From 288727a23d47b00dbf1d670265d03161b50c4086 Mon Sep 17 00:00:00 2001 From: Rahul Joshi Date: Mon, 29 Sep 2025 11:32:30 -0700 Subject: [PATCH 1/2] Test clang-format based unix line ending --- llvm/.clang-format | 2 +- llvm/include/llvm/ADT/Any.h | 336 +- llvm/lib/Support/APInt.cpp | 6378 +++++++++++++++++------------------ 3 files changed, 3358 insertions(+), 3358 deletions(-) diff --git a/llvm/.clang-format b/llvm/.clang-format index 5bead5f39dd3c..ecb44bfabd9aa 100644 --- a/llvm/.clang-format +++ b/llvm/.clang-format @@ -1,2 +1,2 @@ BasedOnStyle: LLVM - +LineEnding: LF diff --git a/llvm/include/llvm/ADT/Any.h b/llvm/include/llvm/ADT/Any.h index a29aaa3439715..b605da1d88d9d 100644 --- a/llvm/include/llvm/ADT/Any.h +++ b/llvm/include/llvm/ADT/Any.h @@ -1,168 +1,168 @@ -//===- Any.h - Generic type erased holder of any type -----------*- C++ -*-===// -// -// 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 -// -//===----------------------------------------------------------------------===// -/// -/// \file -/// This file provides Any, a non-template class modeled in the spirit of -/// std::any. The idea is to provide a type-safe replacement for C's void*. -/// It can hold a value of any copy-constructible copy-assignable type -/// -//===----------------------------------------------------------------------===// - -#ifndef LLVM_ADT_ANY_H -#define LLVM_ADT_ANY_H - -#include "llvm/ADT/STLForwardCompat.h" -#include "llvm/Support/Compiler.h" - -#include -#include -#include - -namespace llvm { - -class LLVM_ABI Any { - - // The `Typeid::Id` static data member below is a globally unique - // identifier for the type `T`. It is explicitly marked with default - // visibility so that when `-fvisibility=hidden` is used, the loader still - // merges duplicate definitions across DSO boundaries. - // We also cannot mark it as `const`, otherwise msvc merges all definitions - // when lto is enabled, making any comparison return true. - template struct TypeId { static char Id; }; - - struct StorageBase { - virtual ~StorageBase() = default; - virtual std::unique_ptr clone() const = 0; - virtual const void *id() const = 0; - }; - - template struct StorageImpl : public StorageBase { - explicit StorageImpl(const T &Value) : Value(Value) {} - - explicit StorageImpl(T &&Value) : Value(std::move(Value)) {} - - std::unique_ptr clone() const override { - return std::make_unique>(Value); - } - - const void *id() const override { return &TypeId::Id; } - - T Value; - - private: - StorageImpl &operator=(const StorageImpl &Other) = delete; - StorageImpl(const StorageImpl &Other) = delete; - }; - -public: - Any() = default; - - Any(const Any &Other) - : Storage(Other.Storage ? Other.Storage->clone() : nullptr) {} - - // When T is Any or T is not copy-constructible we need to explicitly disable - // the forwarding constructor so that the copy constructor gets selected - // instead. - template , Any>>, - // We also disable this overload when an `Any` object can be - // converted to the parameter type because in that case, - // this constructor may combine with that conversion during - // overload resolution for determining copy - // constructibility, and then when we try to determine copy - // constructibility below we may infinitely recurse. This is - // being evaluated by the standards committee as a potential - // DR in `std::any` as well, but we're going ahead and - // adopting it to work-around usage of `Any` with types that - // need to be implicitly convertible from an `Any`. - std::negation>>, - std::is_copy_constructible>>::value, - int> = 0> - Any(T &&Value) { - Storage = - std::make_unique>>(std::forward(Value)); - } - - Any(Any &&Other) : Storage(std::move(Other.Storage)) {} - - Any &swap(Any &Other) { - std::swap(Storage, Other.Storage); - return *this; - } - - Any &operator=(Any Other) { - Storage = std::move(Other.Storage); - return *this; - } - - bool has_value() const { return !!Storage; } - - void reset() { Storage.reset(); } - -private: - // Only used for the internal llvm::Any implementation - template bool isa() const { - if (!Storage) - return false; - return Storage->id() == &Any::TypeId>::Id; - } - - template friend T any_cast(const Any &Value); - template friend T any_cast(Any &Value); - template friend T any_cast(Any &&Value); - template friend const T *any_cast(const Any *Value); - template friend T *any_cast(Any *Value); - - std::unique_ptr Storage; -}; - -// Define the type id and initialize with a non-zero value. -// Initializing with a zero value means the variable can end up in either the -// .data or the .bss section. This can lead to multiple definition linker errors -// when some object files are compiled with a compiler that puts the variable -// into .data but they are linked to object files from a different compiler that -// put the variable into .bss. To prevent this issue from happening, initialize -// the variable with a non-zero value, which forces it to land in .data (because -// .bss is zero-initialized). -// See also https://github.com/llvm/llvm-project/issues/62270 -template char Any::TypeId::Id = 1; - -template T any_cast(const Any &Value) { - assert(Value.isa() && "Bad any cast!"); - return static_cast(*any_cast>(&Value)); -} - -template T any_cast(Any &Value) { - assert(Value.isa() && "Bad any cast!"); - return static_cast(*any_cast>(&Value)); -} - -template T any_cast(Any &&Value) { - assert(Value.isa() && "Bad any cast!"); - return static_cast(std::move(*any_cast>(&Value))); -} - -template const T *any_cast(const Any *Value) { - using U = remove_cvref_t; - if (!Value || !Value->isa()) - return nullptr; - return &static_cast &>(*Value->Storage).Value; -} - -template T *any_cast(Any *Value) { - using U = std::decay_t; - if (!Value || !Value->isa()) - return nullptr; - return &static_cast &>(*Value->Storage).Value; -} - -} // end namespace llvm - -#endif // LLVM_ADT_ANY_H +//===- Any.h - Generic type erased holder of any type -----------*- C++ -*-===// +// +// 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 +// +//===----------------------------------------------------------------------===// +/// +/// \file +/// This file provides Any, a non-template class modeled in the spirit of +/// std::any. The idea is to provide a type-safe replacement for C's void*. +/// It can hold a value of any copy-constructible copy-assignable type +/// +//===----------------------------------------------------------------------===// + +#ifndef LLVM_ADT_ANY_H +#define LLVM_ADT_ANY_H + +#include "llvm/ADT/STLForwardCompat.h" +#include "llvm/Support/Compiler.h" + +#include +#include +#include + +namespace llvm { + +class LLVM_ABI Any { + + // The `Typeid::Id` static data member below is a globally unique + // identifier for the type `T`. It is explicitly marked with default + // visibility so that when `-fvisibility=hidden` is used, the loader still + // merges duplicate definitions across DSO boundaries. + // We also cannot mark it as `const`, otherwise msvc merges all definitions + // when lto is enabled, making any comparison return true. + template struct TypeId { static char Id; }; + + struct StorageBase { + virtual ~StorageBase() = default; + virtual std::unique_ptr clone() const = 0; + virtual const void *id() const = 0; + }; + + template struct StorageImpl : public StorageBase { + explicit StorageImpl(const T &Value) : Value(Value) {} + + explicit StorageImpl(T &&Value) : Value(std::move(Value)) {} + + std::unique_ptr clone() const override { + return std::make_unique>(Value); + } + + const void *id() const override { return &TypeId::Id; } + + T Value; + + private: + StorageImpl &operator=(const StorageImpl &Other) = delete; + StorageImpl(const StorageImpl &Other) = delete; + }; + +public: + Any() = default; + + Any(const Any &Other) + : Storage(Other.Storage ? Other.Storage->clone() : nullptr) {} + + // When T is Any or T is not copy-constructible we need to explicitly disable + // the forwarding constructor so that the copy constructor gets selected + // instead. + template , Any>>, + // We also disable this overload when an `Any` object can be + // converted to the parameter type because in that case, + // this constructor may combine with that conversion during + // overload resolution for determining copy + // constructibility, and then when we try to determine copy + // constructibility below we may infinitely recurse. This is + // being evaluated by the standards committee as a potential + // DR in `std::any` as well, but we're going ahead and + // adopting it to work-around usage of `Any` with types that + // need to be implicitly convertible from an `Any`. + std::negation>>, + std::is_copy_constructible>>::value, + int> = 0> + Any(T &&Value) { + Storage = + std::make_unique>>(std::forward(Value)); + } + + Any(Any &&Other) : Storage(std::move(Other.Storage)) {} + + Any &swap(Any &Other) { + std::swap(Storage, Other.Storage); + return *this; + } + + Any &operator=(Any Other) { + Storage = std::move(Other.Storage); + return *this; + } + + bool has_value() const { return !!Storage; } + + void reset() { Storage.reset(); } + +private: + // Only used for the internal llvm::Any implementation + template bool isa() const { + if (!Storage) + return false; + return Storage->id() == &Any::TypeId>::Id; + } + + template friend T any_cast(const Any &Value); + template friend T any_cast(Any &Value); + template friend T any_cast(Any &&Value); + template friend const T *any_cast(const Any *Value); + template friend T *any_cast(Any *Value); + + std::unique_ptr Storage; +}; + +// Define the type id and initialize with a non-zero value. +// Initializing with a zero value means the variable can end up in either the +// .data or the .bss section. This can lead to multiple definition linker errors +// when some object files are compiled with a compiler that puts the variable +// into .data but they are linked to object files from a different compiler that +// put the variable into .bss. To prevent this issue from happening, initialize +// the variable with a non-zero value, which forces it to land in .data (because +// .bss is zero-initialized). +// See also https://github.com/llvm/llvm-project/issues/62270 +template char Any::TypeId::Id = 1; + +template T any_cast(const Any &Value) { + assert(Value.isa() && "Bad any cast!"); + return static_cast(*any_cast>(&Value)); +} + +template T any_cast(Any &Value) { + assert(Value.isa() && "Bad any cast!"); + return static_cast(*any_cast>(&Value)); +} + +template T any_cast(Any &&Value) { + assert(Value.isa() && "Bad any cast!"); + return static_cast(std::move(*any_cast>(&Value))); +} + +template const T *any_cast(const Any *Value) { + using U = remove_cvref_t; + if (!Value || !Value->isa()) + return nullptr; + return &static_cast &>(*Value->Storage).Value; +} + +template T *any_cast(Any *Value) { + using U = std::decay_t; + if (!Value || !Value->isa()) + return nullptr; + return &static_cast &>(*Value->Storage).Value; +} + +} // end namespace llvm + +#endif // LLVM_ADT_ANY_H diff --git a/llvm/lib/Support/APInt.cpp b/llvm/lib/Support/APInt.cpp index f6fd5f9ddd633..c4cc080578007 100644 --- a/llvm/lib/Support/APInt.cpp +++ b/llvm/lib/Support/APInt.cpp @@ -1,3189 +1,3189 @@ -//===-- 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/SmallString.h" -#include "llvm/ADT/StringRef.h" -#include "llvm/ADT/bit.h" -#include "llvm/Config/llvm-config.h" -#include "llvm/Support/Alignment.h" -#include "llvm/Support/Debug.h" -#include "llvm/Support/ErrorHandling.h" -#include "llvm/Support/MathExtras.h" -#include "llvm/Support/raw_ostream.h" -#include -#include - -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) { - return new uint64_t[numWords](); -} - -/// 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 UINT_MAX; -} - - -void APInt::initSlowCase(uint64_t val, bool isSigned) { - if (isSigned && int64_t(val) < 0) { - U.pVal = getMemory(getNumWords()); - U.pVal[0] = val; - memset(&U.pVal[1], 0xFF, APINT_WORD_SIZE * (getNumWords() - 1)); - clearUnusedBits(); - } else { - U.pVal = getClearedMemory(getNumWords()); - U.pVal[0] = val; - } -} - -void APInt::initSlowCase(const APInt& that) { - U.pVal = getMemory(getNumWords()); - memcpy(U.pVal, that.U.pVal, getNumWords() * APINT_WORD_SIZE); -} - -void APInt::initFromArray(ArrayRef bigVal) { - assert(bigVal.data() && "Null pointer detected!"); - if (isSingleWord()) - U.VAL = bigVal[0]; - else { - // Get memory, cleared to 0 - U.pVal = getClearedMemory(getNumWords()); - // Calculate the number of words to copy - unsigned words = std::min(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 bigVal) : BitWidth(numBits) { - initFromArray(bigVal); -} - -APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[]) - : BitWidth(numBits) { - initFromArray(ArrayRef(bigVal, numWords)); -} - -APInt::APInt(unsigned numbits, StringRef Str, uint8_t radix) - : BitWidth(numbits) { - fromString(numbits, Str, radix); -} - -void APInt::reallocate(unsigned NewBitWidth) { - // If the number of words is the same we can just change the width and stop. - if (getNumWords() == getNumWords(NewBitWidth)) { - BitWidth = NewBitWidth; - return; - } - - // If we have an allocation, delete it. - if (!isSingleWord()) - delete [] U.pVal; - - // Update BitWidth. - BitWidth = NewBitWidth; - - // If we are supposed to have an allocation, create it. - if (!isSingleWord()) - U.pVal = getMemory(getNumWords()); -} - -void APInt::assignSlowCase(const APInt &RHS) { - // Don't do anything for X = X - if (this == &RHS) - return; - - // Adjust the bit width and handle allocations as necessary. - reallocate(RHS.getBitWidth()); - - // Copy the data. - if (isSingleWord()) - U.VAL = RHS.U.VAL; - else - memcpy(U.pVal, RHS.U.pVal, getNumWords() * APINT_WORD_SIZE); -} - -/// This method 'profiles' an APInt for use with FoldingSet. -void APInt::Profile(FoldingSetNodeID& ID) const { - ID.AddInteger(BitWidth); - - if (isSingleWord()) { - ID.AddInteger(U.VAL); - return; - } - - unsigned NumWords = getNumWords(); - for (unsigned i = 0; i < NumWords; ++i) - ID.AddInteger(U.pVal[i]); -} - -bool APInt::isAligned(Align A) const { - if (isZero()) - return true; - const unsigned TrailingZeroes = countr_zero(); - const unsigned MinimumTrailingZeroes = Log2(A); - return TrailingZeroes >= MinimumTrailingZeroes; -} - -/// 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, /*isSigned=*/false, - /*implicitTrunc=*/true); - - APInt Result(getMemory(getNumWords()), getBitWidth()); - tcMultiply(Result.U.pVal, U.pVal, RHS.U.pVal, getNumWords()); - Result.clearUnusedBits(); - return Result; -} - -void APInt::andAssignSlowCase(const APInt &RHS) { - WordType *dst = U.pVal, *rhs = RHS.U.pVal; - for (size_t i = 0, e = getNumWords(); i != e; ++i) - dst[i] &= rhs[i]; -} - -void APInt::orAssignSlowCase(const APInt &RHS) { - WordType *dst = U.pVal, *rhs = RHS.U.pVal; - for (size_t i = 0, e = getNumWords(); i != e; ++i) - dst[i] |= rhs[i]; -} - -void APInt::xorAssignSlowCase(const APInt &RHS) { - WordType *dst = U.pVal, *rhs = RHS.U.pVal; - for (size_t i = 0, e = getNumWords(); i != e; ++i) - dst[i] ^= rhs[i]; -} - -APInt &APInt::operator*=(const APInt &RHS) { - *this = *this * RHS; - return *this; -} - -APInt& APInt::operator*=(uint64_t RHS) { - if (isSingleWord()) { - U.VAL *= RHS; - } else { - unsigned NumWords = getNumWords(); - tcMultiplyPart(U.pVal, U.pVal, RHS, 0, NumWords, NumWords, false); - } - return clearUnusedBits(); -} - -bool APInt::equalSlowCase(const APInt &RHS) const { - return std::equal(U.pVal, U.pVal + getNumWords(), RHS.U.pVal); -} - -int APInt::compare(const APInt& RHS) const { - assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); - if (isSingleWord()) - return U.VAL < RHS.U.VAL ? -1 : U.VAL > RHS.U.VAL; - - return tcCompare(U.pVal, RHS.U.pVal, getNumWords()); -} - -int APInt::compareSigned(const APInt& RHS) const { - assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); - if (isSingleWord()) { - int64_t lhsSext = SignExtend64(U.VAL, BitWidth); - int64_t rhsSext = SignExtend64(RHS.U.VAL, BitWidth); - return lhsSext < rhsSext ? -1 : lhsSext > rhsSext; - } - - bool lhsNeg = isNegative(); - bool rhsNeg = RHS.isNegative(); - - // If the sign bits don't match, then (LHS < RHS) if LHS is negative - if (lhsNeg != rhsNeg) - return lhsNeg ? -1 : 1; - - // Otherwise we can just use an unsigned comparison, because even negative - // numbers compare correctly this way if both have the same signed-ness. - return tcCompare(U.pVal, RHS.U.pVal, getNumWords()); -} - -void APInt::setBitsSlowCase(unsigned loBit, unsigned hiBit) { - unsigned loWord = whichWord(loBit); - unsigned hiWord = whichWord(hiBit); - - // Create an initial mask for the low word with zeros below loBit. - uint64_t loMask = WORDTYPE_MAX << whichBit(loBit); - - // If hiBit is not aligned, we need a high mask. - unsigned hiShiftAmt = whichBit(hiBit); - if (hiShiftAmt != 0) { - // Create a high mask with zeros above hiBit. - uint64_t hiMask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - hiShiftAmt); - // If loWord and hiWord are equal, then we combine the masks. Otherwise, - // set the bits in hiWord. - if (hiWord == loWord) - loMask &= hiMask; - else - U.pVal[hiWord] |= hiMask; - } - // Apply the mask to the low word. - U.pVal[loWord] |= loMask; - - // Fill any words between loWord and hiWord with all ones. - for (unsigned word = loWord + 1; word < hiWord; ++word) - U.pVal[word] = WORDTYPE_MAX; -} - -void APInt::clearBitsSlowCase(unsigned LoBit, unsigned HiBit) { - unsigned LoWord = whichWord(LoBit); - unsigned HiWord = whichWord(HiBit); - - // Create an initial mask for the low word with ones 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 ones above HiBit. - uint64_t HiMask = ~(WORDTYPE_MAX >> (APINT_BITS_PER_WORD - HiShiftAmt)); - // If LoWord and HiWord are equal, then we combine the masks. Otherwise, - // clear 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 zeros. - for (unsigned Word = LoWord + 1; Word < HiWord; ++Word) - U.pVal[Word] = 0; -} - -// Complement a bignum in-place. -static void tcComplement(APInt::WordType *dst, unsigned parts) { - for (unsigned i = 0; i < parts; i++) - dst[i] = ~dst[i]; -} - -/// Toggle every bit to its opposite value. -void APInt::flipAllBitsSlowCase() { - tcComplement(U.pVal, getNumWords()); - clearUnusedBits(); -} - -/// Concatenate the bits from "NewLSB" onto the bottom of *this. This is -/// equivalent to: -/// (this->zext(NewWidth) << NewLSB.getBitWidth()) | NewLSB.zext(NewWidth) -/// In the slow case, we know the result is large. -APInt APInt::concatSlowCase(const APInt &NewLSB) const { - unsigned NewWidth = getBitWidth() + NewLSB.getBitWidth(); - APInt Result = NewLSB.zext(NewWidth); - Result.insertBits(*this, NewLSB.getBitWidth()); - return Result; -} - -/// Toggle a given bit to its opposite value whose position is given -/// as "bitPosition". -/// Toggles a given bit to its opposite value. -void APInt::flipBit(unsigned bitPosition) { - assert(bitPosition < BitWidth && "Out of the bit-width range!"); - setBitVal(bitPosition, !