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 #define DEBUG_TYPE "apint"
16 #include "llvm/ADT/APInt.h"
17 #include "llvm/ADT/StringRef.h"
18 #include "llvm/ADT/FoldingSet.h"
19 #include "llvm/ADT/SmallString.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 /// A utility function for allocating memory, checking for allocation failures,
31 /// and ensuring the contents are zeroed.
32 inline static uint64_t* getClearedMemory(unsigned numWords) {
33 uint64_t * result = new uint64_t[numWords];
34 assert(result && "APInt memory allocation fails!");
35 memset(result, 0, numWords * sizeof(uint64_t));
39 /// A utility function for allocating memory and checking for allocation
40 /// failure. The content is not zeroed.
41 inline static uint64_t* getMemory(unsigned numWords) {
42 uint64_t * result = new uint64_t[numWords];
43 assert(result && "APInt memory allocation fails!");
47 /// A utility function that converts a character to a digit.
48 inline static unsigned getDigit(char cdigit, uint8_t radix) {
73 void APInt::initSlowCase(unsigned numBits, uint64_t val, bool isSigned) {
74 pVal = getClearedMemory(getNumWords());
76 if (isSigned && int64_t(val) < 0)
77 for (unsigned i = 1; i < getNumWords(); ++i)
81 void APInt::initSlowCase(const APInt& that) {
82 pVal = getMemory(getNumWords());
83 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE);
87 APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[])
88 : BitWidth(numBits), VAL(0) {
89 assert(BitWidth && "Bitwidth too small");
90 assert(bigVal && "Null pointer detected!");
94 // Get memory, cleared to 0
95 pVal = getClearedMemory(getNumWords());
96 // Calculate the number of words to copy
97 unsigned words = std::min<unsigned>(numWords, getNumWords());
98 // Copy the words from bigVal to pVal
99 memcpy(pVal, bigVal, words * APINT_WORD_SIZE);
101 // Make sure unused high bits are cleared
105 APInt::APInt(unsigned numbits, const StringRef& Str, uint8_t radix)
106 : BitWidth(numbits), VAL(0) {
107 assert(BitWidth && "Bitwidth too small");
108 fromString(numbits, Str, radix);
111 APInt& APInt::AssignSlowCase(const APInt& RHS) {
112 // Don't do anything for X = X
116 if (BitWidth == RHS.getBitWidth()) {
117 // assume same bit-width single-word case is already handled
118 assert(!isSingleWord());
119 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE);
123 if (isSingleWord()) {
124 // assume case where both are single words is already handled
125 assert(!RHS.isSingleWord());
127 pVal = getMemory(RHS.getNumWords());
128 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
129 } else if (getNumWords() == RHS.getNumWords())
130 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
131 else if (RHS.isSingleWord()) {
136 pVal = getMemory(RHS.getNumWords());
137 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
139 BitWidth = RHS.BitWidth;
140 return clearUnusedBits();
143 APInt& APInt::operator=(uint64_t RHS) {
148 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE);
150 return clearUnusedBits();
153 /// Profile - This method 'profiles' an APInt for use with FoldingSet.
154 void APInt::Profile(FoldingSetNodeID& ID) const {
155 ID.AddInteger(BitWidth);
157 if (isSingleWord()) {
162 unsigned NumWords = getNumWords();
163 for (unsigned i = 0; i < NumWords; ++i)
164 ID.AddInteger(pVal[i]);
167 /// add_1 - This function adds a single "digit" integer, y, to the multiple
168 /// "digit" integer array, x[]. x[] is modified to reflect the addition and
169 /// 1 is returned if there is a carry out, otherwise 0 is returned.
170 /// @returns the carry of the addition.
171 static bool add_1(uint64_t dest[], uint64_t x[], unsigned len, uint64_t y) {
172 for (unsigned i = 0; i < len; ++i) {
175 y = 1; // Carry one to next digit.
177 y = 0; // No need to carry so exit early
184 /// @brief Prefix increment operator. Increments the APInt by one.
185 APInt& APInt::operator++() {
189 add_1(pVal, pVal, getNumWords(), 1);
190 return clearUnusedBits();
193 /// sub_1 - This function subtracts a single "digit" (64-bit word), y, from
194 /// the multi-digit integer array, x[], propagating the borrowed 1 value until
195 /// no further borrowing is neeeded or it runs out of "digits" in x. The result
196 /// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted.
197 /// In other words, if y > x then this function returns 1, otherwise 0.
198 /// @returns the borrow out of the subtraction
199 static bool sub_1(uint64_t x[], unsigned len, uint64_t y) {
200 for (unsigned i = 0; i < len; ++i) {
204 y = 1; // We have to "borrow 1" from next "digit"
206 y = 0; // No need to borrow
207 break; // Remaining digits are unchanged so exit early
213 /// @brief Prefix decrement operator. Decrements the APInt by one.
214 APInt& APInt::operator--() {
218 sub_1(pVal, getNumWords(), 1);
219 return clearUnusedBits();
222 /// add - This function adds the integer array x to the integer array Y and
223 /// places the result in dest.
224 /// @returns the carry out from the addition
225 /// @brief General addition of 64-bit integer arrays
226 static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y,
229 for (unsigned i = 0; i< len; ++i) {
230 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x
231 dest[i] = x[i] + y[i] + carry;
232 carry = dest[i] < limit || (carry && dest[i] == limit);
237 /// Adds the RHS APint to this APInt.
238 /// @returns this, after addition of RHS.
239 /// @brief Addition assignment operator.
240 APInt& APInt::operator+=(const APInt& RHS) {
241 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
245 add(pVal, pVal, RHS.pVal, getNumWords());
247 return clearUnusedBits();
250 /// Subtracts the integer array y from the integer array x
251 /// @returns returns the borrow out.
