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Diffstat (limited to 'contrib/llvm/lib/Support/APInt.cpp')
| -rw-r--r-- | contrib/llvm/lib/Support/APInt.cpp | 2890 |
1 files changed, 2890 insertions, 0 deletions
diff --git a/contrib/llvm/lib/Support/APInt.cpp b/contrib/llvm/lib/Support/APInt.cpp new file mode 100644 index 000000000000..89f96bd57740 --- /dev/null +++ b/contrib/llvm/lib/Support/APInt.cpp @@ -0,0 +1,2890 @@ +//===-- 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/FoldingSet.h" +#include "llvm/ADT/Hashing.h" +#include "llvm/ADT/SmallString.h" +#include "llvm/ADT/StringRef.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 <cstdlib> +#include <cstring> +#include <limits> +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 || radix == 36) { + r = cdigit - '0'; + if (r <= 9) + return r; + + r = cdigit - 'A'; + if (r <= radix - 11U) + return r + 10; + + r = cdigit - 'a'; + if (r <= radix - 11U) + return r + 10; + + radix = 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); +} + +void APInt::initFromArray(ArrayRef<uint64_t> bigVal) { + assert(BitWidth && "Bitwidth too small"); + assert(bigVal.data() && "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>(bigVal.size(), getNumWords()); + // Copy the words from bigVal to pVal + memcpy(pVal, bigVal.data(), words * APINT_WORD_SIZE); + } + // Make sure unused high bits are cleared + clearUnusedBits(); +} + +APInt::APInt(unsigned numBits, ArrayRef<uint64_t> bigVal) + : BitWidth(numBits), VAL(0) { + initFromArray(bigVal); +} + +APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[]) + : BitWidth(numBits), VAL(0) { + initFromArray(makeArrayRef(bigVal, numWords)); +} + +APInt::APInt(unsigned numbits, 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 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 + clearAllBits(); + 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 + clearAllBits(); + unsigned wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords; + memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE); + clearUnusedBits(); + + // 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(); +} + +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; +} + +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::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.flipAllBits(); + ++lhs; + } + if (rhsNeg) { + // Sign bit is set so perform two's complement to make it positive + rhs.flipAllBits(); + ++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); +} + +void APInt::setBit(unsigned bitPosition) { + if (isSingleWord()) + VAL |= maskBit(bitPosition); + else + pVal[whichWord(bitPosition)] |= maskBit(bitPosition); +} + +/// Set the given bit to 0 whose position is given as "bitPosition". +/// @brief Set a given bit to 0. +void APInt::clearBit(unsigned bitPosition) { + if (isSingleWord()) + VAL &= ~maskBit(bitPosition); + else + pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition); +} + +/// @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. +void APInt::flipBit(unsigned bitPosition) { + assert(bitPosition < BitWidth && "Out of the bit-width range!"); + if ((*this)[bitPosition]) clearBit(bitPosition); + else setBit(bitPosition); +} + +unsigned APInt::getBitsNeeded(StringRef str, uint8_t radix) { + assert(!str.empty() && "Invalid string length"); + assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 || + radix == 36) && + "Radix should be 2, 8, 10, 16, or 36!"); + + 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; + + // FIXME: base 36 + + // 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 + = radix == 10? (slen == 1 ? 4 : slen * 64/18) + : (slen == 1 ? 7 : slen * 16/3); + + // 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; + } +} + +hash_code llvm::hash_value(const APInt &Arg) { + if (Arg.isSingleWord()) + return hash_combine(Arg.VAL); + + return hash_combine_range(Arg.pVal, Arg.pVal + Arg.getNumWords()); +} + +/// 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); +} + +unsigned APInt::countLeadingZerosSlowCase() const { + // Treat the most significand word differently because it might have + // meaningless bits set beyond the precision. + unsigned BitsInMSW = BitWidth % APINT_BITS_PER_WORD; + integerPart MSWMask; + if (BitsInMSW) MSWMask = (integerPart(1) << BitsInMSW) - 1; + else { + MSWMask = ~integerPart(0); + BitsInMSW = APINT_BITS_PER_WORD; + } + + unsigned i = getNumWords(); + integerPart MSW = pVal[i-1] & MSWMask; + if (MSW) + return llvm::countLeadingZeros(MSW) - (APINT_BITS_PER_WORD - BitsInMSW); + + unsigned Count = BitsInMSW; + for (--i; i > 0u; --i) { + if (pVal[i-1] == 0) + Count += APINT_BITS_PER_WORD; + else { + Count += llvm::countLeadingZeros(pVal[i-1]); + break; + } + } + 