forked from OSchip/llvm-project
3111 lines
98 KiB
C++
3111 lines
98 KiB
C++
//===-- APInt.cpp - Implement APInt class ---------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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//
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// This file implements a class to represent arbitrary precision integer
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// constant values and provide a variety of arithmetic operations on them.
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//
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//===----------------------------------------------------------------------===//
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#include "llvm/ADT/APInt.h"
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#include "llvm/ADT/ArrayRef.h"
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#include "llvm/ADT/FoldingSet.h"
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#include "llvm/ADT/Hashing.h"
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#include "llvm/ADT/Optional.h"
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#include "llvm/ADT/SmallString.h"
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#include "llvm/ADT/StringRef.h"
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#include "llvm/ADT/bit.h"
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#include "llvm/Config/llvm-config.h"
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#include "llvm/Support/Debug.h"
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#include "llvm/Support/ErrorHandling.h"
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#include "llvm/Support/MathExtras.h"
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#include "llvm/Support/raw_ostream.h"
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#include <climits>
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#include <cmath>
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#include <cstdlib>
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#include <cstring>
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using namespace llvm;
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#define DEBUG_TYPE "apint"
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/// A utility function for allocating memory, checking for allocation failures,
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/// and ensuring the contents are zeroed.
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inline static uint64_t* getClearedMemory(unsigned numWords) {
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uint64_t *result = new uint64_t[numWords];
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memset(result, 0, numWords * sizeof(uint64_t));
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return result;
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}
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/// A utility function for allocating memory and checking for allocation
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/// failure. The content is not zeroed.
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inline static uint64_t* getMemory(unsigned numWords) {
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return new uint64_t[numWords];
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}
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/// A utility function that converts a character to a digit.
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inline static unsigned getDigit(char cdigit, uint8_t radix) {
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unsigned r;
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if (radix == 16 || radix == 36) {
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r = cdigit - '0';
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if (r <= 9)
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return r;
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r = cdigit - 'A';
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if (r <= radix - 11U)
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return r + 10;
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r = cdigit - 'a';
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if (r <= radix - 11U)
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return r + 10;
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radix = 10;
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}
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r = cdigit - '0';
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if (r < radix)
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return r;
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return -1U;
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}
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void APInt::initSlowCase(uint64_t val, bool isSigned) {
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U.pVal = getClearedMemory(getNumWords());
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U.pVal[0] = val;
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if (isSigned && int64_t(val) < 0)
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for (unsigned i = 1; i < getNumWords(); ++i)
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U.pVal[i] = WORDTYPE_MAX;
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clearUnusedBits();
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}
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void APInt::initSlowCase(const APInt& that) {
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U.pVal = getMemory(getNumWords());
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memcpy(U.pVal, that.U.pVal, getNumWords() * APINT_WORD_SIZE);
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}
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void APInt::initFromArray(ArrayRef<uint64_t> bigVal) {
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assert(BitWidth && "Bitwidth too small");
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assert(bigVal.data() && "Null pointer detected!");
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if (isSingleWord())
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U.VAL = bigVal[0];
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else {
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// Get memory, cleared to 0
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U.pVal = getClearedMemory(getNumWords());
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// Calculate the number of words to copy
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unsigned words = std::min<unsigned>(bigVal.size(), getNumWords());
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// Copy the words from bigVal to pVal
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memcpy(U.pVal, bigVal.data(), words * APINT_WORD_SIZE);
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}
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// Make sure unused high bits are cleared
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clearUnusedBits();
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}
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APInt::APInt(unsigned numBits, ArrayRef<uint64_t> bigVal)
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: BitWidth(numBits) {
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initFromArray(bigVal);
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}
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APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[])
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: BitWidth(numBits) {
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initFromArray(makeArrayRef(bigVal, numWords));
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}
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APInt::APInt(unsigned numbits, StringRef Str, uint8_t radix)
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: BitWidth(numbits) {
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assert(BitWidth && "Bitwidth too small");
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fromString(numbits, Str, radix);
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}
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void APInt::reallocate(unsigned NewBitWidth) {
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// If the number of words is the same we can just change the width and stop.
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if (getNumWords() == getNumWords(NewBitWidth)) {
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BitWidth = NewBitWidth;
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return;
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}
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// If we have an allocation, delete it.
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if (!isSingleWord())
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delete [] U.pVal;
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// Update BitWidth.
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BitWidth = NewBitWidth;
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// If we are supposed to have an allocation, create it.
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if (!isSingleWord())
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U.pVal = getMemory(getNumWords());
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}
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void APInt::AssignSlowCase(const APInt& RHS) {
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// Don't do anything for X = X
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if (this == &RHS)
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return;
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// Adjust the bit width and handle allocations as necessary.
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reallocate(RHS.getBitWidth());
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// Copy the data.
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if (isSingleWord())
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U.VAL = RHS.U.VAL;
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else
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memcpy(U.pVal, RHS.U.pVal, getNumWords() * APINT_WORD_SIZE);
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}
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/// This method 'profiles' an APInt for use with FoldingSet.
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void APInt::Profile(FoldingSetNodeID& ID) const {
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ID.AddInteger(BitWidth);
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if (isSingleWord()) {
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ID.AddInteger(U.VAL);
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return;
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}
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unsigned NumWords = getNumWords();
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for (unsigned i = 0; i < NumWords; ++i)
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ID.AddInteger(U.pVal[i]);
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}
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/// Prefix increment operator. Increments the APInt by one.
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APInt& APInt::operator++() {
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if (isSingleWord())
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++U.VAL;
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else
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tcIncrement(U.pVal, getNumWords());
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return clearUnusedBits();
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}
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/// Prefix decrement operator. Decrements the APInt by one.
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APInt& APInt::operator--() {
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if (isSingleWord())
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--U.VAL;
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else
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tcDecrement(U.pVal, getNumWords());
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return clearUnusedBits();
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}
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/// Adds the RHS APInt to this APInt.
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/// @returns this, after addition of RHS.
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/// Addition assignment operator.
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APInt& APInt::operator+=(const APInt& RHS) {
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assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
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if (isSingleWord())
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U.VAL += RHS.U.VAL;
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else
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tcAdd(U.pVal, RHS.U.pVal, 0, getNumWords());
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return clearUnusedBits();
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}
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APInt& APInt::operator+=(uint64_t RHS) {
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if (isSingleWord())
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U.VAL += RHS;
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else
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tcAddPart(U.pVal, RHS, getNumWords());
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return clearUnusedBits();
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}
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/// Subtracts the RHS APInt from this APInt
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/// @returns this, after subtraction
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/// Subtraction assignment operator.
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APInt& APInt::operator-=(const APInt& RHS) {
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assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
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if (isSingleWord())
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U.VAL -= RHS.U.VAL;
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else
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tcSubtract(U.pVal, RHS.U.pVal, 0, getNumWords());
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return clearUnusedBits();
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}
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APInt& APInt::operator-=(uint64_t RHS) {
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if (isSingleWord())
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U.VAL -= RHS;
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else
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tcSubtractPart(U.pVal, RHS, getNumWords());
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return clearUnusedBits();
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}
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APInt APInt::operator*(const APInt& RHS) const {
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assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
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if (isSingleWord())
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return APInt(BitWidth, U.VAL * RHS.U.VAL);
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APInt Result(getMemory(getNumWords()), getBitWidth());
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tcMultiply(Result.U.pVal, U.pVal, RHS.U.pVal, getNumWords());
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Result.clearUnusedBits();
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return Result;
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}
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void APInt::AndAssignSlowCase(const APInt& RHS) {
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tcAnd(U.pVal, RHS.U.pVal, getNumWords());
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}
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void APInt::OrAssignSlowCase(const APInt& RHS) {
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tcOr(U.pVal, RHS.U.pVal, getNumWords());
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}
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void APInt::XorAssignSlowCase(const APInt& RHS) {
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tcXor(U.pVal, RHS.U.pVal, getNumWords());
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}
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APInt& APInt::operator*=(const APInt& RHS) {
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assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
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*this = *this * RHS;
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return *this;
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}
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APInt& APInt::operator*=(uint64_t RHS) {
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if (isSingleWord()) {
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U.VAL *= RHS;
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} else {
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unsigned NumWords = getNumWords();
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tcMultiplyPart(U.pVal, U.pVal, RHS, 0, NumWords, NumWords, false);
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}
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return clearUnusedBits();
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}
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bool APInt::EqualSlowCase(const APInt& RHS) const {
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return std::equal(U.pVal, U.pVal + getNumWords(), RHS.U.pVal);
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}
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int APInt::compare(const APInt& RHS) const {
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assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
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if (isSingleWord())
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return U.VAL < RHS.U.VAL ? -1 : U.VAL > RHS.U.VAL;
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return tcCompare(U.pVal, RHS.U.pVal, getNumWords());
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}
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int APInt::compareSigned(const APInt& RHS) const {
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assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
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if (isSingleWord()) {
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int64_t lhsSext = SignExtend64(U.VAL, BitWidth);
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int64_t rhsSext = SignExtend64(RHS.U.VAL, BitWidth);
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return lhsSext < rhsSext ? -1 : lhsSext > rhsSext;
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}
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bool lhsNeg = isNegative();
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bool rhsNeg = RHS.isNegative();
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// If the sign bits don't match, then (LHS < RHS) if LHS is negative
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if (lhsNeg != rhsNeg)
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return lhsNeg ? -1 : 1;
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// Otherwise we can just use an unsigned comparison, because even negative
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// numbers compare correctly this way if both have the same signed-ness.
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return tcCompare(U.pVal, RHS.U.pVal, getNumWords());
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}
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void APInt::setBitsSlowCase(unsigned loBit, unsigned hiBit) {
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unsigned loWord = whichWord(loBit);
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unsigned hiWord = whichWord(hiBit);
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// Create an initial mask for the low word with zeros below loBit.
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uint64_t loMask = WORDTYPE_MAX << whichBit(loBit);
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// If hiBit is not aligned, we need a high mask.
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unsigned hiShiftAmt = whichBit(hiBit);
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if (hiShiftAmt != 0) {
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// Create a high mask with zeros above hiBit.
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uint64_t hiMask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - hiShiftAmt);
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// If loWord and hiWord are equal, then we combine the masks. Otherwise,
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// set the bits in hiWord.
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if (hiWord == loWord)
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loMask &= hiMask;
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else
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U.pVal[hiWord] |= hiMask;
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}
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// Apply the mask to the low word.
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U.pVal[loWord] |= loMask;
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// Fill any words between loWord and hiWord with all ones.
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for (unsigned word = loWord + 1; word < hiWord; ++word)
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U.pVal[word] = WORDTYPE_MAX;
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}
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/// Toggle every bit to its opposite value.
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void APInt::flipAllBitsSlowCase() {
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tcComplement(U.pVal, getNumWords());
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clearUnusedBits();
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}
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/// Toggle a given bit to its opposite value whose position is given
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/// as "bitPosition".
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/// Toggles a given bit to its opposite value.
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void APInt::flipBit(unsigned bitPosition) {
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assert(bitPosition < BitWidth && "Out of the bit-width range!");
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if ((*this)[bitPosition]) clearBit(bitPosition);
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else setBit(bitPosition);
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}
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void APInt::insertBits(const APInt &subBits, unsigned bitPosition) {
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unsigned subBitWidth = subBits.getBitWidth();
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assert(0 < subBitWidth && (subBitWidth + bitPosition) <= BitWidth &&
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"Illegal bit insertion");
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// Insertion is a direct copy.
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if (subBitWidth == BitWidth) {
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*this = subBits;
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return;
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}
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// Single word result can be done as a direct bitmask.
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if (isSingleWord()) {
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uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - subBitWidth);
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U.VAL &= ~(mask << bitPosition);
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U.VAL |= (subBits.U.VAL << bitPosition);
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return;
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}
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unsigned loBit = whichBit(bitPosition);
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unsigned loWord = whichWord(bitPosition);
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unsigned hi1Word = whichWord(bitPosition + subBitWidth - 1);
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// Insertion within a single word can be done as a direct bitmask.
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if (loWord == hi1Word) {
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uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - subBitWidth);
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U.pVal[loWord] &= ~(mask << loBit);
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U.pVal[loWord] |= (subBits.U.VAL << loBit);
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return;
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}
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// Insert on word boundaries.
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if (loBit == 0) {
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// Direct copy whole words.
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unsigned numWholeSubWords = subBitWidth / APINT_BITS_PER_WORD;
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memcpy(U.pVal + loWord, subBits.getRawData(),
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numWholeSubWords * APINT_WORD_SIZE);
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// Mask+insert remaining bits.
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unsigned remainingBits = subBitWidth % APINT_BITS_PER_WORD;
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if (remainingBits != 0) {
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uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - remainingBits);
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U.pVal[hi1Word] &= ~mask;
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U.pVal[hi1Word] |= subBits.getWord(subBitWidth - 1);
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}
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return;
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}
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// General case - set/clear individual bits in dst based on src.
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// TODO - there is scope for optimization here, but at the moment this code
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// path is barely used so prefer readability over performance.
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for (unsigned i = 0; i != subBitWidth; ++i) {
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if (subBits[i])
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setBit(bitPosition + i);
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else
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clearBit(bitPosition + i);
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}
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}
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void APInt::insertBits(uint64_t subBits, unsigned bitPosition, unsigned numBits) {
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uint64_t maskBits = maskTrailingOnes<uint64_t>(numBits);
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subBits &= maskBits;
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if (isSingleWord()) {
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U.VAL &= ~(maskBits << bitPosition);
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U.VAL |= subBits << bitPosition;
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return;
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}
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unsigned loBit = whichBit(bitPosition);
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unsigned loWord = whichWord(bitPosition);
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unsigned hiWord = whichWord(bitPosition + numBits - 1);
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if (loWord == hiWord) {
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U.pVal[loWord] &= ~(maskBits << loBit);
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U.pVal[loWord] |= subBits << loBit;
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return;
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}
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static_assert(8 * sizeof(WordType) <= 64, "This code assumes only two words affected");
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unsigned wordBits = 8 * sizeof(WordType);
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U.pVal[loWord] &= ~(maskBits << loBit);
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U.pVal[loWord] |= subBits << loBit;
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U.pVal[hiWord] &= ~(maskBits >> (wordBits - loBit));
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U.pVal[hiWord] |= subBits >> (wordBits - loBit);
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}
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APInt APInt::extractBits(unsigned numBits, unsigned bitPosition) const {
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assert(numBits > 0 && "Can't extract zero bits");
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assert(bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth &&
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"Illegal bit extraction");
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if (isSingleWord())
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return APInt(numBits, U.VAL >> bitPosition);
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unsigned loBit = whichBit(bitPosition);
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unsigned loWord = whichWord(bitPosition);
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unsigned hiWord = whichWord(bitPosition + numBits - 1);
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// Single word result extracting bits from a single word source.
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if (loWord == hiWord)
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return APInt(numBits, U.pVal[loWord] >> loBit);
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// Extracting bits that start on a source word boundary can be done
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// as a fast memory copy.
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if (loBit == 0)
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return APInt(numBits, makeArrayRef(U.pVal + loWord, 1 + hiWord - loWord));
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// General case - shift + copy source words directly into place.
