| for (; i < getNumWords() && pVal[i] == 0; ++i) |
| Count += APINT_BITS_PER_WORD; |
| if (i < getNumWords()) |
| Count += CountTrailingZeros_64(pVal[i]); |
| return std::min(Count, BitWidth); |
| } |
| |
| unsigned APInt::countTrailingOnesSlowCase() const { |
| unsigned Count = 0; |
| unsigned i = 0; |
| for (; i < getNumWords() && pVal[i] == -1ULL; ++i) |
| Count += APINT_BITS_PER_WORD; |
| if (i < getNumWords()) |
| Count += CountTrailingOnes_64(pVal[i]); |
| return std::min(Count, BitWidth); |
| } |
| |
| unsigned APInt::countPopulationSlowCase() const { |
| unsigned Count = 0; |
| for (unsigned i = 0; i < getNumWords(); ++i) |
| Count += CountPopulation_64(pVal[i]); |
| return Count; |
| } |
| |
| APInt APInt::byteSwap() const { |
| assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!"); |
| if (BitWidth == 16) |
| return APInt(BitWidth, ByteSwap_16(uint16_t(VAL))); |
| else if (BitWidth == 32) |
| return APInt(BitWidth, ByteSwap_32(unsigned(VAL))); |
| else if (BitWidth == 48) { |
| unsigned Tmp1 = unsigned(VAL >> 16); |
| Tmp1 = ByteSwap_32(Tmp1); |
| uint16_t Tmp2 = uint16_t(VAL); |
| Tmp2 = ByteSwap_16(Tmp2); |
| return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1); |
| } else if (BitWidth == 64) |
| return APInt(BitWidth, ByteSwap_64(VAL)); |
| else { |
| APInt Result(BitWidth, 0); |
| char *pByte = (char*)Result.pVal; |
| for (unsigned i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) { |
| char Tmp = pByte[i]; |
| pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i]; |
| pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp; |
| } |
| return Result; |
| } |
| } |
| |
| APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1, |
| const APInt& API2) { |
| APInt A = API1, B = API2; |
| while (!!B) { |
| APInt T = B; |
| B = APIntOps::urem(A, B); |
| A = T; |
| } |
| return A; |
| } |
| |
| APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) { |
| union { |
| double D; |
| uint64_t I; |
| } T; |
| T.D = Double; |
| |
| // Get the sign bit from the highest order bit |
| bool isNeg = T.I >> 63; |
| |
| // Get the 11-bit exponent and adjust for the 1023 bit bias |
| int64_t exp = ((T.I >> 52) & 0x7ff) - 1023; |
| |
| // If the exponent is negative, the value is < 0 so just return 0. |
| if (exp < 0) |
| return APInt(width, 0u); |
| |
| // Extract the mantissa by clearing the top 12 bits (sign + exponent). |
| uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52; |
| |
| // If the exponent doesn't shift all bits out of the mantissa |
| if (exp < 52) |
| return isNeg ? -APInt(width, mantissa >> (52 - exp)) : |
| APInt(width, mantissa >> (52 - exp)); |
| |
| // If the client didn't provide enough bits for us to shift the mantissa into |
| // then the result is undefined, just return 0 |
| if (width <= exp - 52) |
| return APInt(width, 0); |
| |
| // Otherwise, we have to shift the mantissa bits up to the right location |
| APInt Tmp(width, mantissa); |
| Tmp = Tmp.shl((unsigned)exp - 52); |
| return isNeg ? -Tmp : Tmp; |
| } |
| |
| /// RoundToDouble - This function converts this APInt to a double. |
| /// The layout for double is as following (IEEE Standard 754): |
| /// -------------------------------------- |
| /// | Sign Exponent Fraction Bias | |
| /// |-------------------------------------- | |
| /// | 1[63] 11[62-52] 52[51-00] 1023 | |
| /// -------------------------------------- |
| double APInt::roundToDouble(bool isSigned) const { |
| |
| // Handle the simple case where the value is contained in one uint64_t. |
| // It is wrong to optimize getWord(0) to VAL; there might be more than one word. |
| if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) { |
| if (isSigned) { |
| int64_t sext = (int64_t(getWord(0)) << (64-BitWidth)) >> (64-BitWidth); |
| return double(sext); |
| } else |
| return double(getWord(0)); |
| } |
| |
| // Determine if the value is negative. |
| bool isNeg = isSigned ? (*this)[BitWidth-1] : false; |
| |
| // Construct the absolute value if we're negative. |
| APInt Tmp(isNeg ? -(*this) : (*this)); |
| |
| // Figure out how many bits we're using. |
| unsigned n = Tmp.getActiveBits(); |
| |
| // The exponent (without bias normalization) is just the number of bits |
| // we are using. Note that the sign bit is gone since we constructed the |
| // absolute value. |
| uint64_t exp = n; |
| |
| // Return infinity for exponent overflow |
| if (exp > 1023) { |
| if (!isSigned || !isNeg) |
| return std::numeric_limits<double>::infinity(); |
| else |
| return -std::numeric_limits<double>::infinity(); |
| } |
| exp += 1023; // Increment for 1023 bias |
| |
| // Number of bits in mantissa is 52. To obtain the mantissa value, we must |
| // extract the high 52 bits from the correct words in pVal. |
| uint64_t mantissa; |
| unsigned hiWord = whichWord(n-1); |
| if (hiWord == 0) { |
| mantissa = Tmp.pVal[0]; |
| if (n > 52) |
| mantissa >>= n - 52; // shift down, we want the top 52 bits. |
| } else { |
| assert(hiWord > 0 && "huh?"); |
| uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD); |
| uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD); |
| mantissa = hibits | lobits; |
| } |
| |
| // The leading bit of mantissa is implicit, so get rid of it. |
| uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0; |
| union { |
| double D; |
| uint64_t I; |
| } T; |
| T.I = sign | (exp << 52) | mantissa; |
| return T.D; |
| } |
| |
| // Truncate to new width. |
| APInt &APInt::trunc(unsigned width) { |
| assert(width < BitWidth && "Invalid APInt Truncate request"); |
| assert(width && "Can't truncate to 0 bits"); |
| unsigned wordsBefore = getNumWords(); |
| BitWidth = width; |
| unsigned wordsAfter = getNumWords(); |
| if (wordsBefore != wordsAfter) { |
| if (wordsAfter == 1) { |
| uint64_t *tmp = pVal; |
| VAL = pVal[0]; |
| delete [] tmp; |
| } else { |
| uint64_t *newVal = getClearedMemory(wordsAfter); |
| for (unsigned i = 0; i < wordsAfter; ++i) |
| newVal[i] = pVal[i]; |
| delete [] pVal; |
| pVal = newVal; |
| } |
| } |
| return clearUnusedBits(); |
| } |
| |
| // Sign extend to a new width. |
| APInt &APInt::sext(unsigned width) { |
| assert(width > BitWidth && "Invalid APInt SignExtend request"); |
| // If the sign bit isn't set, this is the same as zext. |
| if (!isNegative()) { |
| zext(width); |
| return *this; |
| } |
| |
| // The sign bit is set. First, get some facts |
| unsigned wordsBefore = getNumWords(); |
| unsigned wordBits = BitWidth % APINT_BITS_PER_WORD; |
| BitWidth = width; |
| unsigned wordsAfter = getNumWords(); |
| |
| // Mask the high order word appropriately |
| if (wordsBefore == wordsAfter) { |
| unsigned newWordBits = width % APINT_BITS_PER_WORD; |
| // The extension is contained to the wordsBefore-1th word. |
| uint64_t mask = ~0ULL; |
| if (newWordBits) |
| mask >>= APINT_BITS_PER_WORD - newWordBits; |
| mask <<= wordBits; |
| if (wordsBefore == 1) |
| VAL |= mask; |
| else |
| pVal[wordsBefore-1] |= mask; |
| return clearUnusedBits(); |
| } |
| |
| uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits; |
| uint64_t *newVal = getMemory(wordsAfter); |
| if (wordsBefore == 1) |
| newVal[0] = VAL | mask; |
| else { |
| for (unsigned i = 0; i < wordsBefore; ++i) |
| newVal[i] = pVal[i]; |
| newVal[wordsBefore-1] |= mask; |
| } |
| for (unsigned i = wordsBefore; i < wordsAfter; i++) |
| newVal[i] = -1ULL; |
| if (wordsBefore != 1) |
| delete [] pVal; |
| pVal = newVal; |
| return clearUnusedBits(); |
| } |
| |
| // Zero extend to a new width. |
| APInt &APInt::zext(unsigned width) { |
| assert(width > BitWidth && "Invalid APInt ZeroExtend request"); |
| unsigned wordsBefore = getNumWords(); |
| BitWidth = width; |
| unsigned wordsAfter = getNumWords(); |
| if (wordsBefore != wordsAfter) { |
| uint64_t *newVal = getClearedMemory(wordsAfter); |
| if (wordsBefore == 1) |
| newVal[0] = VAL; |
