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 /// 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 /// 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 /// 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 /// 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 APInt Result(val, getBitWidth());
458 // 0^0==1 so clear the high bits in case they got set.
459 Result.clearUnusedBits();
463 APInt APInt::operator*(const APInt& RHS) const {
464 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
466 return APInt(BitWidth, VAL * RHS.VAL);
472 APInt APInt::operator+(const APInt& RHS) const {
473 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
475 return APInt(BitWidth, VAL + RHS.VAL);
476 APInt Result(BitWidth, 0);
477 add(Result.pVal, this->pVal, RHS.pVal, getNumWords());
478 Result.clearUnusedBits();
482 APInt APInt::operator-(const APInt& RHS) const {
483 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
485 return APInt(BitWidth, VAL - RHS.VAL);
486 APInt Result(BitWidth, 0);
487 sub(Result.pVal, this->pVal, RHS.pVal, getNumWords());
488 Result.clearUnusedBits();
492 bool APInt::EqualSlowCase(const APInt& RHS) const {
493 // Get some facts about the number of bits used in the two operands.
494 unsigned n1 = getActiveBits();
495 unsigned n2 = RHS.getActiveBits();
497 // If the number of bits isn't the same, they aren't equal
501 // If the number of bits fits in a word, we only need to compare the low word.
502 if (n1 <= APINT_BITS_PER_WORD)
503 return pVal[0] == RHS.pVal[0];
505 // Otherwise, compare everything
506 for (int i = whichWord(n1 - 1); i >= 0; --i)
507 if (pVal[i] != RHS.pVal[i])
512 bool APInt::EqualSlowCase(uint64_t Val) const {
513 unsigned n = getActiveBits();
514 if (n <= APINT_BITS_PER_WORD)
515 return pVal[0] == Val;
520 bool APInt::ult(const APInt& RHS) const {
521 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
523 return VAL < RHS.VAL;
525 // Get active bit length of both operands
526 unsigned n1 = getActiveBits();
527 unsigned n2 = RHS.getActiveBits();
529 // If magnitude of LHS is less than RHS, return true.
533 // If magnitude of RHS is greather than LHS, return false.
537 // If they bot fit in a word, just compare the low order word
538 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD)
539 return pVal[0] < RHS.pVal[0];
541 // Otherwise, compare all words
542 unsigned topWord = whichWord(std::max(n1,n2)-1);
543 for (int i = topWord; i >= 0; --i) {
544 if (pVal[i] > RHS.pVal[i])
546 if (pVal[i] < RHS.pVal[i])
552 bool APInt::slt(const APInt& RHS) const {
553 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
554 if (isSingleWord()) {
555 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
556 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth);
557 return lhsSext < rhsSext;
562 bool lhsNeg = isNegative();
563 bool rhsNeg = rhs.isNegative();
565 // Sign bit is set so perform two's complement to make it positive
570 // Sign bit is set so perform two's complement to make it positive
575 // Now we have unsigned values to compare so do the comparison if necessary
576 // based on the negativeness of the values.
588 void APInt::setBit(unsigned bitPosition) {
590 VAL |= maskBit(bitPosition);
592 pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
595 /// Set the given bit to 0 whose position is given as "bitPosition".
596 /// @brief Set a given bit to 0.
597 void APInt::clearBit(unsigned bitPosition) {
599 VAL &= ~maskBit(bitPosition);
601 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
604 /// @brief Toggle every bit to its opposite value.
606 /// Toggle a given bit to its opposite value whose position is given
607 /// as "bitPosition".
608 /// @brief Toggles a given bit to its opposite value.
609 void APInt::flipBit(unsigned bitPosition) {
610 assert(bitPosition < BitWidth && "Out of the bit-width range!");
611 if ((*this)[bitPosition]) clearBit(bitPosition);
612 else setBit(bitPosition);
615 unsigned APInt::getBitsNeeded(StringRef str, uint8_t radix) {
616 assert(!str.empty() && "Invalid string length");
617 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||
619 "Radix should be 2, 8, 10, 16, or 36!");
621 size_t slen = str.size();
623 // Each computation below needs to know if it's negative.
624 StringRef::iterator p = str.begin();
625 unsigned isNegative = *p == '-';
626 if (*p == '-' || *p == '+') {
629 assert(slen && "String is only a sign, needs a value.");
632 // For radixes of power-of-two values, the bits required is accurately and
635 return slen + isNegative;
637 return slen * 3 + isNegative;
639 return slen * 4 + isNegative;
643 // This is grossly inefficient but accurate. We could probably do something
644 // with a computation of roughly slen*64/20 and then adjust by the value of
645 // the first few digits. But, I'm not sure how accurate that could be.
647 // Compute a sufficient number of bits that is always large enough but might
648 // be too large. This avoids the assertion in the constructor. This
649 // calculation doesn't work appropriately for the numbers 0-9, so just use 4
650 // bits in that case.
652 = radix == 10? (slen == 1 ? 4 : slen * 64/18)
653 : (slen == 1 ? 7 : slen * 16/3);
655 // Convert to the actual binary value.
656 APInt tmp(sufficient, StringRef(p, slen), radix);
658 // Compute how many bits are required. If the log is infinite, assume we need
660 unsigned log = tmp.logBase2();
661 if (log == (unsigned)-1) {
662 return isNegative + 1;
664 return isNegative + log + 1;
668 hash_code llvm::hash_value(const APInt &Arg) {
669 if (Arg.isSingleWord())
670 return hash_combine(Arg.VAL);
672 return hash_combine_range(Arg.pVal, Arg.pVal + Arg.getNumWords());
675 bool APInt::isSplat(unsigned SplatSizeInBits) const {
676 assert(getBitWidth() % SplatSizeInBits == 0 &&
677 "SplatSizeInBits must divide width!");
678 // We can check that all parts of an integer are equal by making use of a
679 // little trick: rotate and check if it's still the same value.
680 return *this == rotl(SplatSizeInBits);
683 /// This function returns the high "numBits" bits of this APInt.
684 APInt APInt::getHiBits(unsigned numBits) const {
685 return APIntOps::lshr(*this, BitWidth - numBits);
688 /// This function returns the low "numBits" bits of this APInt.
689 APInt APInt::getLoBits(unsigned numBits) const {
690 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
694 unsigned APInt::countLeadingZerosSlowCase() const {
695 // Treat the most significand word differently because it might have
696 // meaningless bits set beyond the precision.
697 unsigned BitsInMSW = BitWidth % APINT_BITS_PER_WORD;
699 if (BitsInMSW) MSWMask = (integerPart(1) << BitsInMSW) - 1;
701 MSWMask = ~integerPart(0);
702 BitsInMSW = APINT_BITS_PER_WORD;
705 unsigned i = getNumWords();
706 integerPart MSW = pVal[i-1] & MSWMask;
708 return llvm::countLeadingZeros(MSW) - (APINT_BITS_PER_WORD - BitsInMSW);
710 unsigned Count = BitsInMSW;
711 for (--i; i > 0u; --i) {
713 Count += APINT_BITS_PER_WORD;
715 Count += llvm::countLeadingZeros(pVal[i-1]);
722 unsigned APInt::countLeadingOnes() const {
724 return llvm::countLeadingOnes(VAL << (APINT_BITS_PER_WORD - BitWidth));
726 unsigned highWordBits = BitWidth % APINT_BITS_PER_WORD;
729 highWordBits = APINT_BITS_PER_WORD;
732 shift = APINT_BITS_PER_WORD - highWordBits;
734 int i = getNumWords() - 1;
735 unsigned Count = llvm::countLeadingOnes(pVal[i] << shift);
736 if (Count == highWordBits) {
737 for (i--; i >= 0; --i) {
738 if (pVal[i] == -1ULL)
739 Count += APINT_BITS_PER_WORD;
741 Count += llvm::countLeadingOnes(pVal[i]);
749 unsigned APInt::countTrailingZeros() const {
751 return std::min(unsigned(llvm::countTrailingZeros(VAL)), BitWidth);
754 for (; i < getNumWords() && pVal[i] == 0; ++i)
755 Count += APINT_BITS_PER_WORD;
756 if (i < getNumWords())
757 Count += llvm::countTrailingZeros(pVal[i]);
758 return std::min(Count, BitWidth);
761 unsigned APInt::countTrailingOnesSlowCase() const {
764 for (; i < getNumWords() && pVal[i] == -1ULL; ++i)
765 Count += APINT_BITS_PER_WORD;
766 if (i < getNumWords())
767 Count += llvm::countTrailingOnes(pVal[i]);
768 return std::min(Count, BitWidth);
771 unsigned APInt::countPopulationSlowCase() const {
773 for (unsigned i = 0; i < getNumWords(); ++i)
774 Count += llvm::countPopulation(pVal[i]);
778 /// Perform a logical right-shift from Src to Dst, which must be equal or
779 /// non-overlapping, of Words words, by Shift, which must be less than 64.
