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llvm-project/llvm/lib/Support/APInt.cpp

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//===-- APInt.cpp - Implement APInt class ---------------------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file was developed by Sheng Zhou and is distributed under the
// University of Illinois Open Source License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file implements a class to represent arbitrary precision integer
// constant values and provide a variety of arithmetic operations on them.
//
//===----------------------------------------------------------------------===//
#define DEBUG_TYPE "apint"
#include "llvm/ADT/APInt.h"
#include "llvm/DerivedTypes.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/MathExtras.h"
#include <math.h>
#include <limits>
#include <cstring>
#include <cstdlib>
#ifndef NDEBUG
#include <iomanip>
#endif
using namespace llvm;
/// A utility function for allocating memory, checking for allocation failures,
/// and ensuring the contents are zeroed.
inline static uint64_t* getClearedMemory(uint32_t numWords) {
uint64_t * result = new uint64_t[numWords];
assert(result && "APInt memory allocation fails!");
memset(result, 0, numWords * sizeof(uint64_t));
return result;
}
/// A utility function for allocating memory and checking for allocation
/// failure. The content is not zeroed.
inline static uint64_t* getMemory(uint32_t numWords) {
uint64_t * result = new uint64_t[numWords];
assert(result && "APInt memory allocation fails!");
return result;
}
APInt::APInt(uint32_t numBits, uint64_t val, bool isSigned)
: BitWidth(numBits), VAL(0) {
assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small");
assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large");
if (isSingleWord())
VAL = val;
else {
pVal = getClearedMemory(getNumWords());
pVal[0] = val;
if (isSigned && int64_t(val) < 0)
for (unsigned i = 1; i < getNumWords(); ++i)
pVal[i] = -1ULL;
}
clearUnusedBits();
}
APInt::APInt(uint32_t numBits, uint32_t numWords, uint64_t bigVal[])
: BitWidth(numBits), VAL(0) {
assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small");
assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large");
assert(bigVal && "Null pointer detected!");
if (isSingleWord())
VAL = bigVal[0];
else {
// Get memory, cleared to 0
pVal = getClearedMemory(getNumWords());
// Calculate the number of words to copy
uint32_t words = std::min<uint32_t>(numWords, getNumWords());
// Copy the words from bigVal to pVal
memcpy(pVal, bigVal, words * APINT_WORD_SIZE);
}
// Make sure unused high bits are cleared
clearUnusedBits();
}
APInt::APInt(uint32_t numbits, const char StrStart[], uint32_t slen,
uint8_t radix)
: BitWidth(numbits), VAL(0) {
fromString(numbits, StrStart, slen, radix);
}
APInt::APInt(uint32_t numbits, const std::string& Val, uint8_t radix)
: BitWidth(numbits), VAL(0) {
assert(!Val.empty() && "String empty?");
fromString(numbits, Val.c_str(), Val.size(), radix);
}
APInt::APInt(const APInt& that)
: BitWidth(that.BitWidth), VAL(0) {
if (isSingleWord())
VAL = that.VAL;
else {
pVal = getMemory(getNumWords());
memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE);
}
}
APInt::~APInt() {
if (!isSingleWord() && pVal)
delete [] pVal;
}
APInt& APInt::operator=(const APInt& RHS) {
// Don't do anything for X = X
if (this == &RHS)
return *this;
// If the bitwidths are the same, we can avoid mucking with memory
if (BitWidth == RHS.getBitWidth()) {
if (isSingleWord())
VAL = RHS.VAL;
else
memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE);
return *this;
}
if (isSingleWord())
if (RHS.isSingleWord())
VAL = RHS.VAL;
else {
VAL = 0;
pVal = getMemory(RHS.getNumWords());
memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
}
else if (getNumWords() == RHS.getNumWords())
memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
else if (RHS.isSingleWord()) {
delete [] pVal;
VAL = RHS.VAL;
} else {
delete [] pVal;
pVal = getMemory(RHS.getNumWords());
memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
}
BitWidth = RHS.BitWidth;
return clearUnusedBits();
}
APInt& APInt::operator=(uint64_t RHS) {
if (isSingleWord())
VAL = RHS;
else {
pVal[0] = RHS;
memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE);
}
return clearUnusedBits();
}
/// add_1 - This function adds a single "digit" integer, y, to the multiple
/// "digit" integer array, x[]. x[] is modified to reflect the addition and
/// 1 is returned if there is a carry out, otherwise 0 is returned.
/// @returns the carry of the addition.
static bool add_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
for (uint32_t i = 0; i < len; ++i) {
dest[i] = y + x[i];
if (dest[i] < y)
y = 1; // Carry one to next digit.
else {
y = 0; // No need to carry so exit early
break;
}
}
return y;
}
/// @brief Prefix increment operator. Increments the APInt by one.
APInt& APInt::operator++() {
if (isSingleWord())
++VAL;
else
add_1(pVal, pVal, getNumWords(), 1);
return clearUnusedBits();
}
/// sub_1 - This function subtracts a single "digit" (64-bit word), y, from
/// the multi-digit integer array, x[], propagating the borrowed 1 value until
/// no further borrowing is neeeded or it runs out of "digits" in x. The result
/// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted.
/// In other words, if y > x then this function returns 1, otherwise 0.
/// @returns the borrow out of the subtraction
static bool sub_1(uint64_t x[], uint32_t len, uint64_t y) {
for (uint32_t i = 0; i < len; ++i) {
uint64_t X = x[i];
x[i] -= y;
if (y > X)
y = 1; // We have to "borrow 1" from next "digit"
else {
y = 0; // No need to borrow
break; // Remaining digits are unchanged so exit early
}
}
return bool(y);
}
/// @brief Prefix decrement operator. Decrements the APInt by one.
APInt& APInt::operator--() {
if (isSingleWord())
--VAL;
else
sub_1(pVal, getNumWords(), 1);
return clearUnusedBits();
}
/// add - This function adds the integer array x to the integer array Y and
/// places the result in dest.
/// @returns the carry out from the addition
/// @brief General addition of 64-bit integer arrays
static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y,
uint32_t len) {
bool carry = false;
for (uint32_t i = 0; i< len; ++i) {
uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x
dest[i] = x[i] + y[i] + carry;
carry = dest[i] < limit || (carry && dest[i] == limit);
}
return carry;
}
/// Adds the RHS APint to this APInt.