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]); + break; + } + } + } + return Count; +} + +unsigned APInt::countTrailingZeros() const { + if (isSingleWord()) + return std::min(unsigned(llvm::countTrailingZeros(VAL)), BitWidth); + unsigned Count = 0; + unsigned i = 0; + for (; i < getNumWords() && pVal[i] == 0; ++i) + Count += APINT_BITS_PER_WORD; + if (i < getNumWords()) + Count += llvm::countTrailingZeros(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; +} + +/// Perform a logical right-shift from Src to Dst, which must be equal or +/// non-overlapping, of Words words, by Shift, which must be less than 64. +static void lshrNear(uint64_t *Dst, uint64_t *Src, unsigned Words, + unsigned Shift) { + uint64_t Carry = 0; + for (int I = Words - 1; I >= 0; --I) { + uint64_t Tmp = Src[I]; + Dst[I] = (Tmp >> Shift) | Carry; + Carry = Tmp << (64 - Shift); + } +} + +APInt APInt::byteSwap() const { + assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!"); + if (BitWidth == 16) + return APInt(BitWidth, ByteSwap_16(uint16_t(VAL))); + if (BitWidth == 32) + return APInt(BitWidth, ByteSwap_32(unsigned(VAL))); + 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); + } + if (BitWidth == 64) + return APInt(BitWidth, ByteSwap_64(VAL)); + + APInt Result(getNumWords() * APINT_BITS_PER_WORD, 0); + for (unsigned I = 0, N = getNumWords(); I != N; ++I) + Result.pVal[I] = ByteSwap_64(pVal[N - I - 1]); + if (Result.BitWidth != BitWidth) { + lshrNear(Result.pVal, Result.pVal, getNumWords(), + Result.BitWidth - BitWidth); + Result.BitWidth = BitWidth; + } + 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) const { + assert(width < BitWidth && "Invalid APInt Truncate request"); + assert(width && "Can't truncate to 0 bits"); + + if (width <= APINT_BITS_PER_WORD) + return APInt(width, getRawData()[0]); + + APInt Result(getMemory(getNumWords(width)), width); + + // Copy full words. + unsigned i; + for (i = 0; i != width / APINT_BITS_PER_WORD; i++) + Result.pVal[i] = pVal[i]; + + // Truncate and copy any partial word. + unsigned bits = (0 - width) % APINT_BITS_PER_WORD; + if (bits != 0) + Result.pVal[i] = pVal[i] << bits >> bits; + + return Result; +} + +// Sign extend to a new width. +APInt APInt::sext(unsigned width) const { + assert(width > BitWidth && "Invalid APInt SignExtend request"); + + if (width <= APINT_BITS_PER_WORD) { + uint64_t val = VAL << (APINT_BITS_PER_WORD - BitWidth); + val = (int64_t)val >> (width - BitWidth); + return APInt(width, val >> (APINT_BITS_PER_WORD - width)); + } + + APInt Result(getMemory(getNumWords(width)), width); + + // Copy full words. + unsigned i; + uint64_t word = 0; + for (i = 0; i != BitWidth / APINT_BITS_PER_WORD; i++) { + word = getRawData()[i]; + Result.pVal[i] = word; + } + + // Read and sign-extend any partial word. + unsigned bits = (0 - BitWidth) % APINT_BITS_PER_WORD; + if (bits != 0) + word = (int64_t)getRawData()[i] << bits >> bits; + else + word = (int64_t)word >> (APINT_BITS_PER_WORD - 1); + + // Write remaining full words. + for (; i != width / APINT_BITS_PER_WORD; i++) { + Result.pVal[i] = word; + word = (int64_t)word >> (APINT_BITS_PER_WORD - 1); + } + + // Write any partial word. + bits = (0 - width) % APINT_BITS_PER_WORD; + if (bits != 0) + Result.pVal[i] = word << bits >> bits; + + return Result; +} + +// Zero extend to a new width. +APInt APInt::zext(unsigned width) const { + assert(width > BitWidth && "Invalid APInt ZeroExtend request"); + + if (width <= APINT_BITS_PER_WORD) + return APInt(width, VAL); + + APInt Result(getMemory(getNumWords(width)), width); + + // Copy words. + unsigned i; + for (i = 0; i != getNumWords(); i++) + Result.pVal[i] = getRawData()[i]; + + // Zero remaining words. + memset(&Result.pVal[i], 0, (Result.getNumWords() - i) * APINT_WORD_SIZE); + + return Result; +} + +APInt APInt::zextOrTrunc(unsigned width) const { + if (BitWidth < width) + return zext(width); + if (BitWidth > width) + return trunc(width); + return *this; +} + +APInt APInt::sextOrTrunc(unsigned width) const { + if (BitWidth < width) + return sext(width); + if (BitWidth > width) + return trunc(width); + return *this; +} + +APInt APInt::zextOrSelf(unsigned width) const { + if (BitWidth < width) + return zext(width); + return *this; +} + +APInt APInt::sextOrSelf(unsigned width) const { + if (BitWidth < width) + return sext(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) { + lshrNear(val, pVal, getNumWords(), 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 { + rotateAmt %= BitWidth; + if (rotateAmt == 0) + return *this; + return shl(rotateAmt) | lshr(BitWidth - rotateAmt); +} + +APInt APInt::rotr(const APInt &rotateAmt) const { + return