| else |
| for (unsigned i = 0; i < wordsBefore; ++i) |
| newVal[i] = pVal[i]; |
| if (wordsBefore != 1) |
| delete [] pVal; |
| pVal = newVal; |
| } |
| return *this; |
| } |
| |
| APInt &APInt::zextOrTrunc(unsigned width) { |
| if (BitWidth < width) |
| return zext(width); |
| if (BitWidth > width) |
| return trunc(width); |
| return *this; |
| } |
| |
| APInt &APInt::sextOrTrunc(unsigned width) { |
| if (BitWidth < width) |
| return sext(width); |
| if (BitWidth > width) |
| return trunc(width); |
| return *this; |
| } |
| |
| /// Arithmetic right-shift this APInt by shiftAmt. |
| /// @brief Arithmetic right-shift function. |
| APInt APInt::ashr(const APInt &shiftAmt) const { |
| return ashr((unsigned)shiftAmt.getLimitedValue(BitWidth)); |
| } |
| |
| /// Arithmetic right-shift this APInt by shiftAmt. |
| /// @brief Arithmetic right-shift function. |
| APInt APInt::ashr(unsigned shiftAmt) const { |
| assert(shiftAmt <= BitWidth && "Invalid shift amount"); |
| // Handle a degenerate case |
| if (shiftAmt == 0) |
| return *this; |
| |
| // Handle single word shifts with built-in ashr |
| if (isSingleWord()) { |
| if (shiftAmt == BitWidth) |
| return APInt(BitWidth, 0); // undefined |
| else { |
| unsigned SignBit = APINT_BITS_PER_WORD - BitWidth; |
| return APInt(BitWidth, |
| (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt)); |
| } |
| } |
| |
| // If all the bits were shifted out, the result is, technically, undefined. |
| // We return -1 if it was negative, 0 otherwise. We check this early to avoid |
| // issues in the algorithm below. |
| if (shiftAmt == BitWidth) { |
| if (isNegative()) |
| return APInt(BitWidth, -1ULL, true); |
| else |
| return APInt(BitWidth, 0); |
| } |
| |
| // Create some space for the result. |
| uint64_t * val = new uint64_t[getNumWords()]; |
| |
| // Compute some values needed by the following shift algorithms |
| unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word |
| unsigned offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift |
| unsigned breakWord = getNumWords() - 1 - offset; // last word affected |
| unsigned bitsInWord = whichBit(BitWidth); // how many bits in last word? |
| if (bitsInWord == 0) |
| bitsInWord = APINT_BITS_PER_WORD; |
| |
| // If we are shifting whole words, just move whole words |
| if (wordShift == 0) { |
| // Move the words containing significant bits |
| for (unsigned i = 0; i <= breakWord; ++i) |
| val[i] = pVal[i+offset]; // move whole word |
| |
| // Adjust the top significant word for sign bit fill, if negative |
| if (isNegative()) |
| if (bitsInWord < APINT_BITS_PER_WORD) |
| val[breakWord] |= ~0ULL << bitsInWord; // set high bits |
| } else { |
| // Shift the low order words |
| for (unsigned i = 0; i < breakWord; ++i) { |
| // This combines the shifted corresponding word with the low bits from |
| // the next word (shifted into this word's high bits). |
| val[i] = (pVal[i+offset] >> wordShift) | |
| (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift)); |
| } |
| |
| // Shift the break word. In this case there are no bits from the next word |
| // to include in this word. |
| val[breakWord] = pVal[breakWord+offset] >> wordShift; |
| |
| // Deal with sign extenstion in the break word, and possibly the word before |
| // it. |
| if (isNegative()) { |
| if (wordShift > bitsInWord) { |
| if (breakWord > 0) |
| val[breakWord-1] |= |
| ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord)); |
| val[breakWord] |= ~0ULL; |
| } else |
| val[breakWord] |= (~0ULL << (bitsInWord - wordShift)); |
| } |
| } |
| |
| // Remaining words are 0 or -1, just assign them. |
| uint64_t fillValue = (isNegative() ? -1ULL : 0); |
| for (unsigned i = breakWord+1; i < getNumWords(); ++i) |
| val[i] = fillValue; |
| return APInt(val, BitWidth).clearUnusedBits(); |
| } |
| |
| /// Logical right-shift this APInt by shiftAmt. |
| /// @brief Logical right-shift function. |
| APInt APInt::lshr(const APInt &shiftAmt) const { |
| return lshr((unsigned)shiftAmt.getLimitedValue(BitWidth)); |
| } |
| |
| /// Logical right-shift this APInt by shiftAmt. |
| /// @brief Logical right-shift function. |
| APInt APInt::lshr(unsigned shiftAmt) const { |
| if (isSingleWord()) { |
| if (shiftAmt == BitWidth) |
| return APInt(BitWidth, 0); |
| else |
| return APInt(BitWidth, this->VAL >> shiftAmt); |
| } |
| |
| // If all the bits were shifted out, the result is 0. This avoids issues |
| // with shifting by the size of the integer type, which produces undefined |
| // results. We define these "undefined results" to always be 0. |
| if (shiftAmt == BitWidth) |
| return APInt(BitWidth, 0); |
| |
| // If none of the bits are shifted out, the result is *this. This avoids |
| // issues with shifting by the size of the integer type, which produces |
| // undefined results in the code below. This is also an optimization. |
| if (shiftAmt == 0) |
| return *this; |
| |
| // Create some space for the result. |
| uint64_t * val = new uint64_t[getNumWords()]; |
| |
| // If we are shifting less than a word, compute the shift with a simple carry |
| if (shiftAmt < APINT_BITS_PER_WORD) { |
| uint64_t carry = 0; |
| for (int i = getNumWords()-1; i >= 0; --i) { |
| val[i] = (pVal[i] >> shiftAmt) | carry; |
| carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt); |
| } |
| return APInt(val, BitWidth).clearUnusedBits(); |
| } |
| |
| // Compute some values needed by the remaining shift algorithms |
| unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; |
| unsigned offset = shiftAmt / APINT_BITS_PER_WORD; |
| |
| // If we are shifting whole words, just move whole words |
| if (wordShift == 0) { |
| for (unsigned i = 0; i < getNumWords() - offset; ++i) |
| val[i] = pVal[i+offset]; |
| for (unsigned i = getNumWords()-offset; i < getNumWords(); i++) |
| val[i] = 0; |
| return APInt(val,BitWidth).clearUnusedBits(); |
| } |
| |
| // Shift the low order words |
| unsigned breakWord = getNumWords() - offset -1; |
| for (unsigned i = 0; i < breakWord; ++i) |
| val[i] = (pVal[i+offset] >> wordShift) | |
| (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift)); |
| // Shift the break word. |
| val[breakWord] = pVal[breakWord+offset] >> wordShift; |
| |
| // Remaining words are 0 |
| for (unsigned i = breakWord+1; i < getNumWords(); ++i) |
| val[i] = 0; |
| return APInt(val, BitWidth).clearUnusedBits(); |
| } |
| |
| /// Left-shift this APInt by shiftAmt. |
| /// @brief Left-shift function. |
| APInt APInt::shl(const APInt &shiftAmt) const { |
| // It's undefined behavior in C to shift by BitWidth or greater. |
| return shl((unsigned)shiftAmt.getLimitedValue(BitWidth)); |
| } |
| |
| APInt APInt::shlSlowCase(unsigned shiftAmt) const { |
| // If all the bits were shifted out, the result is 0. This avoids issues |
| // with shifting by the size of the integer type, which produces undefined |
| // results. We define these "undefined results" to always be 0. |
| if (shiftAmt == BitWidth) |
| return APInt(BitWidth, 0); |
| |
| // If none of the bits are shifted out, the result is *this. This avoids a |
| // lshr by the words size in the loop below which can produce incorrect |
| // results. It also avoids the expensive computation below for a common case. |
| if (shiftAmt == 0) |
| return *this; |
| |
| // Create some space for the result. |
| uint64_t * val = new uint64_t[getNumWords()]; |
| |
| // If we are shifting less than a word, do it the easy way |
| if (shiftAmt < APINT_BITS_PER_WORD) { |
| uint64_t carry = 0; |
| for (unsigned i = 0; i < getNumWords(); i++) { |
| val[i] = pVal[i] << shiftAmt | carry; |
| carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt); |
| } |
| return APInt(val, BitWidth).clearUnusedBits(); |
| } |
| |
| // Compute some values needed by the remaining shift algorithms |
| unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; |