/// @returns this, after addition of RHS.
/// @brief Addition assignment operator.
APInt& APInt::operator+=(const APInt& RHS) {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord())
VAL += RHS.VAL;
else {
add(pVal, pVal, RHS.pVal, getNumWords());
}
return clearUnusedBits();
}
/// Subtracts the integer array y from the integer array x
/// @returns returns the borrow out.
/// @brief Generalized subtraction of 64-bit integer arrays.
static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y,
uint32_t len) {
bool borrow = false;
for (uint32_t i = 0; i < len; ++i) {
uint64_t x_tmp = borrow ? x[i] - 1 : x[i];
borrow = y[i] > x_tmp || (borrow && x[i] == 0);
dest[i] = x_tmp - y[i];
}
return borrow;
}
/// Subtracts the RHS APInt from this APInt
/// @returns this, after subtraction
/// @brief Subtraction assignment operator.
APInt& APInt::operator-=(const APInt& RHS) {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord())
VAL -= RHS.VAL;
else
sub(pVal, pVal, RHS.pVal, getNumWords());
return clearUnusedBits();
}
/// Multiplies an integer array, x by a a uint64_t integer and places the result
/// into dest.
/// @returns the carry out of the multiplication.
/// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer.
static uint64_t mul_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
// Split y into high 32-bit part (hy) and low 32-bit part (ly)
uint64_t ly = y & 0xffffffffULL, hy = y >> 32;
uint64_t carry = 0;
// For each digit of x.
for (uint32_t i = 0; i < len; ++i) {
// Split x into high and low words
uint64_t lx = x[i] & 0xffffffffULL;
uint64_t hx = x[i] >> 32;
// hasCarry - A flag to indicate if there is a carry to the next digit.
// hasCarry == 0, no carry
// hasCarry == 1, has carry
// hasCarry == 2, no carry and the calculation result == 0.
uint8_t hasCarry = 0;
dest[i] = carry + lx * ly;
// Determine if the add above introduces carry.
hasCarry = (dest[i] < carry) ? 1 : 0;
carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0);
// The upper limit of carry can be (2^32 - 1)(2^32 - 1) +
// (2^32 - 1) + 2^32 = 2^64.
hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
carry += (lx * hy) & 0xffffffffULL;
dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL);
carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) +
(carry >> 32) + ((lx * hy) >> 32) + hx * hy;
}
return carry;
}
/// Multiplies integer array x by integer array y and stores the result into
/// the integer array dest. Note that dest's size must be >= xlen + ylen.
/// @brief Generalized multiplicate of integer arrays.
static void mul(uint64_t dest[], uint64_t x[], uint32_t xlen, uint64_t y[],
uint32_t ylen) {
dest[xlen] = mul_1(dest, x, xlen, y[0]);
for (uint32_t i = 1; i < ylen; ++i) {
uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32;
uint64_t carry = 0, lx = 0, hx = 0;
for (uint32_t j = 0; j < xlen; ++j) {
lx = x[j] & 0xffffffffULL;
hx = x[j] >> 32;
// hasCarry - A flag to indicate if has carry.
// hasCarry == 0, no carry
// hasCarry == 1, has carry
// hasCarry == 2, no carry and the calculation result == 0.
uint8_t hasCarry = 0;
uint64_t resul = carry + lx * ly;
hasCarry = (resul < carry) ? 1 : 0;
carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32);
hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
carry += (lx * hy) & 0xffffffffULL;
resul = (carry << 32) | (resul & 0xffffffffULL);
dest[i+j] += resul;
carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+
(carry >> 32) + (dest[i+j] < resul ? 1 : 0) +
((lx * hy) >> 32) + hx * hy;
}
dest[i+xlen] = carry;
}
}
APInt& APInt::operator*=(const APInt& RHS) {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord()) {
VAL *= RHS.VAL;
clearUnusedBits();
return *this;
}
// Get some bit facts about LHS and check for zero
uint32_t lhsBits = getActiveBits();
uint32_t lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1;
if (!lhsWords)
// 0 * X ===> 0
return *this;
// Get some bit facts about RHS and check for zero
uint32_t rhsBits = RHS.getActiveBits();
uint32_t rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1;
if (!rhsWords) {
// X * 0 ===> 0
clear();
return *this;
}
// Allocate space for the result
uint32_t destWords = rhsWords + lhsWords;
uint64_t *dest = getMemory(destWords);
// Perform the long multiply
mul(dest, pVal, lhsWords, RHS.pVal, rhsWords);
// Copy result back into *this
clear();
uint32_t wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords;
memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE);
// delete dest array and return
delete[] dest;
return *this;
}
APInt& APInt::operator&=(const APInt& RHS) {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord()) {
VAL &= RHS.VAL;
return *this;
}
uint32_t numWords = getNumWords();
for (uint32_t i = 0; i < numWords; ++i)
pVal[i] &= RHS.pVal[i];
return *this;
}
APInt& APInt::operator|=(const APInt& RHS) {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord()) {
VAL |= RHS.VAL;
return *this;
}
uint32_t numWords = getNumWords();
for (uint32_t i = 0; i < numWords; ++i)
pVal[i] |= RHS.pVal[i];
return *this;
}
APInt& APInt::operator^=(const APInt& RHS) {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord()) {
VAL ^= RHS.VAL;
this->clearUnusedBits();
return *this;
}
uint32_t numWords = getNumWords();
for (uint32_t i = 0; i < numWords; ++i)
pVal[i] ^= RHS.pVal[i];
return clearUnusedBits();
}
APInt APInt::operator&(const APInt& RHS) const {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord())
return APInt(getBitWidth(), VAL & RHS.VAL);
uint32_t numWords = getNumWords();
uint64_t* val = getMemory(numWords);
for (uint32_t i = 0; i < numWords; ++i)
val[i] = pVal[i] & RHS.pVal[i];
return APInt(val, getBitWidth());
}
APInt APInt::operator|(const APInt& RHS) const {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord())
return APInt(getBitWidth(), VAL | RHS.VAL);
uint32_t numWords = getNumWords();
uint64_t *val = getMemory(numWords);
for (uint32_t i = 0; i < numWords; ++i)
val[i] = pVal[i] | RHS.pVal[i];
return APInt(val, getBitWidth());
}
APInt APInt::operator^(const APInt& RHS) const {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord())
return APInt(BitWidth, VAL ^ RHS.VAL);
uint32_t numWords = getNumWords();
uint64_t *val = getMemory(numWords);
for (uint32_t i = 0; i < numWords; ++i)
val[i] = pVal[i] ^ RHS.pVal[i];
// 0^0==1 so clear the high bits in case they got set.
