diff options
Diffstat (limited to 'contrib/llvm-project/llvm/lib/Support/APInt.cpp')
| -rw-r--r-- | contrib/llvm-project/llvm/lib/Support/APInt.cpp | 2989 |
1 files changed, 2989 insertions, 0 deletions
diff --git a/contrib/llvm-project/llvm/lib/Support/APInt.cpp b/contrib/llvm-project/llvm/lib/Support/APInt.cpp new file mode 100644 index 000000000000..43173311cd80 --- /dev/null +++ b/contrib/llvm-project/llvm/lib/Support/APInt.cpp @@ -0,0 +1,2989 @@ +//===-- 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(BitWidth && "Bitwidth too small"); + 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) { + assert(BitWidth && "Bitwidth too small"); + 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) { + tcAnd(U.pVal, RHS.U.pVal, getNumWords()); +} + +void APInt::OrAssignSlowCase(const APInt& RHS) { + tcOr(U.pVal, RHS.U.pVal, getNumWords()); +} + +void APInt::XorAssignSlowCase(const APInt& RHS) { + tcXor(U.pVal, RHS.U.pVal, getNumWords()); +} + +APInt& APInt::operator*=(const APInt& RHS) { + assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); + *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; +} + +/// Toggle every bit to its opposite value. +void APInt::flipAllBitsSlowCase() { + tcComplement(U.pVal, getNumWords()); + clearUnusedBits(); +} + +/// 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!"); + if ((*this)[bitPosition]) clearBit(bitPosition); + else setBit(bitPosition); +} + +void APInt::insertBits(const APInt &subBits, unsigned bitPosition) { + unsigned subBitWidth = subBits.getBitWidth(); + assert(0 < subBitWidth && (subBitWidth + bitPosition) <= BitWidth && + "Illegal bit insertion"); + + // 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) { + if (subBits[i]) + setBit(bitPosition + i); + else + clearBit(bitPosition + i); + } +} + +APInt APInt::extractBits(unsigned numBits, unsigned bitPosition) const { + assert(numBits > 0 && "Can't extract zero bits"); + 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(); +} + +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.U.VAL); + + return hash_combine_range(Arg.U.pVal, Arg.U.pVal + Arg.getNumWords()); +} + +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 % 16 == 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 == 48) { + unsigned Tmp1 = unsigned(U.VAL >> 16); + Tmp1 = ByteSwap_32(Tmp1); + uint16_t Tmp2 = uint16_t(U.VAL); + Tmp2 = ByteSwap_16(Tmp2); + return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1); + } + if (BitWidth == 64) + return APInt(BitWidth, ByteSwap_64(U.VAL)); + + 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)); + 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"); + 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.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; +} + +// 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::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) { + 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 { + 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 { + 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() ? 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]); +} + +/// 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(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.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 { + 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); +} + + +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 (*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 = 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()); +} + +/// 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(); +} + +#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!"); + +/* Some handy functions local to this file. */ + +/* 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++) { + WordType 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 <<= 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) { + Dst[i] = Dst[i + WordShift] >> BitShift; + if (i + 1 != WordsToMove) + Dst[i] |= Dst[i + WordShift + 1] << (APINT_BITS_PER_WORD - BitShift); + } + } + + // Fill in the remainder with 0s. + std::memset(Dst + WordsToMove, 0, WordShift * APINT_WORD_SIZE); +} + +/* Bitwise and of two bignums. */ +void APInt::tcAnd(WordType *dst, const