X-Git-Url: http://demsky.eecs.uci.edu/git/?a=blobdiff_plain;f=lib%2FSupport%2FAPInt.cpp;h=23f89bb66f9e562204cd136d5ed21c9ad5f414a4;hb=c0d892732d3b19af18a1dda15dd3aaa65ddddcd4;hp=9d43ae4f16be59f308a6fbd354379786da16dca9;hpb=61eb180a53320c113fee615bb9d459624e2817f7;p=oota-llvm.git diff --git a/lib/Support/APInt.cpp b/lib/Support/APInt.cpp index 9d43ae4f16b..23f89bb66f9 100644 --- a/lib/Support/APInt.cpp +++ b/lib/Support/APInt.cpp @@ -2,140 +2,191 @@ // // 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 is distributed under the University of Illinois Open Source +// License. See LICENSE.TXT for details. // //===----------------------------------------------------------------------===// // -// This file implements a class to represent arbitrary precision integral -// constant values. +// This file implements a class to represent arbitrary precision integer +// constant values and provide a variety of arithmetic operations on them. // //===----------------------------------------------------------------------===// #include "llvm/ADT/APInt.h" -#include "llvm/DerivedTypes.h" +#include "llvm/ADT/FoldingSet.h" +#include "llvm/ADT/Hashing.h" +#include "llvm/ADT/SmallString.h" +#include "llvm/ADT/StringRef.h" +#include "llvm/Support/Debug.h" +#include "llvm/Support/ErrorHandling.h" #include "llvm/Support/MathExtras.h" -#include +#include "llvm/Support/raw_ostream.h" +#include #include +#include +#include using namespace llvm; -// A utility function for allocating memory, checking for allocation failures, -// and ensuring the contents is zeroed. -inline static uint64_t* getClearedMemory(uint32_t numWords) { +#define DEBUG_TYPE "apint" + +/// A utility function for allocating memory, checking for allocation failures, +/// and ensuring the contents are zeroed. +inline static uint64_t* getClearedMemory(unsigned numWords) { uint64_t * result = new uint64_t[numWords]; 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. -inline static uint64_t* getMemory(uint32_t numWords) { +/// A utility function for allocating memory and checking for allocation +/// failure. The content is not zeroed. +inline static uint64_t* getMemory(unsigned numWords) { uint64_t * result = new uint64_t[numWords]; assert(result && "APInt memory allocation fails!"); return result; } -APInt::APInt(uint32_t numBits, uint64_t val) - : BitWidth(numBits), pVal(0) { - assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small"); - assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large"); - if (isSingleWord()) - VAL = val & (~uint64_t(0ULL) >> (APINT_BITS_PER_WORD - BitWidth)); - else { - pVal = getClearedMemory(getNumWords()); - pVal[0] = val; +/// A utility function that converts a character to a digit. +inline static unsigned getDigit(char cdigit, uint8_t radix) { + unsigned r; + + if (radix == 16 || radix == 36) { + r = cdigit - '0'; + if (r <= 9) + return r; + + r = cdigit - 'A'; + if (r <= radix - 11U) + return r + 10; + + r = cdigit - 'a'; + if (r <= radix - 11U) + return r + 10; + + radix = 10; } + + r = cdigit - '0'; + if (r < radix) + return r; + + return -1U; +} + + +void APInt::initSlowCase(unsigned numBits, uint64_t val, bool isSigned) { + pVal = getClearedMemory(getNumWords()); + pVal[0] = val; + if (isSigned && int64_t(val) < 0) + for (unsigned i = 1; i < getNumWords(); ++i) + pVal[i] = -1ULL; +} + +void APInt::initSlowCase(const APInt& that) { + pVal = getMemory(getNumWords()); + memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE); } -APInt::APInt(uint32_t numBits, uint32_t numWords, uint64_t bigVal[]) - : BitWidth(numBits), pVal(0) { - assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small"); - assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large"); - assert(bigVal && "Null pointer detected!"); +void APInt::initFromArray(ArrayRef bigVal) { + assert(BitWidth && "Bitwidth too small"); + assert(bigVal.data() && "Null pointer detected!"); if (isSingleWord()) - VAL = bigVal[0] & (~uint64_t(0ULL) >> (APINT_BITS_PER_WORD - BitWidth)); + VAL = bigVal[0]; else { - pVal = getMemory(getNumWords()); - // Calculate the actual length of bigVal[]. - uint32_t maxN = std::max(numWords, getNumWords()); - uint32_t minN = std::min(numWords, getNumWords()); - memcpy(pVal, bigVal, (minN - 1) * APINT_WORD_SIZE); - pVal[minN-1] = bigVal[minN-1] & - (~uint64_t(0ULL) >> - (APINT_BITS_PER_WORD - BitWidth % APINT_BITS_PER_WORD)); - if (maxN == getNumWords()) - memset(pVal+numWords, 0, (getNumWords() - numWords) * APINT_WORD_SIZE); - } -} - -/// @brief Create a new APInt by translating the char array represented -/// integer value. -APInt::APInt(uint32_t numbits, const char StrStart[], uint32_t slen, - uint8_t radix) - : BitWidth(numbits), pVal(0) { - fromString(numbits, StrStart, slen, radix); -} - -/// @brief Create a new APInt by translating the string represented -/// integer value. -APInt::APInt(uint32_t numbits, const std::string& Val, uint8_t radix) - : BitWidth(numbits), pVal(0) { - assert(!Val.empty() && "String empty?"); - fromString(numbits, Val.c_str(), Val.size(), radix); -} - -/// @brief Copy constructor -APInt::APInt(const APInt& APIVal) - : BitWidth(APIVal.BitWidth), pVal(0) { - if (isSingleWord()) - VAL = APIVal.VAL; - else { - pVal = getMemory(getNumWords()); - memcpy(pVal, APIVal.pVal, getNumWords() * APINT_WORD_SIZE); + // Get memory, cleared to 0 + pVal = getClearedMemory(getNumWords()); + // Calculate the number of words to copy + unsigned words = std::min(bigVal.size(), getNumWords()); + // Copy the words from bigVal to pVal + memcpy(pVal, bigVal.data(), words * APINT_WORD_SIZE); } + // Make sure unused high bits are cleared + clearUnusedBits(); } -APInt::~APInt() { - if (!isSingleWord() && pVal) - delete[] pVal; +APInt::APInt(unsigned numBits, ArrayRef bigVal) + : BitWidth(numBits), VAL(0) { + initFromArray(bigVal); } -/// @brief Copy assignment operator. Create a new object from the given -/// APInt one by initialization. -APInt& APInt::operator=(const APInt& RHS) { - assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); - if (isSingleWord()) - VAL = RHS.VAL; - else +APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[]) + : BitWidth(numBits), VAL(0) { + initFromArray(makeArrayRef(bigVal, numWords)); +} + +APInt::APInt(unsigned numbits, StringRef Str, uint8_t radix) + : BitWidth(numbits), VAL(0) { + assert(BitWidth && "Bitwidth too small"); + fromString(numbits, Str, radix); +} + +APInt& APInt::AssignSlowCase(const APInt& RHS) { + // Don't do anything for X = X + if (this == &RHS) + return *this; + + if (BitWidth == RHS.getBitWidth()) { + // assume same bit-width single-word case is already handled + assert(!isSingleWord()); memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE); - return *this; + return *this; + } + + if (isSingleWord()) { + // assume case where both are single words is already handled + assert(!RHS.isSingleWord()); + 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(); } -/// @brief Assignment operator. Assigns a common case integer value to -/// the APInt. APInt& APInt::operator=(uint64_t RHS) { - if (isSingleWord()) + if (isSingleWord()) VAL = RHS; else { pVal[0] = RHS; memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE); } - return *this; + return clearUnusedBits(); +} + +/// This method 'profiles' an APInt for use with FoldingSet. +void APInt::Profile(FoldingSetNodeID& ID) const { + ID.AddInteger(BitWidth); + + if (isSingleWord()) { + ID.AddInteger(VAL); + return; + } + + unsigned NumWords = getNumWords(); + for (unsigned i = 0; i < NumWords; ++i) + ID.AddInteger(pVal[i]); } -/// add_1 - This function adds a single "digit" integer, y, to the multiple +/// 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 uint64_t add_1(uint64_t dest[], - uint64_t x[], uint32_t len, - uint64_t y) { - for (uint32_t i = 0; i < len; ++i) { +static bool add_1(uint64_t dest[], uint64_t x[], unsigned len, uint64_t y) { + for (unsigned i = 0; i < len; ++i) { dest[i] = y + x[i]; if (dest[i] < y) - y = 1; + y = 1; // Carry one to next digit. else { - y = 0; + y = 0; // No need to carry so exit early break; } } @@ -144,133 +195,111 @@ static uint64_t add_1(uint64_t dest[], /// @brief Prefix increment operator. Increments the APInt by one. APInt& APInt::operator++() { - if (isSingleWord()) + if (isSingleWord()) ++VAL; else add_1(pVal, pVal, getNumWords(), 1); - clearUnusedBits(); - return *this; + 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 +/// 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. -static uint64_t sub_1(uint64_t x[], uint32_t len, - uint64_t y) { - for (uint32_t i = 0; i < len; ++i) { +/// @returns the borrow out of the subtraction +static bool sub_1(uint64_t x[], unsigned len, uint64_t y) { + for (unsigned i = 0; i < len; ++i) { uint64_t X = x[i]; x[i] -= y; - if (y > X) + 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 y; + return bool(y); } /// @brief Prefix decrement operator. Decrements the APInt by one. APInt& APInt::operator--() { - if (isSingleWord()) + if (isSingleWord()) --VAL; else sub_1(pVal, getNumWords(), 1); - clearUnusedBits(); - return *this; -} - -/// add - This function adds the integer array x[] by integer array -/// y[] and returns the carry. -static uint64_t add(uint64_t dest[], uint64_t x[], - uint64_t y[], uint32_t len) { - uint32_t carry = 0; - for (uint32_t i = 0; i< len; ++i) { - carry += x[i]; - dest[i] = carry + y[i]; - carry = carry < x[i] ? 1 : (dest[i] < carry ? 