| //===-- APInt.cpp - Implement APInt class ---------------------------------===// |
| // |
| // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
| // See https://llvm.org/LICENSE.txt for license information. |
| // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| // |
| //===----------------------------------------------------------------------===// |
| // |
| // This file implements a class to represent arbitrary precision integer |
| // constant values and provide a variety of arithmetic operations on them. |
| // |
| //===----------------------------------------------------------------------===// |
| |
| #include "llvm/ADT/APInt.h" |
| #include "llvm/ADT/ArrayRef.h" |
| #include "llvm/ADT/FoldingSet.h" |
| #include "llvm/ADT/Hashing.h" |
| #include "llvm/ADT/Optional.h" |
| #include "llvm/ADT/SmallString.h" |
| #include "llvm/ADT/StringRef.h" |
| #include "llvm/ADT/bit.h" |
| #include "llvm/Config/llvm-config.h" |
| #include "llvm/Support/Debug.h" |
| #include "llvm/Support/ErrorHandling.h" |
| #include "llvm/Support/MathExtras.h" |
| #include "llvm/Support/raw_ostream.h" |
| #include <climits> |
| #include <cmath> |
| #include <cstdlib> |
| #include <cstring> |
| using namespace llvm; |
| |
| #define DEBUG_TYPE "apint" |
| |
| /// 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]; |
| 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) { |
| return new uint64_t[numWords]; |
| } |
| |
| /// 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(uint64_t val, bool isSigned) { |
| U.pVal = getClearedMemory(getNumWords()); |
| U.pVal[0] = val; |
| if (isSigned && int64_t(val) < 0) |
| for (unsigned i = 1; i < getNumWords(); ++i) |
| U.pVal[i] = WORDTYPE_MAX; |
| clearUnusedBits(); |
| } |
| |
| void APInt::initSlowCase(const APInt& that) { |
| U.pVal = getMemory(getNumWords()); |
| memcpy(U.pVal, that.U.pVal, getNumWords() * APINT_WORD_SIZE); |
| } |
| |
| void APInt::initFromArray(ArrayRef<uint64_t> bigVal) { |
| assert(bigVal.data() && "Null pointer detected!"); |
| if (isSingleWord()) |
| U.VAL = bigVal[0]; |
| else { |
| // Get memory, cleared to 0 |
| U.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(U.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) { |
| initFromArray(bigVal); |
| } |
| |
| APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[]) |
| : BitWidth(numBits) { |
| initFromArray(makeArrayRef(bigVal, numWords)); |
| } |
| |
| APInt::APInt(unsigned numbits, StringRef Str, uint8_t radix) |
| : BitWidth(numbits) { |
| fromString(numbits, Str, radix); |
| } |
| |
| void APInt::reallocate(unsigned NewBitWidth) { |
| // If the number of words is the same we can just change the width and stop. |
| if (getNumWords() == getNumWords(NewBitWidth)) { |
| BitWidth = NewBitWidth; |
| return; |
| } |
| |
| // If we have an allocation, delete it. |
| if (!isSingleWord()) |
| delete [] U.pVal; |
| |
| // Update BitWidth. |
| BitWidth = NewBitWidth; |
| |
| // If we are supposed to have an allocation, create it. |
| if (!isSingleWord()) |
| U.pVal = getMemory(getNumWords()); |
| } |
| |
| void APInt::assignSlowCase(const APInt &RHS) { |
| // Don't do anything for X = X |
| if (this == &RHS) |
| return; |
| |
| // Adjust the bit width and handle allocations as necessary. |
| reallocate(RHS.getBitWidth()); |
| |
| // Copy the data. |
| if (isSingleWord()) |
| U.VAL = RHS.U.VAL; |
| else |
| memcpy(U.pVal, RHS.U.pVal, getNumWords() * APINT_WORD_SIZE); |
| } |
| |
| /// This method 'profiles' an APInt for use with FoldingSet. |
| void APInt::Profile(FoldingSetNodeID& ID) const { |
| ID.AddInteger(BitWidth); |
| |
| if (isSingleWord()) { |
| ID.AddInteger(U.VAL); |
| return; |
| } |
| |
| unsigned NumWords = getNumWords(); |
| for (unsigned i = 0; i < NumWords; ++i) |
| ID.AddInteger(U.pVal[i]); |
| } |
| |
| /// Prefix increment operator. Increments the APInt by one. |
| APInt& APInt::operator++() { |
| if (isSingleWord()) |
| ++U.VAL; |
| else |
| tcIncrement(U.pVal, getNumWords()); |
| return clearUnusedBits(); |
| } |
| |
| /// Prefix decrement operator. Decrements the APInt by one. |
| APInt& APInt::operator--() { |
| if (isSingleWord()) |
| --U.VAL; |
| else |
| tcDecrement(U.pVal, getNumWords()); |
| return clearUnusedBits(); |
| } |
| |
| /// Adds the RHS APInt to this APInt. |
| /// @returns this, after addition of RHS. |
| /// Addition assignment operator. |
| APInt& APInt::operator+=(const APInt& RHS) { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) |
| U.VAL += RHS.U.VAL; |
| else |
| tcAdd(U.pVal, RHS.U.pVal, 0, getNumWords()); |
| return clearUnusedBits(); |
| } |
| |
| APInt& APInt::operator+=(uint64_t RHS) { |
| if (isSingleWord()) |
| U.VAL += RHS; |
| else |
| tcAddPart(U.pVal, RHS, getNumWords()); |
| return clearUnusedBits(); |
| } |
| |
| /// Subtracts the RHS APInt from this APInt |
| /// @returns this, after subtraction |
| /// Subtraction assignment operator. |
| APInt& APInt::operator-=(const APInt& RHS) { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) |
| U.VAL -= RHS.U.VAL; |
| else |
| tcSubtract(U.pVal, RHS.U.pVal, 0, getNumWords()); |
| return clearUnusedBits(); |
| } |
| |
| APInt& APInt::operator-=(uint64_t RHS) { |
| if (isSingleWord()) |
| U.VAL -= RHS; |
| else |
| tcSubtractPart(U.pVal, RHS, getNumWords()); |
| return clearUnusedBits(); |
| } |
| |
| APInt APInt::operator*(const APInt& RHS) const { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| if (isSingleWord()) |
| return APInt(BitWidth, U.VAL * RHS.U.VAL); |
| |
| APInt Result(getMemory(getNumWords()), getBitWidth()); |
| tcMultiply(Result.U.pVal, U.pVal, RHS.U.pVal, getNumWords()); |
| Result.clearUnusedBits(); |
| return Result; |
| } |
| |
| void APInt::andAssignSlowCase(const APInt &RHS) { |
| WordType *dst = U.pVal, *rhs = RHS.U.pVal; |
| for (size_t i = 0, e = getNumWords(); i != e; ++i) |
| dst[i] &= rhs[i]; |
| } |
| |
| void APInt::orAssignSlowCase(const APInt &RHS) { |
| WordType *dst = U.pVal, *rhs = RHS.U.pVal; |
| for (size_t i = 0, e = getNumWords(); i != e; ++i) |
| dst[i] |= rhs[i]; |
| } |
| |
| void APInt::xorAssignSlowCase(const APInt &RHS) { |
| WordType *dst = U.pVal, *rhs = RHS.U.pVal; |
| for (size_t i = 0, e = getNumWords(); i != e; ++i) |
| dst[i] ^= rhs[i]; |
| } |
| |
| APInt &APInt::operator*=(const APInt &RHS) { |
| *this = *this * RHS; |
| return *this; |
| } |
| |
| APInt& APInt::operator*=(uint64_t RHS) { |
| if (isSingleWord()) { |
| U.VAL *= RHS; |
| } else { |
| unsigned NumWords = getNumWords(); |
| tcMultiplyPart(U.pVal, U.pVal, RHS, 0, NumWords, NumWords, false); |
| } |
| return clearUnusedBits(); |
| } |
| |
| bool APInt::equalSlowCase(const APInt &RHS) const { |
| return std::equal(U.pVal, U.pVal + getNumWords(), RHS.U.pVal); |
| } |
| |
| int APInt::compare(const APInt& RHS) const { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); |
| if (isSingleWord()) |
| return U.VAL < RHS.U.VAL ? -1 : U.VAL > RHS.U.VAL; |
| |
| return tcCompare(U.pVal, RHS.U.pVal, getNumWords()); |
| } |
| |
| int APInt::compareSigned(const APInt& RHS) const { |
| assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); |
| if (isSingleWord()) { |
| int64_t lhsSext = SignExtend64(U.VAL, BitWidth); |
| int64_t rhsSext = SignExtend64(RHS.U.VAL, BitWidth); |
| return lhsSext < rhsSext ? -1 : lhsSext > rhsSext; |
| } |
| |
| bool lhsNeg = isNegative(); |
| bool rhsNeg = RHS.isNegative(); |
| |
| // If the sign bits don't match, then (LHS < RHS) if LHS is negative |
| if (lhsNeg != rhsNeg) |
| return lhsNeg ? -1 : 1; |
| |
| // Otherwise we can just use an unsigned comparison, because even negative |
| // numbers compare correctly this way if both have the same signed-ness. |