| unsigned offset = shiftAmt / APINT_BITS_PER_WORD; |
| |
| // If we are shifting whole words, just move whole words |
| if (wordShift == 0) { |
| for (unsigned i = 0; i < offset; i++) |
| val[i] = 0; |
| for (unsigned i = offset; i < getNumWords(); i++) |
| val[i] = pVal[i-offset]; |
| return APInt(val,BitWidth).clearUnusedBits(); |
| } |
| |
| // Copy whole words from this to Result. |
| unsigned i = getNumWords() - 1; |
| for (; i > offset; --i) |
| val[i] = pVal[i-offset] << wordShift | |
| pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift); |
| val[offset] = pVal[0] << wordShift; |
| for (i = 0; i < offset; ++i) |
| val[i] = 0; |
| return APInt(val, BitWidth).clearUnusedBits(); |
| } |
| |
| APInt APInt::rotl(const APInt &rotateAmt) const { |
| return rotl((unsigned)rotateAmt.getLimitedValue(BitWidth)); |
| } |
| |
| APInt APInt::rotl(unsigned rotateAmt) const { |
| if (rotateAmt == 0) |
| return *this; |
| // Don't get too fancy, just use existing shift/or facilities |
| APInt hi(*this); |
| APInt lo(*this); |
| hi.shl(rotateAmt); |
| lo.lshr(BitWidth - rotateAmt); |
| return hi | lo; |
| } |
| |
| APInt APInt::rotr(const APInt &rotateAmt) const { |
| return rotr((unsigned)rotateAmt.getLimitedValue(BitWidth)); |
| } |
| |
| APInt APInt::rotr(unsigned rotateAmt) const { |
| if (rotateAmt == 0) |
| return *this; |
| // Don't get too fancy, just use existing shift/or facilities |
| APInt hi(*this); |
| APInt lo(*this); |
| lo.lshr(rotateAmt); |
| hi.shl(BitWidth - rotateAmt); |
| return hi | lo; |
| } |
| |
| // Square Root - this method computes and returns the square root of "this". |
| // Three mechanisms are used for computation. For small values (<= 5 bits), |
| // a table lookup is done. This gets some performance for common cases. For |
| // values using less than 52 bits, the value is converted to double and then |
| // the libc sqrt function is called. The result is rounded and then converted |
| // back to a uint64_t which is then used to construct the result. Finally, |
| // the Babylonian method for computing square roots is used. |
| APInt APInt::sqrt() const { |
| |
| // Determine the magnitude of the value. |
| unsigned magnitude = getActiveBits(); |
| |
| // Use a fast table for some small values. This also gets rid of some |
| // rounding errors in libc sqrt for small values. |
| if (magnitude <= 5) { |
| static const uint8_t results[32] = { |
| /* 0 */ 0, |
| /* 1- 2 */ 1, 1, |
| /* 3- 6 */ 2, 2, 2, 2, |
| /* 7-12 */ 3, 3, 3, 3, 3, 3, |
| /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4, |
| /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, |
| /* 31 */ 6 |
| }; |
| return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]); |
| } |
| |
| // If the magnitude of the value fits in less than 52 bits (the precision of |
| // an IEEE double precision floating point value), then we can use the |
| // libc sqrt function which will probably use a hardware sqrt computation. |
| // This should be faster than the algorithm below. |
| if (magnitude < 52) { |
| #ifdef _MSC_VER |
| // Amazingly, VC++ doesn't have round(). |
| return APInt(BitWidth, |
| uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0]))) + 0.5); |
| #else |
| return APInt(BitWidth, |
| uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0]))))); |
| #endif |
| } |
| |
| // Okay, all the short cuts are exhausted. We must compute it. The following |
| // is a classical Babylonian method for computing the square root. This code |
| // was adapted to APINt from a wikipedia article on such computations. |
| // See http://www.wikipedia.org/ and go to the page named |
| // Calculate_an_integer_square_root. |
| unsigned nbits = BitWidth, i = 4; |
| APInt testy(BitWidth, 16); |
| APInt x_old(BitWidth, 1); |
| APInt x_new(BitWidth, 0); |
| APInt two(BitWidth, 2); |
| |
| // Select a good starting value using binary logarithms. |
| for (;; i += 2, testy = testy.shl(2)) |
| if (i >= nbits || this->ule(testy)) { |
| x_old = x_old.shl(i / 2); |
| break; |
| } |
| |
| // Use the Babylonian method to arrive at the integer square root: |
| for (;;) { |
| x_new = (this->udiv(x_old) + x_old).udiv(two); |
| if (x_old.ule(x_new)) |
| break; |
| x_old = x_new; |
| } |
| |
| // Make sure we return the closest approximation |
| // NOTE: The rounding calculation below is correct. It will produce an |
| // off-by-one discrepancy with results from pari/gp. That discrepancy has been |
| // determined to be a rounding issue with pari/gp as it begins to use a |
| // floating point representation after 192 bits. There are no discrepancies |
| // between this algorithm and pari/gp for bit widths < 192 bits. |
| APInt square(x_old * x_old); |
| APInt nextSquare((x_old + 1) * (x_old +1)); |
| if (this->ult(square)) |
| return x_old; |
| else if (this->ule(nextSquare)) { |
| APInt midpoint((nextSquare - square).udiv(two)); |
| APInt offset(*this - square); |
| if (offset.ult(midpoint)) |
| return x_old; |
| else |
| return x_old + 1; |
| } else |
| llvm_unreachable("Error in APInt::sqrt computation"); |
| return x_old + 1; |
| } |
| |
| /// Computes the multiplicative inverse of this APInt for a given modulo. The |
| /// iterative extended Euclidean algorithm is used to solve for this value, |
| /// however we simplify it to speed up calculating only the inverse, and take |
| /// advantage of div+rem calculations. We also use some tricks to avoid copying |
| /// (potentially large) APInts around. |
| APInt APInt::multiplicativeInverse(const APInt& modulo) const { |
| assert(ult(modulo) && "This APInt must be smaller than the modulo"); |
| |
| // Using the properties listed at the following web page (accessed 06/21/08): |
| // http://www.numbertheory.org/php/euclid.html |
| // (especially the properties numbered 3, 4 and 9) it can be proved that |
| // BitWidth bits suffice for all the computations in the algorithm implemented |
| // below. More precisely, this number of bits suffice if the multiplicative |
| // inverse exists, but may not suffice for the general extended Euclidean |
| // algorithm. |
| |
| APInt r[2] = { modulo, *this }; |
| APInt t[2] = { APInt(BitWidth, 0), APInt(BitWidth, 1) }; |
| APInt q(BitWidth, 0); |
| |
| unsigned i; |
| for (i = 0; r[i^1] != 0; i ^= 1) { |
| // An overview of the math without the confusing bit-flipping: |
| // q = r[i-2] / r[i-1] |
| // r[i] = r[i-2] % r[i-1] |
| // t[i] = t[i-2] - t[i-1] * q |
| udivrem(r[i], r[i^1], q, r[i]); |
| t[i] -= t[i^1] * q; |
| } |
| |
| // If this APInt and the modulo are not coprime, there is no multiplicative |
| // inverse, so return 0. We check this by looking at the next-to-last |
| // remainder, which is the gcd(*this,modulo) as calculated by the Euclidean |
| // algorithm. |
| if (r[i] != 1) |
| return APInt(BitWidth, 0); |
| |
| // The next-to-last t is the multiplicative inverse. However, we are |
| // interested in a positive inverse. Calcuate a positive one from a negative |
| // one if necessary. A simple addition of the modulo suffices because |
| // abs(t[i]) is known to be less than *this/2 (see the link above). |
| return t[i].isNegative() ? t[i] + modulo : t[i]; |
| } |
| |
| /// Calculate the magic numbers required to implement a signed integer division |
| /// by a constant as a sequence of multiplies, adds and shifts. Requires that |
| /// the divisor not be 0, 1, or -1. Taken from "Hacker's Delight", Henry S. |
| /// Warren, Jr., chapter 10. |
| APInt::ms APInt::magic() const { |
| const APInt& d = *this; |
| unsigned p; |
| APInt ad, anc, delta, q1, r1, q2, r2, t; |
| APInt signedMin = APInt::getSignedMinValue(d.getBitWidth()); |
| struct ms mag; |
| |
| ad = d.abs(); |
| t = signedMin + (d.lshr(d.getBitWidth() - 1)); |
| anc = t - 1 - t.urem(ad); // absolute value of nc |
| p = d.getBitWidth() - 1; // initialize p |