1 : 0); + return clearUnusedBits(); +} + +/// 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, + unsigned len) { + bool carry = false; + for (unsigned 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; } -/// @brief Addition assignment operator. Adds this APInt by the given APInt& -/// RHS and assigns the result to this APInt. +/// 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.isSingleWord() ? RHS.VAL : RHS.pVal[0]; + if (isSingleWord()) + VAL += RHS.VAL; else { - if (RHS.isSingleWord()) add_1(pVal, pVal, getNumWords(), RHS.VAL); - else { - if (getNumWords() <= RHS.getNumWords()) - add(pVal, pVal, RHS.pVal, getNumWords()); - else { - uint64_t carry = add(pVal, pVal, RHS.pVal, RHS.getNumWords()); - add_1(pVal + RHS.getNumWords(), pVal + RHS.getNumWords(), - getNumWords() - RHS.getNumWords(), carry); - } - } + add(pVal, pVal, RHS.pVal, getNumWords()); } - clearUnusedBits(); - return *this; -} - -/// sub - This function subtracts the integer array x[] by -/// integer array y[], and returns the borrow-out carry. -static uint64_t sub(uint64_t dest[], uint64_t x[], - uint64_t y[], uint32_t len) { - // Carry indicator. - uint64_t cy = 0; - - for (uint32_t i = 0; i < len; ++i) { - uint64_t Y = y[i], X = x[i]; - Y += cy; - - cy = Y < cy ? 1 : 0; - Y = X - Y; - cy += Y > X ? 1 : 0; - dest[i] = Y; + 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, + unsigned len) { + bool borrow = false; + for (unsigned 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 cy; + return borrow; } -/// @brief Subtraction assignment operator. Subtracts this APInt by the given -/// APInt &RHS and assigns the result to this APInt. +/// 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.isSingleWord() ? RHS.VAL : RHS.pVal[0]; - else { - if (RHS.isSingleWord()) - sub_1(pVal, getNumWords(), RHS.VAL); - else { - if (RHS.getNumWords() < getNumWords()) { - uint64_t carry = sub(pVal, pVal, RHS.pVal, RHS.getNumWords()); - sub_1(pVal + RHS.getNumWords(), getNumWords() - RHS.getNumWords(), - carry); - } - else - sub(pVal, pVal, RHS.pVal, getNumWords()); - } - } - clearUnusedBits(); - return *this; + if (isSingleWord()) + VAL -= RHS.VAL; + else + sub(pVal, pVal, RHS.pVal, getNumWords()); + return clearUnusedBits(); } -/// mul_1 - This function performs the multiplication operation on a -/// large integer (represented as an integer array) and a uint64_t integer. -/// @returns the carry of the multiplication. -static uint64_t mul_1(uint64_t dest[], - uint64_t x[], uint32_t len, - uint64_t y) { - // Split y into high 32-bit part and low 32-bit part. +/// Multiplies an integer array, x, by 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[], unsigned 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, lx, hx; - for (uint32_t i = 0; i < len; ++i) { - lx = x[i] & 0xffffffffULL; - hx = x[i] >> 32; - // hasCarry - A flag to indicate if has carry. + uint64_t carry = 0; + + // For each digit of x. + for (unsigned 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. @@ -279,30 +308,28 @@ static uint64_t mul_1(uint64_t dest[], // 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) + + // 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 = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) + (carry >> 32) + ((lx * hy) >> 32) + hx * hy; } - return carry; } -/// mul - This function multiplies integer array x[] by integer array y[] and -/// stores the result into integer array dest[]. -/// Note the array dest[]'s size should no less than xlen + ylen. -static void mul(uint64_t dest[], uint64_t x[], uint32_t xlen, - uint64_t y[], uint32_t ylen) { +/// 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[], unsigned xlen, uint64_t y[], + unsigned ylen) { dest[xlen] = mul_1(dest, x, xlen, y[0]); - - for (uint32_t i = 1; i < ylen; ++i) { + for (unsigned i = 1; i < ylen; ++i) { uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32; - uint64_t carry = 0, lx, hx; - for (uint32_t j = 0; j < xlen; ++j) { + uint64_t carry = 0, lx = 0, hx = 0; + for (unsigned j = 0; j < xlen; ++j) { lx = x[j] & 0xffffffffULL; hx = x[j] >> 32; // hasCarry - A flag to indicate if has carry. @@ -319,226 +346,209 @@ static void mul(uint64_t dest[], uint64_t x[], uint32_t xlen, 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) + + (carry >> 32) + (dest[i+j] < resul ? 1 : 0) + ((lx * hy) >> 32) + hx * hy; } dest[i+xlen] = carry; } } -/// @brief Multiplication assignment operator. Multiplies this APInt by the -/// given APInt& RHS and assigns the result to this APInt. APInt& APInt::operator*=(const APInt& RHS) { assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); - if (isSingleWord()) + if (isSingleWord()) { VAL *= RHS.VAL; - else { - // one-based first non-zero bit position. - uint32_t first = getActiveBits(); - uint32_t xlen = !first ? 0 : whichWord(first - 1) + 1; - if (!xlen) - return *this; - else if (RHS.isSingleWord()) - mul_1(pVal, pVal, xlen, RHS.VAL); - else { - first = RHS.getActiveBits(); - uint32_t ylen = !first ? 0 : whichWord(first - 1) + 1; - if (!ylen) { - memset(pVal, 0, getNumWords() * APINT_WORD_SIZE); - return *this; - } - uint64_t *dest = getMemory(xlen+ylen); - mul(dest, pVal, xlen, RHS.pVal, ylen); - memcpy(pVal, dest, ((xlen + ylen >= getNumWords()) ? - getNumWords() : xlen + ylen) * APINT_WORD_SIZE); - delete[] dest; - } + clearUnusedBits(); + return *this; + } + + // Get some bit facts about LHS and check for zero + unsigned lhsBits = getActiveBits(); + unsigned lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1; + if (!lhsWords) + // 0 * X ===> 0 + return *this; + + // Get some bit facts about RHS and check for zero + unsigned rhsBits = RHS.getActiveBits(); + unsigned rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1; + if (!rhsWords) { + // X * 0 ===> 0 + clearAllBits(); + return *this; } + + // Allocate space for the result + unsigned destWords = rhsWords + lhsWords; + uint64_t *dest = getMemory(destWords); + + // Perform the long multiply + mul(dest, pVal, lhsWords, RHS.pVal, rhsWords); + + // Copy result back into *this + clearAllBits(); + unsigned wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords; + memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE); clearUnusedBits(); + + // delete dest array and return + delete[] dest; return *this; } -/// @brief Bitwise AND assignment operator. Performs bitwise AND operation on -/// this APInt and the given APInt& RHS, assigns the result to this APInt. 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) + unsigned numWords = getNumWords(); + for (unsigned i = 0; i < numWords; ++i) pVal[i] &= RHS.pVal[i]; return *this; } -/// @brief Bitwise OR assignment operator. Performs bitwise OR operation on -/// this APInt and the given APInt& RHS, assigns the result to this APInt. 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) + unsigned numWords = getNumWords(); + for (unsigned i = 0; i < numWords; ++i) pVal[i] |= RHS.pVal[i]; return *this; } -/// @brief Bitwise XOR assignment operator. Performs bitwise XOR operation on -/// this APInt and the given APInt& RHS, assigns the result to this APInt. 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) + } + unsigned numWords = getNumWords(); + for (unsigned i = 0; i < numWords; ++i) pVal[i] ^= RHS.pVal[i]; - return *this; -} - -/// @brief Bitwise AND operator. Performs bitwise AND operation on this APInt -/// and the given APInt& RHS. -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); - - APInt Result(*this); - uint32_t numWords = getNumWords(); - for (uint32_t i = 0; i < numWords; ++i) - Result.pVal[i] &= RHS.pVal[i]; - return Result; + return clearUnusedBits(); } -/// @brief Bitwise OR operator. Performs bitwise OR operation on this APInt -/// and the given APInt& RHS. -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); - APInt Result(*this); - uint32_t numWords = getNumWords(); - for (uint32_t i = 0; i < numWords; ++i) - Result.pVal[i] |= RHS.pVal[i]; - return Result; +APInt APInt::AndSlowCase(const APInt& RHS) const { + unsigned numWords = getNumWords(); + uint64_t* val = getMemory(numWords); + for (unsigned i = 0; i < numWords; ++i) + val[i] = pVal[i] & RHS.pVal[i]; + return APInt(val, getBitWidth()); } -/// @brief Bitwise XOR operator. Performs bitwise XOR operation on this APInt -/// and the given APInt& RHS. -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); - APInt Result(*this); - uint32_t numWords = getNumWords(); - for (uint32_t i = 0; i < numWords; ++i) - Result.pVal[i] ^= RHS.pVal[i]; - return Result; +APInt APInt::OrSlowCase(const APInt& RHS) const { + unsigned numWords = getNumWords(); + uint64_t *val = getMemory(numWords); + for (unsigned i = 0; i < numWords; ++i) + val[i] = pVal[i] | RHS.pVal[i]; + return APInt(val, getBitWidth()); } -/// @brief Logical negation operator. Performs logical negation operation on -/// this APInt. -bool APInt::operator !() const { - if (isSingleWord()) - return !VAL; +APInt APInt::XorSlowCase(const APInt& RHS) const { + unsigned numWords = getNumWords(); + uint64_t *val = getMemory(numWords); + for (unsigned i = 0; i < numWords; ++i) + val[i] = pVal[i] ^ RHS.pVal[i]; - for (uint32_t i = 0; i < getNumWords(); ++i) - if (pVal[i]) - return false; - return true; + APInt Result(val, getBitWidth()); + // 0^0==1 so clear the high bits in case they got set. + Result.clearUnusedBits(); + return Result; } -/// @brief Multiplication operator. Multiplies this APInt by the given APInt& -/// RHS. 