| return tcCompare(U.pVal, RHS.U.pVal, getNumWords()); |
| } |
| |
| void APInt::setBitsSlowCase(unsigned loBit, unsigned hiBit) { |
| unsigned loWord = whichWord(loBit); |
| unsigned hiWord = whichWord(hiBit); |
| |
| // Create an initial mask for the low word with zeros below loBit. |
| uint64_t loMask = WORDTYPE_MAX << whichBit(loBit); |
| |
| // If hiBit is not aligned, we need a high mask. |
| unsigned hiShiftAmt = whichBit(hiBit); |
| if (hiShiftAmt != 0) { |
| // Create a high mask with zeros above hiBit. |
| uint64_t hiMask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - hiShiftAmt); |
| // If loWord and hiWord are equal, then we combine the masks. Otherwise, |
| // set the bits in hiWord. |
| if (hiWord == loWord) |
| loMask &= hiMask; |
| else |
| U.pVal[hiWord] |= hiMask; |
| } |
| // Apply the mask to the low word. |
| U.pVal[loWord] |= loMask; |
| |
| // Fill any words between loWord and hiWord with all ones. |
| for (unsigned word = loWord + 1; word < hiWord; ++word) |
| U.pVal[word] = WORDTYPE_MAX; |
| } |
| |
| // Complement a bignum in-place. |
| static void tcComplement(APInt::WordType *dst, unsigned parts) { |
| for (unsigned i = 0; i < parts; i++) |
| dst[i] = ~dst[i]; |
| } |
| |
| /// Toggle every bit to its opposite value. |
| void APInt::flipAllBitsSlowCase() { |
| tcComplement(U.pVal, getNumWords()); |
| clearUnusedBits(); |
| } |
| |
| /// Concatenate the bits from "NewLSB" onto the bottom of *this. This is |
| /// equivalent to: |
| /// (this->zext(NewWidth) << NewLSB.getBitWidth()) | NewLSB.zext(NewWidth) |
| /// In the slow case, we know the result is large. |
| APInt APInt::concatSlowCase(const APInt &NewLSB) const { |
| unsigned NewWidth = getBitWidth() + NewLSB.getBitWidth(); |
| APInt Result = NewLSB.zextOrSelf(NewWidth); |
| Result.insertBits(*this, NewLSB.getBitWidth()); |
| return Result; |
| } |
| |
| /// Toggle a given bit to its opposite value whose position is given |
| /// as "bitPosition". |
| /// Toggles a given bit to its opposite value. |
| void APInt::flipBit(unsigned bitPosition) { |
| assert(bitPosition < BitWidth && "Out of the bit-width range!"); |
| setBitVal(bitPosition, !(*this)[bitPosition]); |
| } |
| |
| void APInt::insertBits(const APInt &subBits, unsigned bitPosition) { |
| unsigned subBitWidth = subBits.getBitWidth(); |
| assert((subBitWidth + bitPosition) <= BitWidth && "Illegal bit insertion"); |
| |
| // inserting no bits is a noop. |
| if (subBitWidth == 0) |
| return; |
| |
| // Insertion is a direct copy. |
| if (subBitWidth == BitWidth) { |
| *this = subBits; |
| return; |
| } |
| |
| // Single word result can be done as a direct bitmask. |
| if (isSingleWord()) { |
| uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - subBitWidth); |
| U.VAL &= ~(mask << bitPosition); |
| U.VAL |= (subBits.U.VAL << bitPosition); |
| return; |
| } |
| |
| unsigned loBit = whichBit(bitPosition); |
| unsigned loWord = whichWord(bitPosition); |
| unsigned hi1Word = whichWord(bitPosition + subBitWidth - 1); |
| |
| // Insertion within a single word can be done as a direct bitmask. |
| if (loWord == hi1Word) { |
| uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - subBitWidth); |
| U.pVal[loWord] &= ~(mask << loBit); |
| U.pVal[loWord] |= (subBits.U.VAL << loBit); |
| return; |
| } |
| |
| // Insert on word boundaries. |
| if (loBit == 0) { |
| // Direct copy whole words. |
| unsigned numWholeSubWords = subBitWidth / APINT_BITS_PER_WORD; |
| memcpy(U.pVal + loWord, subBits.getRawData(), |
| numWholeSubWords * APINT_WORD_SIZE); |
| |
| // Mask+insert remaining bits. |
| unsigned remainingBits = subBitWidth % APINT_BITS_PER_WORD; |
| if (remainingBits != 0) { |
| uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - remainingBits); |
| U.pVal[hi1Word] &= ~mask; |
| U.pVal[hi1Word] |= subBits.getWord(subBitWidth - 1); |
| } |
| return; |
| } |
| |
| // General case - set/clear individual bits in dst based on src. |
| // TODO - there is scope for optimization here, but at the moment this code |
| // path is barely used so prefer readability over performance. |
| for (unsigned i = 0; i != subBitWidth; ++i) |
| setBitVal(bitPosition + i, subBits[i]); |
| } |
| |
| void APInt::insertBits(uint64_t subBits, unsigned bitPosition, unsigned numBits) { |
| uint64_t maskBits = maskTrailingOnes<uint64_t>(numBits); |
| subBits &= maskBits; |
| if (isSingleWord()) { |
| U.VAL &= ~(maskBits << bitPosition); |
| U.VAL |= subBits << bitPosition; |
| return; |
| } |
| |
| unsigned loBit = whichBit(bitPosition); |
| unsigned loWord = whichWord(bitPosition); |
| unsigned hiWord = whichWord(bitPosition + numBits - 1); |
| if (loWord == hiWord) { |
| U.pVal[loWord] &= ~(maskBits << loBit); |
| U.pVal[loWord] |= subBits << loBit; |
| return; |
| } |
| |
| static_assert(8 * sizeof(WordType) <= 64, "This code assumes only two words affected"); |
| unsigned wordBits = 8 * sizeof(WordType); |
| U.pVal[loWord] &= ~(maskBits << loBit); |
| U.pVal[loWord] |= subBits << loBit; |
| |
| U.pVal[hiWord] &= ~(maskBits >> (wordBits - loBit)); |
| U.pVal[hiWord] |= subBits >> (wordBits - loBit); |
| } |
| |
| APInt APInt::extractBits(unsigned numBits, unsigned bitPosition) const { |
| assert(bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth && |
| "Illegal bit extraction"); |
| |
| if (isSingleWord()) |
| return APInt(numBits, U.VAL >> bitPosition); |
| |
| unsigned loBit = whichBit(bitPosition); |
| unsigned loWord = whichWord(bitPosition); |
| unsigned hiWord = whichWord(bitPosition + numBits - 1); |
| |
| // Single word result extracting bits from a single word source. |
| if (loWord == hiWord) |
| return APInt(numBits, U.pVal[loWord] >> loBit); |
| |
| // Extracting bits that start on a source word boundary can be done |
| // as a fast memory copy. |
| if (loBit == 0) |
| return APInt(numBits, makeArrayRef(U.pVal + loWord, 1 + hiWord - loWord)); |
| |
| // General case - shift + copy source words directly into place. |
| APInt Result(numBits, 0); |
| unsigned NumSrcWords = getNumWords(); |
| unsigned NumDstWords = Result.getNumWords(); |
| |
| uint64_t *DestPtr = Result.isSingleWord() ? &Result.U.VAL : Result.U.pVal; |
| for (unsigned word = 0; word < NumDstWords; ++word) { |
| uint64_t w0 = U.pVal[loWord + word]; |
| uint64_t w1 = |
| (loWord + word + 1) < NumSrcWords ? U.pVal[loWord + word + 1] : 0; |
| DestPtr[word] = (w0 >> loBit) | (w1 << (APINT_BITS_PER_WORD - loBit)); |
| } |
| |
| return Result.clearUnusedBits(); |
| } |
| |
| uint64_t APInt::extractBitsAsZExtValue(unsigned numBits, |
| unsigned bitPosition) const { |
| assert(numBits > 0 && "Can't extract zero bits"); |
| assert(bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth && |
| "Illegal bit extraction"); |
| assert(numBits <= 64 && "Illegal bit extraction"); |
| |
| uint64_t maskBits = maskTrailingOnes<uint64_t>(numBits); |
| if (isSingleWord()) |
| return (U.VAL >> bitPosition) & maskBits; |
| |
| unsigned loBit = whichBit(bitPosition); |
| unsigned loWord = whichWord(bitPosition); |
| unsigned hiWord = whichWord(bitPosition + numBits - 1); |
| if (loWord == hiWord) |
| return (U.pVal[loWord] >> loBit) & maskBits; |
| |
| static_assert(8 * sizeof(WordType) <= 64, "This code assumes only two words affected"); |
| unsigned wordBits = 8 * sizeof(WordType); |
| uint64_t retBits = U.pVal[loWord] >> loBit; |
| retBits |= U.pVal[hiWord] << (wordBits - loBit); |
| retBits &= maskBits; |
| return retBits; |
| } |
| |
| 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. If the log is exact and value is negative, then the value is |
| // MinSignedValue with (log + 1) bits. |
| unsigned log = tmp.logBase2(); |