(*this)[bitPosition]); -} - -void APInt::insertBits(const APInt &subBits, unsigned bitPosition) { - unsigned subBitWidth = subBits.getBitWidth(); - assert((subBitWidth + bitPosition) <= BitWidth && "Illegal bit insertion"); - - // inserting no bits is a noop. - if (subBitWidth == 0) - return; - - // Insertion is a direct copy. - if (subBitWidth == BitWidth) { - *this = subBits; - return; - } - - // Single word result can be done as a direct bitmask. - if (isSingleWord()) { - uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - subBitWidth); - U.VAL &= ~(mask << bitPosition); - U.VAL |= (subBits.U.VAL << bitPosition); - return; - } - - unsigned loBit = whichBit(bitPosition); - unsigned loWord = whichWord(bitPosition); - unsigned hi1Word = whichWord(bitPosition + subBitWidth - 1); - - // Insertion within a single word can be done as a direct bitmask. - if (loWord == hi1Word) { - uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - subBitWidth); - U.pVal[loWord] &= ~(mask << loBit); - U.pVal[loWord] |= (subBits.U.VAL << loBit); - return; - } - - // Insert on word boundaries. - if (loBit == 0) { - // Direct copy whole words. - unsigned numWholeSubWords = subBitWidth / APINT_BITS_PER_WORD; - memcpy(U.pVal + loWord, subBits.getRawData(), - numWholeSubWords * APINT_WORD_SIZE); - - // Mask+insert remaining bits. - unsigned remainingBits = subBitWidth % APINT_BITS_PER_WORD; - if (remainingBits != 0) { - uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - remainingBits); - U.pVal[hi1Word] &= ~mask; - U.pVal[hi1Word] |= subBits.getWord(subBitWidth - 1); - } - return; - } - - // General case - set/clear individual bits in dst based on src. - // TODO - there is scope for optimization here, but at the moment this code - // path is barely used so prefer readability over performance. - for (unsigned i = 0; i != subBitWidth; ++i) - setBitVal(bitPosition + i, subBits[i]); -} - -void APInt::insertBits(uint64_t subBits, unsigned bitPosition, unsigned numBits) { - uint64_t maskBits = maskTrailingOnes(numBits); - subBits &= maskBits; - if (isSingleWord()) { - U.VAL &= ~(maskBits << bitPosition); - U.VAL |= subBits << bitPosition; - return; - } - - unsigned loBit = whichBit(bitPosition); - unsigned loWord = whichWord(bitPosition); - unsigned hiWord = whichWord(bitPosition + numBits - 1); - if (loWord == hiWord) { - U.pVal[loWord] &= ~(maskBits << loBit); - U.pVal[loWord] |= subBits << loBit; - return; - } - - static_assert(8 * sizeof(WordType) <= 64, "This code assumes only two words affected"); - unsigned wordBits = 8 * sizeof(WordType); - U.pVal[loWord] &= ~(maskBits << loBit); - U.pVal[loWord] |= subBits << loBit; - - U.pVal[hiWord] &= ~(maskBits >> (wordBits - loBit)); - U.pVal[hiWord] |= subBits >> (wordBits - loBit); -} - -APInt APInt::extractBits(unsigned numBits, unsigned bitPosition) const { - assert(bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth && - "Illegal bit extraction"); - - if (isSingleWord()) - return APInt(numBits, U.VAL >> bitPosition, /*isSigned=*/false, - /*implicitTrunc=*/true); - - 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, /*isSigned=*/false, - /*implicitTrunc=*/true); - - // Extracting bits that start on a source word boundary can be done - // as a fast memory copy. - if (loBit == 0) - return APInt(numBits, ArrayRef(U.pVal + loWord, 1 + hiWord - loWord)); - - // General case - shift + copy source words directly into place. - APInt Result(numBits, 0); - unsigned NumSrcWords = getNumWords(); - unsigned NumDstWords = Result.getNumWords(); - - uint64_t *DestPtr = Result.isSingleWord() ? &Result.U.VAL : Result.U.pVal; - for (unsigned word = 0; word < NumDstWords; ++word) { - uint64_t w0 = U.pVal[loWord + word]; - uint64_t w1 = - (loWord + word + 1) < NumSrcWords ? U.pVal[loWord + word + 1] : 0; - DestPtr[word] = (w0 >> loBit) | (w1 << (APINT_BITS_PER_WORD - loBit)); - } - - return Result.clearUnusedBits(); -} - -uint64_t APInt::extractBitsAsZExtValue(unsigned numBits, - unsigned bitPosition) const { - assert(bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth && - "Illegal bit extraction"); - assert(numBits <= 64 && "Illegal bit extraction"); - - uint64_t maskBits = maskTrailingOnes(numBits); - if (isSingleWord()) - return (U.VAL >> bitPosition) & maskBits; - - static_assert(APINT_BITS_PER_WORD >= 64, - "This code assumes only two words affected"); - unsigned loBit = whichBit(bitPosition); - unsigned loWord = whichWord(bitPosition); - unsigned hiWord = whichWord(bitPosition + numBits - 1); - if (loWord == hiWord) - return (U.pVal[loWord] >> loBit) & maskBits; - - uint64_t retBits = U.pVal[loWord] >> loBit; - retBits |= U.pVal[hiWord] << (APINT_BITS_PER_WORD - loBit); - retBits &= maskBits; - return retBits; -} - -unsigned APInt::getSufficientBitsNeeded(StringRef Str, uint8_t Radix) { - assert(!Str.empty() && "Invalid string length"); - size_t StrLen = Str.size(); - - // Each computation below needs to know if it's negative. - unsigned IsNegative = false; - if (Str[0] == '-' || Str[0] == '+') { - IsNegative = Str[0] == '-'; - StrLen--; - assert(StrLen && "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 StrLen + IsNegative; - if (Radix == 8) - return StrLen * 3 + IsNegative; - if (Radix == 16) - return StrLen * 4 + IsNegative; - - // 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. - if (Radix == 10) - return (StrLen == 1 ? 4 : StrLen * 64 / 18) + IsNegative; - - assert(Radix == 36); - return (StrLen == 1 ? 7 : StrLen * 16 / 3) + IsNegative; -} - -unsigned APInt::getBitsNeeded(StringRef str, uint8_t radix) { - // Compute a sufficient number of bits that is always large enough but might - // be too large. - unsigned sufficient = getSufficientBitsNeeded(str, radix); - - // For bases 2, 8, and 16, the sufficient number of bits is exact and we can - // return the value directly. For bases 10 and 36, we need to do extra work. - if (radix == 2 || radix == 8 || radix == 16) - return sufficient; - - // 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. - 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."); - } - - - // Convert to the actual binary value. - APInt tmp(sufficient, StringRef(p, slen), radix); - - // Compute how many bits are required. If the log is infinite, assume we need - // just bit. If the log is exact and value is negative, then the value is - // MinSignedValue with (log + 1) bits. - unsigned log = tmp.logBase2(); - if (log == (unsigned)-1) { - return isNegative + 1; - } else if (isNegative && tmp.isPowerOf2()) { - return isNegative + log; - } else { - return isNegative + log + 1; - } -} - -hash_code llvm::hash_value(const APInt &Arg) { - if (Arg.isSingleWord()) - return hash_combine(Arg.BitWidth, Arg.U.VAL); - - return hash_combine( - Arg.BitWidth, - hash_combine_range(Arg.U.pVal, Arg.U.pVal + Arg.getNumWords())); -} - -unsigned DenseMapInfo::getHashValue(const APInt &Key) { - return static_cast(hash_value(Key)); -} - -bool APInt::isSplat(unsigned SplatSizeInBits) const { - assert(getBitWidth() % SplatSizeInBits == 0 && - "SplatSizeInBits must divide width!"); - // We can check that all parts of an integer are equal by making use of a - // little trick: rotate and check if it's still the same value. - return *this == rotl(SplatSizeInBits); -} - -/// This function returns the high "numBits" bits of this APInt. -APInt APInt::getHiBits(unsigned numBits) const { - return this->lshr(BitWidth - numBits); -} - -/// This function returns the low "numBits" bits of this APInt. -APInt APInt::getLoBits(unsigned numBits) const { - APInt Result(getLowBitsSet(BitWidth, numBits)); - Result &= *this; - return Result; -} - -/// Return a value containing V broadcasted over NewLen bits. -APInt APInt::getSplat(unsigned NewLen, const APInt &V) { - assert(NewLen >= V.getBitWidth() && "Can't splat to smaller bit width!"); - - APInt Val = V.zext(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::countl_zero(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::countl_one(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::countl_one(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::countr_zero(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::countr_one(U.pVal[i]); - assert(Count <= BitWidth); - return Count; -} - -unsigned APInt::countPopulationSlowCase() const { - unsigned Count = 0; - for (unsigned i = 0; i < getNumWords(); ++i) - Count += llvm::popcount(U.pVal[i]); - return Count; -} - -bool APInt::intersectsSlowCase(const APInt &RHS) const { - for (unsigned i = 0, e = getNumWords(); i != e; ++i) - if ((U.pVal[i] & RHS.U.pVal[i]) != 0) - return true; - - return false; -} - -bool APInt::isSubsetOfSlowCase(const APInt &RHS) const { - for (unsigned i = 0, e = getNumWords(); i != e; ++i) - if ((U.pVal[i] & ~RHS.U.pVal[i]) != 0) - return false; - - return true; -} - -APInt APInt::byteSwap() const { - assert(BitWidth >= 16 && BitWidth % 8 == 0 && "Cannot byteswap!"); - if (BitWidth == 16) - return APInt(BitWidth, llvm::byteswap(U.VAL)); - if (BitWidth == 32) - return APInt(BitWidth, llvm::byteswap(U.VAL)); - if (BitWidth <= 64) { - uint64_t Tmp1 = llvm::byteswap(U.VAL); - Tmp1 >>= (64 - BitWidth); - return APInt(BitWidth, Tmp1); - } - - APInt Result(getNumWords() * APINT_BITS_PER_WORD, 0); - for (unsigned I = 0, N = getNumWords(); I != N; ++I) - Result.U.pVal[I] = llvm::byteswap(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(U.VAL)); - case 32: - return APInt(BitWidth, llvm::reverseBits(U.VAL)); - case 16: - return APInt(BitWidth, llvm::reverseBits(U.VAL)); - case 8: - return APInt(BitWidth, llvm::reverseBits(U.VAL)); - case 0: - return *this; - default: - break; - } - - APInt Val(*this); - APInt Reversed(BitWidth, 0); - unsigned S = BitWidth; - - for (; Val != 0; Val.lshrInPlace(1)) { - Reversed <<= 1; - Reversed |= Val[0]; - --S; - } - - Reversed <<= S; - return Reversed; -} - -APInt llvm::APIntOps::GreatestCommonDivisor(APInt A, APInt B) { - // Fast-path a common case. - if (A == B) return A; - - // Corner cases: if either operand is zero, the other is the gcd. - if (!A) return B; - if (!B) return A; - - // Count common powers of 2 and remove all other powers of 2. - unsigned Pow2; - { - unsigned Pow2_A = A.countr_zero(); - unsigned Pow2_B = B.countr_zero(); - 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.countr_zero() - Pow2); - } else { - B -= A; - B.lshrInPlace(B.countr_zero() - Pow2); - } - } - - return A; -} - -APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) { - uint64_t I = bit_cast(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); - } - 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::infinity(); - else - return -std::numeric_limits::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(I); -} - -// Truncate to new width. -APInt APInt::trunc(unsigned width) const { - assert(width <= BitWidth && "Invalid APInt Truncate request"); - - if (width <= APINT_BITS_PER_WORD) - return APInt(width, getRawData()[0], /*isSigned=*/false, - /*implicitTrunc=*/true); - - if (width == BitWidth) - return *this; - - APInt Result(getMemory(getNumWords(width)), width); - - // Copy full words. - unsigned i; - for (i = 0; i != width / APINT_BITS_PER_WORD; i++) - Result.U.pVal[i] = U.pVal[i]; - - // Truncate and copy any partial word. - unsigned bits = (0 - width) % APINT_BITS_PER_WORD; - if (bits != 0) - Result.U.pVal[i] = U.pVal[i] << bits >> bits; - - return Result; -} - -// Truncate to new width with unsigned saturation. -APInt APInt::truncUSat(unsigned width) const { - assert(width <= BitWidth && "Invalid APInt Truncate request"); - - // Can we just losslessly truncate it? - if (isIntN(width)) - return trunc(width); - // If not, then just return the new limit. - return APInt::getMaxValue(width); -} - -// Truncate to new width with signed saturation. -APInt APInt::truncSSat(unsigned width) const { - assert(width <= BitWidth && "Invalid APInt Truncate request"); - - // Can we just losslessly truncate it? - if (isSignedIntN(width)) - return trunc(width); - // If not, then just return the new limits. - return isNegative() ? APInt::getSignedMinValue(width) - : APInt::getSignedMaxValue(width); -} - -// Sign extend to a new width. -APInt APInt::sext(unsigned Width) const { - assert(Width >= BitWidth && "Invalid APInt SignExtend request"); - - if (Width <= APINT_BITS_PER_WORD) - return APInt(Width, SignExtend64(U.VAL, BitWidth), /*isSigned=*/true); - - if (Width == BitWidth) - return *this; - - 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); - - if (width == BitWidth) - return *this; - - 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; -} - -/// 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. Use an arithmetic - // shift to preserve the sign bit. - U.pVal[WordsToMove - 1] = - (int64_t)U.pVal[WordShift + WordsToMove - 1] >> BitShift; - } - } - - // Fill in the remainder based on the original sign. - std::memset(U.pVal + WordsToMove, Negative ? -1 : 0, - WordShift * APINT_WORD_SIZE); - clearUnusedBits(); -} - -/// Logical right-shift this APInt by shiftAmt. -/// Logical right-shift function. -void APInt::lshrInPlace(const APInt &shiftAmt) { - lshrInPlace((unsigned)shiftAmt.getLimitedValue(BitWidth)); -} - -/// Logical right-shift this APInt by shiftAmt. -/// Logical right-shift function. -void APInt::lshrSlowCase(unsigned ShiftAmt) { - tcShiftRight(U.pVal, getNumWords(), ShiftAmt); -} - -/// Left-shift this APInt by shiftAmt. -/// Left-shift function. -APInt &APInt::operator<<=(const APInt &shiftAmt) { - // It's undefined behavior in C to shift by BitWidth or greater. - *this <<= (unsigned)shiftAmt.getLimitedValue(BitWidth); - return *this; -} - -void APInt::shlSlowCase(unsigned ShiftAmt) { - tcShiftLeft(U.pVal, getNumWords(), ShiftAmt); - clearUnusedBits(); -} - -// Calculate the rotate amount modulo the bit width. -static unsigned rotateModulo(unsigned BitWidth, const APInt &rotateAmt) { - if (LLVM_UNLIKELY(BitWidth == 0)) - return 0; - unsigned rotBitWidth = rotateAmt.getBitWidth(); - APInt rot = rotateAmt; - if (rotBitWidth < BitWidth) { - // Extend the rotate APInt, so that the urem doesn't divide by 0. - // e.g. APInt(1, 32) would give APInt(1, 0). - rot = rotateAmt.zext(BitWidth); - } - rot = rot.urem(APInt(rot.getBitWidth(), BitWidth)); - return rot.getLimitedValue(BitWidth); -} - -APInt APInt::rotl(const APInt &rotateAmt) const { - return rotl(rotateModulo(BitWidth, rotateAmt)); -} - -APInt APInt::rotl(unsigned rotateAmt) const { - if (LLVM_UNLIKELY(BitWidth == 0)) - return *this; - rotateAmt %= BitWidth; - if (rotateAmt == 0) - return *this; - return shl(rotateAmt) | lshr(BitWidth - rotateAmt); -} - -APInt APInt::rotr(const APInt &rotateAmt) const { - return rotr(rotateModulo(BitWidth, rotateAmt)); -} - -APInt APInt::rotr(unsigned rotateAmt) const { - if (BitWidth == 0) - return *this; - rotateAmt %= BitWidth; - if (rotateAmt == 0) - return *this; - return lshr(rotateAmt) | shl(BitWidth - rotateAmt); -} - -/// \returns the nearest log base 2 of this APInt. Ties round up. -/// -/// NOTE: When we have a BitWidth of 1, we define: -/// -/// log2(0) = UINT32_MAX -/// log2(1) = 0 -/// -/// to get around any mathematical concerns resulting from -/// referencing 2 in a space where 2 does no exist. -unsigned APInt::nearestLogBase2() const { - // Special case when we have a bitwidth of 1. If VAL is 1, then we - // get 0. If VAL is 0, we get WORDTYPE_MAX which gets truncated to - // UINT32_MAX. - if (BitWidth == 1) - return U.VAL - 1; - - // Handle the zero case. - if (isZero()) - return UINT32_MAX; - - // The non-zero case is handled by computing: - // - // nearestLogBase2(x) = logBase2(x) + x[logBase2(x)-1]. - // - // where x[i] is referring to the value of the ith bit of x. - unsigned lg = logBase2(); - return lg + unsigned((*this)[lg - 1]); -} - -// Square Root - this method computes and returns the square root of "this". -// Three mechanisms are used for computation. For small values (<= 5 bits), -// a table lookup is done. This gets some performance for common cases. For -// values using less than 52 bits, the value is converted to double and then -// the libc sqrt function is called. The result is rounded and then converted -// back to a uint64_t which is then used to construct the result. Finally, -// the Babylonian method for computing square roots is used. -APInt APInt::sqrt() const { - - // Determine the magnitude of the value. - unsigned magnitude = getActiveBits(); - - // Use a fast table for some small values. This also gets rid of some - // rounding errors in libc sqrt for small values. - if (magnitude <= 5) { - static const uint8_t results[32] = { - /* 0 */ 0, - /* 1- 2 */ 1, 1, - /* 3- 6 */ 2, 2, 2, 2, - /* 7-12 */ 3, 3, 3, 3, 3, 3, - /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4, - /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, - /* 31 */ 6 - }; - return APInt(BitWidth, results[ (isSingleWord() ? U.VAL : U.pVal[0]) ]); - } - - // If the magnitude of the value fits in less than 52 bits (the precision of - // an IEEE double precision floating point value), then we can use the - // libc sqrt function which will probably use a hardware sqrt computation. - // This should be faster than the algorithm below. - if (magnitude < 52) { - return APInt(BitWidth, - uint64_t(::round(::sqrt(double(isSingleWord() ? U.VAL - : U.pVal[0]))))); - } - - // Okay, all the short cuts are exhausted. We must compute it. The following - // is a classical Babylonian method for computing the square root. This code - // was adapted to APInt from a wikipedia article on such computations. - // See http://www.wikipedia.org/ and go to the page named - // Calculate_an_integer_square_root. - unsigned nbits = BitWidth, i = 4; - APInt testy(BitWidth, 16); - APInt x_old(BitWidth, 1); - APInt x_new(BitWidth, 0); - APInt two(BitWidth, 2); - - // Select a good starting value using binary logarithms. - for (;; i += 2, testy = testy.shl(2)) - if (i >= nbits || this->ule(testy)) { - x_old = x_old.shl(i / 2); - break; - } - - // Use the Babylonian method to arrive at the integer square root: - for (;;) { - x_new = (this->udiv(x_old) + x_old).udiv(two); - if (x_old.ule(x_new)) - break; - x_old = x_new; - } - - // Make sure we return the closest approximation - // NOTE: The rounding calculation below is correct. It will produce an - // off-by-one discrepancy with results from pari/gp. That discrepancy has been - // determined to be a rounding issue with pari/gp as it begins to use a - // floating point representation after 192 bits. There are no discrepancies - // between this algorithm and pari/gp for bit widths < 192 bits. - APInt square(x_old * x_old); - APInt nextSquare((x_old + 1) * (x_old +1)); - if (this->ult(square)) - return x_old; - assert(this->ule(nextSquare) && "Error in APInt::sqrt computation"); - APInt midpoint((nextSquare - square).udiv(two)); - APInt offset(*this - square); - if (offset.ult(midpoint)) - return x_old; - return x_old + 1; -} - -/// \returns the multiplicative inverse of an odd APInt modulo 2^BitWidth. -APInt APInt::multiplicativeInverse() const { - assert((*this)[0] && - "multiplicative inverse is only defined for odd numbers!"); - - // Use Newton's method. - APInt Factor = *this; - APInt T; - while (!