1 //===-- APInt.cpp - Implement APInt class ---------------------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file implements a class to represent arbitrary precision integer
11 // constant values and provide a variety of arithmetic operations on them.
13 //===----------------------------------------------------------------------===//
15 #include "llvm/ADT/APInt.h"
16 #include "llvm/ADT/FoldingSet.h"
17 #include "llvm/ADT/Hashing.h"
18 #include "llvm/ADT/SmallString.h"
19 #include "llvm/ADT/StringRef.h"
20 #include "llvm/Support/Debug.h"
21 #include "llvm/Support/ErrorHandling.h"
22 #include "llvm/Support/MathExtras.h"
23 #include "llvm/Support/raw_ostream.h"
30 #define DEBUG_TYPE "apint"
32 /// A utility function for allocating memory, checking for allocation failures,
33 /// and ensuring the contents are zeroed.
34 inline static uint64_t* getClearedMemory(unsigned numWords) {
35 uint64_t * result = new uint64_t[numWords];
36 assert(result && "APInt memory allocation fails!");
37 memset(result, 0, numWords * sizeof(uint64_t));
41 /// A utility function for allocating memory and checking for allocation
42 /// failure. The content is not zeroed.
43 inline static uint64_t* getMemory(unsigned numWords) {
44 uint64_t * result = new uint64_t[numWords];
45 assert(result && "APInt memory allocation fails!");
49 /// A utility function that converts a character to a digit.
50 inline static unsigned getDigit(char cdigit, uint8_t radix) {
53 if (radix == 16 || radix == 36) {
77 void APInt::initSlowCase(unsigned numBits, uint64_t val, bool isSigned) {
78 pVal = getClearedMemory(getNumWords());
80 if (isSigned && int64_t(val) < 0)
81 for (unsigned i = 1; i < getNumWords(); ++i)
85 void APInt::initSlowCase(const APInt& that) {
86 pVal = getMemory(getNumWords());
87 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE);
90 void APInt::initFromArray(ArrayRef<uint64_t> bigVal) {
91 assert(BitWidth && "Bitwidth too small");
92 assert(bigVal.data() && "Null pointer detected!");
96 // Get memory, cleared to 0
97 pVal = getClearedMemory(getNumWords());
98 // Calculate the number of words to copy
99 unsigned words = std::min<unsigned>(bigVal.size(), getNumWords());
100 // Copy the words from bigVal to pVal
101 memcpy(pVal, bigVal.data(), words * APINT_WORD_SIZE);
103 // Make sure unused high bits are cleared
107 APInt::APInt(unsigned numBits, ArrayRef<uint64_t> bigVal)
108 : BitWidth(numBits), VAL(0) {
109 initFromArray(bigVal);
112 APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[])
113 : BitWidth(numBits), VAL(0) {
114 initFromArray(makeArrayRef(bigVal, numWords));
117 APInt::APInt(unsigned numbits, StringRef Str, uint8_t radix)
118 : BitWidth(numbits), VAL(0) {
119 assert(BitWidth && "Bitwidth too small");
120 fromString(numbits, Str, radix);
123 APInt& APInt::AssignSlowCase(const APInt& RHS) {
124 // Don't do anything for X = X
128 if (BitWidth == RHS.getBitWidth()) {
129 // assume same bit-width single-word case is already handled
130 assert(!isSingleWord());
131 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE);
135 if (isSingleWord()) {
136 // assume case where both are single words is already handled
137 assert(!RHS.isSingleWord());
139 pVal = getMemory(RHS.getNumWords());
140 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
141 } else if (getNumWords() == RHS.getNumWords())
142 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
143 else if (RHS.isSingleWord()) {
148 pVal = getMemory(RHS.getNumWords());
149 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
151 BitWidth = RHS.BitWidth;
152 return clearUnusedBits();
155 APInt& APInt::operator=(uint64_t RHS) {
160 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE);
162 return clearUnusedBits();
165 /// Profile - This method 'profiles' an APInt for use with FoldingSet.
166 void APInt::Profile(FoldingSetNodeID& ID) const {
167 ID.AddInteger(BitWidth);
169 if (isSingleWord()) {
174 unsigned NumWords = getNumWords();
175 for (unsigned i = 0; i < NumWords; ++i)
176 ID.AddInteger(pVal[i]);
179 /// add_1 - This function adds a single "digit" integer, y, to the multiple
180 /// "digit" integer array, x[]. x[] is modified to reflect the addition and
181 /// 1 is returned if there is a carry out, otherwise 0 is returned.
182 /// @returns the carry of the addition.
183 static bool add_1(uint64_t dest[], uint64_t x[], unsigned len, uint64_t y) {
184 for (unsigned i = 0; i < len; ++i) {
187 y = 1; // Carry one to next digit.
189 y = 0; // No need to carry so exit early
196 /// @brief Prefix increment operator. Increments the APInt by one.
197 APInt& APInt::operator++() {
201 add_1(pVal, pVal, getNumWords(), 1);
202 return clearUnusedBits();
205 /// sub_1 - This function subtracts a single "digit" (64-bit word), y, from
206 /// the multi-digit integer array, x[], propagating the borrowed 1 value until
207 /// no further borrowing is neeeded or it runs out of "digits" in x. The result
208 /// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted.
209 /// In other words, if y > x then this function returns 1, otherwise 0.
210 /// @returns the borrow out of the subtraction
211 static bool sub_1(uint64_t x[], unsigned len, uint64_t y) {
212 for (unsigned i = 0; i < len; ++i) {
216 y = 1; // We have to "borrow 1" from next "digit"
218 y = 0; // No need to borrow
219 break; // Remaining digits are unchanged so exit early
225 /// @brief Prefix decrement operator. Decrements the APInt by one.
226 APInt& APInt::operator--() {
230 sub_1(pVal, getNumWords(), 1);
231 return clearUnusedBits();
234 /// add - This function adds the integer array x to the integer array Y and
235 /// places the result in dest.
236 /// @returns the carry out from the addition
237 /// @brief General addition of 64-bit integer arrays
238 static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y,
241 for (unsigned i = 0; i< len; ++i) {
242 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x
243 dest[i] = x[i] + y[i] + carry;
244 carry = dest[i] < limit || (carry && dest[i] == limit);
249 /// Adds the RHS APint to this APInt.
250 /// @returns this, after addition of RHS.
251 /// @brief Addition assignment operator.
252 APInt& APInt::operator+=(const APInt& RHS) {
253 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
257 add(pVal, pVal, RHS.pVal, getNumWords());
259 return clearUnusedBits();
262 /// Subtracts the integer array y from the integer array x
263 /// @returns returns the borrow out.
264 /// @brief Generalized subtraction of 64-bit integer arrays.
265 static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y,
268 for (unsigned i = 0; i < len; ++i) {
269 uint64_t x_tmp = borrow ? x[i] - 1 : x[i];
270 borrow = y[i] > x_tmp || (borrow && x[i] == 0);
271 dest[i] = x_tmp - y[i];
276 /// Subtracts the RHS APInt from this APInt
277 /// @returns this, after subtraction
278 /// @brief Subtraction assignment operator.
279 APInt& APInt::operator-=(const APInt& RHS) {
280 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
284 sub(pVal, pVal, RHS.pVal, getNumWords());
285 return clearUnusedBits();
288 /// Multiplies an integer array, x, by a uint64_t integer and places the result
290 /// @returns the carry out of the multiplication.
291 /// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer.
292 static uint64_t mul_1(uint64_t dest[], uint64_t x[], unsigned len, uint64_t y) {
293 // Split y into high 32-bit part (hy) and low 32-bit part (ly)
294 uint64_t ly = y & 0xffffffffULL, hy = y >> 32;
297 // For each digit of x.
298 for (unsigned i = 0; i < len; ++i) {
299 // Split x into high and low words
300 uint64_t lx = x[i] & 0xffffffffULL;
301 uint64_t hx = x[i] >> 32;
302 // hasCarry - A flag to indicate if there is a carry to the next digit.
303 // hasCarry == 0, no carry
304 // hasCarry == 1, has carry
305 // hasCarry == 2, no carry and the calculation result == 0.
306 uint8_t hasCarry = 0;
307 dest[i] = carry + lx * ly;
308 // Determine if the add above introduces carry.
309 hasCarry = (dest[i] < carry) ? 1 : 0;
310 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0);
311 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) +
312 // (2^32 - 1) + 2^32 = 2^64.
313 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
315 carry += (lx * hy) & 0xffffffffULL;
316 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL);
317 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) +
318 (carry >> 32) + ((lx * hy) >> 32) + hx * hy;
323 /// Multiplies integer array x by integer array y and stores the result into
324 /// the integer array dest. Note that dest's size must be >= xlen + ylen.
325 /// @brief Generalized multiplicate of integer arrays.
326 static void mul(uint64_t dest[], uint64_t x[], unsigned xlen, uint64_t y[],
328 dest[xlen] = mul_1(dest, x, xlen, y[0]);
329 for (unsigned i = 1; i < ylen; ++i) {
330 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32;
331 uint64_t carry = 0, lx = 0, hx = 0;
332 for (unsigned j = 0; j < xlen; ++j) {
333 lx = x[j] & 0xffffffffULL;
335 // hasCarry - A flag to indicate if has carry.
336 // hasCarry == 0, no carry
337 // hasCarry == 1, has carry
338 // hasCarry == 2, no carry and the calculation result == 0.