| q1 = signedMin.udiv(anc); // initialize q1 = 2p/abs(nc) |
| r1 = signedMin - q1*anc; // initialize r1 = rem(2p,abs(nc)) |
| q2 = signedMin.udiv(ad); // initialize q2 = 2p/abs(d) |
| r2 = signedMin - q2*ad; // initialize r2 = rem(2p,abs(d)) |
| do { |
| p = p + 1; |
| q1 = q1<<1; // update q1 = 2p/abs(nc) |
| r1 = r1<<1; // update r1 = rem(2p/abs(nc)) |
| if (r1.uge(anc)) { // must be unsigned comparison |
| q1 = q1 + 1; |
| r1 = r1 - anc; |
| } |
| q2 = q2<<1; // update q2 = 2p/abs(d) |
| r2 = r2<<1; // update r2 = rem(2p/abs(d)) |
| if (r2.uge(ad)) { // must be unsigned comparison |
| q2 = q2 + 1; |
| r2 = r2 - ad; |
| } |
| delta = ad - r2; |
| } while (q1.ule(delta) || (q1 == delta && r1 == 0)); |
| |
| mag.m = q2 + 1; |
| if (d.isNegative()) mag.m = -mag.m; // resulting magic number |
| mag.s = p - d.getBitWidth(); // resulting shift |
| return mag; |
| } |
| |
| /// Calculate the magic numbers required to implement an unsigned integer |
| /// division by a constant as a sequence of multiplies, adds and shifts. |
| /// Requires that the divisor not be 0. Taken from "Hacker's Delight", Henry |
| /// S. Warren, Jr., chapter 10. |
| APInt::mu APInt::magicu() const { |
| const APInt& d = *this; |
| unsigned p; |
| APInt nc, delta, q1, r1, q2, r2; |
| struct mu magu; |
| magu.a = 0; // initialize "add" indicator |
| APInt allOnes = APInt::getAllOnesValue(d.getBitWidth()); |
| APInt signedMin = APInt::getSignedMinValue(d.getBitWidth()); |
| APInt signedMax = APInt::getSignedMaxValue(d.getBitWidth()); |
| |
| nc = allOnes - (-d).urem(d); |
| p = d.getBitWidth() - 1; // initialize p |
| q1 = signedMin.udiv(nc); // initialize q1 = 2p/nc |
| r1 = signedMin - q1*nc; // initialize r1 = rem(2p,nc) |
| q2 = signedMax.udiv(d); // initialize q2 = (2p-1)/d |
| r2 = signedMax - q2*d; // initialize r2 = rem((2p-1),d) |
| do { |
| p = p + 1; |
| if (r1.uge(nc - r1)) { |
| q1 = q1 + q1 + 1; // update q1 |
| r1 = r1 + r1 - nc; // update r1 |
| } |
| else { |
| q1 = q1+q1; // update q1 |
| r1 = r1+r1; // update r1 |
| } |
| if ((r2 + 1).uge(d - r2)) { |
| if (q2.uge(signedMax)) magu.a = 1; |
| q2 = q2+q2 + 1; // update q2 |
| r2 = r2+r2 + 1 - d; // update r2 |
| } |
| else { |
| if (q2.uge(signedMin)) magu.a = 1; |
| q2 = q2+q2; // update q2 |
| r2 = r2+r2 + 1; // update r2 |
| } |
| delta = d - 1 - r2; |
| } while (p < d.getBitWidth()*2 && |
| (q1.ult(delta) || (q1 == delta && r1 == 0))); |
| magu.m = q2 + 1; // resulting magic number |
| magu.s = p - d.getBitWidth(); // resulting shift |
| return magu; |
| } |
| |
| /// Implementation of Knuth's Algorithm D (Division of nonnegative integers) |
| /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The |
| /// variables here have the same names as in the algorithm. Comments explain |
| /// the algorithm and any deviation from it. |
| static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r, |
| unsigned m, unsigned n) { |
| assert(u && "Must provide dividend"); |
| assert(v && "Must provide divisor"); |
| assert(q && "Must provide quotient"); |
| assert(u != v && u != q && v != q && "Must us different memory"); |
| assert(n>1 && "n must be > 1"); |
| |
| // Knuth uses the value b as the base of the number system. In our case b |
| // is 2^31 so we just set it to -1u. |
| uint64_t b = uint64_t(1) << 32; |
| |
| #if 0 |
| DEBUG(errs() << "KnuthDiv: m=" << m << " n=" << n << '\n'); |
| DEBUG(errs() << "KnuthDiv: original:"); |
| DEBUG(for (int i = m+n; i >=0; i--) errs() << " " << u[i]); |
| DEBUG(errs() << " by"); |
| DEBUG(for (int i = n; i >0; i--) errs() << " " << v[i-1]); |
| DEBUG(errs() << '\n'); |
| #endif |
| // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of |
| // u and v by d. Note that we have taken Knuth's advice here to use a power |
| // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of |
| // 2 allows us to shift instead of multiply and it is easy to determine the |
| // shift amount from the leading zeros. We are basically normalizing the u |
| // and v so that its high bits are shifted to the top of v's range without |
| // overflow. Note that this can require an extra word in u so that u must |
| // be of length m+n+1. |
| unsigned shift = CountLeadingZeros_32(v[n-1]); |
| unsigned v_carry = 0; |
| unsigned u_carry = 0; |
| if (shift) { |
| for (unsigned i = 0; i < m+n; ++i) { |
| unsigned u_tmp = u[i] >> (32 - shift); |
| u[i] = (u[i] << shift) | u_carry; |
| u_carry = u_tmp; |
| } |
| for (unsigned i = 0; i < n; ++i) { |
| unsigned v_tmp = v[i] >> (32 - shift); |
| v[i] = (v[i] << shift) | v_carry; |
| v_carry = v_tmp; |
| } |
| } |
| u[m+n] = u_carry; |
| #if 0 |
| DEBUG(errs() << "KnuthDiv: normal:"); |
| DEBUG(for (int i = m+n; i >=0; i--) errs() << " " << u[i]); |
| DEBUG(errs() << " by"); |
| DEBUG(for (int i = n; i >0; i--) errs() << " " << v[i-1]); |
| DEBUG(errs() << '\n'); |
| #endif |
| |
| // D2. [Initialize j.] Set j to m. This is the loop counter over the places. |
| int j = m; |
| do { |
| DEBUG(errs() << "KnuthDiv: quotient digit #" << j << '\n'); |
| // D3. [Calculate q'.]. |
| // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q') |
| // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r') |
| // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease |
| // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test |
| // on v[n-2] determines at high speed most of the cases in which the trial |
| // value qp is one too large, and it eliminates all cases where qp is two |
| // too large. |
| uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]); |
| DEBUG(errs() << "KnuthDiv: dividend == " << dividend << '\n'); |
| uint64_t qp = dividend / v[n-1]; |
| uint64_t rp = dividend % v[n-1]; |
| if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) { |
| qp--; |
| rp += v[n-1]; |
| if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2])) |
| qp--; |
| } |
| DEBUG(errs() << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n'); |
| |
| // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with |
| // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation |
| // consists of a simple multiplication by a one-place number, combined with |
| // a subtraction. |
| bool isNeg = false; |
| for (unsigned i = 0; i < n; ++i) { |
| uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32); |
| uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]); |
| bool borrow = subtrahend > u_tmp; |
| DEBUG(errs() << "KnuthDiv: u_tmp == " << u_tmp |
| << ", subtrahend == " << subtrahend |
| << ", borrow = " << borrow << '\n'); |
| |
| uint64_t result = u_tmp - subtrahend; |
| unsigned k = j + i; |
| u[k++] = (unsigned)(result & (b-1)); // subtract low word |
| u[k++] = (unsigned)(result >> 32); // subtract high word |
| while (borrow && k <= m+n) { // deal with borrow to the left |
| borrow = u[k] == 0; |
| u[k]--; |
| k++; |
| } |
| isNeg |= borrow; |
| DEBUG(errs() << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " << |
| u[j+i+1] << '\n'); |
| } |
| DEBUG(errs() << "KnuthDiv: after subtraction:"); |
| DEBUG(for (int i = m+n; i >=0; i--) errs() << " " << u[i]); |
| DEBUG(errs() << '\n'); |
| // The digits (u[j+n]...u[j]) should be kept positive; if the result of |
| // this step is actually negative, (u[j+n]...u[j]) should be left as the |
| // true value plus b**(n+1), namely as the b's complement of |
| // the true value, and a "borrow" to the left should be remembered. |
| // |
| if (isNeg) { |
| bool carry = true; // true because b's complement is "complement + 1" |
| for (unsigned i = 0; i <= m+n; ++i) { |
| u[i] = ~u[i] + carry; // b's complement |
| carry = carry && u[i] == 0; |
| } |
| } |
| DEBUG(errs() << "KnuthDiv: after complement:"); |
| DEBUG(for (int i = m+n; i >=0; i--) errs() << " " << u[i]); |
| DEBUG(errs() << '\n'); |
| |
| // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was |