WordType *rhs, unsigned parts) { + for (unsigned i = 0; i < parts; i++) + dst[i] &= rhs[i]; +} + +/* Bitwise inclusive or of two bignums. */ +void APInt::tcOr(WordType *dst, const WordType *rhs, unsigned parts) { + for (unsigned i = 0; i < parts; i++) + dst[i] |= rhs[i]; +} + +/* Bitwise exclusive or of two bignums. */ +void APInt::tcXor(WordType *dst, const WordType *rhs, unsigned parts) { + for (unsigned i = 0; i < parts; i++) + dst[i] ^= rhs[i]; +} + +/* Complement a bignum in-place. */ +void APInt::tcComplement(WordType *dst, unsigned parts) { + for (unsigned i = 0; i < parts; i++) + dst[i] = ~dst[i]; +} + +/* Comparison (unsigned) of two bignums. */ +int APInt::tcCompare(const WordType *lhs, const WordType *rhs, + unsigned parts) { + while (parts) { + parts--; + if (lhs[parts] != rhs[parts]) + return (lhs[parts] > rhs[parts]) ? 1 : -1; + } + + return 0; +} + +/* Set the least significant BITS bits of a bignum, clear the + rest. */ +void APInt::tcSetLeastSignificantBits(WordType *dst, unsigned parts, + unsigned bits) { + unsigned i = 0; + while (bits > APINT_BITS_PER_WORD) { + dst[i++] = ~(WordType) 0; + bits -= APINT_BITS_PER_WORD; + } + + if (bits) + dst[i++] = ~(WordType) 0 >> (APINT_BITS_PER_WORD - bits); + + while (i < parts) + dst[i++] = 0; +} + +APInt llvm::APIntOps::RoundingUDiv(const APInt &A, const APInt &B, + APInt::Rounding RM) { + // Currently udivrem always rounds down. + switch (RM) { + case APInt::Rounding::DOWN: + case APInt::Rounding::TOWARD_ZERO: + return A.udiv(B); + case APInt::Rounding::UP: { + APInt Quo, Rem; + APInt::udivrem(A, B, Quo, Rem); + if (Rem == 0) + return Quo; + return Quo + 1; + } + } + llvm_unreachable("Unknown APInt::Rounding enum"); +} + +APInt llvm::APIntOps::RoundingSDiv(const APInt &A, const APInt &B, + APInt::Rounding RM) { + switch (RM) { + case APInt::Rounding::DOWN: + case APInt::Rounding::UP: { + APInt Quo, Rem; + APInt::sdivrem(A, B, Quo, Rem); + if (Rem == 0) + return Quo; + // This algorithm deals with arbitrary rounding mode used by sdivrem. + // We want to check whether the non-integer part of the mathematical value + // is negative or not. If the non-integer part is negative, we need to round + // down from Quo; otherwise, if it's positive or 0, we return Quo, as it's + // already rounded down. + if (RM == APInt::Rounding::DOWN) { + if (Rem.isNegative() != B.isNegative()) + return Quo - 1; + return Quo; + } + if (Rem.isNegative() != B.isNegative()) + return Quo; + return Quo + 1; + } + // Currently sdiv rounds twards zero. + case APInt::Rounding::TOWARD_ZERO: + return A.sdiv(B); + } + llvm_unreachable("Unknown APInt::Rounding enum"); +} + +Optional<APInt> +llvm::APIntOps::SolveQuadraticEquationWrap(APInt A, APInt B, APInt C, + unsigned RangeWidth) { + unsigned CoeffWidth = A.getBitWidth(); + assert(CoeffWidth == B.getBitWidth() && CoeffWidth == C.getBitWidth()); + assert(RangeWidth <= CoeffWidth && + "Value range width should be less than coefficient width"); + assert(RangeWidth > 1 && "Value range bit width should be > 1"); + + LLVM_DEBUG(dbgs() << __func__ << ": solving " << A << "x^2 + " << B + << "x + " << C << ", rw:" << RangeWidth << '\n'); + + // Identify 0 as a (non)solution immediately. + if (C.sextOrTrunc(RangeWidth).isNullValue() ) { + LLVM_DEBUG(dbgs() << __func__ << ": zero solution\n"); + return APInt(CoeffWidth, 0); + } + + // The result of APInt arithmetic has the same bit width as the operands, + // so it can actually lose high bits. A product of two n-bit integers needs + // 2n-1 bits to represent the full value. + // The operation done below (on quadratic coefficients) that can produce + // the largest value is the evaluation of the equation during bisection, + // which needs 3 times the bitwidth of the coefficient, so the total number + // of required bits is 3n. + // + // The purpose of this extension is to simulate the set Z of all integers, + // where n+1 > n for all n in Z. In Z it makes sense to talk about positive + // and negative numbers (not so much in a modulo arithmetic). The method + // used to solve the equation is based on the standard formula for real + // numbers, and uses the concepts of "positive" and "negative" with their + // usual meanings. + CoeffWidth *= 3; + A = A.sext(CoeffWidth); + B = B.sext(CoeffWidth); + C = C.sext(CoeffWidth); + + // Make A > 0 for simplicity. Negate cannot overflow at this point because + // the bit width has increased. + if (A.isNegative()) { + A.negate(); + B.negate(); + C.negate(); + } + + // Solving an equation q(x) = 0 with coefficients in modular arithmetic + // is really solving a set of equations q(x) = kR for k = 0, 1, 2, ..., + // and R = 2^BitWidth. + // Since we're trying not only to find exact solutions, but also values + // that "wrap around", such a set will always have a solution, i.e. an x + // that satisfies at least one of the equations, or such that |q(x)| + // exceeds kR, while |q(x-1)| for the same k does not. + // + // We need to find a value k, such that Ax^2 + Bx + C = kR will have a + // positive solution n (in the above sense), and also such that the n + // will be the least among all solutions corresponding to k = 0, 1, ... + // (more precisely, the least element in the set + // { n(k) | k is such that a solution n(k) exists }). + // + // Consider the parabola (over real numbers) that corresponds to the + // quadratic equation. Since A > 0, the arms of the parabola will point + // up. Picking different values of k will shift it up and down by R. + // + // We want to shift the parabola in such a way as to reduce the problem + // of solving q(x) = kR to solving shifted_q(x) = 0. + // (The interesting solutions are the ceilings of the real number + // solutions.) + APInt R = APInt::getOneBitSet(CoeffWidth, RangeWidth); + APInt TwoA = 2 * A; + APInt SqrB = B * B; + bool PickLow; + + auto RoundUp = [] (const APInt &V, const APInt &A) -> APInt { + assert(A.isStrictlyPositive()); + APInt T = V.abs().urem(A); + if (T.isNullValue()) + return V; + return V.isNegative() ? V+T : V+(A-T); + }; + + // The vertex of the parabola is at -B/2A, but since A > 0, it's negative + // iff B is positive. + if (B.isNonNegative()) { + // If B >= 0, the vertex it at a negative location (or at 0), so in + // order to have a non-negative solution we need to pick k that makes + // C-kR negative. To satisfy all the requirements for the solution + // that we are looking for, it needs to be closest to 0 of all k. + C = C.srem(R); + if (C.isStrictlyPositive()) + C -= R; + // Pick the greater solution. + PickLow = false; + } else { + // If B < 0, the vertex is at a positive location. For any solution + // to exist, the discriminant must be non-negative. This means that + // C-kR <= B^2/4A is a necessary condition for k, i.e. there is a + // lower bound on values of k: kR >= C - B^2/4A. + APInt LowkR = C - SqrB.udiv(2*TwoA); // udiv because all values > 0. + // Round LowkR up (towards +inf) to the nearest kR. + LowkR = RoundUp(LowkR, R); + + // If there exists k meeting the condition above, and such that + // C-kR > 0, there will be two positive real number solutions of + // q(x) = kR. Out of all such values of k, pick the one that makes + // C-kR closest to 0, (i.e. pick maximum k such that C-kR > 0). + // In other words, find maximum k such that LowkR <= kR < C. + if (C.sgt(LowkR)) { + // If LowkR < C, then such a k is guaranteed to exist because + // LowkR itself is a multiple of R. + C -= -RoundUp(-C, R); // C = C - RoundDown(C, R) + // Pick the smaller solution. + PickLow = true; + } else { + // If C-kR < 0 for all potential k's, it means that one solution + // will be negative, while the other will be positive. The positive + // solution will shift towards 0 if the parabola is moved up. + // Pick the kR closest to the lower bound (i.e. make C-kR closest + // to 0, or in other words, out of all parabolas that have solutions, + // pick the one that is the farthest "up"). + // Since LowkR is itself a multiple of R, simply take C-LowkR. + C -= LowkR; + // Pick the greater solution. + PickLow = false; + } + } + + LLVM_DEBUG(dbgs() << __func__ << ": updated coefficients " << A << "x^2 + " + << B << "x + " << C << ", rw:" << RangeWidth << '\n'); + + APInt D = SqrB - 4*A*C; + assert(D.isNonNegative() && "Negative discriminant"); + APInt SQ = D.sqrt(); + + APInt Q = SQ * SQ; + bool InexactSQ = Q != D; + // The calculated SQ may actually be greater than the exact (non-integer) + // value. If