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; - Result.clearUnusedBits(); return Result; } -/// @brief Addition operator. Adds this APInt by the given APInt& RHS. APInt APInt::operator+(const APInt& RHS) const { assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); - APInt API(*this); - API += RHS; - API.clearUnusedBits(); - return API; + if (isSingleWord()) + return APInt(BitWidth, VAL + RHS.VAL); + APInt Result(BitWidth, 0); + add(Result.pVal, this->pVal, RHS.pVal, getNumWords()); + Result.clearUnusedBits(); + return Result; } -/// @brief Subtraction operator. Subtracts this APInt by the given APInt& RHS APInt APInt::operator-(const APInt& RHS) const { assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); - APInt API(*this); - API -= RHS; - return API; + if (isSingleWord()) + return APInt(BitWidth, VAL - RHS.VAL); + APInt Result(BitWidth, 0); + sub(Result.pVal, this->pVal, RHS.pVal, getNumWords()); + Result.clearUnusedBits(); + return Result; } -/// @brief Array-indexing support. -bool APInt::operator[](uint32_t bitPosition) const { - return (maskBit(bitPosition) & (isSingleWord() ? - VAL : pVal[whichWord(bitPosition)])) != 0; -} +bool APInt::EqualSlowCase(const APInt& RHS) const { + // Get some facts about the number of bits used in the two operands. + unsigned n1 = getActiveBits(); + unsigned n2 = RHS.getActiveBits(); -/// @brief Equality operator. Compare this APInt with the given APInt& RHS -/// for the validity of the equality relationship. -bool APInt::operator==(const APInt& RHS) const { - uint32_t n1 = getActiveBits(); - uint32_t n2 = RHS.getActiveBits(); - if (n1 != n2) return false; - else if (isSingleWord()) - return VAL == (RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0]); - else { - if (n1 <= APINT_BITS_PER_WORD) - return pVal[0] == (RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0]); - for (int i = whichWord(n1 - 1); i >= 0; --i) - if (pVal[i] != RHS.pVal[i]) return false; - } + // 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; } -/// @brief Equality operator. Compare this APInt with the given uint64_t value -/// for the validity of the equality relationship. -bool APInt::operator==(uint64_t Val) const { - if (isSingleWord()) - return VAL == Val; - else { - uint32_t n = getActiveBits(); - if (n <= APINT_BITS_PER_WORD) - return pVal[0] == Val; - else - return false; - } +bool APInt::EqualSlowCase(uint64_t Val) const { + unsigned n = getActiveBits(); + if (n <= APINT_BITS_PER_WORD) + return pVal[0] == Val; + else + return false; } -/// @brief Unsigned less than comparison bool APInt::ult(const APInt& RHS) const { assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); if (isSingleWord()) return VAL < RHS.VAL; - else { - uint32_t n1 = getActiveBits(); - uint32_t n2 = RHS.getActiveBits(); - if (n1 < n2) - return true; - else if (n2 < n1) + + // Get active bit length of both operands + unsigned n1 = getActiveBits(); + unsigned 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 + unsigned topWord = whichWord(std::max(n1,n2)-1); + for (int i = topWord; i >= 0; --i) { + if (pVal[i] > RHS.pVal[i]) return false; - else if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD) - return pVal[0] < RHS.pVal[0]; - for (int i = whichWord(n1 - 1); i >= 0; --i) { - if (pVal[i] > RHS.pVal[i]) return false; - else if (pVal[i] < RHS.pVal[i]) return true; - } + if (pVal[i] < RHS.pVal[i]) + return true; } return false; } -/// @brief Signed less than comparison bool APInt::slt(const APInt& RHS) const { assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); if (isSingleWord()) { @@ -548,230 +558,263 @@ bool APInt::slt(const APInt& RHS) const { } APInt lhs(*this); - APInt rhs(*this); - bool lhsNegative = false; - bool rhsNegative = false; - if (lhs[BitWidth-1]) { - lhsNegative = true; - lhs.flip(); - lhs++; - } - if (rhs[BitWidth-1]) { - rhsNegative = true; - rhs.flip(); - rhs++; - } - if (lhsNegative) - if (rhsNegative) - return !lhs.ult(rhs); + 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.flipAllBits(); + ++lhs; + } + if (rhsNeg) { + // Sign bit is set so perform two's complement to make it positive + rhs.flipAllBits(); + ++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 (rhsNegative) + else if (rhsNeg) return false; - else + else return lhs.ult(rhs); } -/// Set the given bit to 1 whose poition is given as "bitPosition". -/// @brief Set a given bit to 1. -APInt& APInt::set(uint32_t bitPosition) { - if (isSingleWord()) VAL |= maskBit(bitPosition); - else pVal[whichWord(bitPosition)] |= maskBit(bitPosition); - return *this; -} - -/// @brief Set every bit to 1. -APInt& APInt::set() { - if (isSingleWord()) - VAL = ~0ULL >> (APINT_BITS_PER_WORD - BitWidth); - else { - for (uint32_t i = 0; i < getNumWords() - 1; ++i) - pVal[i] = -1ULL; - pVal[getNumWords() - 1] = ~0ULL >> - (APINT_BITS_PER_WORD - BitWidth % APINT_BITS_PER_WORD); - } - return *this; +void APInt::setBit(unsigned bitPosition) { + if (isSingleWord()) + VAL |= maskBit(bitPosition); + else + pVal[whichWord(bitPosition)] |= maskBit(bitPosition); } /// 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()) +void APInt::clearBit(unsigned bitPosition) { + if (isSingleWord()) VAL &= ~maskBit(bitPosition); - else + 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 API(*this); - API.flip(); - return API; } /// @brief Toggle every bit to its opposite value. -APInt& APInt::flip() { - if (isSingleWord()) VAL = (~(VAL << - (APINT_BITS_PER_WORD - BitWidth))) >> (APINT_BITS_PER_WORD - BitWidth); - else { - uint32_t i = 0; - for (; i < getNumWords() - 1; ++i) - pVal[i] = ~pVal[i]; - uint32_t offset = - APINT_BITS_PER_WORD - (BitWidth - APINT_BITS_PER_WORD * (i - 1)); - pVal[i] = (~(pVal[i] << offset)) >> offset; - } - return *this; -} -/// Toggle a given bit to its opposite value whose position is given +/// 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) { +void APInt::flipBit(unsigned bitPosition) { assert(bitPosition < BitWidth && "Out of the bit-width range!"); - if ((*this)[bitPosition]) clear(bitPosition); - else set(bitPosition); - return *this; + if ((*this)[bitPosition]) clearBit(bitPosition); + else setBit(bitPosition); } -/// getMaxValue - This function returns the largest value -/// for an APInt of the specified bit-width and if isSign == true, -/// it should be largest signed value, otherwise unsigned value. -APInt APInt::getMaxValue(uint32_t numBits, bool isSign) { - APInt Result(numBits, 0); - Result.set(); - if (isSign) - Result.clear(numBits - 1); - return Result; -} +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!"); -/// getMinValue - This function returns the smallest value for -/// an APInt of the given bit-width and if isSign == true, -/// it should be smallest signed value, otherwise zero. -APInt APInt::getMinValue(uint32_t numBits, bool isSign) { - APInt Result(numBits, 0); - if (isSign) - Result.set(numBits - 1); - return Result; + 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. + unsigned log = tmp.logBase2(); + if (log == (unsigned)-1) { + return isNegative + 1; + } else { + return isNegative + log + 1; + } } -/// getAllOnesValue - This function returns an all-ones value for -/// an APInt of the specified bit-width. -APInt APInt::getAllOnesValue(uint32_t numBits) { - return getMaxValue(numBits, false); +hash_code llvm::hash_value(const APInt &Arg) { + if (Arg.isSingleWord()) + return hash_combine(Arg.VAL); + + return hash_combine_range(Arg.pVal, Arg.pVal + Arg.getNumWords()); } -/// getNullValue - This function creates an '0' value for an -/// APInt of the specified bit-width. -APInt APInt::getNullValue(uint32_t numBits) { - return getMinValue(numBits, false); +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); } -/// HiBits - This function returns the high "numBits" bits of this APInt. -APInt APInt::getHiBits(uint32_t numBits) const { +/// This function returns the high "numBits" bits of this APInt. +APInt APInt::getHiBits(unsigned 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), +/// This function returns the low "numBits" bits of this APInt. +APInt APInt::getLoBits(unsigned numBits) const { + return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits), BitWidth - numBits); } -bool APInt::isPowerOf2() const { - return (!!*this) && !(*this & (*this - APInt(BitWidth,1))); -} +unsigned APInt::countLeadingZerosSlowCase() const { + // Treat the most significand word differently because it might have + // meaningless bits set beyond the precision. + unsigned BitsInMSW = BitWidth % APINT_BITS_PER_WORD; + integerPart MSWMask; + if (BitsInMSW) MSWMask = (integerPart(1) << BitsInMSW) - 1; + else { + MSWMask = ~integerPart(0); + BitsInMSW = APINT_BITS_PER_WORD; + } -/// countLeadingZeros - This function is a APInt version corresponding to -/// llvm/include/llvm/Support/MathExtras.h's function -/// countLeadingZeros_{32, 64}. It performs platform optimal form of counting -/// the number of zeros from the most significant bit to the first one bit. -/// @returns numWord() * 64 if the value is zero. -uint32_t APInt::countLeadingZeros() const { - if (isSingleWord()) - return CountLeadingZeros_64(VAL) - (APINT_BITS_PER_WORD - BitWidth); - uint32_t Count = 0; - for (uint32_t i = getNumWords(); i > 0u; --i) { - uint32_t tmp = CountLeadingZeros_64(pVal[i-1]); - Count += tmp; - if (tmp != APINT_BITS_PER_WORD) - if (i == getNumWords()) - Count -= (APINT_BITS_PER_WORD - whichBit(BitWidth)); + unsigned i = getNumWords(); + integerPart MSW = pVal[i-1] & MSWMask; + if (MSW) + return llvm::countLeadingZeros(MSW) - (APINT_BITS_PER_WORD - BitsInMSW); + + unsigned Count = BitsInMSW; + for (--i; i > 0u; --i) { + if (pVal[i-1] == 0) + Count += APINT_BITS_PER_WORD; + else { + Count += llvm::countLeadingZeros(pVal[i-1]); break; + } } return Count; } -/// countTrailingZeros - This function is a APInt version corresponding to -/// llvm/include/llvm/Support/MathExtras.h's function -/// countTrailingZeros_{32, 64}. It performs platform optimal form of counting -/// the number of zeros from the least significant bit to the first one bit. -/// @returns numWord() * 64 if the value is zero. -uint32_t APInt::countTrailingZeros() const { +unsigned APInt::countLeadingOnes() const { if (isSingleWord()) - return CountTrailingZeros_64(VAL); - APInt Tmp( ~(*this) & ((*this) - APInt(BitWidth,1)) ); - return getNumWords() * APINT_BITS_PER_WORD - Tmp.countLeadingZeros(); + return llvm::countLeadingOnes(VAL << (APINT_BITS_PER_WORD - BitWidth)); + + 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(pVal[i] << shift); + if (Count == highWordBits) { + for (i--; i >= 0; --i) { + if (pVal[i] == -1ULL) + Count += APINT_BITS_PER_WORD; + else { + Count += llvm::countLeadingOnes(pVal[i]); + break; + } + } + } + return Count; } -/// countPopulation - This function is a APInt version corresponding to -/// llvm/include/llvm/Support/MathExtras.h's function -/// countPopulation_{32, 64}. It counts the number of set bits in a value. -/// @returns 0 if the value is zero. -uint32_t APInt::countPopulation() const { +unsigned APInt::countTrailingZeros() 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 std::min(unsigned(llvm::countTrailingZeros(VAL)), BitWidth); + unsigned Count = 0; + unsigned i = 0; + for (; i < getNumWords() && pVal[i] == 0; ++i) + Count += APINT_BITS_PER_WORD; + if (i < getNumWords()) + Count += llvm::countTrailingZeros(pVal[i]); + return std::min(Count, BitWidth); +} + +unsigned APInt::countTrailingOnesSlowCase() const { + unsigned Count = 0; + unsigned i = 0; + for (; i < getNumWords() && pVal[i] == -1ULL; ++i) + Count += APINT_BITS_PER_WORD; + if (i < getNumWords()) + Count += llvm::countTrailingOnes(pVal[i]); + return std::min(Count, BitWidth); +} + +unsigned APInt::countPopulationSlowCase() const { + unsigned Count = 0; + for (unsigned i = 0; i < getNumWords(); ++i) + Count += llvm::countPopulation(pVal[i]); return Count; } +/// Perform a logical right-shift from Src to Dst, which must be equal or +/// non-overlapping, of Words words, by Shift, which must be less than 64. +static void lshrNear(uint64_t *Dst, uint64_t *Src, unsigned Words, + unsigned Shift) { + uint64_t Carry = 0; + for (int I = Words - 1; I >= 0; --I) { + uint64_t Tmp = Src[I]; + Dst[I] = (Tmp >> Shift) | Carry; + Carry = Tmp << (64 - Shift); + } +} -/// byteSwap - This function returns a byte-swapped representation of the -/// this APInt. APInt APInt::byteSwap() const { assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!"); if (BitWidth == 16) - return APInt(BitWidth, ByteSwap_16(VAL)); - else if (BitWidth == 32) - return APInt(BitWidth, ByteSwap_32(VAL)); - else if (BitWidth == 48) { - uint64_t Tmp1 = ((VAL >> 32) << 16) | (VAL & 0xFFFF); + return APInt(BitWidth, ByteSwap_16(uint16_t(VAL))); + if (BitWidth == 32) + return APInt(BitWidth, ByteSwap_32(unsigned(VAL))); + if (BitWidth == 48) { + unsigned Tmp1 = unsigned(VAL >> 16); Tmp1 = ByteSwap_32(Tmp1); - uint64_t Tmp2 = (VAL >> 16) & 0xFFFF; + uint16_t Tmp2 = uint16_t(VAL); Tmp2 = ByteSwap_16(Tmp2); - return - APInt(BitWidth, - (Tmp1 & 0xff) | ((Tmp1<<16) & 0xffff00000000ULL) | (Tmp2 << 16)); - } else if (BitWidth == 64) + return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1); + } + 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 Result(getNumWords() * APINT_BITS_PER_WORD, 0); + for (unsigned I = 0, N = getNumWords(); I != N; ++I) + Result.pVal[I] = ByteSwap_64(pVal[N - I - 1]); + if (Result.BitWidth != BitWidth) { + lshrNear(Result.pVal, Result.pVal, getNumWords(), + Result.BitWidth - BitWidth); + Result.BitWidth = BitWidth; } + return Result; } -/// GreatestCommonDivisor - This function returns the greatest common -/// divisor of the two APInt values using Enclid's algorithm. -APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1, +APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1, const APInt& API2) { APInt A = API1, B = API2; while (!!B) { @@ -782,43 +825,59 @@ APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1, return A; } -/// DoubleRoundToAPInt - This function convert a double value to -/// a APInt value. -APInt llvm::APIntOps::RoundDoubleToAPInt(double Double) { +APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned 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(64ull, 0u); - uint64_t mantissa = ((T.I << 12) >> 12) | (1ULL << 52); + 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(64u, mantissa >> (52 - exp)) : - APInt(64u, mantissa >> (52 - exp)); - APInt Tmp(exp + 1, mantissa); - Tmp = Tmp.shl(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((unsigned)exp - 52); return isNeg ? -Tmp : Tmp; } -/// RoundToDouble - This function convert this APInt to a double. +/// 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 = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth); + int64_t sext = (int64_t(getWord(0)) << (64-BitWidth)) >> (64-BitWidth); return double(sext); } else - return double(VAL); + return double(getWord(0)); } // Determine if the value is negative. @@ -828,7 +887,7 @@ double APInt::roundToDouble(bool isSigned) const { APInt Tmp(isNeg ? -(*this) : (*this)); // Figure out how many bits we're using. - uint32_t n = Tmp.getActiveBits(); + 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 @@ -838,9 +897,9 @@ double APInt::roundToDouble(bool isSigned) const { // Return infinity for exponent overflow if (exp > 1023) { if (!isSigned || !isNeg) - return double(1.0E300 * 1.0E300); // positive infinity - else - return double(-1.0E300 * 1.0E300); // negative infinity + return std::numeric_limits::infinity(); + else + return -std::numeric_limits::infinity(); } exp += 1023; // Increment for 1023 bias @@ -870,253 +929,708 @@ double APInt::roundToDouble(bool isSigned) const { } // Truncate to new width. -void APInt::trunc(uint32_t 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.pVal[i] = pVal[i]; + + // Truncate and copy any partial word. + unsigned bits = (0 - width) % APINT_BITS_PER_WORD; + if (bits != 0) + Result.pVal[i] = pVal[i] << bits >> bits; + + return Result; } // Sign extend to a new width. -void APInt::sext(uint32_t width) { +APInt APInt::sext(unsigned width) const { assert(width > BitWidth && "Invalid APInt SignExtend request"); -} - -// Zero extend to a new width. -void APInt::zext(uint32_t width) { - assert(width > BitWidth && "Invalid APInt ZeroExtend request"); -} -/// Arithmetic right-shift this APInt by shiftAmt. -/// @brief Arithmetic right-shift function. -APInt APInt::ashr(uint32_t shiftAmt) const { - APInt API(*this); - if (API.isSingleWord()) - API.VAL = - (((int64_t(API.VAL) << (APINT_BITS_PER_WORD - API.BitWidth)) >> - (APINT_BITS_PER_WORD - API.BitWidth)) >> shiftAmt) & - (~uint64_t(0UL) >> (APINT_BITS_PER_WORD - API.BitWidth)); - else { - if (shiftAmt >= API.BitWidth) { - memset(API.pVal, API[API.BitWidth-1] ? 1 : 0, - (API.getNumWords()-1) * APINT_WORD_SIZE); - API.pVal[API.getNumWords() - 1] = - ~uint64_t(0UL) >> - (APINT_BITS_PER_WORD - API.BitWidth % APINT_BITS_PER_WORD); - } else { - uint32_t i = 0; - for (; i < API.BitWidth - shiftAmt; ++i) - if (API[i+shiftAmt]) - API.set(i); - else - API.clear(i); - for (; i < API.BitWidth; ++i) - if (API[API.BitWidth-1]) - API.set(i); - else API.clear(i); - } + if (width <= APINT_BITS_PER_WORD) { + uint64_t val = VAL << (APINT_BITS_PER_WORD - BitWidth); + val = (int64_t)val >> (width - BitWidth); + return APInt(width, val >> (APINT_BITS_PER_WORD - width)); } - return API; -} -/// Logical right-shift this APInt by shiftAmt. -/// @brief Logical right-shift function. -APInt APInt::lshr(uint32_t shiftAmt) const { - APInt API(*this); - if (API.isSingleWord()) - API.VAL >>= shiftAmt; - else { - if (shiftAmt >= API.BitWidth) - memset(API.pVal, 0, API.getNumWords() * APINT_WORD_SIZE); - uint32_t i = 0; - for (i = 0; i < API.BitWidth - shiftAmt; ++i) - if (API[i+shiftAmt]) API.set(i); - else API.clear(i); - for (; i < API.BitWidth; ++i) - API.clear(i); + APInt Result(getMemory(getNumWords(width)), width); + + // Copy full words. + unsigned i; + uint64_t word = 0; + for (i = 0; i != BitWidth / APINT_BITS_PER_WORD; i++) { + word = getRawData()[i]; + Result.pVal[i] = word; } - return API; -} -/// Left-shift this APInt by shiftAmt. -/// @brief Left-shift function. -APInt APInt::shl(uint32_t shiftAmt) const { - APInt API(*this); - if (API.isSingleWord()) - API.VAL <<= shiftAmt; - else if (shiftAmt >= API.BitWidth) - memset(API.pVal, 0, API.getNumWords() * APINT_WORD_SIZE); - else { - if (uint32_t offset = shiftAmt / APINT_BITS_PER_WORD) { - for (uint32_t i = API.getNumWords() - 1; i > offset - 1; --i) - API.pVal[i] = API.pVal[i-offset]; - memset(API.pVal, 0, offset * APINT_WORD_SIZE); - } - shiftAmt %= APINT_BITS_PER_WORD; - uint32_t i; - for (i = API.getNumWords() - 1; i > 0; --i) - API.pVal[i] = (API.pVal[i] << shiftAmt) | - (API.pVal[i-1] >> (APINT_BITS_PER_WORD - shiftAmt)); - API.pVal[i] <<= shiftAmt; - } - API.clearUnusedBits(); - return API; -} - -#if 0 -/// subMul - This function substracts x[len-1:0] * y from -/// dest[offset+len-1:offset], and returns the most significant -/// word of the product, minus the borrow-out from the subtraction. -static uint32_t subMul(uint32_t dest[], uint32_t offset, - uint32_t x[], uint32_t len, uint32_t y) { - uint64_t yl = (uint64_t) y & 0xffffffffL; - uint32_t carry = 0; - uint32_t j = 0; - do { - uint64_t prod = ((uint64_t) x[j] & 0xffffffffUL) * yl; - uint32_t prod_low = (uint32_t) prod; - uint32_t prod_high = (uint32_t) (prod >> 32); - prod_low += carry; - carry = (prod_low < carry ? 