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APInt Result(numBits, 0);
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unsigned NumSrcWords = getNumWords();
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unsigned NumDstWords = Result.getNumWords();
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uint64_t *DestPtr = Result.isSingleWord() ? &Result.U.VAL : Result.U.pVal;
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for (unsigned word = 0; word < NumDstWords; ++word) {
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uint64_t w0 = U.pVal[loWord + word];
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uint64_t w1 =
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(loWord + word + 1) < NumSrcWords ? U.pVal[loWord + word + 1] : 0;
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DestPtr[word] = (w0 >> loBit) | (w1 << (APINT_BITS_PER_WORD - loBit));
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}
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return Result.clearUnusedBits();
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}
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uint64_t APInt::extractBitsAsZExtValue(unsigned numBits,
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unsigned bitPosition) const {
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assert(numBits > 0 && "Can't extract zero bits");
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assert(bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth &&
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"Illegal bit extraction");
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assert(numBits <= 64 && "Illegal bit extraction");
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uint64_t maskBits = maskTrailingOnes<uint64_t>(numBits);
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if (isSingleWord())
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return (U.VAL >> bitPosition) & maskBits;
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unsigned loBit = whichBit(bitPosition);
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unsigned loWord = whichWord(bitPosition);
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unsigned hiWord = whichWord(bitPosition + numBits - 1);
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if (loWord == hiWord)
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return (U.pVal[loWord] >> loBit) & maskBits;
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static_assert(8 * sizeof(WordType) <= 64, "This code assumes only two words affected");
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unsigned wordBits = 8 * sizeof(WordType);
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uint64_t retBits = U.pVal[loWord] >> loBit;
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retBits |= U.pVal[hiWord] << (wordBits - loBit);
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retBits &= maskBits;
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return retBits;
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}
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unsigned APInt::getBitsNeeded(StringRef str, uint8_t radix) {
|
|
assert(!str.empty() && "Invalid string length");
|
|
assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||
|
|
radix == 36) &&
|
|
"Radix should be 2, 8, 10, 16, or 36!");
|
|
|
|
size_t slen = str.size();
|
|
|
|
// Each computation below needs to know if it's negative.
|
|
StringRef::iterator p = str.begin();
|
|
unsigned isNegative = *p == '-';
|
|
if (*p == '-' || *p == '+') {
|
|
p++;
|
|
slen--;
|
|
assert(slen && "String is only a sign, needs a value.");
|
|
}
|
|
|
|
// For radixes of power-of-two values, the bits required is accurately and
|
|
// easily computed
|
|
if (radix == 2)
|
|
return slen + isNegative;
|
|
if (radix == 8)
|
|
return slen * 3 + isNegative;
|
|
if (radix == 16)
|
|
return slen * 4 + isNegative;
|
|
|
|
// FIXME: base 36
|
|
|
|
// This is grossly inefficient but accurate. We could probably do something
|
|
// with a computation of roughly slen*64/20 and then adjust by the value of
|
|
// the first few digits. But, I'm not sure how accurate that could be.
|
|
|
|
// Compute a sufficient number of bits that is always large enough but might
|
|
// be too large. This avoids the assertion in the constructor. This
|
|
// calculation doesn't work appropriately for the numbers 0-9, so just use 4
|
|
// bits in that case.
|
|
unsigned sufficient
|
|
= radix == 10? (slen == 1 ? 4 : slen * 64/18)
|
|
: (slen == 1 ? 7 : slen * 16/3);
|
|
|
|
// Convert to the actual binary value.
|
|
APInt tmp(sufficient, StringRef(p, slen), radix);
|
|
|
|
// Compute how many bits are required. If the log is infinite, assume we need
|
|
// just bit. If the log is exact and value is negative, then the value is
|
|
// MinSignedValue with (log + 1) bits.
|
|
unsigned log = tmp.logBase2();
|
|
if (log == (unsigned)-1) {
|
|
return isNegative + 1;
|
|
} else if (isNegative && tmp.isPowerOf2()) {
|
|
return isNegative + log;
|
|
} else {
|
|
return isNegative + log + 1;
|
|
}
|
|
}
|
|
|
|
hash_code llvm::hash_value(const APInt &Arg) {
|
|
if (Arg.isSingleWord())
|
|
return hash_combine(Arg.U.VAL);
|
|
|
|
return hash_combine_range(Arg.U.pVal, Arg.U.pVal + Arg.getNumWords());
|
|
}
|
|
|
|
bool APInt::isSplat(unsigned SplatSizeInBits) const {
|
|
assert(getBitWidth() % SplatSizeInBits == 0 &&
|
|
"SplatSizeInBits must divide width!");
|
|
// We can check that all parts of an integer are equal by making use of a
|
|
// little trick: rotate and check if it's still the same value.
|
|
return *this == rotl(SplatSizeInBits);
|
|
}
|
|
|
|
/// This function returns the high "numBits" bits of this APInt.
|
|
APInt APInt::getHiBits(unsigned numBits) const {
|
|
return this->lshr(BitWidth - numBits);
|
|
}
|
|
|
|
/// This function returns the low "numBits" bits of this APInt.
|
|
APInt APInt::getLoBits(unsigned numBits) const {
|
|
APInt Result(getLowBitsSet(BitWidth, numBits));
|
|
Result &= *this;
|
|
return Result;
|
|
}
|
|
|
|
/// Return a value containing V broadcasted over NewLen bits.
|
|
APInt APInt::getSplat(unsigned NewLen, const APInt &V) {
|
|
assert(NewLen >= V.getBitWidth() && "Can't splat to smaller bit width!");
|
|
|
|
APInt Val = V.zextOrSelf(NewLen);
|
|
for (unsigned I = V.getBitWidth(); I < NewLen; I <<= 1)
|
|
Val |= Val << I;
|
|
|
|
return Val;
|
|
}
|
|
|
|
unsigned APInt::countLeadingZerosSlowCase() const {
|
|
unsigned Count = 0;
|
|
for (int i = getNumWords()-1; i >= 0; --i) {
|
|
uint64_t V = U.pVal[i];
|
|
if (V == 0)
|
|
Count += APINT_BITS_PER_WORD;
|
|
else {
|
|
Count += llvm::countLeadingZeros(V);
|
|
break;
|
|
}
|
|
}
|
|
// Adjust for unused bits in the most significant word (they are zero).
|
|
unsigned Mod = BitWidth % APINT_BITS_PER_WORD;
|
|
Count -= Mod > 0 ? APINT_BITS_PER_WORD - Mod : 0;
|
|
return Count;
|
|
}
|
|
|
|
unsigned APInt::countLeadingOnesSlowCase() const {
|
|
unsigned highWordBits = BitWidth % APINT_BITS_PER_WORD;
|
|
unsigned shift;
|
|
if (!highWordBits) {
|
|
highWordBits = APINT_BITS_PER_WORD;
|
|
shift = 0;
|
|
} else {
|
|
shift = APINT_BITS_PER_WORD - highWordBits;
|
|
}
|
|
int i = getNumWords() - 1;
|
|
unsigned Count = llvm::countLeadingOnes(U.pVal[i] << shift);
|
|
if (Count == highWordBits) {
|
|
for (i--; i >= 0; --i) {
|
|
if (U.pVal[i] == WORDTYPE_MAX)
|
|
Count += APINT_BITS_PER_WORD;
|
|
else {
|
|
Count += llvm::countLeadingOnes(U.pVal[i]);
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
return Count;
|
|
}
|
|
|
|
unsigned APInt::countTrailingZerosSlowCase() const {
|
|
unsigned Count = 0;
|
|
unsigned i = 0;
|
|
for (; i < getNumWords() && U.pVal[i] == 0; ++i)
|
|
Count += APINT_BITS_PER_WORD;
|
|
if (i < getNumWords())
|
|
Count += llvm::countTrailingZeros(U.pVal[i]);
|
|
return std::min(Count, BitWidth);
|
|
}
|
|
|
|
unsigned APInt::countTrailingOnesSlowCase() const {
|
|
unsigned Count = 0;
|
|
unsigned i = 0;
|
|
for (; i < getNumWords() && U.pVal[i] == WORDTYPE_MAX; ++i)
|
|
Count += APINT_BITS_PER_WORD;
|
|
if (i < getNumWords())
|
|
Count += llvm::countTrailingOnes(U.pVal[i]);
|
|
assert(Count <= BitWidth);
|
|
return Count;
|
|
}
|
|
|
|
unsigned APInt::countPopulationSlowCase() const {
|
|
unsigned Count = 0;
|
|
for (unsigned i = 0; i < getNumWords(); ++i)
|
|
Count += llvm::countPopulation(U.pVal[i]);
|
|
return Count;
|
|
}
|
|
|
|
bool APInt::intersectsSlowCase(const APInt &RHS) const {
|
|
for (unsigned i = 0, e = getNumWords(); i != e; ++i)
|
|
if ((U.pVal[i] & RHS.U.pVal[i]) != 0)
|
|
return true;
|
|
|
|
return false;
|
|
}
|
|
|
|
bool APInt::isSubsetOfSlowCase(const APInt &RHS) const {
|
|
for (unsigned i = 0, e = getNumWords(); i != e; ++i)
|
|
if ((U.pVal[i] & ~RHS.U.pVal[i]) != 0)
|
|
return false;
|
|
|
|
return true;
|
|
}
|
|
|
|
APInt APInt::byteSwap() const {
|
|
assert(BitWidth >= 16 && BitWidth % 8 == 0 && "Cannot byteswap!");
|
|
if (BitWidth == 16)
|
|
return APInt(BitWidth, ByteSwap_16(uint16_t(U.VAL)));
|
|
if (BitWidth == 32)
|
|
return APInt(BitWidth, ByteSwap_32(unsigned(U.VAL)));
|
|
if (BitWidth <= 64) {
|
|
uint64_t Tmp1 = ByteSwap_64(U.VAL);
|
|
Tmp1 >>= (64 - BitWidth);
|
|
return APInt(BitWidth, Tmp1);
|
|
}
|
|
|
|
APInt Result(getNumWords() * APINT_BITS_PER_WORD, 0);
|
|
for (unsigned I = 0, N = getNumWords(); I != N; ++I)
|
|
Result.U.pVal[I] = ByteSwap_64(U.pVal[N - I - 1]);
|
|
if (Result.BitWidth != BitWidth) {
|
|
Result.lshrInPlace(Result.BitWidth - BitWidth);
|
|
Result.BitWidth = BitWidth;
|
|
}
|
|
return Result;
|
|
}
|
|
|
|
APInt APInt::reverseBits() const {
|
|
switch (BitWidth) {
|
|
case 64:
|
|
return APInt(BitWidth, llvm::reverseBits<uint64_t>(U.VAL));
|
|
case 32:
|
|
return APInt(BitWidth, llvm::reverseBits<uint32_t>(U.VAL));
|
|
case 16:
|
|
return APInt(BitWidth, llvm::reverseBits<uint16_t>(U.VAL));
|
|
case 8:
|
|
return APInt(BitWidth, llvm::reverseBits<uint8_t>(U.VAL));
|
|
default:
|
|
break;
|
|
}
|
|
|
|
APInt Val(*this);
|
|
APInt Reversed(BitWidth, 0);
|
|
unsigned S = BitWidth;
|
|
|
|
for (; Val != 0; Val.lshrInPlace(1)) {
|
|
Reversed <<= 1;
|
|
Reversed |= Val[0];
|
|
--S;
|
|
}
|
|
|
|
Reversed <<= S;
|
|
return Reversed;
|
|
}
|
|
|
|
APInt llvm::APIntOps::GreatestCommonDivisor(APInt A, APInt B) {
|
|
// Fast-path a common case.
|
|
if (A == B) return A;
|
|
|
|
// Corner cases: if either operand is zero, the other is the gcd.
|
|
if (!A) return B;
|
|
if (!B) return A;
|
|
|
|
// Count common powers of 2 and remove all other powers of 2.
|
|
unsigned Pow2;
|
|
{
|
|
unsigned Pow2_A = A.countTrailingZeros();
|
|
unsigned Pow2_B = B.countTrailingZeros();
|
|
if (Pow2_A > Pow2_B) {
|
|
A.lshrInPlace(Pow2_A - Pow2_B);
|
|
Pow2 = Pow2_B;
|
|
} else if (Pow2_B > Pow2_A) {
|
|
B.lshrInPlace(Pow2_B - Pow2_A);
|
|
Pow2 = Pow2_A;
|
|
} else {
|
|
Pow2 = Pow2_A;
|
|
}
|
|
}
|
|
|
|
// Both operands are odd multiples of 2^Pow_2:
|
|
//
|
|
// gcd(a, b) = gcd(|a - b| / 2^i, min(a, b))
|
|
//
|
|
// This is a modified version of Stein's algorithm, taking advantage of
|
|
// efficient countTrailingZeros().
|
|
while (A != B) {
|
|
if (A.ugt(B)) {
|
|
A -= B;
|
|
A.lshrInPlace(A.countTrailingZeros() - Pow2);
|
|
} else {
|
|
B -= A;
|
|
B.lshrInPlace(B.countTrailingZeros() - Pow2);
|
|
}
|
|
}
|
|
|
|
return A;
|
|
}
|
|
|
|
APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) {
|
|
uint64_t I = bit_cast<uint64_t>(Double);
|
|
|
|
// Get the sign bit from the highest order bit
|
|
bool isNeg = I >> 63;
|
|
|
|
// Get the 11-bit exponent and adjust for the 1023 bit bias
|
|
int64_t exp = ((I >> 52) & 0x7ff) - 1023;
|
|
|
|
// If the exponent is negative, the value is < 0 so just return 0.
|
|
if (exp < 0)
|
|
return APInt(width, 0u);
|
|
|
|
// Extract the mantissa by clearing the top 12 bits (sign + exponent).
|
|
uint64_t mantissa = (I & (~0ULL >> 12)) | 1ULL << 52;
|
|
|
|
// If the exponent doesn't shift all bits out of the mantissa
|
|
if (exp < 52)
|
|
return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
|
|
APInt(width, mantissa >> (52 - exp));
|
|
|
|
// If the client didn't provide enough bits for us to shift the mantissa into
|
|
// then the result is undefined, just return 0
|
|
if (width <= exp - 52)
|
|
return APInt(width, 0);
|
|
|
|
// Otherwise, we have to shift the mantissa bits up to the right location
|
|
APInt Tmp(width, mantissa);
|
|
Tmp <<= (unsigned)exp - 52;
|
|
return isNeg ? -Tmp : Tmp;
|
|
}
|
|
|
|
/// This function converts this APInt to a double.
|
|
/// The layout for double is as following (IEEE Standard 754):
|
|
/// --------------------------------------
|
|
/// | Sign Exponent Fraction Bias |
|
|
/// |-------------------------------------- |
|
|
/// | 1[63] 11[62-52] 52[51-00] 1023 |
|
|
/// --------------------------------------
|
|
double APInt::roundToDouble(bool isSigned) const {
|
|
|
|
// Handle the simple case where the value is contained in one uint64_t.
|
|
// It is wrong to optimize getWord(0) to VAL; there might be more than one word.
|
|
if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
|
|
if (isSigned) {
|
|
int64_t sext = SignExtend64(getWord(0), BitWidth);
|
|
return double(sext);
|
|
} else
|
|
return double(getWord(0));
|
|
}
|
|
|
|
// Determine if the value is negative.
|
|
bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
|
|
|
|
// Construct the absolute value if we're negative.
|
|
APInt Tmp(isNeg ? -(*this) : (*this));
|
|
|
|
// Figure out how many bits we're using.
|
|
unsigned n = Tmp.getActiveBits();
|
|
|
|
// The exponent (without bias normalization) is just the number of bits
|
|
// we are using. Note that the sign bit is gone since we constructed the
|
|
// absolute value.
|
|
uint64_t exp = n;
|
|
|
|
// Return infinity for exponent overflow
|
|
if (exp > 1023) {
|
|
if (!isSigned || !isNeg)
|
|
return std::numeric_limits<double>::infinity();
|
|
else
|
|
return -std::numeric_limits<double>::infinity();
|
|
}
|
|
exp += 1023; // Increment for 1023 bias
|
|
|
|
// Number of bits in mantissa is 52. To obtain the mantissa value, we must
|
|
// extract the high 52 bits from the correct words in pVal.
|
|
uint64_t mantissa;
|
|
unsigned hiWord = whichWord(n-1);
|
|
if (hiWord == 0) {
|
|
mantissa = Tmp.U.pVal[0];
|
|
if (n > 52)
|
|
mantissa >>= n - 52; // shift down, we want the top 52 bits.
|
|
} else {
|
|
assert(hiWord > 0 && "huh?");
|
|
uint64_t hibits = Tmp.U.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
|
|
uint64_t lobits = Tmp.U.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
|
|
mantissa = hibits | lobits;
|
|
}
|
|
|
|
// The leading bit of mantissa is implicit, so get rid of it.
|
|
uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
|
|
uint64_t I = sign | (exp << 52) | mantissa;
|
|
return bit_cast<double>(I);
|
|
}
|
|
|
|
// Truncate to new width.
