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 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 /// HiBits - This function returns the high "numBits" bits of this APInt.
676 APInt APInt::getHiBits(unsigned numBits) const {
677 return APIntOps::lshr(*this, BitWidth - numBits);
680 /// LoBits - This function returns the low "numBits" bits of this APInt.
681 APInt APInt::getLoBits(unsigned numBits) const {
682 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
686 unsigned APInt::countLeadingZerosSlowCase() const {
687 // Treat the most significand word differently because it might have
688 // meaningless bits set beyond the precision.
689 unsigned BitsInMSW = BitWidth % APINT_BITS_PER_WORD;
691 if (BitsInMSW) MSWMask = (integerPart(1) << BitsInMSW) - 1;
693 MSWMask = ~integerPart(0);
694 BitsInMSW = APINT_BITS_PER_WORD;
697 unsigned i = getNumWords();
698 integerPart MSW = pVal[i-1] & MSWMask;
700 return llvm::countLeadingZeros(MSW) - (APINT_BITS_PER_WORD - BitsInMSW);
702 unsigned Count = BitsInMSW;
703 for (--i; i > 0u; --i) {
705 Count += APINT_BITS_PER_WORD;
707 Count += llvm::countLeadingZeros(pVal[i-1]);
714 unsigned APInt::countLeadingOnes() const {
716 return CountLeadingOnes_64(VAL << (APINT_BITS_PER_WORD - BitWidth));
718 unsigned highWordBits = BitWidth % APINT_BITS_PER_WORD;
721 highWordBits = APINT_BITS_PER_WORD;
724 shift = APINT_BITS_PER_WORD - highWordBits;
726 int i = getNumWords() - 1;
727 unsigned Count = CountLeadingOnes_64(pVal[i] << shift);
728 if (Count == highWordBits) {
729 for (i--; i >= 0; --i) {
730 if (pVal[i] == -1ULL)
731 Count += APINT_BITS_PER_WORD;
733 Count += CountLeadingOnes_64(pVal[i]);
741 unsigned APInt::countTrailingZeros() const {
743 return std::min(unsigned(llvm::countTrailingZeros(VAL)), BitWidth);
746 for (; i < getNumWords() && pVal[i] == 0; ++i)
747 Count += APINT_BITS_PER_WORD;
748 if (i < getNumWords())
749 Count += llvm::countTrailingZeros(pVal[i]);
750 return std::min(Count, BitWidth);
753 unsigned APInt::countTrailingOnesSlowCase() const {
756 for (; i < getNumWords() && pVal[i] == -1ULL; ++i)
757 Count += APINT_BITS_PER_WORD;
758 if (i < getNumWords())
759 Count += CountTrailingOnes_64(pVal[i]);
760 return std::min(Count, BitWidth);
763 unsigned APInt::countPopulationSlowCase() const {
765 for (unsigned i = 0; i < getNumWords(); ++i)
766 Count += CountPopulation_64(pVal[i]);
770 /// Perform a logical right-shift from Src to Dst, which must be equal or
771 /// non-overlapping, of Words words, by Shift, which must be less than 64.
772 static void lshrNear(uint64_t *Dst, uint64_t *Src, unsigned Words,
775 for (int I = Words - 1; I >= 0; --I) {
776 uint64_t Tmp = Src[I];
777 Dst[I] = (Tmp >> Shift) | Carry;
778 Carry = Tmp << (64 - Shift);
782 APInt APInt::byteSwap() const {
783 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
785 return APInt(BitWidth, ByteSwap_16(uint16_t(VAL)));
787 return APInt(BitWidth, ByteSwap_32(unsigned(VAL)));
788 if (BitWidth == 48) {
789 unsigned Tmp1 = unsigned(VAL >> 16);
790 Tmp1 = ByteSwap_32(Tmp1);
791 uint16_t Tmp2 = uint16_t(VAL);
792 Tmp2 = ByteSwap_16(Tmp2);
793 return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1);
796 return APInt(BitWidth, ByteSwap_64(VAL));
798 APInt Result(getNumWords() * APINT_BITS_PER_WORD, 0);
799 for (unsigned I = 0, N = getNumWords(); I != N; ++I)
800 Result.pVal[I] = ByteSwap_64(pVal[N - I - 1]);
801 if (Result.BitWidth != BitWidth) {
802 lshrNear(Result.pVal, Result.pVal, getNumWords(),
803 Result.BitWidth - BitWidth);
804 Result.BitWidth = BitWidth;
809 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
811 APInt A = API1, B = API2;
814 B = APIntOps::urem(A, B);
820 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) {
827 // Get the sign bit from the highest order bit
828 bool isNeg = T.I >> 63;
830 // Get the 11-bit exponent and adjust for the 1023 bit bias
831 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
833 // If the exponent is negative, the value is < 0 so just return 0.
835 return APInt(width, 0u);
837 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
838 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
840 // If the exponent doesn't shift all bits out of the mantissa
842 return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
843 APInt(width, mantissa >> (52 - exp));
845 // If the client didn't provide enough bits for us to shift the mantissa into
846 // then the result is undefined, just return 0
847 if (width <= exp - 52)
848 return APInt(width, 0);
850 // Otherwise, we have to shift the mantissa bits up to the right location
851 APInt Tmp(width, mantissa);
852 Tmp = Tmp.shl((unsigned)exp - 52);
853 return isNeg ? -Tmp : Tmp;
856 /// RoundToDouble - This function converts this APInt to a double.
857 /// The layout for double is as following (IEEE Standard 754):
858 /// --------------------------------------
859 /// | Sign Exponent Fraction Bias |
860 /// |-------------------------------------- |
861 /// | 1[63] 11[62-52] 52[51-00] 1023 |
862 /// --------------------------------------
863 double APInt::roundToDouble(bool isSigned) const {
865 // Handle the simple case where the value is contained in one uint64_t.
866 // It is wrong to optimize getWord(0) to VAL; there might be more than one word.
867 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
869 int64_t sext = (int64_t(getWord(0)) << (64-BitWidth)) >> (64-BitWidth);
872 return double(getWord(0));
875 // Determine if the value is negative.
876 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
878 // Construct the absolute value if we're negative.
879 APInt Tmp(isNeg ? -(*this) : (*this));
881 // Figure out how many bits we're using.
882 unsigned n = Tmp.getActiveBits();
884 // The exponent (without bias normalization) is just the number of bits
885 // we are using. Note that the sign bit is gone since we constructed the
889 // Return infinity for exponent overflow
891 if (!isSigned || !isNeg)
892 return std::numeric_limits<double>::infinity();
894 return -std::numeric_limits<double>::infinity();
896 exp += 1023; // Increment for 1023 bias
898 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
899 // extract the high 52 bits from the correct words in pVal.
901 unsigned hiWord = whichWord(n-1);
903 mantissa = Tmp.pVal[0];
905 mantissa >>= n - 52; // shift down, we want the top 52 bits.
907 assert(hiWord > 0 && "huh?");
908 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
909 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
910 mantissa = hibits | lobits;
913 // The leading bit of mantissa is implicit, so get rid of it.
914 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
919 T.I = sign | (exp << 52) | mantissa;
923 // Truncate to new width.
924 APInt APInt::trunc(unsigned width) const {
925 assert(width < BitWidth && "Invalid APInt Truncate request");
926 assert(width && "Can't truncate to 0 bits");
928 if (width <= APINT_BITS_PER_WORD)
929 return APInt(width, getRawData()[0]);
931 APInt Result(getMemory(getNumWords(width)), width);
935 for (i = 0; i != width / APINT_BITS_PER_WORD; i++)
936 Result.pVal[i] = pVal[i];
938 // Truncate and copy any partial word.
939 unsigned bits = (0 - width) % APINT_BITS_PER_WORD;
941 Result.pVal[i] = pVal[i] << bits >> bits;
946 // Sign extend to a new width.