252 /// @brief Generalized subtraction of 64-bit integer arrays.
253 static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y,
256 for (unsigned i = 0; i < len; ++i) {
257 uint64_t x_tmp = borrow ? x[i] - 1 : x[i];
258 borrow = y[i] > x_tmp || (borrow && x[i] == 0);
259 dest[i] = x_tmp - y[i];
264 /// Subtracts the RHS APInt from this APInt
265 /// @returns this, after subtraction
266 /// @brief Subtraction assignment operator.
267 APInt& APInt::operator-=(const APInt& RHS) {
268 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
272 sub(pVal, pVal, RHS.pVal, getNumWords());
273 return clearUnusedBits();
276 /// Multiplies an integer array, x, by a uint64_t integer and places the result
278 /// @returns the carry out of the multiplication.
279 /// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer.
280 static uint64_t mul_1(uint64_t dest[], uint64_t x[], unsigned len, uint64_t y) {
281 // Split y into high 32-bit part (hy) and low 32-bit part (ly)
282 uint64_t ly = y & 0xffffffffULL, hy = y >> 32;
285 // For each digit of x.
286 for (unsigned i = 0; i < len; ++i) {
287 // Split x into high and low words
288 uint64_t lx = x[i] & 0xffffffffULL;
289 uint64_t hx = x[i] >> 32;
290 // hasCarry - A flag to indicate if there is a carry to the next digit.
291 // hasCarry == 0, no carry
292 // hasCarry == 1, has carry
293 // hasCarry == 2, no carry and the calculation result == 0.
294 uint8_t hasCarry = 0;
295 dest[i] = carry + lx * ly;
296 // Determine if the add above introduces carry.
297 hasCarry = (dest[i] < carry) ? 1 : 0;
298 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0);
299 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) +
300 // (2^32 - 1) + 2^32 = 2^64.
301 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
303 carry += (lx * hy) & 0xffffffffULL;
304 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL);
305 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) +
306 (carry >> 32) + ((lx * hy) >> 32) + hx * hy;
311 /// Multiplies integer array x by integer array y and stores the result into
312 /// the integer array dest. Note that dest's size must be >= xlen + ylen.
313 /// @brief Generalized multiplicate of integer arrays.
314 static void mul(uint64_t dest[], uint64_t x[], unsigned xlen, uint64_t y[],
316 dest[xlen] = mul_1(dest, x, xlen, y[0]);
317 for (unsigned i = 1; i < ylen; ++i) {
318 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32;
319 uint64_t carry = 0, lx = 0, hx = 0;
320 for (unsigned j = 0; j < xlen; ++j) {
321 lx = x[j] & 0xffffffffULL;
323 // hasCarry - A flag to indicate if has carry.
324 // hasCarry == 0, no carry
325 // hasCarry == 1, has carry
326 // hasCarry == 2, no carry and the calculation result == 0.
327 uint8_t hasCarry = 0;
328 uint64_t resul = carry + lx * ly;
329 hasCarry = (resul < carry) ? 1 : 0;
330 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32);
331 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
333 carry += (lx * hy) & 0xffffffffULL;
334 resul = (carry << 32) | (resul & 0xffffffffULL);
336 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+
337 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) +
338 ((lx * hy) >> 32) + hx * hy;
340 dest[i+xlen] = carry;
344 APInt& APInt::operator*=(const APInt& RHS) {
345 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
346 if (isSingleWord()) {
352 // Get some bit facts about LHS and check for zero
353 unsigned lhsBits = getActiveBits();
354 unsigned lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1;
359 // Get some bit facts about RHS and check for zero
360 unsigned rhsBits = RHS.getActiveBits();
361 unsigned rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1;
368 // Allocate space for the result
369 unsigned destWords = rhsWords + lhsWords;
370 uint64_t *dest = getMemory(destWords);
372 // Perform the long multiply
373 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords);
375 // Copy result back into *this
377 unsigned wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords;
378 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE);
380 // delete dest array and return
385 APInt& APInt::operator&=(const APInt& RHS) {
386 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
387 if (isSingleWord()) {
391 unsigned numWords = getNumWords();
392 for (unsigned i = 0; i < numWords; ++i)
393 pVal[i] &= RHS.pVal[i];
397 APInt& APInt::operator|=(const APInt& RHS) {
398 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
399 if (isSingleWord()) {
403 unsigned numWords = getNumWords();
404 for (unsigned i = 0; i < numWords; ++i)
405 pVal[i] |= RHS.pVal[i];
409 APInt& APInt::operator^=(const APInt& RHS) {
410 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
411 if (isSingleWord()) {
413 this->clearUnusedBits();
416 unsigned numWords = getNumWords();
417 for (unsigned i = 0; i < numWords; ++i)
418 pVal[i] ^= RHS.pVal[i];
419 return clearUnusedBits();
422 APInt APInt::AndSlowCase(const APInt& RHS) const {
423 unsigned numWords = getNumWords();
424 uint64_t* val = getMemory(numWords);
425 for (unsigned i = 0; i < numWords; ++i)
426 val[i] = pVal[i] & RHS.pVal[i];
427 return APInt(val, getBitWidth());
430 APInt APInt::OrSlowCase(const APInt& RHS) const {
431 unsigned numWords = getNumWords();
432 uint64_t *val = getMemory(numWords);
433 for (unsigned i = 0; i < numWords; ++i)
434 val[i] = pVal[i] | RHS.pVal[i];
435 return APInt(val, getBitWidth());
438 APInt APInt::XorSlowCase(const APInt& RHS) const {
439 unsigned numWords = getNumWords();
440 uint64_t *val = getMemory(numWords);
441 for (unsigned i = 0; i < numWords; ++i)
442 val[i] = pVal[i] ^ RHS.pVal[i];
444 // 0^0==1 so clear the high bits in case they got set.