| // negative, go to step D6; otherwise go on to step D7. |
| q[j] = (unsigned)qp; |
| if (isNeg) { |
| // D6. [Add back]. The probability that this step is necessary is very |
| // small, on the order of only 2/b. Make sure that test data accounts for |
| // this possibility. Decrease q[j] by 1 |
| q[j]--; |
| // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]). |
| // A carry will occur to the left of u[j+n], and it should be ignored |
| // since it cancels with the borrow that occurred in D4. |
| bool carry = false; |
| for (unsigned i = 0; i < n; i++) { |
| unsigned limit = std::min(u[j+i],v[i]); |
| u[j+i] += v[i] + carry; |
| carry = u[j+i] < limit || (carry && u[j+i] == limit); |
| } |
| u[j+n] += carry; |
| } |
| DEBUG(errs() << "KnuthDiv: after correction:"); |
| DEBUG(for (int i = m+n; i >=0; i--) errs() <<" " << u[i]); |
| DEBUG(errs() << "\nKnuthDiv: digit result = " << q[j] << '\n'); |
| |
| // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3. |
| } while (--j >= 0); |
| |
| DEBUG(errs() << "KnuthDiv: quotient:"); |
| DEBUG(for (int i = m; i >=0; i--) errs() <<" " << q[i]); |
| DEBUG(errs() << '\n'); |
| |
| // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired |
| // remainder may be obtained by dividing u[...] by d. If r is non-null we |
| // compute the remainder (urem uses this). |
| if (r) { |
| // The value d is expressed by the "shift" value above since we avoided |
| // multiplication by d by using a shift left. So, all we have to do is |
| // shift right here. In order to mak |
| if (shift) { |
| unsigned carry = 0; |
| DEBUG(errs() << "KnuthDiv: remainder:"); |
| for (int i = n-1; i >= 0; i--) { |
| r[i] = (u[i] >> shift) | carry; |
| carry = u[i] << (32 - shift); |
| DEBUG(errs() << " " << r[i]); |
| } |
| } else { |
| for (int i = n-1; i >= 0; i--) { |
| r[i] = u[i]; |
| DEBUG(errs() << " " << r[i]); |
| } |
| } |
| DEBUG(errs() << '\n'); |
| } |
| #if 0 |
| DEBUG(errs() << '\n'); |
| #endif |
| } |
| |
| void APInt::divide(const APInt LHS, unsigned lhsWords, |
| const APInt &RHS, unsigned rhsWords, |
| APInt *Quotient, APInt *Remainder) |
| { |
| assert(lhsWords >= rhsWords && "Fractional result"); |
| |
| // First, compose the values into an array of 32-bit words instead of |
| // 64-bit words. This is a necessity of both the "short division" algorithm |
| // and the the Knuth "classical algorithm" which requires there to be native |
| // operations for +, -, and * on an m bit value with an m*2 bit result. We |
| // can't use 64-bit operands here because we don't have native results of |
| // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't |
| // work on large-endian machines. |
| uint64_t mask = ~0ull >> (sizeof(unsigned)*CHAR_BIT); |
| unsigned n = rhsWords * 2; |
| unsigned m = (lhsWords * 2) - n; |
| |
| // Allocate space for the temporary values we need either on the stack, if |
| // it will fit, or on the heap if it won't. |
| unsigned SPACE[128]; |
| unsigned *U = 0; |
| unsigned *V = 0; |
| unsigned *Q = 0; |
| unsigned *R = 0; |
| if ((Remainder?4:3)*n+2*m+1 <= 128) { |
| U = &SPACE[0]; |
| V = &SPACE[m+n+1]; |
| Q = &SPACE[(m+n+1) + n]; |
| if (Remainder) |
| R = &SPACE[(m+n+1) + n + (m+n)]; |
| } else { |
| U = new unsigned[m + n + 1]; |
| V = new unsigned[n]; |
| Q = new unsigned[m+n]; |
| if (Remainder) |
| R = new unsigned[n]; |
| } |
| |
| // Initialize the dividend |
| memset(U, 0, (m+n+1)*sizeof(unsigned)); |
| for (unsigned i = 0; i < lhsWords; ++i) { |
| uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]); |
| U[i * 2] = (unsigned)(tmp & mask); |
| U[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT)); |
| } |
| U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm. |
| |
| // Initialize the divisor |
| memset(V, 0, (n)*sizeof(unsigned)); |
| for (unsigned i = 0; i < rhsWords; ++i) { |
| uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]); |
| V[i * 2] = (unsigned)(tmp & mask); |
| V[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT)); |
| } |
| |
| // initialize the quotient and remainder |
| memset(Q, 0, (m+n) * sizeof(unsigned)); |
| if (Remainder) |
| memset(R, 0, n * sizeof(unsigned)); |
| |
| // Now, adjust m and n for the Knuth division. n is the number of words in |
| // the divisor. m is the number of words by which the dividend exceeds the |
| // divisor (i.e. m+n is the length of the dividend). These sizes must not |
| // contain any zero words or the Knuth algorithm fails. |
| for (unsigned i = n; i > 0 && V[i-1] == 0; i--) { |
| n--; |
| m++; |
| } |
| for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--) |
| m--; |
| |
| // If we're left with only a single word for the divisor, Knuth doesn't work |
| // so we implement the short division algorithm here. This is much simpler |
| // and faster because we are certain that we can divide a 64-bit quantity |
| // by a 32-bit quantity at hardware speed and short division is simply a |
| // series of such operations. This is just like doing short division but we |
| // are using base 2^32 instead of base 10. |
| assert(n != 0 && "Divide by zero?"); |
| if (n == 1) { |
| unsigned divisor = V[0]; |
| unsigned remainder = 0; |
| for (int i = m+n-1; i >= 0; i--) { |
| uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i]; |
| if (partial_dividend == 0) { |
| Q[i] = 0; |
| remainder = 0; |
| } else if (partial_dividend < divisor) { |
| Q[i] = 0; |
| remainder = (unsigned)partial_dividend; |
| } else if (partial_dividend == divisor) { |
| Q[i] = 1; |
| remainder = 0; |
| } else { |
| Q[i] = (unsigned)(partial_dividend / divisor); |
| remainder = (unsigned)(partial_dividend - (Q[i] * divisor)); |
| } |
| } |
| if (R) |
| R[0] = remainder; |
| } else { |
| // Now we're ready to invoke the Knuth classical divide algorithm. In this |
| // case n > 1. |
| KnuthDiv(U, V, Q, R, m, n); |
| } |
| |
| // If the caller wants the quotient |
| if (Quotient) { |
| // Set up the Quotient value's memory. |
| if (Quotient->BitWidth != LHS.BitWidth) { |
| if (Quotient->isSingleWord()) |
| Quotient->VAL = 0; |
| else |
| delete [] Quotient->pVal; |
| Quotient->BitWidth = LHS.BitWidth; |
| if (!Quotient->isSingleWord()) |
| Quotient->pVal = getClearedMemory(Quotient->getNumWords()); |
| } else |
| Quotient->clear(); |
| |
| // The quotient is in Q. Reconstitute the quotient into Quotient's low |
| // order words. |
| if (lhsWords == 1) { |
| uint64_t tmp = |
| uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2)); |
| if (Quotient->isSingleWord()) |
| Quotient->VAL = tmp; |
| else |
| Quotient->pVal[0] = tmp; |
| } else { |
| assert(!Quotient->isSingleWord() && "Quotient APInt not large enough"); |
| for (unsigned i = 0; i < lhsWords; ++i) |
| Quotient->pVal[i] = |
| uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2)); |
| } |
| } |
| |
| // If the caller wants the remainder |
| if (Remainder) { |
| // Set up the Remainder value's memory. |
| if (Remainder->BitWidth != RHS.BitWidth) { |
| if (Remainder->isSingleWord()) |
| Remainder->VAL = 0; |
| else |
| delete [] Remainder->pVal; |
| Remainder->BitWidth = RHS.BitWidth; |
| if (!Remainder->isSingleWord()) |
| Remainder->pVal = getClearedMemory(Remainder->getNumWords()); |
| } else |
| Remainder->clear(); |
| |
| // The remainder is in R. Reconstitute the remainder into Remainder's low |
| // order words. |
| if (rhsWords == 1) { |
| uint64_t tmp = |
| uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2)); |
| if (Remainder->isSingleWord()) |
| Remainder->VAL = tmp; |
| else |
| Remainder->pVal[0] = tmp; |
| } else { |
| assert(!Remainder->isSingleWord() && "Remainder APInt not large enough"); |
| for (unsigned i = 0; i < rhsWords; ++i) |
| Remainder->pVal[i] = |
| uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2)); |
| } |
| } |
| |
| // Clean up the memory we allocated. |
| if (U != &SPACE[0]) { |