| if (log == (unsigned)-1) { |
| return isNegative + 1; |
| } else if (isNegative && tmp.isPowerOf2()) { |
| return isNegative + log; |
| } else { |
| return isNegative + log + 1; |
| } |
| } |
| |
| hash_code llvm::hash_value(const APInt &Arg) { |
| if (Arg.isSingleWord()) |
| return hash_combine(Arg.BitWidth, Arg.U.VAL); |
| |
| return hash_combine( |
| Arg.BitWidth, |
| hash_combine_range(Arg.U.pVal, Arg.U.pVal + Arg.getNumWords())); |
| } |
| |
| unsigned DenseMapInfo<APInt, void>::getHashValue(const APInt &Key) { |
| return static_cast<unsigned>(hash_value(Key)); |
| } |
| |
| bool APInt::isSplat(unsigned SplatSizeInBits) const { |
| assert(getBitWidth() % SplatSizeInBits == 0 && |
| "SplatSizeInBits must divide width!"); |
| // We can check that all parts of an integer are equal by making use of a |
| // little trick: rotate and check if it's still the same value. |
| return *this == rotl(SplatSizeInBits); |
| } |
| |
| /// This function returns the high "numBits" bits of this APInt. |
| APInt APInt::getHiBits(unsigned numBits) const { |
| return this->lshr(BitWidth - numBits); |
| } |
| |
| /// This function returns the low "numBits" bits of this APInt. |
| APInt APInt::getLoBits(unsigned numBits) const { |
| APInt Result(getLowBitsSet(BitWidth, numBits)); |
| Result &= *this; |
| return Result; |
| } |
| |
| /// Return a value containing V broadcasted over NewLen bits. |
| APInt APInt::getSplat(unsigned NewLen, const APInt &V) { |
| assert(NewLen >= V.getBitWidth() && "Can't splat to smaller bit width!"); |
| |
| APInt Val = V.zextOrSelf(NewLen); |
| for (unsigned I = V.getBitWidth(); I < NewLen; I <<= 1) |
| Val |= Val << I; |
| |
| return Val; |
| } |
| |
| unsigned APInt::countLeadingZerosSlowCase() const { |
| unsigned Count = 0; |
| for (int i = getNumWords()-1; i >= 0; --i) { |
| uint64_t V = U.pVal[i]; |
| if (V == 0) |
| Count += APINT_BITS_PER_WORD; |
| else { |
| Count += llvm::countLeadingZeros(V); |
| break; |
| } |
| } |
| // Adjust for unused bits in the most significant word (they are zero). |
| unsigned Mod = BitWidth % APINT_BITS_PER_WORD; |
| Count -= Mod > 0 ? APINT_BITS_PER_WORD - Mod : 0; |
| return Count; |
| } |
| |
| unsigned APInt::countLeadingOnesSlowCase() const { |
| 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 = llvm::countLeadingOnes(U.pVal[i] << shift); |
| if (Count == highWordBits) { |
| for (i--; i >= 0; --i) { |
| if (U.pVal[i] == WORDTYPE_MAX) |
| Count += APINT_BITS_PER_WORD; |
| else { |
| Count += llvm::countLeadingOnes(U.pVal[i]); |
| break; |
| } |
| } |
| } |
| return Count; |
| } |
| |
| unsigned APInt::countTrailingZerosSlowCase() const { |
| unsigned Count = 0; |
| unsigned i = 0; |
| for (; i < getNumWords() && U.pVal[i] == 0; ++i) |
| Count += APINT_BITS_PER_WORD; |
| if (i < getNumWords()) |
| Count += llvm::countTrailingZeros(U.pVal[i]); |
| return std::min(Count, BitWidth); |
| } |
| |
| unsigned APInt::countTrailingOnesSlowCase() const { |
| unsigned Count = 0; |
| unsigned i = 0; |
| for (; i < getNumWords() && U.pVal[i] == WORDTYPE_MAX; ++i) |
| Count += APINT_BITS_PER_WORD; |
| if (i < getNumWords()) |
| Count += llvm::countTrailingOnes(U.pVal[i]); |
| assert(Count <= BitWidth); |
| return Count; |
| } |
| |
| unsigned APInt::countPopulationSlowCase() const { |
| unsigned Count = 0; |
| for (unsigned i = 0; i < getNumWords(); ++i) |
| Count += llvm::countPopulation(U.pVal[i]); |
| return Count; |
| } |
| |
| bool APInt::intersectsSlowCase(const APInt &RHS) const { |
| for (unsigned i = 0, e = getNumWords(); i != e; ++i) |
| if ((U.pVal[i] & RHS.U.pVal[i]) != 0) |
| return true; |
| |
| return false; |
| } |
| |
| bool APInt::isSubsetOfSlowCase(const APInt &RHS) const { |
| for (unsigned i = 0, e = getNumWords(); i != e; ++i) |
| if ((U.pVal[i] & ~RHS.U.pVal[i]) != 0) |
| return false; |
| |
| return true; |
| } |
| |
| APInt APInt::byteSwap() const { |
| assert(BitWidth >= 16 && BitWidth % 8 == 0 && "Cannot byteswap!"); |
| if (BitWidth == 16) |
| return APInt(BitWidth, ByteSwap_16(uint16_t(U.VAL))); |
| if (BitWidth == 32) |
| return APInt(BitWidth, ByteSwap_32(unsigned(U.VAL))); |
| if (BitWidth <= 64) { |
| uint64_t Tmp1 = ByteSwap_64(U.VAL); |
| Tmp1 >>= (64 - BitWidth); |
| return APInt(BitWidth, Tmp1); |
| } |
| |
| APInt Result(getNumWords() * APINT_BITS_PER_WORD, 0); |
| for (unsigned I = 0, N = getNumWords(); I != N; ++I) |
| Result.U.pVal[I] = ByteSwap_64(U.pVal[N - I - 1]); |
| if (Result.BitWidth != BitWidth) { |
| Result.lshrInPlace(Result.BitWidth - BitWidth); |
| Result.BitWidth = BitWidth; |
| } |
| return Result; |
| } |
| |
| APInt APInt::reverseBits() const { |
| switch (BitWidth) { |
| case 64: |
| return APInt(BitWidth, llvm::reverseBits<uint64_t>(U.VAL)); |
| case 32: |
| return APInt(BitWidth, llvm::reverseBits<uint32_t>(U.VAL)); |
| case 16: |
| return APInt(BitWidth, llvm::reverseBits<uint16_t>(U.VAL)); |
| case 8: |
| return APInt(BitWidth, llvm::reverseBits<uint8_t>(U.VAL)); |
| case 0: |
| return *this; |
| default: |
| break; |
| } |
| |
| APInt Val(*this); |
| APInt Reversed(BitWidth, 0); |
| unsigned S = BitWidth; |
| |
| for (; Val != 0; Val.lshrInPlace(1)) { |
| Reversed <<= 1; |
| Reversed |= Val[0]; |
| --S; |
| } |
| |
| Reversed <<= S; |
| return Reversed; |
| } |
| |
| APInt llvm::APIntOps::GreatestCommonDivisor(APInt A, APInt B) { |
| // Fast-path a common case. |
| if (A == B) return A; |
| |
| // Corner cases: if either operand is zero, the other is the gcd. |
| if (!A) return B; |
| if (!B) return A; |
| |
| // Count common powers of 2 and remove all other powers of 2. |
| unsigned Pow2; |
| { |
| unsigned Pow2_A = A.countTrailingZeros(); |
| unsigned Pow2_B = B.countTrailingZeros(); |
| if (Pow2_A > Pow2_B) { |
| A.lshrInPlace(Pow2_A - Pow2_B); |
| Pow2 = Pow2_B; |
| } else if (Pow2_B > Pow2_A) { |
| B.lshrInPlace(Pow2_B - Pow2_A); |
| Pow2 = Pow2_A; |
| } else { |
| Pow2 = Pow2_A; |
| } |
| } |
| |
| // Both operands are odd multiples of 2^Pow_2: |
| // |
| // gcd(a, b) = gcd(|a - b| / 2^i, min(a, b)) |
| // |
| // This is a modified version of Stein's algorithm, taking advantage of |
| // efficient countTrailingZeros(). |
| while (A != B) { |
| if (A.ugt(B)) { |
| A -= B; |
| A.lshrInPlace(A.countTrailingZeros() - Pow2); |
| } else { |
| B -= A; |
| B.lshrInPlace(B.countTrailingZeros() - Pow2); |
| } |
| } |
| |
| return A; |
| } |
| |
| APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) { |
| uint64_t I = bit_cast<uint64_t>(Double); |
| |
| // Get the sign bit from the highest order bit |
| bool isNeg = I >> 63; |
| |
| // Get the 11-bit exponent and adjust for the 1023 bit bias |
| int64_t exp = ((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 = (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 <<= (unsigned)exp - 52; |
| return isNeg ? -Tmp : Tmp; |
| } |
| |
| /// 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 = SignExtend64(getWord(0), 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.U.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.U.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD); |
| uint64_t lobits = Tmp.U.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; |
| uint64_t I = sign | (exp << 52) | mantissa; |
| return bit_cast<double>(I); |
| } |
| |
| // Truncate to new width. |
| APInt APInt::trunc(unsigned width) const { |
| assert(width < BitWidth && "Invalid APInt Truncate request"); |
| |
| 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.U.pVal[i] = U.pVal[i]; |
| |
| // Truncate and copy any partial word. |
| unsigned bits = (0 - width) % APINT_BITS_PER_WORD; |
| if (bits != 0) |
| Result.U.pVal[i] = U.pVal[i] << bits >> bits; |
| |