947 APInt APInt::sext(unsigned width) const {
948 assert(width > BitWidth && "Invalid APInt SignExtend request");
950 if (width <= APINT_BITS_PER_WORD) {
951 uint64_t val = VAL << (APINT_BITS_PER_WORD - BitWidth);
952 val = (int64_t)val >> (width - BitWidth);
953 return APInt(width, val >> (APINT_BITS_PER_WORD - width));
956 APInt Result(getMemory(getNumWords(width)), width);
961 for (i = 0; i != BitWidth / APINT_BITS_PER_WORD; i++) {
962 word = getRawData()[i];
963 Result.pVal[i] = word;
966 // Read and sign-extend any partial word.
967 unsigned bits = (0 - BitWidth) % APINT_BITS_PER_WORD;
969 word = (int64_t)getRawData()[i] << bits >> bits;
971 word = (int64_t)word >> (APINT_BITS_PER_WORD - 1);
973 // Write remaining full words.
974 for (; i != width / APINT_BITS_PER_WORD; i++) {
975 Result.pVal[i] = word;
976 word = (int64_t)word >> (APINT_BITS_PER_WORD - 1);
979 // Write any partial word.
980 bits = (0 - width) % APINT_BITS_PER_WORD;
982 Result.pVal[i] = word << bits >> bits;
987 // Zero extend to a new width.
988 APInt APInt::zext(unsigned width) const {
989 assert(width > BitWidth && "Invalid APInt ZeroExtend request");
991 if (width <= APINT_BITS_PER_WORD)
992 return APInt(width, VAL);
994 APInt Result(getMemory(getNumWords(width)), width);
998 for (i = 0; i != getNumWords(); i++)
999 Result.pVal[i] = getRawData()[i];
1001 // Zero remaining words.
1002 memset(&Result.pVal[i], 0, (Result.getNumWords() - i) * APINT_WORD_SIZE);
1007 APInt APInt::zextOrTrunc(unsigned width) const {
1008 if (BitWidth < width)
1010 if (BitWidth > width)
1011 return trunc(width);
1015 APInt APInt::sextOrTrunc(unsigned width) const {
1016 if (BitWidth < width)
1018 if (BitWidth > width)
1019 return trunc(width);
1023 APInt APInt::zextOrSelf(unsigned width) const {
1024 if (BitWidth < width)
1029 APInt APInt::sextOrSelf(unsigned width) const {
1030 if (BitWidth < width)
1035 /// Arithmetic right-shift this APInt by shiftAmt.
1036 /// @brief Arithmetic right-shift function.
1037 APInt APInt::ashr(const APInt &shiftAmt) const {
1038 return ashr((unsigned)shiftAmt.getLimitedValue(BitWidth));
1041 /// Arithmetic right-shift this APInt by shiftAmt.
1042 /// @brief Arithmetic right-shift function.
1043 APInt APInt::ashr(unsigned shiftAmt) const {
1044 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1045 // Handle a degenerate case
1049 // Handle single word shifts with built-in ashr
1050 if (isSingleWord()) {
1051 if (shiftAmt == BitWidth)
1052 return APInt(BitWidth, 0); // undefined
1054 unsigned SignBit = APINT_BITS_PER_WORD - BitWidth;
1055 return APInt(BitWidth,
1056 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1060 // If all the bits were shifted out, the result is, technically, undefined.
1061 // We return -1 if it was negative, 0 otherwise. We check this early to avoid
1062 // issues in the algorithm below.
1063 if (shiftAmt == BitWidth) {
1065 return APInt(BitWidth, -1ULL, true);
1067 return APInt(BitWidth, 0);
1070 // Create some space for the result.
1071 uint64_t * val = new uint64_t[getNumWords()];
1073 // Compute some values needed by the following shift algorithms
1074 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word
1075 unsigned offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift
1076 unsigned breakWord = getNumWords() - 1 - offset; // last word affected
1077 unsigned bitsInWord = whichBit(BitWidth); // how many bits in last word?
1078 if (bitsInWord == 0)
1079 bitsInWord = APINT_BITS_PER_WORD;
1081 // If we are shifting whole words, just move whole words
1082 if (wordShift == 0) {
1083 // Move the words containing significant bits
1084 for (unsigned i = 0; i <= breakWord; ++i)
1085 val[i] = pVal[i+offset]; // move whole word
1087 // Adjust the top significant word for sign bit fill, if negative
1089 if (bitsInWord < APINT_BITS_PER_WORD)
1090 val[breakWord] |= ~0ULL << bitsInWord; // set high bits
1092 // Shift the low order words
1093 for (unsigned i = 0; i < breakWord; ++i) {
1094 // This combines the shifted corresponding word with the low bits from
1095 // the next word (shifted into this word's high bits).
1096 val[i] = (pVal[i+offset] >> wordShift) |
1097 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1100 // Shift the break word. In this case there are no bits from the next word
1101 // to include in this word.
1102 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1104 // Deal with sign extension in the break word, and possibly the word before
1107 if (wordShift > bitsInWord) {
1110 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord));
1111 val[breakWord] |= ~0ULL;
1113 val[breakWord] |= (~0ULL << (bitsInWord - wordShift));
1117 // Remaining words are 0 or -1, just assign them.
1118 uint64_t fillValue = (isNegative() ? -1ULL : 0);
1119 for (unsigned i = breakWord+1; i < getNumWords(); ++i)
1121 APInt Result(val, BitWidth);
1122 Result.clearUnusedBits();
1126 /// Logical right-shift this APInt by shiftAmt.
1127 /// @brief Logical right-shift function.
1128 APInt APInt::lshr(const APInt &shiftAmt) const {
1129 return lshr((unsigned)shiftAmt.getLimitedValue(BitWidth));
1132 /// Logical right-shift this APInt by shiftAmt.
1133 /// @brief Logical right-shift function.
1134 APInt APInt::lshr(unsigned shiftAmt) const {
1135 if (isSingleWord()) {
1136 if (shiftAmt >= BitWidth)
1137 return APInt(BitWidth, 0);
1139 return APInt(BitWidth, this->VAL >> shiftAmt);
1142 // If all the bits were shifted out, the result is 0. This avoids issues
1143 // with shifting by the size of the integer type, which produces undefined
1144 // results. We define these "undefined results" to always be 0.
1145 if (shiftAmt >= BitWidth)
1146 return APInt(BitWidth, 0);
1148 // If none of the bits are shifted out, the result is *this. This avoids
1149 // issues with shifting by the size of the integer type, which produces
1150 // undefined results in the code below. This is also an optimization.
1154 // Create some space for the result.
1155 uint64_t * val = new uint64_t[getNumWords()];
1157 // If we are shifting less than a word, compute the shift with a simple carry
1158 if (shiftAmt < APINT_BITS_PER_WORD) {
1159 lshrNear(val, pVal, getNumWords(), shiftAmt);
1160 APInt Result(val, BitWidth);
1161 Result.clearUnusedBits();
1165 // Compute some values needed by the remaining shift algorithms
1166 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD;
1167 unsigned offset = shiftAmt / APINT_BITS_PER_WORD;
1169 // If we are shifting whole words, just move whole words
1170 if (wordShift == 0) {
1171 for (unsigned i = 0; i < getNumWords() - offset; ++i)
1172 val[i] = pVal[i+offset];
1173 for (unsigned i = getNumWords()-offset; i < getNumWords(); i++)
1175 APInt Result(val, BitWidth);
1176 Result.clearUnusedBits();
1180 // Shift the low order words
1181 unsigned breakWord = getNumWords() - offset -1;
1182 for (unsigned i = 0; i < breakWord; ++i)
1183 val[i] = (pVal[i+offset] >> wordShift) |
1184 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1185 // Shift the break word.
1186 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1188 // Remaining words are 0
1189 for (unsigned i = breakWord+1; i < getNumWords(); ++i)
1191 APInt Result(val, BitWidth);
1192 Result.clearUnusedBits();
1196 /// Left-shift this APInt by shiftAmt.
1197 /// @brief Left-shift function.
1198 APInt APInt::shl(const APInt &shiftAmt) const {
1199 // It's undefined behavior in C to shift by BitWidth or greater.