(T = *this * Factor).isOne()) - Factor *= 2 - std::move(T); - return Factor; -} - -/// 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 = llvm::countl_zero(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 = qp * uint64_t(v[i]); - int64_t subres = int64_t(u[j+i]) - borrow - Lo_32(p); - u[j+i] = Lo_32(subres); - borrow = Hi_32(p) - Hi_32(subres); - DEBUG_KNUTH(dbgs() << "KnuthDiv: u[j+i] = " << u[j + i] - << ", borrow = " << borrow << '\n'); - } - bool isNeg = u[j+n] < borrow; - u[j+n] -= Lo_32(borrow); - - DEBUG_KNUTH(dbgs() << "KnuthDiv: after subtraction:"); - DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]); - DEBUG_KNUTH(dbgs() << '\n'); - - // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was - // negative, go to step D6; otherwise go on to step D7. - q[j] = Lo_32(qp); - if (isNeg) { - // D6. [Add back]. The probability that this step is necessary is very - // small, on the order of only 2/b. Make sure that test data accounts for - // this possibility. Decrease q[j] by 1 - q[j]--; - // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]). - // A carry will occur to the left of u[j+n], and it should be ignored - // since it cancels with the borrow that occurred in D4. - bool carry = false; - for (unsigned i = 0; i < n; i++) { - uint32_t limit = std::min(u[j+i],v[i]); - u[j+i] += v[i] + carry; - carry = u[j+i] < limit || (carry && u[j+i] == limit); - } - u[j+n] += carry; - } - DEBUG_KNUTH(dbgs() << "KnuthDiv: after correction:"); - DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]); - DEBUG_KNUTH(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n'); - - // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3. - } while (--j >= 0); - - DEBUG_KNUTH(dbgs() << "KnuthDiv: quotient:"); - DEBUG_KNUTH(for (int i = m; i >= 0; i--) dbgs() << " " << q[i]); - DEBUG_KNUTH(dbgs() << '\n'); - - // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired - // remainder may be obtained by dividing u[...] by d. If r is non-null we - // compute the remainder (urem uses this). - if (r) { - // The value d is expressed by the "shift" value above since we avoided - // multiplication by d by using a shift left. So, all we have to do is - // shift right here. - if (shift) { - uint32_t carry = 0; - DEBUG_KNUTH(dbgs() << "KnuthDiv: remainder:"); - for (int i = n-1; i >= 0; i--) { - r[i] = (u[i] >> shift) | carry; - carry = u[i] << (32 - shift); - DEBUG_KNUTH(dbgs() << " " << r[i]); - } - } else { - for (int i = n-1; i >= 0; i--) { - r[i] = u[i]; - DEBUG_KNUTH(dbgs() << " " << r[i]); - } - } - DEBUG_KNUTH(dbgs() << '\n'); - } - DEBUG_KNUTH(dbgs() << '\n'); -} - -void APInt::divide(const WordType *LHS, unsigned lhsWords, const WordType *RHS, - unsigned rhsWords, WordType *Quotient, WordType *Remainder) { - assert(lhsWords >= rhsWords && "Fractional result"); - - // First, compose the values into an array of 32-bit words instead of - // 64-bit words. This is a necessity of both the "short division" algorithm - // and the Knuth "classical algorithm" which requires there to be native - // operations for +, -, and * on an m bit value with an m*2 bit result. We - // can't use 64-bit operands here because we don't have native results of - // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't - // work on large-endian machines. - unsigned n = rhsWords * 2; - unsigned m = (lhsWords * 2) - n; - - // Allocate space for the temporary values we need either on the stack, if - // it will fit, or on the heap if it won't. - uint32_t SPACE[128]; - uint32_t *U = nullptr; - uint32_t *V = nullptr; - uint32_t *Q = nullptr; - uint32_t *R = nullptr; - if ((Remainder?4:3)*n+2*m+1 <= 128) { - U = &SPACE[0]; - V = &SPACE[m+n+1]; - Q = &SPACE[(m+n+1) + n]; - if (Remainder) - R = &SPACE[(m+n+1) + n + (m+n)]; - } else { - U = new uint32_t[m + n + 1]; - V = new uint32_t[n]; - Q = new uint32_t[m+n]; - if (Remainder) - R = new uint32_t[n]; - } - - // Initialize the dividend - memset(U, 0, (m+n+1)*sizeof(uint32_t)); - for (unsigned i = 0; i < lhsWords; ++i) { - uint64_t tmp = LHS[i]; - U[i * 2] = Lo_32(tmp); - U[i * 2 + 1] = Hi_32(tmp); - } - U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm. - - // Initialize the divisor - memset(V, 0, (n)*sizeof(uint32_t)); - for (unsigned i = 0; i < rhsWords; ++i) { - uint64_t tmp = RHS[i]; - V[i * 2] = Lo_32(tmp); - V[i * 2 + 1] = Hi_32(tmp); - } - - // initialize the quotient and remainder - memset(Q, 0, (m+n) * sizeof(uint32_t)); - if (Remainder) - memset(R, 0, n * sizeof(uint32_t)); - - // Now, adjust m and n for the Knuth division. n is the number of words in - // the divisor. m is the number of words by which the dividend exceeds the - // divisor (i.e. m+n is the length of the dividend). These sizes must not - // contain any zero words or the Knuth algorithm fails. - for (unsigned i = n; i > 0 && V[i-1] == 0; i--) { - n--; - m++; - } - for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--) - m--; - - // If we're left with only a single word for the divisor, Knuth doesn't work - // so we implement the short division algorithm here. This is much simpler - // and faster because we are certain that we can divide a 64-bit quantity - // by a 32-bit quantity at hardware speed and short division is simply a - // series of such operations. This is just like doing short division but we - // are using base 2^32 instead of base 10. - assert(n != 0 && "Divide by zero?"); - if (n == 1) { - uint32_t divisor = V[0]; - uint32_t remainder = 0; - for (int i = m; i >= 0; i--) { - uint64_t partial_dividend = Make_64(remainder, U[i]); - if (partial_dividend == 0) { - Q[i] = 0; - remainder = 0; - } else if (partial_dividend < divisor) { - Q[i] = 0; - remainder = Lo_32(partial_dividend); - } else if (partial_dividend == divisor) { - Q[i] = 1; - remainder = 0; - } else { - Q[i] = Lo_32(partial_dividend / divisor); - remainder = Lo_32(partial_dividend - (Q[i] * divisor)); - } - } - if (R) - R[0] = remainder; - } else { - // Now we're ready to invoke the Knuth classical divide algorithm. In this - // case n > 1. - KnuthDiv(U, V, Q, R, m, n); - } - - // If the caller wants the quotient - if (Quotient) { - for (unsigned i = 0; i < lhsWords; ++i) - Quotient[i] = Make_64(Q[i*2+1], Q[i*2]); - } - - // If the caller wants the remainder - if (Remainder) { - for (unsigned i = 0; i < rhsWords; ++i) - Remainder[i] = Make_64(R[i*2+1], R[i*2]); - } - - // Clean up the memory we allocated. - if (U != &SPACE[0]) { - delete [] U; - delete [] V; - delete [] Q; - delete [] R; - } -} - -APInt APInt::udiv(const APInt &RHS) const { - assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); - - // First, deal with the easy case - if (isSingleWord()) { - assert(RHS.U.VAL != 0 && "Divide by zero?"); - return APInt(BitWidth, U.VAL / RHS.U.VAL); - } - - // Get some facts about the LHS and RHS number of bits and words - unsigned lhsWords = getNumWords(getActiveBits()); - unsigned rhsBits = RHS.getActiveBits(); - unsigned rhsWords = getNumWords(rhsBits); - assert(rhsWords && "Divided by zero???"); - - // Deal with some degenerate cases - if (!lhsWords) - // 0 / X ===> 0 - return APInt(BitWidth, 0); - if (rhsBits == 1) - // X / 1 ===> X - return *this; - if (lhsWords < rhsWords || this->ult(RHS)) - // X / Y ===> 0, iff X < Y - return APInt(BitWidth, 0); - if (*this == RHS) - // X / X ===> 1 - return APInt(BitWidth, 1); - if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1. - // All high words are zero, just use native divide - return APInt(BitWidth, this->U.pVal[0] / RHS.U.pVal[0]); - - // We have to compute it the hard way. Invoke the Knuth divide algorithm. - APInt Quotient(BitWidth, 0); // to hold result. - divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal, nullptr); - return Quotient; -} - -APInt APInt::udiv(uint64_t RHS) const { - assert(RHS != 0 && "Divide by zero?"); - - // First, deal with the easy case - if (isSingleWord()) - return APInt(BitWidth, U.VAL / RHS); - - // Get some facts about the LHS words. - unsigned lhsWords = getNumWords(getActiveBits()); - - // Deal with some degenerate cases - if (!lhsWords) - // 0 / X ===> 0 - return APInt(BitWidth, 0); - if (RHS == 1) - // X / 1 ===> X - return *this; - if (this->ult(RHS)) - // X / Y ===> 0, iff X < Y - return APInt(BitWidth, 0); - if (*this == RHS) - // X / X ===> 1 - return APInt(BitWidth, 1); - if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1. - // All high words are zero, just use native divide - return APInt(BitWidth, this->U.pVal[0] / RHS); - - // We have to compute it the hard way. Invoke the Knuth divide algorithm. - APInt Quotient(BitWidth, 0); // to hold result. - divide(U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, nullptr); - return Quotient; -} - -APInt APInt::sdiv(const APInt &RHS) const { - if (isNegative()) { - if (RHS.isNegative()) - return (-(*this)).udiv(-RHS); - return -((-(*this)).udiv(RHS)); - } - if (RHS.isNegative()) - return -(this->udiv(-RHS)); - return this->udiv(RHS); -} - -APInt APInt::sdiv(int64_t RHS) const { - if (isNegative()) { - if (RHS < 0) - return (-(*this)).udiv(-RHS); - return -((-(*this)).udiv(RHS)); - } - if (RHS < 0) - return -(this->udiv(-RHS)); - return this->udiv(RHS); -} - -APInt APInt::urem(const APInt &RHS) const { - assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); - if (isSingleWord()) { - assert(RHS.U.VAL != 0 && "Remainder by zero?"); - return APInt(BitWidth, U.VAL % RHS.U.VAL); - } - - // Get some facts about the LHS - unsigned lhsWords = getNumWords(getActiveBits()); - - // Get some facts about the RHS - unsigned rhsBits = RHS.getActiveBits(); - unsigned rhsWords = getNumWords(rhsBits); - assert(rhsWords && "Performing remainder operation by zero ???"); - - // Check the degenerate cases - if (lhsWords == 0) - // 0 % Y ===> 0 - return APInt(BitWidth, 0); - if (rhsBits == 1) - // X % 1 ===> 0 - return APInt(BitWidth, 0); - if (lhsWords < rhsWords || this->ult(RHS)) - // X % Y ===> X, iff X < Y - return *this; - if (*this == RHS) - // X % X == 0; - return APInt(BitWidth, 0); - if (lhsWords == 1) - // All high words are zero, just use native remainder - return APInt(BitWidth, U.pVal[0] % RHS.U.pVal[0]); - - // We have to compute it the hard way. Invoke the Knuth divide algorithm. - APInt Remainder(BitWidth, 0); - divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, nullptr, Remainder.U.pVal); - return Remainder; -} - -uint64_t APInt::urem(uint64_t RHS) const { - assert(RHS != 0 && "Remainder by zero?"); - - if (isSingleWord()) - return U.VAL % RHS; - - // Get some facts about the LHS - unsigned lhsWords = getNumWords(getActiveBits()); - - // Check the degenerate cases - if (lhsWords == 0) - // 0 % Y ===> 0 - return 0; - if (RHS == 1) - // X % 1 ===> 0 - return 0; - if (this->ult(RHS)) - // X % Y ===> X, iff X < Y - return getZExtValue(); - if (*this == RHS) - // X % X == 0; - return 0; - if (lhsWords == 1) - // All high words are zero, just use native remainder - return U.pVal[0] % RHS; - - // We have to compute it the hard way. Invoke the Knuth divide algorithm. - uint64_t Remainder; - divide(U.pVal, lhsWords, &RHS, 1, nullptr, &Remainder); - return Remainder; -} - -APInt APInt::srem(const APInt &RHS) const { - if (isNegative()) { - if (RHS.isNegative()) - return -((-(*this)).urem(-RHS)); - return -((-(*this)).urem(RHS)); - } - if (RHS.isNegative()) - return this->urem(-RHS); - return this->urem(RHS); -} - -int64_t APInt::srem(int64_t RHS) const { - if (isNegative()) { - if (RHS < 0) - return -((-(*this)).urem(-RHS)); - return -((-(*this)).urem(RHS)); - } - if (RHS < 0) - return this->urem(-RHS); - return this->urem(RHS); -} - -void APInt::udivrem(const APInt &LHS, const APInt &RHS, - APInt &Quotient, APInt &Remainder) { - assert(LHS.BitWidth == RHS.BitWidth && "Bit widths must be the same"); - unsigned BitWidth = LHS.BitWidth; - - // First, deal with the easy case - if (LHS.isSingleWord()) { - assert(RHS.U.VAL != 0 && "Divide by zero?"); - uint64_t QuotVal = LHS.U.VAL / RHS.U.VAL; - uint64_t RemVal = LHS.U.VAL % RHS.U.VAL; - Quotient = APInt(BitWidth, QuotVal); - Remainder = APInt(BitWidth, RemVal); - return; - } - - // Get some size facts about the dividend and divisor - unsigned lhsWords = getNumWords(LHS.getActiveBits()); - unsigned rhsBits = RHS.getActiveBits(); - unsigned rhsWords = getNumWords(rhsBits); - assert(rhsWords && "Performing divrem operation by zero ???"); - - // Check the degenerate cases - if (lhsWords == 0) { - Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0 - Remainder = APInt(BitWidth, 0); // 0 % Y ===> 0 - return; - } - - if (rhsBits == 1) { - Quotient = LHS; // X / 1 ===> X - Remainder = APInt(BitWidth, 0); // X % 1 ===> 0 - } - - if (lhsWords < rhsWords || LHS.ult(RHS)) { - Remainder = LHS; // X % Y ===> X, iff X < Y - Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y - return; - } - - if (LHS == RHS) { - Quotient = APInt(BitWidth, 1); // X / X ===> 1 - Remainder = APInt(BitWidth, 0); // X % X ===> 0; - return; - } - - // Make sure there is enough space to hold the results. - // NOTE: This assumes that reallocate won't affect any bits if it doesn't - // change the size. This is necessary if Quotient or Remainder is aliased - // with LHS or RHS. - Quotient.reallocate(BitWidth); - Remainder.reallocate(BitWidth); - - if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1. - // There is only one word to consider so use the native versions. - uint64_t lhsValue = LHS.U.pVal[0]; - uint64_t rhsValue = RHS.U.pVal[0]; - Quotient = lhsValue / rhsValue; - Remainder = lhsValue % rhsValue; - return; - } - - // Okay, lets do it the long way - divide(LHS.U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal, - Remainder.U.pVal); - // Clear the rest of the Quotient and Remainder. - std::memset(Quotient.U.pVal + lhsWords, 0, - (getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE); - std::memset(Remainder.U.pVal + rhsWords, 0, - (getNumWords(BitWidth) - rhsWords) * APINT_WORD_SIZE); -} - -void APInt::udivrem(const APInt &LHS, uint64_t RHS, APInt &Quotient, - uint64_t &Remainder) { - assert(RHS != 0 && "Divide by zero?"); - unsigned BitWidth = LHS.BitWidth; - - // First, deal with the easy case - if (LHS.isSingleWord()) { - uint64_t QuotVal = LHS.U.VAL / RHS; - Remainder = LHS.U.VAL % RHS; - Quotient = APInt(BitWidth, QuotVal); - return; - } - - // Get some size facts about the dividend and divisor - unsigned lhsWords = getNumWords(LHS.getActiveBits()); - - // Check the degenerate cases - if (lhsWords == 0) { - Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0 - Remainder = 0; // 0 % Y ===> 0 - return; - } - - if (RHS == 1) { - Quotient = LHS; // X / 1 ===> X - Remainder = 0; // X % 1 ===> 0 - return; - } - - if (LHS.ult(RHS)) { - Remainder = LHS.getZExtValue(); // X % Y ===> X, iff X < Y - Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y - return; - } - - if (LHS == RHS) { - Quotient = APInt(BitWidth, 1); // X / X ===> 1 - Remainder = 0; // X % X ===> 0; - return; - } - - // Make sure there is enough space to hold the results. - // NOTE: This assumes that reallocate won't affect any bits if it doesn't - // change the size. This is necessary if Quotient is aliased with LHS. - Quotient.reallocate(BitWidth); - - if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1. - // There is only one word to consider so use the native versions. - uint64_t lhsValue = LHS.U.pVal[0]; - Quotient = lhsValue / RHS; - Remainder = lhsValue % RHS; - return; - } - - // Okay, lets do it the long way - divide(LHS.U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, &Remainder); - // Clear the rest of the Quotient. - std::memset(Quotient.U.pVal + lhsWords, 0, - (getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE); -} - -void