1 : 0) + prod_high; - uint32_t x_j = dest[offset+j]; - prod_low = x_j - prod_low; - if (prod_low > x_j) ++carry; - dest[offset+j] = prod_low; - } while (++j < len); - return carry; -} + // Read and sign-extend any partial word. + unsigned bits = (0 - BitWidth) % APINT_BITS_PER_WORD; + if (bits != 0) + word = (int64_t)getRawData()[i] << bits >> bits; + else + word = (int64_t)word >> (APINT_BITS_PER_WORD - 1); -/// unitDiv - This function divides N by D, -/// and returns (remainder << 32) | quotient. -/// Assumes (N >> 32) < D. -static uint64_t unitDiv(uint64_t N, uint32_t D) { - uint64_t q, r; // q: quotient, r: remainder. - uint64_t a1 = N >> 32; // a1: high 32-bit part of N. - uint64_t a0 = N & 0xffffffffL; // a0: low 32-bit part of N - if (a1 < ((D - a1 - (a0 >> 31)) & 0xffffffffL)) { - q = N / D; - r = N % D; - } - else { - // Compute c1*2^32 + c0 = a1*2^32 + a0 - 2^31*d - uint64_t c = N - ((uint64_t) D << 31); - // Divide (c1*2^32 + c0) by d - q = c / D; - r = c % D; - // Add 2^31 to quotient - q += 1 << 31; + // Write remaining full words. + for (; i != width / APINT_BITS_PER_WORD; i++) { + Result.pVal[i] = word; + word = (int64_t)word >> (APINT_BITS_PER_WORD - 1); } - return (r << 32) | (q & 0xFFFFFFFFl); + // Write any partial word. + bits = (0 - width) % APINT_BITS_PER_WORD; + if (bits != 0) + Result.pVal[i] = word << bits >> bits; + + return Result; } -#endif +// Zero extend to a new width. +APInt APInt::zext(unsigned width) const { + assert(width > BitWidth && "Invalid APInt ZeroExtend request"); -/// div - This is basically Knuth's formulation of the classical algorithm. -/// Correspondance with Knuth's notation: -/// Knuth's u[0:m+n] == zds[nx:0]. -/// Knuth's v[1:n] == y[ny-1:0] -/// Knuth's n == ny. -/// Knuth's m == nx-ny. -/// Our nx == Knuth's m+n. -/// Could be re-implemented using gmp's mpn_divrem: -/// zds[nx] = mpn_divrem (&zds[ny], 0, zds, nx, y, ny). + if (width <= APINT_BITS_PER_WORD) + return APInt(width, VAL); -/// 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) { + APInt Result(getMemory(getNumWords(width)), width); + + // Copy words. + unsigned i; + for (i = 0; i != getNumWords(); i++) + Result.pVal[i] = getRawData()[i]; + + // Zero remaining words. + memset(&Result.pVal[i], 0, (Result.getNumWords() - i) * 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. +/// @brief Arithmetic right-shift function. +APInt APInt::ashr(const APInt &shiftAmt) const { + return ashr((unsigned)shiftAmt.getLimitedValue(BitWidth)); +} + +/// Arithmetic right-shift this APInt by shiftAmt. +/// @brief Arithmetic right-shift function. +APInt APInt::ashr(unsigned 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 { + unsigned 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, true); + 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 + unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word + unsigned offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift + unsigned breakWord = getNumWords() - 1 - offset; // last word affected + unsigned 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 (unsigned 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 (unsigned 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 extension 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 (unsigned i = breakWord+1; i < getNumWords(); ++i) + val[i] = fillValue; + APInt Result(val, BitWidth); + Result.clearUnusedBits(); + return Result; +} + +/// Logical right-shift this APInt by shiftAmt. +/// @brief Logical right-shift function. +APInt APInt::lshr(const APInt &shiftAmt) const { + return lshr((unsigned)shiftAmt.getLimitedValue(BitWidth)); +} + +/// Logical right-shift this APInt by shiftAmt. +/// @brief Logical right-shift function. +APInt APInt::lshr(unsigned 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); + + // If none of the bits are shifted out, the result is *this. This avoids + // issues with shifting by the size of the integer type, which produces + // undefined results in the code below. This is also an optimization. + if (shiftAmt == 0) + return *this; + + // 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) { + lshrNear(val, pVal, getNumWords(), shiftAmt); + APInt Result(val, BitWidth); + Result.clearUnusedBits(); + return Result; + } + + // Compute some values needed by the remaining shift algorithms + unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; + unsigned offset = shiftAmt / APINT_BITS_PER_WORD; + + // If we are shifting whole words, just move whole words + if (wordShift == 0) { + for (unsigned i = 0; i < getNumWords() - offset; ++i) + val[i] = pVal[i+offset]; + for (unsigned i = getNumWords()-offset; i < getNumWords(); i++) + val[i] = 0; + APInt Result(val, BitWidth); + Result.clearUnusedBits(); + return Result; + } + + // Shift the low order words + unsigned breakWord = getNumWords() - offset -1; + for (unsigned 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 (unsigned i = breakWord+1; i < getNumWords(); ++i) + val[i] = 0; + APInt Result(val, BitWidth); + Result.clearUnusedBits(); + return Result; +} + +/// Left-shift this APInt by shiftAmt. +/// @brief Left-shift function. +APInt APInt::shl(const APInt &shiftAmt) const { + // It's undefined behavior in C to shift by BitWidth or greater. + return shl((unsigned)shiftAmt.getLimitedValue(BitWidth)); +} + +APInt APInt::shlSlowCase(unsigned shiftAmt) const { + // 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); + + // If none of the bits are shifted out, the result is *this. This avoids a + // lshr by the words size in the loop below which can produce incorrect + // results. It also avoids the expensive computation below for a common case. + if (shiftAmt == 0) + return *this; + + // 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 (unsigned i = 0; i < getNumWords(); i++) { + val[i] = pVal[i] << shiftAmt | carry; + carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt); + } + APInt Result(val, BitWidth); + Result.clearUnusedBits(); + return Result; + } + + // Compute some values needed by the remaining shift algorithms + unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; + unsigned offset = shiftAmt / APINT_BITS_PER_WORD; + + // If we are shifting whole words, just move whole words + if (wordShift == 0) { + for (unsigned i = 0; i < offset; i++) + val[i] = 0; + for (unsigned i = offset; i < getNumWords(); i++) + val[i] = pVal[i-offset]; + APInt Result(val, BitWidth); + Result.clearUnusedBits(); + return Result; + } + + // Copy whole words from this to Result. + unsigned 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; + APInt Result(val, BitWidth); + Result.clearUnusedBits(); + return Result; +} + +APInt APInt::rotl(const APInt &rotateAmt) const { + return rotl((unsigned)rotateAmt.getLimitedValue(BitWidth)); +} + +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((unsigned)rotateAmt.getLimitedValue(BitWidth)); +} + +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() ? 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) { + return APInt(BitWidth, + uint64_t(::round(::sqrt(double(isSingleWord()?VAL: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. +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. Calcuate 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). + return t[i].isNegative() ? t[i] + modulo : 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(unsigned *u, unsigned *v, unsigned *q, unsigned* 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"); - // 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; - - // 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 + // b denotes the base of the number system. In our case b is 2^32. + LLVM_CONSTEXPR uint64_t b = uint64_t(1) << 32; + + DEBUG(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n'); + DEBUG(dbgs() << "KnuthDiv: original:"); + DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]); + DEBUG(dbgs() << " by"); + DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]); + DEBUG(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. - uint32_t shift = CountLeadingZeros_32(v[n-1]); - uint32_t v_carry = 0; - uint32_t u_carry = 0; + unsigned shift = countLeadingZeros(v[n-1]); + unsigned v_carry = 0; + unsigned u_carry = 0; if (shift) { - for (uint32_t i = 0; i < m+n; ++i) { - uint32_t u_tmp = u[i] >> (32 - shift); + for (unsigned i = 0; i < m+n; ++i) { + unsigned 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); + for (unsigned i = 0; i < n; ++i) { + unsigned v_tmp = v[i] >> (32 - shift); v[i] = (v[i] << shift) | v_carry; v_carry = v_tmp; } } u[m+n] = u_carry; + DEBUG(dbgs() << "KnuthDiv: normal:"); + DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]); + DEBUG(dbgs() << " by"); + DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]); + DEBUG(dbgs() << '\n'); + // D2. [Initialize j.] Set j to m. This is the loop counter over the places. int j = m; do { - // D3. [Calculate q'.]. + DEBUG(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, 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 qp = ((uint64_t(u[j+n]) << 32) | uint64_t(u[j+n-1])) / v[n-1]; - uint64_t rp = ((uint64_t(u[j+n]) << 32) | uint64_t(u[j+n-1])) % v[n-1]; + // 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(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) - if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) { + if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2])) qp--; - rp += v[n-1]; - } - - // D4. [Multiply and subtract.] Replace u with u - q*v (for each word). - uint32_t borrow = 0; - for (uint32_t i = 0; i < n; i++) { - uint32_t save = u[j+i]; - u[j+i] = uint64_t(u[j+i]) - (qp * v[i]) - borrow; - if (u[j+i] > save) { - borrow = 1; - u[j+i+1] += b; - } else { - borrow = 0; - } } - if (borrow) - u[j+n] += 1; + DEBUG(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 - (unsigned)p; + u[j+i] = (unsigned)subres; + borrow = (p >> 32) - (subres >> 32); + DEBUG(dbgs() << "KnuthDiv: u[j+i] = " << u[j+i] + << ", borrow = " << borrow << '\n'); + } + bool isNeg = u[j+n] < borrow; + u[j+n] -= (unsigned)borrow; + + DEBUG(dbgs() << "KnuthDiv: after subtraction:"); + DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]); + DEBUG(dbgs() << '\n'); - // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was + // 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 (borrow) { - // D6. [Add back]. The probability that this step is necessary is very + q[j] = (unsigned)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. Decreate qj by 1 and add v[...] to u[...]