| delete [] U; |
| delete [] V; |
| delete [] Q; |
| delete [] R; |
| } |
| } |
| |
| APInt APInt::udiv(const APInt& RHS) const { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| |
| // First, deal with the easy case |
| if (isSingleWord()) { |
| assert(RHS.VAL != 0 && "Divide by zero?"); |
| return APInt(BitWidth, VAL / RHS.VAL); |
| } |
| |
| // Get some facts about the LHS and RHS number of bits and words |
| unsigned rhsBits = RHS.getActiveBits(); |
| unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); |
| assert(rhsWords && "Divided by zero???"); |
| unsigned lhsBits = this->getActiveBits(); |
| unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1); |
| |
| // Deal with some degenerate cases |
| if (!lhsWords) |
| // 0 / X ===> 0 |
| return APInt(BitWidth, 0); |
| else if (lhsWords < rhsWords || this->ult(RHS)) { |
| // X / Y ===> 0, iff X < Y |
| return APInt(BitWidth, 0); |
| } else if (*this == RHS) { |
| // X / X ===> 1 |
| return APInt(BitWidth, 1); |
| } else if (lhsWords == 1 && rhsWords == 1) { |
| // All high words are zero, just use native divide |
| return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]); |
| } |
| |
| // We have to compute it the hard way. Invoke the Knuth divide algorithm. |
| APInt Quotient(1,0); // to hold result. |
| divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0); |
| return Quotient; |
| } |
| |
| APInt APInt::urem(const APInt& RHS) const { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) { |
| assert(RHS.VAL != 0 && "Remainder by zero?"); |
| return APInt(BitWidth, VAL % RHS.VAL); |
| } |
| |
| // Get some facts about the LHS |
| unsigned lhsBits = getActiveBits(); |
| unsigned lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1); |
| |
| // Get some facts about the RHS |
| unsigned rhsBits = RHS.getActiveBits(); |
| unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); |
| assert(rhsWords && "Performing remainder operation by zero ???"); |
| |
| // Check the degenerate cases |
| if (lhsWords == 0) { |
| // 0 % Y ===> 0 |
| return APInt(BitWidth, 0); |
| } else if (lhsWords < rhsWords || this->ult(RHS)) { |
| // X % Y ===> X, iff X < Y |
| return *this; |
| } else if (*this == RHS) { |
| // X % X == 0; |
| return APInt(BitWidth, 0); |
| } else if (lhsWords == 1) { |
| // All high words are zero, just use native remainder |
| return APInt(BitWidth, pVal[0] % RHS.pVal[0]); |
| } |
| |
| // We have to compute it the hard way. Invoke the Knuth divide algorithm. |
| APInt Remainder(1,0); |
| divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder); |
| return Remainder; |
| } |
| |
| void APInt::udivrem(const APInt &LHS, const APInt &RHS, |
| APInt &Quotient, APInt &Remainder) { |
| // Get some size facts about the dividend and divisor |
| unsigned lhsBits = LHS.getActiveBits(); |
| unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1); |
| unsigned rhsBits = RHS.getActiveBits(); |
| unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); |
| |
| // Check the degenerate cases |
| if (lhsWords == 0) { |
| Quotient = 0; // 0 / Y ===> 0 |
| Remainder = 0; // 0 % Y ===> 0 |
| return; |
| } |
| |
| if (lhsWords < rhsWords || LHS.ult(RHS)) { |
| Remainder = LHS; // X % Y ===> X, iff X < Y |
| Quotient = 0; // X / Y ===> 0, iff X < Y |
| return; |
| } |
| |
| if (LHS == RHS) { |
| Quotient = 1; // X / X ===> 1 |
| Remainder = 0; // X % X ===> 0; |
| return; |
| } |
| |
| if (lhsWords == 1 && rhsWords == 1) { |
| // There is only one word to consider so use the native versions. |
| uint64_t lhsValue = LHS.isSingleWord() ? LHS.VAL : LHS.pVal[0]; |
| uint64_t rhsValue = RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0]; |
| Quotient = APInt(LHS.getBitWidth(), lhsValue / rhsValue); |
| Remainder = APInt(LHS.getBitWidth(), lhsValue % rhsValue); |
| return; |
| } |
| |
| // Okay, lets do it the long way |
| divide(LHS, lhsWords, RHS, rhsWords, &Quotient, &Remainder); |
| } |
| |
| void APInt::fromString(unsigned numbits, const StringRef& str, uint8_t radix) { |
| // Check our assumptions here |
| assert(!str.empty() && "Invalid string length"); |
| assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) && |
| "Radix should be 2, 8, 10, or 16!"); |
| |
| StringRef::iterator p = str.begin(); |
| size_t slen = str.size(); |
| bool isNeg = *p == '-'; |
| if (*p == '-' || *p == '+') { |
| p++; |
| slen--; |
| assert(slen && "String is only a sign, needs a value."); |
| } |
| assert((slen <= numbits || radix != 2) && "Insufficient bit width"); |
| assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width"); |
| assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width"); |
| assert((((slen-1)*64)/22 <= numbits || radix != 10) |
| && "Insufficient bit width"); |
| |
| // Allocate memory |
| if (!isSingleWord()) |
| pVal = getClearedMemory(getNumWords()); |
| |
| // Figure out if we can shift instead of multiply |
| unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0); |
| |
| // Set up an APInt for the digit to add outside the loop so we don't |
| // constantly construct/destruct it. |
| APInt apdigit(getBitWidth(), 0); |
| APInt apradix(getBitWidth(), radix); |
| |
| // Enter digit traversal loop |
| for (StringRef::iterator e = str.end(); p != e; ++p) { |
| unsigned digit = getDigit(*p, radix); |
| assert(digit < radix && "Invalid character in digit string"); |
| |
| // Shift or multiply the value by the radix |
| if (slen > 1) { |
| if (shift) |
| *this <<= shift; |
| else |
| *this *= apradix; |
| } |
| |
| // Add in the digit we just interpreted |
| if (apdigit.isSingleWord()) |
| apdigit.VAL = digit; |
| else |
| apdigit.pVal[0] = digit; |
| *this += apdigit; |
| } |
| // If its negative, put it in two's complement form |
| if (isNeg) { |
| (*this)--; |
| this->flip(); |
| } |
| } |
| |
| void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix, |
| bool Signed) const { |
| assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2) && |
| "Radix should be 2, 8, 10, or 16!"); |
| |
| // First, check for a zero value and just short circuit the logic below. |
| if (*this == 0) { |
| Str.push_back('0'); |
| return; |
| } |
| |
| static const char Digits[] = "0123456789ABCDEF"; |
| |
| if (isSingleWord()) { |
| char Buffer[65]; |
| char *BufPtr = Buffer+65; |
| |
| uint64_t N; |
| if (Signed) { |
| int64_t I = getSExtValue(); |
| if (I < 0) { |
| Str.push_back('-'); |
| I = -I; |
| } |
| N = I; |
| } else { |
| N = getZExtValue(); |
| } |
| |
| while (N) { |
| *--BufPtr = Digits[N % Radix]; |
| N /= Radix; |
| } |
| Str.append(BufPtr, Buffer+65); |
| return; |
| } |
| |
| APInt Tmp(*this); |
| |
| if (Signed && isNegative()) { |
| // They want to print the signed version and it is a negative value |
| // Flip the bits and add one to turn it into the equivalent positive |
| // value and put a '-' in the result. |
| Tmp.flip(); |
| Tmp++; |
| Str.push_back('-'); |
| } |
| |
| // We insert the digits backward, then reverse them to get the right order. |
| unsigned StartDig = Str.size(); |
| |
| // For the 2, 8 and 16 bit cases, we can just shift instead of divide |
| // because the number of bits per digit (1, 3 and 4 respectively) divides |
| // equaly. We just shift until the value is zero. |
| if (Radix != 10) { |
| // Just shift tmp right for each digit width until it becomes zero |
| unsigned ShiftAmt = (Radix == 16 ? 4 : (Radix == 8 ? 3 : 1)); |
| unsigned MaskAmt = Radix - 1; |
| |
| while (Tmp != 0) { |
| unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt; |
| Str.push_back(Digits[Digit]); |
| Tmp = Tmp.lshr(ShiftAmt); |
| } |
| } else { |
| APInt divisor(4, 10); |
| while (Tmp != 0) { |
| APInt APdigit(1, 0); |
| APInt tmp2(Tmp.getBitWidth(), 0); |
| divide(Tmp, Tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2, |
| &APdigit); |
| unsigned Digit = (unsigned)APdigit.getZExtValue(); |