1200 return shl((unsigned)shiftAmt.getLimitedValue(BitWidth));
1203 APInt APInt::shlSlowCase(unsigned shiftAmt) const {
1204 // If all the bits were shifted out, the result is 0. This avoids issues
1205 // with shifting by the size of the integer type, which produces undefined
1206 // results. We define these "undefined results" to always be 0.
1207 if (shiftAmt == BitWidth)
1208 return APInt(BitWidth, 0);
1210 // If none of the bits are shifted out, the result is *this. This avoids a
1211 // lshr by the words size in the loop below which can produce incorrect
1212 // results. It also avoids the expensive computation below for a common case.
1216 // Create some space for the result.
1217 uint64_t * val = new uint64_t[getNumWords()];
1219 // If we are shifting less than a word, do it the easy way
1220 if (shiftAmt < APINT_BITS_PER_WORD) {
1222 for (unsigned i = 0; i < getNumWords(); i++) {
1223 val[i] = pVal[i] << shiftAmt | carry;
1224 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1226 APInt Result(val, BitWidth);
1227 Result.clearUnusedBits();
1231 // Compute some values needed by the remaining shift algorithms
1232 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD;
1233 unsigned offset = shiftAmt / APINT_BITS_PER_WORD;
1235 // If we are shifting whole words, just move whole words
1236 if (wordShift == 0) {
1237 for (unsigned i = 0; i < offset; i++)
1239 for (unsigned i = offset; i < getNumWords(); i++)
1240 val[i] = pVal[i-offset];
1241 APInt Result(val, BitWidth);
1242 Result.clearUnusedBits();
1246 // Copy whole words from this to Result.
1247 unsigned i = getNumWords() - 1;
1248 for (; i > offset; --i)
1249 val[i] = pVal[i-offset] << wordShift |
1250 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1251 val[offset] = pVal[0] << wordShift;
1252 for (i = 0; i < offset; ++i)
1254 APInt Result(val, BitWidth);
1255 Result.clearUnusedBits();
1259 APInt APInt::rotl(const APInt &rotateAmt) const {
1260 return rotl((unsigned)rotateAmt.getLimitedValue(BitWidth));
1263 APInt APInt::rotl(unsigned rotateAmt) const {
1264 rotateAmt %= BitWidth;
1267 return shl(rotateAmt) | lshr(BitWidth - rotateAmt);
1270 APInt APInt::rotr(const APInt &rotateAmt) const {
1271 return rotr((unsigned)rotateAmt.getLimitedValue(BitWidth));
1274 APInt APInt::rotr(unsigned rotateAmt) const {
1275 rotateAmt %= BitWidth;
1278 return lshr(rotateAmt) | shl(BitWidth - rotateAmt);
1281 // Square Root - this method computes and returns the square root of "this".
1282 // Three mechanisms are used for computation. For small values (<= 5 bits),
1283 // a table lookup is done. This gets some performance for common cases. For
1284 // values using less than 52 bits, the value is converted to double and then
1285 // the libc sqrt function is called. The result is rounded and then converted
1286 // back to a uint64_t which is then used to construct the result. Finally,
1287 // the Babylonian method for computing square roots is used.
1288 APInt APInt::sqrt() const {
1290 // Determine the magnitude of the value.
1291 unsigned magnitude = getActiveBits();
1293 // Use a fast table for some small values. This also gets rid of some
1294 // rounding errors in libc sqrt for small values.
1295 if (magnitude <= 5) {
1296 static const uint8_t results[32] = {
1299 /* 3- 6 */ 2, 2, 2, 2,
1300 /* 7-12 */ 3, 3, 3, 3, 3, 3,
1301 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1302 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1305 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]);
1308 // If the magnitude of the value fits in less than 52 bits (the precision of
1309 // an IEEE double precision floating point value), then we can use the
1310 // libc sqrt function which will probably use a hardware sqrt computation.
1311 // This should be faster than the algorithm below.
1312 if (magnitude < 52) {
1314 return APInt(BitWidth,
1315 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0])))));
1317 return APInt(BitWidth,
1318 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0])) + 0.5));
1322 // Okay, all the short cuts are exhausted. We must compute it. The following
1323 // is a classical Babylonian method for computing the square root. This code
1324 // was adapted to APInt from a wikipedia article on such computations.
1325 // See http://www.wikipedia.org/ and go to the page named
1326 // Calculate_an_integer_square_root.
1327 unsigned nbits = BitWidth, i = 4;
1328 APInt testy(BitWidth, 16);
1329 APInt x_old(BitWidth, 1);
1330 APInt x_new(BitWidth, 0);
1331 APInt two(BitWidth, 2);
1333 // Select a good starting value using binary logarithms.
1334 for (;; i += 2, testy = testy.shl(2))
1335 if (i >= nbits || this->ule(testy)) {
1336 x_old = x_old.shl(i / 2);
1340 // Use the Babylonian method to arrive at the integer square root:
1342 x_new = (this->udiv(x_old) + x_old).udiv(two);
1343 if (x_old.ule(x_new))
1348 // Make sure we return the closest approximation
1349 // NOTE: The rounding calculation below is correct. It will produce an
1350 // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1351 // determined to be a rounding issue with pari/gp as it begins to use a
1352 // floating point representation after 192 bits. There are no discrepancies
1353 // between this algorithm and pari/gp for bit widths < 192 bits.
1354 APInt square(x_old * x_old);
1355 APInt nextSquare((x_old + 1) * (x_old +1));
1356 if (this->ult(square))
1358 assert(this->ule(nextSquare) && "Error in APInt::sqrt computation");
1359 APInt midpoint((nextSquare - square).udiv(two));
1360 APInt offset(*this - square);
1361 if (offset.ult(midpoint))
1366 /// Computes the multiplicative inverse of this APInt for a given modulo. The
1367 /// iterative extended Euclidean algorithm is used to solve for this value,
1368 /// however we simplify it to speed up calculating only the inverse, and take
1369 /// advantage of div+rem calculations. We also use some tricks to avoid copying
1370 /// (potentially large) APInts around.
1371 APInt APInt::multiplicativeInverse(const APInt& modulo) const {
1372 assert(ult(modulo) && "This APInt must be smaller than the modulo");
1374 // Using the properties listed at the following web page (accessed 06/21/08):
1375 // http://www.numbertheory.org/php/euclid.html
1376 // (especially the properties numbered 3, 4 and 9) it can be proved that
1377 // BitWidth bits suffice for all the computations in the algorithm implemented
1378 // below. More precisely, this number of bits suffice if the multiplicative
1379 // inverse exists, but may not suffice for the general extended Euclidean
1382 APInt r[2] = { modulo, *this };
1383 APInt t[2] = { APInt(BitWidth, 0), APInt(BitWidth, 1) };
1384 APInt q(BitWidth, 0);
1387 for (i = 0; r[i^1] != 0; i ^= 1) {
1388 // An overview of the math without the confusing bit-flipping:
1389 // q = r[i-2] / r[i-1]
1390 // r[i] = r[i-2] % r[i-1]
1391 // t[i] = t[i-2] - t[i-1] * q
1392 udivrem(r[i], r[i^1], q, r[i]);
1396 // If this APInt and the modulo are not coprime, there is no multiplicative
1397 // inverse, so return 0. We check this by looking at the next-to-last
1398 // remainder, which is the gcd(*this,modulo) as calculated by the Euclidean
1401 return APInt(BitWidth, 0);
1403 // The next-to-last t is the multiplicative inverse. However, we are
1404 // interested in a positive inverse. Calcuate a positive one from a negative
1405 // one if necessary. A simple addition of the modulo suffices because
1406 // abs(t[i]) is known to be less than *this/2 (see the link above).
1407 return t[i].isNegative() ? t[i] + modulo : t[i];
1410 /// Calculate the magic numbers required to implement a signed integer division
1411 /// by a constant as a sequence of multiplies, adds and shifts. Requires that
1412 /// the divisor not be 0, 1, or -1. Taken from "Hacker's Delight", Henry S.
1413 /// Warren, Jr., chapter 10.