|
|
APInt APInt::trunc(unsigned width) const {
|
|
assert(width < BitWidth && "Invalid APInt Truncate request");
|
|
assert(width && "Can't truncate to 0 bits");
|
|
|
|
if (width <= APINT_BITS_PER_WORD)
|
|
return APInt(width, getRawData()[0]);
|
|
|
|
APInt Result(getMemory(getNumWords(width)), width);
|
|
|
|
// Copy full words.
|
|
unsigned i;
|
|
for (i = 0; i != width / APINT_BITS_PER_WORD; i++)
|
|
Result.U.pVal[i] = U.pVal[i];
|
|
|
|
// Truncate and copy any partial word.
|
|
unsigned bits = (0 - width) % APINT_BITS_PER_WORD;
|
|
if (bits != 0)
|
|
Result.U.pVal[i] = U.pVal[i] << bits >> bits;
|
|
|
|
return Result;
|
|
}
|
|
|
|
// Truncate to new width with unsigned saturation.
|
|
APInt APInt::truncUSat(unsigned width) const {
|
|
assert(width < BitWidth && "Invalid APInt Truncate request");
|
|
assert(width && "Can't truncate to 0 bits");
|
|
|
|
// 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");
|
|
assert(width && "Can't truncate to 0 bits");
|
|
|
|
// Can we just losslessly truncate it?
|
|
if (isSignedIntN(width))
|
|
return trunc(width);
|
|
// If not, then just return the new limits.
|
|
return isNegative() ? APInt::getSignedMinValue(width)
|
|
: APInt::getSignedMaxValue(width);
|
|
}
|
|
|
|
// Sign extend to a new width.
|
|
APInt APInt::sext(unsigned Width) const {
|
|
assert(Width > BitWidth && "Invalid APInt SignExtend request");
|
|
|
|
if (Width <= APINT_BITS_PER_WORD)
|
|
return APInt(Width, SignExtend64(U.VAL, BitWidth));
|
|
|
|
APInt Result(getMemory(getNumWords(Width)), Width);
|
|
|
|
// Copy words.
|
|
std::memcpy(Result.U.pVal, getRawData(), getNumWords() * APINT_WORD_SIZE);
|
|
|
|
// Sign extend the last word since there may be unused bits in the input.
|
|
Result.U.pVal[getNumWords() - 1] =
|
|
SignExtend64(Result.U.pVal[getNumWords() - 1],
|
|
((BitWidth - 1) % APINT_BITS_PER_WORD) + 1);
|
|
|
|
// Fill with sign bits.
|
|
std::memset(Result.U.pVal + getNumWords(), isNegative() ? -1 : 0,
|
|
(Result.getNumWords() - getNumWords()) * APINT_WORD_SIZE);
|
|
Result.clearUnusedBits();
|
|
return Result;
|
|
}
|
|
|
|
// Zero extend to a new width.
|
|
APInt APInt::zext(unsigned width) const {
|
|
assert(width > BitWidth && "Invalid APInt ZeroExtend request");
|
|
|
|
if (width <= APINT_BITS_PER_WORD)
|
|
return APInt(width, U.VAL);
|
|
|
|
APInt Result(getMemory(getNumWords(width)), width);
|
|
|
|
// Copy words.
|
|
std::memcpy(Result.U.pVal, getRawData(), getNumWords() * APINT_WORD_SIZE);
|
|
|
|
// Zero remaining words.
|
|
std::memset(Result.U.pVal + getNumWords(), 0,
|
|
(Result.getNumWords() - getNumWords()) * APINT_WORD_SIZE);
|
|
|
|
return Result;
|
|
}
|
|
|
|
APInt APInt::zextOrTrunc(unsigned width) const {
|
|
if (BitWidth < width)
|
|
return zext(width);
|
|
if (BitWidth > width)
|
|
return trunc(width);
|
|
return *this;
|
|
}
|
|
|
|
APInt APInt::sextOrTrunc(unsigned width) const {
|
|
if (BitWidth < width)
|
|
return sext(width);
|
|
if (BitWidth > width)
|
|
return trunc(width);
|
|
return *this;
|
|
}
|
|
|
|
APInt APInt::zextOrSelf(unsigned width) const {
|
|
if (BitWidth < width)
|
|
return zext(width);
|
|
return *this;
|
|
}
|
|
|
|
APInt APInt::sextOrSelf(unsigned width) const {
|
|
if (BitWidth < width)
|
|
return sext(width);
|
|
return *this;
|
|
}
|
|
|
|
/// Arithmetic right-shift this APInt by shiftAmt.
|
|
/// Arithmetic right-shift function.
|
|
void APInt::ashrInPlace(const APInt &shiftAmt) {
|
|
ashrInPlace((unsigned)shiftAmt.getLimitedValue(BitWidth));
|
|
}
|
|
|
|
/// Arithmetic right-shift this APInt by shiftAmt.
|
|
/// Arithmetic right-shift function.
|
|
void APInt::ashrSlowCase(unsigned ShiftAmt) {
|
|
// Don't bother performing a no-op shift.
|
|
if (!ShiftAmt)
|
|
return;
|
|
|
|
// Save the original sign bit for later.
|
|
bool Negative = isNegative();
|
|
|
|
// WordShift is the inter-part shift; BitShift is intra-part shift.
|
|
unsigned WordShift = ShiftAmt / APINT_BITS_PER_WORD;
|
|
unsigned BitShift = ShiftAmt % APINT_BITS_PER_WORD;
|
|
|
|
unsigned WordsToMove = getNumWords() - WordShift;
|
|
if (WordsToMove != 0) {
|
|
// Sign extend the last word to fill in the unused bits.
|
|
U.pVal[getNumWords() - 1] = SignExtend64(
|
|
U.pVal[getNumWords() - 1], ((BitWidth - 1) % APINT_BITS_PER_WORD) + 1);
|
|
|
|
// Fastpath for moving by whole words.
|
|
if (BitShift == 0) {
|
|
std::memmove(U.pVal, U.pVal + WordShift, WordsToMove * APINT_WORD_SIZE);
|
|
} else {
|
|
// Move the words containing significant bits.
|
|
for (unsigned i = 0; i != WordsToMove - 1; ++i)
|
|
U.pVal[i] = (U.pVal[i + WordShift] >> BitShift) |
|
|
(U.pVal[i + WordShift + 1] << (APINT_BITS_PER_WORD - BitShift));
|
|
|
|
// Handle the last word which has no high bits to copy.
|
|
U.pVal[WordsToMove - 1] = U.pVal[WordShift + WordsToMove - 1] >> BitShift;
|
|
// Sign extend one more time.
|
|
U.pVal[WordsToMove - 1] =
|
|
SignExtend64(U.pVal[WordsToMove - 1], APINT_BITS_PER_WORD - BitShift);
|
|
}
|
|
}
|
|
|
|
// Fill in the remainder based on the original sign.
|
|
std::memset(U.pVal + WordsToMove, Negative ? -1 : 0,
|
|
WordShift * APINT_WORD_SIZE);
|
|
clearUnusedBits();
|
|
}
|
|
|
|
/// Logical right-shift this APInt by shiftAmt.
|
|
/// Logical right-shift function.
|
|
void APInt::lshrInPlace(const APInt &shiftAmt) {
|
|
lshrInPlace((unsigned)shiftAmt.getLimitedValue(BitWidth));
|
|
}
|
|
|
|
/// Logical right-shift this APInt by shiftAmt.
|
|
/// Logical right-shift function.
|
|
void APInt::lshrSlowCase(unsigned ShiftAmt) {
|
|
tcShiftRight(U.pVal, getNumWords(), ShiftAmt);
|
|
}
|
|
|
|
/// Left-shift this APInt by shiftAmt.
|
|
/// Left-shift function.
|
|
APInt &APInt::operator<<=(const APInt &shiftAmt) {
|
|
// It's undefined behavior in C to shift by BitWidth or greater.
|
|
*this <<= (unsigned)shiftAmt.getLimitedValue(BitWidth);
|
|
return *this;
|
|
}
|
|
|
|
void APInt::shlSlowCase(unsigned ShiftAmt) {
|
|
tcShiftLeft(U.pVal, getNumWords(), ShiftAmt);
|
|
clearUnusedBits();
|
|
}
|
|
|
|
// Calculate the rotate amount modulo the bit width.
|
|
static unsigned rotateModulo(unsigned BitWidth, const APInt &rotateAmt) {
|
|
unsigned rotBitWidth = rotateAmt.getBitWidth();
|
|
APInt rot = rotateAmt;
|
|
if (rotBitWidth < BitWidth) {
|
|
// Extend the rotate APInt, so that the urem doesn't divide by 0.
|
|
// e.g. APInt(1, 32) would give APInt(1, 0).
|
|
rot = rotateAmt.zext(BitWidth);
|
|
}
|
|
rot = rot.urem(APInt(rot.getBitWidth(), BitWidth));
|
|
return rot.getLimitedValue(BitWidth);
|
|
}
|
|
|
|
APInt APInt::rotl(const APInt &rotateAmt) const {
|
|
return rotl(rotateModulo(BitWidth, rotateAmt));
|
|
}
|
|
|
|
APInt APInt::rotl(unsigned rotateAmt) const {
|
|
rotateAmt %= BitWidth;
|
|
if (rotateAmt == 0)
|
|
return *this;
|
|
return shl(rotateAmt) | lshr(BitWidth - rotateAmt);
|
|
}
|
|
|
|
APInt APInt::rotr(const APInt &rotateAmt) const {
|
|
return rotr(rotateModulo(BitWidth, rotateAmt));
|
|
}
|
|
|
|
APInt APInt::rotr(unsigned rotateAmt) const {
|
|
rotateAmt %= BitWidth;
|
|
if (rotateAmt == 0)
|
|
return *this;
|
|
return lshr(rotateAmt) | shl(BitWidth - rotateAmt);
|
|
}
|
|
|
|
// Square Root - this method computes and returns the square root of "this".
|
|
// Three mechanisms are used for computation. For small values (<= 5 bits),
|
|
// a table lookup is done. This gets some performance for common cases. For
|
|
// values using less than 52 bits, the value is converted to double and then
|
|
// the libc sqrt function is called. The result is rounded and then converted
|
|
// back to a uint64_t which is then used to construct the result. Finally,
|
|
// the Babylonian method for computing square roots is used.
|
|
APInt APInt::sqrt() const {
|
|
|
|
// Determine the magnitude of the value.
|
|
unsigned magnitude = getActiveBits();
|
|
|
|
// Use a fast table for some small values. This also gets rid of some
|
|
// rounding errors in libc sqrt for small values.
|
|
if (magnitude <= 5) {
|
|
static const uint8_t results[32] = {
|
|
/* 0 */ 0,
|
|
/* 1- 2 */ 1, 1,
|
|
/* 3- 6 */ 2, 2, 2, 2,
|
|
/* 7-12 */ 3, 3, 3, 3, 3, 3,
|
|
/* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
|
|
/* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
|
|
/* 31 */ 6
|
|
};
|
|
return APInt(BitWidth, results[ (isSingleWord() ? U.VAL : U.pVal[0]) ]);
|
|
}
|
|
|
|
// If the magnitude of the value fits in less than 52 bits (the precision of
|
|
// an IEEE double precision floating point value), then we can use the
|
|
// libc sqrt function which will probably use a hardware sqrt computation.
|
|
// This should be faster than the algorithm below.
|
|
if (magnitude < 52) {
|
|
return APInt(BitWidth,
|
|
uint64_t(::round(::sqrt(double(isSingleWord() ? U.VAL
|
|
: U.pVal[0])))));
|
|
}
|
|
|
|
// Okay, all the short cuts are exhausted. We must compute it. The following
|
|
// is a classical Babylonian method for computing the square root. This code
|
|
// was adapted to APInt from a wikipedia article on such computations.
|
|
// See http://www.wikipedia.org/ and go to the page named
|
|
// Calculate_an_integer_square_root.
|
|
unsigned nbits = BitWidth, i = 4;
|
|
APInt testy(BitWidth, 16);
|
|
APInt x_old(BitWidth, 1);
|
|
APInt x_new(BitWidth, 0);
|
|
APInt two(BitWidth, 2);
|
|
|
|
// Select a good starting value using binary logarithms.
|
|
for (;; i += 2, testy = testy.shl(2))
|
|
if (i >= nbits || this->ule(testy)) {
|
|
x_old = x_old.shl(i / 2);
|
|
break;
|
|
}
|
|
|
|
// Use the Babylonian method to arrive at the integer square root:
|
|
for (;;) {
|
|
x_new = (this->udiv(x_old) + x_old).udiv(two);
|
|
if (x_old.ule(x_new))
|
|
break;
|
|
x_old = x_new;
|
|
}
|
|
|
|
// Make sure we return the closest approximation
|
|
// NOTE: The rounding calculation below is correct. It will produce an
|
|
// off-by-one discrepancy with results from pari/gp. That discrepancy has been
|
|
// determined to be a rounding issue with pari/gp as it begins to use a
|
|
// floating point representation after 192 bits. There are no discrepancies
|
|
// between this algorithm and pari/gp for bit widths < 192 bits.
|
|
APInt square(x_old * x_old);
|
|
APInt nextSquare((x_old + 1) * (x_old +1));
|
|
if (this->ult(square))
|
|
return x_old;
|
|
assert(this->ule(nextSquare) && "Error in APInt::sqrt computation");
|
|
APInt midpoint((nextSquare - square).udiv(two));
|
|
APInt offset(*this - square);
|
|
if (offset.ult(midpoint))
|
|
return x_old;
|
|
return x_old + 1;
|
|
}
|
|
|
|
/// Computes the multiplicative inverse of this APInt for a given modulo. The
|
|
/// iterative extended Euclidean algorithm is used to solve for this value,
|
|
/// however we simplify it to speed up calculating only the inverse, and take
|
|
/// advantage of div+rem calculations. We also use some tricks to avoid copying
|
|
/// (potentially large) APInts around.
|
|
/// WARNING: a value of '0' may be returned,
|
|
/// signifying that no multiplicative inverse exists!
|
|
APInt APInt::multiplicativeInverse(const APInt& modulo) const {
|
|
assert(ult(modulo) && "This APInt must be smaller than the modulo");
|
|
|
|
// Using the properties listed at the following web page (accessed 06/21/08):
|
|
// http://www.numbertheory.org/php/euclid.html
|
|
// (especially the properties numbered 3, 4 and 9) it can be proved that
|
|
// BitWidth bits suffice for all the computations in the algorithm implemented
|
|
// below. More precisely, this number of bits suffice if the multiplicative
|
|
// inverse exists, but may not suffice for the general extended Euclidean
|
|
// algorithm.
|
|
|
|
APInt r[2] = { modulo, *this };
|
|
APInt t[2] = { APInt(BitWidth, 0), APInt(BitWidth, 1) };
|
|
APInt q(BitWidth, 0);
|
|
|
|
unsigned i;
|
|
for (i = 0; r[i^1] != 0; i ^= 1) {
|
|
// An overview of the math without the confusing bit-flipping:
|
|
// q = r[i-2] / r[i-1]
|
|
// r[i] = r[i-2] % r[i-1]
|
|
// t[i] = t[i-2] - t[i-1] * q
|
|
udivrem(r[i], r[i^1], q, r[i]);
|
|
t[i] -= t[i^1] * q;
|
|
}
|
|
|
|
// If this APInt and the modulo are not coprime, there is no multiplicative
|
|
// inverse, so return 0. We check this by looking at the next-to-last
|
|
// remainder, which is the gcd(*this,modulo) as calculated by the Euclidean
|
|
// algorithm.
|
|
if (r[i] != 1)
|
|
return APInt(BitWidth, 0);
|
|
|
|
// The next-to-last t is the multiplicative inverse. However, we are
|
|
// interested in a positive inverse. Calculate a positive one from a negative
|
|
// one if necessary. A simple addition of the modulo suffices because
|
|
// abs(t[i]) is known to be less than *this/2 (see the link above).