445 return APInt(val, getBitWidth()).clearUnusedBits();
448 bool APInt::operator !() const {
452 for (unsigned i = 0; i < getNumWords(); ++i)
458 APInt APInt::operator*(const APInt& RHS) const {
459 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
461 return APInt(BitWidth, VAL * RHS.VAL);
464 return Result.clearUnusedBits();
467 APInt APInt::operator+(const APInt& RHS) const {
468 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
470 return APInt(BitWidth, VAL + RHS.VAL);
471 APInt Result(BitWidth, 0);
472 add(Result.pVal, this->pVal, RHS.pVal, getNumWords());
473 return Result.clearUnusedBits();
476 APInt APInt::operator-(const APInt& RHS) const {
477 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
479 return APInt(BitWidth, VAL - RHS.VAL);
480 APInt Result(BitWidth, 0);
481 sub(Result.pVal, this->pVal, RHS.pVal, getNumWords());
482 return Result.clearUnusedBits();
485 bool APInt::operator[](unsigned bitPosition) const {
486 return (maskBit(bitPosition) &
487 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0;
490 bool APInt::EqualSlowCase(const APInt& RHS) const {
491 // Get some facts about the number of bits used in the two operands.
492 unsigned n1 = getActiveBits();
493 unsigned n2 = RHS.getActiveBits();
495 // If the number of bits isn't the same, they aren't equal
499 // If the number of bits fits in a word, we only need to compare the low word.
500 if (n1 <= APINT_BITS_PER_WORD)
501 return pVal[0] == RHS.pVal[0];
503 // Otherwise, compare everything
504 for (int i = whichWord(n1 - 1); i >= 0; --i)
505 if (pVal[i] != RHS.pVal[i])
510 bool APInt::EqualSlowCase(uint64_t Val) const {
511 unsigned n = getActiveBits();
512 if (n <= APINT_BITS_PER_WORD)
513 return pVal[0] == Val;
518 bool APInt::ult(const APInt& RHS) const {
519 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
521 return VAL < RHS.VAL;
523 // Get active bit length of both operands
524 unsigned n1 = getActiveBits();
525 unsigned n2 = RHS.getActiveBits();
527 // If magnitude of LHS is less than RHS, return true.
531 // If magnitude of RHS is greather than LHS, return false.
535 // If they bot fit in a word, just compare the low order word
536 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD)
537 return pVal[0] < RHS.pVal[0];
539 // Otherwise, compare all words
540 unsigned topWord = whichWord(std::max(n1,n2)-1);
541 for (int i = topWord; i >= 0; --i) {
542 if (pVal[i] > RHS.pVal[i])
544 if (pVal[i] < RHS.pVal[i])
550 bool APInt::slt(const APInt& RHS) const {
551 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
552 if (isSingleWord()) {
553 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
554 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth);
555 return lhsSext < rhsSext;
560 bool lhsNeg = isNegative();
561 bool rhsNeg = rhs.isNegative();
563 // Sign bit is set so perform two's complement to make it positive
568 // Sign bit is set so perform two's complement to make it positive
573 // Now we have unsigned values to compare so do the comparison if necessary
574 // based on the negativeness of the values.
586 APInt& APInt::set(unsigned bitPosition) {
588 VAL |= maskBit(bitPosition);
590 pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
594 /// Set the given bit to 0 whose position is given as "bitPosition".
595 /// @brief Set a given bit to 0.
596 APInt& APInt::clear(unsigned bitPosition) {
598 VAL &= ~maskBit(bitPosition);
600 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 APInt& APInt::flip(unsigned bitPosition) {
610 assert(bitPosition < BitWidth && "Out of the bit-width range!");
611 if ((*this)[bitPosition]) clear(bitPosition);
612 else set(bitPosition);
616 unsigned APInt::getBitsNeeded(const StringRef& str, uint8_t radix) {
617 assert(!str.empty() && "Invalid string length");
618 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
619 "Radix should be 2, 8, 10, or 16!");
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;
641 // This is grossly inefficient but accurate. We could probably do something
642 // with a computation of roughly slen*64/20 and then adjust by the value of
643 // the first few digits. But, I'm not sure how accurate that could be.
645 // Compute a sufficient number of bits that is always large enough but might
646 // be too large. This avoids the assertion in the constructor. This
647 // calculation doesn't work appropriately for the numbers 0-9, so just use 4
648 // bits in that case.
649 unsigned sufficient = slen == 1 ? 4 : slen * 64/18;
651 // Convert to the actual binary value.
652 APInt tmp(sufficient, StringRef(p, slen), radix);
654 // Compute how many bits are required. If the log is infinite, assume we need
656 unsigned log = tmp.logBase2();
657 if (log == (unsigned)-1) {
658 return isNegative + 1;
660 return isNegative + log + 1;
664 // From http://www.burtleburtle.net, byBob Jenkins.
665 // When targeting x86, both GCC and LLVM seem to recognize this as a
666 // rotate instruction.
667 #define rot(x,k) (((x)<<(k)) | ((x)>>(32-(k))))
669 // From http://www.burtleburtle.net, by Bob Jenkins.
672 a -= c; a ^= rot(c, 4); c += b; \
673 b -= a; b ^= rot(a, 6); a += c; \
674 c -= b; c ^= rot(b, 8); b += a; \
675 a -= c; a ^= rot(c,16); c += b; \
676 b -= a; b ^= rot(a,19); a += c; \
677 c -= b; c ^= rot(b, 4); b += a; \
680 // From http://www.burtleburtle.net, by Bob Jenkins.