. 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. - uint32_t carry = 0; - for (uint32_t i = 0; i < n; i++) { - uint32_t save = u[j+i]; + // 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++) { + unsigned limit = std::min(u[j+i],v[i]); u[j+i] += v[i] + carry; - carry = u[j+i] < save; + carry = u[j+i] < limit || (carry && u[j+i] == limit); } + u[j+n] += carry; } + DEBUG(dbgs() << "KnuthDiv: after correction:"); + DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]); + DEBUG(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); - // D7. [Loop on j.] Decreate j by one. Now if j >= 0, go back to D3. - j--; - } while (j >= 0); + DEBUG(dbgs() << "KnuthDiv: quotient:"); + DEBUG(for (int i = m; i >=0; i--) dbgs() <<" " << q[i]); + DEBUG(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 @@ -1125,65 +1639,88 @@ static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* 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 - uint32_t mask = ~0u >> (32 - shift); - uint32_t carry = 0; - for (int i = n-1; i >= 0; i--) { - uint32_t save = u[i] & mask; - r[i] = (u[i] >> shift) | carry; - carry = save; + if (shift) { + unsigned carry = 0; + DEBUG(dbgs() << "KnuthDiv: remainder:"); + for (int i = n-1; i >= 0; i--) { + r[i] = (u[i] >> shift) | carry; + carry = u[i] << (32 - shift); + DEBUG(dbgs() << " " << r[i]); + } + } else { + for (int i = n-1; i >= 0; i--) { + r[i] = u[i]; + DEBUG(dbgs() << " " << r[i]); + } } + DEBUG(dbgs() << '\n'); } + DEBUG(dbgs() << '\n'); } -// This function makes calling KnuthDiv a little more convenient. It uses -// APInt parameters instead of uint32_t* parameters. It can also divide APInt -// values of different widths. -void APInt::divide(const APInt LHS, uint32_t lhsWords, - const APInt &RHS, uint32_t rhsWords, +void APInt::divide(const APInt LHS, unsigned lhsWords, + const APInt &RHS, unsigned rhsWords, APInt *Quotient, APInt *Remainder) { assert(lhsWords >= rhsWords && "Fractional result"); - // First, compose the values into an array of 32-bit words instead of + // 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 + // 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. - uint64_t mask = ~0ull >> (sizeof(uint32_t)*8); - uint32_t n = rhsWords * 2; - uint32_t m = (lhsWords * 2) - n; - // FIXME: allocate space on stack if m and n are sufficiently small. - uint32_t *U = new uint32_t[m + n + 1]; - memset(U, 0, (m+n+1)*sizeof(uint32_t)); + uint64_t mask = ~0ull >> (sizeof(unsigned)*CHAR_BIT); + 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. + unsigned SPACE[128]; + unsigned *U = nullptr; + unsigned *V = nullptr; + unsigned *Q = nullptr; + unsigned *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 unsigned[m + n + 1]; + V = new unsigned[n]; + Q = new unsigned[m+n]; + if (Remainder) + R = new unsigned[n]; + } + + // Initialize the dividend + memset(U, 0, (m+n+1)*sizeof(unsigned)); for (unsigned i = 0; i < lhsWords; ++i) { - uint64_t tmp = (lhsWords == 1 ? LHS.VAL : LHS.pVal[i]); - U[i * 2] = tmp & mask; - U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8); + uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]); + U[i * 2] = (unsigned)(tmp & mask); + U[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT)); } U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm. - uint32_t *V = new uint32_t[n]; - memset(V, 0, (n)*sizeof(uint32_t)); + // Initialize the divisor + memset(V, 0, (n)*sizeof(unsigned)); for (unsigned i = 0; i < rhsWords; ++i) { - uint64_t tmp = (rhsWords == 1 ? RHS.VAL : RHS.pVal[i]); - V[i * 2] = tmp & mask; - V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8); + uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]); + V[i * 2] = (unsigned)(tmp & mask); + V[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT)); } - // Set up the quotient and remainder - uint32_t *Q = new uint32_t[m+n]; - memset(Q, 0, (m+n) * sizeof(uint32_t)); - uint32_t *R = 0; - if (Remainder) { - R = new uint32_t[n]; - memset(R, 0, n * sizeof(uint32_t)); - } + // initialize the quotient and remainder + memset(Q, 0, (m+n) * sizeof(unsigned)); + if (Remainder) + memset(R, 0, n * sizeof(unsigned)); - // Now, adjust m and n for the Knuth division. n is the number of words in + // 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 + // 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--; @@ -1200,8 +1737,8 @@ void APInt::divide(const APInt LHS, uint32_t lhsWords, // 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; + unsigned divisor = V[0]; + unsigned 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) { @@ -1209,13 +1746,13 @@ void APInt::divide(const APInt LHS, uint32_t lhsWords, remainder = 0; } else if (partial_dividend < divisor) { Q[i] = 0; - remainder = partial_dividend; + remainder = (unsigned)partial_dividend; } else if (partial_dividend == divisor) { Q[i] = 1; remainder = 0; } else { - Q[i] = partial_dividend / divisor; - remainder = partial_dividend - (Q[i] * divisor); + Q[i] = (unsigned)(partial_dividend / divisor); + remainder = (unsigned)(partial_dividend - (Q[i] * divisor)); } } if (R) @@ -1233,17 +1770,19 @@ void APInt::divide(const APInt LHS, uint32_t lhsWords, if (Quotient->isSingleWord()) Quotient->VAL = 0; else - delete Quotient->pVal; + delete [] Quotient->pVal; Quotient->BitWidth = LHS.BitWidth; if (!Quotient->isSingleWord()) - Quotient->pVal = getClearedMemory(lhsWords); + Quotient->pVal = getClearedMemory(Quotient->getNumWords()); } else - Quotient->clear(); + Quotient->clearAllBits(); - // The quotient is in Q. Reconstitute the quotient into Quotient's low + // The quotient is in Q. Reconstitute the quotient into Quotient's low // order words. + // This case is currently dead as all users of divide() handle trivial cases + // earlier. if (lhsWords == 1) { - uint64_t tmp = + uint64_t tmp = uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2)); if (Quotient->isSingleWord()) Quotient->VAL = tmp; @@ -1252,7 +1791,7 @@ void APInt::divide(const APInt LHS, uint32_t lhsWords, } else { assert(!Quotient->isSingleWord() && "Quotient APInt not large enough"); for (unsigned i = 0; i < lhsWords; ++i) - Quotient->pVal[i] = + Quotient->pVal[i] = uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2)); } } @@ -1264,17 +1803,17 @@ void APInt::divide(const APInt LHS, uint32_t lhsWords, if (Remainder->isSingleWord()) Remainder->VAL = 0; else - delete Remainder->pVal; + delete [] Remainder->pVal; Remainder->BitWidth = RHS.BitWidth; if (!Remainder->isSingleWord()) - Remainder->pVal = getClearedMemory(rhsWords); + Remainder->pVal = getClearedMemory(Remainder->getNumWords()); } else - Remainder->clear(); + Remainder->clearAllBits(); // The remainder is in R. Reconstitute the remainder into Remainder's low // order words. if (rhsWords == 1) { - uint64_t tmp = + uint64_t tmp = uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2)); if (Remainder->isSingleWord()) Remainder->VAL = tmp; @@ -1283,20 +1822,20 @@ void APInt::divide(const APInt LHS, uint32_t lhsWords, } else { assert(!Remainder->isSingleWord() && "Remainder APInt not large enough"); for (unsigned i = 0; i < rhsWords; ++i) - Remainder->pVal[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. - delete [] U; - delete [] V; - delete [] Q; - delete [] R; + if (U != &SPACE[0]) { + delete [] U; + delete [] V; + delete [] Q; + delete [] R; + } } -/// Unsigned divide this APInt by APInt RHS. -/// @brief Unsigned division function for APInt. APInt APInt::udiv(const APInt& RHS) const { assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); @@ -1307,41 +1846,44 @@ APInt APInt::udiv(const APInt& RHS) const { } // 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); + unsigned rhsBits = RHS.getActiveBits(); + unsigned 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); - - // Make a temporary to hold the result - APInt Result(*this); + unsigned lhsBits = this->getActiveBits(); + unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1); // Deal with some degenerate cases - if (!lhsWords) - return Result; // 0 / X == 0 - else if (lhsWords < rhsWords || Result.ult(RHS)) { - // X / Y with X < Y == 0 - memset(Result.pVal, 0, Result.getNumWords() * APINT_WORD_SIZE); - return Result; - } else if (Result == RHS) { - // X / X == 1 - memset(Result.pVal, 0, Result.getNumWords() * APINT_WORD_SIZE); - Result.pVal[0] = 1; - return Result; + 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 - Result.pVal[0] /= RHS.pVal[0]; - return Result; + 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); + divide(*this, lhsWords, RHS, rhsWords, &Quotient, nullptr); return Quotient; } -/// Unsigned remainder operation on APInt. -/// @brief Function for unsigned remainder operation. +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::urem(const APInt& RHS) const { assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); if (isSingleWord()) { @@ -1349,186 +1891,1017 @@ APInt APInt::urem(const APInt& RHS) const { return APInt(BitWidth, VAL % RHS.VAL); } - // Make a temporary to hold the result - APInt Result(*this); + // Get some facts about the LHS + unsigned lhsBits = getActiveBits(); + unsigned 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); + unsigned rhsBits = RHS.getActiveBits(); + unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); assert(rhsWords && "Performing remainder operation by zero ???"); - // Get some facts about the LHS - uint32_t lhsBits = Result.getActiveBits(); - uint32_t lhsWords = !lhsBits ? 