780 static void lshrNear(uint64_t *Dst, uint64_t *Src, unsigned Words,
783 for (int I = Words - 1; I >= 0; --I) {
784 uint64_t Tmp = Src[I];
785 Dst[I] = (Tmp >> Shift) | Carry;
786 Carry = Tmp << (64 - Shift);
790 APInt APInt::byteSwap() const {
791 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
793 return APInt(BitWidth, ByteSwap_16(uint16_t(VAL)));
795 return APInt(BitWidth, ByteSwap_32(unsigned(VAL)));
796 if (BitWidth == 48) {
797 unsigned Tmp1 = unsigned(VAL >> 16);
798 Tmp1 = ByteSwap_32(Tmp1);
799 uint16_t Tmp2 = uint16_t(VAL);
800 Tmp2 = ByteSwap_16(Tmp2);
801 return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1);
804 return APInt(BitWidth, ByteSwap_64(VAL));
806 APInt Result(getNumWords() * APINT_BITS_PER_WORD, 0);
807 for (unsigned I = 0, N = getNumWords(); I != N; ++I)
808 Result.pVal[I] = ByteSwap_64(pVal[N - I - 1]);
809 if (Result.BitWidth != BitWidth) {
810 lshrNear(Result.pVal, Result.pVal, getNumWords(),
811 Result.BitWidth - BitWidth);
812 Result.BitWidth = BitWidth;
817 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
819 APInt A = API1, B = API2;
822 B = APIntOps::urem(A, B);
828 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) {
835 // Get the sign bit from the highest order bit
836 bool isNeg = T.I >> 63;
838 // Get the 11-bit exponent and adjust for the 1023 bit bias
839 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
841 // If the exponent is negative, the value is < 0 so just return 0.
843 return APInt(width, 0u);
845 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
846 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
848 // If the exponent doesn't shift all bits out of the mantissa
850 return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
851 APInt(width, mantissa >> (52 - exp));
853 // If the client didn't provide enough bits for us to shift the mantissa into
854 // then the result is undefined, just return 0
855 if (width <= exp - 52)
856 return APInt(width, 0);
858 // Otherwise, we have to shift the mantissa bits up to the right location
859 APInt Tmp(width, mantissa);
860 Tmp = Tmp.shl((unsigned)exp - 52);
861 return isNeg ? -Tmp : Tmp;
864 /// This function converts this APInt to a double.
865 /// The layout for double is as following (IEEE Standard 754):
866 /// --------------------------------------
867 /// | Sign Exponent Fraction Bias |
868 /// |-------------------------------------- |
869 /// | 1[63] 11[62-52] 52[51-00] 1023 |
870 /// --------------------------------------
871 double APInt::roundToDouble(bool isSigned) const {
873 // Handle the simple case where the value is contained in one uint64_t.
874 // It is wrong to optimize getWord(0) to VAL; there might be more than one word.
875 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
877 int64_t sext = (int64_t(getWord(0)) << (64-BitWidth)) >> (64-BitWidth);
880 return double(getWord(0));
883 // Determine if the value is negative.
884 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
886 // Construct the absolute value if we're negative.
887 APInt Tmp(isNeg ? -(*this) : (*this));
889 // Figure out how many bits we're using.
890 unsigned n = Tmp.getActiveBits();
892 // The exponent (without bias normalization) is just the number of bits
893 // we are using. Note that the sign bit is gone since we constructed the
897 // Return infinity for exponent overflow
899 if (!isSigned || !isNeg)
900 return std::numeric_limits<double>::infinity();
902 return -std::numeric_limits<double>::infinity();
904 exp += 1023; // Increment for 1023 bias
906 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
907 // extract the high 52 bits from the correct words in pVal.
909 unsigned hiWord = whichWord(n-1);
911 mantissa = Tmp.pVal[0];
913 mantissa >>= n - 52; // shift down, we want the top 52 bits.
915 assert(hiWord > 0 && "huh?");
916 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
917 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
918 mantissa = hibits | lobits;
921 // The leading bit of mantissa is implicit, so get rid of it.
922 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
927 T.I = sign | (exp << 52) | mantissa;
931 // Truncate to new width.
932 APInt APInt::trunc(unsigned width) const {
933 assert(width < BitWidth && "Invalid APInt Truncate request");
934 assert(width && "Can't truncate to 0 bits");
936 if (width <= APINT_BITS_PER_WORD)
937 return APInt(width, getRawData()[0]);
939 APInt Result(getMemory(getNumWords(width)), width);
943 for (i = 0; i != width / APINT_BITS_PER_WORD; i++)
944 Result.pVal[i] = pVal[i];
946 // Truncate and copy any partial word.
947 unsigned bits = (0 - width) % APINT_BITS_PER_WORD;
949 Result.pVal[i] = pVal[i] << bits >> bits;
954 // Sign extend to a new width.
955 APInt APInt::sext(unsigned width) const {
956 assert(width > BitWidth && "Invalid APInt SignExtend request");
958 if (width <= APINT_BITS_PER_WORD) {
959 uint64_t val = VAL << (APINT_BITS_PER_WORD - BitWidth);
960 val = (int64_t)val >> (width - BitWidth);
961 return APInt(width, val >> (APINT_BITS_PER_WORD - width));
964 APInt Result(getMemory(getNumWords(width)), width);
969 for (i = 0; i != BitWidth / APINT_BITS_PER_WORD; i++) {
970 word = getRawData()[i];
971 Result.pVal[i] = word;
974 // Read and sign-extend any partial word.
975 unsigned bits = (0 - BitWidth) % APINT_BITS_PER_WORD;
977 word = (int64_t)getRawData()[i] << bits >> bits;
979 word = (int64_t)word >> (APINT_BITS_PER_WORD - 1);
981 // Write remaining full words.
982 for (; i != width / APINT_BITS_PER_WORD; i++) {
983 Result.pVal[i] = word;
984 word = (int64_t)word >> (APINT_BITS_PER_WORD - 1);
987 // Write any partial word.
988 bits = (0 - width) % APINT_BITS_PER_WORD;
990 Result.pVal[i] = word << bits >> bits;
995 // Zero extend to a new width.
996 APInt APInt::zext(unsigned width) const {
997 assert(width > BitWidth && "Invalid APInt ZeroExtend request");
999 if (width <= APINT_BITS_PER_WORD)
1000 return APInt(width, VAL);
1002 APInt Result(getMemory(getNumWords(width)), width);
1006 for (i = 0; i != getNumWords(); i++)
1007 Result.pVal[i] = getRawData()[i];
1009 // Zero remaining words.
1010 memset(&Result.pVal[i], 0, (Result.getNumWords() - i) * APINT_WORD_SIZE);
1015 APInt APInt::zextOrTrunc(unsigned width) const {
1016 if (BitWidth < width)
1018 if (BitWidth > width)
1019 return trunc(width);
1023 APInt APInt::sextOrTrunc(unsigned width) const {
1024 if (BitWidth < width)
1026 if (BitWidth > width)
1027 return trunc(width);
1031 APInt APInt::zextOrSelf(unsigned width) const {
1032 if (BitWidth < width)
1037 APInt APInt::sextOrSelf(unsigned width) const {
1038 if (BitWidth < width)
1043 /// Arithmetic right-shift this APInt by shiftAmt.
1044 /// @brief Arithmetic right-shift function.
1045 APInt APInt::ashr(const APInt &shiftAmt) const {
1046 return ashr((unsigned)shiftAmt.getLimitedValue(BitWidth));
1049 /// Arithmetic right-shift this APInt by shiftAmt.
1050 /// @brief Arithmetic right-shift function.
1051 APInt APInt::ashr(unsigned shiftAmt) const {
1052 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1053 // Handle a degenerate case
1057 // Handle single word shifts with built-in ashr
1058 if (isSingleWord()) {
1059 if (shiftAmt == BitWidth)
1060 return APInt(BitWidth, 0); // undefined
1062 unsigned SignBit = APINT_BITS_PER_WORD - BitWidth;
1063 return APInt(BitWidth,
1064 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1068 // If all the bits were shifted out, the result is, technically, undefined.
1069 // We return -1 if it was negative, 0 otherwise. We check this early to avoid
1070 // issues in the algorithm below.
1071 if (shiftAmt == BitWidth) {
1073 return APInt(BitWidth, -1ULL, true);
1075 return APInt(BitWidth, 0);
1078 // Create some space for the result.
1079 uint64_t * val = new uint64_t[getNumWords()];
1081 // Compute some values needed by the following shift algorithms
1082 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word
1083 unsigned offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift
1084 unsigned breakWord = getNumWords() - 1 - offset; // last word affected
1085 unsigned bitsInWord = whichBit(BitWidth); // how many bits in last word?