| return Result; |
| } |
| |
| // Truncate to new width with unsigned saturation. |
| APInt APInt::truncUSat(unsigned width) const { |
| assert(width < BitWidth && "Invalid APInt Truncate request"); |
| |
| // Can we just losslessly truncate it? |
| if (isIntN(width)) |
| return trunc(width); |
| // If not, then just return the new limit. |
| return APInt::getMaxValue(width); |
| } |
| |
| // Truncate to new width with signed saturation. |
| APInt APInt::truncSSat(unsigned width) const { |
| assert(width < BitWidth && "Invalid APInt Truncate request"); |
| |
| // Can we just losslessly truncate it? |
| if (isSignedIntN(width)) |
| return trunc(width); |
| // If not, then just return the new limits. |
| return isNegative() ? APInt::getSignedMinValue(width) |
| : APInt::getSignedMaxValue(width); |
| } |
| |
| // 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) |
| return APInt(Width, SignExtend64(U.VAL, BitWidth)); |
| |
| APInt Result(getMemory(getNumWords(Width)), Width); |
| |
| // Copy words. |
| std::memcpy(Result.U.pVal, getRawData(), getNumWords() * APINT_WORD_SIZE); |
| |
| // Sign extend the last word since there may be unused bits in the input. |
| Result.U.pVal[getNumWords() - 1] = |
| SignExtend64(Result.U.pVal[getNumWords() - 1], |
| ((BitWidth - 1) % APINT_BITS_PER_WORD) + 1); |
| |
| // Fill with sign bits. |
| std::memset(Result.U.pVal + getNumWords(), isNegative() ? -1 : 0, |
| (Result.getNumWords() - getNumWords()) * APINT_WORD_SIZE); |
| Result.clearUnusedBits(); |
| 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, U.VAL); |
| |
| APInt Result(getMemory(getNumWords(width)), width); |
| |
| // Copy words. |
| std::memcpy(Result.U.pVal, getRawData(), getNumWords() * APINT_WORD_SIZE); |
| |
| // Zero remaining words. |
| std::memset(Result.U.pVal + getNumWords(), 0, |
| (Result.getNumWords() - getNumWords()) * 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::truncOrSelf(unsigned width) const { |
| 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. |
| /// Arithmetic right-shift function. |
| void APInt::ashrInPlace(const APInt &shiftAmt) { |
| ashrInPlace((unsigned)shiftAmt.getLimitedValue(BitWidth)); |
| } |
| |
| /// Arithmetic right-shift this APInt by shiftAmt. |
| /// Arithmetic right-shift function. |
| void APInt::ashrSlowCase(unsigned ShiftAmt) { |
| // Don't bother performing a no-op shift. |
| if (!ShiftAmt) |
| return; |
| |
| // Save the original sign bit for later. |
| bool Negative = isNegative(); |
| |
| // WordShift is the inter-part shift; BitShift is intra-part shift. |
| unsigned WordShift = ShiftAmt / APINT_BITS_PER_WORD; |
| unsigned BitShift = ShiftAmt % APINT_BITS_PER_WORD; |
| |
| unsigned WordsToMove = getNumWords() - WordShift; |
| if (WordsToMove != 0) { |
| // Sign extend the last word to fill in the unused bits. |
| U.pVal[getNumWords() - 1] = SignExtend64( |
| U.pVal[getNumWords() - 1], ((BitWidth - 1) % APINT_BITS_PER_WORD) + 1); |
| |
| // Fastpath for moving by whole words. |
| if (BitShift == 0) { |
| std::memmove(U.pVal, U.pVal + WordShift, WordsToMove * APINT_WORD_SIZE); |
| } else { |
| // Move the words containing significant bits. |
| for (unsigned i = 0; i != WordsToMove - 1; ++i) |
| U.pVal[i] = (U.pVal[i + WordShift] >> BitShift) | |
| (U.pVal[i + WordShift + 1] << (APINT_BITS_PER_WORD - BitShift)); |
| |
| // Handle the last word which has no high bits to copy. |
| U.pVal[WordsToMove - 1] = U.pVal[WordShift + WordsToMove - 1] >> BitShift; |
| // Sign extend one more time. |
| U.pVal[WordsToMove - 1] = |
| SignExtend64(U.pVal[WordsToMove - 1], APINT_BITS_PER_WORD - BitShift); |
| } |
| } |
| |
| // Fill in the remainder based on the original sign. |
| std::memset(U.pVal + WordsToMove, Negative ? -1 : 0, |
| WordShift * APINT_WORD_SIZE); |
| clearUnusedBits(); |
| } |
| |
| /// Logical right-shift this APInt by shiftAmt. |
| /// Logical right-shift function. |
| void APInt::lshrInPlace(const APInt &shiftAmt) { |
| lshrInPlace((unsigned)shiftAmt.getLimitedValue(BitWidth)); |
| } |
| |
| /// Logical right-shift this APInt by shiftAmt. |
| /// Logical right-shift function. |
| void APInt::lshrSlowCase(unsigned ShiftAmt) { |
| tcShiftRight(U.pVal, getNumWords(), ShiftAmt); |
| } |
| |
| /// Left-shift this APInt by shiftAmt. |
| /// Left-shift function. |
| APInt &APInt::operator<<=(const APInt &shiftAmt) { |
| // It's undefined behavior in C to shift by BitWidth or greater. |
| *this <<= (unsigned)shiftAmt.getLimitedValue(BitWidth); |
| return *this; |
| } |
| |
| void APInt::shlSlowCase(unsigned ShiftAmt) { |
| tcShiftLeft(U.pVal, getNumWords(), ShiftAmt); |
| clearUnusedBits(); |
| } |
| |
| // Calculate the rotate amount modulo the bit width. |
| static unsigned rotateModulo(unsigned BitWidth, const APInt &rotateAmt) { |
| if (LLVM_UNLIKELY(BitWidth == 0)) |
| return 0; |
| unsigned rotBitWidth = rotateAmt.getBitWidth(); |
| APInt rot = rotateAmt; |
| if (rotBitWidth < BitWidth) { |
| // Extend the rotate APInt, so that the urem doesn't divide by 0. |
| // e.g. APInt(1, 32) would give APInt(1, 0). |
| rot = rotateAmt.zext(BitWidth); |
| } |
| rot = rot.urem(APInt(rot.getBitWidth(), BitWidth)); |
| return rot.getLimitedValue(BitWidth); |
| } |
| |
| APInt APInt::rotl(const APInt &rotateAmt) const { |
| return rotl(rotateModulo(BitWidth, rotateAmt)); |
| } |
| |
| APInt APInt::rotl(unsigned rotateAmt) const { |
| if (LLVM_UNLIKELY(BitWidth == 0)) |
| return *this; |
| rotateAmt %= BitWidth; |
| if (rotateAmt == 0) |
| return *this; |
| return shl(rotateAmt) | lshr(BitWidth - rotateAmt); |
| } |
| |
| APInt APInt::rotr(const APInt &rotateAmt) const { |
| return rotr(rotateModulo(BitWidth, rotateAmt)); |
| } |
| |
| APInt APInt::rotr(unsigned rotateAmt) const { |
| if (BitWidth == 0) |
| return *this; |
| rotateAmt %= BitWidth; |
| if (rotateAmt == 0) |
| return *this; |
| return lshr(rotateAmt) | shl(BitWidth - rotateAmt); |
| } |
| |
| /// \returns the nearest log base 2 of this APInt. Ties round up. |
| /// |
| /// NOTE: When we have a BitWidth of 1, we define: |
| /// |
| /// log2(0) = UINT32_MAX |
| /// log2(1) = 0 |
| /// |
| /// to get around any mathematical concerns resulting from |
| /// referencing 2 in a space where 2 does no exist. |
| unsigned APInt::nearestLogBase2() const { |
| // Special case when we have a bitwidth of 1. If VAL is 1, then we |
| // get 0. If VAL is 0, we get WORDTYPE_MAX which gets truncated to |
| // UINT32_MAX. |
| if (BitWidth == 1) |
| return U.VAL - 1; |
| |
| // Handle the zero case. |
| if (isZero()) |
| return UINT32_MAX; |
| |
| // The non-zero case is handled by computing: |
| // |
| // nearestLogBase2(x) = logBase2(x) + x[logBase2(x)-1]. |
| // |
| // where x[i] is referring to the value of the ith bit of x. |
| unsigned lg = logBase2(); |
| return lg + unsigned((*this)[lg - 1]); |
| } |
| |
| // 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() ? U.VAL : U.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) { |
| return APInt(BitWidth, |
| uint64_t(::round(::sqrt(double(isSingleWord() ? U.VAL |
| : U.pVal[0]))))); |
| } |
| |
| // 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. |
| /// WARNING: a value of '0' may be returned, |
| /// signifying that no multiplicative inverse exists! |
| 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. Calculate 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). |
| if (t[i].isNegative()) |
| t[i] += modulo; |
| |
| return std::move(t[i]); |
| } |
| |
| /// 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(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* 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 use different memory"); |