return APInt(val, getBitWidth()).clearUnusedBits();
}
bool APInt::operator !() const {
if (isSingleWord())
return !VAL;
for (uint32_t i = 0; i < getNumWords(); ++i)
if (pVal[i])
return false;
return true;
}
APInt APInt::operator*(const APInt& RHS) const {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord())
return APInt(BitWidth, VAL * RHS.VAL);
APInt Result(*this);
Result *= RHS;
return Result.clearUnusedBits();
}
APInt APInt::operator+(const APInt& RHS) const {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord())
return APInt(BitWidth, VAL + RHS.VAL);
APInt Result(BitWidth, 0);
add(Result.pVal, this->pVal, RHS.pVal, getNumWords());
return Result.clearUnusedBits();
}
APInt APInt::operator-(const APInt& RHS) const {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord())
return APInt(BitWidth, VAL - RHS.VAL);
APInt Result(BitWidth, 0);
sub(Result.pVal, this->pVal, RHS.pVal, getNumWords());
return Result.clearUnusedBits();
}
bool APInt::operator[](uint32_t bitPosition) const {
return (maskBit(bitPosition) &
(isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0;
}
bool APInt::operator==(const APInt& RHS) const {
assert(BitWidth == RHS.BitWidth && "Comparison requires equal bit widths");
if (isSingleWord())
return VAL == RHS.VAL;
// Get some facts about the number of bits used in the two operands.
uint32_t n1 = getActiveBits();
uint32_t n2 = RHS.getActiveBits();
// If the number of bits isn't the same, they aren't equal
if (n1 != n2)
return false;
// If the number of bits fits in a word, we only need to compare the low word.
if (n1 <= APINT_BITS_PER_WORD)
return pVal[0] == RHS.pVal[0];
// Otherwise, compare everything
for (int i = whichWord(n1 - 1); i >= 0; --i)
if (pVal[i] != RHS.pVal[i])
return false;
return true;
}
bool APInt::operator==(uint64_t Val) const {
if (isSingleWord())
return VAL == Val;
uint32_t n = getActiveBits();
if (n <= APINT_BITS_PER_WORD)
return pVal[0] == Val;
else
return false;
}
bool APInt::ult(const APInt& RHS) const {
assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
if (isSingleWord())
return VAL < RHS.VAL;
// Get active bit length of both operands
uint32_t n1 = getActiveBits();
uint32_t n2 = RHS.getActiveBits();
// If magnitude of LHS is less than RHS, return true.
if (n1 < n2)
return true;
// If magnitude of RHS is greather than LHS, return false.
if (n2 < n1)
return false;
// If they bot fit in a word, just compare the low order word
if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD)
return pVal[0] < RHS.pVal[0];
// Otherwise, compare all words
uint32_t topWord = whichWord(std::max(n1,n2)-1);
for (int i = topWord; i >= 0; --i) {
if (pVal[i] > RHS.pVal[i])
return false;
if (pVal[i] < RHS.pVal[i])
return true;
}
return false;
}
bool APInt::slt(const APInt& RHS) const {
assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
if (isSingleWord()) {
int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth);
return lhsSext < rhsSext;
}
APInt lhs(*this);
APInt rhs(RHS);
bool lhsNeg = isNegative();
bool rhsNeg = rhs.isNegative();
if (lhsNeg) {
// Sign bit is set so perform two's complement to make it positive
lhs.flip();
lhs++;
}
if (rhsNeg) {
// Sign bit is set so perform two's complement to make it positive
rhs.flip();
rhs++;
}
// Now we have unsigned values to compare so do the comparison if necessary
// based on the negativeness of the values.
if (lhsNeg)
if (rhsNeg)
return lhs.ugt(rhs);
else
return true;
else if (rhsNeg)
return false;
else
return lhs.ult(rhs);
}
APInt& APInt::set(uint32_t bitPosition) {
if (isSingleWord())
VAL |= maskBit(bitPosition);
else
pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
return *this;
}
APInt& APInt::set() {
if (isSingleWord()) {
VAL = -1ULL;
return clearUnusedBits();
}
// Set all the bits in all the words.
for (uint32_t i = 0; i < getNumWords(); ++i)
pVal[i] = -1ULL;
// Clear the unused ones
return clearUnusedBits();
}
/// Set the given bit to 0 whose position is given as "bitPosition".
/// @brief Set a given bit to 0.
APInt& APInt::clear(uint32_t bitPosition) {
if (isSingleWord())
VAL &= ~maskBit(bitPosition);
else
pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
return *this;
}
/// @brief Set every bit to 0.
APInt& APInt::clear() {
if (isSingleWord())
VAL = 0;
else
memset(pVal, 0, getNumWords() * APINT_WORD_SIZE);
return *this;
}
/// @brief Bitwise NOT operator. Performs a bitwise logical NOT operation on
/// this APInt.
APInt APInt::operator~() const {
APInt Result(*this);
Result.flip();
return Result;
}
/// @brief Toggle every bit to its opposite value.
APInt& APInt::flip() {
if (isSingleWord()) {
VAL ^= -1ULL;
return clearUnusedBits();
}
for (uint32_t i = 0; i < getNumWords(); ++i)
pVal[i] ^= -1ULL;
return clearUnusedBits();
}
/// Toggle a given bit to its opposite value whose position is given
/// as "bitPosition".
/// @brief Toggles a given bit to its opposite value.
APInt& APInt::flip(uint32_t bitPosition) {
assert(bitPosition < BitWidth && "Out of the bit-width range!");
if ((*this)[bitPosition]) clear(bitPosition);
else set(bitPosition);
return *this;
}
uint32_t APInt::getBitsNeeded(const char* str, uint32_t slen, uint8_t radix) {
assert(str != 0 && "Invalid value string");
assert(slen > 0 && "Invalid string length");
// Each computation below needs to know if its negative
uint32_t isNegative = str[0] == '-';
if (isNegative) {
slen--;
str++;
}
// 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;
// Otherwise it must be radix == 10, the hard case
assert(radix == 10 && "Invalid radix");
// 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.
uint32_t sufficient = slen*64/18;
// Convert to the actual binary value.