APInt::sdivrem(const APInt &LHS, const APInt &RHS, - APInt &Quotient, APInt &Remainder) { - if (LHS.isNegative()) { - if (RHS.isNegative()) - APInt::udivrem(-LHS, -RHS, Quotient, Remainder); - else { - APInt::udivrem(-LHS, RHS, Quotient, Remainder); - Quotient.negate(); - } - Remainder.negate(); - } else if (RHS.isNegative()) { - APInt::udivrem(LHS, -RHS, Quotient, Remainder); - Quotient.negate(); - } else { - APInt::udivrem(LHS, RHS, Quotient, Remainder); - } -} - -void APInt::sdivrem(const APInt &LHS, int64_t RHS, - APInt &Quotient, int64_t &Remainder) { - uint64_t R = Remainder; - if (LHS.isNegative()) { - if (RHS < 0) - APInt::udivrem(-LHS, -RHS, Quotient, R); - else { - APInt::udivrem(-LHS, RHS, Quotient, R); - Quotient.negate(); - } - R = -R; - } else if (RHS < 0) { - APInt::udivrem(LHS, -RHS, Quotient, R); - Quotient.negate(); - } else { - APInt::udivrem(LHS, RHS, Quotient, R); - } - Remainder = R; -} - -APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const { - APInt Res = *this+RHS; - Overflow = isNonNegative() == RHS.isNonNegative() && - Res.isNonNegative() != isNonNegative(); - return Res; -} - -APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const { - APInt Res = *this+RHS; - Overflow = Res.ult(RHS); - return Res; -} - -APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const { - APInt Res = *this - RHS; - Overflow = isNonNegative() != RHS.isNonNegative() && - Res.isNonNegative() != isNonNegative(); - return Res; -} - -APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const { - APInt Res = *this-RHS; - Overflow = Res.ugt(*this); - return Res; -} - -APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const { - // MININT/-1 --> overflow. - Overflow = isMinSignedValue() && RHS.isAllOnes(); - return sdiv(RHS); -} - -APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const { - APInt Res = *this * RHS; - - if (RHS != 0) - Overflow = Res.sdiv(RHS) != *this || - (isMinSignedValue() && RHS.isAllOnes()); - else - Overflow = false; - return Res; -} - -APInt APInt::umul_ov(const APInt &RHS, bool &Overflow) const { - if (countl_zero() + RHS.countl_zero() + 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 { - return sshl_ov(ShAmt.getLimitedValue(getBitWidth()), Overflow); -} - -APInt APInt::sshl_ov(unsigned ShAmt, bool &Overflow) const { - Overflow = ShAmt >= getBitWidth(); - if (Overflow) - return APInt(BitWidth, 0); - - if (isNonNegative()) // Don't allow sign change. - Overflow = ShAmt >= countl_zero(); - else - Overflow = ShAmt >= countl_one(); - - return *this << ShAmt; -} - -APInt APInt::ushl_ov(const APInt &ShAmt, bool &Overflow) const { - return ushl_ov(ShAmt.getLimitedValue(getBitWidth()), Overflow); -} - -APInt APInt::ushl_ov(unsigned ShAmt, bool &Overflow) const { - Overflow = ShAmt >= getBitWidth(); - if (Overflow) - return APInt(BitWidth, 0); - - Overflow = ShAmt > countl_zero(); - - return *this << ShAmt; -} - -APInt APInt::sfloordiv_ov(const APInt &RHS, bool &Overflow) const { - APInt quotient = sdiv_ov(RHS, Overflow); - if ((quotient * RHS != *this) && (isNegative() != RHS.isNegative())) - return quotient - 1; - return quotient; -} - -APInt APInt::sadd_sat(const APInt &RHS) const { - bool Overflow; - APInt Res = sadd_ov(RHS, Overflow); - if (!Overflow) - return Res; - - return isNegative() ? APInt::getSignedMinValue(BitWidth) - : APInt::getSignedMaxValue(BitWidth); -} - -APInt APInt::uadd_sat(const APInt &RHS) const { - bool Overflow; - APInt Res = uadd_ov(RHS, Overflow); - if (!Overflow) - return Res; - - return APInt::getMaxValue(BitWidth); -} - -APInt APInt::ssub_sat(const APInt &RHS) const { - bool Overflow; - APInt Res = ssub_ov(RHS, Overflow); - if (!Overflow) - return Res; - - return isNegative() ? APInt::getSignedMinValue(BitWidth) - : APInt::getSignedMaxValue(BitWidth); -} - -APInt APInt::usub_sat(const APInt &RHS) const { - bool Overflow; - APInt Res = usub_ov(RHS, Overflow); - if (!Overflow) - return Res; - - return APInt(BitWidth, 0); -} - -APInt APInt::smul_sat(const APInt &RHS) const { - bool Overflow; - APInt Res = smul_ov(RHS, Overflow); - if (!Overflow) - return Res; - - // The result is negative if one and only one of inputs is negative. - bool ResIsNegative = isNegative() ^ RHS.isNegative(); - - return ResIsNegative ? APInt::getSignedMinValue(BitWidth) - : APInt::getSignedMaxValue(BitWidth); -} - -APInt APInt::umul_sat(const APInt &RHS) const { - bool Overflow; - APInt Res = umul_ov(RHS, Overflow); - if (!Overflow) - return Res; - - return APInt::getMaxValue(BitWidth); -} - -APInt APInt::sshl_sat(const APInt &RHS) const { - return sshl_sat(RHS.getLimitedValue(getBitWidth())); -} - -APInt APInt::sshl_sat(unsigned RHS) const { - bool Overflow; - APInt Res = sshl_ov(RHS, Overflow); - if (!Overflow) - return Res; - - return isNegative() ? APInt::getSignedMinValue(BitWidth) - : APInt::getSignedMaxValue(BitWidth); -} - -APInt APInt::ushl_sat(const APInt &RHS) const { - return ushl_sat(RHS.getLimitedValue(getBitWidth())); -} - -APInt APInt::ushl_sat(unsigned RHS) const { - bool Overflow; - APInt Res = ushl_ov(RHS, Overflow); - if (!Overflow) - return Res; - - return APInt::getMaxValue(BitWidth); -} - -void APInt::fromString(unsigned numbits, StringRef str, uint8_t radix) { - // Check our assumptions here - assert(!str.empty() && "Invalid string length"); - assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 || - radix == 36) && - "Radix should be 2, 8, 10, 16, or 36!"); - - StringRef::iterator p = str.begin(); - size_t slen = str.size(); - bool isNeg = *p == '-'; - if (*p == '-' || *p == '+') { - p++; - slen--; - assert(slen && "String is only a sign, needs a value."); - } - assert((slen <= numbits || radix != 2) && "Insufficient bit width"); - assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width"); - assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width"); - assert((((slen-1)*64)/22 <= numbits || radix != 10) && - "Insufficient bit width"); - - // Allocate memory if needed - if (isSingleWord()) - U.VAL = 0; - else - U.pVal = getClearedMemory(getNumWords()); - - // Figure out if we can shift instead of multiply - unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0); - - // Enter digit traversal loop - for (StringRef::iterator e = str.end(); p != e; ++p) { - unsigned digit = getDigit(*p, radix); - assert(digit < radix && "Invalid character in digit string"); - - // Shift or multiply the value by the radix - if (slen > 1) { - if (shift) - *this <<= shift; - else - *this *= radix; - } - - // Add in the digit we just interpreted - *this += digit; - } - // If its negative, put it in two's complement form - if (isNeg) - this->negate(); -} - -void APInt::toString(SmallVectorImpl &Str, unsigned Radix, bool Signed, - bool formatAsCLiteral, bool UpperCase, - bool InsertSeparators) 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!"); - } - } - - // Number of digits in a group between separators. - unsigned Grouping = (Radix == 8 || Radix == 10) ? 3 : 4; - - // First, check for a zero value and just short circuit the logic below. - if (isZero()) { - while (*Prefix) { - Str.push_back(*Prefix); - ++Prefix; - }; - Str.push_back('0'); - return; - } - - static const char BothDigits[] = "0123456789abcdefghijklmnopqrstuvwxyz" - "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; - const char *Digits = BothDigits + (UpperCase ? 36 : 0); - - 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; - }; - - int Pos = 0; - while (N) { - if (InsertSeparators && Pos % Grouping == 0 && Pos > 0) - *--BufPtr = '\''; - *--BufPtr = Digits[N % Radix]; - N /= Radix; - Pos++; - } - 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; - - int Pos = 0; - while (Tmp.getBoolValue()) { - unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt; - if (InsertSeparators && Pos % Grouping == 0 && Pos > 0) - Str.push_back('\''); - - Str.push_back(Digits[Digit]); - Tmp.lshrInPlace(ShiftAmt); - Pos++; - } - } else { - int Pos = 0; - while (Tmp.getBoolValue()) { - uint64_t Digit; - udivrem(Tmp, Radix, Tmp, Digit); - assert(Digit < Radix && "divide failed"); - if (InsertSeparators && Pos % Grouping == 0 && Pos > 0) - Str.push_back('\''); - - Str.push_back(Digits[Digit]); - Pos++; - } - } - - // Reverse the digits before returning. - std::reverse(Str.begin()+StartDig, Str.end()); -} - -#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP) -LLVM_DUMP_METHOD void APInt::dump() const { - SmallString<40> S, U; - this->toStringUnsigned(U); - this->toStringSigned(S); - dbgs() << "APInt(" << BitWidth << "b, " - << U << "u " << S << "s)\n"; -} -#endif - -void APInt::print(raw_ostream &OS, bool isSigned) const { - SmallString<40> S; - this->toString(S, 10, isSigned, /* formatAsCLiteral = */false); - OS << S; -} - -// This implements a variety of operations on a representation of -// arbitrary precision, two's-complement, bignum integer values. - -// Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe -// and unrestricting assumption. -static_assert(APInt::APINT_BITS_PER_WORD % 2 == 0, - "Part width must be divisible by 2!"); - -// Returns the integer part with the least significant BITS set. -// BITS cannot be zero. -static inline APInt::WordType lowBitMask(unsigned bits) { - assert(bits != 0 && bits <= APInt::APINT_BITS_PER_WORD); - return ~(APInt::WordType) 0 >> (APInt::APINT_BITS_PER_WORD - bits); -} - -/// Returns the value of the lower half of PART. -static inline APInt::WordType lowHalf(APInt::WordType part) { - return part & lowBitMask(APInt::APINT_BITS_PER_WORD / 2); -} - -/// Returns the value of the upper half of PART. -static inline APInt::WordType highHalf(APInt::WordType part) { - return part >> (APInt::APINT_BITS_PER_WORD / 2); -} - -/// 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 UINT_MAX is returned. -unsigned APInt::tcLSB(const WordType *parts, unsigned n) { - for (unsigned i = 0; i < n; i++) { - if (parts[i] != 0) { - unsigned lsb = llvm::countr_zero(parts[i]); - return lsb + i * APINT_BITS_PER_WORD; - } - } - - return UINT_MAX; -} - -/// Returns the bit number of the most significant set bit of a number. -/// If the input number has no bits set UINT_MAX is returned. -unsigned APInt::tcMSB(const WordType *parts, unsigned n) { - do { - --n; - - if (parts[n] != 0) { - static_assert(sizeof(parts[n]) <= sizeof(uint64_t)); - unsigned msb = llvm::Log2_64(parts[n]); - - return msb + n * APINT_BITS_PER_WORD; - } - } while (n); - - return UINT_MAX; -} - -/// Copy the bit vector of width srcBITS from SRC, starting at bit srcLSB, to -/// DST, of dstCOUNT parts, such that the bit srcLSB becomes the least -/// significant bit of DST. All high bits above srcBITS in DST are zero-filled. -/// */ -void -APInt::tcExtract(WordType *dst, unsigned dstCount, const WordType *src, - unsigned srcBits, unsigned srcLSB) { - unsigned dstParts = (srcBits + APINT_BITS_PER_WORD - 1) / APINT_BITS_PER_WORD; - assert(dstParts <= dstCount); - - unsigned firstSrcPart = srcLSB / APINT_BITS_PER_WORD; - tcAssign(dst, src + firstSrcPart, dstParts); - - unsigned shift = srcLSB % APINT_BITS_PER_WORD; - tcShiftRight(dst, dstParts, shift); - - // We now have (dstParts * APINT_BITS_PER_WORD - shift) bits from SRC - // in DST. If this is less that srcBits, append the rest, else - // clear the high bits. - unsigned n = dstParts * APINT_BITS_PER_WORD - shift; - if (n < srcBits) { - WordType mask = lowBitMask (srcBits - n); - dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask) - << n % APINT_BITS_PER_WORD); - } else if (n > srcBits) { - if (srcBits % APINT_BITS_PER_WORD) - dst[dstParts - 1] &= lowBitMask (srcBits % APINT_BITS_PER_WORD); - } - - // Clear high parts. - while (dstParts < dstCount) - dst[dstParts++] = 0; -} - -//// DST += RHS + C where C is zero or one. Returns the carry flag. -APInt::WordType APInt::tcAdd(WordType *dst, const WordType *rhs, - WordType c, unsigned parts) { - assert(c <= 1); - - for (unsigned i = 0; i < parts; i++) { - WordType l = dst[i]; - if (c) { - dst[i] += rhs[i] + 1; - c = (dst[i] <= l); - } else { - dst[i] += rhs[i]; - c = (dst[i] < l); - } - } - - return c; -} - -/// This function adds a single "word" integer, src, to the multiple -/// "word" integer array, dst[]. dst[] is modified to reflect the addition and -/// 1 is returned if there is a carry out, otherwise 0 is returned. -/// @returns the carry of the addition. -APInt::WordType APInt::tcAddPart(WordType *dst, WordType src, - unsigned parts) { - for (unsigned i = 0; i < parts; ++i) { - dst[i] += src; - if (dst[i] >= src) - return 0; // No need to carry so exit early. - src = 1; // Carry one to next digit. - } - - return 1; -} - -/// DST -= RHS + C where C is zero or one. Returns the carry flag. -APInt::WordType APInt::tcSubtract(WordType *dst, const WordType *rhs, - WordType c, unsigned parts) { - assert(c <= 1); - - for (unsigned i = 0; i < parts; i++) { - WordType l = dst[i]; - if (c) { - dst[i] -= rhs[i] + 1; - c = (dst[i] >= l); - } else { - dst[i] -= rhs[i]; - c = (dst[i] > l); - } - } - - return c; -} - -/// This function subtracts a single "word" (64-bit word), src, from -/// the multi-word integer array, dst[], propagating the borrowed 1 value until -/// no further borrowing is needed or it runs out of "words" in dst. The result -/// is 1 if "borrowing" exhausted the digits in dst, or 0 if dst was not -/// exhausted. In other words, if src > dst then this function returns 1, -/// otherwise 0. -/// @returns the borrow out of the subtraction -APInt::WordType APInt::tcSubtractPart(WordType *dst, WordType src, - unsigned parts) { - for (unsigned i = 0; i < parts; ++i) { - WordType Dst = dst[i]; - dst[i] -= src; - if (src <= Dst) - return 0; // No need to borrow so exit early. - src = 1; // We have to "borrow 1" from next "word" - } - - return 1; -} - -/// Negate a bignum in-place. -void APInt::tcNegate(WordType *dst, unsigned parts) { - tcComplement(dst, parts); - tcIncrement(dst, parts); -} - -/// DST += SRC * MULTIPLIER + CARRY if add is true -/// DST = SRC * MULTIPLIER + CARRY if add is false -/// Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC -/// they must start at the same point, i.e. DST == SRC. -/// If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is -/// returned. Otherwise DST is filled with the least significant -/// DSTPARTS parts of the result, and if all of the omitted higher -/// parts were zero return zero, otherwise overflow occurred and -/// return one. -int APInt::tcMultiplyPart(WordType *dst, const WordType *src, - WordType multiplier, WordType carry, - unsigned srcParts, unsigned dstParts, - bool add) { - // Otherwise our writes of DST kill our later reads of SRC. - assert(dst <= src || dst >= src + srcParts); - assert(dstParts <= srcParts + 1); - - // N loops; minimum of dstParts and srcParts. - unsigned n = std::min(dstParts, srcParts); - - for (unsigned i = 0; i < n; i++) { - // [LOW, HIGH] = MULTIPLIER * SRC[i] + DST[i] + CARRY. - // This cannot overflow, because: - // (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1) - // which is less than n^2. - WordType srcPart = src[i]; - WordType low, mid, high; - if (multiplier == 0 || srcPart == 0) { - low = carry; - high = 0; - } else { - low = lowHalf(srcPart) * lowHalf(multiplier); - high = highHalf(srcPart) * highHalf(multiplier); - - mid = lowHalf(srcPart) * highHalf(multiplier); - high += highHalf(mid); - mid <<= APINT_BITS_PER_WORD / 2; - if (low + mid < low) - high++; - low += mid; - - mid = highHalf(srcPart) * lowHalf(multiplier); - high += highHalf(mid); - mid <<= APINT_BITS_PER_WORD / 2; - if (low + mid < low) - high++; - low += mid; - - // Now add carry. - if (low + carry < low) - high++; - low += carry; - } - - if (add) { - // And now DST[i], and store the new low part there. - if (low + dst[i] < low) - high++; - dst[i] += low; - } else { - dst[i] = low; - } - - carry = high; - } - - if (srcParts < dstParts) { - // Full multiplication, there is no overflow. - assert(srcParts + 1 == dstParts); - dst[srcParts] = carry; - return 0; - } - - // We overflowed if there is carry. - if (carry) - return 1; - - // We would overflow if any significant unwritten parts would be - // non-zero. This is true if any remaining src parts are non-zero - // and the multiplier is non-zero. - if (multiplier) - for (unsigned i = dstParts; i < srcParts; i++) - if (src[i]) - return 1; - - // We fitted in the narrow destination. - return 0; -} - -/// DST = LHS * RHS, where DST has the same width as the operands and -/// is filled with the least significant parts of the result. Returns -/// one if overflow occurred, otherwise zero. DST must be disjoint -/// from both operands. -int APInt::tcMultiply(WordType *dst, const WordType *lhs, - const WordType *rhs, unsigned parts) { - assert(dst != lhs && dst != rhs); - - int overflow = 0; - - for (unsigned i = 0; i < parts; i++) { - // Don't accumulate on the first iteration so we don't need to initalize - // dst to 0. - overflow |= - tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts, parts - i, i != 0); - } - - 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); - - for (unsigned i = 0; i < lhsParts; i++) { - // Don't accumulate on the first iteration so we don't need to initalize - // dst to 0. - tcMultiplyPart(&dst[i], rhs, lhs[i], 0, rhsParts, rhsParts + 1, i != 0); - } -} - -// If RHS is zero LHS and REMAINDER are left unchanged, return one. -// Otherwise set LHS to LHS / RHS with the fractional part discarded, -// set REMAINDER to the remainder, return zero. i.e. -// -// OLD_LHS = RHS * LHS + REMAINDER -// -// SCRATCH is a bignum of the same size as the operands and result for -// use by the routine; its contents need not be initialized and are -// destroyed. LHS, REMAINDER and SCRATCH must be distinct. -int APInt::tcDivide(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 Count 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); -} - -// 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; -} - -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.isZero()) - 