|
|
if (t[i].isNegative())
|
|
t[i] += modulo;
|
|
|
|
return std::move(t[i]);
|
|
}
|
|
|
|
/// Calculate the magic numbers required to implement a signed integer division
|
|
/// by a constant as a sequence of multiplies, adds and shifts. Requires that
|
|
/// the divisor not be 0, 1, or -1. Taken from "Hacker's Delight", Henry S.
|
|
/// Warren, Jr., chapter 10.
|
|
APInt::ms APInt::magic() const {
|
|
const APInt& d = *this;
|
|
unsigned p;
|
|
APInt ad, anc, delta, q1, r1, q2, r2, t;
|
|
APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
|
|
struct ms mag;
|
|
|
|
ad = d.abs();
|
|
t = signedMin + (d.lshr(d.getBitWidth() - 1));
|
|
anc = t - 1 - t.urem(ad); // absolute value of nc
|
|
p = d.getBitWidth() - 1; // initialize p
|
|
q1 = signedMin.udiv(anc); // initialize q1 = 2p/abs(nc)
|
|
r1 = signedMin - q1*anc; // initialize r1 = rem(2p,abs(nc))
|
|
q2 = signedMin.udiv(ad); // initialize q2 = 2p/abs(d)
|
|
r2 = signedMin - q2*ad; // initialize r2 = rem(2p,abs(d))
|
|
do {
|
|
p = p + 1;
|
|
q1 = q1<<1; // update q1 = 2p/abs(nc)
|
|
r1 = r1<<1; // update r1 = rem(2p/abs(nc))
|
|
if (r1.uge(anc)) { // must be unsigned comparison
|
|
q1 = q1 + 1;
|
|
r1 = r1 - anc;
|
|
}
|
|
q2 = q2<<1; // update q2 = 2p/abs(d)
|
|
r2 = r2<<1; // update r2 = rem(2p/abs(d))
|
|
if (r2.uge(ad)) { // must be unsigned comparison
|
|
q2 = q2 + 1;
|
|
r2 = r2 - ad;
|
|
}
|
|
delta = ad - r2;
|
|
} while (q1.ult(delta) || (q1 == delta && r1 == 0));
|
|
|
|
mag.m = q2 + 1;
|
|
if (d.isNegative()) mag.m = -mag.m; // resulting magic number
|
|
mag.s = p - d.getBitWidth(); // resulting shift
|
|
return mag;
|
|
}
|
|
|
|
/// Calculate the magic numbers required to implement an unsigned integer
|
|
/// division by a constant as a sequence of multiplies, adds and shifts.
|
|
/// Requires that the divisor not be 0. Taken from "Hacker's Delight", Henry
|
|
/// S. Warren, Jr., chapter 10.
|
|
/// LeadingZeros can be used to simplify the calculation if the upper bits
|
|
/// of the divided value are known zero.
|
|
APInt::mu APInt::magicu(unsigned LeadingZeros) const {
|
|
const APInt& d = *this;
|
|
unsigned p;
|
|
APInt nc, delta, q1, r1, q2, r2;
|
|
struct mu magu;
|
|
magu.a = 0; // initialize "add" indicator
|
|
APInt allOnes = APInt::getAllOnesValue(d.getBitWidth()).lshr(LeadingZeros);
|
|
APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
|
|
APInt signedMax = APInt::getSignedMaxValue(d.getBitWidth());
|
|
|
|
nc = allOnes - (allOnes - d).urem(d);
|
|
p = d.getBitWidth() - 1; // initialize p
|
|
q1 = signedMin.udiv(nc); // initialize q1 = 2p/nc
|
|
r1 = signedMin - q1*nc; // initialize r1 = rem(2p,nc)
|
|
q2 = signedMax.udiv(d); // initialize q2 = (2p-1)/d
|
|
r2 = signedMax - q2*d; // initialize r2 = rem((2p-1),d)
|
|
do {
|
|
p = p + 1;
|
|
if (r1.uge(nc - r1)) {
|
|
q1 = q1 + q1 + 1; // update q1
|
|
r1 = r1 + r1 - nc; // update r1
|
|
}
|
|
else {
|
|
q1 = q1+q1; // update q1
|
|
r1 = r1+r1; // update r1
|
|
}
|
|
if ((r2 + 1).uge(d - r2)) {
|
|
if (q2.uge(signedMax)) magu.a = 1;
|
|
q2 = q2+q2 + 1; // update q2
|
|
r2 = r2+r2 + 1 - d; // update r2
|
|
}
|
|
else {
|
|
if (q2.uge(signedMin)) magu.a = 1;
|
|
q2 = q2+q2; // update q2
|
|
r2 = r2+r2 + 1; // update r2
|
|
}
|
|
delta = d - 1 - r2;
|
|
} while (p < d.getBitWidth()*2 &&
|
|
(q1.ult(delta) || (q1 == delta && r1 == 0)));
|
|
magu.m = q2 + 1; // resulting magic number
|
|
magu.s = p - d.getBitWidth(); // resulting shift
|
|
return magu;
|
|
}
|
|
|
|
/// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
|
|
/// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
|
|
/// variables here have the same names as in the algorithm. Comments explain
|
|
/// the algorithm and any deviation from it.
|
|
static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
|
|
unsigned m, unsigned n) {
|
|
assert(u && "Must provide dividend");
|
|
assert(v && "Must provide divisor");
|
|
assert(q && "Must provide quotient");
|
|
assert(u != v && u != q && v != q && "Must use different memory");
|
|
assert(n>1 && "n must be > 1");
|
|
|
|
// b denotes the base of the number system. In our case b is 2^32.
|
|
const uint64_t b = uint64_t(1) << 32;
|
|
|
|
// The DEBUG macros here tend to be spam in the debug output if you're not
|
|
// debugging this code. Disable them unless KNUTH_DEBUG is defined.
|
|
#ifdef KNUTH_DEBUG
|
|
#define DEBUG_KNUTH(X) LLVM_DEBUG(X)
|
|
#else
|
|
#define DEBUG_KNUTH(X) do {} while(false)
|
|
#endif
|
|
|
|
DEBUG_KNUTH(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n');
|
|
DEBUG_KNUTH(dbgs() << "KnuthDiv: original:");
|
|
DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]);
|
|
DEBUG_KNUTH(dbgs() << " by");
|
|
DEBUG_KNUTH(for (int i = n; i > 0; i--) dbgs() << " " << v[i - 1]);
|
|
DEBUG_KNUTH(dbgs() << '\n');
|
|
// D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
|
|
// u and v by d. Note that we have taken Knuth's advice here to use a power
|
|
// of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
|
|
// 2 allows us to shift instead of multiply and it is easy to determine the
|
|
// shift amount from the leading zeros. We are basically normalizing the u
|
|
// and v so that its high bits are shifted to the top of v's range without
|
|
// overflow. Note that this can require an extra word in u so that u must
|
|
// be of length m+n+1.
|
|
unsigned shift = countLeadingZeros(v[n-1]);
|
|
uint32_t v_carry = 0;
|
|
uint32_t u_carry = 0;
|
|
if (shift) {
|
|
for (unsigned i = 0; i < m+n; ++i) {
|
|
uint32_t u_tmp = u[i] >> (32 - shift);
|
|
u[i] = (u[i] << shift) | u_carry;
|
|
u_carry = u_tmp;
|
|
}
|
|
for (unsigned i = 0; i < n; ++i) {
|
|
uint32_t v_tmp = v[i] >> (32 - shift);
|
|
v[i] = (v[i] << shift) | v_carry;
|
|
v_carry = v_tmp;
|
|
}
|
|
}
|
|
u[m+n] = u_carry;
|
|
|
|
DEBUG_KNUTH(dbgs() << "KnuthDiv: normal:");
|
|
DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]);
|
|
DEBUG_KNUTH(dbgs() << " by");
|
|
DEBUG_KNUTH(for (int i = n; i > 0; i--) dbgs() << " " << v[i - 1]);
|
|
DEBUG_KNUTH(dbgs() << '\n');
|
|
|
|
// D2. [Initialize j.] Set j to m. This is the loop counter over the places.
|
|
int j = m;
|
|
do {
|
|
DEBUG_KNUTH(dbgs() << "KnuthDiv: quotient digit #" << j << '\n');
|
|
// D3. [Calculate q'.].
|
|
// Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
|
|
// Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
|
|
// Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
|
|
// qp by 1, increase rp by v[n-1], and repeat this test if rp < b. The test
|
|
// on v[n-2] determines at high speed most of the cases in which the trial
|
|
// value qp is one too large, and it eliminates all cases where qp is two
|
|
// too large.
|
|
uint64_t dividend = Make_64(u[j+n], u[j+n-1]);
|
|
DEBUG_KNUTH(dbgs() << "KnuthDiv: dividend == " << dividend << '\n');
|
|
uint64_t qp = dividend / v[n-1];
|
|
uint64_t rp = dividend % v[n-1];
|
|
if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
|
|
qp--;
|
|
rp += v[n-1];
|
|
if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
|
|
qp--;
|
|
}
|
|
DEBUG_KNUTH(dbgs() << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
|
|
|
|
// D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
|
|
// (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
|
|
// consists of a simple multiplication by a one-place number, combined with
|
|
// a subtraction.
|
|
// The digits (u[j+n]...u[j]) should be kept positive; if the result of
|
|
// this step is actually negative, (u[j+n]...u[j]) should be left as the
|
|
// true value plus b**(n+1), namely as the b's complement of
|
|
// the true value, and a "borrow" to the left should be remembered.
|
|
int64_t borrow = 0;
|
|
for (unsigned i = 0; i < n; ++i) {
|
|
uint64_t p = uint64_t(qp) * uint64_t(v[i]);
|
|
int64_t subres = int64_t(u[j+i]) - borrow - Lo_32(p);
|
|
u[j+i] = Lo_32(subres);
|
|
borrow = Hi_32(p) - Hi_32(subres);
|
|
DEBUG_KNUTH(dbgs() << "KnuthDiv: u[j+i] = " << u[j + i]
|
|
<< ", borrow = " << borrow << '\n');
|
|
}
|
|
bool isNeg = u[j+n] < borrow;
|
|
u[j+n] -= Lo_32(borrow);
|
|
|
|
DEBUG_KNUTH(dbgs() << "KnuthDiv: after subtraction:");
|
|
DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]);
|
|
DEBUG_KNUTH(dbgs() << '\n');
|
|
|
|
// D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
|
|
// negative, go to step D6; otherwise go on to step D7.
|
|
q[j] = Lo_32(qp);
|
|
if (isNeg) {
|
|
// D6. [Add back]. The probability that this step is necessary is very
|
|
// small, on the order of only 2/b. Make sure that test data accounts for
|
|
// this possibility. Decrease q[j] by 1
|
|
q[j]--;
|
|
// and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
|
|
// A carry will occur to the left of u[j+n], and it should be ignored
|
|
// since it cancels with the borrow that occurred in D4.
|
|
bool carry = false;
|
|
for (unsigned i = 0; i < n; i++) {
|
|
uint32_t limit = std::min(u[j+i],v[i]);
|
|
u[j+i] += v[i] + carry;
|
|
carry = u[j+i] < limit || (carry && u[j+i] == limit);
|
|
}
|
|
u[j+n] += carry;
|
|
}
|
|
DEBUG_KNUTH(dbgs() << "KnuthDiv: after correction:");
|
|
DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]);
|
|
DEBUG_KNUTH(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n');
|
|
|
|
// D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
|
|
} while (--j >= 0);
|
|
|
|
DEBUG_KNUTH(dbgs() << "KnuthDiv: quotient:");
|
|
DEBUG_KNUTH(for (int i = m; i >= 0; i--) dbgs() << " " << q[i]);
|
|
DEBUG_KNUTH(dbgs() << '\n');
|
|
|
|
// D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
|
|
// remainder may be obtained by dividing u[...] by d. If r is non-null we
|
|
// compute the remainder (urem uses this).
|
|
if (r) {
|
|
// The value d is expressed by the "shift" value above since we avoided
|
|
// multiplication by d by using a shift left. So, all we have to do is
|
|
// shift right here.
|
|
if (shift) {
|
|
uint32_t carry = 0;
|
|
DEBUG_KNUTH(dbgs() << "KnuthDiv: remainder:");
|
|
for (int i = n-1; i >= 0; i--) {
|
|
r[i] = (u[i] >> shift) | carry;
|
|
carry = u[i] << (32 - shift);
|
|
DEBUG_KNUTH(dbgs() << " " << r[i]);
|
|
}
|
|
} else {
|
|
for (int i = n-1; i >= 0; i--) {
|
|
r[i] = u[i];
|
|
DEBUG_KNUTH(dbgs() << " " << r[i]);
|
|
}
|
|
}
|
|
DEBUG_KNUTH(dbgs() << '\n');
|
|
}
|
|
DEBUG_KNUTH(dbgs() << '\n');
|
|
}
|
|
|
|
void APInt::divide(const WordType *LHS, unsigned lhsWords, const WordType *RHS,
|
|
unsigned rhsWords, WordType *Quotient, WordType *Remainder) {
|
|
assert(lhsWords >= rhsWords && "Fractional result");
|
|
|
|
// First, compose the values into an array of 32-bit words instead of
|
|
// 64-bit words. This is a necessity of both the "short division" algorithm
|
|
// and the Knuth "classical algorithm" which requires there to be native
|
|
// operations for +, -, and * on an m bit value with an m*2 bit result. We
|
|
// can't use 64-bit operands here because we don't have native results of
|
|
// 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't
|
|
// work on large-endian machines.
|
|
unsigned n = rhsWords * 2;
|
|
unsigned m = (lhsWords * 2) - n;
|
|
|
|
// Allocate space for the temporary values we need either on the stack, if
|
|
// it will fit, or on the heap if it won't.
|
|
uint32_t SPACE[128];
|
|
uint32_t *U = nullptr;
|
|
uint32_t *V = nullptr;
|
|
uint32_t *Q = nullptr;
|
|
uint32_t *R = nullptr;
|
|
if ((Remainder?4:3)*n+2*m+1 <= 128) {
|
|
U = &SPACE[0];
|
|
V = &SPACE[m+n+1];
|
|
Q = &SPACE[(m+n+1) + n];
|
|
if (Remainder)
|
|
R = &SPACE[(m+n+1) + n + (m+n)];
|
|
} else {
|
|
U = new uint32_t[m + n + 1];
|
|
V = new uint32_t[n];
|
|
Q = new uint32_t[m+n];
|
|
if (Remainder)
|
|
R = new uint32_t[n];
|
|
}
|
|
|
|
// Initialize the dividend
|
|
memset(U, 0, (m+n+1)*sizeof(uint32_t));
|
|
for (unsigned i = 0; i < lhsWords; ++i) {
|
|
uint64_t tmp = LHS[i];
|
|
U[i * 2] = Lo_32(tmp);
|
|
U[i * 2 + 1] = Hi_32(tmp);
|
|
}
|
|
U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
|
|
|
|
// Initialize the divisor
|
|
memset(V, 0, (n)*sizeof(uint32_t));
|
|
for (unsigned i = 0; i < rhsWords; ++i) {
|
|
uint64_t tmp = RHS[i];
|
|
V[i * 2] = Lo_32(tmp);
|
|
V[i * 2 + 1] = Hi_32(tmp);
|
|
}
|
|
|
|
// initialize the quotient and remainder
|
|
memset(Q, 0, (m+n) * sizeof(uint32_t));
|
|
if (Remainder)
|
|
memset(R, 0, n * sizeof(uint32_t));
|
|
|
|
// Now, adjust m and n for the Knuth division. n is the number of words in
|
|
// the divisor. m is the number of words by which the dividend exceeds the
|
|
// divisor (i.e. m+n is the length of the dividend). These sizes must not
|
|
// contain any zero words or the Knuth algorithm fails.
|
|
for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
|
|
n--;
|
|
m++;
|
|
}
|
|
for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
|
|
m--;
|
|
|
|
// If we're left with only a single word for the divisor, Knuth doesn't work
|
|
// so we implement the short division algorithm here. This is much simpler
|
|
// and faster because we are certain that we can divide a 64-bit quantity
|
|
// by a 32-bit quantity at hardware speed and short division is simply a
|
|
// series of such operations. This is just like doing short division but we
|
|
// are using base 2^32 instead of base 10.