1086 if (bitsInWord == 0)
1087 bitsInWord = APINT_BITS_PER_WORD;
1089 // If we are shifting whole words, just move whole words
1090 if (wordShift == 0) {
1091 // Move the words containing significant bits
1092 for (unsigned i = 0; i <= breakWord; ++i)
1093 val[i] = pVal[i+offset]; // move whole word
1095 // Adjust the top significant word for sign bit fill, if negative
1097 if (bitsInWord < APINT_BITS_PER_WORD)
1098 val[breakWord] |= ~0ULL << bitsInWord; // set high bits
1100 // Shift the low order words
1101 for (unsigned i = 0; i < breakWord; ++i) {
1102 // This combines the shifted corresponding word with the low bits from
1103 // the next word (shifted into this word's high bits).
1104 val[i] = (pVal[i+offset] >> wordShift) |
1105 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1108 // Shift the break word. In this case there are no bits from the next word
1109 // to include in this word.
1110 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1112 // Deal with sign extension in the break word, and possibly the word before
1115 if (wordShift > bitsInWord) {
1118 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord));
1119 val[breakWord] |= ~0ULL;
1121 val[breakWord] |= (~0ULL << (bitsInWord - wordShift));
1125 // Remaining words are 0 or -1, just assign them.
1126 uint64_t fillValue = (isNegative() ? -1ULL : 0);
1127 for (unsigned i = breakWord+1; i < getNumWords(); ++i)
1129 APInt Result(val, BitWidth);
1130 Result.clearUnusedBits();
1134 /// Logical right-shift this APInt by shiftAmt.
1135 /// @brief Logical right-shift function.
1136 APInt APInt::lshr(const APInt &shiftAmt) const {
1137 return lshr((unsigned)shiftAmt.getLimitedValue(BitWidth));
1140 /// Logical right-shift this APInt by shiftAmt.
1141 /// @brief Logical right-shift function.
1142 APInt APInt::lshr(unsigned shiftAmt) const {
1143 if (isSingleWord()) {
1144 if (shiftAmt >= BitWidth)
1145 return APInt(BitWidth, 0);
1147 return APInt(BitWidth, this->VAL >> shiftAmt);
1150 // If all the bits were shifted out, the result is 0. This avoids issues
1151 // with shifting by the size of the integer type, which produces undefined
1152 // results. We define these "undefined results" to always be 0.
1153 if (shiftAmt >= BitWidth)
1154 return APInt(BitWidth, 0);
1156 // If none of the bits are shifted out, the result is *this. This avoids
1157 // issues with shifting by the size of the integer type, which produces
1158 // undefined results in the code below. This is also an optimization.
1162 // Create some space for the result.
1163 uint64_t * val = new uint64_t[getNumWords()];
1165 // If we are shifting less than a word, compute the shift with a simple carry
1166 if (shiftAmt < APINT_BITS_PER_WORD) {
1167 lshrNear(val, pVal, getNumWords(), shiftAmt);
1168 APInt Result(val, BitWidth);
1169 Result.clearUnusedBits();
1173 // Compute some values needed by the remaining shift algorithms
1174 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD;
1175 unsigned offset = shiftAmt / APINT_BITS_PER_WORD;
1177 // If we are shifting whole words, just move whole words
1178 if (wordShift == 0) {
1179 for (unsigned i = 0; i < getNumWords() - offset; ++i)
1180 val[i] = pVal[i+offset];
1181 for (unsigned i = getNumWords()-offset; i < getNumWords(); i++)
1183 APInt Result(val, BitWidth);
1184 Result.clearUnusedBits();
1188 // Shift the low order words
1189 unsigned breakWord = getNumWords() - offset -1;
1190 for (unsigned i = 0; i < breakWord; ++i)
1191 val[i] = (pVal[i+offset] >> wordShift) |
1192 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1193 // Shift the break word.
1194 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1196 // Remaining words are 0
1197 for (unsigned i = breakWord+1; i < getNumWords(); ++i)
1199 APInt Result(val, BitWidth);
1200 Result.clearUnusedBits();
1204 /// Left-shift this APInt by shiftAmt.
1205 /// @brief Left-shift function.
1206 APInt APInt::shl(const APInt &shiftAmt) const {
1207 // It's undefined behavior in C to shift by BitWidth or greater.
1208 return shl((unsigned)shiftAmt.getLimitedValue(BitWidth));
1211 APInt APInt::shlSlowCase(unsigned shiftAmt) const {
1212 // If all the bits were shifted out, the result is 0. This avoids issues
1213 // with shifting by the size of the integer type, which produces undefined
1214 // results. We define these "undefined results" to always be 0.
1215 if (shiftAmt == BitWidth)
1216 return APInt(BitWidth, 0);
1218 // If none of the bits are shifted out, the result is *this. This avoids a
1219 // lshr by the words size in the loop below which can produce incorrect
1220 // results. It also avoids the expensive computation below for a common case.
1224 // Create some space for the result.
1225 uint64_t * val = new uint64_t[getNumWords()];
1227 // If we are shifting less than a word, do it the easy way
1228 if (shiftAmt < APINT_BITS_PER_WORD) {
1230 for (unsigned i = 0; i < getNumWords(); i++) {
1231 val[i] = pVal[i] << shiftAmt | carry;
1232 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1234 APInt Result(val, BitWidth);
1235 Result.clearUnusedBits();
1239 // Compute some values needed by the remaining shift algorithms
1240 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD;
1241 unsigned offset = shiftAmt / APINT_BITS_PER_WORD;
1243 // If we are shifting whole words, just move whole words
1244 if (wordShift == 0) {
1245 for (unsigned i = 0; i < offset; i++)
1247 for (unsigned i = offset; i < getNumWords(); i++)
1248 val[i] = pVal[i-offset];
1249 APInt Result(val, BitWidth);
1250 Result.clearUnusedBits();
1254 // Copy whole words from this to Result.
1255 unsigned i = getNumWords() - 1;
1256 for (; i > offset; --i)
1257 val[i] = pVal[i-offset] << wordShift |
1258 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1259 val[offset] = pVal[0] << wordShift;
1260 for (i = 0; i < offset; ++i)
1262 APInt Result(val, BitWidth);
1263 Result.clearUnusedBits();
1267 APInt APInt::rotl(const APInt &rotateAmt) const {
1268 return rotl((unsigned)rotateAmt.getLimitedValue(BitWidth));
1271 APInt APInt::rotl(unsigned rotateAmt) const {
1272 rotateAmt %= BitWidth;
1275 return shl(rotateAmt) | lshr(BitWidth - rotateAmt);
1278 APInt APInt::rotr(const APInt &rotateAmt) const {
1279 return rotr((unsigned)rotateAmt.getLimitedValue(BitWidth));
1282 APInt APInt::rotr(unsigned rotateAmt) const {
1283 rotateAmt %= BitWidth;
1286 return lshr(rotateAmt) | shl(BitWidth - rotateAmt);
1289 // Square Root - this method computes and returns the square root of "this".
1290 // Three mechanisms are used for computation. For small values (<= 5 bits),
1291 // a table lookup is done. This gets some performance for common cases. For
1292 // values using less than 52 bits, the value is converted to double and then
1293 // the libc sqrt function is called. The result is rounded and then converted
1294 // back to a uint64_t which is then used to construct the result. Finally,
1295 // the Babylonian method for computing square roots is used.
1296 APInt APInt::sqrt() const {
1298 // Determine the magnitude of the value.
1299 unsigned magnitude = getActiveBits();
1301 // Use a fast table for some small values. This also gets rid of some
1302 // rounding errors in libc sqrt for small values.
1303 if (magnitude <= 5) {
1304 static const uint8_t results[32] = {
1307 /* 3- 6 */ 2, 2, 2, 2,
1308 /* 7-12 */ 3, 3, 3, 3, 3, 3,
1309 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1310 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1313 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]);
1316 // If the magnitude of the value fits in less than 52 bits (the precision of
1317 // an IEEE double precision floating point value), then we can use the
1318 // libc sqrt function which will probably use a hardware sqrt computation.
1319 // This should be faster than the algorithm below.
1320 if (magnitude < 52) {
1321 return APInt(BitWidth,
1322 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0])))));
1325 // Okay, all the short cuts are exhausted. We must compute it. The following
1326 // is a classical Babylonian method for computing the square root. This code
1327 // was adapted to APInt from a wikipedia article on such computations.
1328 // See http://www.wikipedia.org/ and go to the page named
1329 // Calculate_an_integer_square_root.
1330 unsigned nbits = BitWidth, i = 4;
1331 APInt testy(BitWidth, 16);
1332 APInt x_old(BitWidth, 1);
1333 APInt x_new(BitWidth, 0);
1334 APInt two(BitWidth, 2);
1336 // Select a good starting value using binary logarithms.