| assert(n>1 && "n must be > 1"); |
| |
| // b denotes the base of the number system. In our case b is 2^32. |
| const uint64_t b = uint64_t(1) << 32; |
| |
| // The DEBUG macros here tend to be spam in the debug output if you're not |
| // debugging this code. Disable them unless KNUTH_DEBUG is defined. |
| #ifdef KNUTH_DEBUG |
| #define DEBUG_KNUTH(X) LLVM_DEBUG(X) |
| #else |
| #define DEBUG_KNUTH(X) do {} while(false) |
| #endif |
| |
| DEBUG_KNUTH(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n'); |
| DEBUG_KNUTH(dbgs() << "KnuthDiv: original:"); |
| DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]); |
| DEBUG_KNUTH(dbgs() << " by"); |
| DEBUG_KNUTH(for (int i = n; i > 0; i--) dbgs() << " " << v[i - 1]); |
| DEBUG_KNUTH(dbgs() << '\n'); |
| // 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]); |
| uint32_t v_carry = 0; |
| uint32_t u_carry = 0; |
| if (shift) { |
| for (unsigned i = 0; i < m+n; ++i) { |
| uint32_t u_tmp = u[i] >> (32 - shift); |
| u[i] = (u[i] << shift) | u_carry; |
| u_carry = u_tmp; |
| } |
| for (unsigned i = 0; i < n; ++i) { |
| uint32_t v_tmp = v[i] >> (32 - shift); |
| v[i] = (v[i] << shift) | v_carry; |
| v_carry = v_tmp; |
| } |
| } |
| u[m+n] = u_carry; |
| |
| DEBUG_KNUTH(dbgs() << "KnuthDiv: normal:"); |
| DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]); |
| DEBUG_KNUTH(dbgs() << " by"); |
| DEBUG_KNUTH(for (int i = n; i > 0; i--) dbgs() << " " << v[i - 1]); |
| DEBUG_KNUTH(dbgs() << '\n'); |
| |
| // D2. [Initialize j.] Set j to m. This is the loop counter over the places. |
| int j = m; |
| do { |
| DEBUG_KNUTH(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, increase 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 = Make_64(u[j+n], u[j+n-1]); |
| DEBUG_KNUTH(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_KNUTH(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. |
| // 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. |
| int64_t borrow = 0; |
| for (unsigned i = 0; i < n; ++i) { |
| uint64_t p = uint64_t(qp) * uint64_t(v[i]); |
| int64_t subres = int64_t(u[j+i]) - borrow - Lo_32(p); |
| u[j+i] = Lo_32(subres); |
| borrow = Hi_32(p) - Hi_32(subres); |
| DEBUG_KNUTH(dbgs() << "KnuthDiv: u[j+i] = " << u[j + i] |
| << ", borrow = " << borrow << '\n'); |
| } |
| bool isNeg = u[j+n] < borrow; |
| u[j+n] -= Lo_32(borrow); |
| |
| DEBUG_KNUTH(dbgs() << "KnuthDiv: after subtraction:"); |
| DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]); |
| DEBUG_KNUTH(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] = Lo_32(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++) { |
| uint32_t 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_KNUTH(dbgs() << "KnuthDiv: after correction:"); |
| DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]); |
| DEBUG_KNUTH(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_KNUTH(dbgs() << "KnuthDiv: quotient:"); |
| DEBUG_KNUTH(for (int i = m; i >= 0; i--) dbgs() << " " << q[i]); |
| DEBUG_KNUTH(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. |
| if (shift) { |
| uint32_t carry = 0; |
| DEBUG_KNUTH(dbgs() << "KnuthDiv: remainder:"); |
| for (int i = n-1; i >= 0; i--) { |
| r[i] = (u[i] >> shift) | carry; |
| carry = u[i] << (32 - shift); |
| DEBUG_KNUTH(dbgs() << " " << r[i]); |
| } |
| } else { |
| for (int i = n-1; i >= 0; i--) { |
| r[i] = u[i]; |
| DEBUG_KNUTH(dbgs() << " " << r[i]); |
| } |
| } |
| DEBUG_KNUTH(dbgs() << '\n'); |
| } |
| DEBUG_KNUTH(dbgs() << '\n'); |
| } |
| |
| void APInt::divide(const WordType *LHS, unsigned lhsWords, const WordType *RHS, |
| unsigned rhsWords, WordType *Quotient, WordType *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. |
| 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. |
| uint32_t SPACE[128]; |
| uint32_t *U = nullptr; |
| uint32_t *V = nullptr; |
| uint32_t *Q = nullptr; |
| uint32_t *R = nullptr; |
| 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 uint32_t[m + n + 1]; |
| V = new uint32_t[n]; |
| Q = new uint32_t[m+n]; |
| if (Remainder) |
| R = new uint32_t[n]; |
| } |
| |
| // Initialize the dividend |
| memset(U, 0, (m+n+1)*sizeof(uint32_t)); |
| for (unsigned i = 0; i < lhsWords; ++i) { |
| uint64_t tmp = LHS[i]; |
| U[i * 2] = Lo_32(tmp); |
| U[i * 2 + 1] = Hi_32(tmp); |
| } |
| U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm. |
| |
| // Initialize the divisor |
| memset(V, 0, (n)*sizeof(uint32_t)); |
| for (unsigned i = 0; i < rhsWords; ++i) { |
| uint64_t tmp = RHS[i]; |
| V[i * 2] = Lo_32(tmp); |
| V[i * 2 + 1] = Hi_32(tmp); |
| } |
| |
| // initialize the quotient and remainder |
| memset(Q, 0, (m+n) * sizeof(uint32_t)); |
| if (Remainder) |
| memset(R, 0, n * sizeof(uint32_t)); |
| |
| // 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) { |
| uint32_t divisor = V[0]; |
| uint32_t remainder = 0; |
| for (int i = m; i >= 0; i--) { |
| uint64_t partial_dividend = Make_64(remainder, U[i]); |
| if (partial_dividend == 0) { |
| Q[i] = 0; |
| remainder = 0; |
| } else if (partial_dividend < divisor) { |
| Q[i] = 0; |
| remainder = Lo_32(partial_dividend); |
| } else if (partial_dividend == divisor) { |
| Q[i] = 1; |
| remainder = 0; |
| } else { |
| Q[i] = Lo_32(partial_dividend / divisor); |
| remainder = Lo_32(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) { |
| for (unsigned i = 0; i < lhsWords; ++i) |
| Quotient[i] = Make_64(Q[i*2+1], Q[i*2]); |
| } |
| |
| // If the caller wants the remainder |
| if (Remainder) { |
| for (unsigned i = 0; i < rhsWords; ++i) |
| Remainder[i] = Make_64(R[i*2+1], R[i*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.U.VAL != 0 && "Divide by zero?"); |
| return APInt(BitWidth, U.VAL / RHS.U.VAL); |
| } |
| |
| // Get some facts about the LHS and RHS number of bits and words |
| unsigned lhsWords = getNumWords(getActiveBits()); |
| unsigned rhsBits = RHS.getActiveBits(); |
| unsigned rhsWords = getNumWords(rhsBits); |
| assert(rhsWords && "Divided by zero???"); |
| |
| // Deal with some degenerate cases |
| if (!lhsWords) |
| // 0 / X ===> 0 |
| return APInt(BitWidth, 0); |
| if (rhsBits == 1) |
| // X / 1 ===> X |
| return *this; |
| if (lhsWords < rhsWords || this->ult(RHS)) |
| // X / Y ===> 0, iff X < Y |
| return APInt(BitWidth, 0); |
| if (*this == RHS) |
| // X / X ===> 1 |
| return APInt(BitWidth, 1); |
| if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1. |
| // All high words are zero, just use native divide |
| return APInt(BitWidth, this->U.pVal[0] / RHS.U.pVal[0]); |
| |
| // We have to compute it the hard way. Invoke the Knuth divide algorithm. |
| APInt Quotient(BitWidth, 0); // to hold result. |
| divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal, nullptr); |
| return Quotient; |
| } |
| |
| APInt APInt::udiv(uint64_t RHS) const { |
| assert(RHS != 0 && "Divide by zero?"); |
| |
| // First, deal with the easy case |
| if (isSingleWord()) |
| return APInt(BitWidth, U.VAL / RHS); |
| |
| // Get some facts about the LHS words. |
| unsigned lhsWords = getNumWords(getActiveBits()); |
| |
| // Deal with some degenerate cases |
| if (!lhsWords) |
| // 0 / X ===> 0 |
| return APInt(BitWidth, 0); |
| if (RHS == 1) |
| // X / 1 ===> X |
| return *this; |
| if (this->ult(RHS)) |
| // X / Y ===> 0, iff X < Y |
| return APInt(BitWidth, 0); |
| if (*this == RHS) |
| // X / X ===> 1 |
| return APInt(BitWidth, 1); |
| if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1. |
| // All high words are zero, just use native divide |
| return APInt(BitWidth, this->U.pVal[0] / RHS); |
| |
| // We have to compute it the hard way. Invoke the Knuth divide algorithm. |
| APInt Quotient(BitWidth, 0); // to hold result. |