339 uint8_t hasCarry = 0;
340 uint64_t resul = carry + lx * ly;
341 hasCarry = (resul < carry) ? 1 : 0;
342 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32);
343 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
345 carry += (lx * hy) & 0xffffffffULL;
346 resul = (carry << 32) | (resul & 0xffffffffULL);
348 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+
349 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) +
350 ((lx * hy) >> 32) + hx * hy;
352 dest[i+xlen] = carry;
356 APInt& APInt::operator*=(const APInt& RHS) {
357 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
358 if (isSingleWord()) {
364 // Get some bit facts about LHS and check for zero
365 unsigned lhsBits = getActiveBits();
366 unsigned lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1;
371 // Get some bit facts about RHS and check for zero
372 unsigned rhsBits = RHS.getActiveBits();
373 unsigned rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1;
380 // Allocate space for the result
381 unsigned destWords = rhsWords + lhsWords;
382 uint64_t *dest = getMemory(destWords);
384 // Perform the long multiply
385 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords);
387 // Copy result back into *this
389 unsigned wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords;
390 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE);
393 // delete dest array and return
398 APInt& APInt::operator&=(const APInt& RHS) {
399 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
400 if (isSingleWord()) {
404 unsigned numWords = getNumWords();
405 for (unsigned i = 0; i < numWords; ++i)
406 pVal[i] &= RHS.pVal[i];
410 APInt& APInt::operator|=(const APInt& RHS) {
411 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
412 if (isSingleWord()) {
416 unsigned numWords = getNumWords();
417 for (unsigned i = 0; i < numWords; ++i)
418 pVal[i] |= RHS.pVal[i];
422 APInt& APInt::operator^=(const APInt& RHS) {
423 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
424 if (isSingleWord()) {
426 this->clearUnusedBits();
429 unsigned numWords = getNumWords();
430 for (unsigned i = 0; i < numWords; ++i)
431 pVal[i] ^= RHS.pVal[i];
432 return clearUnusedBits();
435 APInt APInt::AndSlowCase(const APInt& RHS) const {
436 unsigned numWords = getNumWords();
437 uint64_t* val = getMemory(numWords);
438 for (unsigned i = 0; i < numWords; ++i)
439 val[i] = pVal[i] & RHS.pVal[i];
440 return APInt(val, getBitWidth());
443 APInt APInt::OrSlowCase(const APInt& RHS) const {
444 unsigned numWords = getNumWords();
445 uint64_t *val = getMemory(numWords);
446 for (unsigned i = 0; i < numWords; ++i)
447 val[i] = pVal[i] | RHS.pVal[i];
448 return APInt(val, getBitWidth());
451 APInt APInt::XorSlowCase(const APInt& RHS) const {
452 unsigned numWords = getNumWords();
453 uint64_t *val = getMemory(numWords);
454 for (unsigned i = 0; i < numWords; ++i)
455 val[i] = pVal[i] ^ RHS.pVal[i];
457 // 0^0==1 so clear the high bits in case they got set.
458 return APInt(val, getBitWidth()).clearUnusedBits();
461 APInt APInt::operator*(const APInt& RHS) const {
462 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
464 return APInt(BitWidth, VAL * RHS.VAL);
470 APInt APInt::operator+(const APInt& RHS) const {
471 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
473 return APInt(BitWidth, VAL + RHS.VAL);
474 APInt Result(BitWidth, 0);
475 add(Result.pVal, this->pVal, RHS.pVal, getNumWords());
476 return Result.clearUnusedBits();
479 APInt APInt::operator-(const APInt& RHS) const {
480 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
482 return APInt(BitWidth, VAL - RHS.VAL);
483 APInt Result(BitWidth, 0);
484 sub(Result.pVal, this->pVal, RHS.pVal, getNumWords());
485 return Result.clearUnusedBits();
488 bool APInt::EqualSlowCase(const APInt& RHS) const {
489 // Get some facts about the number of bits used in the two operands.
490 unsigned n1 = getActiveBits();
491 unsigned n2 = RHS.getActiveBits();
493 // If the number of bits isn't the same, they aren't equal
497 // If the number of bits fits in a word, we only need to compare the low word.
498 if (n1 <= APINT_BITS_PER_WORD)
499 return pVal[0] == RHS.pVal[0];
501 // Otherwise, compare everything
502 for (int i = whichWord(n1 - 1); i >= 0; --i)
503 if (pVal[i] != RHS.pVal[i])
508 bool APInt::EqualSlowCase(uint64_t Val) const {
509 unsigned n = getActiveBits();
510 if (n <= APINT_BITS_PER_WORD)
511 return pVal[0] == Val;
516 bool APInt::ult(const APInt& RHS) const {
517 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
519 return VAL < RHS.VAL;
521 // Get active bit length of both operands
522 unsigned n1 = getActiveBits();
523 unsigned n2 = RHS.getActiveBits();
525 // If magnitude of LHS is less than RHS, return true.
529 // If magnitude of RHS is greather than LHS, return false.
533 // If they bot fit in a word, just compare the low order word
534 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD)
535 return pVal[0] < RHS.pVal[0];
537 // Otherwise, compare all words
538 unsigned topWord = whichWord(std::max(n1,n2)-1);
539 for (int i = topWord; i >= 0; --i) {
540 if (pVal[i] > RHS.pVal[i])
542 if (pVal[i] < RHS.pVal[i])
548 bool APInt::slt(const APInt& RHS) const {
549 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
550 if (isSingleWord()) {
551 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
552 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth);
553 return lhsSext < rhsSext;
558 bool lhsNeg = isNegative();
559 bool rhsNeg = rhs.isNegative();
561 // Sign bit is set so perform two's complement to make it positive
566 // Sign bit is set so perform two's complement to make it positive
571 // Now we have unsigned values to compare so do the comparison if necessary
572 // based on the negativeness of the values.
584 void APInt::setBit(unsigned bitPosition) {
586 VAL |= maskBit(bitPosition);
588 pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
591 /// Set the given bit to 0 whose position is given as "bitPosition".
592 /// @brief Set a given bit to 0.
593 void APInt::clearBit(unsigned bitPosition) {
595 VAL &= ~maskBit(bitPosition);
597 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
600 /// @brief Toggle every bit to its opposite value.
602 /// Toggle a given bit to its opposite value whose position is given
603 /// as "bitPosition".
604 /// @brief Toggles a given bit to its opposite value.
605 void APInt::flipBit(unsigned bitPosition) {
606 assert(bitPosition < BitWidth && "Out of the bit-width range!");
607 if ((*this)[bitPosition]) clearBit(bitPosition);
608 else setBit(bitPosition);
611 unsigned APInt::getBitsNeeded(StringRef str, uint8_t radix) {
612 assert(!str.empty() && "Invalid string length");
613 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||
615 "Radix should be 2, 8, 10, 16, or 36!");
617 size_t slen = str.size();
619 // Each computation below needs to know if it's negative.
620 StringRef::iterator p = str.begin();
621 unsigned isNegative = *p == '-';
622 if (*p == '-' || *p == '+') {
625 assert(slen && "String is only a sign, needs a value.");
628 // For radixes of power-of-two values, the bits required is accurately and
631 return slen + isNegative;
633 return slen * 3 + isNegative;
635 return slen * 4 + isNegative;
639 // This is grossly inefficient but accurate. We could probably do something
640 // with a computation of roughly slen*64/20 and then adjust by the value of
641 // the first few digits. But, I'm not sure how accurate that could be.
643 // Compute a sufficient number of bits that is always large enough but might
644 // be too large. This avoids the assertion in the constructor. This
645 // calculation doesn't work appropriately for the numbers 0-9, so just use 4
646 // bits in that case.
648 = radix == 10? (slen == 1 ? 4 : slen * 64/18)
649 : (slen == 1 ? 7 : slen * 16/3);
651 // Convert to the actual binary value.
652 APInt tmp(sufficient, StringRef(p, slen), radix);
654 // Compute how many bits are required. If the log is infinite, assume we need
656 unsigned log = tmp.logBase2();
657 if (log == (unsigned)-1) {
658 return isNegative + 1;
660 return isNegative + log + 1;
664 hash_code llvm::hash_value(const APInt &Arg) {
665 if (Arg.isSingleWord())
666 return hash_combine(Arg.VAL);
668 return hash_combine_range(Arg.pVal, Arg.pVal + Arg.getNumWords());
671 /// HiBits - This function returns the high "numBits" bits of this APInt.
672 APInt APInt::getHiBits(unsigned numBits) const {
673 return APIntOps::lshr(*this, BitWidth - numBits);
676 /// LoBits - This function returns the low "numBits" bits of this APInt.
677 APInt APInt::getLoBits(unsigned numBits) const {
678 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
682 unsigned APInt::countLeadingZerosSlowCase() const {
683 // Treat the most significand word differently because it might have
684 // meaningless bits set beyond the precision.
685 unsigned BitsInMSW = BitWidth % APINT_BITS_PER_WORD;
687 if (BitsInMSW) MSWMask = (integerPart(1) << BitsInMSW) - 1;
689 MSWMask = ~integerPart(0);
690 BitsInMSW = APINT_BITS_PER_WORD;
693 unsigned i = getNumWords();
694 integerPart MSW = pVal[i-1] & MSWMask;
696 return llvm::countLeadingZeros(MSW) - (APINT_BITS_PER_WORD - BitsInMSW);
698 unsigned Count = BitsInMSW;
699 for (--i; i > 0u; --i) {
701 Count += APINT_BITS_PER_WORD;
703 Count += llvm::countLeadingZeros(pVal[i-1]);
710 unsigned APInt::countLeadingOnes() const {
712 return CountLeadingOnes_64(VAL << (APINT_BITS_PER_WORD - BitWidth));
714 unsigned highWordBits = BitWidth % APINT_BITS_PER_WORD;
717 highWordBits = APINT_BITS_PER_WORD;
720 shift = APINT_BITS_PER_WORD - highWordBits;
722 int i = getNumWords() - 1;
723 unsigned Count = CountLeadingOnes_64(pVal[i] << shift);
724 if (Count == highWordBits) {
725 for (i--; i >= 0; --i) {
726 if (pVal[i] == -1ULL)
727 Count += APINT_BITS_PER_WORD;
729 Count += CountLeadingOnes_64(pVal[i]);
737 unsigned APInt::countTrailingZeros() const {
739 return std::min(unsigned(llvm::countTrailingZeros(VAL)), BitWidth);
742 for (; i < getNumWords() && pVal[i] == 0; ++i)
743 Count += APINT_BITS_PER_WORD;
744 if (i < getNumWords())
745 Count += llvm::countTrailingZeros(pVal[i]);
746 return std::min(Count, BitWidth);
749 unsigned APInt::countTrailingOnesSlowCase() const {
752 for (; i < getNumWords() && pVal[i] == -1ULL; ++i)
753 Count += APINT_BITS_PER_WORD;
754 if (i < getNumWords())
755 Count += CountTrailingOnes_64(pVal[i]);
756 return std::min(Count, BitWidth);
759 unsigned APInt::countPopulationSlowCase() const {
761 for (unsigned i = 0; i < getNumWords(); ++i)
762 Count += CountPopulation_64(pVal[i]);
766 /// Perform a logical right-shift from Src to Dst, which must be equal or
767 /// non-overlapping, of Words words, by Shift, which must be less than 64.