1337 for (;; i += 2, testy = testy.shl(2))
1338 if (i >= nbits || this->ule(testy)) {
1339 x_old = x_old.shl(i / 2);
1343 // Use the Babylonian method to arrive at the integer square root:
1345 x_new = (this->udiv(x_old) + x_old).udiv(two);
1346 if (x_old.ule(x_new))
1351 // Make sure we return the closest approximation
1352 // NOTE: The rounding calculation below is correct. It will produce an
1353 // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1354 // determined to be a rounding issue with pari/gp as it begins to use a
1355 // floating point representation after 192 bits. There are no discrepancies
1356 // between this algorithm and pari/gp for bit widths < 192 bits.
1357 APInt square(x_old * x_old);
1358 APInt nextSquare((x_old + 1) * (x_old +1));
1359 if (this->ult(square))
1361 assert(this->ule(nextSquare) && "Error in APInt::sqrt computation");
1362 APInt midpoint((nextSquare - square).udiv(two));
1363 APInt offset(*this - square);
1364 if (offset.ult(midpoint))
1369 /// Computes the multiplicative inverse of this APInt for a given modulo. The
1370 /// iterative extended Euclidean algorithm is used to solve for this value,
1371 /// however we simplify it to speed up calculating only the inverse, and take
1372 /// advantage of div+rem calculations. We also use some tricks to avoid copying
1373 /// (potentially large) APInts around.
1374 APInt APInt::multiplicativeInverse(const APInt& modulo) const {
1375 assert(ult(modulo) && "This APInt must be smaller than the modulo");
1377 // Using the properties listed at the following web page (accessed 06/21/08):
1378 // http://www.numbertheory.org/php/euclid.html
1379 // (especially the properties numbered 3, 4 and 9) it can be proved that
1380 // BitWidth bits suffice for all the computations in the algorithm implemented
1381 // below. More precisely, this number of bits suffice if the multiplicative
1382 // inverse exists, but may not suffice for the general extended Euclidean
1385 APInt r[2] = { modulo, *this };
1386 APInt t[2] = { APInt(BitWidth, 0), APInt(BitWidth, 1) };
1387 APInt q(BitWidth, 0);
1390 for (i = 0; r[i^1] != 0; i ^= 1) {
1391 // An overview of the math without the confusing bit-flipping:
1392 // q = r[i-2] / r[i-1]
1393 // r[i] = r[i-2] % r[i-1]
1394 // t[i] = t[i-2] - t[i-1] * q
1395 udivrem(r[i], r[i^1], q, r[i]);
1399 // If this APInt and the modulo are not coprime, there is no multiplicative
1400 // inverse, so return 0. We check this by looking at the next-to-last
1401 // remainder, which is the gcd(*this,modulo) as calculated by the Euclidean
1404 return APInt(BitWidth, 0);
1406 // The next-to-last t is the multiplicative inverse. However, we are
1407 // interested in a positive inverse. Calcuate a positive one from a negative
1408 // one if necessary. A simple addition of the modulo suffices because
1409 // abs(t[i]) is known to be less than *this/2 (see the link above).
1410 return t[i].isNegative() ? t[i] + modulo : t[i];
1413 /// Calculate the magic numbers required to implement a signed integer division
1414 /// by a constant as a sequence of multiplies, adds and shifts. Requires that
1415 /// the divisor not be 0, 1, or -1. Taken from "Hacker's Delight", Henry S.
1416 /// Warren, Jr., chapter 10.
1417 APInt::ms APInt::magic() const {
1418 const APInt& d = *this;
1420 APInt ad, anc, delta, q1, r1, q2, r2, t;
1421 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
1425 t = signedMin + (d.lshr(d.getBitWidth() - 1));
1426 anc = t - 1 - t.urem(ad); // absolute value of nc
1427 p = d.getBitWidth() - 1; // initialize p
1428 q1 = signedMin.udiv(anc); // initialize q1 = 2p/abs(nc)
1429 r1 = signedMin - q1*anc; // initialize r1 = rem(2p,abs(nc))
1430 q2 = signedMin.udiv(ad); // initialize q2 = 2p/abs(d)
1431 r2 = signedMin - q2*ad; // initialize r2 = rem(2p,abs(d))
1434 q1 = q1<<1; // update q1 = 2p/abs(nc)
1435 r1 = r1<<1; // update r1 = rem(2p/abs(nc))
1436 if (r1.uge(anc)) { // must be unsigned comparison
1440 q2 = q2<<1; // update q2 = 2p/abs(d)
1441 r2 = r2<<1; // update r2 = rem(2p/abs(d))
1442 if (r2.uge(ad)) { // must be unsigned comparison
1447 } while (q1.ult(delta) || (q1 == delta && r1 == 0));
1450 if (d.isNegative()) mag.m = -mag.m; // resulting magic number
1451 mag.s = p - d.getBitWidth(); // resulting shift
1455 /// Calculate the magic numbers required to implement an unsigned integer
1456 /// division by a constant as a sequence of multiplies, adds and shifts.
1457 /// Requires that the divisor not be 0. Taken from "Hacker's Delight", Henry
1458 /// S. Warren, Jr., chapter 10.
1459 /// LeadingZeros can be used to simplify the calculation if the upper bits
1460 /// of the divided value are known zero.
1461 APInt::mu APInt::magicu(unsigned LeadingZeros) const {
1462 const APInt& d = *this;
1464 APInt nc, delta, q1, r1, q2, r2;
1466 magu.a = 0; // initialize "add" indicator
1467 APInt allOnes = APInt::getAllOnesValue(d.getBitWidth()).lshr(LeadingZeros);
1468 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
1469 APInt signedMax = APInt::getSignedMaxValue(d.getBitWidth());
1471 nc = allOnes - (allOnes - d).urem(d);
1472 p = d.getBitWidth() - 1; // initialize p
1473 q1 = signedMin.udiv(nc); // initialize q1 = 2p/nc
1474 r1 = signedMin - q1*nc; // initialize r1 = rem(2p,nc)
1475 q2 = signedMax.udiv(d); // initialize q2 = (2p-1)/d
1476 r2 = signedMax - q2*d; // initialize r2 = rem((2p-1),d)
1479 if (r1.uge(nc - r1)) {
1480 q1 = q1 + q1 + 1; // update q1
1481 r1 = r1 + r1 - nc; // update r1
1484 q1 = q1+q1; // update q1
1485 r1 = r1+r1; // update r1
1487 if ((r2 + 1).uge(d - r2)) {
1488 if (q2.uge(signedMax)) magu.a = 1;
1489 q2 = q2+q2 + 1; // update q2
1490 r2 = r2+r2 + 1 - d; // update r2
1493 if (q2.uge(signedMin)) magu.a = 1;
1494 q2 = q2+q2; // update q2
1495 r2 = r2+r2 + 1; // update r2
1498 } while (p < d.getBitWidth()*2 &&
1499 (q1.ult(delta) || (q1 == delta && r1 == 0)));
1500 magu.m = q2 + 1; // resulting magic number
1501 magu.s = p - d.getBitWidth(); // resulting shift
1505 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1506 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1507 /// variables here have the same names as in the algorithm. Comments explain
1508 /// the algorithm and any deviation from it.
1509 static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
1510 unsigned m, unsigned n) {
1511 assert(u && "Must provide dividend");
1512 assert(v && "Must provide divisor");
1513 assert(q && "Must provide quotient");
1514 assert(u != v && u != q && v != q && "Must use different memory");
1515 assert(n>1 && "n must be > 1");
1517 // b denotes the base of the number system. In our case b is 2^32.
1518 LLVM_CONSTEXPR uint64_t b = uint64_t(1) << 32;
1520 DEBUG(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n');
1521 DEBUG(dbgs() << "KnuthDiv: original:");
1522 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1523 DEBUG(dbgs() << " by");
1524 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
1525 DEBUG(dbgs() << '\n');
1526 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1527 // u and v by d. Note that we have taken Knuth's advice here to use a power
1528 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1529 // 2 allows us to shift instead of multiply and it is easy to determine the
1530 // shift amount from the leading zeros. We are basically normalizing the u
1531 // and v so that its high bits are shifted to the top of v's range without
1532 // overflow. Note that this can require an extra word in u so that u must
1533 // be of length m+n+1.
1534 unsigned shift = countLeadingZeros(v[n-1]);
1535 unsigned v_carry = 0;
1536 unsigned u_carry = 0;
1538 for (unsigned i = 0; i < m+n; ++i) {
1539 unsigned u_tmp = u[i] >> (32 - shift);
1540 u[i] = (u[i] << shift) | u_carry;
1543 for (unsigned i = 0; i < n; ++i) {
1544 unsigned v_tmp = v[i] >> (32 - shift);
1545 v[i] = (v[i] << shift) | v_carry;
1551 DEBUG(dbgs() << "KnuthDiv: normal:");
1552 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1553 DEBUG(dbgs() << " by");
1554 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
1555 DEBUG(dbgs() << '\n');
1557 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1560 DEBUG(dbgs() << "KnuthDiv: quotient digit #" << j << '\n');
1561 // D3. [Calculate q'.].