681 #define final(a,b,c) \
683 c ^= b; c -= rot(b,14); \
684 a ^= c; a -= rot(c,11); \
685 b ^= a; b -= rot(a,25); \
686 c ^= b; c -= rot(b,16); \
687 a ^= c; a -= rot(c,4); \
688 b ^= a; b -= rot(a,14); \
689 c ^= b; c -= rot(b,24); \
692 // hashword() was adapted from http://www.burtleburtle.net, by Bob
693 // Jenkins. k is a pointer to an array of uint32_t values; length is
694 // the length of the key, in 32-bit chunks. This version only handles
695 // keys that are a multiple of 32 bits in size.
696 static inline uint32_t hashword(const uint64_t *k64, size_t length)
698 const uint32_t *k = reinterpret_cast<const uint32_t *>(k64);
701 /* Set up the internal state */
702 a = b = c = 0xdeadbeef + (((uint32_t)length)<<2);
704 /*------------------------------------------------- handle most of the key */
715 /*------------------------------------------- handle the last 3 uint32_t's */
716 switch (length) { /* all the case statements fall through */
721 case 0: /* case 0: nothing left to add */
724 /*------------------------------------------------------ report the result */
728 // hashword8() was adapted from http://www.burtleburtle.net, by Bob
729 // Jenkins. This computes a 32-bit hash from one 64-bit word. When
730 // targeting x86 (32 or 64 bit), both LLVM and GCC compile this
731 // function into about 35 instructions when inlined.
732 static inline uint32_t hashword8(const uint64_t k64)
735 a = b = c = 0xdeadbeef + 4;
737 a += k64 & 0xffffffff;
745 uint64_t APInt::getHashValue() const {
748 hash = hashword8(VAL);
750 hash = hashword(pVal, getNumWords()*2);
754 /// HiBits - This function returns the high "numBits" bits of this APInt.
755 APInt APInt::getHiBits(unsigned numBits) const {
756 return APIntOps::lshr(*this, BitWidth - numBits);
759 /// LoBits - This function returns the low "numBits" bits of this APInt.
760 APInt APInt::getLoBits(unsigned numBits) const {
761 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
765 bool APInt::isPowerOf2() const {
766 return (!!*this) && !(*this & (*this - APInt(BitWidth,1)));
769 unsigned APInt::countLeadingZerosSlowCase() const {
770 // Treat the most significand word differently because it might have
771 // meaningless bits set beyond the precision.
772 unsigned BitsInMSW = BitWidth % APINT_BITS_PER_WORD;
774 if (BitsInMSW) MSWMask = (integerPart(1) << BitsInMSW) - 1;
776 MSWMask = ~integerPart(0);
777 BitsInMSW = APINT_BITS_PER_WORD;
780 unsigned i = getNumWords();
781 integerPart MSW = pVal[i-1] & MSWMask;
783 return CountLeadingZeros_64(MSW) - (APINT_BITS_PER_WORD - BitsInMSW);
785 unsigned Count = BitsInMSW;
786 for (--i; i > 0u; --i) {
788 Count += APINT_BITS_PER_WORD;
790 Count += CountLeadingZeros_64(pVal[i-1]);
797 static unsigned countLeadingOnes_64(uint64_t V, unsigned skip) {
801 while (V && (V & (1ULL << 63))) {
808 unsigned APInt::countLeadingOnes() const {
810 return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth);
812 unsigned highWordBits = BitWidth % APINT_BITS_PER_WORD;
815 highWordBits = APINT_BITS_PER_WORD;
818 shift = APINT_BITS_PER_WORD - highWordBits;
820 int i = getNumWords() - 1;
821 unsigned Count = countLeadingOnes_64(pVal[i], shift);
822 if (Count == highWordBits) {
823 for (i--; i >= 0; --i) {
824 if (pVal[i] == -1ULL)
825 Count += APINT_BITS_PER_WORD;
827 Count += countLeadingOnes_64(pVal[i], 0);
835 unsigned APInt::countTrailingZeros() const {
837 return std::min(unsigned(CountTrailingZeros_64(VAL)), BitWidth);
840 for (; i < getNumWords() && pVal[i] == 0; ++i)
841 Count += APINT_BITS_PER_WORD;
842 if (i < getNumWords())
843 Count += CountTrailingZeros_64(pVal[i]);
844 return std::min(Count, BitWidth);
847 unsigned APInt::countTrailingOnesSlowCase() const {
850 for (; i < getNumWords() && pVal[i] == -1ULL; ++i)
851 Count += APINT_BITS_PER_WORD;
852 if (i < getNumWords())
853 Count += CountTrailingOnes_64(pVal[i]);
854 return std::min(Count, BitWidth);
857 unsigned APInt::countPopulationSlowCase() const {
859 for (unsigned i = 0; i < getNumWords(); ++i)
860 Count += CountPopulation_64(pVal[i]);
864 APInt APInt::byteSwap() const {
865 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
867 return APInt(BitWidth, ByteSwap_16(uint16_t(VAL)));
868 else if (BitWidth == 32)
869 return APInt(BitWidth, ByteSwap_32(unsigned(VAL)));
870 else if (BitWidth == 48) {
871 unsigned Tmp1 = unsigned(VAL >> 16);
872 Tmp1 = ByteSwap_32(Tmp1);
873 uint16_t Tmp2 = uint16_t(VAL);
874 Tmp2 = ByteSwap_16(Tmp2);
875 return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1);
876 } else if (BitWidth == 64)
877 return APInt(BitWidth, ByteSwap_64(VAL));
879 APInt Result(BitWidth, 0);
880 char *pByte = (char*)Result.pVal;
881 for (unsigned i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) {
883 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i];
884 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp;
890 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
892 APInt A = API1, B = API2;
895 B = APIntOps::urem(A, B);
901 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) {
908 // Get the sign bit from the highest order bit
909 bool isNeg = T.I >> 63;
911 // Get the 11-bit exponent and adjust for the 1023 bit bias
912 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
914 // If the exponent is negative, the value is < 0 so just return 0.