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.isZero()) - 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 towards zero. - case APInt::Rounding::TOWARD_ZERO: - return A.sdiv(B); - } - llvm_unreachable("Unknown APInt::Rounding enum"); -} - -std::optional -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).isZero()) { - 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.isZero()) - 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, decrement 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.isZero()) { - 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.isZero() != VY.isZero(); - // 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 std::nullopt; - } - - X += 1; - LLVM_DEBUG(dbgs() << __func__ << ": solution (wrap): " << X << '\n'); - return X; -} - -std::optional -llvm::APIntOps::GetMostSignificantDifferentBit(const APInt &A, const APInt &B) { - assert(A.getBitWidth() == B.getBitWidth() && "Must have the same bitwidth"); - if (A == B) - return std::nullopt; - return A.getBitWidth() - ((A ^ B).countl_zero() + 1); -} - -APInt llvm::APIntOps::ScaleBitMask(const APInt &A, unsigned NewBitWidth, - bool MatchAllBits) { - unsigned OldBitWidth = A.getBitWidth(); - assert((((OldBitWidth % NewBitWidth) == 0) || - ((NewBitWidth % OldBitWidth) == 0)) && - "One size should be a multiple of the other one. " - "Can't do fractional scaling."); - - // Check for matching bitwidths. - if (OldBitWidth == NewBitWidth) - return A; - - APInt NewA = APInt::getZero(NewBitWidth); - - // Check for null input. - if (A.isZero()) - return NewA; - - if (NewBitWidth > OldBitWidth) { - // Repeat bits. - unsigned Scale = NewBitWidth / OldBitWidth; - for (unsigned i = 0; i != OldBitWidth; ++i) - if (A[i]) - NewA.setBits(i * Scale, (i + 1) * Scale); - } else { - unsigned Scale = OldBitWidth / NewBitWidth; - for (unsigned i = 0; i != NewBitWidth; ++i) { - if (MatchAllBits) { - if (A.extractBits(Scale, i * Scale).isAllOnes()) - NewA.setBit(i); - } else { - if (!A.extractBits(Scale, i * Scale).isZero()) - NewA.setBit(i); - } - } - } - - return NewA; -} - -/// 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, const uint8_t *Src, - unsigned LoadBytes) { - assert((IntVal.getBitWidth()+7)/8 >= LoadBytes && "Integer too small!"); - uint8_t *Dst = reinterpret_cast( - const_cast(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); - } -} - -APInt APIntOps::avgFloorS(const APInt &C1, const APInt &C2) { - // Return floor((C1 + C2) / 2) - return (C1 & C2) + (C1 ^ C2).ashr(1); -} - -APInt APIntOps::avgFloorU(const APInt &C1, const APInt &C2) { - // Return floor((C1 + C2) / 2) - return (C1 & C2) + (C1 ^ C2).lshr(1); -} - -APInt APIntOps::avgCeilS(const APInt &C1, const APInt &C2) { - // Return ceil((C1 + C2) / 2) - return (C1 | C2) - (C1 ^ C2).ashr(1); -} - -APInt APIntOps::avgCeilU(const APInt &C1, const APInt &C2) { - // Return ceil((C1 + C2) / 2) - return (C1 | C2) - (C1 ^ C2).lshr(1); -} - -APInt APIntOps::mulhs(const APInt &C1, const APInt &C2) { - assert(C1.getBitWidth() == C2.getBitWidth() && "Unequal bitwidths"); - unsigned FullWidth = C1.getBitWidth() * 2; - APInt C1Ext = C1.sext(FullWidth); - APInt C2Ext = C2.sext(FullWidth); - return (C1Ext * C2Ext).extractBits(C1.getBitWidth(), C1.getBitWidth()); -} - -APInt APIntOps::mulhu(const APInt &C1, const APInt &C2) { - assert(C1.getBitWidth() == C2.getBitWidth() && "Unequal bitwidths"); - unsigned FullWidth = C1.getBitWidth() * 2; - APInt C1Ext = C1.zext(FullWidth); - APInt C2Ext = C2.zext(FullWidth); - return (C1Ext * C2Ext).extractBits(C1.getBitWidth(), C1.getBitWidth()); -} - -APInt APIntOps::mulsExtended(const APInt &C1, const APInt &C2) { - assert(C1.getBitWidth() == C2.getBitWidth() && "Unequal bitwidths"); - unsigned FullWidth = C1.getBitWidth() * 2; - APInt C1Ext = C1.sext(FullWidth); - APInt C2Ext = C2.sext(FullWidth); - return C1Ext * C2Ext; -} - -APInt APIntOps::muluExtended(const APInt &C1, const APInt &C2) { - assert(C1.getBitWidth() == C2.getBitWidth() && "Unequal bitwidths"); - unsigned FullWidth = C1.getBitWidth() * 2; - APInt C1Ext = C1.zext(FullWidth); - APInt C2Ext = C2.zext(FullWidth); - return C1Ext * C2Ext; -} - -APInt APIntOps::pow(const APInt &X, int64_t N) { - assert(N >= 0 && "negative exponents not supported."); - APInt Acc = APInt(X.getBitWidth(), 1); - if (N == 0) - return Acc; - APInt Base = X; - int64_t RemainingExponent = N; - while (RemainingExponent > 0) { - while (RemainingExponent % 2 == 0) { - Base *= Base; - RemainingExponent /= 2; - } - --RemainingExponent; - Acc *= Base; - } - return Acc; -} - -APInt llvm::APIntOps::fshl(const APInt &Hi, const APInt &Lo, - const APInt &Shift) { - assert(Hi.getBitWidth() == Lo.getBitWidth()); - unsigned ShiftAmt = rotateModulo(Hi.getBitWidth(), Shift); - if (ShiftAmt == 0) - return Hi; - return Hi.shl(ShiftAmt) | Lo.lshr(Hi.getBitWidth() - ShiftAmt); -} - -APInt llvm::APIntOps::fshr(const APInt &Hi, const APInt &Lo, - const APInt &Shift) { - assert(Hi.getBitWidth() == Lo.getBitWidth()); - unsigned ShiftAmt = rotateModulo(Hi.getBitWidth(), Shift); - if (ShiftAmt == 0) - return Lo; - return Hi.shl(Hi.getBitWidth() - ShiftAmt) | Lo.lshr(ShiftAmt); -} +//===-- 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/SmallString.h" +#include "llvm/ADT/StringRef.h" +#include "llvm/ADT/bit.h" +#include "llvm/Config/llvm-config.h" +#include "llvm/Support/Alignment.h" +#include "llvm/Support/Debug.h" +#include "llvm/Support/ErrorHandling.h" +#include "llvm/Support/MathExtras.h" +#include "llvm/Support/raw_ostream.h" +#include +#include + +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) { + return new uint64_t[numWords](); +} + +/// 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 UINT_MAX; +} + + +void APInt::initSlowCase(uint64_t val, bool isSigned) { + if (isSigned && int64_t(val) < 0) { + U.pVal = getMemory(getNumWords()); + U.pVal[0] = val; + memset(&U.pVal[1], 0xFF, APINT_WORD_SIZE * (getNumWords() - 1)); + clearUnusedBits(); + } else { + U.pVal = getClearedMemory(getNumWords()); + U.pVal[0] = val; + } +} + +void APInt::initSlowCase(const APInt& that) { + U.pVal = getMemory(getNumWords()); + memcpy(U.pVal, that.U.pVal, getNumWords() * APINT_WORD_SIZE); +} + +void APInt::initFromArray(ArrayRef bigVal) { + assert(bigVal.data() && "Null pointer detected!"); + if (isSingleWord()) + U.VAL = bigVal[0]; + else { + // Get memory, cleared to 0 + U.pVal = getClearedMemory(getNumWords()); + // Calculate the number of words to copy + unsigned words = std::min(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 bigVal) : BitWidth(numBits) { + initFromArray(bigVal); +} + +APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[]) + : BitWidth(numBits) { + initFromArray(ArrayRef(bigVal, numWords)); +} + +APInt::APInt(unsigned numbits, StringRef Str, uint8_t radix) + : BitWidth(numbits) { + fromString(numbits, Str, radix); +} + +void APInt::reallocate(unsigned NewBitWidth) { + // If the number of words is the same we can just change the width and stop. + if (getNumWords() == getNumWords(NewBitWidth)) { + BitWidth = NewBitWidth; + return; + } + + // If we have an allocation, delete it. + if (!isSingleWord()) + delete [] U.pVal; + + // Update BitWidth. + BitWidth = NewBitWidth; + + // If we are supposed to have an allocation, create it. + if (!isSingleWord()) + U.pVal = getMemory(getNumWords()); +} + +void APInt::assignSlowCase(const APInt &RHS) { + // Don't do anything for X = X + if (this == &RHS) + return; + + // Adjust the bit width and handle allocations as necessary. + reallocate(RHS.getBitWidth()); + + // Copy the data. + if (isSingleWord()) + U.VAL = RHS.U.VAL; + else + memcpy(U.pVal, RHS.U.pVal, getNumWords() * APINT_WORD_SIZE); +} + +/// This method 'profiles' an APInt for use with FoldingSet. +void APInt::Profile(FoldingSetNodeID& ID) const { + ID.AddInteger(BitWidth); + + if (isSingleWord()) { + ID.AddInteger(U.VAL); + return; + } + + unsigned NumWords = getNumWords(); + for (unsigned i = 0; i < NumWords; ++i) + ID.AddInteger(U.pVal[i]); +} + +bool APInt::isAligned(Align A) const { + if (isZero()) + return true; + const unsigned TrailingZeroes = countr_zero(); + const unsigned MinimumTrailingZeroes = Log2(A); + return TrailingZeroes >= MinimumTrailingZeroes; +} + +/// 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, /*isSigned=*/false, + /*implicitTrunc=*/true); + + APInt Result(getMemory(getNumWords()), getBitWidth()); + tcMultiply(Result.U.pVal, U.pVal, RHS.U.pVal, getNumWords()); + Result.clearUnusedBits(); + return Result; +} + +void APInt::andAssignSlowCase(const APInt &RHS) { + WordType *dst = U.pVal, *rhs = RHS.U.pVal; + for (size_t i = 0, e = getNumWords(); i != e; ++i) + dst[i] &= rhs[i]; +} + +void APInt::orAssignSlowCase(const APInt &RHS) { + WordType *dst = U.pVal, *rhs = RHS.U.pVal; + for (size_t i = 0, e = getNumWords(); i != e; ++i) + dst[i] |= rhs[i]; +} + +void APInt::xorAssignSlowCase(const APInt &RHS) { + WordType *dst = U.pVal, *rhs = RHS.U.pVal; + for (size_t i = 0, e = getNumWords(); i != e; ++i) + dst[i] ^= rhs[i]; +} + +APInt &APInt::operator*=(const APInt &RHS) { + *this = *this * RHS; + return *this; +} + +APInt& APInt::operator*=(uint64_t RHS) { + if (isSingleWord()) { + U.VAL *= RHS; + } else { + unsigned NumWords = getNumWords(); + tcMultiplyPart(U.pVal, U.pVal, RHS, 0, NumWords, NumWords, false); + } + return clearUnusedBits(); +} + +bool APInt::equalSlowCase(const APInt &RHS) const { + return std::equal(U.pVal, U.pVal + getNumWords(), RHS.U.pVal); +} + +int APInt::compare(const APInt& RHS) const { + assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); + if (isSingleWord()) + return U.VAL < RHS.U.VAL ? -1 : U.VAL > RHS.U.VAL; + + return tcCompare(U.pVal, RHS.U.pVal, getNumWords()); +} + +int APInt::compareSigned(const APInt& RHS) const { + assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); + if (isSingleWord()) { + int64_t lhsSext = SignExtend64(U.VAL, BitWidth); + int64_t rhsSext = SignExtend64(RHS.U.VAL, BitWidth); + return lhsSext < rhsSext ? -1 : lhsSext > rhsSext; + } + + bool lhsNeg = isNegative(); + bool rhsNeg = RHS.isNegative(); + + // If the sign bits don't match, then (LHS < RHS) if LHS is negative + if (lhsNeg != rhsNeg) + return lhsNeg ? -1 : 1; + + // Otherwise we can just use an unsigned comparison, because even negative + // numbers compare correctly this way if both have the same signed-ness. + return tcCompare(U.pVal, RHS.U.pVal, getNumWords()); +} + +void APInt::setBitsSlowCase(unsigned loBit, unsigned hiBit) { + unsigned loWord = whichWord(loBit); + unsigned hiWord = whichWord(hiBit); + + // Create an initial mask for the low word with zeros below loBit. + uint64_t loMask = WORDTYPE_MAX << whichBit(loBit); + + // If hiBit is not aligned, we need a high mask. + unsigned hiShiftAmt = whichBit(hiBit); + if (hiShiftAmt != 0) { + // Create a high mask with zeros above hiBit. + uint64_t hiMask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - hiShiftAmt); + // If loWord and hiWord are equal, then we combine the masks. Otherwise, + // set the bits in hiWord. + if (hiWord == loWord) + loMask &= hiMask; + else + U.pVal[hiWord] |= hiMask; + } + // Apply the mask to the low word. + U.pVal[loWord] |= loMask; + + // Fill any words between loWord and hiWord with all ones. + for (unsigned word = loWord + 1; word < hiWord; ++word) + U.pVal[word] = WORDTYPE_MAX; +} + +void APInt::clearBitsSlowCase(unsigned LoBit, unsigned HiBit) { + unsigned LoWord = whichWord(LoBit); + unsigned HiWord = whichWord(HiBit); + + // Create an initial mask for the low word with ones 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 ones above HiBit. + uint64_t HiMask = ~(WORDTYPE_MAX >> (APINT_BITS_PER_WORD - HiShiftAmt)); + // If LoWord and HiWord are equal, then we combine the masks. Otherwise, + // clear 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 zeros. + for (unsigned Word = LoWord + 1; Word < HiWord; ++Word) + U.pVal[Word] = 0; +} + +// Complement a bignum in-place. +static void tcComplement(APInt::WordType *dst, unsigned parts) { + for (unsigned i = 0; i < parts; i++) + dst[i] = ~dst[i]; +} + +/// Toggle every bit to its opposite value. +void APInt::flipAllBitsSlowCase() { + tcComplement(U.pVal, getNumWords()); + clearUnusedBits(); +} + +/// Concatenate the bits from "NewLSB" onto the bottom of *this. This is +/// equivalent to: +/// (this->zext(NewWidth) << NewLSB.getBitWidth()) | NewLSB.zext(NewWidth) +/// In the slow case, we know the result is large. +APInt APInt::concatSlowCase(const APInt &NewLSB) const { + unsigned NewWidth = getBitWidth() + NewLSB.getBitWidth(); + APInt Result = NewLSB.zext(NewWidth); + Result.insertBits(*this, NewLSB.getBitWidth()); + return Result; +} + +/// Toggle a given bit to its opposite value whose position is given +/// as "bitPosition". +/// Toggles a given bit to its opposite value. +void APInt::flipBit(unsigned bitPosition) { + assert(bitPosition < BitWidth && "Out of the bit-width range!"); + setBitVal(bitPosition, !(*this)[bitPosition]); +} + +void APInt::insertBits(const APInt &subBits, unsigned bitPosition) { + unsigned subBitWidth = subBits.getBitWidth(); + assert((subBitWidth + bitPosition) <= BitWidth && "Illegal bit insertion"); + + // inserting no bits is a noop. + if (subBitWidth == 0) + return; + + // Insertion is a direct copy. + if (subBitWidth == BitWidth) { + *this = subBits; + return; + } + + // Single word result can be done as a direct bitmask. + if (isSingleWord()) { + uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - subBitWidth); + U.VAL &= ~(mask << bitPosition); + U.VAL |= (subBits.U.VAL << bitPosition); + return; + } + + unsigned loBit = whichBit(bitPosition); + unsigned loWord = whichWord(bitPosition); + unsigned hi1Word = whichWord(bitPosition + subBitWidth - 1); + + // Insertion within a single word can be done as a direct bitmask. + if (loWord == hi1Word) { + uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - subBitWidth); + U.pVal[loWord] &= ~(mask << loBit); + U.pVal[loWord] |= (subBits.U.VAL << loBit); + return; + } + + // Insert on word boundaries. + if (loBit == 0) { + // Direct copy whole words. + unsigned numWholeSubWords = subBitWidth / APINT_BITS_PER_WORD; + memcpy(U.pVal + loWord, subBits.getRawData(), + numWholeSubWords * APINT_WORD_SIZE); + + // Mask+insert remaining bits. + unsigned remainingBits = subBitWidth % APINT_BITS_PER_WORD; + if (remainingBits != 0) { + uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - remainingBits); + U.pVal[hi1Word] &= ~mask; + U.pVal[hi1Word] |= subBits.getWord(subBitWidth - 1); + } + return; + } + + // General case - set/clear individual bits in dst based on src. + // TODO - there is scope for optimization here, but at the moment this code + // path is barely used so prefer readability over performance. + for (unsigned i = 0; i != subBitWidth; ++i) + setBitVal(bitPosition + i, subBits[i]); +} + +void APInt::insertBits(uint64_t subBits, unsigned bitPosition, unsigned numBits) { + uint64_t maskBits = maskTrailingOnes(numBits); + subBits &= maskBits; + if (isSingleWord()) { + U.VAL &= ~(maskBits << bitPosition); + U.VAL |= subBits << bitPosition; + return; + } + + unsigned loBit = whichBit(bitPosition); + unsigned loWord = whichWord(bitPosition); + unsigned hiWord = whichWord(bitPosition + numBits - 1); + if (loWord == hiWord) { + U.pVal[loWord] &= ~(maskBits << loBit); + U.pVal[loWord] |= subBits << loBit; + return; + } + + static_assert(8 * sizeof(WordType) <= 64, "This code assumes only two words affected"); + unsigned wordBits = 8 * sizeof(WordType); + U.pVal[loWord] &= ~(maskBits << loBit); + U.pVal[loWord] |= subBits << loBit; + + U.pVal[hiWord] &= ~(maskBits >> (wordBits - loBit)); + U.pVal[hiWord] |= subBits >> (wordBits - loBit); +} + +APInt APInt::extractBits(unsigned numBits, unsigned bitPosition) const { + assert(bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth && + "Illegal bit extraction"); + + if (isSingleWord()) + return APInt(numBits, U.VAL >> bitPosition, /*isSigned=*/false, + /*implicitTrunc=*/true); + + 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, /*isSigned=*/false, + /*implicitTrunc=*/true); + + // Extracting bits that start on a source word boundary can be done + // as a fast memory copy. + if (loBit == 0) + return APInt(numBits, ArrayRef(U.pVal + loWord, 1 + hiWord - loWord)); + + // General case - shift + copy source words directly into place. + APInt Result(numBits, 0); + unsigned NumSrcWords = getNumWords(); + unsigned NumDstWords = Result.getNumWords(); + + uint64_t *DestPtr = Result.isSingleWord() ? &Result.U.VAL : Result.U.pVal; + for (unsigned word = 0; word < NumDstWords; ++word) { + uint64_t w0 = U.pVal[loWord + word]; + uint64_t w1 = + (loWord + word + 1) < NumSrcWords ? U.pVal[loWord + word + 1] : 0; + DestPtr[word] = (w0 >> loBit) | (w1 << (APINT_BITS_PER_WORD - loBit)); + } + + return Result.clearUnusedBits(); +} + +uint64_t APInt::extractBitsAsZExtValue(unsigned numBits, + unsigned bitPosition) const { + assert(bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth && + "Illegal bit extraction"); + assert(numBits <= 64 && "Illegal bit extraction"); + + uint64_t maskBits = maskTrailingOnes(numBits); + if (isSingleWord()) + return (U.VAL >> bitPosition) & maskBits; + + static_assert(APINT_BITS_PER_WORD >= 64, + "This code assumes only two words affected"); + unsigned loBit = whichBit(bitPosition); + unsigned loWord = whichWord(bitPosition); + unsigned hiWord = whichWord(bitPosition + numBits - 1); + if (loWord == hiWord) + return (U.pVal[loWord] >> loBit) & maskBits; + + uint64_t retBits = U.pVal[loWord] >> loBit; + retBits |= U.pVal[hiWord] << (APINT_BITS_PER_WORD - loBit); + retBits &= maskBits; + return retBits; +} + +unsigned APInt::getSufficientBitsNeeded(StringRef Str, uint8_t Radix) { + assert(!Str.empty() && "Invalid string length"); + size_t StrLen = Str.size(); + + // Each computation below needs to know if it's negative. + unsigned IsNegative = false; + if (Str[0] == '-' || Str[0] == '+') { + IsNegative = Str[0] == '-'; + StrLen--; + assert(StrLen && "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 StrLen + IsNegative; + if (Radix == 8) + return StrLen * 3 + IsNegative; + if (Radix == 16) + return StrLen * 4 + IsNegative; + + // 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. + if (Radix == 10) + return (StrLen == 1 ? 