APInt tmp(sufficient, str, slen, radix);
// Compute how many bits are required.
return isNegative + tmp.logBase2() + 1;
}
uint64_t APInt::getHashValue() const {
// Put the bit width into the low order bits.
uint64_t hash = BitWidth;
// Add the sum of the words to the hash.
if (isSingleWord())
hash += VAL << 6; // clear separation of up to 64 bits
else
for (uint32_t i = 0; i < getNumWords(); ++i)
hash += pVal[i] << 6; // clear sepration of up to 64 bits
return hash;
}
/// HiBits - This function returns the high "numBits" bits of this APInt.
APInt APInt::getHiBits(uint32_t numBits) const {
return APIntOps::lshr(*this, BitWidth - numBits);
}
/// LoBits - This function returns the low "numBits" bits of this APInt.
APInt APInt::getLoBits(uint32_t numBits) const {
return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
BitWidth - numBits);
}
bool APInt::isPowerOf2() const {
return (!!*this) && !(*this & (*this - APInt(BitWidth,1)));
}
uint32_t APInt::countLeadingZeros() const {
uint32_t Count = 0;
if (isSingleWord())
Count = CountLeadingZeros_64(VAL);
else {
for (uint32_t i = getNumWords(); i > 0u; --i) {
if (pVal[i-1] == 0)
Count += APINT_BITS_PER_WORD;
else {
Count += CountLeadingZeros_64(pVal[i-1]);
break;
}
}
}
uint32_t remainder = BitWidth % APINT_BITS_PER_WORD;
if (remainder)
Count -= APINT_BITS_PER_WORD - remainder;
return Count;
}
static uint32_t countLeadingOnes_64(uint64_t V, uint32_t skip) {
uint32_t Count = 0;
if (skip)
V <<= skip;
while (V && (V & (1ULL << 63))) {
Count++;
V <<= 1;
}
return Count;
}
uint32_t APInt::countLeadingOnes() const {
if (isSingleWord())
return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth);
uint32_t highWordBits = BitWidth % APINT_BITS_PER_WORD;
uint32_t shift = (highWordBits == 0 ? 0 : APINT_BITS_PER_WORD - highWordBits);
int i = getNumWords() - 1;
uint32_t Count = countLeadingOnes_64(pVal[i], shift);
if (Count == highWordBits) {
for (i--; i >= 0; --i) {
if (pVal[i] == -1ULL)
Count += APINT_BITS_PER_WORD;
else {
Count += countLeadingOnes_64(pVal[i], 0);
break;
}
}
}
return Count;
}
uint32_t APInt::countTrailingZeros() const {
if (isSingleWord())
return CountTrailingZeros_64(VAL);
uint32_t Count = 0;
uint32_t i = 0;
for (; i < getNumWords() && pVal[i] == 0; ++i)
Count += APINT_BITS_PER_WORD;
if (i < getNumWords())
Count += CountTrailingZeros_64(pVal[i]);
return Count;
}
uint32_t APInt::countPopulation() const {
if (isSingleWord())
return CountPopulation_64(VAL);
uint32_t Count = 0;
for (uint32_t i = 0; i < getNumWords(); ++i)
Count += CountPopulation_64(pVal[i]);
return Count;
}
APInt APInt::byteSwap() const {
assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
if (BitWidth == 16)
return APInt(BitWidth, ByteSwap_16(uint16_t(VAL)));
else if (BitWidth == 32)
return APInt(BitWidth, ByteSwap_32(uint32_t(VAL)));
else if (BitWidth == 48) {
uint32_t Tmp1 = uint32_t(VAL >> 16);
Tmp1 = ByteSwap_32(Tmp1);
uint16_t Tmp2 = uint16_t(VAL);
Tmp2 = ByteSwap_16(Tmp2);
return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1);
} else if (BitWidth == 64)
return APInt(BitWidth, ByteSwap_64(VAL));
else {
APInt Result(BitWidth, 0);
char *pByte = (char*)Result.pVal;
for (uint32_t i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) {
char Tmp = pByte[i];
pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i];
pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp;
}
return Result;
}
}
APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
const APInt& API2) {
APInt A = API1, B = API2;
while (!!B) {
APInt T = B;
B = APIntOps::urem(A, B);
A = T;
}
return A;
}
APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, uint32_t width) {
union {
double D;
uint64_t I;
} T;
T.D = Double;
// Get the sign bit from the highest order bit
bool isNeg = T.I >> 63;
// Get the 11-bit exponent and adjust for the 1023 bit bias
int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
// If the exponent is negative, the value is < 0 so just return 0.
if (exp < 0)
return APInt(width, 0u);
// Extract the mantissa by clearing the top 12 bits (sign + exponent).
uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
// If the exponent doesn't shift all bits out of the mantissa
if (exp < 52)
return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
APInt(width, mantissa >> (52 - exp));
// If the client didn't provide enough bits for us to shift the mantissa into
// then the result is undefined, just return 0
if (width <= exp - 52)
return APInt(width, 0);
// Otherwise, we have to shift the mantissa bits up to the right location
APInt Tmp(width, mantissa);
Tmp = Tmp.shl(exp - 52);
return isNeg ? -Tmp : Tmp;
}
/// RoundToDouble - This function convert 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.
if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
if (isSigned) {
int64_t sext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
return double(sext);
} else
return double(VAL);
}
// 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.
uint32_t n = Tmp.getActiveBits();
// The exponent (without bias normalization) is just the number of bits
// we are using. Note that the sign bit is gone since we constructed the
// absolute value.
uint64_t exp = n;
// Return infinity for exponent overflow
if (exp > 1023) {
if (!isSigned || !isNeg)
return std::numeric_limits<double>::infinity();
else
return -std::numeric_limits<double>::infinity();
}
exp += 1023; // Increment for 1023 bias
// Number of bits in mantissa is 52. To obtain the mantissa value, we must
// extract the high 52 bits from the correct words in pVal.
uint64_t mantissa;
unsigned hiWord = whichWord(n-1);
if (hiWord == 0) {
mantissa = Tmp.pVal[0];
if (n > 52)
mantissa >>= n - 52; // shift down, we want the top 52 bits.
} else {
assert(hiWord > 0 && "huh?");
uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
mantissa = hibits | lobits;
}
// The leading bit of mantissa is implicit, so get rid of it.
uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
union {
double D;
uint64_t I;
} T;
T.I = sign | (exp << 52) | mantissa;
return T.D;
}
// Truncate to new width.