1414 APInt::ms APInt::magic() const {
1415 const APInt& d = *this;
1417 APInt ad, anc, delta, q1, r1, q2, r2, t;
1418 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
1422 t = signedMin + (d.lshr(d.getBitWidth() - 1));
1423 anc = t - 1 - t.urem(ad); // absolute value of nc
1424 p = d.getBitWidth() - 1; // initialize p
1425 q1 = signedMin.udiv(anc); // initialize q1 = 2p/abs(nc)
1426 r1 = signedMin - q1*anc; // initialize r1 = rem(2p,abs(nc))
1427 q2 = signedMin.udiv(ad); // initialize q2 = 2p/abs(d)
1428 r2 = signedMin - q2*ad; // initialize r2 = rem(2p,abs(d))
1431 q1 = q1<<1; // update q1 = 2p/abs(nc)
1432 r1 = r1<<1; // update r1 = rem(2p/abs(nc))
1433 if (r1.uge(anc)) { // must be unsigned comparison
1437 q2 = q2<<1; // update q2 = 2p/abs(d)
1438 r2 = r2<<1; // update r2 = rem(2p/abs(d))
1439 if (r2.uge(ad)) { // must be unsigned comparison
1444 } while (q1.ult(delta) || (q1 == delta && r1 == 0));
1447 if (d.isNegative()) mag.m = -mag.m; // resulting magic number
1448 mag.s = p - d.getBitWidth(); // resulting shift
1452 /// Calculate the magic numbers required to implement an unsigned integer
1453 /// division by a constant as a sequence of multiplies, adds and shifts.
1454 /// Requires that the divisor not be 0. Taken from "Hacker's Delight", Henry
1455 /// S. Warren, Jr., chapter 10.
1456 /// LeadingZeros can be used to simplify the calculation if the upper bits
1457 /// of the divided value are known zero.
1458 APInt::mu APInt::magicu(unsigned LeadingZeros) const {
1459 const APInt& d = *this;
1461 APInt nc, delta, q1, r1, q2, r2;
1463 magu.a = 0; // initialize "add" indicator
1464 APInt allOnes = APInt::getAllOnesValue(d.getBitWidth()).lshr(LeadingZeros);
1465 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
1466 APInt signedMax = APInt::getSignedMaxValue(d.getBitWidth());
1468 nc = allOnes - (allOnes - d).urem(d);
1469 p = d.getBitWidth() - 1; // initialize p
1470 q1 = signedMin.udiv(nc); // initialize q1 = 2p/nc
1471 r1 = signedMin - q1*nc; // initialize r1 = rem(2p,nc)
1472 q2 = signedMax.udiv(d); // initialize q2 = (2p-1)/d
1473 r2 = signedMax - q2*d; // initialize r2 = rem((2p-1),d)
1476 if (r1.uge(nc - r1)) {
1477 q1 = q1 + q1 + 1; // update q1
1478 r1 = r1 + r1 - nc; // update r1
1481 q1 = q1+q1; // update q1
1482 r1 = r1+r1; // update r1
1484 if ((r2 + 1).uge(d - r2)) {
1485 if (q2.uge(signedMax)) magu.a = 1;
1486 q2 = q2+q2 + 1; // update q2
1487 r2 = r2+r2 + 1 - d; // update r2
1490 if (q2.uge(signedMin)) magu.a = 1;
1491 q2 = q2+q2; // update q2
1492 r2 = r2+r2 + 1; // update r2
1495 } while (p < d.getBitWidth()*2 &&
1496 (q1.ult(delta) || (q1 == delta && r1 == 0)));
1497 magu.m = q2 + 1; // resulting magic number
1498 magu.s = p - d.getBitWidth(); // resulting shift
1502 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1503 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1504 /// variables here have the same names as in the algorithm. Comments explain
1505 /// the algorithm and any deviation from it.
1506 static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
1507 unsigned m, unsigned n) {
1508 assert(u && "Must provide dividend");
1509 assert(v && "Must provide divisor");
1510 assert(q && "Must provide quotient");
1511 assert(u != v && u != q && v != q && "Must us different memory");
1512 assert(n>1 && "n must be > 1");
1514 // Knuth uses the value b as the base of the number system. In our case b
1515 // is 2^31 so we just set it to -1u.
1516 uint64_t b = uint64_t(1) << 32;
1519 DEBUG(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n');
1520 DEBUG(dbgs() << "KnuthDiv: original:");
1521 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1522 DEBUG(dbgs() << " by");
1523 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
1524 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');
1558 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1561 DEBUG(dbgs() << "KnuthDiv: quotient digit #" << j << '\n');
1562 // D3. [Calculate q'.].
1563 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1564 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1565 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1566 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1567 // on v[n-2] determines at high speed most of the cases in which the trial
1568 // value qp is one too large, and it eliminates all cases where qp is two
1570 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1571 DEBUG(dbgs() << "KnuthDiv: dividend == " << dividend << '\n');
1572 uint64_t qp = dividend / v[n-1];
1573 uint64_t rp = dividend % v[n-1];
1574 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1577 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1580 DEBUG(dbgs() << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1582 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1583 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1584 // consists of a simple multiplication by a one-place number, combined with
1587 for (unsigned i = 0; i < n; ++i) {
1588 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1589 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1590 bool borrow = subtrahend > u_tmp;
1591 DEBUG(dbgs() << "KnuthDiv: u_tmp == " << u_tmp
1592 << ", subtrahend == " << subtrahend
1593 << ", borrow = " << borrow << '\n');
1595 uint64_t result = u_tmp - subtrahend;
1597 u[k++] = (unsigned)(result & (b-1)); // subtract low word
1598 u[k++] = (unsigned)(result >> 32); // subtract high word
1599 while (borrow && k <= m+n) { // deal with borrow to the left
1605 DEBUG(dbgs() << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1608 DEBUG(dbgs() << "KnuthDiv: after subtraction:");
1609 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1610 DEBUG(dbgs() << '\n');
1611 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1612 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1613 // true value plus b**(n+1), namely as the b's complement of
1614 // the true value, and a "borrow" to the left should be remembered.
1617 bool carry = true; // true because b's complement is "complement + 1"
1618 for (unsigned i = 0; i <= m+n; ++i) {
1619 u[i] = ~u[i] + carry; // b's complement
1620 carry = carry && u[i] == 0;
1623 DEBUG(dbgs() << "KnuthDiv: after complement:");
1624 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1625 DEBUG(dbgs() << '\n');
1627 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1628 // negative, go to step D6; otherwise go on to step D7.
1629 q[j] = (unsigned)qp;
1631 // D6. [Add back]. The probability that this step is necessary is very
1632 // small, on the order of only 2/b. Make sure that test data accounts for
1633 // this possibility. Decrease q[j] by 1
1635 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1636 // A carry will occur to the left of u[j+n], and it should be ignored
1637 // since it cancels with the borrow that occurred in D4.
1639 for (unsigned i = 0; i < n; i++) {
1640 unsigned limit = std::min(u[j+i],v[i]);
1641 u[j+i] += v[i] + carry;
1642 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1646 DEBUG(dbgs() << "KnuthDiv: after correction:");
1647 DEBUG(for (int i = m+n; i >=0; i--) dbgs() <<" " << u[i]);
1648 DEBUG(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n');
1650 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1653 DEBUG(dbgs() << "KnuthDiv: quotient:");
1654 DEBUG(for (int i = m; i >=0; i--) dbgs() <<" " << q[i]);
1655 DEBUG(dbgs() << '\n');
1657 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1658 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1659 // compute the remainder (urem uses this).