|
|
assert(n != 0 && "Divide by zero?");
|
|
if (n == 1) {
|
|
uint32_t divisor = V[0];
|
|
uint32_t remainder = 0;
|
|
for (int i = m; i >= 0; i--) {
|
|
uint64_t partial_dividend = Make_64(remainder, U[i]);
|
|
if (partial_dividend == 0) {
|
|
Q[i] = 0;
|
|
remainder = 0;
|
|
} else if (partial_dividend < divisor) {
|
|
Q[i] = 0;
|
|
remainder = Lo_32(partial_dividend);
|
|
} else if (partial_dividend == divisor) {
|
|
Q[i] = 1;
|
|
remainder = 0;
|
|
} else {
|
|
Q[i] = Lo_32(partial_dividend / divisor);
|
|
remainder = Lo_32(partial_dividend - (Q[i] * divisor));
|
|
}
|
|
}
|
|
if (R)
|
|
R[0] = remainder;
|
|
} else {
|
|
// Now we're ready to invoke the Knuth classical divide algorithm. In this
|
|
// case n > 1.
|
|
KnuthDiv(U, V, Q, R, m, n);
|
|
}
|
|
|
|
// If the caller wants the quotient
|
|
if (Quotient) {
|
|
for (unsigned i = 0; i < lhsWords; ++i)
|
|
Quotient[i] = Make_64(Q[i*2+1], Q[i*2]);
|
|
}
|
|
|
|
// If the caller wants the remainder
|
|
if (Remainder) {
|
|
for (unsigned i = 0; i < rhsWords; ++i)
|
|
Remainder[i] = Make_64(R[i*2+1], R[i*2]);
|
|
}
|
|
|
|
// Clean up the memory we allocated.
|
|
if (U != &SPACE[0]) {
|
|
delete [] U;
|
|
delete [] V;
|
|
delete [] Q;
|
|
delete [] R;
|
|
}
|
|
}
|
|
|
|
APInt APInt::udiv(const APInt &RHS) const {
|
|
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
|
|
|
|
// First, deal with the easy case
|
|
if (isSingleWord()) {
|
|
assert(RHS.U.VAL != 0 && "Divide by zero?");
|
|
return APInt(BitWidth, U.VAL / RHS.U.VAL);
|
|
}
|
|
|
|
// Get some facts about the LHS and RHS number of bits and words
|
|
unsigned lhsWords = getNumWords(getActiveBits());
|
|
unsigned rhsBits = RHS.getActiveBits();
|
|
unsigned rhsWords = getNumWords(rhsBits);
|
|
assert(rhsWords && "Divided by zero???");
|
|
|
|
// Deal with some degenerate cases
|
|
if (!lhsWords)
|
|
// 0 / X ===> 0
|
|
return APInt(BitWidth, 0);
|
|
if (rhsBits == 1)
|
|
// X / 1 ===> X
|
|
return *this;
|
|
if (lhsWords < rhsWords || this->ult(RHS))
|
|
// X / Y ===> 0, iff X < Y
|
|
return APInt(BitWidth, 0);
|
|
if (*this == RHS)
|
|
// X / X ===> 1
|
|
return APInt(BitWidth, 1);
|
|
if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1.
|
|
// All high words are zero, just use native divide
|
|
return APInt(BitWidth, this->U.pVal[0] / RHS.U.pVal[0]);
|
|
|
|
// We have to compute it the hard way. Invoke the Knuth divide algorithm.
|
|
APInt Quotient(BitWidth, 0); // to hold result.
|
|
divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal, nullptr);
|
|
return Quotient;
|
|
}
|
|
|
|
APInt APInt::udiv(uint64_t RHS) const {
|
|
assert(RHS != 0 && "Divide by zero?");
|
|
|
|
// First, deal with the easy case
|
|
if (isSingleWord())
|
|
return APInt(BitWidth, U.VAL / RHS);
|
|
|
|
// Get some facts about the LHS words.
|
|
unsigned lhsWords = getNumWords(getActiveBits());
|
|
|
|
// Deal with some degenerate cases
|
|
if (!lhsWords)
|
|
// 0 / X ===> 0
|
|
return APInt(BitWidth, 0);
|
|
if (RHS == 1)
|
|
// X / 1 ===> X
|
|
return *this;
|
|
if (this->ult(RHS))
|
|
// X / Y ===> 0, iff X < Y
|
|
return APInt(BitWidth, 0);
|
|
if (*this == RHS)
|
|
// X / X ===> 1
|
|
return APInt(BitWidth, 1);
|
|
if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1.
|
|
// All high words are zero, just use native divide
|
|
return APInt(BitWidth, this->U.pVal[0] / RHS);
|
|
|
|
// We have to compute it the hard way. Invoke the Knuth divide algorithm.
|
|
APInt Quotient(BitWidth, 0); // to hold result.
|
|
divide(U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, nullptr);
|
|
return Quotient;
|
|
}
|
|
|
|
APInt APInt::sdiv(const APInt &RHS) const {
|
|
if (isNegative()) {
|
|
if (RHS.isNegative())
|
|
return (-(*this)).udiv(-RHS);
|
|
return -((-(*this)).udiv(RHS));
|
|
}
|
|
if (RHS.isNegative())
|
|
return -(this->udiv(-RHS));
|
|
return this->udiv(RHS);
|
|
}
|
|
|
|
APInt APInt::sdiv(int64_t RHS) const {
|
|
if (isNegative()) {
|
|
if (RHS < 0)
|
|
return (-(*this)).udiv(-RHS);
|
|
return -((-(*this)).udiv(RHS));
|
|
}
|
|
if (RHS < 0)
|
|
return -(this->udiv(-RHS));
|
|
return this->udiv(RHS);
|
|
}
|
|
|
|
APInt APInt::urem(const APInt &RHS) const {
|
|
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
|
|
if (isSingleWord()) {
|
|
assert(RHS.U.VAL != 0 && "Remainder by zero?");
|
|
return APInt(BitWidth, U.VAL % RHS.U.VAL);
|
|
}
|
|
|
|
// Get some facts about the LHS
|
|
unsigned lhsWords = getNumWords(getActiveBits());
|
|
|
|
// Get some facts about the RHS
|
|
unsigned rhsBits = RHS.getActiveBits();
|
|
unsigned rhsWords = getNumWords(rhsBits);
|
|
assert(rhsWords && "Performing remainder operation by zero ???");
|
|
|
|
// Check the degenerate cases
|
|
if (lhsWords == 0)
|
|
// 0 % Y ===> 0
|
|
return APInt(BitWidth, 0);
|
|
if (rhsBits == 1)
|
|
// X % 1 ===> 0
|
|
return APInt(BitWidth, 0);
|
|
if (lhsWords < rhsWords || this->ult(RHS))
|
|
// X % Y ===> X, iff X < Y
|
|
return *this;
|
|
if (*this == RHS)
|
|
// X % X == 0;
|
|
return APInt(BitWidth, 0);
|
|
if (lhsWords == 1)
|
|
// All high words are zero, just use native remainder
|
|
return APInt(BitWidth, U.pVal[0] % RHS.U.pVal[0]);
|
|
|
|
// We have to compute it the hard way. Invoke the Knuth divide algorithm.
|
|
APInt Remainder(BitWidth, 0);
|
|
divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, nullptr, Remainder.U.pVal);
|
|
return Remainder;
|
|
}
|
|
|
|
uint64_t APInt::urem(uint64_t RHS) const {
|
|
assert(RHS != 0 && "Remainder by zero?");
|
|
|
|
if (isSingleWord())
|
|
return U.VAL % RHS;
|
|
|
|
// Get some facts about the LHS
|
|
unsigned lhsWords = getNumWords(getActiveBits());
|
|
|
|
// Check the degenerate cases
|
|
if (lhsWords == 0)
|
|
// 0 % Y ===> 0
|
|
return 0;
|
|
if (RHS == 1)
|
|
// X % 1 ===> 0
|
|
return 0;
|
|
if (this->ult(RHS))
|
|
// X % Y ===> X, iff X < Y
|
|
return getZExtValue();
|
|
if (*this == RHS)
|
|
// X % X == 0;
|
|
return 0;
|
|
if (lhsWords == 1)
|
|
// All high words are zero, just use native remainder
|
|
return U.pVal[0] % RHS;
|
|
|
|
// We have to compute it the hard way. Invoke the Knuth divide algorithm.
|
|
uint64_t Remainder;
|
|
divide(U.pVal, lhsWords, &RHS, 1, nullptr, &Remainder);
|
|
return Remainder;
|
|
}
|
|
|
|
APInt APInt::srem(const APInt &RHS) const {
|
|
if (isNegative()) {
|
|
if (RHS.isNegative())
|
|
return -((-(*this)).urem(-RHS));
|
|
return -((-(*this)).urem(RHS));
|
|
}
|
|
if (RHS.isNegative())
|
|
return this->urem(-RHS);
|
|
return this->urem(RHS);
|
|
}
|
|
|
|
int64_t APInt::srem(int64_t RHS) const {
|
|
if (isNegative()) {
|
|
if (RHS < 0)
|
|
return -((-(*this)).urem(-RHS));
|
|
return -((-(*this)).urem(RHS));
|
|
}
|
|
if (RHS < 0)
|
|
return this->urem(-RHS);
|
|
return this->urem(RHS);
|
|
}
|
|
|
|
void APInt::udivrem(const APInt &LHS, const APInt &RHS,
|
|
APInt &Quotient, APInt &Remainder) {
|
|
assert(LHS.BitWidth == RHS.BitWidth && "Bit widths must be the same");
|
|
unsigned BitWidth = LHS.BitWidth;
|
|
|
|
// First, deal with the easy case
|
|
if (LHS.isSingleWord()) {
|
|
assert(RHS.U.VAL != 0 && "Divide by zero?");
|
|
uint64_t QuotVal = LHS.U.VAL / RHS.U.VAL;
|
|
uint64_t RemVal = LHS.U.VAL % RHS.U.VAL;
|
|
Quotient = APInt(BitWidth, QuotVal);
|
|
Remainder = APInt(BitWidth, RemVal);
|
|
return;
|
|
}
|
|
|
|
// Get some size facts about the dividend and divisor
|
|
unsigned lhsWords = getNumWords(LHS.getActiveBits());
|
|
unsigned rhsBits = RHS.getActiveBits();
|
|
unsigned rhsWords = getNumWords(rhsBits);
|
|
assert(rhsWords && "Performing divrem operation by zero ???");
|
|
|
|
// Check the degenerate cases
|
|
if (lhsWords == 0) {
|
|
Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0
|
|
Remainder = APInt(BitWidth, 0); // 0 % Y ===> 0
|
|
return;
|
|
}
|
|
|
|
if (rhsBits == 1) {
|
|
Quotient = LHS; // X / 1 ===> X
|
|
Remainder = APInt(BitWidth, 0); // X % 1 ===> 0
|
|
}
|
|
|
|
if (lhsWords < rhsWords || LHS.ult(RHS)) {
|
|
Remainder = LHS; // X % Y ===> X, iff X < Y
|
|
Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y
|
|
return;
|
|
}
|
|
|
|
if (LHS == RHS) {
|
|
Quotient = APInt(BitWidth, 1); // X / X ===> 1
|
|
Remainder = APInt(BitWidth, 0); // X % X ===> 0;
|
|
return;
|
|
}
|
|
|
|
// Make sure there is enough space to hold the results.
|
|
// NOTE: This assumes that reallocate won't affect any bits if it doesn't
|
|
// change the size. This is necessary if Quotient or Remainder is aliased
|
|
// with LHS or RHS.
|
|
Quotient.reallocate(BitWidth);
|
|
Remainder.reallocate(BitWidth);
|
|
|
|
if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1.
|
|
// There is only one word to consider so use the native versions.
|
|
uint64_t lhsValue = LHS.U.pVal[0];
|
|
uint64_t rhsValue = RHS.U.pVal[0];
|
|
Quotient = lhsValue / rhsValue;
|
|
Remainder = lhsValue % rhsValue;
|
|
return;
|
|
}
|
|
|
|
// Okay, lets do it the long way
|
|
divide(LHS.U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal,
|
|
Remainder.U.pVal);
|
|
// Clear the rest of the Quotient and Remainder.
|
|
std::memset(Quotient.U.pVal + lhsWords, 0,
|
|
(getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE);
|
|
std::memset(Remainder.U.pVal + rhsWords, 0,
|
|
(getNumWords(BitWidth) - rhsWords) * APINT_WORD_SIZE);
|
|
}
|
|
|
|
void APInt::udivrem(const APInt &LHS, uint64_t RHS, APInt &Quotient,
|
|
uint64_t &Remainder) {
|
|
assert(RHS != 0 && "Divide by zero?");
|
|
unsigned BitWidth = LHS.BitWidth;
|
|
|
|
// First, deal with the easy case
|
|
if (LHS.isSingleWord()) {
|
|
uint64_t QuotVal = LHS.U.VAL / RHS;
|
|
Remainder = LHS.U.VAL % RHS;
|
|
Quotient = APInt(BitWidth, QuotVal);
|
|
return;
|
|
}
|
|
|
|
// Get some size facts about the dividend and divisor
|
|
unsigned lhsWords = getNumWords(LHS.getActiveBits());
|
|
|
|
// Check the degenerate cases
|
|
if (lhsWords == 0) {
|
|
Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0
|
|
Remainder = 0; // 0 % Y ===> 0
|
|
return;
|
|
}
|
|
|
|
if (RHS == 1) {
|
|
Quotient = LHS; // X / 1 ===> X
|
|
Remainder = 0; // X % 1 ===> 0
|
|
return;
|
|
}
|
|
|
|
if (LHS.ult(RHS)) {
|
|
Remainder = LHS.getZExtValue(); // X % Y ===> X, iff X < Y
|
|
Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y
|
|
return;
|
|
}
|
|
|
|
if (LHS == RHS) {
|
|
Quotient = APInt(BitWidth, 1); // X / X ===> 1
|
|
Remainder = 0; // X % X ===> 0;
|
|
return;
|
|
}
|
|
|
|
// Make sure there is enough space to hold the results.
|
|
// NOTE: This assumes that reallocate won't affect any bits if it doesn't
|
|
// change the size. This is necessary if Quotient is aliased with LHS.
|
|
Quotient.reallocate(BitWidth);
|
|
|
|
if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1.
|
|
// There is only one word to consider so use the native versions.
|
|
uint64_t lhsValue = LHS.U.pVal[0];
|
|
Quotient = lhsValue / RHS;
|
|
Remainder = lhsValue % RHS;
|
|
return;
|
|
}
|
|
|
|
// Okay, lets do it the long way
|
|
divide(LHS.U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, &Remainder);
|
|
// Clear the rest of the Quotient.