916 return APInt(width, 0u);
918 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
919 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
921 // If the exponent doesn't shift all bits out of the mantissa
923 return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
924 APInt(width, mantissa >> (52 - exp));
926 // If the client didn't provide enough bits for us to shift the mantissa into
927 // then the result is undefined, just return 0
928 if (width <= exp - 52)
929 return APInt(width, 0);
931 // Otherwise, we have to shift the mantissa bits up to the right location
932 APInt Tmp(width, mantissa);
933 Tmp = Tmp.shl((unsigned)exp - 52);
934 return isNeg ? -Tmp : Tmp;
937 /// RoundToDouble - This function converts this APInt to a double.
938 /// The layout for double is as following (IEEE Standard 754):
939 /// --------------------------------------
940 /// | Sign Exponent Fraction Bias |
941 /// |-------------------------------------- |
942 /// | 1[63] 11[62-52] 52[51-00] 1023 |
943 /// --------------------------------------
944 double APInt::roundToDouble(bool isSigned) const {
946 // Handle the simple case where the value is contained in one uint64_t.
947 // It is wrong to optimize getWord(0) to VAL; there might be more than one word.
948 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
950 int64_t sext = (int64_t(getWord(0)) << (64-BitWidth)) >> (64-BitWidth);
953 return double(getWord(0));
956 // Determine if the value is negative.
957 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
959 // Construct the absolute value if we're negative.
960 APInt Tmp(isNeg ? -(*this) : (*this));
962 // Figure out how many bits we're using.
963 unsigned n = Tmp.getActiveBits();
965 // The exponent (without bias normalization) is just the number of bits
966 // we are using. Note that the sign bit is gone since we constructed the
970 // Return infinity for exponent overflow
972 if (!isSigned || !isNeg)
973 return std::numeric_limits<double>::infinity();
975 return -std::numeric_limits<double>::infinity();
977 exp += 1023; // Increment for 1023 bias
979 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
980 // extract the high 52 bits from the correct words in pVal.
982 unsigned hiWord = whichWord(n-1);
984 mantissa = Tmp.pVal[0];
986 mantissa >>= n - 52; // shift down, we want the top 52 bits.
988 assert(hiWord > 0 && "huh?");
989 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
990 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
991 mantissa = hibits | lobits;
994 // The leading bit of mantissa is implicit, so get rid of it.
995 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
1000 T.I = sign | (exp << 52) | mantissa;
1004 // Truncate to new width.
1005 APInt &APInt::trunc(unsigned width) {
1006 assert(width < BitWidth && "Invalid APInt Truncate request");
1007 assert(width && "Can't truncate to 0 bits");
1008 unsigned wordsBefore = getNumWords();
1010 unsigned wordsAfter = getNumWords();
1011 if (wordsBefore != wordsAfter) {
1012 if (wordsAfter == 1) {
1013 uint64_t *tmp = pVal;
1017 uint64_t *newVal = getClearedMemory(wordsAfter);
1018 for (unsigned i = 0; i < wordsAfter; ++i)
1019 newVal[i] = pVal[i];
1024 return clearUnusedBits();
1027 // Sign extend to a new width.
1028 APInt &APInt::sext(unsigned width) {
1029 assert(width > BitWidth && "Invalid APInt SignExtend request");
1030 // If the sign bit isn't set, this is the same as zext.
1031 if (!isNegative()) {
1036 // The sign bit is set. First, get some facts
1037 unsigned wordsBefore = getNumWords();
1038 unsigned wordBits = BitWidth % APINT_BITS_PER_WORD;
1040 unsigned wordsAfter = getNumWords();
1042 // Mask the high order word appropriately
1043 if (wordsBefore == wordsAfter) {
1044 unsigned newWordBits = width % APINT_BITS_PER_WORD;
1045 // The extension is contained to the wordsBefore-1th word.
1046 uint64_t mask = ~0ULL;
1048 mask >>= APINT_BITS_PER_WORD - newWordBits;
1050 if (wordsBefore == 1)
1053 pVal[wordsBefore-1] |= mask;
1054 return clearUnusedBits();
1057 uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits;
1058 uint64_t *newVal = getMemory(wordsAfter);
1059 if (wordsBefore == 1)
1060 newVal[0] = VAL | mask;
1062 for (unsigned i = 0; i < wordsBefore; ++i)
1063 newVal[i] = pVal[i];
1064 newVal[wordsBefore-1] |= mask;
1066 for (unsigned i = wordsBefore; i < wordsAfter; i++)
1068 if (wordsBefore != 1)
1071 return clearUnusedBits();
1074 // Zero extend to a new width.
1075 APInt &APInt::zext(unsigned width) {
1076 assert(width > BitWidth && "Invalid APInt ZeroExtend request");
1077 unsigned wordsBefore = getNumWords();
1079 unsigned wordsAfter = getNumWords();
1080 if (wordsBefore != wordsAfter) {
1081 uint64_t *newVal = getClearedMemory(wordsAfter);
1082 if (wordsBefore == 1)
1085 for (unsigned i = 0; i < wordsBefore; ++i)
1086 newVal[i] = pVal[i];
1087 if (wordsBefore != 1)
1094 APInt &APInt::zextOrTrunc(unsigned width) {
1095 if (BitWidth < width)
1097 if (BitWidth > width)
1098 return trunc(width);
1102 APInt &APInt::sextOrTrunc(unsigned width) {
1103 if (BitWidth < width)
1105 if (BitWidth > width)
1106 return trunc(width);
1110 /// Arithmetic right-shift this APInt by shiftAmt.