1661 // The value d is expressed by the "shift" value above since we avoided
1662 // multiplication by d by using a shift left. So, all we have to do is
1663 // shift right here. In order to mak
1666 DEBUG(dbgs() << "KnuthDiv: remainder:");
1667 for (int i = n-1; i >= 0; i--) {
1668 r[i] = (u[i] >> shift) | carry;
1669 carry = u[i] << (32 - shift);
1670 DEBUG(dbgs() << " " << r[i]);
1673 for (int i = n-1; i >= 0; i--) {
1675 DEBUG(dbgs() << " " << r[i]);
1678 DEBUG(dbgs() << '\n');
1681 DEBUG(dbgs() << '\n');
1685 void APInt::divide(const APInt LHS, unsigned lhsWords,
1686 const APInt &RHS, unsigned rhsWords,
1687 APInt *Quotient, APInt *Remainder)
1689 assert(lhsWords >= rhsWords && "Fractional result");
1691 // First, compose the values into an array of 32-bit words instead of
1692 // 64-bit words. This is a necessity of both the "short division" algorithm
1693 // and the Knuth "classical algorithm" which requires there to be native
1694 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1695 // can't use 64-bit operands here because we don't have native results of
1696 // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't
1697 // work on large-endian machines.
1698 uint64_t mask = ~0ull >> (sizeof(unsigned)*CHAR_BIT);
1699 unsigned n = rhsWords * 2;
1700 unsigned m = (lhsWords * 2) - n;
1702 // Allocate space for the temporary values we need either on the stack, if
1703 // it will fit, or on the heap if it won't.
1704 unsigned SPACE[128];
1705 unsigned *U = nullptr;
1706 unsigned *V = nullptr;
1707 unsigned *Q = nullptr;
1708 unsigned *R = nullptr;
1709 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1712 Q = &SPACE[(m+n+1) + n];
1714 R = &SPACE[(m+n+1) + n + (m+n)];
1716 U = new unsigned[m + n + 1];
1717 V = new unsigned[n];
1718 Q = new unsigned[m+n];
1720 R = new unsigned[n];
1723 // Initialize the dividend
1724 memset(U, 0, (m+n+1)*sizeof(unsigned));
1725 for (unsigned i = 0; i < lhsWords; ++i) {
1726 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1727 U[i * 2] = (unsigned)(tmp & mask);
1728 U[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT));
1730 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1732 // Initialize the divisor
1733 memset(V, 0, (n)*sizeof(unsigned));
1734 for (unsigned i = 0; i < rhsWords; ++i) {
1735 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1736 V[i * 2] = (unsigned)(tmp & mask);
1737 V[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT));
1740 // initialize the quotient and remainder
1741 memset(Q, 0, (m+n) * sizeof(unsigned));
1743 memset(R, 0, n * sizeof(unsigned));
1745 // Now, adjust m and n for the Knuth division. n is the number of words in
1746 // the divisor. m is the number of words by which the dividend exceeds the
1747 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1748 // contain any zero words or the Knuth algorithm fails.
1749 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1753 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1756 // If we're left with only a single word for the divisor, Knuth doesn't work
1757 // so we implement the short division algorithm here. This is much simpler
1758 // and faster because we are certain that we can divide a 64-bit quantity
1759 // by a 32-bit quantity at hardware speed and short division is simply a
1760 // series of such operations. This is just like doing short division but we
1761 // are using base 2^32 instead of base 10.
1762 assert(n != 0 && "Divide by zero?");
1764 unsigned divisor = V[0];
1765 unsigned remainder = 0;
1766 for (int i = m+n-1; i >= 0; i--) {
1767 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1768 if (partial_dividend == 0) {
1771 } else if (partial_dividend < divisor) {
1773 remainder = (unsigned)partial_dividend;
1774 } else if (partial_dividend == divisor) {
1778 Q[i] = (unsigned)(partial_dividend / divisor);
1779 remainder = (unsigned)(partial_dividend - (Q[i] * divisor));
1785 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1787 KnuthDiv(U, V, Q, R, m, n);
1790 // If the caller wants the quotient
1792 // Set up the Quotient value's memory.
1793 if (Quotient->BitWidth != LHS.BitWidth) {
1794 if (Quotient->isSingleWord())
1797 delete [] Quotient->pVal;
1798 Quotient->BitWidth = LHS.BitWidth;
1799 if (!Quotient->isSingleWord())
1800 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1802 Quotient->clearAllBits();
1804 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1806 if (lhsWords == 1) {
1808 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1809 if (Quotient->isSingleWord())
1810 Quotient->VAL = tmp;
1812 Quotient->pVal[0] = tmp;
1814 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1815 for (unsigned i = 0; i < lhsWords; ++i)
1817 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1821 // If the caller wants the remainder
1823 // Set up the Remainder value's memory.
1824 if (Remainder->BitWidth != RHS.BitWidth) {
1825 if (Remainder->isSingleWord())
1828 delete [] Remainder->pVal;
1829 Remainder->BitWidth = RHS.BitWidth;
1830 if (!Remainder->isSingleWord())
1831 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1833 Remainder->clearAllBits();
1835 // The remainder is in R. Reconstitute the remainder into Remainder's low
1837 if (rhsWords == 1) {
1839 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1840 if (Remainder->isSingleWord())
1841 Remainder->VAL = tmp;
1843 Remainder->pVal[0] = tmp;
1845 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1846 for (unsigned i = 0; i < rhsWords; ++i)
1847 Remainder->pVal[i] =
1848 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1852 // Clean up the memory we allocated.
1853 if (U != &SPACE[0]) {
1861 APInt APInt::udiv(const APInt& RHS) const {
1862 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1864 // First, deal with the easy case
1865 if (isSingleWord()) {
1866 assert(RHS.VAL != 0 && "Divide by zero?");
1867 return APInt(BitWidth, VAL / RHS.VAL);
1870 // Get some facts about the LHS and RHS number of bits and words
1871 unsigned rhsBits = RHS.getActiveBits();
1872 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1873 assert(rhsWords && "Divided by zero???");
1874 unsigned lhsBits = this->getActiveBits();
1875 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1877 // Deal with some degenerate cases
1880 return APInt(BitWidth, 0);
1881 else if (lhsWords < rhsWords || this->ult(RHS)) {
1882 // X / Y ===> 0, iff X < Y
1883 return APInt(BitWidth, 0);
1884 } else if (*this == RHS) {
1886 return APInt(BitWidth, 1);
1887 } else if (lhsWords == 1 && rhsWords == 1) {
1888 // All high words are zero, just use native divide
1889 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1892 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1893 APInt Quotient(1,0); // to hold result.
1894 divide(*this, lhsWords, RHS, rhsWords, &Quotient, nullptr);
1898 APInt APInt::sdiv(const APInt &RHS) const {
1900 if (RHS.isNegative())
1901 return (-(*this)).udiv(-RHS);
1902 return -((-(*this)).udiv(RHS));
1904 if (RHS.isNegative())
1905 return -(this->udiv(-RHS));
1906 return this->udiv(RHS);
1909 APInt APInt::urem(const APInt& RHS) const {
1910 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1911 if (isSingleWord()) {
1912 assert(RHS.VAL != 0 && "Remainder by zero?");
1913 return APInt(BitWidth, VAL % RHS.VAL);
1916 // Get some facts about the LHS
1917 unsigned lhsBits = getActiveBits();
1918 unsigned lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1920 // Get some facts about the RHS
1921 unsigned rhsBits = RHS.getActiveBits();
1922 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1923 assert(rhsWords && "Performing remainder operation by zero ???");
1925 // Check the degenerate cases
1926 if (lhsWords == 0) {
1928 return APInt(BitWidth, 0);
1929 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1930 // X % Y ===> X, iff X < Y
1932 } else if (*this == RHS) {
1934 return APInt(BitWidth, 0);
1935 } else if (lhsWords == 1) {
1936 // All high words are zero, just use native remainder
1937 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
1940 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1941 APInt Remainder(1,0);
1942 divide(*this, lhsWords, RHS, rhsWords, nullptr, &Remainder);
1946 APInt APInt::srem(const APInt &RHS) const {
1948 if (RHS.isNegative())
1949 return -((-(*this)).urem(-RHS));
1950 return -((-(*this)).urem(RHS));
1952 if (RHS.isNegative())
1953 return this->urem(-RHS);
1954 return this->urem(RHS);
1957 void APInt::udivrem(const APInt &LHS, const APInt &RHS,
1958 APInt &Quotient, APInt &Remainder) {
1959 assert(LHS.BitWidth == RHS.BitWidth && "Bit widths must be the same");
1961 // First, deal with the easy case
1962 if (LHS.isSingleWord()) {
1963 assert(RHS.VAL != 0 && "Divide by zero?");
1964 uint64_t QuotVal = LHS.VAL / RHS.VAL;
1965 uint64_t RemVal = LHS.VAL % RHS.VAL;
1966 Quotient = APInt(LHS.BitWidth, QuotVal);
1967 Remainder = APInt(LHS.BitWidth, RemVal);
1971 // Get some size facts about the dividend and divisor
1972 unsigned lhsBits = LHS.getActiveBits();
1973 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1974 unsigned rhsBits = RHS.getActiveBits();
1975 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1977 // Check the degenerate cases
1978 if (lhsWords == 0) {
1979 Quotient = 0; // 0 / Y ===> 0
1980 Remainder = 0; // 0 % Y ===> 0
1984 if (lhsWords < rhsWords || LHS.ult(RHS)) {
1985 Remainder = LHS; // X % Y ===> X, iff X < Y
1986 Quotient = 0; // X / Y ===> 0, iff X < Y
1991 Quotient = 1; // X / X ===> 1
1992 Remainder = 0; // X % X ===> 0;
1996 if (lhsWords == 1 && rhsWords == 1) {
1997 // There is only one word to consider so use the native versions.