|
|
std::memset(Quotient.U.pVal + lhsWords, 0,
|
|
(getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE);
|
|
}
|
|
|
|
void APInt::sdivrem(const APInt &LHS, const APInt &RHS,
|
|
APInt &Quotient, APInt &Remainder) {
|
|
if (LHS.isNegative()) {
|
|
if (RHS.isNegative())
|
|
APInt::udivrem(-LHS, -RHS, Quotient, Remainder);
|
|
else {
|
|
APInt::udivrem(-LHS, RHS, Quotient, Remainder);
|
|
Quotient.negate();
|
|
}
|
|
Remainder.negate();
|
|
} else if (RHS.isNegative()) {
|
|
APInt::udivrem(LHS, -RHS, Quotient, Remainder);
|
|
Quotient.negate();
|
|
} else {
|
|
APInt::udivrem(LHS, RHS, Quotient, Remainder);
|
|
}
|
|
}
|
|
|
|
void APInt::sdivrem(const APInt &LHS, int64_t RHS,
|
|
APInt &Quotient, int64_t &Remainder) {
|
|
uint64_t R = Remainder;
|
|
if (LHS.isNegative()) {
|
|
if (RHS < 0)
|
|
APInt::udivrem(-LHS, -RHS, Quotient, R);
|
|
else {
|
|
APInt::udivrem(-LHS, RHS, Quotient, R);
|
|
Quotient.negate();
|
|
}
|
|
R = -R;
|
|
} else if (RHS < 0) {
|
|
APInt::udivrem(LHS, -RHS, Quotient, R);
|
|
Quotient.negate();
|
|
} else {
|
|
APInt::udivrem(LHS, RHS, Quotient, R);
|
|
}
|
|
Remainder = R;
|
|
}
|
|
|
|
APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const {
|
|
APInt Res = *this+RHS;
|
|
Overflow = isNonNegative() == RHS.isNonNegative() &&
|
|
Res.isNonNegative() != isNonNegative();
|
|
return Res;
|
|
}
|
|
|
|
APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const {
|
|
APInt Res = *this+RHS;
|
|
Overflow = Res.ult(RHS);
|
|
return Res;
|
|
}
|
|
|
|
APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const {
|
|
APInt Res = *this - RHS;
|
|
Overflow = isNonNegative() != RHS.isNonNegative() &&
|
|
Res.isNonNegative() != isNonNegative();
|
|
return Res;
|
|
}
|
|
|
|
APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const {
|
|
APInt Res = *this-RHS;
|
|
Overflow = Res.ugt(*this);
|
|
return Res;
|
|
}
|
|
|
|
APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const {
|
|
// MININT/-1 --> overflow.
|
|
Overflow = isMinSignedValue() && RHS.isAllOnesValue();
|
|
return sdiv(RHS);
|
|
}
|
|
|
|
APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const {
|
|
APInt Res = *this * RHS;
|
|
|
|
if (*this != 0 && RHS != 0)
|
|
Overflow = Res.sdiv(RHS) != *this || Res.sdiv(*this) != RHS;
|
|
else
|
|
Overflow = false;
|
|
return Res;
|
|
}
|
|
|
|
APInt APInt::umul_ov(const APInt &RHS, bool &Overflow) const {
|
|
if (countLeadingZeros() + RHS.countLeadingZeros() + 2 <= BitWidth) {
|
|
Overflow = true;
|
|
return *this * RHS;
|
|
}
|
|
|
|
APInt Res = lshr(1) * RHS;
|
|
Overflow = Res.isNegative();
|
|
Res <<= 1;
|
|
if ((*this)[0]) {
|
|
Res += RHS;
|
|
if (Res.ult(RHS))
|
|
Overflow = true;
|
|
}
|
|
return Res;
|
|
}
|
|
|
|
APInt APInt::sshl_ov(const APInt &ShAmt, bool &Overflow) const {
|
|
Overflow = ShAmt.uge(getBitWidth());
|
|
if (Overflow)
|
|
return APInt(BitWidth, 0);
|
|
|
|
if (isNonNegative()) // Don't allow sign change.
|
|
Overflow = ShAmt.uge(countLeadingZeros());
|
|
else
|
|
Overflow = ShAmt.uge(countLeadingOnes());
|
|
|
|
return *this << ShAmt;
|
|
}
|
|
|
|
APInt APInt::ushl_ov(const APInt &ShAmt, bool &Overflow) const {
|
|
Overflow = ShAmt.uge(getBitWidth());
|
|
if (Overflow)
|
|
return APInt(BitWidth, 0);
|
|
|
|
Overflow = ShAmt.ugt(countLeadingZeros());
|
|
|
|
return *this << ShAmt;
|
|
}
|
|
|
|
APInt APInt::sadd_sat(const APInt &RHS) const {
|
|
bool Overflow;
|
|
APInt Res = sadd_ov(RHS, Overflow);
|
|
if (!Overflow)
|
|
return Res;
|
|
|
|
return isNegative() ? APInt::getSignedMinValue(BitWidth)
|
|
: APInt::getSignedMaxValue(BitWidth);
|
|
}
|
|
|
|
APInt APInt::uadd_sat(const APInt &RHS) const {
|
|
bool Overflow;
|
|
APInt Res = uadd_ov(RHS, Overflow);
|
|
if (!Overflow)
|
|
return Res;
|
|
|
|
return APInt::getMaxValue(BitWidth);
|
|
}
|
|
|
|
APInt APInt::ssub_sat(const APInt &RHS) const {
|
|
bool Overflow;
|
|
APInt Res = ssub_ov(RHS, Overflow);
|
|
if (!Overflow)
|
|
return Res;
|
|
|
|
return isNegative() ? APInt::getSignedMinValue(BitWidth)
|
|
: APInt::getSignedMaxValue(BitWidth);
|
|
}
|
|
|
|
APInt APInt::usub_sat(const APInt &RHS) const {
|
|
bool Overflow;
|
|
APInt Res = usub_ov(RHS, Overflow);
|
|
if (!Overflow)
|
|
return Res;
|
|
|
|
return APInt(BitWidth, 0);
|
|
}
|
|
|
|
APInt APInt::smul_sat(const APInt &RHS) const {
|
|
bool Overflow;
|
|
APInt Res = smul_ov(RHS, Overflow);
|
|
if (!Overflow)
|
|
return Res;
|
|
|
|
// The result is negative if one and only one of inputs is negative.
|
|
bool ResIsNegative = isNegative() ^ RHS.isNegative();
|
|
|
|
return ResIsNegative ? APInt::getSignedMinValue(BitWidth)
|
|
: APInt::getSignedMaxValue(BitWidth);
|
|
}
|
|
|
|
APInt APInt::umul_sat(const APInt &RHS) const {
|
|
bool Overflow;
|
|
APInt Res = umul_ov(RHS, Overflow);
|
|
if (!Overflow)
|
|
return Res;
|
|
|
|
return APInt::getMaxValue(BitWidth);
|
|
}
|
|
|
|
APInt APInt::sshl_sat(const APInt &RHS) const {
|
|
bool Overflow;
|
|
APInt Res = sshl_ov(RHS, Overflow);
|
|
if (!Overflow)
|
|
return Res;
|
|
|
|
return isNegative() ? APInt::getSignedMinValue(BitWidth)
|
|
: APInt::getSignedMaxValue(BitWidth);
|
|
}
|
|
|
|
APInt APInt::ushl_sat(const APInt &RHS) const {
|
|
bool Overflow;
|
|
APInt Res = ushl_ov(RHS, Overflow);
|
|
if (!Overflow)
|
|
return Res;
|
|
|
|
return APInt::getMaxValue(BitWidth);
|
|
}
|
|
|
|
void APInt::fromString(unsigned numbits, StringRef str, uint8_t radix) {
|
|
// Check our assumptions here
|
|
assert(!str.empty() && "Invalid string length");
|
|
assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||
|
|
radix == 36) &&
|
|
"Radix should be 2, 8, 10, 16, or 36!");
|
|
|
|
StringRef::iterator p = str.begin();
|
|
size_t slen = str.size();
|
|
bool isNeg = *p == '-';
|
|
if (*p == '-' || *p == '+') {
|
|
p++;
|
|
slen--;
|
|
assert(slen && "String is only a sign, needs a value.");
|
|
}
|
|
assert((slen <= numbits || radix != 2) && "Insufficient bit width");
|
|
assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width");
|
|
assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width");
|
|
assert((((slen-1)*64)/22 <= numbits || radix != 10) &&
|
|
"Insufficient bit width");
|
|
|
|
// Allocate memory if needed
|
|
if (isSingleWord())
|
|
U.VAL = 0;
|
|
else
|
|
U.pVal = getClearedMemory(getNumWords());
|
|
|
|
// Figure out if we can shift instead of multiply
|
|
unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
|
|
|
|
// Enter digit traversal loop
|
|
for (StringRef::iterator e = str.end(); p != e; ++p) {
|
|
unsigned digit = getDigit(*p, radix);
|
|
assert(digit < radix && "Invalid character in digit string");
|
|
|
|
// Shift or multiply the value by the radix
|
|
if (slen > 1) {
|
|
if (shift)
|
|
*this <<= shift;
|
|
else
|
|
*this *= radix;
|
|
}
|
|
|
|
// Add in the digit we just interpreted
|
|
*this += digit;
|
|
}
|
|
// If its negative, put it in two's complement form
|
|
if (isNeg)
|
|
this->negate();
|
|
}
|
|
|
|
void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix,
|
|
bool Signed, bool formatAsCLiteral) const {
|
|
assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2 ||
|
|
Radix == 36) &&
|
|
"Radix should be 2, 8, 10, 16, or 36!");
|
|
|
|
const char *Prefix = "";
|
|
if (formatAsCLiteral) {
|
|
switch (Radix) {
|
|
case 2:
|
|
// Binary literals are a non-standard extension added in gcc 4.3:
|
|
// http://gcc.gnu.org/onlinedocs/gcc-4.3.0/gcc/Binary-constants.html
|
|
Prefix = "0b";
|
|
break;
|
|
case 8:
|
|
Prefix = "0";
|
|
break;
|
|
case 10:
|
|
break; // No prefix
|
|
case 16:
|
|
Prefix = "0x";
|
|
break;
|
|
default:
|
|
llvm_unreachable("Invalid radix!");
|
|
}
|
|
}
|
|
|
|
// First, check for a zero value and just short circuit the logic below.
|
|
if (*this == 0) {
|
|
while (*Prefix) {
|
|
Str.push_back(*Prefix);
|
|
++Prefix;
|
|
};
|
|
Str.push_back('0');
|
|
return;
|
|
}
|
|
|
|
static const char Digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
|
|
|
|
if (isSingleWord()) {
|
|
char Buffer[65];
|
|
char *BufPtr = std::end(Buffer);
|
|
|
|
uint64_t N;
|
|
if (!Signed) {
|
|
N = getZExtValue();
|
|
} else {
|
|
int64_t I = getSExtValue();
|
|
if (I >= 0) {
|
|
N = I;
|
|
} else {
|
|
Str.push_back('-');
|
|
N = -(uint64_t)I;
|
|
}
|
|
}
|
|
|
|
while (*Prefix) {
|
|
Str.push_back(*Prefix);
|
|
++Prefix;
|
|
};
|
|
|
|
while (N) {
|
|
*--BufPtr = Digits[N % Radix];
|
|
N /= Radix;
|
|
}
|
|
Str.append(BufPtr, std::end(Buffer));
|
|
return;
|
|
}
|
|
|
|
APInt Tmp(*this);
|
|
|
|
if (Signed && isNegative()) {
|
|
// They want to print the signed version and it is a negative value
|
|
// Flip the bits and add one to turn it into the equivalent positive
|
|
// value and put a '-' in the result.
|
|
Tmp.negate();
|
|
Str.push_back('-');
|
|
}
|
|
|
|
while (*Prefix) {
|
|
Str.push_back(*Prefix);
|
|
++Prefix;
|
|
};
|
|
|
|
// We insert the digits backward, then reverse them to get the right order.
|
|
unsigned StartDig = Str.size();
|
|
|
|
// For the 2, 8 and 16 bit cases, we can just shift instead of divide
|
|
// because the number of bits per digit (1, 3 and 4 respectively) divides
|
|
// equally. We just shift until the value is zero.
|
|
if (Radix == 2 || Radix == 8 || Radix == 16) {
|
|
// Just shift tmp right for each digit width until it becomes zero
|
|
unsigned ShiftAmt = (Radix == 16 ? 4 : (Radix == 8 ? 3 : 1));
|
|
unsigned MaskAmt = Radix - 1;
|
|
|
|
while (Tmp.getBoolValue()) {
|
|
unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt;
|
|
Str.push_back(Digits[Digit]);
|
|
Tmp.lshrInPlace(ShiftAmt);
|
|
}
|
|
} else {
|
|
while (Tmp.getBoolValue()) {
|
|
uint64_t Digit;
|
|
udivrem(Tmp, Radix, Tmp, Digit);
|
|
assert(Digit < Radix && "divide failed");
|
|
Str.push_back(Digits[Digit]);
|
|
}
|
|
}
|
|
|
|
// Reverse the digits before returning.
|
|
std::reverse(Str.begin()+StartDig, Str.end());
|
|
}
|
|
|
|
/// Returns the APInt as a std::string. Note that this is an inefficient method.
|
|
/// It is better to pass in a SmallVector/SmallString to the methods above.
|
|
std::string APInt::toString(unsigned Radix = 10, bool Signed = true) const {
|
|
SmallString<40> S;
|
|
toString(S, Radix, Signed, /* formatAsCLiteral = */false);
|
|
return std::string(S.str());
|
|
}
|
|
|
|
#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
|
|
LLVM_DUMP_METHOD void APInt::dump() const {
|
|
SmallString<40> S, U;
|
|
this->toStringUnsigned(U);
|
|
this->toStringSigned(S);
|
|
dbgs() << "APInt(" << BitWidth << "b, "
|
|
<< U << "u " << S << "s)\n";
|
|
}
|
|
#endif
|
|
|
|
void APInt::print(raw_ostream &OS, bool isSigned) const {
|
|
SmallString<40> S;
|
|
this->toString(S, 10, isSigned, /* formatAsCLiteral = */false);
|
|
OS << S;
|
|
}
|
|
|
|
// This implements a variety of operations on a representation of
|
|
// arbitrary precision, two's-complement, bignum integer values.
|
|
|
|
// Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe
|
|
// and unrestricting assumption.
|
|
static_assert(APInt::APINT_BITS_PER_WORD % 2 == 0,
|
|
"Part width must be divisible by 2!");
|
|
|
|
/* Some handy functions local to this file. */
|
|
|
|
/* Returns the integer part with the least significant BITS set.
|
|
BITS cannot be zero. */
|
|
static inline APInt::WordType lowBitMask(unsigned bits) {
|
|
assert(bits != 0 && bits <= APInt::APINT_BITS_PER_WORD);
|
|
|
|
return ~(APInt::WordType) 0 >> (APInt::APINT_BITS_PER_WORD - bits);
|
|
}
|
|
|
|
/* Returns the value of the lower half of PART. */
|
|
static inline APInt::WordType lowHalf(APInt::WordType part) {
|
|
return part & lowBitMask(APInt::APINT_BITS_PER_WORD / 2);
|
|
}
|
|
|
|
/* Returns the value of the upper half of PART. */
|
|
static inline APInt::WordType highHalf(APInt::WordType part) {
|
|
return part >> (APInt::APINT_BITS_PER_WORD / 2);
|
|
}
|
|
|
|
/* Returns the bit number of the most significant set bit of a part.
|
|
If the input number has no bits set -1U is returned. */
|
|
static unsigned partMSB(APInt::WordType value) {
|
|
return findLastSet(value, ZB_Max);
|
|
}
|
|
|
|
/* Returns the bit number of the least significant set bit of a
|
|
part. If the input number has no bits set -1U is returned. */
|
|
static unsigned partLSB(APInt::WordType value) {
|
|
return findFirstSet(value, ZB_Max);
|
|
}
|
|
|
|
/* Sets the least significant part of a bignum to the input value, and
|
|
zeroes out higher parts. */
|
|
void APInt::tcSet(WordType *dst, WordType part, unsigned parts) {
|
|
assert(parts > 0);
|
|
|
|
dst[0] = part;
|
|
for (unsigned i = 1; i < parts; i++)
|
|
dst[i] = 0;
|
|
}
|
|
|
|
/* Assign one bignum to another. */
|
|
void APInt::tcAssign(WordType *dst, const WordType *src, unsigned parts) {
|
|
for (unsigned i = 0; i < parts; i++)
|
|
dst[i] = src[i];
|
|
}
|
|
|
|
/* Returns true if a bignum is zero, false otherwise. */
|
|
bool APInt::tcIsZero(const WordType *src, unsigned parts) {
|
|
for (unsigned i = 0; i < parts; i++)
|
|
if (src[i])
|
|
return false;
|
|
|
|
return true;
|
|
}
|
|
|
|
/* Extract the given bit of a bignum; returns 0 or 1. */
|
|
int APInt::tcExtractBit(const WordType *parts, unsigned bit) {
|
|
return (parts[whichWord(bit)] & maskBit(bit)) != 0;
|
|
}
|
|
|
|
/* Set the given bit of a bignum. */
|
|
void APInt::tcSetBit(WordType *parts, unsigned bit) {
|
|
parts[whichWord(bit)] |= maskBit(bit);
|
|
}
|
|
|
|
/* Clears the given bit of a bignum. */
|
|
void APInt::tcClearBit(WordType *parts, unsigned bit) {
|
|
parts[whichWord(bit)] &= ~maskBit(bit);
|
|
}
|
|
|
|
/* Returns the bit number of the least significant set bit of a
|
|
number. If the input number has no bits set -1U is returned. */
|
|
unsigned APInt::tcLSB(const WordType *parts, unsigned n) {
|
|
for (unsigned i = 0; i < n; i++) {
|
|
if (parts[i] != 0) {
|
|
unsigned lsb = partLSB(parts[i]);
|
|
|
|
return lsb + i * APINT_BITS_PER_WORD;
|
|
}
|
|
}
|
|
|
|
return -1U;
|
|
}
|
|
|
|
/* Returns the bit number of the most significant set bit of a number.