1562 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1563 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1564 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1565 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1566 // on v[n-2] determines at high speed most of the cases in which the trial
1567 // value qp is one too large, and it eliminates all cases where qp is two
1569 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1570 DEBUG(dbgs() << "KnuthDiv: dividend == " << dividend << '\n');
1571 uint64_t qp = dividend / v[n-1];
1572 uint64_t rp = dividend % v[n-1];
1573 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1576 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1579 DEBUG(dbgs() << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1581 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1582 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1583 // consists of a simple multiplication by a one-place number, combined with
1585 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1586 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1587 // true value plus b**(n+1), namely as the b's complement of
1588 // the true value, and a "borrow" to the left should be remembered.
1590 for (unsigned i = 0; i < n; ++i) {
1591 uint64_t p = uint64_t(qp) * uint64_t(v[i]);
1592 int64_t subres = int64_t(u[j+i]) - borrow - (unsigned)p;
1593 u[j+i] = (unsigned)subres;
1594 borrow = (p >> 32) - (subres >> 32);
1595 DEBUG(dbgs() << "KnuthDiv: u[j+i] = " << u[j+i]
1596 << ", borrow = " << borrow << '\n');
1598 bool isNeg = u[j+n] < borrow;
1599 u[j+n] -= (unsigned)borrow;
1601 DEBUG(dbgs() << "KnuthDiv: after subtraction:");
1602 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1603 DEBUG(dbgs() << '\n');
1605 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1606 // negative, go to step D6; otherwise go on to step D7.
1607 q[j] = (unsigned)qp;
1609 // D6. [Add back]. The probability that this step is necessary is very
1610 // small, on the order of only 2/b. Make sure that test data accounts for
1611 // this possibility. Decrease q[j] by 1
1613 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1614 // A carry will occur to the left of u[j+n], and it should be ignored
1615 // since it cancels with the borrow that occurred in D4.
1617 for (unsigned i = 0; i < n; i++) {
1618 unsigned limit = std::min(u[j+i],v[i]);
1619 u[j+i] += v[i] + carry;
1620 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1624 DEBUG(dbgs() << "KnuthDiv: after correction:");
1625 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1626 DEBUG(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n');
1628 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1631 DEBUG(dbgs() << "KnuthDiv: quotient:");
1632 DEBUG(for (int i = m; i >=0; i--) dbgs() <<" " << q[i]);
1633 DEBUG(dbgs() << '\n');
1635 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1636 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1637 // compute the remainder (urem uses this).
1639 // The value d is expressed by the "shift" value above since we avoided
1640 // multiplication by d by using a shift left. So, all we have to do is
1641 // shift right here. In order to mak
1644 DEBUG(dbgs() << "KnuthDiv: remainder:");
1645 for (int i = n-1; i >= 0; i--) {
1646 r[i] = (u[i] >> shift) | carry;
1647 carry = u[i] << (32 - shift);
1648 DEBUG(dbgs() << " " << r[i]);
1651 for (int i = n-1; i >= 0; i--) {
1653 DEBUG(dbgs() << " " << r[i]);
1656 DEBUG(dbgs() << '\n');
1658 DEBUG(dbgs() << '\n');
1661 void APInt::divide(const APInt LHS, unsigned lhsWords,
1662 const APInt &RHS, unsigned rhsWords,
1663 APInt *Quotient, APInt *Remainder)
1665 assert(lhsWords >= rhsWords && "Fractional result");
1667 // First, compose the values into an array of 32-bit words instead of
1668 // 64-bit words. This is a necessity of both the "short division" algorithm
1669 // and the Knuth "classical algorithm" which requires there to be native
1670 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1671 // can't use 64-bit operands here because we don't have native results of
1672 // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't
1673 // work on large-endian machines.
1674 uint64_t mask = ~0ull >> (sizeof(unsigned)*CHAR_BIT);
1675 unsigned n = rhsWords * 2;
1676 unsigned m = (lhsWords * 2) - n;
1678 // Allocate space for the temporary values we need either on the stack, if
1679 // it will fit, or on the heap if it won't.
1680 unsigned SPACE[128];
1681 unsigned *U = nullptr;
1682 unsigned *V = nullptr;
1683 unsigned *Q = nullptr;
1684 unsigned *R = nullptr;
1685 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1688 Q = &SPACE[(m+n+1) + n];
1690 R = &SPACE[(m+n+1) + n + (m+n)];
1692 U = new unsigned[m + n + 1];
1693 V = new unsigned[n];
1694 Q = new unsigned[m+n];
1696 R = new unsigned[n];
1699 // Initialize the dividend
1700 memset(U, 0, (m+n+1)*sizeof(unsigned));
1701 for (unsigned i = 0; i < lhsWords; ++i) {
1702 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1703 U[i * 2] = (unsigned)(tmp & mask);
1704 U[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT));
1706 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1708 // Initialize the divisor
1709 memset(V, 0, (n)*sizeof(unsigned));
1710 for (unsigned i = 0; i < rhsWords; ++i) {
1711 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1712 V[i * 2] = (unsigned)(tmp & mask);
1713 V[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT));
1716 // initialize the quotient and remainder
1717 memset(Q, 0, (m+n) * sizeof(unsigned));
1719 memset(R, 0, n * sizeof(unsigned));
1721 // Now, adjust m and n for the Knuth division. n is the number of words in
1722 // the divisor. m is the number of words by which the dividend exceeds the
1723 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1724 // contain any zero words or the Knuth algorithm fails.
1725 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1729 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1732 // If we're left with only a single word for the divisor, Knuth doesn't work
1733 // so we implement the short division algorithm here. This is much simpler
1734 // and faster because we are certain that we can divide a 64-bit quantity
1735 // by a 32-bit quantity at hardware speed and short division is simply a
1736 // series of such operations. This is just like doing short division but we
1737 // are using base 2^32 instead of base 10.
1738 assert(n != 0 && "Divide by zero?");
1740 unsigned divisor = V[0];
1741 unsigned remainder = 0;
1742 for (int i = m+n-1; i >= 0; i--) {
1743 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1744 if (partial_dividend == 0) {
1747 } else if (partial_dividend < divisor) {
1749 remainder = (unsigned)partial_dividend;
1750 } else if (partial_dividend == divisor) {
1754 Q[i] = (unsigned)(partial_dividend / divisor);
1755 remainder = (unsigned)(partial_dividend - (Q[i] * divisor));
1761 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1763 KnuthDiv(U, V, Q, R, m, n);
1766 // If the caller wants the quotient
1768 // Set up the Quotient value's memory.
1769 if (Quotient->BitWidth != LHS.BitWidth) {
1770 if (Quotient->isSingleWord())
1773 delete [] Quotient->pVal;
1774 Quotient->BitWidth = LHS.BitWidth;
1775 if (!Quotient->isSingleWord())
1776 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1778 Quotient->clearAllBits();
1780 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1782 // This case is currently dead as all users of divide() handle trivial cases
1784 if (lhsWords == 1) {
1786 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1787 if (Quotient->isSingleWord())
1788 Quotient->VAL = tmp;
1790 Quotient->pVal[0] = tmp;
1792 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1793 for (unsigned i = 0; i < lhsWords; ++i)
1795 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1799 // If the caller wants the remainder
1801 // Set up the Remainder value's memory.
1802 if (Remainder->BitWidth != RHS.BitWidth) {
1803 if (Remainder->isSingleWord())
1806 delete [] Remainder->pVal;
1807 Remainder->BitWidth = RHS.BitWidth;
1808 if (!Remainder->isSingleWord())
1809 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1811 Remainder->clearAllBits();
1813 // The remainder is in R. Reconstitute the remainder into Remainder's low
1815 if (rhsWords == 1) {
1817 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1818 if (Remainder->isSingleWord())
1819 Remainder->VAL = tmp;
1821 Remainder->pVal[0] = tmp;
1823 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1824 for (unsigned i = 0; i < rhsWords; ++i)
1825 Remainder->pVal[i] =
1826 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1830 // Clean up the memory we allocated.