768 static void lshrNear(uint64_t *Dst, uint64_t *Src, unsigned Words,
771 for (int I = Words - 1; I >= 0; --I) {
772 uint64_t Tmp = Src[I];
773 Dst[I] = (Tmp >> Shift) | Carry;
774 Carry = Tmp << (64 - Shift);
778 APInt APInt::byteSwap() const {
779 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
781 return APInt(BitWidth, ByteSwap_16(uint16_t(VAL)));
783 return APInt(BitWidth, ByteSwap_32(unsigned(VAL)));
784 if (BitWidth == 48) {
785 unsigned Tmp1 = unsigned(VAL >> 16);
786 Tmp1 = ByteSwap_32(Tmp1);
787 uint16_t Tmp2 = uint16_t(VAL);
788 Tmp2 = ByteSwap_16(Tmp2);
789 return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1);
792 return APInt(BitWidth, ByteSwap_64(VAL));
794 APInt Result(getNumWords() * APINT_BITS_PER_WORD, 0);
795 for (unsigned I = 0, N = getNumWords(); I != N; ++I)
796 Result.pVal[I] = ByteSwap_64(pVal[N - I - 1]);
797 if (Result.BitWidth != BitWidth) {
798 lshrNear(Result.pVal, Result.pVal, getNumWords(),
799 Result.BitWidth - BitWidth);
800 Result.BitWidth = BitWidth;
805 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
807 APInt A = API1, B = API2;
810 B = APIntOps::urem(A, B);
816 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) {
823 // Get the sign bit from the highest order bit
824 bool isNeg = T.I >> 63;
826 // Get the 11-bit exponent and adjust for the 1023 bit bias
827 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
829 // If the exponent is negative, the value is < 0 so just return 0.
831 return APInt(width, 0u);
833 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
834 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
836 // If the exponent doesn't shift all bits out of the mantissa
838 return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
839 APInt(width, mantissa >> (52 - exp));
841 // If the client didn't provide enough bits for us to shift the mantissa into
842 // then the result is undefined, just return 0
843 if (width <= exp - 52)
844 return APInt(width, 0);
846 // Otherwise, we have to shift the mantissa bits up to the right location
847 APInt Tmp(width, mantissa);
848 Tmp = Tmp.shl((unsigned)exp - 52);
849 return isNeg ? -Tmp : Tmp;
852 /// RoundToDouble - This function converts this APInt to a double.
853 /// The layout for double is as following (IEEE Standard 754):
854 /// --------------------------------------
855 /// | Sign Exponent Fraction Bias |
856 /// |-------------------------------------- |
857 /// | 1[63] 11[62-52] 52[51-00] 1023 |
858 /// --------------------------------------
859 double APInt::roundToDouble(bool isSigned) const {
861 // Handle the simple case where the value is contained in one uint64_t.
862 // It is wrong to optimize getWord(0) to VAL; there might be more than one word.
863 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
865 int64_t sext = (int64_t(getWord(0)) << (64-BitWidth)) >> (64-BitWidth);
868 return double(getWord(0));
871 // Determine if the value is negative.
872 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
874 // Construct the absolute value if we're negative.
875 APInt Tmp(isNeg ? -(*this) : (*this));
877 // Figure out how many bits we're using.
878 unsigned n = Tmp.getActiveBits();
880 // The exponent (without bias normalization) is just the number of bits
881 // we are using. Note that the sign bit is gone since we constructed the
885 // Return infinity for exponent overflow
887 if (!isSigned || !isNeg)
888 return std::numeric_limits<double>::infinity();
890 return -std::numeric_limits<double>::infinity();
892 exp += 1023; // Increment for 1023 bias
894 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
895 // extract the high 52 bits from the correct words in pVal.
897 unsigned hiWord = whichWord(n-1);
899 mantissa = Tmp.pVal[0];
901 mantissa >>= n - 52; // shift down, we want the top 52 bits.
903 assert(hiWord > 0 && "huh?");
904 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
905 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
906 mantissa = hibits | lobits;
909 // The leading bit of mantissa is implicit, so get rid of it.
910 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
915 T.I = sign | (exp << 52) | mantissa;
919 // Truncate to new width.
920 APInt APInt::trunc(unsigned width) const {
921 assert(width < BitWidth && "Invalid APInt Truncate request");
922 assert(width && "Can't truncate to 0 bits");
924 if (width <= APINT_BITS_PER_WORD)
925 return APInt(width, getRawData()[0]);
927 APInt Result(getMemory(getNumWords(width)), width);
931 for (i = 0; i != width / APINT_BITS_PER_WORD; i++)
932 Result.pVal[i] = pVal[i];
934 // Truncate and copy any partial word.
935 unsigned bits = (0 - width) % APINT_BITS_PER_WORD;
937 Result.pVal[i] = pVal[i] << bits >> bits;
942 // Sign extend to a new width.
943 APInt APInt::sext(unsigned width) const {
944 assert(width > BitWidth && "Invalid APInt SignExtend request");
946 if (width <= APINT_BITS_PER_WORD) {
947 uint64_t val = VAL << (APINT_BITS_PER_WORD - BitWidth);
948 val = (int64_t)val >> (width - BitWidth);
949 return APInt(width, val >> (APINT_BITS_PER_WORD - width));
952 APInt Result(getMemory(getNumWords(width)), width);
957 for (i = 0; i != BitWidth / APINT_BITS_PER_WORD; i++) {
958 word = getRawData()[i];
959 Result.pVal[i] = word;
962 // Read and sign-extend any partial word.
963 unsigned bits = (0 - BitWidth) % APINT_BITS_PER_WORD;
965 word = (int64_t)getRawData()[i] << bits >> bits;
967 word = (int64_t)word >> (APINT_BITS_PER_WORD - 1);
969 // Write remaining full words.
970 for (; i != width / APINT_BITS_PER_WORD; i++) {
971 Result.pVal[i] = word;
972 word = (int64_t)word >> (APINT_BITS_PER_WORD - 1);
975 // Write any partial word.
976 bits = (0 - width) % APINT_BITS_PER_WORD;
978 Result.pVal[i] = word << bits >> bits;
983 // Zero extend to a new width.
984 APInt APInt::zext(unsigned width) const {
985 assert(width > BitWidth && "Invalid APInt ZeroExtend request");
987 if (width <= APINT_BITS_PER_WORD)
988 return APInt(width, VAL);
990 APInt Result(getMemory(getNumWords(width)), width);
994 for (i = 0; i != getNumWords(); i++)
995 Result.pVal[i] = getRawData()[i];
997 // Zero remaining words.
998 memset(&Result.pVal[i], 0, (Result.getNumWords() - i) * APINT_WORD_SIZE);
1003 APInt APInt::zextOrTrunc(unsigned width) const {
1004 if (BitWidth < width)
1006 if (BitWidth > width)
1007 return trunc(width);
1011 APInt APInt::sextOrTrunc(unsigned width) const {
1012 if (BitWidth < width)
1014 if (BitWidth > width)
1015 return trunc(width);
1019 APInt APInt::zextOrSelf(unsigned width) const {
1020 if (BitWidth < width)
1025 APInt APInt::sextOrSelf(unsigned width) const {
1026 if (BitWidth < width)
1031 /// Arithmetic right-shift this APInt by shiftAmt.
1032 /// @brief Arithmetic right-shift function.
1033 APInt APInt::ashr(const APInt &shiftAmt) const {
1034 return ashr((unsigned)shiftAmt.getLimitedValue(BitWidth));
1037 /// Arithmetic right-shift this APInt by shiftAmt.
1038 /// @brief Arithmetic right-shift function.
1039 APInt APInt::ashr(unsigned shiftAmt) const {
1040 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1041 // Handle a degenerate case
1045 // Handle single word shifts with built-in ashr
1046 if (isSingleWord()) {
1047 if (shiftAmt == BitWidth)
1048 return APInt(BitWidth, 0); // undefined
1050 unsigned SignBit = APINT_BITS_PER_WORD - BitWidth;
1051 return APInt(BitWidth,
1052 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1056 // If all the bits were shifted out, the result is, technically, undefined.
1057 // We return -1 if it was negative, 0 otherwise. We check this early to avoid
1058 // issues in the algorithm below.
1059 if (shiftAmt == BitWidth) {
1061 return APInt(BitWidth, -1ULL, true);
1063 return APInt(BitWidth, 0);
1066 // Create some space for the result.
1067 uint64_t * val = new uint64_t[getNumWords()];
1069 // Compute some values needed by the following shift algorithms
1070 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word
1071 unsigned offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift
1072 unsigned breakWord = getNumWords() - 1 - offset; // last word affected
1073 unsigned bitsInWord = whichBit(BitWidth); // how many bits in last word?
1074 if (bitsInWord == 0)
1075 bitsInWord = APINT_BITS_PER_WORD;
1077 // If we are shifting whole words, just move whole words
1078 if (wordShift == 0) {
1079 // Move the words containing significant bits
1080 for (unsigned i = 0; i <= breakWord; ++i)
1081 val[i] = pVal[i+offset]; // move whole word
1083 // Adjust the top significant word for sign bit fill, if negative
1085 if (bitsInWord < APINT_BITS_PER_WORD)
1086 val[breakWord] |= ~0ULL << bitsInWord; // set high bits
1088 // Shift the low order words
1089 for (unsigned i = 0; i < breakWord; ++i) {
1090 // This combines the shifted corresponding word with the low bits from
1091 // the next word (shifted into this word's high bits).
1092 val[i] = (pVal[i+offset] >> wordShift) |
1093 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1096 // Shift the break word. In this case there are no bits from the next word
1097 // to include in this word.
1098 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1100 // Deal with sign extension in the break word, and possibly the word before
1103 if (wordShift > bitsInWord) {
1106 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord));
1107 val[breakWord] |= ~0ULL;
1109 val[breakWord] |= (~0ULL << (bitsInWord - wordShift));
1113 // Remaining words are 0 or -1, just assign them.