| assert(Digit < Radix && "divide failed"); |
| Str.push_back(Digits[Digit]); |
| Tmp = tmp2; |
| } |
| } |
| |
| // Reverse the digits before returning. |
| std::reverse(Str.begin()+StartDig, Str.end()); |
| } |
| |
| /// 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. |
| std::string APInt::toString(unsigned Radix = 10, bool Signed = true) const { |
| SmallString<40> S; |
| toString(S, Radix, Signed); |
| return S.str(); |
| } |
| |
| |
| void APInt::dump() const { |
| SmallString<40> S, U; |
| this->toStringUnsigned(U); |
| this->toStringSigned(S); |
| errs() << "APInt(" << BitWidth << "b, " |
| << U.str() << "u " << S.str() << "s)"; |
| } |
| |
| void APInt::print(raw_ostream &OS, bool isSigned) const { |
| SmallString<40> S; |
| this->toString(S, 10, isSigned); |
| OS << S.str(); |
| } |
| |
| // This implements a variety of operations on a representation of |
| // arbitrary precision, two's-complement, bignum integer values. |
| |
| // Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe |
| // and unrestricting assumption. |
| #define COMPILE_TIME_ASSERT(cond) extern int CTAssert[(cond) ? 1 : -1] |
| COMPILE_TIME_ASSERT(integerPartWidth % 2 == 0); |
| |
| /* Some handy functions local to this file. */ |
| namespace { |
| |
| /* Returns the integer part with the least significant BITS set. |
| BITS cannot be zero. */ |
| static inline integerPart |
| lowBitMask(unsigned int bits) |
| { |
| assert (bits != 0 && bits <= integerPartWidth); |
| |
| return ~(integerPart) 0 >> (integerPartWidth - bits); |
| } |
| |
| /* Returns the value of the lower half of PART. */ |
| static inline integerPart |
| lowHalf(integerPart part) |
| { |
| return part & lowBitMask(integerPartWidth / 2); |
| } |
| |
| /* Returns the value of the upper half of PART. */ |
| static inline integerPart |
| highHalf(integerPart part) |
| { |
| return part >> (integerPartWidth / 2); |
| } |
| |
| /* Returns the bit number of the most significant set bit of a part. |
| If the input number has no bits set -1U is returned. */ |
| static unsigned int |
| partMSB(integerPart value) |
| { |
| unsigned int n, msb; |
| |
| if (value == 0) |
| return -1U; |
| |
| n = integerPartWidth / 2; |
| |
| msb = 0; |
| do { |
| if (value >> n) { |
| value >>= n; |
| msb += n; |
| } |
| |
| n >>= 1; |
| } while (n); |
| |
| return msb; |
| } |
| |
| /* Returns the bit number of the least significant set bit of a |
| part. If the input number has no bits set -1U is returned. */ |
| static unsigned int |
| partLSB(integerPart value) |
| { |
| unsigned int n, lsb; |
| |
| if (value == 0) |
| return -1U; |
| |
| lsb = integerPartWidth - 1; |
| n = integerPartWidth / 2; |
| |
| do { |
| if (value << n) { |
| value <<= n; |
| lsb -= n; |
| } |
| |
| n >>= 1; |
| } while (n); |
| |
| return lsb; |
| } |
| } |
| |
| /* Sets the least significant part of a bignum to the input value, and |
| zeroes out higher parts. */ |
| void |
| APInt::tcSet(integerPart *dst, integerPart part, unsigned int parts) |
| { |
| unsigned int i; |
| |
| assert (parts > 0); |
| |
| dst[0] = part; |
| for(i = 1; i < parts; i++) |
| dst[i] = 0; |
| } |
| |
| /* Assign one bignum to another. */ |
| void |
| APInt::tcAssign(integerPart *dst, const integerPart *src, unsigned int parts) |
| { |
| unsigned int i; |
| |
| for(i = 0; i < parts; i++) |
| dst[i] = src[i]; |
| } |
| |
| /* Returns true if a bignum is zero, false otherwise. */ |
| bool |
| APInt::tcIsZero(const integerPart *src, unsigned int parts) |
| { |
| unsigned int i; |
| |
| for(i = 0; i < parts; i++) |
| if (src[i]) |
| return false; |
| |
| return true; |
| } |
| |
| /* Extract the given bit of a bignum; returns 0 or 1. */ |
| int |
| APInt::tcExtractBit(const integerPart *parts, unsigned int bit) |
| { |
| return(parts[bit / integerPartWidth] |
| & ((integerPart) 1 << bit % integerPartWidth)) != 0; |
| } |
| |
| /* Set the given bit of a bignum. */ |
| void |
| APInt::tcSetBit(integerPart *parts, unsigned int bit) |
| { |
| parts[bit / integerPartWidth] |= (integerPart) 1 << (bit % integerPartWidth); |
| } |
| |
| /* Returns the bit number of the least significant set bit of a |
| number. If the input number has no bits set -1U is returned. */ |
| unsigned int |
| APInt::tcLSB(const integerPart *parts, unsigned int n) |
| { |
| unsigned int i, lsb; |
| |
| for(i = 0; i < n; i++) { |
| if (parts[i] != 0) { |
| lsb = partLSB(parts[i]); |
| |
| return lsb + i * integerPartWidth; |
| } |
| } |
| |
| return -1U; |
| } |
| |
| /* Returns the bit number of the most significant set bit of a number. |
| If the input number has no bits set -1U is returned. */ |
| unsigned int |
| APInt::tcMSB(const integerPart *parts, unsigned int n) |
| { |
| unsigned int msb; |
| |
| do { |
| --n; |
| |
| if (parts[n] != 0) { |
| msb = partMSB(parts[n]); |
| |
| return msb + n * integerPartWidth; |
| } |
| } while (n); |
| |
| return -1U; |
| } |
| |
| /* 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. */ |
| void |
| APInt::tcExtract(integerPart *dst, unsigned int dstCount,const integerPart *src, |
| unsigned int srcBits, unsigned int srcLSB) |
| { |
| unsigned int firstSrcPart, dstParts, shift, n; |
| |
| dstParts = (srcBits + integerPartWidth - 1) / integerPartWidth; |
| assert (dstParts <= dstCount); |
| |
| firstSrcPart = srcLSB / integerPartWidth; |
| tcAssign (dst, src + firstSrcPart, dstParts); |
| |
| shift = srcLSB % integerPartWidth; |
| tcShiftRight (dst, dstParts, shift); |
| |
| /* We now have (dstParts * integerPartWidth - shift) bits from SRC |
| in DST. If this is less that srcBits, append the rest, else |
| clear the high bits. */ |
| n = dstParts * integerPartWidth - shift; |
| if (n < srcBits) { |
| integerPart mask = lowBitMask (srcBits - n); |
| dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask) |
| << n % integerPartWidth); |
| } else if (n > srcBits) { |
| if (srcBits % integerPartWidth) |
| dst[dstParts - 1] &= lowBitMask (srcBits % integerPartWidth); |
| } |
| |
| /* Clear high parts. */ |
| while (dstParts < dstCount) |
| dst[dstParts++] = 0; |
| } |
| |
| /* DST += RHS + C where C is zero or one. Returns the carry flag. */ |
| integerPart |
| APInt::tcAdd(integerPart *dst, const integerPart *rhs, |
| integerPart c, unsigned int parts) |
| { |
| unsigned int i; |
| |
| assert(c <= 1); |
| |
| for(i = 0; i < parts; i++) { |
| integerPart l; |
| |
| l = dst[i]; |
| if (c) { |
| dst[i] += rhs[i] + 1; |
| c = (dst[i] <= l); |
| } else { |
| dst[i] += rhs[i]; |
| c = (dst[i] < l); |
| } |
| } |
| |
| return c; |
| } |
| |
| /* DST -= RHS + C where C is zero or one. Returns the carry flag. */ |
| integerPart |
| APInt::tcSubtract(integerPart *dst, const integerPart *rhs, |
| integerPart c, unsigned int parts) |
| { |
| unsigned int i; |
| |
| assert(c <= 1); |
| |
| for(i = 0; i < parts; i++) { |
| integerPart l; |
| |
| l = dst[i]; |
| if (c) { |
| dst[i] -= rhs[i] + 1; |
| c = (dst[i] >= l); |
| } else { |
| dst[i] -= rhs[i]; |
| c = (dst[i] > l); |
| } |
| } |
| |
| return c; |
| } |
| |
| /* Negate a bignum in-place. */ |
| void |
| APInt::tcNegate(integerPart *dst, unsigned int parts) |
| { |
| tcComplement(dst, parts); |
| tcIncrement(dst, parts); |
| } |
| |
| /* DST += SRC * MULTIPLIER + CARRY if add is true |
| DST = SRC * MULTIPLIER + CARRY 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 == SRCPARTS + 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. */ |
| int |
| APInt::tcMultiplyPart(integerPart *dst, const integerPart *src, |
| integerPart multiplier, integerPart carry, |
| unsigned int srcParts, unsigned int dstParts, |
| bool add) |
| { |
| unsigned int i, n; |
| |
| /* Otherwise our writes of DST kill our later reads of SRC. */ |
| assert(dst <= src || dst >= src + srcParts); |
| assert(dstParts <= srcParts + 1); |
| |