1111 /// @brief Arithmetic right-shift function.
1112 APInt APInt::ashr(const APInt &shiftAmt) const {
1113 return ashr((unsigned)shiftAmt.getLimitedValue(BitWidth));
1116 /// Arithmetic right-shift this APInt by shiftAmt.
1117 /// @brief Arithmetic right-shift function.
1118 APInt APInt::ashr(unsigned shiftAmt) const {
1119 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1120 // Handle a degenerate case
1124 // Handle single word shifts with built-in ashr
1125 if (isSingleWord()) {
1126 if (shiftAmt == BitWidth)
1127 return APInt(BitWidth, 0); // undefined
1129 unsigned SignBit = APINT_BITS_PER_WORD - BitWidth;
1130 return APInt(BitWidth,
1131 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1135 // If all the bits were shifted out, the result is, technically, undefined.
1136 // We return -1 if it was negative, 0 otherwise. We check this early to avoid
1137 // issues in the algorithm below.
1138 if (shiftAmt == BitWidth) {
1140 return APInt(BitWidth, -1ULL, true);
1142 return APInt(BitWidth, 0);
1145 // Create some space for the result.
1146 uint64_t * val = new uint64_t[getNumWords()];
1148 // Compute some values needed by the following shift algorithms
1149 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word
1150 unsigned offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift
1151 unsigned breakWord = getNumWords() - 1 - offset; // last word affected
1152 unsigned bitsInWord = whichBit(BitWidth); // how many bits in last word?
1153 if (bitsInWord == 0)
1154 bitsInWord = APINT_BITS_PER_WORD;
1156 // If we are shifting whole words, just move whole words
1157 if (wordShift == 0) {
1158 // Move the words containing significant bits
1159 for (unsigned i = 0; i <= breakWord; ++i)
1160 val[i] = pVal[i+offset]; // move whole word
1162 // Adjust the top significant word for sign bit fill, if negative
1164 if (bitsInWord < APINT_BITS_PER_WORD)
1165 val[breakWord] |= ~0ULL << bitsInWord; // set high bits
1167 // Shift the low order words
1168 for (unsigned i = 0; i < breakWord; ++i) {
1169 // This combines the shifted corresponding word with the low bits from
1170 // the next word (shifted into this word's high bits).
1171 val[i] = (pVal[i+offset] >> wordShift) |
1172 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1175 // Shift the break word. In this case there are no bits from the next word
1176 // to include in this word.
1177 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1179 // Deal with sign extenstion in the break word, and possibly the word before
1182 if (wordShift > bitsInWord) {
1185 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord));
1186 val[breakWord] |= ~0ULL;
1188 val[breakWord] |= (~0ULL << (bitsInWord - wordShift));
1192 // Remaining words are 0 or -1, just assign them.
1193 uint64_t fillValue = (isNegative() ? -1ULL : 0);
1194 for (unsigned i = breakWord+1; i < getNumWords(); ++i)
1196 return APInt(val, BitWidth).clearUnusedBits();
1199 /// Logical right-shift this APInt by shiftAmt.
1200 /// @brief Logical right-shift function.
1201 APInt APInt::lshr(const APInt &shiftAmt) const {
1202 return lshr((unsigned)shiftAmt.getLimitedValue(BitWidth));
1205 /// Logical right-shift this APInt by shiftAmt.
1206 /// @brief Logical right-shift function.
1207 APInt APInt::lshr(unsigned shiftAmt) const {
1208 if (isSingleWord()) {
1209 if (shiftAmt == BitWidth)
1210 return APInt(BitWidth, 0);
1212 return APInt(BitWidth, this->VAL >> shiftAmt);
1215 // If all the bits were shifted out, the result is 0. This avoids issues
1216 // with shifting by the size of the integer type, which produces undefined
1217 // results. We define these "undefined results" to always be 0.
1218 if (shiftAmt == BitWidth)
1219 return APInt(BitWidth, 0);
1221 // If none of the bits are shifted out, the result is *this. This avoids
1222 // issues with shifting by the size of the integer type, which produces
1223 // undefined results in the code below. This is also an optimization.
1227 // Create some space for the result.
1228 uint64_t * val = new uint64_t[getNumWords()];
1230 // If we are shifting less than a word, compute the shift with a simple carry
1231 if (shiftAmt < APINT_BITS_PER_WORD) {
1233 for (int i = getNumWords()-1; i >= 0; --i) {
1234 val[i] = (pVal[i] >> shiftAmt) | carry;
1235 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1237 return APInt(val, BitWidth).clearUnusedBits();
1240 // Compute some values needed by the remaining shift algorithms
1241 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD;
1242 unsigned offset = shiftAmt / APINT_BITS_PER_WORD;
1244 // If we are shifting whole words, just move whole words
1245 if (wordShift == 0) {
1246 for (unsigned i = 0; i < getNumWords() - offset; ++i)
1247 val[i] = pVal[i+offset];
1248 for (unsigned i = getNumWords()-offset; i < getNumWords(); i++)
1250 return APInt(val,BitWidth).clearUnusedBits();
1253 // Shift the low order words
1254 unsigned breakWord = getNumWords() - offset -1;
1255 for (unsigned i = 0; i < breakWord; ++i)
1256 val[i] = (pVal[i+offset] >> wordShift) |
1257 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1258 // Shift the break word.