1998 uint64_t lhsValue = LHS.isSingleWord() ? LHS.VAL : LHS.pVal[0];
1999 uint64_t rhsValue = RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0];
2000 Quotient = APInt(LHS.getBitWidth(), lhsValue / rhsValue);
2001 Remainder = APInt(LHS.getBitWidth(), lhsValue % rhsValue);
2005 // Okay, lets do it the long way
2006 divide(LHS, lhsWords, RHS, rhsWords, &Quotient, &Remainder);
2009 void APInt::sdivrem(const APInt &LHS, const APInt &RHS,
2010 APInt &Quotient, APInt &Remainder) {
2011 if (LHS.isNegative()) {
2012 if (RHS.isNegative())
2013 APInt::udivrem(-LHS, -RHS, Quotient, Remainder);
2015 APInt::udivrem(-LHS, RHS, Quotient, Remainder);
2016 Quotient = -Quotient;
2018 Remainder = -Remainder;
2019 } else if (RHS.isNegative()) {
2020 APInt::udivrem(LHS, -RHS, Quotient, Remainder);
2021 Quotient = -Quotient;
2023 APInt::udivrem(LHS, RHS, Quotient, Remainder);
2027 APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const {
2028 APInt Res = *this+RHS;
2029 Overflow = isNonNegative() == RHS.isNonNegative() &&
2030 Res.isNonNegative() != isNonNegative();
2034 APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const {
2035 APInt Res = *this+RHS;
2036 Overflow = Res.ult(RHS);
2040 APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const {
2041 APInt Res = *this - RHS;
2042 Overflow = isNonNegative() != RHS.isNonNegative() &&
2043 Res.isNonNegative() != isNonNegative();
2047 APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const {
2048 APInt Res = *this-RHS;
2049 Overflow = Res.ugt(*this);
2053 APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const {
2054 // MININT/-1 --> overflow.
2055 Overflow = isMinSignedValue() && RHS.isAllOnesValue();
2059 APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const {
2060 APInt Res = *this * RHS;
2062 if (*this != 0 && RHS != 0)
2063 Overflow = Res.sdiv(RHS) != *this || Res.sdiv(*this) != RHS;
2069 APInt APInt::umul_ov(const APInt &RHS, bool &Overflow) const {
2070 APInt Res = *this * RHS;
2072 if (*this != 0 && RHS != 0)
2073 Overflow = Res.udiv(RHS) != *this || Res.udiv(*this) != RHS;
2079 APInt APInt::sshl_ov(const APInt &ShAmt, bool &Overflow) const {
2080 Overflow = ShAmt.uge(getBitWidth());
2082 return APInt(BitWidth, 0);
2084 if (isNonNegative()) // Don't allow sign change.
2085 Overflow = ShAmt.uge(countLeadingZeros());
2087 Overflow = ShAmt.uge(countLeadingOnes());
2089 return *this << ShAmt;
2092 APInt APInt::ushl_ov(const APInt &ShAmt, bool &Overflow) const {
2093 Overflow = ShAmt.uge(getBitWidth());
2095 return APInt(BitWidth, 0);
2097 Overflow = ShAmt.ugt(countLeadingZeros());
2099 return *this << ShAmt;
2105 void APInt::fromString(unsigned numbits, StringRef str, uint8_t radix) {
2106 // Check our assumptions here
2107 assert(!str.empty() && "Invalid string length");
2108 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||
2110 "Radix should be 2, 8, 10, 16, or 36!");
2112 StringRef::iterator p = str.begin();
2113 size_t slen = str.size();
2114 bool isNeg = *p == '-';
2115 if (*p == '-' || *p == '+') {
2118 assert(slen && "String is only a sign, needs a value.");
2120 assert((slen <= numbits || radix != 2) && "Insufficient bit width");
2121 assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width");
2122 assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width");
2123 assert((((slen-1)*64)/22 <= numbits || radix != 10) &&
2124 "Insufficient bit width");
2127 if (!isSingleWord())
2128 pVal = getClearedMemory(getNumWords());
2130 // Figure out if we can shift instead of multiply
2131 unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
2133 // Set up an APInt for the digit to add outside the loop so we don't
2134 // constantly construct/destruct it.
2135 APInt apdigit(getBitWidth(), 0);
2136 APInt apradix(getBitWidth(), radix);
2138 // Enter digit traversal loop
2139 for (StringRef::iterator e = str.end(); p != e; ++p) {
2140 unsigned digit = getDigit(*p, radix);
2141 assert(digit < radix && "Invalid character in digit string");
2143 // Shift or multiply the value by the radix
2151 // Add in the digit we just interpreted
2152 if (apdigit.isSingleWord())
2153 apdigit.VAL = digit;
2155 apdigit.pVal[0] = digit;
2158 // If its negative, put it in two's complement form
2161 this->flipAllBits();
2165 void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix,
2166 bool Signed, bool formatAsCLiteral) const {
2167 assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2 ||
2169 "Radix should be 2, 8, 10, 16, or 36!");
2171 const char *Prefix = "";
2172 if (formatAsCLiteral) {
2175 // Binary literals are a non-standard extension added in gcc 4.3:
2176 // http://gcc.gnu.org/onlinedocs/gcc-4.3.0/gcc/Binary-constants.html
2188 llvm_unreachable("Invalid radix!");
2192 // First, check for a zero value and just short circuit the logic below.
2195 Str.push_back(*Prefix);
2202 static const char Digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
2204 if (isSingleWord()) {
2206 char *BufPtr = Buffer+65;
2212 int64_t I = getSExtValue();
2222 Str.push_back(*Prefix);
2227 *--BufPtr = Digits[N % Radix];
2230 Str.append(BufPtr, Buffer+65);
2236 if (Signed && isNegative()) {
2237 // They want to print the signed version and it is a negative value
2238 // Flip the bits and add one to turn it into the equivalent positive
2239 // value and put a '-' in the result.
2246 Str.push_back(*Prefix);
2250 // We insert the digits backward, then reverse them to get the right order.
2251 unsigned StartDig = Str.size();
2253 // For the 2, 8 and 16 bit cases, we can just shift instead of divide
2254 // because the number of bits per digit (1, 3 and 4 respectively) divides
2255 // equaly. We just shift until the value is zero.