1831 if (U != &SPACE[0]) {
1839 APInt APInt::udiv(const APInt& RHS) const {
1840 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1842 // First, deal with the easy case
1843 if (isSingleWord()) {
1844 assert(RHS.VAL != 0 && "Divide by zero?");
1845 return APInt(BitWidth, VAL / RHS.VAL);
1848 // Get some facts about the LHS and RHS number of bits and words
1849 unsigned rhsBits = RHS.getActiveBits();
1850 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1851 assert(rhsWords && "Divided by zero???");
1852 unsigned lhsBits = this->getActiveBits();
1853 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1855 // Deal with some degenerate cases
1858 return APInt(BitWidth, 0);
1859 else if (lhsWords < rhsWords || this->ult(RHS)) {
1860 // X / Y ===> 0, iff X < Y
1861 return APInt(BitWidth, 0);
1862 } else if (*this == RHS) {
1864 return APInt(BitWidth, 1);
1865 } else if (lhsWords == 1 && rhsWords == 1) {
1866 // All high words are zero, just use native divide
1867 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1870 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1871 APInt Quotient(1,0); // to hold result.
1872 divide(*this, lhsWords, RHS, rhsWords, &Quotient, nullptr);
1876 APInt APInt::sdiv(const APInt &RHS) const {
1878 if (RHS.isNegative())
1879 return (-(*this)).udiv(-RHS);
1880 return -((-(*this)).udiv(RHS));
1882 if (RHS.isNegative())
1883 return -(this->udiv(-RHS));
1884 return this->udiv(RHS);
1887 APInt APInt::urem(const APInt& RHS) const {
1888 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1889 if (isSingleWord()) {
1890 assert(RHS.VAL != 0 && "Remainder by zero?");
1891 return APInt(BitWidth, VAL % RHS.VAL);
1894 // Get some facts about the LHS
1895 unsigned lhsBits = getActiveBits();
1896 unsigned lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1898 // Get some facts about the RHS
1899 unsigned rhsBits = RHS.getActiveBits();
1900 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1901 assert(rhsWords && "Performing remainder operation by zero ???");
1903 // Check the degenerate cases
1904 if (lhsWords == 0) {
1906 return APInt(BitWidth, 0);
1907 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1908 // X % Y ===> X, iff X < Y
1910 } else if (*this == RHS) {
1912 return APInt(BitWidth, 0);
1913 } else if (lhsWords == 1) {
1914 // All high words are zero, just use native remainder
1915 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
1918 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1919 APInt Remainder(1,0);
1920 divide(*this, lhsWords, RHS, rhsWords, nullptr, &Remainder);
1924 APInt APInt::srem(const APInt &RHS) const {
1926 if (RHS.isNegative())
1927 return -((-(*this)).urem(-RHS));
1928 return -((-(*this)).urem(RHS));
1930 if (RHS.isNegative())
1931 return this->urem(-RHS);
1932 return this->urem(RHS);
1935 void APInt::udivrem(const APInt &LHS, const APInt &RHS,
1936 APInt &Quotient, APInt &Remainder) {
1937 assert(LHS.BitWidth == RHS.BitWidth && "Bit widths must be the same");
1939 // First, deal with the easy case
1940 if (LHS.isSingleWord()) {
1941 assert(RHS.VAL != 0 && "Divide by zero?");
1942 uint64_t QuotVal = LHS.VAL / RHS.VAL;
1943 uint64_t RemVal = LHS.VAL % RHS.VAL;
1944 Quotient = APInt(LHS.BitWidth, QuotVal);
1945 Remainder = APInt(LHS.BitWidth, RemVal);
1949 // Get some size facts about the dividend and divisor
1950 unsigned lhsBits = LHS.getActiveBits();
1951 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1952 unsigned rhsBits = RHS.getActiveBits();
1953 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1955 // Check the degenerate cases
1956 if (lhsWords == 0) {
1957 Quotient = 0; // 0 / Y ===> 0
1958 Remainder = 0; // 0 % Y ===> 0
1962 if (lhsWords < rhsWords || LHS.ult(RHS)) {
1963 Remainder = LHS; // X % Y ===> X, iff X < Y
1964 Quotient = 0; // X / Y ===> 0, iff X < Y
1969 Quotient = 1; // X / X ===> 1
1970 Remainder = 0; // X % X ===> 0;
1974 if (lhsWords == 1 && rhsWords == 1) {
1975 // There is only one word to consider so use the native versions.
1976 uint64_t lhsValue = LHS.isSingleWord() ? LHS.VAL : LHS.pVal[0];
1977 uint64_t rhsValue = RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0];
1978 Quotient = APInt(LHS.getBitWidth(), lhsValue / rhsValue);
1979 Remainder = APInt(LHS.getBitWidth(), lhsValue % rhsValue);
1983 // Okay, lets do it the long way
1984 divide(LHS, lhsWords, RHS, rhsWords, &Quotient, &Remainder);
1987 void APInt::sdivrem(const APInt &LHS, const APInt &RHS,
1988 APInt &Quotient, APInt &Remainder) {
1989 if (LHS.isNegative()) {
1990 if (RHS.isNegative())
1991 APInt::udivrem(-LHS, -RHS, Quotient, Remainder);
1993 APInt::udivrem(-LHS, RHS, Quotient, Remainder);
1994 Quotient = -Quotient;
1996 Remainder = -Remainder;
1997 } else if (RHS.isNegative()) {
1998 APInt::udivrem(LHS, -RHS, Quotient, Remainder);
1999 Quotient = -Quotient;
2001 APInt::udivrem(LHS, RHS, Quotient, Remainder);
2005 APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const {
2006 APInt Res = *this+RHS;
2007 Overflow = isNonNegative() == RHS.isNonNegative() &&
2008 Res.isNonNegative() != isNonNegative();
2012 APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const {
2013 APInt Res = *this+RHS;
2014 Overflow = Res.ult(RHS);
2018 APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const {
2019 APInt Res = *this - RHS;
2020 Overflow = isNonNegative() != RHS.isNonNegative() &&
2021 Res.isNonNegative() != isNonNegative();
2025 APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const {
2026 APInt Res = *this-RHS;
2027 Overflow = Res.ugt(*this);
2031 APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const {
2032 // MININT/-1 --> overflow.
2033 Overflow = isMinSignedValue() && RHS.isAllOnesValue();
2037 APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const {
2038 APInt Res = *this * RHS;
2040 if (*this != 0 && RHS != 0)
2041 Overflow = Res.sdiv(RHS) != *this || Res.sdiv(*this) != RHS;
2047 APInt APInt::umul_ov(const APInt &RHS, bool &Overflow) const {
2048 APInt Res = *this * RHS;
2050 if (*this != 0 && RHS != 0)
2051 Overflow = Res.udiv(RHS) != *this || Res.udiv(*this) != RHS;
2057 APInt APInt::sshl_ov(const APInt &ShAmt, bool &Overflow) const {
2058 Overflow = ShAmt.uge(getBitWidth());
2060 return APInt(BitWidth, 0);
2062 if (isNonNegative()) // Don't allow sign change.
2063 Overflow = ShAmt.uge(countLeadingZeros());
2065 Overflow = ShAmt.uge(countLeadingOnes());
2067 return *this << ShAmt;
2070 APInt APInt::ushl_ov(const APInt &ShAmt, bool &Overflow) const {
2071 Overflow = ShAmt.uge(getBitWidth());
2073 return APInt(BitWidth, 0);
2075 Overflow = ShAmt.ugt(countLeadingZeros());
2077 return *this << ShAmt;
2083 void APInt::fromString(unsigned numbits, StringRef str, uint8_t radix) {
2084 // Check our assumptions here
2085 assert(!str.empty() && "Invalid string length");
2086 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||
2088 "Radix should be 2, 8, 10, 16, or 36!");
2090 StringRef::iterator p = str.begin();
2091 size_t slen = str.size();
2092 bool isNeg = *p == '-';
2093 if (*p == '-' || *p == '+') {
2096 assert(slen && "String is only a sign, needs a value.");
2098 assert((slen <= numbits || radix != 2) && "Insufficient bit width");
2099 assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width");
2100 assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width");
2101 assert((((slen-1)*64)/22 <= numbits || radix != 10) &&
2102 "Insufficient bit width");
2105 if (!isSingleWord())
2106 pVal = getClearedMemory(getNumWords());
2108 // Figure out if we can shift instead of multiply
2109 unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
2111 // Set up an APInt for the digit to add outside the loop so we don't
2112 // constantly construct/destruct it.
2113 APInt apdigit(getBitWidth(), 0);
2114 APInt apradix(getBitWidth(), radix);
2116 // Enter digit traversal loop
2117 for (StringRef::iterator e = str.end(); p != e; ++p) {
2118 unsigned digit = getDigit(*p, radix);
2119 assert(digit < radix && "Invalid character in digit string");
2121 // Shift or multiply the value by the radix
2129 // Add in the digit we just interpreted
2130 if (apdigit.isSingleWord())
2131 apdigit.VAL = digit;
2133 apdigit.pVal[0] = digit;
2136 // If its negative, put it in two's complement form
2139 this->flipAllBits();
2143 void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix,
2144 bool Signed, bool formatAsCLiteral) const {
2145 assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2 ||
2147 "Radix should be 2, 8, 10, 16, or 36!");
2149 const char *Prefix = "";
2150 if (formatAsCLiteral) {
2153 // Binary literals are a non-standard extension added in gcc 4.3:
2154 // http://gcc.gnu.org/onlinedocs/gcc-4.3.0/gcc/Binary-constants.html
2166 llvm_unreachable("Invalid radix!");
2170 // First, check for a zero value and just short circuit the logic below.