1114 uint64_t fillValue = (isNegative() ? -1ULL : 0);
1115 for (unsigned i = breakWord+1; i < getNumWords(); ++i)
1117 return APInt(val, BitWidth).clearUnusedBits();
1120 /// Logical right-shift this APInt by shiftAmt.
1121 /// @brief Logical right-shift function.
1122 APInt APInt::lshr(const APInt &shiftAmt) const {
1123 return lshr((unsigned)shiftAmt.getLimitedValue(BitWidth));
1126 /// Logical right-shift this APInt by shiftAmt.
1127 /// @brief Logical right-shift function.
1128 APInt APInt::lshr(unsigned shiftAmt) const {
1129 if (isSingleWord()) {
1130 if (shiftAmt >= BitWidth)
1131 return APInt(BitWidth, 0);
1133 return APInt(BitWidth, this->VAL >> shiftAmt);
1136 // If all the bits were shifted out, the result is 0. This avoids issues
1137 // with shifting by the size of the integer type, which produces undefined
1138 // results. We define these "undefined results" to always be 0.
1139 if (shiftAmt >= BitWidth)
1140 return APInt(BitWidth, 0);
1142 // If none of the bits are shifted out, the result is *this. This avoids
1143 // issues with shifting by the size of the integer type, which produces
1144 // undefined results in the code below. This is also an optimization.
1148 // Create some space for the result.
1149 uint64_t * val = new uint64_t[getNumWords()];
1151 // If we are shifting less than a word, compute the shift with a simple carry
1152 if (shiftAmt < APINT_BITS_PER_WORD) {
1153 lshrNear(val, pVal, getNumWords(), shiftAmt);
1154 return APInt(val, BitWidth).clearUnusedBits();
1157 // Compute some values needed by the remaining shift algorithms
1158 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD;
1159 unsigned offset = shiftAmt / APINT_BITS_PER_WORD;
1161 // If we are shifting whole words, just move whole words
1162 if (wordShift == 0) {
1163 for (unsigned i = 0; i < getNumWords() - offset; ++i)
1164 val[i] = pVal[i+offset];
1165 for (unsigned i = getNumWords()-offset; i < getNumWords(); i++)
1167 return APInt(val,BitWidth).clearUnusedBits();
1170 // Shift the low order words
1171 unsigned breakWord = getNumWords() - offset -1;
1172 for (unsigned i = 0; i < breakWord; ++i)
1173 val[i] = (pVal[i+offset] >> wordShift) |
1174 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1175 // Shift the break word.
1176 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1178 // Remaining words are 0
1179 for (unsigned i = breakWord+1; i < getNumWords(); ++i)
1181 return APInt(val, BitWidth).clearUnusedBits();
1184 /// Left-shift this APInt by shiftAmt.
1185 /// @brief Left-shift function.
1186 APInt APInt::shl(const APInt &shiftAmt) const {
1187 // It's undefined behavior in C to shift by BitWidth or greater.
1188 return shl((unsigned)shiftAmt.getLimitedValue(BitWidth));
1191 APInt APInt::shlSlowCase(unsigned shiftAmt) const {
1192 // If all the bits were shifted out, the result is 0. This avoids issues
1193 // with shifting by the size of the integer type, which produces undefined
1194 // results. We define these "undefined results" to always be 0.
1195 if (shiftAmt == BitWidth)
1196 return APInt(BitWidth, 0);
1198 // If none of the bits are shifted out, the result is *this. This avoids a
1199 // lshr by the words size in the loop below which can produce incorrect
1200 // results. It also avoids the expensive computation below for a common case.
1204 // Create some space for the result.
1205 uint64_t * val = new uint64_t[getNumWords()];
1207 // If we are shifting less than a word, do it the easy way
1208 if (shiftAmt < APINT_BITS_PER_WORD) {
1210 for (unsigned i = 0; i < getNumWords(); i++) {
1211 val[i] = pVal[i] << shiftAmt | carry;
1212 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1214 return APInt(val, BitWidth).clearUnusedBits();
1217 // Compute some values needed by the remaining shift algorithms
1218 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD;
1219 unsigned offset = shiftAmt / APINT_BITS_PER_WORD;
1221 // If we are shifting whole words, just move whole words
1222 if (wordShift == 0) {
1223 for (unsigned i = 0; i < offset; i++)
1225 for (unsigned i = offset; i < getNumWords(); i++)
1226 val[i] = pVal[i-offset];
1227 return APInt(val,BitWidth).clearUnusedBits();
1230 // Copy whole words from this to Result.
1231 unsigned i = getNumWords() - 1;
1232 for (; i > offset; --i)
1233 val[i] = pVal[i-offset] << wordShift |
1234 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1235 val[offset] = pVal[0] << wordShift;
1236 for (i = 0; i < offset; ++i)
1238 return APInt(val, BitWidth).clearUnusedBits();
1241 APInt APInt::rotl(const APInt &rotateAmt) const {
1242 return rotl((unsigned)rotateAmt.getLimitedValue(BitWidth));
1245 APInt APInt::rotl(unsigned rotateAmt) const {
1246 rotateAmt %= BitWidth;
1249 return shl(rotateAmt) | lshr(BitWidth - rotateAmt);
1252 APInt APInt::rotr(const APInt &rotateAmt) const {
1253 return rotr((unsigned)rotateAmt.getLimitedValue(BitWidth));
1256 APInt APInt::rotr(unsigned rotateAmt) const {
1257 rotateAmt %= BitWidth;
1260 return lshr(rotateAmt) | shl(BitWidth - rotateAmt);
1263 // Square Root - this method computes and returns the square root of "this".
1264 // Three mechanisms are used for computation. For small values (<= 5 bits),
1265 // a table lookup is done. This gets some performance for common cases. For
1266 // values using less than 52 bits, the value is converted to double and then
1267 // the libc sqrt function is called. The result is rounded and then converted
1268 // back to a uint64_t which is then used to construct the result. Finally,
1269 // the Babylonian method for computing square roots is used.
1270 APInt APInt::sqrt() const {
1272 // Determine the magnitude of the value.
1273 unsigned magnitude = getActiveBits();
1275 // Use a fast table for some small values. This also gets rid of some
1276 // rounding errors in libc sqrt for small values.
1277 if (magnitude <= 5) {
1278 static const uint8_t results[32] = {
1281 /* 3- 6 */ 2, 2, 2, 2,
1282 /* 7-12 */ 3, 3, 3, 3, 3, 3,
1283 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1284 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1287 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]);
1290 // If the magnitude of the value fits in less than 52 bits (the precision of
1291 // an IEEE double precision floating point value), then we can use the
1292 // libc sqrt function which will probably use a hardware sqrt computation.
1293 // This should be faster than the algorithm below.
1294 if (magnitude < 52) {
1296 return APInt(BitWidth,
1297 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0])))));
1299 return APInt(BitWidth,
1300 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0])) + 0.5));
1304 // Okay, all the short cuts are exhausted. We must compute it. The following
1305 // is a classical Babylonian method for computing the square root. This code
1306 // was adapted to APINt from a wikipedia article on such computations.
1307 // See http://www.wikipedia.org/ and go to the page named
1308 // Calculate_an_integer_square_root.
1309 unsigned nbits = BitWidth, i = 4;
1310 APInt testy(BitWidth, 16);
1311 APInt x_old(BitWidth, 1);
1312 APInt x_new(BitWidth, 0);
1313 APInt two(BitWidth, 2);
1315 // Select a good starting value using binary logarithms.
1316 for (;; i += 2, testy = testy.shl(2))
1317 if (i >= nbits || this->ule(testy)) {
1318 x_old = x_old.shl(i / 2);
1322 // Use the Babylonian method to arrive at the integer square root:
1324 x_new = (this->udiv(x_old) + x_old).udiv(two);
1325 if (x_old.ule(x_new))
1330 // Make sure we return the closest approximation
1331 // NOTE: The rounding calculation below is correct. It will produce an
1332 // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1333 // determined to be a rounding issue with pari/gp as it begins to use a
1334 // floating point representation after 192 bits. There are no discrepancies
1335 // between this algorithm and pari/gp for bit widths < 192 bits.
1336 APInt square(x_old * x_old);
1337 APInt nextSquare((x_old + 1) * (x_old +1));
1338 if (this->ult(square))
1340 assert(this->ule(nextSquare) && "Error in APInt::sqrt computation");
1341 APInt midpoint((nextSquare - square).udiv(two));
1342 APInt offset(*this - square);
1343 if (offset.ult(midpoint))
1348 /// Computes the multiplicative inverse of this APInt for a given modulo. The
1349 /// iterative extended Euclidean algorithm is used to solve for this value,
1350 /// however we simplify it to speed up calculating only the inverse, and take
1351 /// advantage of div+rem calculations. We also use some tricks to avoid copying
1352 /// (potentially large) APInts around.
1353 APInt APInt::multiplicativeInverse(const APInt& modulo) const {
1354 assert(ult(modulo) && "This APInt must be smaller than the modulo");
1356 // Using the properties listed at the following web page (accessed 06/21/08):
1357 // http://www.numbertheory.org/php/euclid.html
1358 // (especially the properties numbered 3, 4 and 9) it can be proved that
1359 // BitWidth bits suffice for all the computations in the algorithm implemented
1360 // below. More precisely, this number of bits suffice if the multiplicative
1361 // inverse exists, but may not suffice for the general extended Euclidean
1364 APInt r[2] = { modulo, *this };
1365 APInt t[2] = { APInt(BitWidth, 0), APInt(BitWidth, 1) };
1366 APInt q(BitWidth, 0);
1369 for (i = 0; r[i^1] != 0; i ^= 1) {
1370 // An overview of the math without the confusing bit-flipping:
1371 // q = r[i-2] / r[i-1]
1372 // r[i] = r[i-2] % r[i-1]
1373 // t[i] = t[i-2] - t[i-1] * q
1374 udivrem(r[i], r[i^1], q, r[i]);
1378 // If this APInt and the modulo are not coprime, there is no multiplicative
1379 // inverse, so return 0. We check this by looking at the next-to-last
1380 // remainder, which is the gcd(*this,modulo) as calculated by the Euclidean
1383 return APInt(BitWidth, 0);
1385 // The next-to-last t is the multiplicative inverse. However, we are
1386 // interested in a positive inverse. Calcuate a positive one from a negative
1387 // one if necessary. A simple addition of the modulo suffices because
1388 // abs(t[i]) is known to be less than *this/2 (see the link above).