0 : (Result.whichWord(lhsBits - 1) + 1); - // Check the degenerate cases if (lhsWords == 0) { - // 0 % Y == 0 - memset(Result.pVal, 0, Result.getNumWords() * APINT_WORD_SIZE); - return Result; - } else if (lhsWords < rhsWords || Result.ult(RHS)) { - // X % Y == X iff X < Y - return Result; - } else if (Result == RHS) { + // 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; - memset(Result.pVal, 0, Result.getNumWords() * APINT_WORD_SIZE); - return Result; + return APInt(BitWidth, 0); } else if (lhsWords == 1) { // All high words are zero, just use native remainder - Result.pVal[0] %= RHS.pVal[0]; - return Result; + return APInt(BitWidth, pVal[0] % RHS.pVal[0]); } - // We have to compute it the hard way. Invoke the Knute divide algorithm. + // We have to compute it the hard way. Invoke the Knuth divide algorithm. APInt Remainder(1,0); - divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder); + divide(*this, lhsWords, RHS, rhsWords, nullptr, &Remainder); return Remainder; } -/// @brief Converts a char array into an integer. -void APInt::fromString(uint32_t numbits, const char *StrStart, uint32_t slen, - uint8_t radix) { - assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) && - "Radix should be 2, 8, 10, or 16!"); - assert(StrStart && "String is null?"); - uint32_t size = 0; - // If the radix is a power of 2, read the input - // from most significant to least significant. - if ((radix & (radix - 1)) == 0) { - uint32_t nextBitPos = 0; - uint32_t bits_per_digit = radix / 8 + 2; - uint64_t resDigit = 0; - BitWidth = slen * bits_per_digit; - if (getNumWords() > 1) - pVal = getMemory(getNumWords()); - for (int i = slen - 1; i >= 0; --i) { - uint64_t digit = StrStart[i] - '0'; - resDigit |= digit << nextBitPos; - nextBitPos += bits_per_digit; - if (nextBitPos >= APINT_BITS_PER_WORD) { - if (isSingleWord()) { - VAL = resDigit; - break; - } - pVal[size++] = resDigit; - nextBitPos -= APINT_BITS_PER_WORD; - resDigit = digit >> (bits_per_digit - nextBitPos); - } +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); +} + +void APInt::udivrem(const APInt &LHS, const APInt &RHS, + APInt &Quotient, APInt &Remainder) { + assert(LHS.BitWidth == RHS.BitWidth && "Bit widths must be the same"); + + // First, deal with the easy case + if (LHS.isSingleWord()) { + assert(RHS.VAL != 0 && "Divide by zero?"); + uint64_t QuotVal = LHS.VAL / RHS.VAL; + uint64_t RemVal = LHS.VAL % RHS.VAL; + Quotient = APInt(LHS.BitWidth, QuotVal); + Remainder = APInt(LHS.BitWidth, RemVal); + return; + } + + // Get some size facts about the dividend and divisor + unsigned lhsBits = LHS.getActiveBits(); + unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1); + unsigned rhsBits = RHS.getActiveBits(); + unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); + + // Check the degenerate cases + if (lhsWords == 0) { + Quotient = 0; // 0 / Y ===> 0 + Remainder = 0; // 0 % Y ===> 0 + return; + } + + if (lhsWords < rhsWords || LHS.ult(RHS)) { + Remainder = LHS; // X % Y ===> X, iff X < Y + Quotient = 0; // X / Y ===> 0, iff X < Y + return; + } + + if (LHS == RHS) { + Quotient = 1; // X / X ===> 1 + Remainder = 0; // X % X ===> 0; + return; + } + + if (lhsWords == 1 && rhsWords == 1) { + // There is only one word to consider so use the native versions. + uint64_t lhsValue = LHS.isSingleWord() ? LHS.VAL : LHS.pVal[0]; + uint64_t rhsValue = RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0]; + Quotient = APInt(LHS.getBitWidth(), lhsValue / rhsValue); + Remainder = APInt(LHS.getBitWidth(), lhsValue % rhsValue); + return; + } + + // Okay, lets do it the long way + divide(LHS, lhsWords, RHS, rhsWords, &Quotient, &Remainder); +} + +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 = -Quotient; } - if (!isSingleWord() && size <= getNumWords()) - pVal[size] = resDigit; - } else { // General case. The radix is not a power of 2. - // For 10-radix, the max value of 64-bit integer is 18446744073709551615, - // and its digits number is 20. - const uint32_t chars_per_word = 20; - if (slen < chars_per_word || - (slen == chars_per_word && // In case the value <= 2^64 - 1 - strcmp(StrStart, "18446744073709551615") <= 0)) { - BitWidth = APINT_BITS_PER_WORD; - VAL = strtoull(StrStart, 0, 10); - } else { // In case the value > 2^64 - 1 - BitWidth = (slen / chars_per_word + 1) * APINT_BITS_PER_WORD; - pVal = getClearedMemory(getNumWords()); - uint32_t str_pos = 0; - while (str_pos < slen) { - uint32_t chunk = slen - str_pos; - if (chunk > chars_per_word - 1) - chunk = chars_per_word - 1; - uint64_t resDigit = StrStart[str_pos++] - '0'; - uint64_t big_base = radix; - while (--chunk > 0) { - resDigit = resDigit * radix + StrStart[str_pos++] - '0'; - big_base *= radix; - } - - uint64_t carry; - if (!size) - carry = resDigit; - else { - carry = mul_1(pVal, pVal, size, big_base); - carry += add_1(pVal, pVal, size, resDigit); - } - - if (carry) pVal[size++] = carry; - } + Remainder = -Remainder; + } else if (RHS.isNegative()) { + APInt::udivrem(LHS, -RHS, Quotient, Remainder); + Quotient = -Quotient; + } else { + APInt::udivrem(LHS, RHS, Quotient, Remainder); + } +} + +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 { + APInt Res = *this * RHS; + + if (*this != 0 && RHS != 0) + Overflow = Res.udiv(RHS) != *this || Res.udiv(*this) != RHS; + else + Overflow = false; + 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; +} + + + + +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 (!isSingleWord()) + pVal = getClearedMemory(getNumWords()); + + // Figure out if we can shift instead of multiply + unsigned 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 (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 *= 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->flipAllBits(); } } -/// to_string - This function translates the APInt into a string. -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(); +void APInt::toString(SmallVectorImpl &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 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); + char Buffer[65]; + char *BufPtr = Buffer+65; + + uint64_t N; + if (!Signed) { + N = getZExtValue(); } 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; + int64_t I = getSExtValue(); + if (I >= 0) { + N = I; + } else { + Str.push_back('-'); + N = -(uint64_t)I; } } - 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; - } + + while (*Prefix) { + Str.push_back(*Prefix); + ++Prefix; + }; + + while (N) { + *--BufPtr = Digits[N % Radix]; + N /= Radix; } - return result; + Str.append(BufPtr, Buffer+65); + return; } - APInt tmp(*this); - APInt divisor(4, radix); - APInt zero(tmp.getBitWidth(), 0); - size_t insert_at = 0; - if (wantSigned && tmp[BitWidth-1]) { + 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.flip(); - tmp++; - result = "-"; - insert_at = 1; - } - if (tmp == 0) - result = "0"; - else while (tmp.ne(zero)) { - APInt APdigit(1,0); - divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), 0, &APdigit); - uint32_t digit = APdigit.getValue(); - assert(digit < radix && "urem failed"); - result.insert(insert_at,digits[digit]); - APInt tmp2(tmp.getBitWidth(), 0); - divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2, 0); - tmp = tmp2; + Tmp.flipAllBits(); + ++Tmp; + Str.push_back('-'); } - return result; + 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 + // equaly. 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 != 0) { + unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt; + Str.push_back(Digits[Digit]); + Tmp = Tmp.lshr(ShiftAmt); + } + } else { + APInt divisor(Radix == 10? 4 : 8, Radix); + while (Tmp != 0) { + APInt APdigit(1, 0); + APInt tmp2(Tmp.getBitWidth(), 0); + divide(Tmp, Tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2, + &APdigit); + unsigned Digit = (unsigned)APdigit.getZExtValue(); + assert(Digit < Radix && "divide failed"); + Str.push_back(Digits[Digit]); + Tmp = tmp2; + } + } + + // Reverse the digits before returning. + std::reverse(Str.begin()+StartDig, Str.end()); +} + +/// Returns the APInt as a std::string. Note that this is an inefficient method. +/// It is better to pass in a SmallVector/SmallString to the methods above. +std::string APInt::toString(unsigned Radix = 10, bool Signed = true) const { + SmallString<40> S; + toString(S, Radix, Signed, /* formatAsCLiteral = */false); + return S.str(); +} + + +void APInt::dump() const { + SmallString<40> S, U; + this->toStringUnsigned(U); + this->toStringSigned(S); + dbgs() << "APInt(" << BitWidth << "b, " + << U << "u " << S << "s)"; +} + +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(integerPartWidth % 2 == 0, "Part width must be divisible by 2!"); + +/* Some handy functions local to this file. */ +namespace { + + /* Returns the integer part with the least significant BITS set. + BITS cannot be zero. */ + static inline integerPart + lowBitMask(unsigned int bits) + { + assert(bits != 0 && bits <= integerPartWidth); + + return ~(integerPart) 0 >> (integerPartWidth - bits); + } + + /* Returns the value of the lower half of PART. */ + static inline integerPart + lowHalf(integerPart part) + { + return part & lowBitMask(integerPartWidth / 2); + } + + /* Returns the value of the upper half of PART. */ + static inline integerPart + highHalf(integerPart part) + { + return part >> (integerPartWidth / 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 int + partMSB(integerPart 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 int + partLSB(integerPart 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(integerPart *dst, integerPart part, unsigned int parts) +{ + unsigned int i; + + assert(parts > 0); + + dst[0] = part; + for (i = 1; i < parts; i++) + dst[i] = 0; +} + +/* Assign one bignum to another. */ +void +APInt::tcAssign(integerPart *dst, const integerPart *src, unsigned int parts) +{ + unsigned int i; + + for (i = 0; i < parts; i++) + dst[i] = src[i]; +} + +/* Returns true if a