2173 Str.push_back(*Prefix);
2180 static const char Digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
2182 if (isSingleWord()) {
2184 char *BufPtr = Buffer+65;
2190 int64_t I = getSExtValue();
2200 Str.push_back(*Prefix);
2205 *--BufPtr = Digits[N % Radix];
2208 Str.append(BufPtr, Buffer+65);
2214 if (Signed && isNegative()) {
2215 // They want to print the signed version and it is a negative value
2216 // Flip the bits and add one to turn it into the equivalent positive
2217 // value and put a '-' in the result.
2224 Str.push_back(*Prefix);
2228 // We insert the digits backward, then reverse them to get the right order.
2229 unsigned StartDig = Str.size();
2231 // For the 2, 8 and 16 bit cases, we can just shift instead of divide
2232 // because the number of bits per digit (1, 3 and 4 respectively) divides
2233 // equaly. We just shift until the value is zero.
2234 if (Radix == 2 || Radix == 8 || Radix == 16) {
2235 // Just shift tmp right for each digit width until it becomes zero
2236 unsigned ShiftAmt = (Radix == 16 ? 4 : (Radix == 8 ? 3 : 1));
2237 unsigned MaskAmt = Radix - 1;
2240 unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt;
2241 Str.push_back(Digits[Digit]);
2242 Tmp = Tmp.lshr(ShiftAmt);
2245 APInt divisor(Radix == 10? 4 : 8, Radix);
2247 APInt APdigit(1, 0);
2248 APInt tmp2(Tmp.getBitWidth(), 0);
2249 divide(Tmp, Tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
2251 unsigned Digit = (unsigned)APdigit.getZExtValue();
2252 assert(Digit < Radix && "divide failed");
2253 Str.push_back(Digits[Digit]);
2258 // Reverse the digits before returning.
2259 std::reverse(Str.begin()+StartDig, Str.end());
2262 /// Returns the APInt as a std::string. Note that this is an inefficient method.
2263 /// It is better to pass in a SmallVector/SmallString to the methods above.
2264 std::string APInt::toString(unsigned Radix = 10, bool Signed = true) const {
2266 toString(S, Radix, Signed, /* formatAsCLiteral = */false);
2271 void APInt::dump() const {
2272 SmallString<40> S, U;
2273 this->toStringUnsigned(U);
2274 this->toStringSigned(S);
2275 dbgs() << "APInt(" << BitWidth << "b, "
2276 << U << "u " << S << "s)";
2279 void APInt::print(raw_ostream &OS, bool isSigned) const {
2281 this->toString(S, 10, isSigned, /* formatAsCLiteral = */false);
2285 // This implements a variety of operations on a representation of
2286 // arbitrary precision, two's-complement, bignum integer values.
2288 // Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe
2289 // and unrestricting assumption.
2290 static_assert(integerPartWidth % 2 == 0, "Part width must be divisible by 2!");
2292 /* Some handy functions local to this file. */
2295 /* Returns the integer part with the least significant BITS set.
2296 BITS cannot be zero. */
2297 static inline integerPart
2298 lowBitMask(unsigned int bits)
2300 assert(bits != 0 && bits <= integerPartWidth);
2302 return ~(integerPart) 0 >> (integerPartWidth - bits);
2305 /* Returns the value of the lower half of PART. */
2306 static inline integerPart
2307 lowHalf(integerPart part)
2309 return part & lowBitMask(integerPartWidth / 2);
2312 /* Returns the value of the upper half of PART. */
2313 static inline integerPart
2314 highHalf(integerPart part)
2316 return part >> (integerPartWidth / 2);
2319 /* Returns the bit number of the most significant set bit of a part.
2320 If the input number has no bits set -1U is returned. */
2322 partMSB(integerPart value)
2324 return findLastSet(value, ZB_Max);
2327 /* Returns the bit number of the least significant set bit of a
2328 part. If the input number has no bits set -1U is returned. */
2330 partLSB(integerPart value)
2332 return findFirstSet(value, ZB_Max);
2336 /* Sets the least significant part of a bignum to the input value, and
2337 zeroes out higher parts. */
2339 APInt::tcSet(integerPart *dst, integerPart part, unsigned int parts)
2346 for (i = 1; i < parts; i++)
2350 /* Assign one bignum to another. */
2352 APInt::tcAssign(integerPart *dst, const integerPart *src, unsigned int parts)
2356 for (i = 0; i < parts; i++)
2360 /* Returns true if a bignum is zero, false otherwise. */
2362 APInt::tcIsZero(const integerPart *src, unsigned int parts)
2366 for (i = 0; i < parts; i++)
2373 /* Extract the given bit of a bignum; returns 0 or 1. */
2375 APInt::tcExtractBit(const integerPart *parts, unsigned int bit)
2377 return (parts[bit / integerPartWidth] &
2378 ((integerPart) 1 << bit % integerPartWidth)) != 0;
2381 /* Set the given bit of a bignum. */
2383 APInt::tcSetBit(integerPart *parts, unsigned int bit)
2385 parts[bit / integerPartWidth] |= (integerPart) 1 << (bit % integerPartWidth);
2388 /* Clears the given bit of a bignum. */
2390 APInt::tcClearBit(integerPart *parts, unsigned int bit)
2392 parts[bit / integerPartWidth] &=
2393 ~((integerPart) 1 << (bit % integerPartWidth));
2396 /* Returns the bit number of the least significant set bit of a
2397 number. If the input number has no bits set -1U is returned. */
2399 APInt::tcLSB(const integerPart *parts, unsigned int n)
2401 unsigned int i, lsb;
2403 for (i = 0; i < n; i++) {
2404 if (parts[i] != 0) {
2405 lsb = partLSB(parts[i]);
2407 return lsb + i * integerPartWidth;
2414 /* Returns the bit number of the most significant set bit of a number.
2415 If the input number has no bits set -1U is returned. */
2417 APInt::tcMSB(const integerPart *parts, unsigned int n)
2424 if (parts[n] != 0) {
2425 msb = partMSB(parts[n]);
2427 return msb + n * integerPartWidth;
2434 /* Copy the bit vector of width srcBITS from SRC, starting at bit
2435 srcLSB, to DST, of dstCOUNT parts, such that the bit srcLSB becomes
2436 the least significant bit of DST. All high bits above srcBITS in
2437 DST are zero-filled. */
2439 APInt::tcExtract(integerPart *dst, unsigned int dstCount,const integerPart *src,
2440 unsigned int srcBits, unsigned int srcLSB)
2442 unsigned int firstSrcPart, dstParts, shift, n;
2444 dstParts = (srcBits + integerPartWidth - 1) / integerPartWidth;
2445 assert(dstParts <= dstCount);
2447 firstSrcPart = srcLSB / integerPartWidth;
2448 tcAssign (dst, src + firstSrcPart, dstParts);
2450 shift = srcLSB % integerPartWidth;
2451 tcShiftRight (dst, dstParts, shift);
2453 /* We now have (dstParts * integerPartWidth - shift) bits from SRC
2454 in DST. If this is less that srcBits, append the rest, else
2455 clear the high bits. */
2456 n = dstParts * integerPartWidth - shift;
2458 integerPart mask = lowBitMask (srcBits - n);
2459 dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask)
2460 << n % integerPartWidth);
2461 } else if (n > srcBits) {
2462 if (srcBits % integerPartWidth)
2463 dst[dstParts - 1] &= lowBitMask (srcBits % integerPartWidth);
2466 /* Clear high parts. */
2467 while (dstParts < dstCount)
2468 dst[dstParts++] = 0;
2471 /* DST += RHS + C where C is zero or one. Returns the carry flag. */
2473 APInt::tcAdd(integerPart *dst, const integerPart *rhs,
2474 integerPart c, unsigned int parts)
2480 for (i = 0; i < parts; i++) {
2485 dst[i] += rhs[i] + 1;
2496 /* DST -= RHS + C where C is zero or one. Returns the carry flag. */
2498 APInt::tcSubtract(integerPart *dst, const integerPart *rhs,
2499 integerPart c, unsigned int parts)
2505 for (i = 0; i < parts; i++) {
2510 dst[i] -= rhs[i] + 1;
2521 /* Negate a bignum in-place. */
2523 APInt::tcNegate(integerPart *dst, unsigned int parts)
2525 tcComplement(dst, parts);
2526 tcIncrement(dst, parts);
2529 /* DST += SRC * MULTIPLIER + CARRY if add is true
2530 DST = SRC * MULTIPLIER + CARRY if add is false
2532 Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC
2533 they must start at the same point, i.e. DST == SRC.