| divide(U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, nullptr); |
| 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::sdiv(int64_t RHS) const { |
| if (isNegative()) { |
| if (RHS < 0) |
| return (-(*this)).udiv(-RHS); |
| return -((-(*this)).udiv(RHS)); |
| } |
| if (RHS < 0) |
| 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.U.VAL != 0 && "Remainder by zero?"); |
| return APInt(BitWidth, U.VAL % RHS.U.VAL); |
| } |
| |
| // Get some facts about the LHS |
| unsigned lhsWords = getNumWords(getActiveBits()); |
| |
| // Get some facts about the RHS |
| unsigned rhsBits = RHS.getActiveBits(); |
| unsigned rhsWords = getNumWords(rhsBits); |
| assert(rhsWords && "Performing remainder operation by zero ???"); |
| |
| // Check the degenerate cases |
| if (lhsWords == 0) |
| // 0 % Y ===> 0 |
| return APInt(BitWidth, 0); |
| if (rhsBits == 1) |
| // X % 1 ===> 0 |
| return APInt(BitWidth, 0); |
| if (lhsWords < rhsWords || this->ult(RHS)) |
| // X % Y ===> X, iff X < Y |
| return *this; |
| if (*this == RHS) |
| // X % X == 0; |
| return APInt(BitWidth, 0); |
| if (lhsWords == 1) |
| // All high words are zero, just use native remainder |
| return APInt(BitWidth, U.pVal[0] % RHS.U.pVal[0]); |
| |
| // We have to compute it the hard way. Invoke the Knuth divide algorithm. |
| APInt Remainder(BitWidth, 0); |
| divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, nullptr, Remainder.U.pVal); |
| return Remainder; |
| } |
| |
| uint64_t APInt::urem(uint64_t RHS) const { |
| assert(RHS != 0 && "Remainder by zero?"); |
| |
| if (isSingleWord()) |
| return U.VAL % RHS; |
| |
| // Get some facts about the LHS |
| unsigned lhsWords = getNumWords(getActiveBits()); |
| |
| // Check the degenerate cases |
| if (lhsWords == 0) |
| // 0 % Y ===> 0 |
| return 0; |
| if (RHS == 1) |
| // X % 1 ===> 0 |
| return 0; |
| if (this->ult(RHS)) |
| // X % Y ===> X, iff X < Y |
| return getZExtValue(); |
| if (*this == RHS) |
| // X % X == 0; |
| return 0; |
| if (lhsWords == 1) |
| // All high words are zero, just use native remainder |
| return U.pVal[0] % RHS; |
| |
| // We have to compute it the hard way. Invoke the Knuth divide algorithm. |
| uint64_t Remainder; |
| divide(U.pVal, lhsWords, &RHS, 1, nullptr, &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); |
| } |
| |
| int64_t APInt::srem(int64_t RHS) const { |
| if (isNegative()) { |
| if (RHS < 0) |
| return -((-(*this)).urem(-RHS)); |
| return -((-(*this)).urem(RHS)); |
| } |
| if (RHS < 0) |
| return this->urem(-RHS); |
| return this->urem(RHS); |
| } |
| |
| void APInt::udivrem(const APInt &LHS, const APInt &RHS, |
| APInt &Quotient, APInt &Remainder) { |
| assert(LHS.BitWidth == RHS.BitWidth && "Bit widths must be the same"); |
| unsigned BitWidth = LHS.BitWidth; |
| |
| // First, deal with the easy case |
| if (LHS.isSingleWord()) { |
| assert(RHS.U.VAL != 0 && "Divide by zero?"); |
| uint64_t QuotVal = LHS.U.VAL / RHS.U.VAL; |
| uint64_t RemVal = LHS.U.VAL % RHS.U.VAL; |
| Quotient = APInt(BitWidth, QuotVal); |
| Remainder = APInt(BitWidth, RemVal); |
| return; |
| } |
| |
| // Get some size facts about the dividend and divisor |
| unsigned lhsWords = getNumWords(LHS.getActiveBits()); |
| unsigned rhsBits = RHS.getActiveBits(); |
| unsigned rhsWords = getNumWords(rhsBits); |
| assert(rhsWords && "Performing divrem operation by zero ???"); |
| |
| // Check the degenerate cases |
| if (lhsWords == 0) { |
| Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0 |
| Remainder = APInt(BitWidth, 0); // 0 % Y ===> 0 |
| return; |
| } |
| |
| if (rhsBits == 1) { |
| Quotient = LHS; // X / 1 ===> X |
| Remainder = APInt(BitWidth, 0); // X % 1 ===> 0 |
| } |
| |
| if (lhsWords < rhsWords || LHS.ult(RHS)) { |
| Remainder = LHS; // X % Y ===> X, iff X < Y |
| Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y |
| return; |
| } |
| |
| if (LHS == RHS) { |
| Quotient = APInt(BitWidth, 1); // X / X ===> 1 |
| Remainder = APInt(BitWidth, 0); // X % X ===> 0; |
| return; |
| } |
| |
| // Make sure there is enough space to hold the results. |
| // NOTE: This assumes that reallocate won't affect any bits if it doesn't |
| // change the size. This is necessary if Quotient or Remainder is aliased |
| // with LHS or RHS. |
| Quotient.reallocate(BitWidth); |
| Remainder.reallocate(BitWidth); |
| |
| if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1. |
| // There is only one word to consider so use the native versions. |
| uint64_t lhsValue = LHS.U.pVal[0]; |
| uint64_t rhsValue = RHS.U.pVal[0]; |
| Quotient = lhsValue / rhsValue; |
| Remainder = lhsValue % rhsValue; |
| return; |
| } |
| |
| // Okay, lets do it the long way |
| divide(LHS.U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal, |
| Remainder.U.pVal); |
| // Clear the rest of the Quotient and Remainder. |
| std::memset(Quotient.U.pVal + lhsWords, 0, |
| (getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE); |
| std::memset(Remainder.U.pVal + rhsWords, 0, |
| (getNumWords(BitWidth) - rhsWords) * APINT_WORD_SIZE); |
| } |
| |
| void APInt::udivrem(const APInt &LHS, uint64_t RHS, APInt &Quotient, |
| uint64_t &Remainder) { |
| assert(RHS != 0 && "Divide by zero?"); |
| unsigned BitWidth = LHS.BitWidth; |
| |
| // First, deal with the easy case |
| if (LHS.isSingleWord()) { |
| uint64_t QuotVal = LHS.U.VAL / RHS; |
| Remainder = LHS.U.VAL % RHS; |
| Quotient = APInt(BitWidth, QuotVal); |
| return; |
| } |
| |
| // Get some size facts about the dividend and divisor |
| unsigned lhsWords = getNumWords(LHS.getActiveBits()); |
| |
| // Check the degenerate cases |
| if (lhsWords == 0) { |
| Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0 |
| Remainder = 0; // 0 % Y ===> 0 |
| return; |
| } |
| |
| if (RHS == 1) { |
| Quotient = LHS; // X / 1 ===> X |
| Remainder = 0; // X % 1 ===> 0 |
| return; |
| } |
| |
| if (LHS.ult(RHS)) { |
| Remainder = LHS.getZExtValue(); // X % Y ===> X, iff X < Y |
| Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y |
| return; |
| } |
| |
| if (LHS == RHS) { |
| Quotient = APInt(BitWidth, 1); // X / X ===> 1 |
| Remainder = 0; // X % X ===> 0; |
| return; |
| } |
| |
| // Make sure there is enough space to hold the results. |
| // NOTE: This assumes that reallocate won't affect any bits if it doesn't |
| // change the size. This is necessary if Quotient is aliased with LHS. |
| Quotient.reallocate(BitWidth); |
| |
| if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1. |
| // There is only one word to consider so use the native versions. |
| uint64_t lhsValue = LHS.U.pVal[0]; |
| Quotient = lhsValue / RHS; |
| Remainder = lhsValue % RHS; |
| return; |
| } |
| |
| // Okay, lets do it the long way |
| divide(LHS.U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, &Remainder); |
| // Clear the rest of the Quotient. |
| std::memset(Quotient.U.pVal + lhsWords, 0, |
| (getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE); |
| } |
| |
| 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.negate(); |
| } |
| Remainder.negate(); |
| } else if (RHS.isNegative()) { |
| APInt::udivrem(LHS, -RHS, Quotient, Remainder); |
| Quotient.negate(); |
| } else { |
| APInt::udivrem(LHS, RHS, Quotient, Remainder); |
| } |
| } |
| |
| void APInt::sdivrem(const APInt &LHS, int64_t RHS, |
| APInt &Quotient, int64_t &Remainder) { |
| uint64_t R = Remainder; |
| if (LHS.isNegative()) { |
| if (RHS < 0) |
| APInt::udivrem(-LHS, -RHS, Quotient, R); |
| else { |
| APInt::udivrem(-LHS, RHS, Quotient, R); |
| Quotient.negate(); |
| } |
| R = -R; |
| } else if (RHS < 0) { |
| APInt::udivrem(LHS, -RHS, Quotient, R); |
| Quotient.negate(); |
| } else { |
| APInt::udivrem(LHS, RHS, Quotient, R); |