|
|
If the input number has no bits set -1U is returned. */
|
|
unsigned APInt::tcMSB(const WordType *parts, unsigned n) {
|
|
do {
|
|
--n;
|
|
|
|
if (parts[n] != 0) {
|
|
unsigned msb = partMSB(parts[n]);
|
|
|
|
return msb + n * APINT_BITS_PER_WORD;
|
|
}
|
|
} while (n);
|
|
|
|
return -1U;
|
|
}
|
|
|
|
/* Copy the bit vector of width srcBITS from SRC, starting at bit
|
|
srcLSB, to DST, of dstCOUNT parts, such that the bit srcLSB becomes
|
|
the least significant bit of DST. All high bits above srcBITS in
|
|
DST are zero-filled. */
|
|
void
|
|
APInt::tcExtract(WordType *dst, unsigned dstCount, const WordType *src,
|
|
unsigned srcBits, unsigned srcLSB) {
|
|
unsigned dstParts = (srcBits + APINT_BITS_PER_WORD - 1) / APINT_BITS_PER_WORD;
|
|
assert(dstParts <= dstCount);
|
|
|
|
unsigned firstSrcPart = srcLSB / APINT_BITS_PER_WORD;
|
|
tcAssign (dst, src + firstSrcPart, dstParts);
|
|
|
|
unsigned shift = srcLSB % APINT_BITS_PER_WORD;
|
|
tcShiftRight (dst, dstParts, shift);
|
|
|
|
/* We now have (dstParts * APINT_BITS_PER_WORD - shift) bits from SRC
|
|
in DST. If this is less that srcBits, append the rest, else
|
|
clear the high bits. */
|
|
unsigned n = dstParts * APINT_BITS_PER_WORD - shift;
|
|
if (n < srcBits) {
|
|
WordType mask = lowBitMask (srcBits - n);
|
|
dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask)
|
|
<< n % APINT_BITS_PER_WORD);
|
|
} else if (n > srcBits) {
|
|
if (srcBits % APINT_BITS_PER_WORD)
|
|
dst[dstParts - 1] &= lowBitMask (srcBits % APINT_BITS_PER_WORD);
|
|
}
|
|
|
|
/* Clear high parts. */
|
|
while (dstParts < dstCount)
|
|
dst[dstParts++] = 0;
|
|
}
|
|
|
|
/* DST += RHS + C where C is zero or one. Returns the carry flag. */
|
|
APInt::WordType APInt::tcAdd(WordType *dst, const WordType *rhs,
|
|
WordType c, unsigned parts) {
|
|
assert(c <= 1);
|
|
|
|
for (unsigned i = 0; i < parts; i++) {
|
|
WordType l = dst[i];
|
|
if (c) {
|
|
dst[i] += rhs[i] + 1;
|
|
c = (dst[i] <= l);
|
|
} else {
|
|
dst[i] += rhs[i];
|
|
c = (dst[i] < l);
|
|
}
|
|
}
|
|
|
|
return c;
|
|
}
|
|
|
|
/// This function adds a single "word" integer, src, to the multiple
|
|
/// "word" integer array, dst[]. dst[] is modified to reflect the addition and
|
|
/// 1 is returned if there is a carry out, otherwise 0 is returned.
|
|
/// @returns the carry of the addition.
|
|
APInt::WordType APInt::tcAddPart(WordType *dst, WordType src,
|
|
unsigned parts) {
|
|
for (unsigned i = 0; i < parts; ++i) {
|
|
dst[i] += src;
|
|
if (dst[i] >= src)
|
|
return 0; // No need to carry so exit early.
|
|
src = 1; // Carry one to next digit.
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
/* DST -= RHS + C where C is zero or one. Returns the carry flag. */
|
|
APInt::WordType APInt::tcSubtract(WordType *dst, const WordType *rhs,
|
|
WordType c, unsigned parts) {
|
|
assert(c <= 1);
|
|
|
|
for (unsigned i = 0; i < parts; i++) {
|
|
WordType l = dst[i];
|
|
if (c) {
|
|
dst[i] -= rhs[i] + 1;
|
|
c = (dst[i] >= l);
|
|
} else {
|
|
dst[i] -= rhs[i];
|
|
c = (dst[i] > l);
|
|
}
|
|
}
|
|
|
|
return c;
|
|
}
|
|
|
|
/// This function subtracts a single "word" (64-bit word), src, from
|
|
/// the multi-word integer array, dst[], propagating the borrowed 1 value until
|
|
/// no further borrowing is needed or it runs out of "words" in dst. The result
|
|
/// is 1 if "borrowing" exhausted the digits in dst, or 0 if dst was not
|
|
/// exhausted. In other words, if src > dst then this function returns 1,
|
|
/// otherwise 0.
|
|
/// @returns the borrow out of the subtraction
|
|
APInt::WordType APInt::tcSubtractPart(WordType *dst, WordType src,
|
|
unsigned parts) {
|
|
for (unsigned i = 0; i < parts; ++i) {
|
|
WordType Dst = dst[i];
|
|
dst[i] -= src;
|
|
if (src <= Dst)
|
|
return 0; // No need to borrow so exit early.
|
|
src = 1; // We have to "borrow 1" from next "word"
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
/* Negate a bignum in-place. */
|
|
void APInt::tcNegate(WordType *dst, unsigned parts) {
|
|
tcComplement(dst, parts);
|
|
tcIncrement(dst, parts);
|
|
}
|
|
|
|
/* DST += SRC * MULTIPLIER + CARRY if add is true
|
|
DST = SRC * MULTIPLIER + CARRY if add is false
|
|
|
|
Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC
|
|
they must start at the same point, i.e. DST == SRC.
|
|
|
|
If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is
|
|
returned. Otherwise DST is filled with the least significant
|
|
DSTPARTS parts of the result, and if all of the omitted higher
|
|
parts were zero return zero, otherwise overflow occurred and
|
|
return one. */
|
|
int APInt::tcMultiplyPart(WordType *dst, const WordType *src,
|
|
WordType multiplier, WordType carry,
|
|
unsigned srcParts, unsigned dstParts,
|
|
bool add) {
|
|
/* Otherwise our writes of DST kill our later reads of SRC. */
|
|
assert(dst <= src || dst >= src + srcParts);
|
|
assert(dstParts <= srcParts + 1);
|
|
|
|
/* N loops; minimum of dstParts and srcParts. */
|
|
unsigned n = std::min(dstParts, srcParts);
|
|
|
|
for (unsigned i = 0; i < n; i++) {
|
|
WordType low, mid, high, srcPart;
|
|
|
|
/* [ LOW, HIGH ] = MULTIPLIER * SRC[i] + DST[i] + CARRY.
|
|
|
|
This cannot overflow, because
|
|
|
|
(n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1)
|
|
|
|
which is less than n^2. */
|
|
|
|
srcPart = src[i];
|
|
|
|
if (multiplier == 0 || srcPart == 0) {
|
|
low = carry;
|
|
high = 0;
|
|
} else {
|
|
low = lowHalf(srcPart) * lowHalf(multiplier);
|
|
high = highHalf(srcPart) * highHalf(multiplier);
|
|
|
|
mid = lowHalf(srcPart) * highHalf(multiplier);
|
|
high += highHalf(mid);
|
|
mid <<= APINT_BITS_PER_WORD / 2;
|
|
if (low + mid < low)
|
|
high++;
|
|
low += mid;
|
|
|
|
mid = highHalf(srcPart) * lowHalf(multiplier);
|
|
high += highHalf(mid);
|
|
mid <<= APINT_BITS_PER_WORD / 2;
|
|
if (low + mid < low)
|
|
high++;
|
|
low += mid;
|
|
|
|
/* Now add carry. */
|
|
if (low + carry < low)
|
|
high++;
|
|
low += carry;
|
|
}
|
|
|
|
if (add) {
|
|
/* And now DST[i], and store the new low part there. */
|
|
if (low + dst[i] < low)
|
|
high++;
|
|
dst[i] += low;
|
|
} else
|
|
dst[i] = low;
|
|
|
|
carry = high;
|
|
}
|
|
|
|
if (srcParts < dstParts) {
|
|
/* Full multiplication, there is no overflow. */
|
|
assert(srcParts + 1 == dstParts);
|
|
dst[srcParts] = carry;
|
|
return 0;
|
|
}
|
|
|
|
/* We overflowed if there is carry. */
|
|
if (carry)
|
|
return 1;
|
|
|
|
/* We would overflow if any significant unwritten parts would be
|
|
non-zero. This is true if any remaining src parts are non-zero
|
|
and the multiplier is non-zero. */
|
|
if (multiplier)
|
|
for (unsigned i = dstParts; i < srcParts; i++)
|
|
if (src[i])
|
|
return 1;
|
|
|
|
/* We fitted in the narrow destination. */
|
|
return 0;
|
|
}
|
|
|
|
/* DST = LHS * RHS, where DST has the same width as the operands and
|
|
is filled with the least significant parts of the result. Returns
|
|
one if overflow occurred, otherwise zero. DST must be disjoint
|
|
from both operands. */
|
|
int APInt::tcMultiply(WordType *dst, const WordType *lhs,
|
|
const WordType *rhs, unsigned parts) {
|
|
assert(dst != lhs && dst != rhs);
|
|
|
|
int overflow = 0;
|
|
tcSet(dst, 0, parts);
|
|
|
|
for (unsigned i = 0; i < parts; i++)
|
|
overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts,
|
|
parts - i, true);
|
|
|
|
return overflow;
|
|
}
|
|
|
|
/// DST = LHS * RHS, where DST has width the sum of the widths of the
|
|
/// operands. No overflow occurs. DST must be disjoint from both operands.
|
|
void APInt::tcFullMultiply(WordType *dst, const WordType *lhs,
|
|
const WordType *rhs, unsigned lhsParts,
|
|
unsigned rhsParts) {
|
|
/* Put the narrower number on the LHS for less loops below. */
|
|
if (lhsParts > rhsParts)
|
|
return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts);
|
|
|
|
assert(dst != lhs && dst != rhs);
|
|
|
|
tcSet(dst, 0, rhsParts);
|
|
|
|
for (unsigned i = 0; i < lhsParts; i++)
|
|
tcMultiplyPart(&dst[i], rhs, lhs[i], 0, rhsParts, rhsParts + 1, true);
|
|
}
|
|
|
|
/* If RHS is zero LHS and REMAINDER are left unchanged, return one.
|
|
Otherwise set LHS to LHS / RHS with the fractional part discarded,
|
|
set REMAINDER to the remainder, return zero. i.e.
|
|
|
|
OLD_LHS = RHS * LHS + REMAINDER
|
|
|
|
SCRATCH is a bignum of the same size as the operands and result for
|
|
use by the routine; its contents need not be initialized and are
|
|
destroyed. LHS, REMAINDER and SCRATCH must be distinct.
|
|
*/
|
|
int APInt::tcDivide(WordType *lhs, const WordType *rhs,
|
|
WordType *remainder, WordType *srhs,
|
|
unsigned parts) {
|
|
assert(lhs != remainder && lhs != srhs && remainder != srhs);
|
|
|
|
unsigned shiftCount = tcMSB(rhs, parts) + 1;
|
|
if (shiftCount == 0)
|
|
return true;
|
|
|
|
shiftCount = parts * APINT_BITS_PER_WORD - shiftCount;
|
|
unsigned n = shiftCount / APINT_BITS_PER_WORD;
|
|
WordType mask = (WordType) 1 << (shiftCount % APINT_BITS_PER_WORD);
|
|
|
|
tcAssign(srhs, rhs, parts);
|
|
tcShiftLeft(srhs, parts, shiftCount);
|
|
tcAssign(remainder, lhs, parts);
|
|
tcSet(lhs, 0, parts);
|
|
|
|
/* Loop, subtracting SRHS if REMAINDER is greater and adding that to
|
|
the total. */
|
|
for (;;) {
|
|
int compare = tcCompare(remainder, srhs, parts);
|
|
if (compare >= 0) {
|
|
tcSubtract(remainder, srhs, 0, parts);
|
|
lhs[n] |= mask;
|
|
}
|
|
|
|
if (shiftCount == 0)
|
|
break;
|
|
shiftCount--;
|
|
tcShiftRight(srhs, parts, 1);
|
|
if ((mask >>= 1) == 0) {
|
|
mask = (WordType) 1 << (APINT_BITS_PER_WORD - 1);
|
|
n--;
|
|
}
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
/// Shift a bignum left Cound bits in-place. Shifted in bits are zero. There are
|
|
/// no restrictions on Count.
|
|
void APInt::tcShiftLeft(WordType *Dst, unsigned Words, unsigned Count) {
|
|
// Don't bother performing a no-op shift.
|
|
if (!Count)
|
|
return;
|
|
|
|
// WordShift is the inter-part shift; BitShift is the intra-part shift.
|
|
unsigned WordShift = std::min(Count / APINT_BITS_PER_WORD, Words);
|
|
unsigned BitShift = Count % APINT_BITS_PER_WORD;
|
|
|
|
// Fastpath for moving by whole words.
|
|
if (BitShift == 0) {
|
|
std::memmove(Dst + WordShift, Dst, (Words - WordShift) * APINT_WORD_SIZE);
|
|
} else {
|
|
while (Words-- > WordShift) {
|
|
Dst[Words] = Dst[Words - WordShift] << BitShift;
|
|
if (Words > WordShift)
|
|
Dst[Words] |=
|
|
Dst[Words - WordShift - 1] >> (APINT_BITS_PER_WORD - BitShift);
|
|
}
|
|
}
|
|
|
|
// Fill in the remainder with 0s.
|
|
std::memset(Dst, 0, WordShift * APINT_WORD_SIZE);
|
|
}
|
|
|
|
/// Shift a bignum right Count bits in-place. Shifted in bits are zero. There
|
|
/// are no restrictions on Count.
|
|
void APInt::tcShiftRight(WordType *Dst, unsigned Words, unsigned Count) {
|
|
// Don't bother performing a no-op shift.
|
|
if (!Count)
|
|
return;
|
|
|
|
// WordShift is the inter-part shift; BitShift is the intra-part shift.
|
|
unsigned WordShift = std::min(Count / APINT_BITS_PER_WORD, Words);
|
|
unsigned BitShift = Count % APINT_BITS_PER_WORD;
|
|
|
|
unsigned WordsToMove = Words - WordShift;
|
|
// Fastpath for moving by whole words.
|
|
if (BitShift == 0) {
|
|
std::memmove(Dst, Dst + WordShift, WordsToMove * APINT_WORD_SIZE);
|
|
} else {
|
|
for (unsigned i = 0; i != WordsToMove; ++i) {
|
|
Dst[i] = Dst[i + WordShift] >> BitShift;
|
|
if (i + 1 != WordsToMove)
|
|
Dst[i] |= Dst[i + WordShift + 1] << (APINT_BITS_PER_WORD - BitShift);
|
|
}
|
|
}
|
|
|
|
// Fill in the remainder with 0s.