1389 return t[i].isNegative() ? t[i] + modulo : t[i];
1392 /// Calculate the magic numbers required to implement a signed integer division
1393 /// by a constant as a sequence of multiplies, adds and shifts. Requires that
1394 /// the divisor not be 0, 1, or -1. Taken from "Hacker's Delight", Henry S.
1395 /// Warren, Jr., chapter 10.
1396 APInt::ms APInt::magic() const {
1397 const APInt& d = *this;
1399 APInt ad, anc, delta, q1, r1, q2, r2, t;
1400 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
1404 t = signedMin + (d.lshr(d.getBitWidth() - 1));
1405 anc = t - 1 - t.urem(ad); // absolute value of nc
1406 p = d.getBitWidth() - 1; // initialize p
1407 q1 = signedMin.udiv(anc); // initialize q1 = 2p/abs(nc)
1408 r1 = signedMin - q1*anc; // initialize r1 = rem(2p,abs(nc))
1409 q2 = signedMin.udiv(ad); // initialize q2 = 2p/abs(d)
1410 r2 = signedMin - q2*ad; // initialize r2 = rem(2p,abs(d))
1413 q1 = q1<<1; // update q1 = 2p/abs(nc)
1414 r1 = r1<<1; // update r1 = rem(2p/abs(nc))
1415 if (r1.uge(anc)) { // must be unsigned comparison
1419 q2 = q2<<1; // update q2 = 2p/abs(d)
1420 r2 = r2<<1; // update r2 = rem(2p/abs(d))
1421 if (r2.uge(ad)) { // must be unsigned comparison
1426 } while (q1.ult(delta) || (q1 == delta && r1 == 0));
1429 if (d.isNegative()) mag.m = -mag.m; // resulting magic number
1430 mag.s = p - d.getBitWidth(); // resulting shift
1434 /// Calculate the magic numbers required to implement an unsigned integer
1435 /// division by a constant as a sequence of multiplies, adds and shifts.
1436 /// Requires that the divisor not be 0. Taken from "Hacker's Delight", Henry
1437 /// S. Warren, Jr., chapter 10.
1438 /// LeadingZeros can be used to simplify the calculation if the upper bits
1439 /// of the divided value are known zero.
1440 APInt::mu APInt::magicu(unsigned LeadingZeros) const {
1441 const APInt& d = *this;
1443 APInt nc, delta, q1, r1, q2, r2;
1445 magu.a = 0; // initialize "add" indicator
1446 APInt allOnes = APInt::getAllOnesValue(d.getBitWidth()).lshr(LeadingZeros);
1447 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
1448 APInt signedMax = APInt::getSignedMaxValue(d.getBitWidth());
1450 nc = allOnes - (allOnes - d).urem(d);
1451 p = d.getBitWidth() - 1; // initialize p
1452 q1 = signedMin.udiv(nc); // initialize q1 = 2p/nc
1453 r1 = signedMin - q1*nc; // initialize r1 = rem(2p,nc)
1454 q2 = signedMax.udiv(d); // initialize q2 = (2p-1)/d
1455 r2 = signedMax - q2*d; // initialize r2 = rem((2p-1),d)
1458 if (r1.uge(nc - r1)) {
1459 q1 = q1 + q1 + 1; // update q1
1460 r1 = r1 + r1 - nc; // update r1
1463 q1 = q1+q1; // update q1
1464 r1 = r1+r1; // update r1
1466 if ((r2 + 1).uge(d - r2)) {
1467 if (q2.uge(signedMax)) magu.a = 1;
1468 q2 = q2+q2 + 1; // update q2
1469 r2 = r2+r2 + 1 - d; // update r2
1472 if (q2.uge(signedMin)) magu.a = 1;
1473 q2 = q2+q2; // update q2
1474 r2 = r2+r2 + 1; // update r2
1477 } while (p < d.getBitWidth()*2 &&
1478 (q1.ult(delta) || (q1 == delta && r1 == 0)));
1479 magu.m = q2 + 1; // resulting magic number
1480 magu.s = p - d.getBitWidth(); // resulting shift
1484 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1485 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1486 /// variables here have the same names as in the algorithm. Comments explain
1487 /// the algorithm and any deviation from it.
1488 static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
1489 unsigned m, unsigned n) {
1490 assert(u && "Must provide dividend");
1491 assert(v && "Must provide divisor");
1492 assert(q && "Must provide quotient");
1493 assert(u != v && u != q && v != q && "Must us different memory");
1494 assert(n>1 && "n must be > 1");
1496 // Knuth uses the value b as the base of the number system. In our case b
1497 // is 2^31 so we just set it to -1u.
1498 uint64_t b = uint64_t(1) << 32;
1501 DEBUG(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n');
1502 DEBUG(dbgs() << "KnuthDiv: original:");
1503 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1504 DEBUG(dbgs() << " by");
1505 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
1506 DEBUG(dbgs() << '\n');
1508 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1509 // u and v by d. Note that we have taken Knuth's advice here to use a power
1510 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1511 // 2 allows us to shift instead of multiply and it is easy to determine the
1512 // shift amount from the leading zeros. We are basically normalizing the u
1513 // and v so that its high bits are shifted to the top of v's range without
1514 // overflow. Note that this can require an extra word in u so that u must
1515 // be of length m+n+1.
1516 unsigned shift = countLeadingZeros(v[n-1]);
1517 unsigned v_carry = 0;
1518 unsigned u_carry = 0;
1520 for (unsigned i = 0; i < m+n; ++i) {
1521 unsigned u_tmp = u[i] >> (32 - shift);
1522 u[i] = (u[i] << shift) | u_carry;
1525 for (unsigned i = 0; i < n; ++i) {
1526 unsigned v_tmp = v[i] >> (32 - shift);
1527 v[i] = (v[i] << shift) | v_carry;
1533 DEBUG(dbgs() << "KnuthDiv: normal:");
1534 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1535 DEBUG(dbgs() << " by");
1536 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
1537 DEBUG(dbgs() << '\n');
1540 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1543 DEBUG(dbgs() << "KnuthDiv: quotient digit #" << j << '\n');
1544 // D3. [Calculate q'.].
1545 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1546 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1547 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1548 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1549 // on v[n-2] determines at high speed most of the cases in which the trial
1550 // value qp is one too large, and it eliminates all cases where qp is two
1552 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1553 DEBUG(dbgs() << "KnuthDiv: dividend == " << dividend << '\n');
1554 uint64_t qp = dividend / v[n-1];
1555 uint64_t rp = dividend % v[n-1];
1556 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1559 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1562 DEBUG(dbgs() << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1564 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1565 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1566 // consists of a simple multiplication by a one-place number, combined with
1569 for (unsigned i = 0; i < n; ++i) {
1570 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1571 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1572 bool borrow = subtrahend > u_tmp;
1573 DEBUG(dbgs() << "KnuthDiv: u_tmp == " << u_tmp
1574 << ", subtrahend == " << subtrahend
1575 << ", borrow = " << borrow << '\n');
1577 uint64_t result = u_tmp - subtrahend;
1579 u[k++] = (unsigned)(result & (b-1)); // subtract low word
1580 u[k++] = (unsigned)(result >> 32); // subtract high word
1581 while (borrow && k <= m+n) { // deal with borrow to the left
1587 DEBUG(dbgs() << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1590 DEBUG(dbgs() << "KnuthDiv: after subtraction:");
1591 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1592 DEBUG(dbgs() << '\n');
1593 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1594 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1595 // true value plus b**(n+1), namely as the b's complement of
1596 // the true value, and a "borrow" to the left should be remembered.
1599 bool carry = true; // true because b's complement is "complement + 1"
1600 for (unsigned i = 0; i <= m+n; ++i) {
1601 u[i] = ~u[i] + carry; // b's complement
1602 carry = carry && u[i] == 0;
1605 DEBUG(dbgs() << "KnuthDiv: after complement:");
1606 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1607 DEBUG(dbgs() << '\n');
1609 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1610 // negative, go to step D6; otherwise go on to step D7.
1611 q[j] = (unsigned)qp;
1613 // D6. [Add back]. The probability that this step is necessary is very
1614 // small, on the order of only 2/b. Make sure that test data accounts for
1615 // this possibility. Decrease q[j] by 1
1617 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1618 // A carry will occur to the left of u[j+n], and it should be ignored
1619 // since it cancels with the borrow that occurred in D4.
1621 for (unsigned i = 0; i < n; i++) {
1622 unsigned limit = std::min(u[j+i],v[i]);
1623 u[j+i] += v[i] + carry;
1624 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1628 DEBUG(dbgs() << "KnuthDiv: after correction:");
1629 DEBUG(for (int i = m+n; i >=0; i--) dbgs() <<" " << u[i]);
1630 DEBUG(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n');
1632 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1635 DEBUG(dbgs() << "KnuthDiv: quotient:");
1636 DEBUG(for (int i = m; i >=0; i--) dbgs() <<" " << q[i]);
1637 DEBUG(dbgs() << '\n');
1639 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1640 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1641 // compute the remainder (urem uses this).
1643 // The value d is expressed by the "shift" value above since we avoided
1644 // multiplication by d by using a shift left. So, all we have to do is
1645 // shift right here. In order to mak
1648 DEBUG(dbgs() << "KnuthDiv: remainder:");
1649 for (int i = n-1; i >= 0; i--) {
1650 r[i] = (u[i] >> shift) | carry;
1651 carry = u[i] << (32 - shift);
1652 DEBUG(dbgs() << " " << r[i]);
1655 for (int i = n-1; i >= 0; i--) {
1657 DEBUG(dbgs() << " " << r[i]);
1660 DEBUG(dbgs() << '\n');
1663 DEBUG(dbgs() << '\n');
1667 void APInt::divide(const APInt LHS, unsigned lhsWords,
1668 const APInt &RHS, unsigned rhsWords,
1669 APInt *Quotient, APInt *Remainder)
1671 assert(lhsWords >= rhsWords && "Fractional result");
1673 // First, compose the values into an array of 32-bit words instead of
1674 // 64-bit words. This is a necessity of both the "short division" algorithm
1675 // and the Knuth "classical algorithm" which requires there to be native
1676 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1677 // can't use 64-bit operands here because we don't have native results of
1678 // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't
1679 // work on large-endian machines.