2256 if (Radix == 2 || Radix == 8 || Radix == 16) {
2257 // Just shift tmp right for each digit width until it becomes zero
2258 unsigned ShiftAmt = (Radix == 16 ? 4 : (Radix == 8 ? 3 : 1));
2259 unsigned MaskAmt = Radix - 1;
2262 unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt;
2263 Str.push_back(Digits[Digit]);
2264 Tmp = Tmp.lshr(ShiftAmt);
2267 APInt divisor(Radix == 10? 4 : 8, Radix);
2269 APInt APdigit(1, 0);
2270 APInt tmp2(Tmp.getBitWidth(), 0);
2271 divide(Tmp, Tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
2273 unsigned Digit = (unsigned)APdigit.getZExtValue();
2274 assert(Digit < Radix && "divide failed");
2275 Str.push_back(Digits[Digit]);
2280 // Reverse the digits before returning.
2281 std::reverse(Str.begin()+StartDig, Str.end());
2284 /// toString - This returns the APInt as a std::string. Note that this is an
2285 /// inefficient method. It is better to pass in a SmallVector/SmallString
2286 /// to the methods above.
2287 std::string APInt::toString(unsigned Radix = 10, bool Signed = true) const {
2289 toString(S, Radix, Signed, /* formatAsCLiteral = */false);
2294 void APInt::dump() const {
2295 SmallString<40> S, U;
2296 this->toStringUnsigned(U);
2297 this->toStringSigned(S);
2298 dbgs() << "APInt(" << BitWidth << "b, "
2299 << U.str() << "u " << S.str() << "s)";
2302 void APInt::print(raw_ostream &OS, bool isSigned) const {
2304 this->toString(S, 10, isSigned, /* formatAsCLiteral = */false);
2308 // This implements a variety of operations on a representation of
2309 // arbitrary precision, two's-complement, bignum integer values.
2311 // Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe
2312 // and unrestricting assumption.
2313 static_assert(integerPartWidth % 2 == 0, "Part width must be divisible by 2!");
2315 /* Some handy functions local to this file. */
2318 /* Returns the integer part with the least significant BITS set.
2319 BITS cannot be zero. */
2320 static inline integerPart
2321 lowBitMask(unsigned int bits)
2323 assert(bits != 0 && bits <= integerPartWidth);
2325 return ~(integerPart) 0 >> (integerPartWidth - bits);
2328 /* Returns the value of the lower half of PART. */
2329 static inline integerPart
2330 lowHalf(integerPart part)
2332 return part & lowBitMask(integerPartWidth / 2);
2335 /* Returns the value of the upper half of PART. */
2336 static inline integerPart
2337 highHalf(integerPart part)
2339 return part >> (integerPartWidth / 2);
2342 /* Returns the bit number of the most significant set bit of a part.
2343 If the input number has no bits set -1U is returned. */
2345 partMSB(integerPart value)
2347 return findLastSet(value, ZB_Max);
2350 /* Returns the bit number of the least significant set bit of a
2351 part. If the input number has no bits set -1U is returned. */
2353 partLSB(integerPart value)
2355 return findFirstSet(value, ZB_Max);
2359 /* Sets the least significant part of a bignum to the input value, and
2360 zeroes out higher parts. */
2362 APInt::tcSet(integerPart *dst, integerPart part, unsigned int parts)
2369 for (i = 1; i < parts; i++)
2373 /* Assign one bignum to another. */
2375 APInt::tcAssign(integerPart *dst, const integerPart *src, unsigned int parts)
2379 for (i = 0; i < parts; i++)
2383 /* Returns true if a bignum is zero, false otherwise. */
2385 APInt::tcIsZero(const integerPart *src, unsigned int parts)
2389 for (i = 0; i < parts; i++)
2396 /* Extract the given bit of a bignum; returns 0 or 1. */
2398 APInt::tcExtractBit(const integerPart *parts, unsigned int bit)
2400 return (parts[bit / integerPartWidth] &
2401 ((integerPart) 1 << bit % integerPartWidth)) != 0;
2404 /* Set the given bit of a bignum. */
2406 APInt::tcSetBit(integerPart *parts, unsigned int bit)
2408 parts[bit / integerPartWidth] |= (integerPart) 1 << (bit % integerPartWidth);
2411 /* Clears the given bit of a bignum. */
2413 APInt::tcClearBit(integerPart *parts, unsigned int bit)
2415 parts[bit / integerPartWidth] &=
2416 ~((integerPart) 1 << (bit % integerPartWidth));
2419 /* Returns the bit number of the least significant set bit of a
2420 number. If the input number has no bits set -1U is returned. */
2422 APInt::tcLSB(const integerPart *parts, unsigned int n)
2424 unsigned int i, lsb;
2426 for (i = 0; i < n; i++) {
2427 if (parts[i] != 0) {
2428 lsb = partLSB(parts[i]);
2430 return lsb + i * integerPartWidth;
2437 /* Returns the bit number of the most significant set bit of a number.
2438 If the input number has no bits set -1U is returned. */
2440 APInt::tcMSB(const integerPart *parts, unsigned int n)
2447 if (parts[n] != 0) {
2448 msb = partMSB(parts[n]);
2450 return msb + n * integerPartWidth;
2457 /* Copy the bit vector of width srcBITS from SRC, starting at bit
2458 srcLSB, to DST, of dstCOUNT parts, such that the bit srcLSB becomes
2459 the least significant bit of DST. All high bits above srcBITS in
2460 DST are zero-filled. */
2462 APInt::tcExtract(integerPart *dst, unsigned int dstCount,const integerPart *src,
2463 unsigned int srcBits, unsigned int srcLSB)
2465 unsigned int firstSrcPart, dstParts, shift, n;
2467 dstParts = (srcBits + integerPartWidth - 1) / integerPartWidth;
2468 assert(dstParts <= dstCount);
2470 firstSrcPart = srcLSB / integerPartWidth;
2471 tcAssign (dst, src + firstSrcPart, dstParts);
2473 shift = srcLSB % integerPartWidth;
2474 tcShiftRight (dst, dstParts, shift);
2476 /* We now have (dstParts * integerPartWidth - shift) bits from SRC
2477 in DST. If this is less that srcBits, append the rest, else
2478 clear the high bits. */
2479 n = dstParts * integerPartWidth - shift;
2481 integerPart mask = lowBitMask (srcBits - n);
2482 dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask)
2483 << n % integerPartWidth);
2484 } else if (n > srcBits) {
2485 if (srcBits % integerPartWidth)
2486 dst[dstParts - 1] &= lowBitMask (srcBits % integerPartWidth);
2489 /* Clear high parts. */
2490 while (dstParts < dstCount)
2491 dst[dstParts++] = 0;
2494 /* DST += RHS + C where C is zero or one. Returns the carry flag. */
2496 APInt::tcAdd(integerPart *dst, const integerPart *rhs,
2497 integerPart c, unsigned int parts)
2503 for (i = 0; i < parts; i++) {
2508 dst[i] += rhs[i] + 1;
2519 /* DST -= RHS + C where C is zero or one. Returns the carry flag. */
2521 APInt::tcSubtract(integerPart *dst, const integerPart *rhs,
2522 integerPart c, unsigned int parts)
2528 for (i = 0; i < parts; i++) {
2533 dst[i] -= rhs[i] + 1;
2544 /* Negate a bignum in-place. */
2546 APInt::tcNegate(integerPart *dst, unsigned int parts)
2548 tcComplement(dst, parts);
2549 tcIncrement(dst, parts);
2552 /* DST += SRC * MULTIPLIER + CARRY if add is true
2553 DST = SRC * MULTIPLIER + CARRY if add is false
2555 Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC
2556 they must start at the same point, i.e. DST == SRC.
2558 If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is
2559 returned. Otherwise DST is filled with the least significant
2560 DSTPARTS parts of the result, and if all of the omitted higher
2561 parts were zero return zero, otherwise overflow occurred and
2564 APInt::tcMultiplyPart(integerPart *dst, const integerPart *src,
2565 integerPart multiplier, integerPart carry,
2566 unsigned int srcParts, unsigned int dstParts,
2571 /* Otherwise our writes of DST kill our later reads of SRC. */
2572 assert(dst <= src || dst >= src + srcParts);
2573 assert(dstParts <= srcParts + 1);
2575 /* N loops; minimum of dstParts and srcParts. */
2576 n = dstParts < srcParts ? dstParts: srcParts;
2578 for (i = 0; i < n; i++) {
2579 integerPart low, mid, high, srcPart;
2581 /* [ LOW, HIGH ] = MULTIPLIER * SRC[i] + DST[i] + CARRY.