| /* N loops; minimum of dstParts and srcParts. */ |
| n = dstParts < srcParts ? dstParts: srcParts; |
| |
| for(i = 0; i < n; i++) { |
| integerPart low, mid, high, srcPart; |
| |
| /* [ LOW, HIGH ] = MULTIPLIER * SRC[i] + DST[i] + CARRY. |
| |
| This cannot overflow, because |
| |
| (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1) |
| |
| which is less than n^2. */ |
| |
| srcPart = src[i]; |
| |
| if (multiplier == 0 || srcPart == 0) { |
| low = carry; |
| high = 0; |
| } else { |
| low = lowHalf(srcPart) * lowHalf(multiplier); |
| high = highHalf(srcPart) * highHalf(multiplier); |
| |
| mid = lowHalf(srcPart) * highHalf(multiplier); |
| high += highHalf(mid); |
| mid <<= integerPartWidth / 2; |
| if (low + mid < low) |
| high++; |
| low += mid; |
| |
| mid = highHalf(srcPart) * lowHalf(multiplier); |
| high += highHalf(mid); |
| mid <<= integerPartWidth / 2; |
| if (low + mid < low) |
| high++; |
| low += mid; |
| |
| /* Now add carry. */ |
| if (low + carry < low) |
| high++; |
| low += carry; |
| } |
| |
| if (add) { |
| /* And now DST[i], and store the new low part there. */ |
| if (low + dst[i] < low) |
| high++; |
| dst[i] += low; |
| } else |
| dst[i] = low; |
| |
| carry = high; |
| } |
| |
| if (i < dstParts) { |
| /* Full multiplication, there is no overflow. */ |
| assert(i + 1 == dstParts); |
| dst[i] = carry; |
| return 0; |
| } else { |
| /* We overflowed if there is carry. */ |
| if (carry) |
| return 1; |
| |
| /* We would overflow if any significant unwritten parts would be |
| non-zero. This is true if any remaining src parts are non-zero |
| and the multiplier is non-zero. */ |
| if (multiplier) |
| for(; i < srcParts; i++) |
| if (src[i]) |
| return 1; |
| |
| /* We fitted in the narrow destination. */ |
| return 0; |
| } |
| } |
| |
| /* 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. */ |
| int |
| APInt::tcMultiply(integerPart *dst, const integerPart *lhs, |
| const integerPart *rhs, unsigned int parts) |
| { |
| unsigned int i; |
| int overflow; |
| |
| assert(dst != lhs && dst != rhs); |
| |
| overflow = 0; |
| tcSet(dst, 0, parts); |
| |
| for(i = 0; i < parts; i++) |
| overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts, |
| parts - i, true); |
| |
| return overflow; |
| } |
| |
| /* 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. */ |
| unsigned int |
| APInt::tcFullMultiply(integerPart *dst, const integerPart *lhs, |
| const integerPart *rhs, unsigned int lhsParts, |
| unsigned int rhsParts) |
| { |
| /* Put the narrower number on the LHS for less loops below. */ |
| if (lhsParts > rhsParts) { |
| return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts); |
| } else { |
| unsigned int n; |
| |
| assert(dst != lhs && dst != rhs); |
| |
| tcSet(dst, 0, rhsParts); |
| |
| for(n = 0; n < lhsParts; n++) |
| tcMultiplyPart(&dst[n], rhs, lhs[n], 0, rhsParts, rhsParts + 1, true); |
| |
| n = lhsParts + rhsParts; |
| |
| return n - (dst[n - 1] == 0); |
| } |
| } |
| |
| /* 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. |
| */ |
| int |
| APInt::tcDivide(integerPart *lhs, const integerPart *rhs, |
| integerPart *remainder, integerPart *srhs, |
| unsigned int parts) |
| { |
| unsigned int n, shiftCount; |
| integerPart mask; |
| |
| assert(lhs != remainder && lhs != srhs && remainder != srhs); |
| |
| shiftCount = tcMSB(rhs, parts) + 1; |
| if (shiftCount == 0) |
| return true; |
| |
| shiftCount = parts * integerPartWidth - shiftCount; |
| n = shiftCount / integerPartWidth; |
| mask = (integerPart) 1 << (shiftCount % integerPartWidth); |
| |
| tcAssign(srhs, rhs, parts); |
| tcShiftLeft(srhs, parts, shiftCount); |
| tcAssign(remainder, lhs, parts); |
| tcSet(lhs, 0, parts); |
| |
| /* Loop, subtracting SRHS if REMAINDER is greater and adding that to |
| the total. */ |
| for(;;) { |
| int compare; |
| |
| compare = tcCompare(remainder, srhs, parts); |
| if (compare >= 0) { |
| tcSubtract(remainder, srhs, 0, parts); |
| lhs[n] |= mask; |
| } |
| |
| if (shiftCount == 0) |
| break; |
| shiftCount--; |
| tcShiftRight(srhs, parts, 1); |
| if ((mask >>= 1) == 0) |
| mask = (integerPart) 1 << (integerPartWidth - 1), n--; |
| } |
| |
| return false; |
| } |
| |
| /* Shift a bignum left COUNT bits in-place. Shifted in bits are zero. |
| There are no restrictions on COUNT. */ |
| void |
| APInt::tcShiftLeft(integerPart *dst, unsigned int parts, unsigned int count) |
| { |
| if (count) { |
| unsigned int jump, shift; |
| |
| /* Jump is the inter-part jump; shift is is intra-part shift. */ |
| jump = count / integerPartWidth; |
| shift = count % integerPartWidth; |
| |
| while (parts > jump) { |
| integerPart part; |
| |
| parts--; |
| |
| /* dst[i] comes from the two parts src[i - jump] and, if we have |
| an intra-part shift, src[i - jump - 1]. */ |
| part = dst[parts - jump]; |
| if (shift) { |
| part <<= shift; |
| if (parts >= jump + 1) |
| part |= dst[parts - jump - 1] >> (integerPartWidth - shift); |
| } |
| |
| dst[parts] = part; |
| } |
| |
| while (parts > 0) |
| dst[--parts] = 0; |
| } |
| } |
| |
| /* Shift a bignum right COUNT bits in-place. Shifted in bits are |
| zero. There are no restrictions on COUNT. */ |
| void |
| APInt::tcShiftRight(integerPart *dst, unsigned int parts, unsigned int count) |
| { |
| if (count) { |
| unsigned int i, jump, shift; |
| |
| /* Jump is the inter-part jump; shift is is intra-part shift. */ |
| jump = count / integerPartWidth; |
| shift = count % integerPartWidth; |
| |
| /* Perform the shift. This leaves the most significant COUNT bits |
| of the result at zero. */ |
| for(i = 0; i < parts; i++) { |
| integerPart part; |
| |
| if (i + jump >= parts) { |
| part = 0; |
| } else { |
| part = dst[i + jump]; |
| if (shift) { |
| part >>= shift; |
| if (i + jump + 1 < parts) |
| part |= dst[i + jump + 1] << (integerPartWidth - shift); |
| } |
| } |
| |
| dst[i] = part; |
| } |
| } |
| } |
| |
| /* Bitwise and of two bignums. */ |
| void |
| APInt::tcAnd(integerPart *dst, const integerPart *rhs, unsigned int parts) |
| { |
| unsigned int i; |
| |
| for(i = 0; i < parts; i++) |
| dst[i] &= rhs[i]; |
| } |
| |
| /* Bitwise inclusive or of two bignums. */ |
| void |
| APInt::tcOr(integerPart *dst, const integerPart *rhs, unsigned int parts) |
| { |
| unsigned int i; |
| |
| for(i = 0; i < parts; i++) |
| dst[i] |= rhs[i]; |
| } |
| |
| /* Bitwise exclusive or of two bignums. */ |
| void |
| APInt::tcXor(integerPart *dst, const integerPart *rhs, unsigned int parts) |
| { |
| unsigned int i; |
| |
| for(i = 0; i < parts; i++) |
| dst[i] ^= rhs[i]; |
| } |
| |
| /* Complement a bignum in-place. */ |
| void |
| APInt::tcComplement(integerPart *dst, unsigned int parts) |
| { |
| unsigned int i; |
| |
| for(i = 0; i < parts; i++) |
| dst[i] = ~dst[i]; |
| } |
| |
| /* Comparison (unsigned) of two bignums. */ |
| int |
| APInt::tcCompare(const integerPart *lhs, const integerPart *rhs, |
| unsigned int parts) |
| { |
| while (parts) { |
| parts--; |
| if (lhs[parts] == rhs[parts]) |
| continue; |
| |
| if (lhs[parts] > rhs[parts]) |
| return 1; |
| else |
| return -1; |
| } |
| |
| return 0; |
| } |
| |
| /* Increment a bignum in-place, return the carry flag. */ |
| integerPart |
| APInt::tcIncrement(integerPart *dst, unsigned int parts) |
| { |
| unsigned int i; |
| |
| for(i = 0; i < parts; i++) |
| if (++dst[i] != 0) |
| break; |
| |
| return i == parts; |
| } |
| |
| /* Set the least significant BITS bits of a bignum, clear the |
| rest. */ |
| void |
| APInt::tcSetLeastSignificantBits(integerPart *dst, unsigned int parts, |
| unsigned int bits) |
| { |
| unsigned int i; |
| |
| i = 0; |
| while (bits > integerPartWidth) { |
| dst[i++] = ~(integerPart) 0; |
| bits -= integerPartWidth; |
| } |
| |
| if (bits) |
| dst[i++] = ~(integerPart) 0 >> (integerPartWidth - bits); |
| |
| while (i < parts) |
| dst[i++] = 0; |
| } |