1680 uint64_t mask = ~0ull >> (sizeof(unsigned)*CHAR_BIT);
1681 unsigned n = rhsWords * 2;
1682 unsigned m = (lhsWords * 2) - n;
1684 // Allocate space for the temporary values we need either on the stack, if
1685 // it will fit, or on the heap if it won't.
1686 unsigned SPACE[128];
1687 unsigned *U = nullptr;
1688 unsigned *V = nullptr;
1689 unsigned *Q = nullptr;
1690 unsigned *R = nullptr;
1691 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1694 Q = &SPACE[(m+n+1) + n];
1696 R = &SPACE[(m+n+1) + n + (m+n)];
1698 U = new unsigned[m + n + 1];
1699 V = new unsigned[n];
1700 Q = new unsigned[m+n];
1702 R = new unsigned[n];
1705 // Initialize the dividend
1706 memset(U, 0, (m+n+1)*sizeof(unsigned));
1707 for (unsigned i = 0; i < lhsWords; ++i) {
1708 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1709 U[i * 2] = (unsigned)(tmp & mask);
1710 U[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT));
1712 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1714 // Initialize the divisor
1715 memset(V, 0, (n)*sizeof(unsigned));
1716 for (unsigned i = 0; i < rhsWords; ++i) {
1717 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1718 V[i * 2] = (unsigned)(tmp & mask);
1719 V[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT));
1722 // initialize the quotient and remainder
1723 memset(Q, 0, (m+n) * sizeof(unsigned));
1725 memset(R, 0, n * sizeof(unsigned));
1727 // Now, adjust m and n for the Knuth division. n is the number of words in
1728 // the divisor. m is the number of words by which the dividend exceeds the
1729 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1730 // contain any zero words or the Knuth algorithm fails.
1731 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1735 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1738 // If we're left with only a single word for the divisor, Knuth doesn't work
1739 // so we implement the short division algorithm here. This is much simpler
1740 // and faster because we are certain that we can divide a 64-bit quantity
1741 // by a 32-bit quantity at hardware speed and short division is simply a
1742 // series of such operations. This is just like doing short division but we
1743 // are using base 2^32 instead of base 10.
1744 assert(n != 0 && "Divide by zero?");
1746 unsigned divisor = V[0];
1747 unsigned remainder = 0;
1748 for (int i = m+n-1; i >= 0; i--) {
1749 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1750 if (partial_dividend == 0) {
1753 } else if (partial_dividend < divisor) {
1755 remainder = (unsigned)partial_dividend;
1756 } else if (partial_dividend == divisor) {
1760 Q[i] = (unsigned)(partial_dividend / divisor);
1761 remainder = (unsigned)(partial_dividend - (Q[i] * divisor));
1767 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1769 KnuthDiv(U, V, Q, R, m, n);
1772 // If the caller wants the quotient
1774 // Set up the Quotient value's memory.
1775 if (Quotient->BitWidth != LHS.BitWidth) {
1776 if (Quotient->isSingleWord())
1779 delete [] Quotient->pVal;
1780 Quotient->BitWidth = LHS.BitWidth;
1781 if (!Quotient->isSingleWord())
1782 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1784 Quotient->clearAllBits();
1786 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1788 if (lhsWords == 1) {
1790 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1791 if (Quotient->isSingleWord())
1792 Quotient->VAL = tmp;
1794 Quotient->pVal[0] = tmp;
1796 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1797 for (unsigned i = 0; i < lhsWords; ++i)
1799 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1803 // If the caller wants the remainder
1805 // Set up the Remainder value's memory.
1806 if (Remainder->BitWidth != RHS.BitWidth) {
1807 if (Remainder->isSingleWord())
1810 delete [] Remainder->pVal;
1811 Remainder->BitWidth = RHS.BitWidth;
1812 if (!Remainder->isSingleWord())
1813 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1815 Remainder->clearAllBits();
1817 // The remainder is in R. Reconstitute the remainder into Remainder's low
1819 if (rhsWords == 1) {
1821 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1822 if (Remainder->isSingleWord())
1823 Remainder->VAL = tmp;
1825 Remainder->pVal[0] = tmp;
1827 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1828 for (unsigned i = 0; i < rhsWords; ++i)
1829 Remainder->pVal[i] =
1830 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1834 // Clean up the memory we allocated.
1835 if (U != &SPACE[0]) {
1843 APInt APInt::udiv(const APInt& RHS) const {
1844 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1846 // First, deal with the easy case
1847 if (isSingleWord()) {
1848 assert(RHS.VAL != 0 && "Divide by zero?");
1849 return APInt(BitWidth, VAL / RHS.VAL);
1852 // Get some facts about the LHS and RHS number of bits and words
1853 unsigned rhsBits = RHS.getActiveBits();
1854 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1855 assert(rhsWords && "Divided by zero???");
1856 unsigned lhsBits = this->getActiveBits();
1857 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1859 // Deal with some degenerate cases
1862 return APInt(BitWidth, 0);
1863 else if (lhsWords < rhsWords || this->ult(RHS)) {
1864 // X / Y ===> 0, iff X < Y
1865 return APInt(BitWidth, 0);
1866 } else if (*this == RHS) {
1868 return APInt(BitWidth, 1);
1869 } else if (lhsWords == 1 && rhsWords == 1) {
1870 // All high words are zero, just use native divide
1871 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1874 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1875 APInt Quotient(1,0); // to hold result.
1876 divide(*this, lhsWords, RHS, rhsWords, &Quotient, nullptr);
1880 APInt APInt::sdiv(const APInt &RHS) const {
1882 if (RHS.isNegative())
1883 return (-(*this)).udiv(-RHS);
1884 return -((-(*this)).udiv(RHS));
1886 if (RHS.isNegative())
1887 return -(this->udiv(-RHS));
1888 return this->udiv(RHS);
1891 APInt APInt::urem(const APInt& RHS) const {
1892 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1893 if (isSingleWord()) {
1894 assert(RHS.VAL != 0 && "Remainder by zero?");
1895 return APInt(BitWidth, VAL % RHS.VAL);
1898 // Get some facts about the LHS
1899 unsigned lhsBits = getActiveBits();
1900 unsigned lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1902 // Get some facts about the RHS
1903 unsigned rhsBits = RHS.getActiveBits();
1904 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1905 assert(rhsWords && "Performing remainder operation by zero ???");
1907 // Check the degenerate cases
1908 if (lhsWords == 0) {
1910 return APInt(BitWidth, 0);
1911 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1912 // X % Y ===> X, iff X < Y
1914 } else if (*this == RHS) {
1916 return APInt(BitWidth, 0);
1917 } else if (lhsWords == 1) {
1918 // All high words are zero, just use native remainder
1919 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
1922 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1923 APInt Remainder(1,0);
1924 divide(*this, lhsWords, RHS, rhsWords, nullptr, &Remainder);
1928 APInt APInt::srem(const APInt &RHS) const {
1930 if (RHS.isNegative())
1931 return -((-(*this)).urem(-RHS));
1932 return -((-(*this)).urem(RHS));
1934 if (RHS.isNegative())
1935 return this->urem(-RHS);
1936 return this->urem(RHS);
1939 void APInt::udivrem(const APInt &LHS, const APInt &RHS,
1940 APInt &Quotient, APInt &Remainder) {
1941 // Get some size facts about the dividend and divisor
1942 unsigned lhsBits = LHS.getActiveBits();
1943 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1944 unsigned rhsBits = RHS.getActiveBits();
1945 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1947 // Check the degenerate cases
1948 if (lhsWords == 0) {
1949 Quotient = 0; // 0 / Y ===> 0
1950 Remainder = 0; // 0 % Y ===> 0
1954 if (lhsWords < rhsWords || LHS.ult(RHS)) {
1955 Remainder = LHS; // X % Y ===> X, iff X < Y
1956 Quotient = 0; // X / Y ===> 0, iff X < Y
1961 Quotient = 1; // X / X ===> 1
1962 Remainder = 0; // X % X ===> 0;
1966 if (lhsWords == 1 && rhsWords == 1) {
1967 // There is only one word to consider so use the native versions.
1968 uint64_t lhsValue = LHS.isSingleWord() ? LHS.VAL : LHS.pVal[0];
1969 uint64_t rhsValue = RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0];
1970 Quotient = APInt(LHS.getBitWidth(), lhsValue / rhsValue);
1971 Remainder = APInt(LHS.getBitWidth(), lhsValue % rhsValue);
1975 // Okay, lets do it the long way
1976 divide(LHS, lhsWords, RHS, rhsWords, &Quotient, &Remainder);
1979 void APInt::sdivrem(const APInt &LHS, const APInt &RHS,
1980 APInt &Quotient, APInt &Remainder) {
1981 if (LHS.isNegative()) {
1982 if (RHS.isNegative())
1983 APInt::udivrem(-LHS, -RHS, Quotient, Remainder);
1985 APInt::udivrem(-LHS, RHS, Quotient, Remainder);
1986 Quotient = -Quotient;
1988 Remainder = -Remainder;
1989 } else if (RHS.isNegative()) {
1990 APInt::udivrem(LHS, -RHS, Quotient, Remainder);
1991 Quotient = -Quotient;
1993 APInt::udivrem(LHS, RHS, Quotient, Remainder);
1997 APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const {
1998 APInt Res = *this+RHS;
1999 Overflow = isNonNegative() == RHS.isNonNegative() &&
2000 Res.isNonNegative() != isNonNegative();
2004 APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const {
2005 APInt Res = *this+RHS;
2006 Overflow = Res.ult(RHS);
2010 APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const {
2011 APInt Res = *this - RHS;
2012 Overflow = isNonNegative() != RHS.isNonNegative() &&
2013 Res.isNonNegative() != isNonNegative();
2017 APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const {
2018 APInt Res = *this-RHS;
2019 Overflow = Res.ugt(*this);
2023 APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const {
2024 // MININT/-1 --> overflow.