4 : StrLen * 64 / 18) + IsNegative; + + assert(Radix == 36); + return (StrLen == 1 ? 7 : StrLen * 16 / 3) + IsNegative; +} + +unsigned APInt::getBitsNeeded(StringRef str, uint8_t radix) { + // Compute a sufficient number of bits that is always large enough but might + // be too large. + unsigned sufficient = getSufficientBitsNeeded(str, radix); + + // For bases 2, 8, and 16, the sufficient number of bits is exact and we can + // return the value directly. For bases 10 and 36, we need to do extra work. + if (radix == 2 || radix == 8 || radix == 16) + return sufficient; + + // 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. + 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."); + } + + + // Convert to the actual binary value. + APInt tmp(sufficient, StringRef(p, slen), radix); + + // Compute how many bits are required. If the log is infinite, assume we need + // just bit. If the log is exact and value is negative, then the value is + // MinSignedValue with (log + 1) bits. + unsigned log = tmp.logBase2(); + if (log == (unsigned)-1) { + return isNegative + 1; + } else if (isNegative && tmp.isPowerOf2()) { + return isNegative + log; + } else { + return isNegative + log + 1; + } +} + +hash_code llvm::hash_value(const APInt &Arg) { + if (Arg.isSingleWord()) + return hash_combine(Arg.BitWidth, Arg.U.VAL); + + return hash_combine( + Arg.BitWidth, + hash_combine_range(Arg.U.pVal, Arg.U.pVal + Arg.getNumWords())); +} + +unsigned DenseMapInfo::getHashValue(const APInt &Key) { + return static_cast(hash_value(Key)); +} + +bool APInt::isSplat(unsigned SplatSizeInBits) const { + assert(getBitWidth() % SplatSizeInBits == 0 && + "SplatSizeInBits must divide width!"); + // We can check that all parts of an integer are equal by making use of a + // little trick: rotate and check if it's still the same value. + return *this == rotl(SplatSizeInBits); +} + +/// This function returns the high "numBits" bits of this APInt. +APInt APInt::getHiBits(unsigned numBits) const { + return this->lshr(BitWidth - numBits); +} + +/// This function returns the low "numBits" bits of this APInt. +APInt APInt::getLoBits(unsigned numBits) const { + APInt Result(getLowBitsSet(BitWidth, numBits)); + Result &= *this; + return Result; +} + +/// Return a value containing V broadcasted over NewLen bits. +APInt APInt::getSplat(unsigned NewLen, const APInt &V) { + assert(NewLen >= V.getBitWidth() && "Can't splat to smaller bit width!"); + + APInt Val = V.zext(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::countl_zero(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::countl_one(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::countl_one(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::countr_zero(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::countr_one(U.pVal[i]); + assert(Count <= BitWidth); + return Count; +} + +unsigned APInt::countPopulationSlowCase() const { + unsigned Count = 0; + for (unsigned i = 0; i < getNumWords(); ++i) + Count += llvm::popcount(U.pVal[i]); + return Count; +} + +bool APInt::intersectsSlowCase(const APInt &RHS) const { + for (unsigned i = 0, e = getNumWords(); i != e; ++i) + if ((U.pVal[i] & RHS.U.pVal[i]) != 0) + return true; + + return false; +} + +bool APInt::isSubsetOfSlowCase(const APInt &RHS) const { + for (unsigned i = 0, e = getNumWords(); i != e; ++i) + if ((U.pVal[i] & ~RHS.U.pVal[i]) != 0) + return false; + + return true; +} + +APInt APInt::byteSwap() const { + assert(BitWidth >= 16 && BitWidth % 8 == 0 && "Cannot byteswap!"); + if (BitWidth == 16) + return APInt(BitWidth, llvm::byteswap(U.VAL)); + if (BitWidth == 32) + return APInt(BitWidth, llvm::byteswap(U.VAL)); + if (BitWidth <= 64) { + uint64_t Tmp1 = llvm::byteswap(U.VAL); + Tmp1 >>= (64 - BitWidth); + return APInt(BitWidth, Tmp1); + } + + APInt Result(getNumWords() * APINT_BITS_PER_WORD, 0); + for (unsigned I = 0, N = getNumWords(); I != N; ++I) + Result.U.pVal[I] = llvm::byteswap(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(U.VAL)); + case 32: + return APInt(BitWidth, llvm::reverseBits(U.VAL)); + case 16: + return APInt(BitWidth, llvm::reverseBits(U.VAL)); + case 8: + return APInt(BitWidth, llvm::reverseBits(U.VAL)); + case 0: + return *this; + default: + break; + } + + APInt Val(*this); + APInt Reversed(BitWidth, 0); + unsigned S = BitWidth; + + for (; Val != 0; Val.lshrInPlace(1)) { + Reversed <<= 1; + Reversed |= Val[0]; + --S; + } + + Reversed <<= S; + return Reversed; +} + +APInt llvm::APIntOps::GreatestCommonDivisor(APInt A, APInt B) { + // Fast-path a common case. + if (A == B) return A; + + // Corner cases: if either operand is zero, the other is the gcd. + if (!A) return B; + if (!B) return A; + + // Count common powers of 2 and remove all other powers of 2. + unsigned Pow2; + { + unsigned Pow2_A = A.countr_zero(); + unsigned Pow2_B = B.countr_zero(); + 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.countr_zero() - Pow2); + } else { + B -= A; + B.lshrInPlace(B.countr_zero() - Pow2); + } + } + + return A; +} + +APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) { + uint64_t I = bit_cast(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); + } + 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::infinity(); + else + return -std::numeric_limits::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(I); +} + +// Truncate to new width. +APInt APInt::trunc(unsigned width) const { + assert(width <= BitWidth && "Invalid APInt Truncate request"); + + if (width <= APINT_BITS_PER_WORD) + return APInt(width, getRawData()[0], /*isSigned=*/false, + /*implicitTrunc=*/true); + + if (width == BitWidth) + return *this; + + APInt Result(getMemory(getNumWords(width)), width); + + // Copy full words. + unsigned i; + for (i = 0; i != width / APINT_BITS_PER_WORD; i++) + Result.U.pVal[i] = U.pVal[i]; + + // Truncate and copy any partial word. + unsigned bits = (0 - width) % APINT_BITS_PER_WORD; + if (bits != 0) + Result.U.pVal[i] = U.pVal[i] << bits >> bits; + + return Result; +} + +// Truncate to new width with unsigned saturation. +APInt APInt::truncUSat(unsigned width) const { + assert(width <= BitWidth && "Invalid APInt Truncate request"); + + // Can we just losslessly truncate it? + if (isIntN(width)) + return trunc(width); + // If not, then just return the new limit. + return APInt::getMaxValue(width); +} + +// Truncate to new width with signed saturation. +APInt APInt::truncSSat(unsigned width) const { + assert(width <= BitWidth && "Invalid APInt Truncate request"); + + // Can we just losslessly truncate it? + if (isSignedIntN(width)) + return trunc(width); + // If not, then just return the new limits. + return isNegative() ? APInt::getSignedMinValue(width) + : APInt::getSignedMaxValue(width); +} + +// Sign extend to a new width. +APInt APInt::sext(unsigned Width) const { + assert(Width >= BitWidth && "Invalid APInt SignExtend request"); + + if (Width <= APINT_BITS_PER_WORD) + return APInt(Width, SignExtend64(U.VAL, BitWidth), /*isSigned=*/true); + + if (Width == BitWidth) + return *this; + + 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); + + if (width == BitWidth) + return *this; + + 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; +} + +/// 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. Use an arithmetic + // shift to preserve the sign bit. + U.pVal[WordsToMove - 1] = + (int64_t)U.pVal[WordShift + WordsToMove - 1] >> BitShift; + } + } + + // Fill in the remainder based on the original sign. + std::memset(U.pVal + WordsToMove, Negative ? -1 : 0, + WordShift * APINT_WORD_SIZE); + clearUnusedBits(); +} + +/// Logical right-shift this APInt by shiftAmt. +/// Logical right-shift function. +void APInt::lshrInPlace(const APInt &shiftAmt) { + lshrInPlace((unsigned)shiftAmt.getLimitedValue(BitWidth)); +} + +/// Logical right-shift this APInt by shiftAmt. +/// Logical right-shift function. +void APInt::lshrSlowCase(unsigned ShiftAmt) { + tcShiftRight(U.pVal, getNumWords(), ShiftAmt); +} + +/// Left-shift this APInt by shiftAmt. +/// Left-shift function. +APInt &APInt::operator<<=(const APInt &shiftAmt) { + // It's undefined behavior in C to shift by BitWidth or greater. + *this <<= (unsigned)shiftAmt.getLimitedValue(BitWidth); + return *this; +} + +void APInt::shlSlowCase(unsigned ShiftAmt) { + tcShiftLeft(U.pVal, getNumWords(), ShiftAmt); + clearUnusedBits(); +} + +// Calculate the rotate amount modulo the bit width. +static unsigned rotateModulo(unsigned BitWidth, const APInt &rotateAmt) { + if (LLVM_UNLIKELY(BitWidth == 0)) + return 0; + unsigned rotBitWidth = rotateAmt.getBitWidth(); + APInt rot = rotateAmt; + if (rotBitWidth < BitWidth) { + // Extend the rotate APInt, so that the urem doesn't divide by 0. + // e.g. APInt(1, 32) would give APInt(1, 0). + rot = rotateAmt.zext(BitWidth); + } + rot = rot.urem(APInt(rot.getBitWidth(), BitWidth)); + return rot.getLimitedValue(BitWidth); +} + +APInt APInt::rotl(const APInt &rotateAmt) const { + return rotl(rotateModulo(BitWidth, rotateAmt)); +} + +APInt APInt::rotl(unsigned rotateAmt) const { + if (LLVM_UNLIKELY(BitWidth == 0)) + return *this; + rotateAmt %= BitWidth; + if (rotateAmt == 0) + return *this; + return shl(rotateAmt) | lshr(BitWidth - rotateAmt); +} + +APInt APInt::rotr(const APInt &rotateAmt) const { + return rotr(rotateModulo(BitWidth, rotateAmt)); +} + +APInt APInt::rotr(unsigned rotateAmt) const { + if (BitWidth == 0) + return *this; + rotateAmt %= BitWidth; + if (rotateAmt == 0) + return *this; + return lshr(rotateAmt) | shl(BitWidth - rotateAmt); +} + +/// \returns the nearest log base 2 of this APInt. Ties round up. +/// +/// NOTE: When we have a BitWidth of 1, we define: +/// +/// log2(0) = UINT32_MAX +/// log2(1) = 0 +/// +/// to get around any mathematical concerns resulting from +/// referencing 2 in a space where 2 does no exist. +unsigned APInt::nearestLogBase2() const { + // Special case when we have a bitwidth of 1. If VAL is 1, then we + // get 0. If VAL is 0, we get WORDTYPE_MAX which gets truncated to + // UINT32_MAX. + if (BitWidth == 1) + return U.VAL - 1; + + // Handle the zero case. + if (isZero()) + return UINT32_MAX; + + // The non-zero case is handled by computing: + // + // nearestLogBase2(x) = logBase2(x) + x[logBase2(x)-1]. + // + // where x[i] is referring to the value of the ith bit of x. + unsigned lg = logBase2(); + return lg + unsigned((*this)[lg - 1]); +} + +// Square Root - this method computes and returns the square root of "this". +// Three mechanisms are used for computation. For small values (<= 5 bits), +// a table lookup is done. This gets some performance for common cases. For +// values using less than 52 bits, the value is converted to double and then +// the libc sqrt function is called. The result is rounded and then converted +// back to a uint64_t which is then used to construct the result. Finally, +// the Babylonian method for computing square roots is used. +APInt APInt::sqrt() const { + + // Determine the magnitude of the value. + unsigned magnitude = getActiveBits(); + + // Use a fast table for some small values. This also gets rid of some + // rounding errors in libc sqrt for small values. + if (magnitude <= 5) { + static const uint8_t results[32] = { + /* 0 */ 0, + /* 1- 2 */ 1, 1, + /* 3- 6 */ 2, 2, 2, 2, + /* 7-12 */ 3, 3, 3, 3, 3, 3, + /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4, + /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, + /* 31 */ 6 + }; + return APInt(BitWidth, results[ (isSingleWord() ? U.VAL : U.pVal[0]) ]); + } + + // If the magnitude of the value fits in less than 52 bits (the precision of + // an IEEE double precision floating point value), then we can use the + // libc sqrt function which will probably use a hardware sqrt computation. + // This should be faster than the algorithm below. + if (magnitude < 52) { + return APInt(BitWidth, + uint64_t(::round(::sqrt(double(isSingleWord() ? U.VAL + : U.pVal[0]))))); + } + + // Okay, all the short cuts are exhausted. We must compute it. The following + // is a classical Babylonian method for computing the square root. This code + // was adapted to APInt from a wikipedia article on such computations. + // See http://www.wikipedia.org/ and go to the page named + // Calculate_an_integer_square_root. + unsigned nbits = BitWidth, i = 4; + APInt testy(BitWidth, 16); + APInt x_old(BitWidth, 1); + APInt x_new(BitWidth, 0); + APInt two(BitWidth, 2); + + // Select a good starting value using binary logarithms. + for (;; i += 2, testy = testy.shl(2)) + if (i >= nbits || this->ule(testy)) { + x_old = x_old.shl(i / 2); + break; + } + + // Use the Babylonian method to arrive at the integer square root: + for (;;) { + x_new = (this->udiv(x_old) + x_old).udiv(two); + if (x_old.ule(x_new)) + break; + x_old = x_new; + } + + // Make sure we return the closest approximation + // NOTE: The rounding calculation below is correct. It will produce an + // off-by-one discrepancy with results from pari/gp. That discrepancy has been + // determined to be a rounding issue with pari/gp as it begins to use a + // floating point representation after 192 bits. There are no discrepancies + // between this algorithm and pari/gp for bit widths < 192 bits. + APInt square(x_old * x_old); + APInt nextSquare((x_old + 1) * (x_old +1)); + if (this->ult(square)) + return x_old; + assert(this->ule(nextSquare) && "Error in APInt::sqrt computation"); + APInt midpoint((nextSquare - square).udiv(two)); + APInt offset(*this - square); + if (offset.ult(midpoint)) + return x_old; + return x_old + 1; +} + +/// \returns the multiplicative inverse of an odd APInt modulo 2^BitWidth. +APInt APInt::multiplicativeInverse() const { + assert((*this)[0] && + "multiplicative inverse is only defined for odd numbers!"); + + // Use Newton's method. + APInt Factor = *this; + APInt T; + while (!(T = *this * Factor).isOne()) + Factor *= 2 - std::move(T); + return Factor; +} + +/// 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 = llvm::countl_zero(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 = qp * uint64_t(v[i]); + int64_t subres = int64_t(u[j+i]) - borrow - Lo_32(p); + u[j+i] = Lo_32(subres); + borrow = Hi_32(p) - Hi_32(subres); + DEBUG_KNUTH(dbgs() << "KnuthDiv: u[j+i] = " << u[j + i] + << ", borrow = " << borrow << '\n'); + } + bool isNeg = u[j+n] < borrow; + u[j+n] -= Lo_32(borrow); + + DEBUG_KNUTH(dbgs() << "KnuthDiv: after subtraction:"); + DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]); + DEBUG_KNUTH(dbgs() << '\n'); + + // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was + // negative, go to step D6; otherwise go on to step D7. + q[j] = Lo_32(qp); + if (isNeg) { + // D6. [Add back]. The probability that this step is necessary is very + // small, on the order of only 2/b. Make sure that test data accounts for + // this possibility. Decrease q[j] by 1 + q[j]--; + // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]). + // A carry will occur to the left of u[j+n], and it should be ignored + // since it cancels with the borrow that occurred in D4. + bool carry = false; + for (unsigned i = 0; i < n; i++) { + uint32_t limit = std::min(u[j+i],v[i]); + u[j+i] += v[i] + carry; + carry = u[j+i] < limit || (carry && u[j+i] == limit); + } + u[j+n] += carry; + } + DEBUG_KNUTH(dbgs() << "KnuthDiv: after correction:"); + DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]); + DEBUG_KNUTH(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n'); + + // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3. + } while (--j >= 0); + + DEBUG_KNUTH(dbgs() << "KnuthDiv: quotient:"); + DEBUG_KNUTH(for (int i = m; i >= 0; i--) dbgs() << " " << q[i]); + DEBUG_KNUTH(dbgs() << '\n'); + + // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired + // remainder may be obtained by dividing u[...] by d. If r is non-null we + // compute the remainder (urem uses this). + if (r) { + // The value d is expressed by the "shift" value above since we avoided + // multiplication by d by using a shift left. So, all we have to do is + // shift right here. + if (shift) { + uint32_t carry = 0; + DEBUG_KNUTH(dbgs() << "KnuthDiv: remainder:"); + for (int i = n-1; i >= 0; i--) { + r[i] = (u[i] >> shift) | carry; + carry = u[i] << (32 - shift); + DEBUG_KNUTH(dbgs() << " " << r[i]); + } + } else { + for (int i = n-1; i >= 0; i--) { + r[i] = u[i]; + DEBUG_KNUTH(dbgs() << " " << r[i]); + } + } + DEBUG_KNUTH(dbgs() << '\n'); + } + DEBUG_KNUTH(dbgs() << '\n'); +} + +void APInt::divide(const WordType *LHS, unsigned lhsWords, const WordType *RHS, + unsigned rhsWords, WordType *Quotient, WordType *Remainder) { + assert(lhsWords >= rhsWords && "Fractional result"); + + // First, compose the values into an array of 32-bit words instead of + // 64-bit words. This is a necessity of both the "short division" algorithm + // and the Knuth "classical algorithm" which requires there to be native + // operations for +, -, and * on an m bit value with an m*2 bit result. We + // can't use 64-bit operands here because we don't have native results of + // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't + // work on large-endian machines. + unsigned n = rhsWords * 2; + unsigned m = (lhsWords * 2) - n; + + // Allocate space for the temporary values we need either on the stack, if + // it will fit, or on the heap if it won't. + uint32_t SPACE[128]; + uint32_t *U = nullptr; + uint32_t *V = nullptr; + uint32_t *Q = nullptr; + uint32_t *R = nullptr; + if ((Remainder?4:3)*n+2*m+1 <= 128) { + U = &SPACE[0]; + V = &SPACE[m+n+1]; + Q = &SPACE[(m+n+1) + n]; + if (Remainder) + R = &SPACE[(m+n+1) + n + (m+n)]; + } else { + U = new uint32_t[m + n + 1]; + V = new uint32_t[n]; + Q = new uint32_t[m+n]; + if (Remainder) + R = new uint32_t[n]; + } + + // Initialize the dividend + memset(U, 0, (m+n+1)*sizeof(uint32_t)); + for (unsigned i = 0; i < lhsWords; ++i) { + uint64_t tmp = LHS[i]; + U[i * 2] = Lo_32(tmp); + U[i * 2 + 1] = Hi_32(tmp); + } + U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm. + + // Initialize the divisor + memset(V, 0, (n)*sizeof(uint32_t)); + for (unsigned i = 0; i < rhsWords; ++i) { + uint64_t tmp = RHS[i]; + V[i * 2] = Lo_32(tmp); + V[i * 2 + 1] = Hi_32(tmp); + } + + // initialize the quotient and remainder + memset(Q, 0, (m+n) * sizeof(uint32_t)); + if (Remainder) + memset(R, 0, n * sizeof(uint32_t)); + + // Now, adjust m and n for the Knuth division. n is the number of words in + // the divisor. m is the number of words by which the dividend exceeds the + // divisor (i.e. m+n is the length of the dividend). These sizes must not + // contain any zero words or the Knuth algorithm fails. + for (unsigned i = n; i > 0 && V[i-1] == 0; i--) { + n--; + m++; + } + for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--) + m--; + + // If we're left with only a single word for the divisor, Knuth doesn't work + // so we implement the short division algorithm here. This is much simpler + // and faster because we are certain that we can divide a 64-bit quantity + // by a 32-bit quantity at hardware speed and short division is simply a + // series of such operations. This is just like doing short division but we + // are using base 2^32 instead of base 10. + assert(n != 0 && "Divide by zero?"); + if (n == 1) { + uint32_t divisor = V[0]; + uint32_t remainder = 0; + for (int i = m; i >= 0; i--) { + uint64_t partial_dividend = Make_64(remainder, U[i]); + if (partial_dividend == 0) { + Q[i] = 0; + remainder = 0; + } else if (partial_dividend < divisor) { + Q[i] = 0; + remainder = Lo_32(partial_dividend); + } else if (partial_dividend == divisor) { + Q[i] = 1; + remainder = 0; + } else { + Q[i] = Lo_32(partial_dividend / divisor); + remainder = Lo_32(partial_dividend - (Q[i] * divisor)); + } + } + if (R) + R[0] = remainder; + } else { + // Now we're ready to invoke the Knuth classical divide algorithm. In this + // case n > 1. + KnuthDiv(U, V, Q, R, m, n); + } + + // If the caller wants the quotient + if (Quotient) { + for (unsigned i = 0; i < lhsWords; ++i) + Quotient[i] = Make_64(Q[i*2+1], Q[i*2]); + } + + // If the caller wants the remainder + if (Remainder) { + for (unsigned i = 0; i < rhsWords; ++i) + Remainder[i] = Make_64(R[i*2+1], R[i*2]); + } + + // Clean up the memory we allocated. + if (U != &SPACE[0]) { + delete [] U; + delete [] V; + delete [] Q; + delete [] R; + } +} + +APInt APInt::udiv(const APInt &RHS) const { + assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); + + // First, deal with the easy case + if (isSingleWord()) { + assert(RHS.U.VAL != 0 && "Divide by zero?"); + return APInt(BitWidth, U.VAL / RHS.U.VAL); + } + + // Get some facts about the LHS and RHS number of bits and words + unsigned lhsWords = getNumWords(getActiveBits()); + unsigned rhsBits = RHS.getActiveBits(); + unsigned rhsWords = getNumWords(rhsBits); + assert(rhsWords && "Divided by zero???"); + + // Deal with some degenerate cases + if (!lhsWords) + // 0 / X ===> 0 + return APInt(BitWidth, 0); + if (rhsBits == 1) + // X / 1 ===> X + return *this; + if (lhsWords < rhsWords || this->ult(RHS)) + // X / Y ===> 0, iff X < Y + return APInt(BitWidth, 0); + if (*this == RHS) + // X / X ===> 1 + return APInt(BitWidth, 1); + if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1. + // All high words are zero, just use native divide + return APInt(BitWidth, this->U.pVal[0] / RHS.U.pVal[0]); + + // We have to compute it the hard way. Invoke the Knuth divide algorithm. + APInt Quotient(BitWidth, 0); // to hold result. + divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal, nullptr); + return Quotient; +} + +APInt APInt::udiv(uint64_t RHS) const { + assert(RHS != 0 && "Divide by zero?"); + + // First, deal with the easy case + if (isSingleWord()) + return APInt(BitWidth, U.VAL / RHS); + + // Get some facts about the LHS words. + unsigned lhsWords = getNumWords(getActiveBits()); + + // Deal with some degenerate cases + if (!lhsWords) + // 0 / X ===> 0 + return APInt(BitWidth, 0); + if (RHS == 1) + // X / 1 ===> X + return *this; + if (this->ult(RHS)) + // X / Y ===> 0, iff X < Y + return APInt(BitWidth, 0); + if (*this == RHS) + // X / X ===> 1 + return APInt(BitWidth, 1); + if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1. + // All high words are zero, just use native divide + return APInt(BitWidth, this->U.pVal[0] / RHS); + + // We have to compute it the hard way. Invoke the Knuth divide algorithm. + APInt Quotient(BitWidth, 0); // to hold result. + divide(U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, nullptr); + return Quotient; +} + +APInt APInt::sdiv(const APInt &RHS) const { + if (isNegative()) { + if (RHS.isNegative()) + return (-(*this)).udiv(-RHS); + return -((-(*this)).udiv(RHS)); + } + if (RHS.isNegative()) + return -(this->udiv(-RHS)); + return this->udiv(RHS); +} + +APInt APInt::sdiv(int64_t RHS) const { + if (isNegative()) { + if (RHS < 0) + return (-(*this)).udiv(-RHS); + return -((-(*this)).udiv(RHS)); + } + if (RHS < 0) + return -(this->udiv(-RHS)); + return this->udiv(RHS); +} + +APInt APInt::urem(const APInt &RHS) const { + assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); + if (isSingleWord()) { + assert(RHS.U.VAL != 0 && "Remainder by zero?"); + return APInt(BitWidth, U.VAL % RHS.U.VAL); + } + + // Get some facts about the LHS + unsigned lhsWords = getNumWords(getActiveBits()); + + // Get some facts about the RHS + unsigned rhsBits = RHS.getActiveBits(); + unsigned rhsWords = getNumWords(rhsBits); + assert(rhsWords && "Performing remainder operation by zero ???"); + + // Check the degenerate cases + if (lhsWords == 0) + // 0 % Y ===> 0 + return APInt(BitWidth, 0); + if (rhsBits == 1) + // X % 1 ===> 0 + return APInt(BitWidth, 0); + if (lhsWords < rhsWords || this->ult(RHS)) + // X % Y ===> X, iff X < Y + return *this; + if (*this == RHS) + // X % X == 0; + return APInt(BitWidth, 0); + if (lhsWords == 1) + // All high words are zero, just use native remainder + return APInt(BitWidth, U.pVal[0] % RHS.U.pVal[0]); + + // We have to compute it the hard way. Invoke the Knuth divide algorithm. + APInt Remainder(BitWidth, 0); + divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, nullptr, Remainder.U.pVal); + return Remainder; +} + +uint64_t APInt::urem(uint64_t RHS) const { + assert(RHS != 0 && "Remainder by zero?"); + + if (isSingleWord()) + return U.VAL % RHS; + + // Get some facts about the LHS + unsigned lhsWords = getNumWords(getActiveBits()); + + // Check the degenerate cases + if (lhsWords == 0) + // 0 % Y ===> 0 + return 0; + if (RHS == 1) + // X % 1 ===> 0 + return 0; + if (this->ult(RHS)) + // X % Y ===> X, iff X < Y + return getZExtValue(); + if (*this == RHS) + // X % X == 0; + return 0; + if (lhsWords == 1) + // All high words are zero, just use native remainder + return U.pVal[0] % RHS; + + // We have to compute it the hard way. Invoke the Knuth divide algorithm. + uint64_t Remainder; + divide(U.pVal, lhsWords, &RHS, 1, nullptr, &Remainder); + return Remainder; +} + +APInt APInt::srem(const APInt &RHS) const { + if (isNegative()) { + if (RHS.isNegative()) + return -((-(*this)).urem(-RHS)); + return -((-(*this)).urem(RHS)); + } + if (RHS.isNegative()) + return this->urem(-RHS); + return this->urem(RHS); +} + +int64_t APInt::srem(int64_t RHS) const { + if (isNegative()) { + if (RHS < 0) + return -((-(*this)).urem(-RHS)); + return -((-(*this)).urem(RHS)); + } + if (RHS < 0) + return this->urem(-RHS); + return this->urem(RHS); +} + +void APInt::udivrem(const APInt &LHS, const APInt &RHS, + APInt &Quotient, APInt &Remainder) { + assert(LHS.BitWidth == RHS.BitWidth && "Bit widths must be the same"); + unsigned BitWidth = LHS.BitWidth; + + // First, deal with the easy case + if (LHS.isSingleWord()) { + assert(RHS.U.VAL != 0 && "Divide by zero?"); + uint64_t QuotVal = LHS.U.VAL / RHS.U.VAL; + uint64_t RemVal = LHS.U.VAL % RHS.U.VAL; + Quotient = APInt(BitWidth, QuotVal); + Remainder = APInt(BitWidth, RemVal); + return; + } + + // Get some size facts about the dividend and divisor + unsigned lhsWords = getNumWords(LHS.getActiveBits()); + unsigned rhsBits = RHS.getActiveBits(); + unsigned rhsWords = getNumWords(rhsBits); + assert(rhsWords && "Performing divrem operation by zero ???"); + + // Check the degenerate cases + if (lhsWords == 0) { + Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0 + Remainder = APInt(BitWidth, 0); // 0 % Y ===> 0 + return; + } + + if (rhsBits == 1) { + Quotient = LHS; // X / 1 ===> X + Remainder = APInt(BitWidth, 0); // X % 1 ===> 0 + } + + if (lhsWords < rhsWords || LHS.ult(RHS)) { + Remainder = LHS; // X % Y ===> X, iff X < Y + Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y + return; + } + + if (LHS == RHS) { + Quotient = APInt(BitWidth, 1); // X / X ===> 1 + Remainder = APInt(BitWidth, 0); // X % X ===> 0; + return; + } + + // Make sure there is enough space to hold the results. + // NOTE: This assumes that reallocate won't affect any bits if it doesn't + // change the size. This is necessary if Quotient or Remainder is aliased + // with LHS or RHS. + Quotient.reallocate(BitWidth); + Remainder.reallocate(BitWidth); + + if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1. + // There is only one word to consider so use the native versions. + uint64_t lhsValue = LHS.U.pVal[0]; + uint64_t rhsValue = RHS.U.pVal[0]; + Quotient = lhsValue / rhsValue; + Remainder = lhsValue % rhsValue; + return; + } + + // Okay, lets do it the long way + divide(LHS.U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal, + Remainder.U.pVal); + // Clear the rest of the Quotient and Remainder. + std::memset(Quotient.U.pVal + lhsWords, 0, + (getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE); + std::memset(Remainder.U.pVal + rhsWords, 0, + (getNumWords(BitWidth) - rhsWords) * APINT_WORD_SIZE); +} + +void APInt::udivrem(const APInt &LHS, uint64_t RHS, APInt &Quotient, + uint64_t &Remainder) { + assert(RHS != 0 && "Divide by zero?"); + unsigned BitWidth = LHS.BitWidth; + + // First, deal with the easy case + if (LHS.isSingleWord()) { + uint64_t QuotVal = LHS.U.VAL / RHS; + Remainder = LHS.U.VAL % RHS; + Quotient = APInt(BitWidth, QuotVal); + return; + } + + // Get some size facts about the dividend and divisor + unsigned lhsWords = getNumWords(LHS.getActiveBits()); + + // Check the degenerate cases + if (lhsWords == 0) { + Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0 + Remainder = 0; // 0 % Y ===> 0 + return; + } + + if (RHS == 1) { + Quotient = LHS; // X / 1 ===> X + Remainder = 0; // X % 1 ===> 0 + return; + } + + if (LHS.ult(RHS)) { + Remainder = LHS.getZExtValue(); // X % Y ===> X, iff X < Y + Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y + return; + } + + if (LHS == RHS) { + Quotient = APInt(BitWidth, 1); // X / X ===> 1 + Remainder = 0; // X % X ===> 0; + return; + } + + // Make sure there is enough space to hold the results. + // NOTE: This assumes that reallocate won't affect any bits if it doesn't + // change the size. This is necessary if Quotient is aliased with LHS. + Quotient.reallocate(BitWidth); + + if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1. + // There is only one word to consider so use the native versions. + uint64_t lhsValue = LHS.U.pVal[0]; + Quotient = lhsValue / RHS; + Remainder = lhsValue % RHS; + return; + } + + // Okay, lets do it the long way + divide(LHS.U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, &Remainder); + // Clear the rest of the Quotient. + std::memset(Quotient.U.pVal + lhsWords, 0, + (getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE); +} + +void APInt::sdivrem(const APInt &LHS, const APInt &RHS, + APInt &Quotient, APInt &Remainder) { + if (LHS.isNegative()) { + if (RHS.isNegative()) + APInt::udivrem(-LHS, -RHS, Quotient, Remainder); + else { + APInt::udivrem(-LHS, RHS, Quotient, Remainder); + Quotient.negate(); + } + Remainder.negate(); + } else if (RHS.isNegative()) { + APInt::udivrem(LHS, -RHS, Quotient, Remainder); + Quotient.negate(); + } else { + APInt::udivrem(LHS, RHS, Quotient, Remainder); + } +} + +void APInt::sdivrem(const APInt &LHS, int64_t RHS, + APInt &Quotient, int64_t &Remainder) { + uint64_t R = Remainder; + if (LHS.isNegative()) { + if (RHS < 0) + APInt::udivrem(-LHS, -RHS, Quotient, R); + else { + APInt::udivrem(-LHS, RHS, Quotient, R); + Quotient.negate(); + } + R = -R; + } else if (RHS < 0) { + APInt::udivrem(LHS, -RHS, Quotient, R); + Quotient.negate(); + } else { + APInt::udivrem(LHS, RHS, Quotient, R); + } + Remainder = R; +} + +APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const { + APInt Res = *this+RHS; + Overflow = isNonNegative() == RHS.isNonNegative() && + Res.isNonNegative() != isNonNegative(); + return Res; +} + +APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const { + APInt Res = *this+RHS; + Overflow = Res.ult(RHS); + return Res; +} + +APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const { + APInt Res = *this - RHS; + Overflow = isNonNegative() != RHS.isNonNegative() && + Res.isNonNegative() != isNonNegative(); + return Res; +} + +APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const { + APInt Res = *this-RHS; + Overflow = Res.ugt(*this); + return Res; +} + +APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const { + // MININT/-1 --> overflow. + Overflow = isMinSignedValue() && RHS.isAllOnes(); + return sdiv(RHS); +} + +APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const { + APInt Res = *this * RHS; + + if (RHS != 0) + Overflow = Res.sdiv(RHS) != *this || + (isMinSignedValue() && RHS.isAllOnes()); + else + Overflow = false; + return Res; +} + +APInt APInt::umul_ov(const APInt &RHS, bool &Overflow) const { + if (countl_zero() + RHS.countl_zero() + 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 { + return sshl_ov(ShAmt.getLimitedValue(getBitWidth()), Overflow); +} + +APInt APInt::sshl_ov(unsigned ShAmt, bool &Overflow) const { + Overflow = ShAmt >= getBitWidth(); + if (Overflow) + return APInt(BitWidth, 0); + + if (isNonNegative()) // Don't allow sign change. + Overflow = ShAmt >= countl_zero(); + else + Overflow = ShAmt >= countl_one(); + + return *this << ShAmt; +} + +APInt APInt::ushl_ov(const APInt &ShAmt, bool &Overflow) const { + return ushl_ov(ShAmt.getLimitedValue(getBitWidth()), Overflow); +} + +APInt APInt::ushl_ov(unsigned ShAmt, bool &Overflow) const { + Overflow = ShAmt >= getBitWidth(); + if (Overflow) + return APInt(BitWidth, 0); + + Overflow = ShAmt > countl_zero(); + + return *this << ShAmt; +} + +APInt APInt::sfloordiv_ov(const APInt &RHS, bool &Overflow) const { + APInt quotient = sdiv_ov(RHS, Overflow); + if ((quotient * RHS != *this) && (isNegative() != RHS.isNegative())) + return quotient - 1; + return quotient; +} + +APInt APInt::sadd_sat(const APInt &RHS) const { + bool Overflow; + APInt Res = sadd_ov(RHS, Overflow); + if (!Overflow) + return Res; + + return isNegative() ? APInt::getSignedMinValue(BitWidth) + : APInt::getSignedMaxValue(BitWidth); +} + +APInt APInt::uadd_sat(const APInt &RHS) const { + bool Overflow; + APInt Res = uadd_ov(RHS, Overflow); + if (!Overflow) + return Res; + + return APInt::getMaxValue(BitWidth); +} + +APInt APInt::ssub_sat(const APInt &RHS) const { + bool Overflow; + APInt Res = ssub_ov(RHS, Overflow); + if (!Overflow) + return Res; + + return isNegative() ? APInt::getSignedMinValue(BitWidth) + : APInt::getSignedMaxValue(BitWidth); +} + +APInt APInt::usub_sat(const APInt &RHS) const { + bool Overflow; + APInt Res = usub_ov(RHS, Overflow); + if (!Overflow) + return Res; + + return APInt(BitWidth, 0); +} + +APInt APInt::smul_sat(const APInt &RHS) const { + bool Overflow; + APInt Res = smul_ov(RHS, Overflow); + if (!Overflow) + return Res; + + // The result is negative if one and only one of inputs is negative. + bool ResIsNegative = isNegative() ^ RHS.isNegative(); + + return ResIsNegative ? APInt::getSignedMinValue(BitWidth) + : APInt::getSignedMaxValue(BitWidth); +} + +APInt APInt::umul_sat(const APInt &RHS) const { + bool Overflow; + APInt Res = umul_ov(RHS, Overflow); + if (!Overflow) + return Res; + + return APInt::getMaxValue(BitWidth); +} + +APInt APInt::sshl_sat(const APInt &RHS) const { + return sshl_sat(RHS.getLimitedValue(getBitWidth())); +} + +APInt APInt::sshl_sat(unsigned RHS) const { + bool Overflow; + APInt Res = sshl_ov(RHS, Overflow); + if (!Overflow) + return Res; + + return isNegative() ? APInt::getSignedMinValue(BitWidth) + : APInt::getSignedMaxValue(BitWidth); +} + +APInt APInt::ushl_sat(const APInt &RHS) const { + return ushl_sat(RHS.getLimitedValue(getBitWidth())); +} + +APInt APInt::ushl_sat(unsigned RHS) const { + bool Overflow; + APInt Res = ushl_ov(RHS, Overflow); + if (!Overflow) + return Res; + + return APInt::getMaxValue(BitWidth); +} + +void APInt::fromString(unsigned numbits, StringRef str, uint8_t radix) { + // Check our assumptions here + assert(!str.empty() && "Invalid string length"); + assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 || + radix == 36) && + "Radix should be 2, 8, 10, 16, or 36!"); + + StringRef::iterator p = str.begin(); + size_t slen = str.size(); + bool isNeg = *p == '-'; + if (*p == '-' || *p == '+') { + p++; + slen--; + assert(slen && "String is only a sign, needs a value."); + } + assert((slen <= numbits || radix != 2) && "Insufficient bit width"); + assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width"); + assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width"); + assert((((slen-1)*64)/22 <= numbits || radix != 10) && + "Insufficient bit width"); + + // Allocate memory if needed + if (isSingleWord()) + U.VAL = 0; + else + U.pVal = getClearedMemory(getNumWords()); + + // Figure out if we can shift instead of multiply + unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0); + + // Enter digit traversal loop + for (StringRef::iterator e = str.end(); p != e; ++p) { + unsigned digit = getDigit(*p, radix); + assert(digit < radix && "Invalid character in digit string"); + + // Shift or multiply the value by the radix + if (slen > 1) { + if (shift) + *this <<= shift; + else + *this *= radix; + } + + // Add in the digit we just interpreted + *this += digit; + } + // If its negative, put it in two's complement form + if (isNeg) + this->negate(); +} + +void APInt::toString(SmallVectorImpl &Str, unsigned Radix, bool Signed, + bool formatAsCLiteral, bool UpperCase, + bool InsertSeparators) 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!"); + } + } + + // Number of digits in a group between separators. + unsigned Grouping = (Radix == 8 || Radix == 10) ? 