1259 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1261 // Remaining words are 0
1262 for (unsigned i = breakWord+1; i < getNumWords(); ++i)
1264 return APInt(val, BitWidth).clearUnusedBits();
1267 /// Left-shift this APInt by shiftAmt.
1268 /// @brief Left-shift function.
1269 APInt APInt::shl(const APInt &shiftAmt) const {
1270 // It's undefined behavior in C to shift by BitWidth or greater.
1271 return shl((unsigned)shiftAmt.getLimitedValue(BitWidth));
1274 APInt APInt::shlSlowCase(unsigned shiftAmt) const {
1275 // If all the bits were shifted out, the result is 0. This avoids issues
1276 // with shifting by the size of the integer type, which produces undefined
1277 // results. We define these "undefined results" to always be 0.
1278 if (shiftAmt == BitWidth)
1279 return APInt(BitWidth, 0);
1281 // If none of the bits are shifted out, the result is *this. This avoids a
1282 // lshr by the words size in the loop below which can produce incorrect
1283 // results. It also avoids the expensive computation below for a common case.
1287 // Create some space for the result.
1288 uint64_t * val = new uint64_t[getNumWords()];
1290 // If we are shifting less than a word, do it the easy way
1291 if (shiftAmt < APINT_BITS_PER_WORD) {
1293 for (unsigned i = 0; i < getNumWords(); i++) {
1294 val[i] = pVal[i] << shiftAmt | carry;
1295 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1297 return APInt(val, BitWidth).clearUnusedBits();
1300 // Compute some values needed by the remaining shift algorithms
1301 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD;
1302 unsigned offset = shiftAmt / APINT_BITS_PER_WORD;
1304 // If we are shifting whole words, just move whole words
1305 if (wordShift == 0) {
1306 for (unsigned i = 0; i < offset; i++)
1308 for (unsigned i = offset; i < getNumWords(); i++)
1309 val[i] = pVal[i-offset];
1310 return APInt(val,BitWidth).clearUnusedBits();
1313 // Copy whole words from this to Result.
1314 unsigned i = getNumWords() - 1;
1315 for (; i > offset; --i)
1316 val[i] = pVal[i-offset] << wordShift |
1317 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1318 val[offset] = pVal[0] << wordShift;
1319 for (i = 0; i < offset; ++i)
1321 return APInt(val, BitWidth).clearUnusedBits();
1324 APInt APInt::rotl(const APInt &rotateAmt) const {
1325 return rotl((unsigned)rotateAmt.getLimitedValue(BitWidth));
1328 APInt APInt::rotl(unsigned rotateAmt) const {
1331 // Don't get too fancy, just use existing shift/or facilities
1335 lo.lshr(BitWidth - rotateAmt);
1339 APInt APInt::rotr(const APInt &rotateAmt) const {
1340 return rotr((unsigned)rotateAmt.getLimitedValue(BitWidth));
1343 APInt APInt::rotr(unsigned rotateAmt) const {
1346 // Don't get too fancy, just use existing shift/or facilities
1350 hi.shl(BitWidth - rotateAmt);
1354 // Square Root - this method computes and returns the square root of "this".
1355 // Three mechanisms are used for computation. For small values (<= 5 bits),
1356 // a table lookup is done. This gets some performance for common cases. For
1357 // values using less than 52 bits, the value is converted to double and then
1358 // the libc sqrt function is called. The result is rounded and then converted
1359 // back to a uint64_t which is then used to construct the result. Finally,
1360 // the Babylonian method for computing square roots is used.
1361 APInt APInt::sqrt() const {
1363 // Determine the magnitude of the value.
1364 unsigned magnitude = getActiveBits();
1366 // Use a fast table for some small values. This also gets rid of some
1367 // rounding errors in libc sqrt for small values.
1368 if (magnitude <= 5) {
1369 static const uint8_t results[32] = {
1372 /* 3- 6 */ 2, 2, 2, 2,
1373 /* 7-12 */ 3, 3, 3, 3, 3, 3,
1374 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1375 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1378 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]);
1381 // If the magnitude of the value fits in less than 52 bits (the precision of
1382 // an IEEE double precision floating point value), then we can use the
1383 // libc sqrt function which will probably use a hardware sqrt computation.
1384 // This should be faster than the algorithm below.
1385 if (magnitude < 52) {
1387 // Amazingly, VC++ doesn't have round().
1388 return APInt(BitWidth,
1389 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0]))) + 0.5);
1391 return APInt(BitWidth,
1392 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0])))));
1396 // Okay, all the short cuts are exhausted. We must compute it. The following
1397 // is a classical Babylonian method for computing the square root. This code
1398 // was adapted to APINt from a wikipedia article on such computations.
1399 // See http://www.wikipedia.org/ and go to the page named
1400 // Calculate_an_integer_square_root.
1401 unsigned nbits = BitWidth, i = 4;
1402 APInt testy(BitWidth, 16);
1403 APInt x_old(BitWidth, 1);
1404 APInt x_new(BitWidth, 0);
1405 APInt two(BitWidth, 2);
1407 // Select a good starting value using binary logarithms.
1408 for (;; i += 2, testy = testy.shl(2))
1409 if (i >= nbits || this->ule(testy)) {
1410 x_old = x_old.shl(i / 2);
1414 // Use the Babylonian method to arrive at the integer square root:
1416 x_new = (this->udiv(x_old) + x_old).udiv(two);
1417 if (x_old.ule(x_new))
1422 // Make sure we return the closest approximation
1423 // NOTE: The rounding calculation below is correct. It will produce an
1424 // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1425 // determined to be a rounding issue with pari/gp as it begins to use a
1426 // floating point representation after 192 bits. There are no discrepancies
1427 // between this algorithm and pari/gp for bit widths < 192 bits.