| } |
| Remainder = R; |
| } |
| |
| 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.isAllOnes(); |
| return sdiv(RHS); |
| } |
| |
| APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const { |
| APInt Res = *this * RHS; |
| |
| if (RHS != 0) |
| Overflow = Res.sdiv(RHS) != *this || |
| (isMinSignedValue() && RHS.isAllOnes()); |
| else |
| Overflow = false; |
| return Res; |
| } |
| |
| APInt APInt::umul_ov(const APInt &RHS, bool &Overflow) const { |
| if (countLeadingZeros() + RHS.countLeadingZeros() + 2 <= BitWidth) { |
| Overflow = true; |
| return *this * RHS; |
| } |
| |
| APInt Res = lshr(1) * RHS; |
| Overflow = Res.isNegative(); |
| Res <<= 1; |
| if ((*this)[0]) { |
| Res += RHS; |
| if (Res.ult(RHS)) |
| Overflow = true; |
| } |
| return Res; |
| } |
| |
| APInt APInt::sshl_ov(const APInt &ShAmt, bool &Overflow) const { |
| Overflow = ShAmt.uge(getBitWidth()); |
| if (Overflow) |
| return APInt(BitWidth, 0); |
| |
| if (isNonNegative()) // Don't allow sign change. |
| Overflow = ShAmt.uge(countLeadingZeros()); |
| else |
| Overflow = ShAmt.uge(countLeadingOnes()); |
| |
| return *this << ShAmt; |
| } |
| |
| APInt APInt::ushl_ov(const APInt &ShAmt, bool &Overflow) const { |
| Overflow = ShAmt.uge(getBitWidth()); |
| if (Overflow) |
| return APInt(BitWidth, 0); |
| |
| Overflow = ShAmt.ugt(countLeadingZeros()); |
| |
| return *this << ShAmt; |
| } |
| |
| APInt APInt::sadd_sat(const APInt &RHS) const { |
| bool Overflow; |
| APInt Res = sadd_ov(RHS, Overflow); |
| if (!Overflow) |
| return Res; |
| |
| return isNegative() ? APInt::getSignedMinValue(BitWidth) |
| : APInt::getSignedMaxValue(BitWidth); |
| } |
| |
| APInt APInt::uadd_sat(const APInt &RHS) const { |
| bool Overflow; |
| APInt Res = uadd_ov(RHS, Overflow); |
| if (!Overflow) |
| return Res; |
| |
| return APInt::getMaxValue(BitWidth); |
| } |
| |
| APInt APInt::ssub_sat(const APInt &RHS) const { |
| bool Overflow; |
| APInt Res = ssub_ov(RHS, Overflow); |
| if (!Overflow) |
| return Res; |
| |
| return isNegative() ? APInt::getSignedMinValue(BitWidth) |
| : APInt::getSignedMaxValue(BitWidth); |
| } |
| |
| APInt APInt::usub_sat(const APInt &RHS) const { |
| bool Overflow; |
| APInt Res = usub_ov(RHS, Overflow); |
| if (!Overflow) |
| return Res; |
| |
| return APInt(BitWidth, 0); |
| } |
| |
| APInt APInt::smul_sat(const APInt &RHS) const { |
| bool Overflow; |
| APInt Res = smul_ov(RHS, Overflow); |
| if (!Overflow) |
| return Res; |
| |
| // The result is negative if one and only one of inputs is negative. |
| bool ResIsNegative = isNegative() ^ RHS.isNegative(); |
| |
| return ResIsNegative ? APInt::getSignedMinValue(BitWidth) |
| : APInt::getSignedMaxValue(BitWidth); |
| } |
| |
| APInt APInt::umul_sat(const APInt &RHS) const { |
| bool Overflow; |
| APInt Res = umul_ov(RHS, Overflow); |
| if (!Overflow) |
| return Res; |
| |
| return APInt::getMaxValue(BitWidth); |
| } |
| |
| APInt APInt::sshl_sat(const APInt &RHS) const { |
| bool Overflow; |
| APInt Res = sshl_ov(RHS, Overflow); |
| if (!Overflow) |
| return Res; |
| |
| return isNegative() ? APInt::getSignedMinValue(BitWidth) |
| : APInt::getSignedMaxValue(BitWidth); |
| } |
| |
| APInt APInt::ushl_sat(const APInt &RHS) const { |
| bool Overflow; |
| APInt Res = ushl_ov(RHS, Overflow); |
| if (!Overflow) |
| return Res; |
| |
| return APInt::getMaxValue(BitWidth); |
| } |
| |
| 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 needed |
| if (isSingleWord()) |
| U.VAL = 0; |
| else |
| U.pVal = getClearedMemory(getNumWords()); |
| |
| // Figure out if we can shift instead of multiply |
| unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0); |
| |
| // 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 *= radix; |
| } |
| |
| // Add in the digit we just interpreted |
| *this += digit; |
| } |
| // If its negative, put it in two's complement form |
| if (isNeg) |
| this->negate(); |
| } |
| |
| 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 (isZero()) { |
| while (*Prefix) { |
| Str.push_back(*Prefix); |
| ++Prefix; |
| }; |
| Str.push_back('0'); |
| return; |
| } |
| |
| static const char Digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; |
| |
| if (isSingleWord()) { |
| char Buffer[65]; |
| char *BufPtr = std::end(Buffer); |
| |
| 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, std::end(Buffer)); |
| 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.negate(); |
| 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 |
| // equally. 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.getBoolValue()) { |
| unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt; |
| Str.push_back(Digits[Digit]); |
| Tmp.lshrInPlace(ShiftAmt); |
| } |
| } else { |
| while (Tmp.getBoolValue()) { |
| uint64_t Digit; |
| udivrem(Tmp, Radix, Tmp, Digit); |
| assert(Digit < Radix && "divide failed"); |
| Str.push_back(Digits[Digit]); |
| } |
| } |
| |
| // Reverse the digits before returning. |
| std::reverse(Str.begin()+StartDig, Str.end()); |
| } |
| |
| #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP) |
| LLVM_DUMP_METHOD void APInt::dump() const { |
| SmallString<40> S, U; |
| this->toStringUnsigned(U); |
| this->toStringSigned(S); |
| dbgs() << "APInt(" << BitWidth << "b, " |
| << U << "u " << S << "s)\n"; |
| } |
| #endif |
| |
| void APInt::print(raw_ostream &OS, bool isSigned) const { |
| SmallString<40> S; |
| this->toString(S, 10, isSigned, /* formatAsCLiteral = */false); |
| OS << S; |
| } |
| |
| // 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. |
| static_assert(APInt::APINT_BITS_PER_WORD % 2 == 0, |
| "Part width must be divisible by 2!"); |
| |
| // Returns the integer part with the least significant BITS set. |
| // BITS cannot be zero. |
| static inline APInt::WordType lowBitMask(unsigned bits) { |
| assert(bits != 0 && bits <= APInt::APINT_BITS_PER_WORD); |
| return ~(APInt::WordType) 0 >> (APInt::APINT_BITS_PER_WORD - bits); |
| } |
| |
| /// Returns the value of the lower half of PART. |
| static inline APInt::WordType lowHalf(APInt::WordType part) { |
| return part & lowBitMask(APInt::APINT_BITS_PER_WORD / 2); |
| } |
| |
| /// Returns the value of the upper half of PART. |
| static inline APInt::WordType highHalf(APInt::WordType part) { |
| return part >> (APInt::APINT_BITS_PER_WORD / 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 partMSB(APInt::WordType 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 partLSB(APInt::WordType 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(WordType *dst, WordType part, unsigned parts) { |
| assert(parts > 0); |
| dst[0] = part; |
| for (unsigned i = 1; i < parts; i++) |
| dst[i] = 0; |
| } |
| |
| /// Assign one bignum to another. |
| void APInt::tcAssign(WordType *dst, const WordType *src, unsigned parts) { |
| for (unsigned i = 0; i < parts; i++) |
| dst[i] = src[i]; |
| } |
| |
| /// Returns true if a bignum is zero, false otherwise. |
| bool APInt::tcIsZero(const WordType *src, unsigned parts) { |
| for (unsigned 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 WordType *parts, unsigned bit) { |
| return (parts[whichWord(bit)] & maskBit(bit)) != 0; |
| } |
| |
| /// Set the given bit of a bignum. |
| void APInt::tcSetBit(WordType *parts, unsigned bit) { |
| parts[whichWord(bit)] |= maskBit(bit); |
| } |
| |
| /// Clears the given bit of a bignum. |
| void APInt::tcClearBit(WordType *parts, unsigned bit) { |
| parts[whichWord(bit)] &= ~maskBit(bit); |
| } |
| |
| /// 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 APInt::tcLSB(const WordType *parts, unsigned n) { |
| for (unsigned i = 0; i < n; i++) { |
| if (parts[i] != 0) { |
| unsigned lsb = partLSB(parts[i]); |