2025 Overflow = isMinSignedValue() && RHS.isAllOnesValue();
2029 APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const {
2030 APInt Res = *this * RHS;
2032 if (*this != 0 && RHS != 0)
2033 Overflow = Res.sdiv(RHS) != *this || Res.sdiv(*this) != RHS;
2039 APInt APInt::umul_ov(const APInt &RHS, bool &Overflow) const {
2040 APInt Res = *this * RHS;
2042 if (*this != 0 && RHS != 0)
2043 Overflow = Res.udiv(RHS) != *this || Res.udiv(*this) != RHS;
2049 APInt APInt::sshl_ov(unsigned ShAmt, bool &Overflow) const {
2050 Overflow = ShAmt >= getBitWidth();
2052 ShAmt = getBitWidth()-1;
2054 if (isNonNegative()) // Don't allow sign change.
2055 Overflow = ShAmt >= countLeadingZeros();
2057 Overflow = ShAmt >= countLeadingOnes();
2059 return *this << ShAmt;
2065 void APInt::fromString(unsigned numbits, StringRef str, uint8_t radix) {
2066 // Check our assumptions here
2067 assert(!str.empty() && "Invalid string length");
2068 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||
2070 "Radix should be 2, 8, 10, 16, or 36!");
2072 StringRef::iterator p = str.begin();
2073 size_t slen = str.size();
2074 bool isNeg = *p == '-';
2075 if (*p == '-' || *p == '+') {
2078 assert(slen && "String is only a sign, needs a value.");
2080 assert((slen <= numbits || radix != 2) && "Insufficient bit width");
2081 assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width");
2082 assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width");
2083 assert((((slen-1)*64)/22 <= numbits || radix != 10) &&
2084 "Insufficient bit width");
2087 if (!isSingleWord())
2088 pVal = getClearedMemory(getNumWords());
2090 // Figure out if we can shift instead of multiply
2091 unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
2093 // Set up an APInt for the digit to add outside the loop so we don't
2094 // constantly construct/destruct it.
2095 APInt apdigit(getBitWidth(), 0);
2096 APInt apradix(getBitWidth(), radix);
2098 // Enter digit traversal loop
2099 for (StringRef::iterator e = str.end(); p != e; ++p) {
2100 unsigned digit = getDigit(*p, radix);
2101 assert(digit < radix && "Invalid character in digit string");
2103 // Shift or multiply the value by the radix
2111 // Add in the digit we just interpreted
2112 if (apdigit.isSingleWord())
2113 apdigit.VAL = digit;
2115 apdigit.pVal[0] = digit;
2118 // If its negative, put it in two's complement form
2121 this->flipAllBits();
2125 void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix,
2126 bool Signed, bool formatAsCLiteral) const {
2127 assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2 ||
2129 "Radix should be 2, 8, 10, 16, or 36!");
2131 const char *Prefix = "";
2132 if (formatAsCLiteral) {
2135 // Binary literals are a non-standard extension added in gcc 4.3:
2136 // http://gcc.gnu.org/onlinedocs/gcc-4.3.0/gcc/Binary-constants.html
2148 llvm_unreachable("Invalid radix!");
2152 // First, check for a zero value and just short circuit the logic below.
2155 Str.push_back(*Prefix);
2162 static const char Digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
2164 if (isSingleWord()) {
2166 char *BufPtr = Buffer+65;
2172 int64_t I = getSExtValue();
2182 Str.push_back(*Prefix);
2187 *--BufPtr = Digits[N % Radix];
2190 Str.append(BufPtr, Buffer+65);
2196 if (Signed && isNegative()) {
2197 // They want to print the signed version and it is a negative value
2198 // Flip the bits and add one to turn it into the equivalent positive
2199 // value and put a '-' in the result.
2206 Str.push_back(*Prefix);
2210 // We insert the digits backward, then reverse them to get the right order.
2211 unsigned StartDig = Str.size();
2213 // For the 2, 8 and 16 bit cases, we can just shift instead of divide
2214 // because the number of bits per digit (1, 3 and 4 respectively) divides
2215 // equaly. We just shift until the value is zero.
2216 if (Radix == 2 || Radix == 8 || Radix == 16) {
2217 // Just shift tmp right for each digit width until it becomes zero
2218 unsigned ShiftAmt = (Radix == 16 ? 4 : (Radix == 8 ? 3 : 1));
2219 unsigned MaskAmt = Radix - 1;
2222 unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt;
2223 Str.push_back(Digits[Digit]);
2224 Tmp = Tmp.lshr(ShiftAmt);
2227 APInt divisor(Radix == 10? 4 : 8, Radix);
2229 APInt APdigit(1, 0);
2230 APInt tmp2(Tmp.getBitWidth(), 0);
2231 divide(Tmp, Tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
2233 unsigned Digit = (unsigned)APdigit.getZExtValue();
2234 assert(Digit < Radix && "divide failed");
2235 Str.push_back(Digits[Digit]);
2240 // Reverse the digits before returning.
2241 std::reverse(Str.begin()+StartDig, Str.end());
2244 /// toString - This returns the APInt as a std::string. Note that this is an
2245 /// inefficient method. It is better to pass in a SmallVector/SmallString
2246 /// to the methods above.
2247 std::string APInt::toString(unsigned Radix = 10, bool Signed = true) const {
2249 toString(S, Radix, Signed, /* formatAsCLiteral = */false);
2254 void APInt::dump() const {
2255 SmallString<40> S, U;
2256 this->toStringUnsigned(U);
2257 this->toStringSigned(S);
2258 dbgs() << "APInt(" << BitWidth << "b, "
2259 << U.str() << "u " << S.str() << "s)";
2262 void APInt::print(raw_ostream &OS, bool isSigned) const {
2264 this->toString(S, 10, isSigned, /* formatAsCLiteral = */false);
2268 // This implements a variety of operations on a representation of
2269 // arbitrary precision, two's-complement, bignum integer values.
2271 // Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe
2272 // and unrestricting assumption.
2273 #define COMPILE_TIME_ASSERT(cond) extern int CTAssert[(cond) ? 1 : -1]
2274 COMPILE_TIME_ASSERT(integerPartWidth % 2 == 0);
2276 /* Some handy functions local to this file. */
2279 /* Returns the integer part with the least significant BITS set.
2280 BITS cannot be zero. */
2281 static inline integerPart
2282 lowBitMask(unsigned int bits)
2284 assert(bits != 0 && bits <= integerPartWidth);
2286 return ~(integerPart) 0 >> (integerPartWidth - bits);
2289 /* Returns the value of the lower half of PART. */
2290 static inline integerPart
2291 lowHalf(integerPart part)
2293 return part & lowBitMask(integerPartWidth / 2);
2296 /* Returns the value of the upper half of PART. */
2297 static inline integerPart
2298 highHalf(integerPart part)
2300 return part >> (integerPartWidth / 2);
2303 /* Returns the bit number of the most significant set bit of a part.
2304 If the input number has no bits set -1U is returned. */
2306 partMSB(integerPart value)
2308 return findLastSet(value, ZB_Max);
2311 /* Returns the bit number of the least significant set bit of a
2312 part. If the input number has no bits set -1U is returned. */
2314 partLSB(integerPart value)
2316 return findFirstSet(value, ZB_Max);
2320 /* Sets the least significant part of a bignum to the input value, and
2321 zeroes out higher parts. */
2323 APInt::tcSet(integerPart *dst, integerPart part, unsigned int parts)
2330 for (i = 1; i < parts; i++)
2334 /* Assign one bignum to another. */
2336 APInt::tcAssign(integerPart *dst, const integerPart *src, unsigned int parts)
2340 for (i = 0; i < parts; i++)
2344 /* Returns true if a bignum is zero, false otherwise. */
2346 APInt::tcIsZero(const integerPart *src, unsigned int parts)
2350 for (i = 0; i < parts; i++)
2357 /* Extract the given bit of a bignum; returns 0 or 1. */
2359 APInt::tcExtractBit(const integerPart *parts, unsigned int bit)
2361 return (parts[bit / integerPartWidth] &
2362 ((integerPart) 1 << bit % integerPartWidth)) != 0;
2365 /* Set the given bit of a bignum. */
2367 APInt::tcSetBit(integerPart *parts, unsigned int bit)
2369 parts[bit / integerPartWidth] |= (integerPart) 1 << (bit % integerPartWidth);
2372 /* Clears the given bit of a bignum. */
2374 APInt::tcClearBit(integerPart *parts, unsigned int bit)
2376 parts[bit / integerPartWidth] &=
2377 ~((integerPart) 1 << (bit % integerPartWidth));
2380 /* Returns the bit number of the least significant set bit of a
2381 number. If the input number has no bits set -1U is returned. */
2383 APInt::tcLSB(const integerPart *parts, unsigned int n)
2385 unsigned int i, lsb;
2387 for (i = 0; i < n; i++) {
2388 if (parts[i] != 0) {
2389 lsb = partLSB(parts[i]);
2391 return lsb + i * integerPartWidth;
2398 /* Returns the bit number of the most significant set bit of a number.