rotr((unsigned)rotateAmt.getLimitedValue(BitWidth)); +} + +APInt APInt::rotr(unsigned rotateAmt) const { + rotateAmt %= BitWidth; + if (rotateAmt == 0) + return *this; + return lshr(rotateAmt) | shl(BitWidth - rotateAmt); +} + +// 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) { +#if HAVE_ROUND + return APInt(BitWidth, + uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0]))))); +#else + return APInt(BitWidth, + uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0])) + 0.5)); +#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; + assert(this->ule(nextSquare) && "Error in APInt::sqrt computation"); + APInt midpoint((nextSquare - square).udiv(two)); + APInt offset(*this - square); + if (offset.ult(midpoint)) + return x_old; + 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.ult(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. +/// LeadingZeros can be used to simplify the calculation if the upper bits +/// of the divided value are known zero. +APInt::mu APInt::magicu(unsigned LeadingZeros) 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()).lshr(LeadingZeros); + APInt signedMin = APInt::getSignedMinValue(d.getBitWidth()); + APInt signedMax = APInt::getSignedMaxValue(d.getBitWidth()); + + nc = allOnes - (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(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n'); + DEBUG(dbgs() << "KnuthDiv: original:"); + DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]); + DEBUG(dbgs() << " by"); + DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]); + DEBUG(dbgs() << '\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(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(dbgs() << "KnuthDiv: normal:"); + DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]); + DEBUG(dbgs() << " by"); + DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]); + DEBUG(dbgs() << '\n'); +#endif + + // D2. [Initialize j.] Set j to m. This is the loop counter over the places. + int j = m; + do { + DEBUG(dbgs() << "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(dbgs() << "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(dbgs() << "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(dbgs() << "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(dbgs() << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " << + u[j+i+1] << '\n'); + } + DEBUG(dbgs() << "KnuthDiv: after subtraction:"); + DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]); + DEBUG(dbgs() << '\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(dbgs() << "KnuthDiv: after complement:"); + DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]); + DEBUG(dbgs() << '\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(dbgs() << "KnuthDiv: after correction:"); + DEBUG(for (int i = m+n; i >=0; i--) dbgs() <<" " << u[i]); + DEBUG(dbgs() << "\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(dbgs() << "KnuthDiv: quotient:"); + DEBUG(for (int i = m; i >=0; i--) dbgs() <<" " << q[i]); + DEBUG(dbgs() << '\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(dbgs() << "KnuthDiv: remainder:"); + for (int i = n-1; i >= 0; i--) { + r[i] = (u[i] >> shift) | carry; + carry = u[i] << (32 - shift); + DEBUG(dbgs() << " " << r[i]); + } + } else { + for (int i = n-1; i >= 0; i--) { + r[i] = u[i]; + DEBUG(dbgs() << " " << r[i]); + } + } + DEBUG(dbgs() << '\n'); + } +#if 0 + DEBUG(dbgs() << '\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 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->clearAllBits(); + + // 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->clearAllBits(); + + // 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::sdiv(const APInt &RHS) const { + if (isNegative()) { + if (RHS.isNegative()) + return (-(*this)).udiv(-RHS); + return -((-(*this)).udiv(RHS)); + } + if (RHS.isNegative()) + return -(this->udiv(-RHS)); + return this->udiv(RHS); +} + +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; +} + +APInt APInt::srem(const APInt &RHS) const { + if (isNegative()) { + if (RHS.isNegative()) + return -((-(*this)).urem(-RHS)); + return -((-(*this)).urem(RHS)); + } + if (RHS.isNegative()) + return this->urem(-RHS); + return this->urem(RHS); +} + +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::sdivrem(const APInt &LHS, const APInt &RHS, + APInt &Quotient, APInt &Remainder) { + if (LHS.isNegative()) { + if (RHS.isNegative()) + APInt::udivrem(-LHS, -RHS, Quotient, Remainder); + else { + APInt::udivrem(-LHS, RHS, Quotient, Remainder); + Quotient = -Quotient; + } + Remainder = -Remainder; + } else if (RHS.isNegative()) { + APInt::udivrem(LHS, -RHS, Quotient, Remainder); + Quotient = -Quotient; + } else { + APInt::udivrem(LHS, RHS, Quotient, Remainder); + } +} + +APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const { + APInt Res = *this+RHS; + Overflow = isNonNegative() == RHS.isNonNegative() && + Res.isNonNegative() != isNonNegative(); + return Res; +} + +APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const { + APInt Res = *this+RHS; + Overflow = Res.ult(RHS); + return Res; +} + +APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const { + APInt Res = *this - RHS; + Overflow = isNonNegative() != RHS.isNonNegative() && + Res.isNonNegative() != isNonNegative(); + return Res; +} + +APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const { + APInt Res = *this-RHS; + Overflow = Res.ugt(*this); + return Res; +} + +APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const { + // MININT/-1 --> overflow. + Overflow = isMinSignedValue() && RHS.isAllOnesValue(); + return sdiv(RHS); +} + +APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const { + APInt Res = *this * RHS; + + if (*this != 0 && RHS != 0) + Overflow = Res.sdiv(RHS) != *this || Res.sdiv(*this) != RHS; + else + Overflow = false; + return Res; +} + +APInt APInt::umul_ov(const APInt &RHS, bool &Overflow) const { + APInt Res = *this * RHS; + + if (*this != 0 && RHS != 0) + Overflow = Res.udiv(RHS) != *this || Res.udiv(*this) != RHS; + else + Overflow = false; + return Res; +} + +APInt APInt::sshl_ov(unsigned ShAmt, bool &Overflow) const { + Overflow = ShAmt >= getBitWidth(); + if (Overflow) + ShAmt = getBitWidth()-1; + + if (isNonNegative()) // Don't allow sign change. + Overflow = ShAmt >= countLeadingZeros(); + else + Overflow = ShAmt >= countLeadingOnes(); + + return *this << ShAmt; +} + + + + +void APInt::fromString(unsigned numbits, 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 == 36) && + "Radix should be 2, 8, 10, 16, or 36!"); + + 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->flipAllBits(); + } +} + +void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix, + bool Signed, bool formatAsCLiteral) const { + assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2 || + Radix == 36) && + "Radix should be 2, 8, 10, 16, or 36!"); + + const char *Prefix = ""; + if (formatAsCLiteral) { + switch (Radix) { + case 2: + // Binary literals are a non-standard extension added in gcc 4.3: + // http://gcc.gnu.org/onlinedocs/gcc-4.3.0/gcc/Binary-constants.html + Prefix = "0b"; + break; + case 8: + Prefix = "0"; + break; + case 10: + break; // No prefix + case 16: + Prefix = "0x"; + break; + default: + llvm_unreachable("Invalid radix!"); + } + } + + // First, check for a zero value and just short circuit the logic below. + if (*this == 0) { + while (*Prefix) { + Str.push_back(*Prefix); + ++Prefix; + }; + Str.push_back('0'); + return; + } + + static const char Digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; + + if (isSingleWord()) { + char Buffer[65]; + char *BufPtr = Buffer+65; + + uint64_t N; + if (!Signed) { + N = getZExtValue(); + } else { + int64_t I = getSExtValue(); + if (I >= 0) { + N = I; + } else { + Str.push_back('-'); + N = -(uint64_t)I; + } + } + + while (*Prefix) { + Str.push_back(*Prefix); + ++Prefix; + }; + + 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.flipAllBits(); + ++Tmp; + Str.push_back('-'); + } + + while (*Prefix) { + Str.push_back(*Prefix); + ++Prefix; + }; + + // 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 == 2 || Radix == 8 || Radix == 16) { + // 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(Radix == 10? 4 : 8, Radix); + 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, /* formatAsCLiteral = */false); + return S.str(); +} + + +void APInt::dump() const { + SmallString<40> S, U; + this->toStringUnsigned(U); + this->toStringSigned(S); + dbgs() << "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, /* formatAsCLiteral = */false); + 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) + { + return findLastSet(value, ZB_Max); + } + + /* 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) + { + return findFirstSet(value, ZB_Max); + } +} + +/* 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); +} + +/* Clears the given bit of a bignum. */ +void +APInt::tcClearBit(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; +} + +/* Decrement a bignum in-place, return the borrow flag. */ +integerPart +APInt::tcDecrement(integerPart *dst, unsigned int parts) { + for (unsigned int i = 0; i < parts; i++) { + // If the current word is non-zero, then the decrement has no effect on the + // higher-order words of the integer and no borrow can occur. Exit early. + if (dst[i]--) + return 0; + } + // If every word was zero, then there is a borrow. + return 1; +} + + +/* 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; +} |