bignum is zero, false otherwise. */ +bool +APInt::tcIsZero(const integerPart *src, unsigned int parts) +{ + unsigned int i; + + for (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 integerPart *parts, unsigned int bit) +{ + return (parts[bit / integerPartWidth] & + ((integerPart) 1 << bit % integerPartWidth)) != 0; +} + +/* Set the given bit of a bignum. */ +void +APInt::tcSetBit(integerPart *parts, unsigned int bit) +{ + parts[bit / integerPartWidth] |= (integerPart) 1 << (bit % integerPartWidth); +} + +/* Clears the given bit of a bignum. */ +void +APInt::tcClearBit(integerPart *parts, unsigned int bit) +{ + parts[bit / integerPartWidth] &= + ~((integerPart) 1 << (bit % integerPartWidth)); +} + +/* 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 int +APInt::tcLSB(const integerPart *parts, unsigned int n) +{ + unsigned int i, lsb; + + for (i = 0; i < n; i++) { + if (parts[i] != 0) { + lsb = partLSB(parts[i]); + + return lsb + i * integerPartWidth; + } + } + + 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 int +APInt::tcMSB(const integerPart *parts, unsigned int n) +{ + unsigned int msb; + + do { + --n; + + if (parts[n] != 0) { + msb = partMSB(parts[n]); + + return msb + n * integerPartWidth; + } + } 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(integerPart *dst, unsigned int dstCount,const integerPart *src, + unsigned int srcBits, unsigned int srcLSB) +{ + unsigned int firstSrcPart, dstParts, shift, n; + + dstParts = (srcBits + integerPartWidth - 1) / integerPartWidth; + assert(dstParts <= dstCount); + + firstSrcPart = srcLSB / integerPartWidth; + tcAssign (dst, src + firstSrcPart, dstParts); + + shift = srcLSB % integerPartWidth; + tcShiftRight (dst, dstParts, shift); + + /* We now have (dstParts * integerPartWidth - shift) bits from SRC + in DST. If this is less that srcBits, append the rest, else + clear the high bits. */ + n = dstParts * integerPartWidth - shift; + if (n < srcBits) { + integerPart mask = lowBitMask (srcBits - n); + dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask) + << n % integerPartWidth); + } else if (n > srcBits) { + if (srcBits % integerPartWidth) + dst[dstParts - 1] &= lowBitMask (srcBits % integerPartWidth); + } + + /* Clear high parts. */ + while (dstParts < dstCount) + dst[dstParts++] = 0; +} + +/* DST += RHS + C where C is zero or one. Returns the carry flag. */ +integerPart +APInt::tcAdd(integerPart *dst, const integerPart *rhs, + integerPart c, unsigned int parts) +{ + unsigned int i; + + assert(c <= 1); + + for (i = 0; i < parts; i++) { + integerPart l; + + 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; +} + +/* DST -= RHS + C where C is zero or one. Returns the carry flag. */ +integerPart +APInt::tcSubtract(integerPart *dst, const integerPart *rhs, + integerPart c, unsigned int parts) +{ + unsigned int i; + + assert(c <= 1); + + for (i = 0; i < parts; i++) { + integerPart l; + + 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; +} + +/* Negate a bignum in-place. */ +void +APInt::tcNegate(integerPart *dst, unsigned int 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(integerPart *dst, const integerPart *src, + integerPart multiplier, integerPart carry, + unsigned int srcParts, unsigned int dstParts, + bool add) +{ + unsigned int i, n; + + /* 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. */ + n = dstParts < srcParts ? dstParts: srcParts; + + for (i = 0; i < n; i++) { + integerPart 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 <<= integerPartWidth / 2; + if (low + mid < low) + high++; + low += mid; + + mid = highHalf(srcPart) * lowHalf(multiplier); + high += highHalf(mid); + mid <<= integerPartWidth / 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 (i < dstParts) { + /* Full multiplication, there is no overflow. */ + assert(i + 1 == dstParts); + dst[i] = carry; + return 0; + } else { + /* 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 (; 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(integerPart *dst, const integerPart *lhs, + const integerPart *rhs, unsigned int parts) +{ + unsigned int i; + int overflow; + + assert(dst != lhs && dst != rhs); + + overflow = 0; + tcSet(dst, 0, parts); + + for (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. Returns the number of parts required to hold the + result. */ +unsigned int +APInt::tcFullMultiply(integerPart *dst, const integerPart *lhs, + const integerPart *rhs, unsigned int lhsParts, + unsigned int rhsParts) +{ + /* Put the narrower number on the LHS for less loops below. */ + if (lhsParts > rhsParts) { + return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts); + } else { + unsigned int n; + + assert(dst != lhs && dst != rhs); + + tcSet(dst, 0, rhsParts); + + for (n = 0; n < lhsParts; n++) + tcMultiplyPart(&dst[n], rhs, lhs[n], 0, rhsParts, rhsParts + 1, true); + + n = lhsParts + rhsParts; + + return n - (dst[n - 1] == 0); + } +} + +/* If RHS is zero LHS and REMAINDER are left unchanged, return one. + Otherwise set LHS to LHS / RHS with the fractional part discarded, + set REMAINDER to the remainder, return zero. i.e. + + OLD_LHS = RHS * LHS + REMAINDER + + SCRATCH is a bignum of the same size as the operands and result for + use by the routine; its contents need not be initialized and are + destroyed. LHS, REMAINDER and SCRATCH must be distinct. +*/ +int +APInt::tcDivide(integerPart *lhs, const integerPart *rhs, + integerPart *remainder, integerPart *srhs, + unsigned int parts) +{ + unsigned int n, shiftCount; + integerPart mask; + + assert(lhs != remainder && lhs != srhs && remainder != srhs); + + shiftCount = tcMSB(rhs, parts) + 1; + if (shiftCount == 0) + return true; + + shiftCount = parts * integerPartWidth - shiftCount; + n = shiftCount / integerPartWidth; + mask = (integerPart) 1 << (shiftCount % integerPartWidth); + + 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; + + 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 = (integerPart) 1 << (integerPartWidth - 1), n--; + } + + return false; +} + +/* Shift a bignum left COUNT bits in-place. Shifted in bits are zero. + There are no restrictions on COUNT. */ +void +APInt::tcShiftLeft(integerPart *dst, unsigned int parts, unsigned int count) +{ + if (count) { + unsigned int jump, shift; + + /* Jump is the inter-part jump; shift is is intra-part shift. */ + jump = count / integerPartWidth; + shift = count % integerPartWidth; + + while (parts > jump) { + integerPart part; + + parts--; + + /* dst[i] comes from the two parts src[i - jump] and, if we have + an intra-part shift, src[i - jump - 1]. */ + part = dst[parts - jump]; + if (shift) { + part <<= shift; + if (parts >= jump + 1) + part |= dst[parts - jump - 1] >> (integerPartWidth - shift); + } + + dst[parts] = part; + } + + while (parts > 0) + dst[--parts] = 0; + } } +/* Shift a bignum right COUNT bits in-place. Shifted in bits are + zero. There are no restrictions on COUNT. */ +void +APInt::tcShiftRight(integerPart *dst, unsigned int parts, unsigned int count) +{ + if (count) { + unsigned int i, jump, shift; + + /* Jump is the inter-part jump; shift is is intra-part shift. */ + jump = count / integerPartWidth; + shift = count % integerPartWidth; + + /* Perform the shift. This leaves the most significant COUNT bits + of the result at zero. */ + for (i = 0; i < parts; i++) { + integerPart part; + + if (i + jump >= parts) { + part = 0; + } else { + part = dst[i + jump]; + if (shift) { + part >>= shift; + if (i + jump + 1 < parts) + part |= dst[i + jump + 1] << (integerPartWidth - shift); + } + } + + dst[i] = part; + } + } +} + +/* Bitwise and of two bignums. */ +void +APInt::tcAnd(integerPart *dst, const integerPart *rhs, unsigned int parts) +{ + unsigned int i; + + for (i = 0; i < parts; i++) + dst[i] &= rhs[i]; +} + +/* Bitwise inclusive or of two bignums. */ +void +APInt::tcOr(integerPart *dst, const integerPart *rhs, unsigned int parts) +{ + unsigned int i; + + for (i = 0; i < parts; i++) + dst[i] |= rhs[i]; +} + +/* Bitwise exclusive or of two bignums. */ +void +APInt::tcXor(integerPart *dst, const integerPart *rhs, unsigned int parts) +{ + unsigned int i; + + for (i = 0; i < parts; i++) + dst[i] ^= rhs[i]; +} + +/* Complement a bignum in-place. */ +void +APInt::tcComplement(integerPart *dst, unsigned int parts) +{ + unsigned int i; + + for (i = 0; i < parts; i++) + dst[i] = ~dst[i]; +} + +/* Comparison (unsigned) of two bignums. */ +int +APInt::tcCompare(const integerPart *lhs, const integerPart *rhs, + unsigned int parts) +{ + while (parts) { + parts--; + if (lhs[parts] == rhs[parts]) + continue; + + if (lhs[parts] > rhs[parts]) + return 1; + else + return -1; + } + + return 0; +} + +/* Increment a bignum in-place, return the carry flag. */ +integerPart +APInt::tcIncrement(integerPart *dst, unsigned int parts) +{ + unsigned int i; + + for (i = 0; i < parts; i++) + if (++dst[i] != 0) + break; + + return i == parts; +} + +/* Decrement a bignum in-place, return the borrow flag. */ +integerPart +APInt::tcDecrement(integerPart *dst, unsigned int parts) { + for (unsigned int i = 0; i < parts; i++) { + // If the current word is non-zero, then the decrement has no effect on the + // higher-order words of the integer and no borrow can occur. Exit early. + if (dst[i]--) + return 0; + } + // If every word was zero, then there is a borrow. + return 1; +} + + +/* Set the least significant BITS bits of a bignum, clear the + rest. */ +void +APInt::tcSetLeastSignificantBits(integerPart *dst, unsigned int parts, + unsigned int bits) +{ + unsigned int i; + + i = 0; + while (bits > integerPartWidth) { + dst[i++] = ~(integerPart) 0; + bits -= integerPartWidth; + } + + if (bits) + dst[i++] = ~(integerPart) 0 >> (integerPartWidth - bits); + + while (i < parts) + dst[i++] = 0; +}