that's the case, decremement SQ to get a value that is lower. + if (Q.sgt(D)) + SQ -= 1; + + APInt X; + APInt Rem; + + // SQ is rounded down (i.e SQ * SQ <= D), so the roots may be inexact. + // When using the quadratic formula directly, the calculated low root + // may be greater than the exact one, since we would be subtracting SQ. + // To make sure that the calculated root is not greater than the exact + // one, subtract SQ+1 when calculating the low root (for inexact value + // of SQ). + if (PickLow) + APInt::sdivrem(-B - (SQ+InexactSQ), TwoA, X, Rem); + else + APInt::sdivrem(-B + SQ, TwoA, X, Rem); + + // The updated coefficients should be such that the (exact) solution is + // positive. Since APInt division rounds towards 0, the calculated one + // can be 0, but cannot be negative. + assert(X.isNonNegative() && "Solution should be non-negative"); + + if (!InexactSQ && Rem.isNullValue()) { + LLVM_DEBUG(dbgs() << __func__ << ": solution (root): " << X << '\n'); + return X; + } + + assert((SQ*SQ).sle(D) && "SQ = |_sqrt(D)_|, so SQ*SQ <= D"); + // The exact value of the square root of D should be between SQ and SQ+1. + // This implies that the solution should be between that corresponding to + // SQ (i.e. X) and that corresponding to SQ+1. + // + // The calculated X cannot be greater than the exact (real) solution. + // Actually it must be strictly less than the exact solution, while + // X+1 will be greater than or equal to it. + + APInt VX = (A*X + B)*X + C; + APInt VY = VX + TwoA*X + A + B; + bool SignChange = VX.isNegative() != VY.isNegative() || + VX.isNullValue() != VY.isNullValue(); + // If the sign did not change between X and X+1, X is not a valid solution. + // This could happen when the actual (exact) roots don't have an integer + // between them, so they would both be contained between X and X+1. + if (!SignChange) { + LLVM_DEBUG(dbgs() << __func__ << ": no valid solution\n"); + return None; + } + + X += 1; + LLVM_DEBUG(dbgs() << __func__ << ": solution (wrap): " << X << '\n'); + return X; +} + +/// StoreIntToMemory - Fills the StoreBytes bytes of memory starting from Dst +/// with the integer held in IntVal. +void llvm::StoreIntToMemory(const APInt &IntVal, uint8_t *Dst, + unsigned StoreBytes) { + assert((IntVal.getBitWidth()+7)/8 >= StoreBytes && "Integer too small!"); + const uint8_t *Src = (const uint8_t *)IntVal.getRawData(); + + if (sys::IsLittleEndianHost) { + // Little-endian host - the source is ordered from LSB to MSB. Order the + // destination from LSB to MSB: Do a straight copy. + memcpy(Dst, Src, StoreBytes); + } else { + // Big-endian host - the source is an array of 64 bit words ordered from + // LSW to MSW. Each word is ordered from MSB to LSB. Order the destination + // from MSB to LSB: Reverse the word order, but not the bytes in a word. + while (StoreBytes > sizeof(uint64_t)) { + StoreBytes -= sizeof(uint64_t); + // May not be aligned so use memcpy. + memcpy(Dst + StoreBytes, Src, sizeof(uint64_t)); + Src += sizeof(uint64_t); + } + + memcpy(Dst, Src + sizeof(uint64_t) - StoreBytes, StoreBytes); + } +} + +/// LoadIntFromMemory - Loads the integer stored in the LoadBytes bytes starting +/// from Src into IntVal, which is assumed to be wide enough and to hold zero. +void llvm::LoadIntFromMemory(APInt &IntVal, uint8_t *Src, unsigned LoadBytes) { + assert((IntVal.getBitWidth()+7)/8 >= LoadBytes && "Integer too small!"); + uint8_t *Dst = reinterpret_cast<uint8_t *>( + const_cast<uint64_t *>(IntVal.getRawData())); + + if (sys::IsLittleEndianHost) + // Little-endian host - the destination must be ordered from LSB to MSB. + // The source is ordered from LSB to MSB: Do a straight copy. + memcpy(Dst, Src, LoadBytes); + else { + // Big-endian - the destination is an array of 64 bit words ordered from + // LSW to MSW. Each word must be ordered from MSB to LSB. The source is + // ordered from MSB to LSB: Reverse the word order, but not the bytes in + // a word. + while (LoadBytes > sizeof(uint64_t)) { + LoadBytes -= sizeof(uint64_t); + // May not be aligned so use memcpy. + memcpy(Dst, Src + LoadBytes, sizeof(uint64_t)); + Dst += sizeof(uint64_t); + } + + memcpy(Dst + sizeof(uint64_t) - LoadBytes, Src, LoadBytes); + } +} |