APInt &APInt::trunc(uint32_t width) {
assert(width < BitWidth && "Invalid APInt Truncate request");
assert(width >= IntegerType::MIN_INT_BITS && "Can't truncate to 0 bits");
uint32_t wordsBefore = getNumWords();
BitWidth = width;
uint32_t wordsAfter = getNumWords();
if (wordsBefore != wordsAfter) {
if (wordsAfter == 1) {
uint64_t *tmp = pVal;
VAL = pVal[0];
delete [] tmp;
} else {
uint64_t *newVal = getClearedMemory(wordsAfter);
for (uint32_t i = 0; i < wordsAfter; ++i)
newVal[i] = pVal[i];
delete [] pVal;
pVal = newVal;
}
}
return clearUnusedBits();
}
// Sign extend to a new width.
APInt &APInt::sext(uint32_t width) {
assert(width > BitWidth && "Invalid APInt SignExtend request");
assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
// If the sign bit isn't set, this is the same as zext.
if (!isNegative()) {
zext(width);
return *this;
}
// The sign bit is set. First, get some facts
uint32_t wordsBefore = getNumWords();
uint32_t wordBits = BitWidth % APINT_BITS_PER_WORD;
BitWidth = width;
uint32_t wordsAfter = getNumWords();
// Mask the high order word appropriately
if (wordsBefore == wordsAfter) {
uint32_t newWordBits = width % APINT_BITS_PER_WORD;
// The extension is contained to the wordsBefore-1th word.
uint64_t mask = ~0ULL;
if (newWordBits)
mask >>= APINT_BITS_PER_WORD - newWordBits;
mask <<= wordBits;
if (wordsBefore == 1)
VAL |= mask;
else
pVal[wordsBefore-1] |= mask;
return clearUnusedBits();
}
uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits;
uint64_t *newVal = getMemory(wordsAfter);
if (wordsBefore == 1)
newVal[0] = VAL | mask;
else {
for (uint32_t i = 0; i < wordsBefore; ++i)
newVal[i] = pVal[i];
newVal[wordsBefore-1] |= mask;
}
for (uint32_t i = wordsBefore; i < wordsAfter; i++)
newVal[i] = -1ULL;
if (wordsBefore != 1)
delete [] pVal;
pVal = newVal;
return clearUnusedBits();
}
// Zero extend to a new width.
APInt &APInt::zext(uint32_t width) {
assert(width > BitWidth && "Invalid APInt ZeroExtend request");
assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
uint32_t wordsBefore = getNumWords();
BitWidth = width;
uint32_t wordsAfter = getNumWords();
if (wordsBefore != wordsAfter) {
uint64_t *newVal = getClearedMemory(wordsAfter);
if (wordsBefore == 1)
newVal[0] = VAL;
else
for (uint32_t i = 0; i < wordsBefore; ++i)
newVal[i] = pVal[i];
if (wordsBefore != 1)
delete [] pVal;
pVal = newVal;
}
return *this;
}
APInt &APInt::zextOrTrunc(uint32_t width) {
if (BitWidth < width)
return zext(width);
if (BitWidth > width)
return trunc(width);
return *this;
}
APInt &APInt::sextOrTrunc(uint32_t width) {
if (BitWidth < width)
return sext(width);
if (BitWidth > width)
return trunc(width);
return *this;
}
/// Arithmetic right-shift this APInt by shiftAmt.
/// @brief Arithmetic right-shift function.
APInt APInt::ashr(uint32_t shiftAmt) const {
assert(shiftAmt <= BitWidth && "Invalid shift amount");
// Handle a degenerate case
if (shiftAmt == 0)
return *this;
// Handle single word shifts with built-in ashr
if (isSingleWord()) {
if (shiftAmt == BitWidth)
return APInt(BitWidth, 0); // undefined
else {
uint32_t SignBit = APINT_BITS_PER_WORD - BitWidth;
return APInt(BitWidth,
(((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
}
}
// If all the bits were shifted out, the result is, technically, undefined.
// We return -1 if it was negative, 0 otherwise. We check this early to avoid
// issues in the algorithm below.
if (shiftAmt == BitWidth)
if (isNegative())
return APInt(BitWidth, -1ULL);
else
return APInt(BitWidth, 0);
// Create some space for the result.
uint64_t * val = new uint64_t[getNumWords()];
// Compute some values needed by the following shift algorithms
uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word
uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift
uint32_t breakWord = getNumWords() - 1 - offset; // last word affected
uint32_t bitsInWord = whichBit(BitWidth); // how many bits in last word?
if (bitsInWord == 0)
bitsInWord = APINT_BITS_PER_WORD;
// If we are shifting whole words, just move whole words
if (wordShift == 0) {
// Move the words containing significant bits
for (uint32_t i = 0; i <= breakWord; ++i)
val[i] = pVal[i+offset]; // move whole word
// Adjust the top significant word for sign bit fill, if negative
if (isNegative())
if (bitsInWord < APINT_BITS_PER_WORD)
val[breakWord] |= ~0ULL << bitsInWord; // set high bits
} else {
// Shift the low order words
for (uint32_t i = 0; i < breakWord; ++i) {
// This combines the shifted corresponding word with the low bits from
// the next word (shifted into this word's high bits).
val[i] = (pVal[i+offset] >> wordShift) |
(pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
}
// Shift the break word. In this case there are no bits from the next word
// to include in this word.
val[breakWord] = pVal[breakWord+offset] >> wordShift;
// Deal with sign extenstion in the break word, and possibly the word before
// it.
if (isNegative())
if (wordShift > bitsInWord) {
if (breakWord > 0)
val[breakWord-1] |=
~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord));
val[breakWord] |= ~0ULL;
} else
val[breakWord] |= (~0ULL << (bitsInWord - wordShift));
}
// Remaining words are 0 or -1, just assign them.
uint64_t fillValue = (isNegative() ? -1ULL : 0);
for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
val[i] = fillValue;
return APInt(val, BitWidth).clearUnusedBits();
}
/// Logical right-shift this APInt by shiftAmt.
/// @brief Logical right-shift function.