2583 This cannot overflow, because
2585 (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1)
2587 which is less than n^2. */
2591 if (multiplier == 0 || srcPart == 0) {
2595 low = lowHalf(srcPart) * lowHalf(multiplier);
2596 high = highHalf(srcPart) * highHalf(multiplier);
2598 mid = lowHalf(srcPart) * highHalf(multiplier);
2599 high += highHalf(mid);
2600 mid <<= integerPartWidth / 2;
2601 if (low + mid < low)
2605 mid = highHalf(srcPart) * lowHalf(multiplier);
2606 high += highHalf(mid);
2607 mid <<= integerPartWidth / 2;
2608 if (low + mid < low)
2612 /* Now add carry. */
2613 if (low + carry < low)
2619 /* And now DST[i], and store the new low part there. */
2620 if (low + dst[i] < low)
2630 /* Full multiplication, there is no overflow. */
2631 assert(i + 1 == dstParts);
2635 /* We overflowed if there is carry. */
2639 /* We would overflow if any significant unwritten parts would be
2640 non-zero. This is true if any remaining src parts are non-zero
2641 and the multiplier is non-zero. */
2643 for (; i < srcParts; i++)
2647 /* We fitted in the narrow destination. */
2652 /* DST = LHS * RHS, where DST has the same width as the operands and
2653 is filled with the least significant parts of the result. Returns
2654 one if overflow occurred, otherwise zero. DST must be disjoint
2655 from both operands. */
2657 APInt::tcMultiply(integerPart *dst, const integerPart *lhs,
2658 const integerPart *rhs, unsigned int parts)
2663 assert(dst != lhs && dst != rhs);
2666 tcSet(dst, 0, parts);
2668 for (i = 0; i < parts; i++)
2669 overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts,
2675 /* DST = LHS * RHS, where DST has width the sum of the widths of the
2676 operands. No overflow occurs. DST must be disjoint from both
2677 operands. Returns the number of parts required to hold the
2680 APInt::tcFullMultiply(integerPart *dst, const integerPart *lhs,
2681 const integerPart *rhs, unsigned int lhsParts,
2682 unsigned int rhsParts)
2684 /* Put the narrower number on the LHS for less loops below. */
2685 if (lhsParts > rhsParts) {
2686 return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts);
2690 assert(dst != lhs && dst != rhs);
2692 tcSet(dst, 0, rhsParts);
2694 for (n = 0; n < lhsParts; n++)
2695 tcMultiplyPart(&dst[n], rhs, lhs[n], 0, rhsParts, rhsParts + 1, true);
2697 n = lhsParts + rhsParts;
2699 return n - (dst[n - 1] == 0);
2703 /* If RHS is zero LHS and REMAINDER are left unchanged, return one.
2704 Otherwise set LHS to LHS / RHS with the fractional part discarded,
2705 set REMAINDER to the remainder, return zero. i.e.
2707 OLD_LHS = RHS * LHS + REMAINDER
2709 SCRATCH is a bignum of the same size as the operands and result for
2710 use by the routine; its contents need not be initialized and are
2711 destroyed. LHS, REMAINDER and SCRATCH must be distinct.
2714 APInt::tcDivide(integerPart *lhs, const integerPart *rhs,
2715 integerPart *remainder, integerPart *srhs,
2718 unsigned int n, shiftCount;
2721 assert(lhs != remainder && lhs != srhs && remainder != srhs);
2723 shiftCount = tcMSB(rhs, parts) + 1;
2724 if (shiftCount == 0)
2727 shiftCount = parts * integerPartWidth - shiftCount;
2728 n = shiftCount / integerPartWidth;
2729 mask = (integerPart) 1 << (shiftCount % integerPartWidth);
2731 tcAssign(srhs, rhs, parts);
2732 tcShiftLeft(srhs, parts, shiftCount);
2733 tcAssign(remainder, lhs, parts);
2734 tcSet(lhs, 0, parts);
2736 /* Loop, subtracting SRHS if REMAINDER is greater and adding that to
2741 compare = tcCompare(remainder, srhs, parts);
2743 tcSubtract(remainder, srhs, 0, parts);
2747 if (shiftCount == 0)
2750 tcShiftRight(srhs, parts, 1);
2751 if ((mask >>= 1) == 0)
2752 mask = (integerPart) 1 << (integerPartWidth - 1), n--;
2758 /* Shift a bignum left COUNT bits in-place. Shifted in bits are zero.
2759 There are no restrictions on COUNT. */
2761 APInt::tcShiftLeft(integerPart *dst, unsigned int parts, unsigned int count)
2764 unsigned int jump, shift;
2766 /* Jump is the inter-part jump; shift is is intra-part shift. */
2767 jump = count / integerPartWidth;
2768 shift = count % integerPartWidth;
2770 while (parts > jump) {
2775 /* dst[i] comes from the two parts src[i - jump] and, if we have
2776 an intra-part shift, src[i - jump - 1]. */
2777 part = dst[parts - jump];
2780 if (parts >= jump + 1)
2781 part |= dst[parts - jump - 1] >> (integerPartWidth - shift);
2792 /* Shift a bignum right COUNT bits in-place. Shifted in bits are
2793 zero. There are no restrictions on COUNT. */
2795 APInt::tcShiftRight(integerPart *dst, unsigned int parts, unsigned int count)
2798 unsigned int i, jump, shift;
2800 /* Jump is the inter-part jump; shift is is intra-part shift. */
2801 jump = count / integerPartWidth;
2802 shift = count % integerPartWidth;
2804 /* Perform the shift. This leaves the most significant COUNT bits
2805 of the result at zero. */
2806 for (i = 0; i < parts; i++) {
2809 if (i + jump >= parts) {
2812 part = dst[i + jump];
2815 if (i + jump + 1 < parts)
2816 part |= dst[i + jump + 1] << (integerPartWidth - shift);
2825 /* Bitwise and of two bignums. */
2827 APInt::tcAnd(integerPart *dst, const integerPart *rhs, unsigned int parts)
2831 for (i = 0; i < parts; i++)
2835 /* Bitwise inclusive or of two bignums. */
2837 APInt::tcOr(integerPart *dst, const integerPart *rhs, unsigned int parts)
2841 for (i = 0; i < parts; i++)
2845 /* Bitwise exclusive or of two bignums. */
2847 APInt::tcXor(integerPart *dst, const integerPart *rhs, unsigned int parts)
2851 for (i = 0; i < parts; i++)
2855 /* Complement a bignum in-place. */
2857 APInt::tcComplement(integerPart *dst, unsigned int parts)
2861 for (i = 0; i < parts; i++)
2865 /* Comparison (unsigned) of two bignums. */
2867 APInt::tcCompare(const integerPart *lhs, const integerPart *rhs,
2872 if (lhs[parts] == rhs[parts])
2875 if (lhs[parts] > rhs[parts])
2884 /* Increment a bignum in-place, return the carry flag. */
2886 APInt::tcIncrement(integerPart *dst, unsigned int parts)
2890 for (i = 0; i < parts; i++)
2897 /* Decrement a bignum in-place, return the borrow flag. */
2899 APInt::tcDecrement(integerPart *dst, unsigned int parts) {
2900 for (unsigned int i = 0; i < parts; i++) {
2901 // If the current word is non-zero, then the decrement has no effect on the
2902 // higher-order words of the integer and no borrow can occur. Exit early.
2906 // If every word was zero, then there is a borrow.
2911 /* Set the least significant BITS bits of a bignum, clear the
2914 APInt::tcSetLeastSignificantBits(integerPart *dst, unsigned int parts,
2920 while (bits > integerPartWidth) {
2921 dst[i++] = ~(integerPart) 0;
2922 bits -= integerPartWidth;
2926 dst[i++] = ~(integerPart) 0 >> (integerPartWidth - bits);