|
|
std::memset(Dst + WordsToMove, 0, WordShift * APINT_WORD_SIZE);
|
|
}
|
|
|
|
/* Bitwise and of two bignums. */
|
|
void APInt::tcAnd(WordType *dst, const WordType *rhs, unsigned parts) {
|
|
for (unsigned i = 0; i < parts; i++)
|
|
dst[i] &= rhs[i];
|
|
}
|
|
|
|
/* Bitwise inclusive or of two bignums. */
|
|
void APInt::tcOr(WordType *dst, const WordType *rhs, unsigned parts) {
|
|
for (unsigned i = 0; i < parts; i++)
|
|
dst[i] |= rhs[i];
|
|
}
|
|
|
|
/* Bitwise exclusive or of two bignums. */
|
|
void APInt::tcXor(WordType *dst, const WordType *rhs, unsigned parts) {
|
|
for (unsigned i = 0; i < parts; i++)
|
|
dst[i] ^= rhs[i];
|
|
}
|
|
|
|
/* Complement a bignum in-place. */
|
|
void APInt::tcComplement(WordType *dst, unsigned parts) {
|
|
for (unsigned i = 0; i < parts; i++)
|
|
dst[i] = ~dst[i];
|
|
}
|
|
|
|
/* Comparison (unsigned) of two bignums. */
|
|
int APInt::tcCompare(const WordType *lhs, const WordType *rhs,
|
|
unsigned parts) {
|
|
while (parts) {
|
|
parts--;
|
|
if (lhs[parts] != rhs[parts])
|
|
return (lhs[parts] > rhs[parts]) ? 1 : -1;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Set the least significant BITS bits of a bignum, clear the
|
|
rest. */
|
|
void APInt::tcSetLeastSignificantBits(WordType *dst, unsigned parts,
|
|
unsigned bits) {
|
|
unsigned i = 0;
|
|
while (bits > APINT_BITS_PER_WORD) {
|
|
dst[i++] = ~(WordType) 0;
|
|
bits -= APINT_BITS_PER_WORD;
|
|
}
|
|
|
|
if (bits)
|
|
dst[i++] = ~(WordType) 0 >> (APINT_BITS_PER_WORD - bits);
|
|
|
|
while (i < parts)
|
|
dst[i++] = 0;
|
|
}
|
|
|
|
APInt llvm::APIntOps::RoundingUDiv(const APInt &A, const APInt &B,
|
|
APInt::Rounding RM) {
|
|
// Currently udivrem always rounds down.
|
|
switch (RM) {
|
|
case APInt::Rounding::DOWN:
|
|
case APInt::Rounding::TOWARD_ZERO:
|
|
return A.udiv(B);
|
|
case APInt::Rounding::UP: {
|
|
APInt Quo, Rem;
|
|
APInt::udivrem(A, B, Quo, Rem);
|
|
if (Rem == 0)
|
|
return Quo;
|
|
return Quo + 1;
|
|
}
|
|
}
|
|
llvm_unreachable("Unknown APInt::Rounding enum");
|
|
}
|
|
|
|
APInt llvm::APIntOps::RoundingSDiv(const APInt &A, const APInt &B,
|
|
APInt::Rounding RM) {
|
|
switch (RM) {
|
|
case APInt::Rounding::DOWN:
|
|
case APInt::Rounding::UP: {
|
|
APInt Quo, Rem;
|
|
APInt::sdivrem(A, B, Quo, Rem);
|
|
if (Rem == 0)
|
|
return Quo;
|
|
// This algorithm deals with arbitrary rounding mode used by sdivrem.
|
|
// We want to check whether the non-integer part of the mathematical value
|
|
// is negative or not. If the non-integer part is negative, we need to round
|
|
// down from Quo; otherwise, if it's positive or 0, we return Quo, as it's
|
|
// already rounded down.
|
|
if (RM == APInt::Rounding::DOWN) {
|
|
if (Rem.isNegative() != B.isNegative())
|
|
return Quo - 1;
|
|
return Quo;
|
|
}
|
|
if (Rem.isNegative() != B.isNegative())
|
|
return Quo;
|
|
return Quo + 1;
|
|
}
|
|
// Currently sdiv rounds towards zero.
|
|
case APInt::Rounding::TOWARD_ZERO:
|
|
return A.sdiv(B);
|
|
}
|
|
llvm_unreachable("Unknown APInt::Rounding enum");
|
|
}
|
|
|
|
Optional<APInt>
|
|
llvm::APIntOps::SolveQuadraticEquationWrap(APInt A, APInt B, APInt C,
|
|
unsigned RangeWidth) {
|
|
unsigned CoeffWidth = A.getBitWidth();
|
|
assert(CoeffWidth == B.getBitWidth() && CoeffWidth == C.getBitWidth());
|
|
assert(RangeWidth <= CoeffWidth &&
|
|
"Value range width should be less than coefficient width");
|
|
assert(RangeWidth > 1 && "Value range bit width should be > 1");
|
|
|
|
LLVM_DEBUG(dbgs() << __func__ << ": solving " << A << "x^2 + " << B
|
|
<< "x + " << C << ", rw:" << RangeWidth << '\n');
|
|
|
|
// Identify 0 as a (non)solution immediately.
|
|
if (C.sextOrTrunc(RangeWidth).isNullValue() ) {
|
|
LLVM_DEBUG(dbgs() << __func__ << ": zero solution\n");
|
|
return APInt(CoeffWidth, 0);
|
|
}
|
|
|
|
// The result of APInt arithmetic has the same bit width as the operands,
|
|
// so it can actually lose high bits. A product of two n-bit integers needs
|
|
// 2n-1 bits to represent the full value.
|
|
// The operation done below (on quadratic coefficients) that can produce
|
|
// the largest value is the evaluation of the equation during bisection,
|
|
// which needs 3 times the bitwidth of the coefficient, so the total number
|
|
// of required bits is 3n.
|
|
//
|
|
// The purpose of this extension is to simulate the set Z of all integers,
|
|
// where n+1 > n for all n in Z. In Z it makes sense to talk about positive
|
|
// and negative numbers (not so much in a modulo arithmetic). The method
|
|
// used to solve the equation is based on the standard formula for real
|
|
// numbers, and uses the concepts of "positive" and "negative" with their
|
|
// usual meanings.
|
|
CoeffWidth *= 3;
|
|
A = A.sext(CoeffWidth);
|
|
B = B.sext(CoeffWidth);
|
|
C = C.sext(CoeffWidth);
|
|
|
|
// Make A > 0 for simplicity. Negate cannot overflow at this point because
|
|
// the bit width has increased.
|
|
if (A.isNegative()) {
|
|
A.negate();
|
|
B.negate();
|
|
C.negate();
|
|
}
|
|
|
|
// Solving an equation q(x) = 0 with coefficients in modular arithmetic
|
|
// is really solving a set of equations q(x) = kR for k = 0, 1, 2, ...,
|
|
// and R = 2^BitWidth.
|
|
// Since we're trying not only to find exact solutions, but also values
|
|
// that "wrap around", such a set will always have a solution, i.e. an x
|
|
// that satisfies at least one of the equations, or such that |q(x)|
|
|
// exceeds kR, while |q(x-1)| for the same k does not.
|
|
//
|
|
// We need to find a value k, such that Ax^2 + Bx + C = kR will have a
|
|
// positive solution n (in the above sense), and also such that the n
|
|
// will be the least among all solutions corresponding to k = 0, 1, ...
|
|
// (more precisely, the least element in the set
|
|
// { n(k) | k is such that a solution n(k) exists }).
|
|
//
|
|
// Consider the parabola (over real numbers) that corresponds to the
|
|
// quadratic equation. Since A > 0, the arms of the parabola will point
|
|
// up. Picking different values of k will shift it up and down by R.
|
|
//
|
|
// We want to shift the parabola in such a way as to reduce the problem
|
|
// of solving q(x) = kR to solving shifted_q(x) = 0.
|
|
// (The interesting solutions are the ceilings of the real number
|
|
// solutions.)
|
|
APInt R = APInt::getOneBitSet(CoeffWidth, RangeWidth);
|
|
APInt TwoA = 2 * A;
|
|
APInt SqrB = B * B;
|
|
bool PickLow;
|
|
|
|
auto RoundUp = [] (const APInt &V, const APInt &A) -> APInt {
|
|
assert(A.isStrictlyPositive());
|
|
APInt T = V.abs().urem(A);
|
|
if (T.isNullValue())
|
|
return V;
|
|
return V.isNegative() ? V+T : V+(A-T);
|
|
};
|
|
|
|
// The vertex of the parabola is at -B/2A, but since A > 0, it's negative
|
|
// iff B is positive.
|
|
if (B.isNonNegative()) {
|
|
// If B >= 0, the vertex it at a negative location (or at 0), so in
|
|
// order to have a non-negative solution we need to pick k that makes
|
|
// C-kR negative. To satisfy all the requirements for the solution
|
|
// that we are looking for, it needs to be closest to 0 of all k.
|
|
C = C.srem(R);
|
|
if (C.isStrictlyPositive())
|
|
C -= R;
|
|
// Pick the greater solution.
|
|
PickLow = false;
|
|
} else {
|
|
// If B < 0, the vertex is at a positive location. For any solution
|
|
// to exist, the discriminant must be non-negative. This means that
|
|
// C-kR <= B^2/4A is a necessary condition for k, i.e. there is a
|
|
// lower bound on values of k: kR >= C - B^2/4A.
|
|
APInt LowkR = C - SqrB.udiv(2*TwoA); // udiv because all values > 0.
|
|
// Round LowkR up (towards +inf) to the nearest kR.
|
|
LowkR = RoundUp(LowkR, R);
|
|
|
|
// If there exists k meeting the condition above, and such that
|
|
// C-kR > 0, there will be two positive real number solutions of
|
|
// q(x) = kR. Out of all such values of k, pick the one that makes
|
|
// C-kR closest to 0, (i.e. pick maximum k such that C-kR > 0).
|
|
// In other words, find maximum k such that LowkR <= kR < C.
|
|
if (C.sgt(LowkR)) {
|
|
// If LowkR < C, then such a k is guaranteed to exist because
|
|
// LowkR itself is a multiple of R.
|
|
C -= -RoundUp(-C, R); // C = C - RoundDown(C, R)
|
|
// Pick the smaller solution.
|
|
PickLow = true;
|
|
} else {
|
|
// If C-kR < 0 for all potential k's, it means that one solution
|
|
// will be negative, while the other will be positive. The positive
|
|
// solution will shift towards 0 if the parabola is moved up.
|
|
// Pick the kR closest to the lower bound (i.e. make C-kR closest
|
|
// to 0, or in other words, out of all parabolas that have solutions,
|
|
// pick the one that is the farthest "up").
|
|
// Since LowkR is itself a multiple of R, simply take C-LowkR.
|
|
C -= LowkR;
|
|
// Pick the greater solution.
|
|
PickLow = false;
|
|
}
|
|
}
|
|
|
|
LLVM_DEBUG(dbgs() << __func__ << ": updated coefficients " << A << "x^2 + "
|
|
<< B << "x + " << C << ", rw:" << RangeWidth << '\n');
|
|
|
|
APInt D = SqrB - 4*A*C;
|
|
assert(D.isNonNegative() && "Negative discriminant");
|
|
APInt SQ = D.sqrt();
|
|
|
|
APInt Q = SQ * SQ;
|
|
bool InexactSQ = Q != D;
|
|
// The calculated SQ may actually be greater than the exact (non-integer)
|
|
// value. If that's the case, 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.isNullValue()) {
|
|
LLVM_DEBUG(dbgs() << __func__ << ": solution (root): " << X << '\n');
|
|
return X;
|
|
}
|
|
|
|
assert((SQ*SQ).sle(D) && "SQ = |_sqrt(D)_|, so SQ*SQ <= D");
|
|
// The exact value of the square root of D should be between SQ and SQ+1.
|
|
// This implies that the solution should be between that corresponding to
|
|
// SQ (i.e. X) and that corresponding to SQ+1.
|
|
//
|
|
// The calculated X cannot be greater than the exact (real) solution.
|
|
// Actually it must be strictly less than the exact solution, while
|
|
// X+1 will be greater than or equal to it.
|
|
|
|
APInt VX = (A*X + B)*X + C;
|
|
APInt VY = VX + TwoA*X + A + B;
|
|
bool SignChange = VX.isNegative() != VY.isNegative() ||
|
|
VX.isNullValue() != VY.isNullValue();
|
|
// If the sign did not change between X and X+1, X is not a valid solution.
|
|
// This could happen when the actual (exact) roots don't have an integer
|
|
// between them, so they would both be contained between X and X+1.
|
|
if (!SignChange) {
|
|
LLVM_DEBUG(dbgs() << __func__ << ": no valid solution\n");
|
|
return None;
|
|
}
|
|
|
|
X += 1;
|
|
LLVM_DEBUG(dbgs() << __func__ << ": solution (wrap): " << X << '\n');
|
|
return X;
|
|
}
|
|
|
|
Optional<unsigned>
|
|
llvm::APIntOps::GetMostSignificantDifferentBit(const APInt &A, const APInt &B) {
|
|
assert(A.getBitWidth() == B.getBitWidth() && "Must have the same bitwidth");
|
|
if (A == B)
|
|
return llvm::None;
|
|
return A.getBitWidth() - ((A ^ B).countLeadingZeros() + 1);
|
|
}
|
|
|
|
/// StoreIntToMemory - Fills the StoreBytes bytes of memory starting from Dst
|
|
/// with the integer held in IntVal.
|
|
void llvm::StoreIntToMemory(const APInt &IntVal, uint8_t *Dst,
|
|
unsigned StoreBytes) {
|
|
assert((IntVal.getBitWidth()+7)/8 >= StoreBytes && "Integer too small!");
|
|
const uint8_t *Src = (const uint8_t *)IntVal.getRawData();
|
|
|
|
if (sys::IsLittleEndianHost) {
|
|
// Little-endian host - the source is ordered from LSB to MSB. Order the
|
|
// destination from LSB to MSB: Do a straight copy.
|
|
memcpy(Dst, Src, StoreBytes);
|
|
} else {
|
|
// Big-endian host - the source is an array of 64 bit words ordered from
|
|
// LSW to MSW. Each word is ordered from MSB to LSB. Order the destination
|
|
// from MSB to LSB: Reverse the word order, but not the bytes in a word.
|
|
while (StoreBytes > sizeof(uint64_t)) {
|
|
StoreBytes -= sizeof(uint64_t);
|
|
// May not be aligned so use memcpy.
|
|
memcpy(Dst + StoreBytes, Src, sizeof(uint64_t));
|
|
Src += sizeof(uint64_t);
|
|
}
|
|
|
|
memcpy(Dst, Src + sizeof(uint64_t) - StoreBytes, StoreBytes);
|
|
}
|
|
}
|
|
|
|
/// LoadIntFromMemory - Loads the integer stored in the LoadBytes bytes starting
|
|
/// from Src into IntVal, which is assumed to be wide enough and to hold zero.
|
|
void llvm::LoadIntFromMemory(APInt &IntVal, uint8_t *Src, unsigned LoadBytes) {
|
|
assert((IntVal.getBitWidth()+7)/8 >= LoadBytes && "Integer too small!");
|
|
uint8_t *Dst = reinterpret_cast<uint8_t *>(
|
|
const_cast<uint64_t *>(IntVal.getRawData()));
|
|
|
|
if (sys::IsLittleEndianHost)
|
|
// Little-endian host - the destination must be ordered from LSB to MSB.
|
|
// The source is ordered from LSB to MSB: Do a straight copy.
|
|
memcpy(Dst, Src, LoadBytes);
|
|
else {
|
|
// Big-endian - the destination is an array of 64 bit words ordered from
|
|
// LSW to MSW. Each word must be ordered from MSB to LSB. The source is
|
|
// ordered from MSB to LSB: Reverse the word order, but not the bytes in
|
|
// a word.
|
|
while (LoadBytes > sizeof(uint64_t)) {
|
|
LoadBytes -= sizeof(uint64_t);
|
|
// May not be aligned so use memcpy.
|
|
memcpy(Dst, Src + LoadBytes, sizeof(uint64_t));
|
|
Dst += sizeof(uint64_t);
|
|
}
|
|
|
|
memcpy(Dst + sizeof(uint64_t) - LoadBytes, Src, LoadBytes);
|
|
}
|
|
}
|