3 : 4; + + // First, check for a zero value and just short circuit the logic below. + if (isZero()) { + while (*Prefix) { + Str.push_back(*Prefix); + ++Prefix; + }; + Str.push_back('0'); + return; + } + + static const char BothDigits[] = "0123456789abcdefghijklmnopqrstuvwxyz" + "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; + const char *Digits = BothDigits + (UpperCase ? 36 : 0); + + 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; + }; + + int Pos = 0; + while (N) { + if (InsertSeparators && Pos % Grouping == 0 && Pos > 0) + *--BufPtr = '\''; + *--BufPtr = Digits[N % Radix]; + N /= Radix; + Pos++; + } + 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; + + int Pos = 0; + while (Tmp.getBoolValue()) { + unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt; + if (InsertSeparators && Pos % Grouping == 0 && Pos > 0) + Str.push_back('\''); + + Str.push_back(Digits[Digit]); + Tmp.lshrInPlace(ShiftAmt); + Pos++; + } + } else { + int Pos = 0; + while (Tmp.getBoolValue()) { + uint64_t Digit; + udivrem(Tmp, Radix, Tmp, Digit); + assert(Digit < Radix && "divide failed"); + if (InsertSeparators && Pos % Grouping == 0 && Pos > 0) + Str.push_back('\''); + + Str.push_back(Digits[Digit]); + Pos++; + } + } + + // Reverse the digits before returning. + std::reverse(Str.begin()+StartDig, Str.end()); +} + +#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP) +LLVM_DUMP_METHOD void APInt::dump() const { + SmallString<40> S, U; + this->toStringUnsigned(U); + this->toStringSigned(S); + dbgs() << "APInt(" << BitWidth << "b, " + << U << "u " << S << "s)\n"; +} +#endif + +void APInt::print(raw_ostream &OS, bool isSigned) const { + SmallString<40> S; + this->toString(S, 10, isSigned, /* formatAsCLiteral = */false); + OS << S; +} + +// This implements a variety of operations on a representation of +// arbitrary precision, two's-complement, bignum integer values. + +// Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe +// and unrestricting assumption. +static_assert(APInt::APINT_BITS_PER_WORD % 2 == 0, + "Part width must be divisible by 2!"); + +// Returns the integer part with the least significant BITS set. +// BITS cannot be zero. +static inline APInt::WordType lowBitMask(unsigned bits) { + assert(bits != 0 && bits <= APInt::APINT_BITS_PER_WORD); + return ~(APInt::WordType) 0 >> (APInt::APINT_BITS_PER_WORD - bits); +} + +/// Returns the value of the lower half of PART. +static inline APInt::WordType lowHalf(APInt::WordType part) { + return part & lowBitMask(APInt::APINT_BITS_PER_WORD / 2); +} + +/// Returns the value of the upper half of PART. +static inline APInt::WordType highHalf(APInt::WordType part) { + return part >> (APInt::APINT_BITS_PER_WORD / 2); +} + +/// 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 UINT_MAX is returned. +unsigned APInt::tcLSB(const WordType *parts, unsigned n) { + for (unsigned i = 0; i < n; i++) { + if (parts[i] != 0) { + unsigned lsb = llvm::countr_zero(parts[i]); + return lsb + i * APINT_BITS_PER_WORD; + } + } + + return UINT_MAX; +} + +/// Returns the bit number of the most significant set bit of a number. +/// If the input number has no bits set UINT_MAX is returned. +unsigned APInt::tcMSB(const WordType *parts, unsigned n) { + do { + --n; + + if (parts[n] != 0) { + static_assert(sizeof(parts[n]) <= sizeof(uint64_t)); + unsigned msb = llvm::Log2_64(parts[n]); + + return msb + n * APINT_BITS_PER_WORD; + } + } while (n); + + return UINT_MAX; +} + +/// Copy the bit vector of width srcBITS from SRC, starting at bit srcLSB, to +/// DST, of dstCOUNT parts, such that the bit srcLSB becomes the least +/// significant bit of DST. All high bits above srcBITS in DST are zero-filled. +/// */ +void +APInt::tcExtract(WordType *dst, unsigned dstCount, const WordType *src, + unsigned srcBits, unsigned srcLSB) { + unsigned dstParts = (srcBits + APINT_BITS_PER_WORD - 1) / APINT_BITS_PER_WORD; + assert(dstParts <= dstCount); + + unsigned firstSrcPart = srcLSB / APINT_BITS_PER_WORD; + tcAssign(dst, src + firstSrcPart, dstParts); + + unsigned shift = srcLSB % APINT_BITS_PER_WORD; + tcShiftRight(dst, dstParts, shift); + + // We now have (dstParts * APINT_BITS_PER_WORD - shift) bits from SRC + // in DST. If this is less that srcBits, append the rest, else + // clear the high bits. + unsigned n = dstParts * APINT_BITS_PER_WORD - shift; + if (n < srcBits) { + WordType mask = lowBitMask (srcBits - n); + dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask) + << n % APINT_BITS_PER_WORD); + } else if (n > srcBits) { + if (srcBits % APINT_BITS_PER_WORD) + dst[dstParts - 1] &= lowBitMask (srcBits % APINT_BITS_PER_WORD); + } + + // Clear high parts. + while (dstParts < dstCount) + dst[dstParts++] = 0; +} + +//// DST += RHS + C where C is zero or one. Returns the carry flag. +APInt::WordType APInt::tcAdd(WordType *dst, const WordType *rhs, + WordType c, unsigned parts) { + assert(c <= 1); + + for (unsigned i = 0; i < parts; i++) { + WordType l = dst[i]; + if (c) { + dst[i] += rhs[i] + 1; + c = (dst[i] <= l); + } else { + dst[i] += rhs[i]; + c = (dst[i] < l); + } + } + + return c; +} + +/// This function adds a single "word" integer, src, to the multiple +/// "word" integer array, dst[]. dst[] is modified to reflect the addition and +/// 1 is returned if there is a carry out, otherwise 0 is returned. +/// @returns the carry of the addition. +APInt::WordType APInt::tcAddPart(WordType *dst, WordType src, + unsigned parts) { + for (unsigned i = 0; i < parts; ++i) { + dst[i] += src; + if (dst[i] >= src) + return 0; // No need to carry so exit early. + src = 1; // Carry one to next digit. + } + + return 1; +} + +/// DST -= RHS + C where C is zero or one. Returns the carry flag. +APInt::WordType APInt::tcSubtract(WordType *dst, const WordType *rhs, + WordType c, unsigned parts) { + assert(c <= 1); + + for (unsigned i = 0; i < parts; i++) { + WordType l = dst[i]; + if (c) { + dst[i] -= rhs[i] + 1; + c = (dst[i] >= l); + } else { + dst[i] -= rhs[i]; + c = (dst[i] > l); + } + } + + return c; +} + +/// This function subtracts a single "word" (64-bit word), src, from +/// the multi-word integer array, dst[], propagating the borrowed 1 value until +/// no further borrowing is needed or it runs out of "words" in dst. The result +/// is 1 if "borrowing" exhausted the digits in dst, or 0 if dst was not +/// exhausted. In other words, if src > dst then this function returns 1, +/// otherwise 0. +/// @returns the borrow out of the subtraction +APInt::WordType APInt::tcSubtractPart(WordType *dst, WordType src, + unsigned parts) { + for (unsigned i = 0; i < parts; ++i) { + WordType Dst = dst[i]; + dst[i] -= src; + if (src <= Dst) + return 0; // No need to borrow so exit early. + src = 1; // We have to "borrow 1" from next "word" + } + + return 1; +} + +/// Negate a bignum in-place. +void APInt::tcNegate(WordType *dst, unsigned parts) { + tcComplement(dst, parts); + tcIncrement(dst, parts); +} + +/// DST += SRC * MULTIPLIER + CARRY if add is true +/// DST = SRC * MULTIPLIER + CARRY if add is false +/// Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC +/// they must start at the same point, i.e. DST == SRC. +/// If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is +/// returned. Otherwise DST is filled with the least significant +/// DSTPARTS parts of the result, and if all of the omitted higher +/// parts were zero return zero, otherwise overflow occurred and +/// return one. +int APInt::tcMultiplyPart(WordType *dst, const WordType *src, + WordType multiplier, WordType carry, + unsigned srcParts, unsigned dstParts, + bool add) { + // Otherwise our writes of DST kill our later reads of SRC. + assert(dst <= src || dst >= src + srcParts); + assert(dstParts <= srcParts + 1); + + // N loops; minimum of dstParts and srcParts. + unsigned n = std::min(dstParts, srcParts); + + for (unsigned i = 0; i < n; i++) { + // [LOW, HIGH] = MULTIPLIER * SRC[i] + DST[i] + CARRY. + // This cannot overflow, because: + // (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1) + // which is less than n^2. + WordType srcPart = src[i]; + WordType low, mid, high; + if (multiplier == 0 || srcPart == 0) { + low = carry; + high = 0; + } else { + low = lowHalf(srcPart) * lowHalf(multiplier); + high = highHalf(srcPart) * highHalf(multiplier); + + mid = lowHalf(srcPart) * highHalf(multiplier); + high += highHalf(mid); + mid <<= APINT_BITS_PER_WORD / 2; + if (low + mid < low) + high++; + low += mid; + + mid = highHalf(srcPart) * lowHalf(multiplier); + high += highHalf(mid); + mid <<= APINT_BITS_PER_WORD / 2; + if (low + mid < low) + high++; + low += mid; + + // Now add carry. + if (low + carry < low) + high++; + low += carry; + } + + if (add) { + // And now DST[i], and store the new low part there. + if (low + dst[i] < low) + high++; + dst[i] += low; + } else { + dst[i] = low; + } + + carry = high; + } + + if (srcParts < dstParts) { + // Full multiplication, there is no overflow. + assert(srcParts + 1 == dstParts); + dst[srcParts] = carry; + return 0; + } + + // We overflowed if there is carry. + if (carry) + return 1; + + // We would overflow if any significant unwritten parts would be + // non-zero. This is true if any remaining src parts are non-zero + // and the multiplier is non-zero. + if (multiplier) + for (unsigned i = dstParts; i < srcParts; i++) + if (src[i]) + return 1; + + // We fitted in the narrow destination. + return 0; +} + +/// DST = LHS * RHS, where DST has the same width as the operands and +/// is filled with the least significant parts of the result. Returns +/// one if overflow occurred, otherwise zero. DST must be disjoint +/// from both operands. +int APInt::tcMultiply(WordType *dst, const WordType *lhs, + const WordType *rhs, unsigned parts) { + assert(dst != lhs && dst != rhs); + + int overflow = 0; + + for (unsigned i = 0; i < parts; i++) { + // Don't accumulate on the first iteration so we don't need to initalize + // dst to 0. + overflow |= + tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts, parts - i, i != 0); + } + + 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); + + for (unsigned i = 0; i < lhsParts; i++) { + // Don't accumulate on the first iteration so we don't need to initalize + // dst to 0. + tcMultiplyPart(&dst[i], rhs, lhs[i], 0, rhsParts, rhsParts + 1, i != 0); + } +} + +// If RHS is zero LHS and REMAINDER are left unchanged, return one. +// Otherwise set LHS to LHS / RHS with the fractional part discarded, +// set REMAINDER to the remainder, return zero. i.e. +// +// OLD_LHS = RHS * LHS + REMAINDER +// +// SCRATCH is a bignum of the same size as the operands and result for +// use by the routine; its contents need not be initialized and are +// destroyed. LHS, REMAINDER and SCRATCH must be distinct. +int APInt::tcDivide(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 Count 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); +} + +// 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; +} + +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.isZero()) + 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.isZero()) + 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 towards zero. + case APInt::Rounding::TOWARD_ZERO: + return A.sdiv(B); + } + llvm_unreachable("Unknown APInt::Rounding enum"); +} + +std::optional +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).isZero()) { + 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.isZero()) + 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, decrement 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.isZero()) { + 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.isZero() != VY.isZero(); + // 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 std::nullopt; + } + + X += 1; + LLVM_DEBUG(dbgs() << __func__ << ": solution (wrap): " << X << '\n'); + return X; +} + +std::optional +llvm::APIntOps::GetMostSignificantDifferentBit(const APInt &A, const APInt &B) { + assert(A.getBitWidth() == B.getBitWidth() && "Must have the same bitwidth"); + if (A == B) + return std::nullopt; + return A.getBitWidth() - ((A ^ B).countl_zero() + 1); +} + +APInt llvm::APIntOps::ScaleBitMask(const APInt &A, unsigned NewBitWidth, + bool MatchAllBits) { + unsigned OldBitWidth = A.getBitWidth(); + assert((((OldBitWidth % NewBitWidth) == 0) || + ((NewBitWidth % OldBitWidth) == 0)) && + "One size should be a multiple of the other one. " + "Can't do fractional scaling."); + + // Check for matching bitwidths. + if (OldBitWidth == NewBitWidth) + return A; + + APInt NewA = APInt::getZero(NewBitWidth); + + // Check for null input. + if (A.isZero()) + return NewA; + + if (NewBitWidth > OldBitWidth) { + // Repeat bits. + unsigned Scale = NewBitWidth / OldBitWidth; + for (unsigned i = 0; i != OldBitWidth; ++i) + if (A[i]) + NewA.setBits(i * Scale, (i + 1) * Scale); + } else { + unsigned Scale = OldBitWidth / NewBitWidth; + for (unsigned i = 0; i != NewBitWidth; ++i) { + if (MatchAllBits) { + if (A.extractBits(Scale, i * Scale).isAllOnes()) + NewA.setBit(i); + } else { + if (!A.extractBits(Scale, i * Scale).isZero()) + NewA.setBit(i); + } + } + } + + return NewA; +} + +/// 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, const uint8_t *Src, + unsigned LoadBytes) { + assert((IntVal.getBitWidth()+7)/8 >= LoadBytes && "Integer too small!"); + uint8_t *Dst = reinterpret_cast( + const_cast(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); + } +} + +APInt APIntOps::avgFloorS(const APInt &C1, const APInt &C2) { + // Return floor((C1 + C2) / 2) + return (C1 & C2) + (C1 ^ C2).ashr(1); +} + +APInt APIntOps::avgFloorU(const APInt &C1, const APInt &C2) { + // Return floor((C1 + C2) / 2) + return (C1 & C2) + (C1 ^ C2).lshr(1); +} + +APInt APIntOps::avgCeilS(const APInt &C1, const APInt &C2) { + // Return ceil((C1 + C2) / 2) + return (C1 | C2) - (C1 ^ C2).ashr(1); +} + +APInt APIntOps::avgCeilU(const APInt &C1, const APInt &C2) { + // Return ceil((C1 + C2) / 2) + return (C1 | C2) - (C1 ^ C2).lshr(1); +} + +APInt APIntOps::mulhs(const APInt &C1, const APInt &C2) { + assert(C1.getBitWidth() == C2.getBitWidth() && "Unequal bitwidths"); + unsigned FullWidth = C1.getBitWidth() * 2; + APInt C1Ext = C1.sext(FullWidth); + APInt C2Ext = C2.sext(FullWidth); + return (C1Ext * C2Ext).extractBits(C1.getBitWidth(), C1.getBitWidth()); +} + +APInt APIntOps::mulhu(const APInt &C1, const APInt &C2) { + assert(C1.getBitWidth() == C2.getBitWidth() && "Unequal bitwidths"); + unsigned FullWidth = C1.getBitWidth() * 2; + APInt C1Ext = C1.zext(FullWidth); + APInt C2Ext = C2.zext(FullWidth); + return (C1Ext * C2Ext).extractBits(C1.getBitWidth(), C1.getBitWidth()); +} + +APInt APIntOps::mulsExtended(const APInt &C1, const APInt &C2) { + assert(C1.getBitWidth() == C2.getBitWidth() && "Unequal bitwidths"); + unsigned FullWidth = C1.getBitWidth() * 2; + APInt C1Ext = C1.sext(FullWidth); + APInt C2Ext = C2.sext(FullWidth); + return C1Ext * C2Ext; +} + +APInt APIntOps::muluExtended(const APInt &C1, const APInt &C2) { + assert(C1.getBitWidth() == C2.getBitWidth() && "Unequal bitwidths"); + unsigned FullWidth = C1.getBitWidth() * 2; + APInt C1Ext = C1.zext(FullWidth); + APInt C2Ext = C2.zext(FullWidth); + return C1Ext * C2Ext; +} + +APInt APIntOps::pow(const APInt &X, int64_t N) { + assert(N >= 0 && "negative exponents not supported."); + APInt Acc = APInt(X.getBitWidth(), 1); + if (N == 0) + return Acc; + APInt Base = X; + int64_t RemainingExponent = N; + while (RemainingExponent > 0) { + while (RemainingExponent % 2 == 0) { + Base *= Base; + RemainingExponent /= 2; + } + --RemainingExponent; + Acc *= Base; + } + return Acc; +} + +APInt llvm::APIntOps::fshl(const APInt &Hi, const APInt &Lo, + const APInt &Shift) { + assert(Hi.getBitWidth() == Lo.getBitWidth()); + unsigned ShiftAmt = rotateModulo(Hi.getBitWidth(), Shift); + if (ShiftAmt == 0) + return Hi; + return Hi.shl(ShiftAmt) | Lo.lshr(Hi.getBitWidth() - ShiftAmt); +} + +APInt llvm::APIntOps::fshr(const APInt &Hi, const APInt &Lo, + const APInt &Shift) { + assert(Hi.getBitWidth() == Lo.getBitWidth()); + unsigned ShiftAmt = rotateModulo(Hi.getBitWidth(), Shift); + if (ShiftAmt == 0) + return Lo; + return Hi.shl(Hi.getBitWidth() - ShiftAmt) | Lo.lshr(ShiftAmt); +} From bd3ae2330f32b1651a8bfde069c841a5fbb78d33 Mon Sep 17 00:00:00 2001 From: Rahul Joshi Date: Mon, 29 Sep 2025 11:39:34 -0700 Subject: [PATCH 2/2] Add ools/llvm-opt-report/Inputs/q.cpp --- llvm/test/tools/llvm-opt-report/Inputs/q.cpp | 28 ++++++++++---------- 1 file changed, 14 insertions(+), 14 deletions(-) diff --git a/llvm/test/tools/llvm-opt-report/Inputs/q.cpp b/llvm/test/tools/llvm-opt-report/Inputs/q.cpp index 0982c6afdfe5c..a26a750822b12 100644 --- a/llvm/test/tools/llvm-opt-report/Inputs/q.cpp +++ b/llvm/test/tools/llvm-opt-report/Inputs/q.cpp @@ -1,14 +1,14 @@ -void bar(); -void foo(int n) { - for (int i = 0; i < n; ++i) - bar(); -} - -void quack() { - foo(4); -} - -void quack2() { - foo(4); -} - +void bar(); +void foo(int n) { + for (int i = 0; i < n; ++i) + bar(); +} + +void quack() { + foo(4); +} + +void quack2() { + foo(4); +} +