| return lsb + i * APINT_BITS_PER_WORD; |
| } |
| } |
| |
| 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 APInt::tcMSB(const WordType *parts, unsigned n) { |
| do { |
| --n; |
| |
| if (parts[n] != 0) { |
| unsigned msb = partMSB(parts[n]); |
| |
| return msb + n * APINT_BITS_PER_WORD; |
| } |
| } 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(WordType *dst, unsigned dstCount, const WordType *src, |
| unsigned srcBits, unsigned srcLSB) { |
| unsigned dstParts = (srcBits + APINT_BITS_PER_WORD - 1) / APINT_BITS_PER_WORD; |
| assert(dstParts <= dstCount); |
| |
| unsigned firstSrcPart = srcLSB / APINT_BITS_PER_WORD; |
| tcAssign(dst, src + firstSrcPart, dstParts); |
| |
| unsigned shift = srcLSB % APINT_BITS_PER_WORD; |
| tcShiftRight(dst, dstParts, shift); |
| |
| // We now have (dstParts * APINT_BITS_PER_WORD - shift) bits from SRC |
| // in DST. If this is less that srcBits, append the rest, else |
| // clear the high bits. |
| unsigned n = dstParts * APINT_BITS_PER_WORD - shift; |
| if (n < srcBits) { |
| WordType mask = lowBitMask (srcBits - n); |
| dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask) |
| << n % APINT_BITS_PER_WORD); |
| } else if (n > srcBits) { |
| if (srcBits % APINT_BITS_PER_WORD) |
| dst[dstParts - 1] &= lowBitMask (srcBits % APINT_BITS_PER_WORD); |
| } |
| |
| // Clear high parts. |
| while (dstParts < dstCount) |
| dst[dstParts++] = 0; |
| } |
| |
| //// DST += RHS + C where C is zero or one. Returns the carry flag. |
| APInt::WordType APInt::tcAdd(WordType *dst, const WordType *rhs, |
| WordType c, unsigned parts) { |
| assert(c <= 1); |
| |
| for (unsigned i = 0; i < parts; i++) { |
| WordType 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; |
| } |
| |
| /// This function adds a single "word" integer, src, to the multiple |
| /// "word" integer array, dst[]. dst[] 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. |
| APInt::WordType APInt::tcAddPart(WordType *dst, WordType src, |
| unsigned parts) { |
| for (unsigned i = 0; i < parts; ++i) { |
| dst[i] += src; |
| if (dst[i] >= src) |
| return 0; // No need to carry so exit early. |
| src = 1; // Carry one to next digit. |
| } |
| |
| return 1; |
| } |
| |
| /// DST -= RHS + C where C is zero or one. Returns the carry flag. |
| APInt::WordType APInt::tcSubtract(WordType *dst, const WordType *rhs, |
| WordType c, unsigned parts) { |
| assert(c <= 1); |
| |
| for (unsigned i = 0; i < parts; i++) { |
| WordType 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; |
| } |
| |
| /// This function subtracts a single "word" (64-bit word), src, from |
| /// the multi-word integer array, dst[], propagating the borrowed 1 value until |
| /// no further borrowing is needed or it runs out of "words" in dst. The result |
| /// is 1 if "borrowing" exhausted the digits in dst, or 0 if dst was not |
| /// exhausted. In other words, if src > dst then this function returns 1, |
| /// otherwise 0. |
| /// @returns the borrow out of the subtraction |
| APInt::WordType APInt::tcSubtractPart(WordType *dst, WordType src, |
| unsigned parts) { |
| for (unsigned i = 0; i < parts; ++i) { |
| WordType Dst = dst[i]; |
| dst[i] -= src; |
| if (src <= Dst) |
| return 0; // No need to borrow so exit early. |
| src = 1; // We have to "borrow 1" from next "word" |
| } |
| |
| return 1; |
| } |
| |
| /// Negate a bignum in-place. |
| void APInt::tcNegate(WordType *dst, unsigned 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(WordType *dst, const WordType *src, |
| WordType multiplier, WordType carry, |
| unsigned srcParts, unsigned dstParts, |
| bool add) { |
| // 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. |
| unsigned n = std::min(dstParts, srcParts); |
| |
| for (unsigned i = 0; i < n; i++) { |
| // [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. |
| WordType srcPart = src[i]; |
| WordType low, mid, high; |
| 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 <<= APINT_BITS_PER_WORD / 2; |
| if (low + mid < low) |
| high++; |
| low += mid; |
| |
| mid = highHalf(srcPart) * lowHalf(multiplier); |
| high += highHalf(mid); |
| mid <<= APINT_BITS_PER_WORD / 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 (srcParts < dstParts) { |
| // Full multiplication, there is no overflow. |
| assert(srcParts + 1 == dstParts); |
| dst[srcParts] = carry; |
| return 0; |
| } |
| |
| // 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 (unsigned i = dstParts; 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(WordType *dst, const WordType *lhs, |
| const WordType *rhs, unsigned parts) { |
| assert(dst != lhs && dst != rhs); |
| |
| int overflow = 0; |
| tcSet(dst, 0, parts); |
| |
| for (unsigned 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. |
| void APInt::tcFullMultiply(WordType *dst, const WordType *lhs, |
| const WordType *rhs, unsigned lhsParts, |
| unsigned rhsParts) { |
| // Put the narrower number on the LHS for less loops below. |
| if (lhsParts > rhsParts) |
| return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts); |
| |
| assert(dst != lhs && dst != rhs); |
| |
| tcSet(dst, 0, rhsParts); |
| |
| for (unsigned i = 0; i < lhsParts; i++) |
| tcMultiplyPart(&dst[i], rhs, lhs[i], 0, rhsParts, rhsParts + 1, true); |
| } |
| |
| // 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(WordType *lhs, const WordType *rhs, |
| WordType *remainder, WordType *srhs, |
| unsigned parts) { |
| assert(lhs != remainder && lhs != srhs && remainder != srhs); |
| |
| unsigned shiftCount = tcMSB(rhs, parts) + 1; |
| if (shiftCount == 0) |
| return true; |
| |
| shiftCount = parts * APINT_BITS_PER_WORD - shiftCount; |
| unsigned n = shiftCount / APINT_BITS_PER_WORD; |
| WordType mask = (WordType) 1 << (shiftCount % APINT_BITS_PER_WORD); |
| |
| 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 = 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 = (WordType) 1 << (APINT_BITS_PER_WORD - 1); |
| n--; |
| } |
| } |
| |
| return false; |
| } |
| |
| /// Shift a bignum left Cound bits in-place. Shifted in bits are zero. There are |
| /// no restrictions on Count. |
| void APInt::tcShiftLeft(WordType *Dst, unsigned Words, unsigned Count) { |
| // Don't bother performing a no-op shift. |
| if (!Count) |
| return; |
| |
| // WordShift is the inter-part shift; BitShift is the intra-part shift. |
| unsigned WordShift = std::min(Count / APINT_BITS_PER_WORD, Words); |
| unsigned BitShift = Count % APINT_BITS_PER_WORD; |
| |
| // Fastpath for moving by whole words. |
| if (BitShift == 0) { |
| std::memmove(Dst + WordShift, Dst, (Words - WordShift) * APINT_WORD_SIZE); |
| } else { |
| while (Words-- > WordShift) { |
| Dst[Words] = Dst[Words - WordShift] << BitShift; |
| if (Words > WordShift) |
| Dst[Words] |= |
| Dst[Words - WordShift - 1] >> (APINT_BITS_PER_WORD - BitShift); |
| } |
| } |
| |
| // Fill in the remainder with 0s. |
| std::memset(Dst, 0, WordShift * APINT_WORD_SIZE); |
| } |
| |
| /// Shift a bignum right Count bits in-place. Shifted in bits are zero. There |
| /// are no restrictions on Count. |
| void APInt::tcShiftRight(WordType *Dst, unsigned Words, unsigned Count) { |
| // Don't bother performing a no-op shift. |
| if (!Count) |
| return; |
| |
| // WordShift is the inter-part shift; BitShift is the intra-part shift. |
| unsigned WordShift = std::min(Count / APINT_BITS_PER_WORD, Words); |
| unsigned BitShift = Count % APINT_BITS_PER_WORD; |
| |
| unsigned WordsToMove = Words - WordShift; |
| // Fastpath for moving by whole words. |
| if (BitShift == 0) { |
| std::memmove(Dst, Dst + WordShift, WordsToMove * APINT_WORD_SIZE); |
| } else { |
| for (unsigned i = 0; i != WordsToMove; ++i) { |
|