APInt APInt::lshr(uint32_t shiftAmt) const {
if (isSingleWord())
if (shiftAmt == BitWidth)
return APInt(BitWidth, 0);
else
return APInt(BitWidth, this->VAL >> shiftAmt);
// If all the bits were shifted out, the result is 0. This avoids issues
// with shifting by the size of the integer type, which produces undefined
// results. We define these "undefined results" to always be 0.
if (shiftAmt == BitWidth)
return APInt(BitWidth, 0);
// Create some space for the result.
uint64_t * val = new uint64_t[getNumWords()];
// If we are shifting less than a word, compute the shift with a simple carry
if (shiftAmt < APINT_BITS_PER_WORD) {
uint64_t carry = 0;
for (int i = getNumWords()-1; i >= 0; --i) {
val[i] = (pVal[i] >> shiftAmt) | carry;
carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
}
return APInt(val, BitWidth).clearUnusedBits();
}
// Compute some values needed by the remaining shift algorithms
uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
// If we are shifting whole words, just move whole words
if (wordShift == 0) {
for (uint32_t i = 0; i < getNumWords() - offset; ++i)
val[i] = pVal[i+offset];
for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
val[i] = 0;
return APInt(val,BitWidth).clearUnusedBits();
}
// Shift the low order words
uint32_t breakWord = getNumWords() - offset -1;
for (uint32_t i = 0; i < breakWord; ++i)
val[i] = (pVal[i+offset] >> wordShift) |
(pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
// Shift the break word.
val[breakWord] = pVal[breakWord+offset] >> wordShift;
// Remaining words are 0
for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
val[i] = 0;
return APInt(val, BitWidth).clearUnusedBits();
}
/// Left-shift this APInt by shiftAmt.
/// @brief Left-shift function.
APInt APInt::shl(uint32_t shiftAmt) const {
assert(shiftAmt <= BitWidth && "Invalid shift amount");
if (isSingleWord()) {
if (shiftAmt == BitWidth)
return APInt(BitWidth, 0); // avoid undefined shift results
return APInt(BitWidth, VAL << shiftAmt);
}
// If all the bits were shifted out, the result is 0. This avoids issues
// with shifting by the size of the integer type, which produces undefined
// results. We define these "undefined results" to always be 0.
if (shiftAmt == BitWidth)
return APInt(BitWidth, 0);
// Create some space for the result.
uint64_t * val = new uint64_t[getNumWords()];
// If we are shifting less than a word, do it the easy way
if (shiftAmt < APINT_BITS_PER_WORD) {
uint64_t carry = 0;
for (uint32_t i = 0; i < getNumWords(); i++) {
val[i] = pVal[i] << shiftAmt | carry;
carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
}
return APInt(val, BitWidth).clearUnusedBits();
}
// Compute some values needed by the remaining shift algorithms
uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
// If we are shifting whole words, just move whole words
if (wordShift == 0) {
for (uint32_t i = 0; i < offset; i++)
val[i] = 0;
for (uint32_t i = offset; i < getNumWords(); i++)
val[i] = pVal[i-offset];
return APInt(val,BitWidth).clearUnusedBits();
}
// Copy whole words from this to Result.
uint32_t i = getNumWords() - 1;
for (; i > offset; --i)
val[i] = pVal[i-offset] << wordShift |
pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
val[offset] = pVal[0] << wordShift;
for (i = 0; i < offset; ++i)
val[i] = 0;
return APInt(val, BitWidth).clearUnusedBits();
}
// 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.
uint32_t magnitude = getActiveBits();
// Use a fast table for some small values. This also gets rid of some
// rounding errors in libc sqrt for small values.
if (magnitude <= 5) {
static const uint8_t results[32] = {
/* 0 */ 0,
/* 1- 2 */ 1, 1,
/* 3- 6 */ 2, 2, 2, 2,
/* 7-12 */ 3, 3, 3, 3, 3, 3,
/* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
/* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
/* 31 */ 6
};
return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]);
}
// If the magnitude of the value fits in less than 52 bits (the precision of
// an IEEE double precision floating point value), then we can use the
// libc sqrt function which will probably use a hardware sqrt computation.
// This should be faster than the algorithm below.
if (magnitude < 52) {
#ifdef _MSC_VER
// Amazingly, VC++ doesn't have round().
return APInt(BitWidth,
uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0]))) + 0.5);
#else
return APInt(BitWidth,
uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0])))));
#endif
}
// Okay, all the short cuts are exhausted. We must compute it. The following
// is a classical Babylonian method for computing the square root. This code
// was adapted to APINt from a wikipedia article on such computations.
// See http://www.wikipedia.org/ and go to the page named
// Calculate_an_integer_square_root.
uint32_t 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;
else if (this->ule(nextSquare)) {
APInt midpoint((nextSquare - square).udiv(two));
APInt offset(*this - square);
if (offset.ult(midpoint))
return x_old;
else
return x_old + 1;
} else
assert(0 && "Error in APInt::sqrt computation");
return x_old + 1;
}
/// 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,
uint32_t m, uint32_t n) {
assert(u && "Must provide dividend");
assert(v && "Must provide divisor");
assert(q && "Must provide quotient");
assert(u != v && u != q && v != q && "Must us different memory");
assert(n>1 && "n must be > 1");
// Knuth uses the value b as the base of the number system. In our case b
// is 2^31 so we just set it to -1u.
uint64_t b = uint64_t(1) << 32;
DEBUG(cerr << "KnuthDiv: m=" << m << " n=" << n << '\n');
DEBUG(cerr << "KnuthDiv: original:");
DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
DEBUG(cerr << " by");
DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
DEBUG(cerr << '\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.
uint32_t shift = CountLeadingZeros_32(v[n-1]);
uint32_t v_carry = 0;
uint32_t u_carry = 0;
if (shift) {
for (uint32_t 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 (uint32_t 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(cerr << "KnuthDiv: normal:");
DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
DEBUG(cerr << " by");
DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
DEBUG(cerr << '\n');
// D2. [Initialize j.] Set j to m. This is the loop counter over the places.
int j = m;
do {
DEBUG(cerr << "KnuthDiv: quotient digit #" << j << '\n');
// D3. [Calculate q'.].
// Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
// Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
// Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
// qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
// on v[n-2] determines at high speed most of the cases in which the trial
// value qp is one too large, and it eliminates all cases where qp is two
// too large.
uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
DEBUG(cerr << "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(cerr << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
// D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
// (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
// consists of a simple multiplication by a one-place number, combined with
// a subtraction.
bool isNeg = false;
for (uint32_t i = 0; i < n; ++i) {
uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
bool borrow = subtrahend > u_tmp;
DEBUG(cerr << "KnuthDiv: u_tmp == " << u_tmp
<< ", subtrahend == " << subtrahend
<< ", borrow = " << borrow << '\n');
uint64_t result = u_tmp - subtrahend;
uint32_t k = j + i;
u[k++] = result & (b-1); // subtract low word
u[k++] = result >> 32; // subtract high word
while (borrow && k <= m+n) { // deal with borrow to the left
borrow = u[k] == 0;
u[k]--;
k++;
}
isNeg |= borrow;
DEBUG(cerr << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
u[j+i+1] << '\n');
}
DEBUG(cerr << "KnuthDiv: after subtraction:");
DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
DEBUG(cerr << '\n');
// The digits (u[j+n]...u[j]) should be kept positive; if the result of
// this step is actually negative, (u[j+n]...u[j]) should be left as the
// true value plus b**(n+1), namely as the b's complement of
// the true value, and a "borrow" to the left should be remembered.
//
if (isNeg) {
bool carry = true; // true because b's complement is "complement + 1"
for (uint32_t i = 0; i <= m+n; ++i) {
u[i] = ~u[i] + carry; // b's complement
carry = carry && u[i] == 0;
}
}
DEBUG(cerr << "KnuthDiv: after complement:");
DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
DEBUG(cerr << '\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] = 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 (uint32_t 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(cerr << "KnuthDiv: after correction:");
DEBUG(for (int i = m+n; i >=0; i--) cerr <<" " << u[i]);
DEBUG(cerr << "\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(cerr << "KnuthDiv: quotient:");
DEBUG(for (int i = m; i >=0; i--) cerr <<" " << q[i]);
DEBUG(cerr << '\n');
// D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
// remainder may be obtained by dividing u[...] by d. If r is non-null we
// compute the remainder (urem uses this).
if (r) {
// The value d is expressed by the "shift" value above since we avoided
// multiplication by d by using a shift left. So, all we have to do is
// shift right here. In order to mak
if (shift) {
uint32_t carry = 0;
DEBUG(cerr << "KnuthDiv: remainder:");
for (int i = n-1; i >= 0; i--) {
r[i] = (u[i] >> shift) | carry;
carry = u[i] << (32 - shift);
DEBUG(cerr << " " << r[i]);
}
} else {
for (int i = n-1; i >= 0; i--) {
r[i] = u[i];
DEBUG(cerr << " " << r[i]);
}
}
DEBUG(cerr << '\n');
}
DEBUG(cerr << std::setbase(10) << '\n');
}
void APInt::divide(const APInt LHS, uint32_t lhsWords,
const APInt &RHS, uint32_t rhsWords,
APInt *Quotient, APInt *Remainder)
{
assert(lhsWords >= rhsWords && "Fractional result");
// First, compose the values into an array of 32-bit words instead of
// 64-bit words. This is a necessity of both the "short division" algorithm
// and the 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. Furthremore, casting the 64-bit values to 32-bit values won't
// work on large-endian machines.
uint64_t mask = ~0ull >> (sizeof(uint32_t)*8);
uint32_t n = rhsWords * 2;
uint32_t 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 = 0;
uint32_t *V = 0;
uint32_t *Q = 0;
uint32_t *R = 0;
if ((Remainder?4:3)*n+2*m+1 <= 128) {
U = &SPACE[0];
V = &SPACE[m+n+1];
Q = &SPACE[(m+n+1) + n];
if (Remainder)
R = &SPACE[(m+n+1) + n + (m+n)];
} else {
U = new 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.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
U[i * 2] = tmp & mask;
U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
}
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.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
V[i * 2] = tmp & mask;
V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
}
// 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+n-1; i >= 0; i--) {
uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
if (partial_dividend == 0) {
Q[i] = 0;
remainder = 0;
} else if (partial_dividend < divisor) {
Q[i] = 0;
remainder = partial_dividend;
} else if (partial_dividend == divisor) {
Q[i] = 1;
remainder = 0;
} else {
Q[i] = partial_dividend / divisor;
remainder = partial_dividend - (Q[i] * divisor);
}
}
if (R)
R[0] = remainder;
} else {
// Now we're ready to invoke the Knuth classical divide algorithm. In this
// case n > 1.
KnuthDiv(U, V, Q, R, m, n);
}
// If the caller wants the quotient
if (Quotient) {
// Set up the Quotient value's memory.
if (Quotient->BitWidth != LHS.BitWidth) {
if (Quotient->isSingleWord())
Quotient->VAL = 0;
else
delete [] Quotient->pVal;
Quotient->BitWidth = LHS.BitWidth;
if (!Quotient->isSingleWord())
Quotient->pVal = getClearedMemory(Quotient->getNumWords());
} else
Quotient->clear();
// The quotient is in Q. Reconstitute the quotient into Quotient's low
// order words.
if (lhsWords == 1) {
uint64_t tmp =
uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
if (Quotient->isSingleWord())
Quotient->VAL = tmp;
else
Quotient->pVal[0] = tmp;
} else {
assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
for (unsigned i = 0; i < lhsWords; ++i)
Quotient->pVal[i] =
uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
}
}
// If the caller wants the remainder
if (Remainder) {
// Set up the Remainder value's memory.
if (Remainder->BitWidth != RHS.BitWidth) {
if (Remainder->isSingleWord())
Remainder->VAL = 0;
else
delete [] Remainder->pVal;
Remainder->BitWidth = RHS.BitWidth;
if (!Remainder->isSingleWord())
Remainder->pVal = getClearedMemory(Remainder->getNumWords());
} else
Remainder->clear();
// The remainder is in R. Reconstitute the remainder into Remainder's low
// order words.
if (rhsWords == 1) {
uint64_t tmp =
uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
if (Remainder->isSingleWord())
Remainder->VAL = tmp;
else
Remainder->pVal[0] = tmp;
} else {
assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
for (unsigned i = 0; i < rhsWords; ++i)
Remainder->pVal[i] =
uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
}
}
// Clean up the memory we allocated.
if (U != &SPACE[0]) {
delete [] U;
delete [] V;
delete [] Q;
delete [] R;
}
}
APInt APInt::udiv(const APInt& RHS) const {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
// First, deal with the easy case
if (isSingleWord()) {
assert(RHS.VAL != 0 && "Divide by zero?");
return APInt(BitWidth, VAL / RHS.VAL);
}
// Get some facts about the LHS and RHS number of bits and words
uint32_t rhsBits = RHS.getActiveBits();
uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
assert(rhsWords && "Divided by zero???");
uint32_t lhsBits = this->getActiveBits();
uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
// Deal with some degenerate cases
if (!lhsWords)
// 0 / X ===> 0
return APInt(BitWidth, 0);
else if (lhsWords < rhsWords || this->ult(RHS)) {
// X / Y ===> 0, iff X < Y
return APInt(BitWidth, 0);
} else if (*this == RHS) {
// X / X ===> 1
return APInt(BitWidth, 1);
} else if (lhsWords == 1 && rhsWords == 1) {
// All high words are zero, just use native divide
return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
}
// We have to compute it the hard way. Invoke the Knuth divide algorithm.