2399 If the input number has no bits set -1U is returned. */
2401 APInt::tcMSB(const integerPart *parts, unsigned int n)
2408 if (parts[n] != 0) {
2409 msb = partMSB(parts[n]);
2411 return msb + n * integerPartWidth;
2418 /* Copy the bit vector of width srcBITS from SRC, starting at bit
2419 srcLSB, to DST, of dstCOUNT parts, such that the bit srcLSB becomes
2420 the least significant bit of DST. All high bits above srcBITS in
2421 DST are zero-filled. */
2423 APInt::tcExtract(integerPart *dst, unsigned int dstCount,const integerPart *src,
2424 unsigned int srcBits, unsigned int srcLSB)
2426 unsigned int firstSrcPart, dstParts, shift, n;
2428 dstParts = (srcBits + integerPartWidth - 1) / integerPartWidth;
2429 assert(dstParts <= dstCount);
2431 firstSrcPart = srcLSB / integerPartWidth;
2432 tcAssign (dst, src + firstSrcPart, dstParts);
2434 shift = srcLSB % integerPartWidth;
2435 tcShiftRight (dst, dstParts, shift);
2437 /* We now have (dstParts * integerPartWidth - shift) bits from SRC
2438 in DST. If this is less that srcBits, append the rest, else
2439 clear the high bits. */
2440 n = dstParts * integerPartWidth - shift;
2442 integerPart mask = lowBitMask (srcBits - n);
2443 dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask)
2444 << n % integerPartWidth);
2445 } else if (n > srcBits) {
2446 if (srcBits % integerPartWidth)
2447 dst[dstParts - 1] &= lowBitMask (srcBits % integerPartWidth);
2450 /* Clear high parts. */
2451 while (dstParts < dstCount)
2452 dst[dstParts++] = 0;
2455 /* DST += RHS + C where C is zero or one. Returns the carry flag. */
2457 APInt::tcAdd(integerPart *dst, const integerPart *rhs,
2458 integerPart c, unsigned int parts)
2464 for (i = 0; i < parts; i++) {
2469 dst[i] += rhs[i] + 1;
2480 /* DST -= RHS + C where C is zero or one. Returns the carry flag. */
2482 APInt::tcSubtract(integerPart *dst, const integerPart *rhs,
2483 integerPart c, unsigned int parts)
2489 for (i = 0; i < parts; i++) {
2494 dst[i] -= rhs[i] + 1;
2505 /* Negate a bignum in-place. */
2507 APInt::tcNegate(integerPart *dst, unsigned int parts)
2509 tcComplement(dst, parts);
2510 tcIncrement(dst, parts);
2513 /* DST += SRC * MULTIPLIER + CARRY if add is true
2514 DST = SRC * MULTIPLIER + CARRY if add is false
2516 Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC
2517 they must start at the same point, i.e. DST == SRC.
2519 If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is
2520 returned. Otherwise DST is filled with the least significant
2521 DSTPARTS parts of the result, and if all of the omitted higher
2522 parts were zero return zero, otherwise overflow occurred and
2525 APInt::tcMultiplyPart(integerPart *dst, const integerPart *src,
2526 integerPart multiplier, integerPart carry,
2527 unsigned int srcParts, unsigned int dstParts,
2532 /* Otherwise our writes of DST kill our later reads of SRC. */
2533 assert(dst <= src || dst >= src + srcParts);
2534 assert(dstParts <= srcParts + 1);
2536 /* N loops; minimum of dstParts and srcParts. */
2537 n = dstParts < srcParts ? dstParts: srcParts;
2539 for (i = 0; i < n; i++) {
2540 integerPart low, mid, high, srcPart;
2542 /* [ LOW, HIGH ] = MULTIPLIER * SRC[i] + DST[i] + CARRY.
2544 This cannot overflow, because
2546 (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1)
2548 which is less than n^2. */
2552 if (multiplier == 0 || srcPart == 0) {
2556 low = lowHalf(srcPart) * lowHalf(multiplier);
2557 high = highHalf(srcPart) * highHalf(multiplier);
2559 mid = lowHalf(srcPart) * highHalf(multiplier);
2560 high += highHalf(mid);
2561 mid <<= integerPartWidth / 2;
2562 if (low + mid < low)
2566 mid = highHalf(srcPart) * lowHalf(multiplier);
2567 high += highHalf(mid);
2568 mid <<= integerPartWidth / 2;
2569 if (low + mid < low)
2573 /* Now add carry. */
2574 if (low + carry < low)
2580 /* And now DST[i], and store the new low part there. */
2581 if (low + dst[i] < low)
2591 /* Full multiplication, there is no overflow. */
2592 assert(i + 1 == dstParts);
2596 /* We overflowed if there is carry. */
2600 /* We would overflow if any significant unwritten parts would be
2601 non-zero. This is true if any remaining src parts are non-zero
2602 and the multiplier is non-zero. */
2604 for (; i < srcParts; i++)
2608 /* We fitted in the narrow destination. */
2613 /* DST = LHS * RHS, where DST has the same width as the operands and
2614 is filled with the least significant parts of the result. Returns
2615 one if overflow occurred, otherwise zero. DST must be disjoint
2616 from both operands. */
2618 APInt::tcMultiply(integerPart *dst, const integerPart *lhs,
2619 const integerPart *rhs, unsigned int parts)
2624 assert(dst != lhs && dst != rhs);
2627 tcSet(dst, 0, parts);
2629 for (i = 0; i < parts; i++)
2630 overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts,
2636 /* DST = LHS * RHS, where DST has width the sum of the widths of the
2637 operands. No overflow occurs. DST must be disjoint from both
2638 operands. Returns the number of parts required to hold the
2641 APInt::tcFullMultiply(integerPart *dst, const integerPart *lhs,
2642 const integerPart *rhs, unsigned int lhsParts,
2643 unsigned int rhsParts)
2645 /* Put the narrower number on the LHS for less loops below. */
2646 if (lhsParts > rhsParts) {
2647 return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts);
2651 assert(dst != lhs && dst != rhs);
2653 tcSet(dst, 0, rhsParts);
2655 for (n = 0; n < lhsParts; n++)
2656 tcMultiplyPart(&dst[n], rhs, lhs[n], 0, rhsParts, rhsParts + 1, true);
2658 n = lhsParts + rhsParts;
2660 return n - (dst[n - 1] == 0);
2664 /* If RHS is zero LHS and REMAINDER are left unchanged, return one.
2665 Otherwise set LHS to LHS / RHS with the fractional part discarded,
2666 set REMAINDER to the remainder, return zero. i.e.
2668 OLD_LHS = RHS * LHS + REMAINDER
2670 SCRATCH is a bignum of the same size as the operands and result for
2671 use by the routine; its contents need not be initialized and are
2672 destroyed. LHS, REMAINDER and SCRATCH must be distinct.
2675 APInt::tcDivide(integerPart *lhs, const integerPart *rhs,
2676 integerPart *remainder, integerPart *srhs,
2679 unsigned int n, shiftCount;
2682 assert(lhs != remainder && lhs != srhs && remainder != srhs);
2684 shiftCount = tcMSB(rhs, parts) + 1;
2685 if (shiftCount == 0)
2688 shiftCount = parts * integerPartWidth - shiftCount;
2689 n = shiftCount / integerPartWidth;
2690 mask = (integerPart) 1 << (shiftCount % integerPartWidth);
2692 tcAssign(srhs, rhs, parts);
2693 tcShiftLeft(srhs, parts, shiftCount);
2694 tcAssign(remainder, lhs, parts);
2695 tcSet(lhs, 0, parts);
2697 /* Loop, subtracting SRHS if REMAINDER is greater and adding that to
2702 compare = tcCompare(remainder, srhs, parts);
2704 tcSubtract(remainder, srhs, 0, parts);
2708 if (shiftCount == 0)
2711 tcShiftRight(srhs, parts, 1);
2712 if ((mask >>= 1) == 0)
2713 mask = (integerPart) 1 << (integerPartWidth - 1), n--;
2719 /* Shift a bignum left COUNT bits in-place. Shifted in bits are zero.
2720 There are no restrictions on COUNT. */
2722 APInt::tcShiftLeft(integerPart *dst, unsigned int parts, unsigned int count)
2725 unsigned int jump, shift;
2727 /* Jump is the inter-part jump; shift is is intra-part shift. */
2728 jump = count / integerPartWidth;
2729 shift = count % integerPartWidth;
2731 while (parts > jump) {
2736 /* dst[i] comes from the two parts src[i - jump] and, if we have
2737 an intra-part shift, src[i - jump - 1]. */
2738 part = dst[parts - jump];
2741 if (parts >= jump + 1)
2742 part |= dst[parts - jump - 1] >> (integerPartWidth - shift);
2753 /* Shift a bignum right COUNT bits in-place. Shifted in bits are
2754 zero. There are no restrictions on COUNT. */
2756 APInt::tcShiftRight(integerPart *dst, unsigned int parts, unsigned int count)
2759 unsigned int i, jump, shift;
2761 /* Jump is the inter-part jump; shift is is intra-part shift. */
2762 jump = count / integerPartWidth;
2763 shift = count % integerPartWidth;
2765 /* Perform the shift. This leaves the most significant COUNT bits
2766 of the result at zero. */
2767 for (i = 0; i < parts; i++) {
2770 if (i + jump >= parts) {
2773 part = dst[i + jump];
2776 if (i + jump + 1 < parts)
2777 part |= dst[i + jump + 1] << (integerPartWidth - shift);
2786 /* Bitwise and of two bignums. */
2788 APInt::tcAnd(integerPart *dst, const integerPart *rhs, unsigned int parts)
2792 for (i = 0; i < parts; i++)
2796 /* Bitwise inclusive or of two bignums. */
2798 APInt::tcOr(integerPart *dst, const integerPart *rhs, unsigned int parts)
2802 for (i = 0; i < parts; i++)
2806 /* Bitwise exclusive or of two bignums. */
2808 APInt::tcXor(integerPart *dst, const integerPart *rhs, unsigned int parts)
2812 for (i = 0; i < parts; i++)
2816 /* Complement a bignum in-place. */
2818 APInt::tcComplement(integerPart *dst, unsigned int parts)
2822 for (i = 0; i < parts; i++)
2826 /* Comparison (unsigned) of two bignums. */
2828 APInt::tcCompare(const integerPart *lhs, const integerPart *rhs,
2833 if (lhs[parts] == rhs[parts])
2836 if (lhs[parts] > rhs[parts])
2845 /* Increment a bignum in-place, return the carry flag. */
2847 APInt::tcIncrement(integerPart *dst, unsigned int parts)
2851 for (i = 0; i < parts; i++)
2858 /* Decrement a bignum in-place, return the borrow flag. */
2860 APInt::tcDecrement(integerPart *dst, unsigned int parts) {
2861 for (unsigned int i = 0; i < parts; i++) {
2862 // If the current word is non-zero, then the decrement has no effect on the
2863 // higher-order words of the integer and no borrow can occur. Exit early.
2867 // If every word was zero, then there is a borrow.
2872 /* Set the least significant BITS bits of a bignum, clear the
2875 APInt::tcSetLeastSignificantBits(integerPart *dst, unsigned int parts,
2881 while (bits > integerPartWidth) {
2882 dst[i++] = ~(integerPart) 0;
2883 bits -= integerPartWidth;
2887 dst[i++] = ~(integerPart) 0 >> (integerPartWidth - bits);