2535 If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is
2536 returned. Otherwise DST is filled with the least significant
2537 DSTPARTS parts of the result, and if all of the omitted higher
2538 parts were zero return zero, otherwise overflow occurred and
2541 APInt::tcMultiplyPart(integerPart *dst, const integerPart *src,
2542 integerPart multiplier, integerPart carry,
2543 unsigned int srcParts, unsigned int dstParts,
2548 /* Otherwise our writes of DST kill our later reads of SRC. */
2549 assert(dst <= src || dst >= src + srcParts);
2550 assert(dstParts <= srcParts + 1);
2552 /* N loops; minimum of dstParts and srcParts. */
2553 n = dstParts < srcParts ? dstParts: srcParts;
2555 for (i = 0; i < n; i++) {
2556 integerPart low, mid, high, srcPart;
2558 /* [ LOW, HIGH ] = MULTIPLIER * SRC[i] + DST[i] + CARRY.
2560 This cannot overflow, because
2562 (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1)
2564 which is less than n^2. */
2568 if (multiplier == 0 || srcPart == 0) {
2572 low = lowHalf(srcPart) * lowHalf(multiplier);
2573 high = highHalf(srcPart) * highHalf(multiplier);
2575 mid = lowHalf(srcPart) * highHalf(multiplier);
2576 high += highHalf(mid);
2577 mid <<= integerPartWidth / 2;
2578 if (low + mid < low)
2582 mid = highHalf(srcPart) * lowHalf(multiplier);
2583 high += highHalf(mid);
2584 mid <<= integerPartWidth / 2;
2585 if (low + mid < low)
2589 /* Now add carry. */
2590 if (low + carry < low)
2596 /* And now DST[i], and store the new low part there. */
2597 if (low + dst[i] < low)
2607 /* Full multiplication, there is no overflow. */
2608 assert(i + 1 == dstParts);
2612 /* We overflowed if there is carry. */
2616 /* We would overflow if any significant unwritten parts would be
2617 non-zero. This is true if any remaining src parts are non-zero
2618 and the multiplier is non-zero. */
2620 for (; i < srcParts; i++)
2624 /* We fitted in the narrow destination. */
2629 /* DST = LHS * RHS, where DST has the same width as the operands and
2630 is filled with the least significant parts of the result. Returns
2631 one if overflow occurred, otherwise zero. DST must be disjoint
2632 from both operands. */
2634 APInt::tcMultiply(integerPart *dst, const integerPart *lhs,
2635 const integerPart *rhs, unsigned int parts)
2640 assert(dst != lhs && dst != rhs);
2643 tcSet(dst, 0, parts);
2645 for (i = 0; i < parts; i++)
2646 overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts,
2652 /* DST = LHS * RHS, where DST has width the sum of the widths of the
2653 operands. No overflow occurs. DST must be disjoint from both
2654 operands. Returns the number of parts required to hold the
2657 APInt::tcFullMultiply(integerPart *dst, const integerPart *lhs,
2658 const integerPart *rhs, unsigned int lhsParts,
2659 unsigned int rhsParts)
2661 /* Put the narrower number on the LHS for less loops below. */
2662 if (lhsParts > rhsParts) {
2663 return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts);
2667 assert(dst != lhs && dst != rhs);
2669 tcSet(dst, 0, rhsParts);
2671 for (n = 0; n < lhsParts; n++)
2672 tcMultiplyPart(&dst[n], rhs, lhs[n], 0, rhsParts, rhsParts + 1, true);
2674 n = lhsParts + rhsParts;
2676 return n - (dst[n - 1] == 0);
2680 /* If RHS is zero LHS and REMAINDER are left unchanged, return one.
2681 Otherwise set LHS to LHS / RHS with the fractional part discarded,
2682 set REMAINDER to the remainder, return zero. i.e.
2684 OLD_LHS = RHS * LHS + REMAINDER
2686 SCRATCH is a bignum of the same size as the operands and result for
2687 use by the routine; its contents need not be initialized and are
2688 destroyed. LHS, REMAINDER and SCRATCH must be distinct.
2691 APInt::tcDivide(integerPart *lhs, const integerPart *rhs,
2692 integerPart *remainder, integerPart *srhs,
2695 unsigned int n, shiftCount;
2698 assert(lhs != remainder && lhs != srhs && remainder != srhs);
2700 shiftCount = tcMSB(rhs, parts) + 1;
2701 if (shiftCount == 0)
2704 shiftCount = parts * integerPartWidth - shiftCount;
2705 n = shiftCount / integerPartWidth;
2706 mask = (integerPart) 1 << (shiftCount % integerPartWidth);
2708 tcAssign(srhs, rhs, parts);
2709 tcShiftLeft(srhs, parts, shiftCount);
2710 tcAssign(remainder, lhs, parts);
2711 tcSet(lhs, 0, parts);
2713 /* Loop, subtracting SRHS if REMAINDER is greater and adding that to
2718 compare = tcCompare(remainder, srhs, parts);
2720 tcSubtract(remainder, srhs, 0, parts);
2724 if (shiftCount == 0)
2727 tcShiftRight(srhs, parts, 1);
2728 if ((mask >>= 1) == 0)
2729 mask = (integerPart) 1 << (integerPartWidth - 1), n--;
2735 /* Shift a bignum left COUNT bits in-place. Shifted in bits are zero.
2736 There are no restrictions on COUNT. */
2738 APInt::tcShiftLeft(integerPart *dst, unsigned int parts, unsigned int count)
2741 unsigned int jump, shift;
2743 /* Jump is the inter-part jump; shift is is intra-part shift. */
2744 jump = count / integerPartWidth;
2745 shift = count % integerPartWidth;
2747 while (parts > jump) {
2752 /* dst[i] comes from the two parts src[i - jump] and, if we have
2753 an intra-part shift, src[i - jump - 1]. */
2754 part = dst[parts - jump];
2757 if (parts >= jump + 1)
2758 part |= dst[parts - jump - 1] >> (integerPartWidth - shift);
2769 /* Shift a bignum right COUNT bits in-place. Shifted in bits are
2770 zero. There are no restrictions on COUNT. */
2772 APInt::tcShiftRight(integerPart *dst, unsigned int parts, unsigned int count)
2775 unsigned int i, jump, shift;
2777 /* Jump is the inter-part jump; shift is is intra-part shift. */
2778 jump = count / integerPartWidth;
2779 shift = count % integerPartWidth;
2781 /* Perform the shift. This leaves the most significant COUNT bits
2782 of the result at zero. */
2783 for (i = 0; i < parts; i++) {
2786 if (i + jump >= parts) {
2789 part = dst[i + jump];
2792 if (i + jump + 1 < parts)
2793 part |= dst[i + jump + 1] << (integerPartWidth - shift);
2802 /* Bitwise and of two bignums. */
2804 APInt::tcAnd(integerPart *dst, const integerPart *rhs, unsigned int parts)
2808 for (i = 0; i < parts; i++)
2812 /* Bitwise inclusive or of two bignums. */
2814 APInt::tcOr(integerPart *dst, const integerPart *rhs, unsigned int parts)
2818 for (i = 0; i < parts; i++)
2822 /* Bitwise exclusive or of two bignums. */
2824 APInt::tcXor(integerPart *dst, const integerPart *rhs, unsigned int parts)
2828 for (i = 0; i < parts; i++)
2832 /* Complement a bignum in-place. */
2834 APInt::tcComplement(integerPart *dst, unsigned int parts)
2838 for (i = 0; i < parts; i++)
2842 /* Comparison (unsigned) of two bignums. */
2844 APInt::tcCompare(const integerPart *lhs, const integerPart *rhs,
2849 if (lhs[parts] == rhs[parts])
2852 if (lhs[parts] > rhs[parts])
2861 /* Increment a bignum in-place, return the carry flag. */
2863 APInt::tcIncrement(integerPart *dst, unsigned int parts)
2867 for (i = 0; i < parts; i++)
2874 /* Decrement a bignum in-place, return the borrow flag. */
2876 APInt::tcDecrement(integerPart *dst, unsigned int parts) {
2877 for (unsigned int i = 0; i < parts; i++) {
2878 // If the current word is non-zero, then the decrement has no effect on the
2879 // higher-order words of the integer and no borrow can occur. Exit early.
2883 // If every word was zero, then there is a borrow.
2888 /* Set the least significant BITS bits of a bignum, clear the
2891 APInt::tcSetLeastSignificantBits(integerPart *dst, unsigned int parts,
2897 while (bits > integerPartWidth) {
2898 dst[i++] = ~(integerPart) 0;
2899 bits -= integerPartWidth;
2903 dst[i++] = ~(integerPart) 0 >> (integerPartWidth - bits);