APInt Quotient(1,0); // to hold result.
divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0);
return Quotient;
}
APInt APInt::urem(const APInt& RHS) const {
assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
if (isSingleWord()) {
assert(RHS.VAL != 0 && "Remainder by zero?");
return APInt(BitWidth, VAL % RHS.VAL);
}
// Get some facts about the LHS
uint32_t lhsBits = getActiveBits();
uint32_t lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
// Get some facts about the RHS
uint32_t rhsBits = RHS.getActiveBits();
uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
assert(rhsWords && "Performing remainder operation by zero ???");
// Check the degenerate cases
if (lhsWords == 0) {
// 0 % Y ===> 0
return APInt(BitWidth, 0);
} else if (lhsWords < rhsWords || this->ult(RHS)) {
// X % Y ===> X, iff X < Y
return *this;
} else if (*this == RHS) {
// X % X == 0;
return APInt(BitWidth, 0);
} else if (lhsWords == 1) {
// All high words are zero, just use native remainder
return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
}
// We have to compute it the hard way. Invoke the Knute divide algorithm.
APInt Remainder(1,0);
divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder);
return Remainder;
}
void APInt::fromString(uint32_t numbits, const char *str, uint32_t slen,
uint8_t radix) {
// Check our assumptions here
assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
"Radix should be 2, 8, 10, or 16!");
assert(str && "String is null?");
bool isNeg = str[0] == '-';
if (isNeg)
str++, slen--;
assert(slen <= numbits || radix != 2 && "Insufficient bit width");
assert(slen*3 <= numbits || radix != 8 && "Insufficient bit width");
assert(slen*4 <= numbits || radix != 16 && "Insufficient bit width");
assert((slen*64)/22 <= numbits || radix != 10 && "Insufficient bit width");
// Allocate memory
if (!isSingleWord())
pVal = getClearedMemory(getNumWords());
// Figure out if we can shift instead of multiply
uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
// Set up an APInt for the digit to add outside the loop so we don't
// constantly construct/destruct it.
APInt apdigit(getBitWidth(), 0);
APInt apradix(getBitWidth(), radix);
// Enter digit traversal loop
for (unsigned i = 0; i < slen; i++) {
// Get a digit
uint32_t digit = 0;
char cdigit = str[i];
if (isdigit(cdigit))
digit = cdigit - '0';
else if (isxdigit(cdigit))
if (cdigit >= 'a')
digit = cdigit - 'a' + 10;
else if (cdigit >= 'A')
digit = cdigit - 'A' + 10;
else
assert(0 && "huh?");
else
assert(0 && "Invalid character in digit string");
// Shift or multiple the value by the radix
if (shift)
this->shl(shift);
else
*this *= apradix;
// Add in the digit we just interpreted
if (apdigit.isSingleWord())
apdigit.VAL = digit;
else
apdigit.pVal[0] = digit;
*this += apdigit;
}
// If its negative, put it in two's complement form
if (isNeg) {
(*this)--;
this->flip();
}
}
std::string APInt::toString(uint8_t radix, bool wantSigned) const {
assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
"Radix should be 2, 8, 10, or 16!");
static const char *digits[] = {
"0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"
};
std::string result;
uint32_t bits_used = getActiveBits();
if (isSingleWord()) {
char buf[65];
const char *format = (radix == 10 ? (wantSigned ? "%lld" : "%llu") :
(radix == 16 ? "%llX" : (radix == 8 ? "%llo" : 0)));
if (format) {
if (wantSigned) {
int64_t sextVal = (int64_t(VAL) << (APINT_BITS_PER_WORD-BitWidth)) >>
(APINT_BITS_PER_WORD-BitWidth);
sprintf(buf, format, sextVal);
} else
sprintf(buf, format, VAL);
} else {
memset(buf, 0, 65);
uint64_t v = VAL;
while (bits_used) {
uint32_t bit = v & 1;
bits_used--;
buf[bits_used] = digits[bit][0];
v >>=1;
}
}
result = buf;
return result;
}
if (radix != 10) {
uint64_t mask = radix - 1;
uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : 1);
uint32_t nibbles = APINT_BITS_PER_WORD / shift;
for (uint32_t i = 0; i < getNumWords(); ++i) {
uint64_t value = pVal[i];
for (uint32_t j = 0; j < nibbles; ++j) {
result.insert(0, digits[ value & mask ]);
value >>= shift;
}
}
return result;
}
APInt tmp(*this);
APInt divisor(4, radix);
APInt zero(tmp.getBitWidth(), 0);
size_t insert_at = 0;
if (wantSigned && tmp[BitWidth-1]) {
// 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.flip();
tmp++;
result = "-";
insert_at = 1;
}
if (tmp == APInt(tmp.getBitWidth(), 0))
result = "0";
else while (tmp.ne(zero)) {
APInt APdigit(1,0);
APInt tmp2(tmp.getBitWidth(), 0);
divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
&APdigit);
uint32_t digit = APdigit.getZExtValue();
assert(digit < radix && "divide failed");
result.insert(insert_at,digits[digit]);
tmp = tmp2;
}
return result;
}
#ifndef NDEBUG
void APInt::dump() const
{
cerr << "APInt(" << BitWidth << ")=" << std::setbase(16);
if (isSingleWord())
cerr << VAL;
else for (unsigned i = getNumWords(); i > 0; i--) {
cerr << pVal[i-1] << " ";
}
cerr << " U(" << this->toString(10) << ") S(" << this->toStringSigned(10)
<< ")\n" << std::setbase(10);
}
#endif
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