1428 APInt square(x_old * x_old);
1429 APInt nextSquare((x_old + 1) * (x_old +1));
1430 if (this->ult(square))
1432 else if (this->ule(nextSquare)) {
1433 APInt midpoint((nextSquare - square).udiv(two));
1434 APInt offset(*this - square);
1435 if (offset.ult(midpoint))
1440 llvm_unreachable("Error in APInt::sqrt computation");
1444 /// Computes the multiplicative inverse of this APInt for a given modulo. The
1445 /// iterative extended Euclidean algorithm is used to solve for this value,
1446 /// however we simplify it to speed up calculating only the inverse, and take
1447 /// advantage of div+rem calculations. We also use some tricks to avoid copying
1448 /// (potentially large) APInts around.
1449 APInt APInt::multiplicativeInverse(const APInt& modulo) const {
1450 assert(ult(modulo) && "This APInt must be smaller than the modulo");
1452 // Using the properties listed at the following web page (accessed 06/21/08):
1453 // http://www.numbertheory.org/php/euclid.html
1454 // (especially the properties numbered 3, 4 and 9) it can be proved that
1455 // BitWidth bits suffice for all the computations in the algorithm implemented
1456 // below. More precisely, this number of bits suffice if the multiplicative
1457 // inverse exists, but may not suffice for the general extended Euclidean
1460 APInt r[2] = { modulo, *this };
1461 APInt t[2] = { APInt(BitWidth, 0), APInt(BitWidth, 1) };
1462 APInt q(BitWidth, 0);
1465 for (i = 0; r[i^1] != 0; i ^= 1) {
1466 // An overview of the math without the confusing bit-flipping:
1467 // q = r[i-2] / r[i-1]
1468 // r[i] = r[i-2] % r[i-1]
1469 // t[i] = t[i-2] - t[i-1] * q
1470 udivrem(r[i], r[i^1], q, r[i]);
1474 // If this APInt and the modulo are not coprime, there is no multiplicative
1475 // inverse, so return 0. We check this by looking at the next-to-last
1476 // remainder, which is the gcd(*this,modulo) as calculated by the Euclidean
1479 return APInt(BitWidth, 0);
1481 // The next-to-last t is the multiplicative inverse. However, we are
1482 // interested in a positive inverse. Calcuate a positive one from a negative
1483 // one if necessary. A simple addition of the modulo suffices because
1484 // abs(t[i]) is known to be less than *this/2 (see the link above).
1485 return t[i].isNegative() ? t[i] + modulo : t[i];
1488 /// Calculate the magic numbers required to implement a signed integer division
1489 /// by a constant as a sequence of multiplies, adds and shifts. Requires that
1490 /// the divisor not be 0, 1, or -1. Taken from "Hacker's Delight", Henry S.
1491 /// Warren, Jr., chapter 10.
1492 APInt::ms APInt::magic() const {
1493 const APInt& d = *this;
1495 APInt ad, anc, delta, q1, r1, q2, r2, t;
1496 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
1500 t = signedMin + (d.lshr(d.getBitWidth() - 1));
1501 anc = t - 1 - t.urem(ad); // absolute value of nc
1502 p = d.getBitWidth() - 1; // initialize p
1503 q1 = signedMin.udiv(anc); // initialize q1 = 2p/abs(nc)
1504 r1 = signedMin - q1*anc; // initialize r1 = rem(2p,abs(nc))
1505 q2 = signedMin.udiv(ad); // initialize q2 = 2p/abs(d)
1506 r2 = signedMin - q2*ad; // initialize r2 = rem(2p,abs(d))
1509 q1 = q1<<1; // update q1 = 2p/abs(nc)
1510 r1 = r1<<1; // update r1 = rem(2p/abs(nc))
1511 if (r1.uge(anc)) { // must be unsigned comparison
1515 q2 = q2<<1; // update q2 = 2p/abs(d)
1516 r2 = r2<<1; // update r2 = rem(2p/abs(d))
1517 if (r2.uge(ad)) { // must be unsigned comparison
1522 } while (q1.ule(delta) || (q1 == delta && r1 == 0));
1525 if (d.isNegative()) mag.m = -mag.m; // resulting magic number
1526 mag.s = p - d.getBitWidth(); // resulting shift
1530 /// Calculate the magic numbers required to implement an unsigned integer
1531 /// division by a constant as a sequence of multiplies, adds and shifts.
1532 /// Requires that the divisor not be 0. Taken from "Hacker's Delight", Henry
1533 /// S. Warren, Jr., chapter 10.
1534 APInt::mu APInt::magicu() const {
1535 const APInt& d = *this;
1537 APInt nc, delta, q1, r1, q2, r2;
1539 magu.a = 0; // initialize "add" indicator
1540 APInt allOnes = APInt::getAllOnesValue(d.getBitWidth());
1541 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
1542 APInt signedMax = APInt::getSignedMaxValue(d.getBitWidth());
1544 nc = allOnes - (-d).urem(d);
1545 p = d.getBitWidth() - 1; // initialize p
1546 q1 = signedMin.udiv(nc); // initialize q1 = 2p/nc
1547 r1 = signedMin - q1*nc; // initialize r1 = rem(2p,nc)
1548 q2 = signedMax.udiv(d); // initialize q2 = (2p-1)/d
1549 r2 = signedMax - q2*d; // initialize r2 = rem((2p-1),d)
1552 if (r1.uge(nc - r1)) {
1553 q1 = q1 + q1 + 1; // update q1
1554 r1 = r1 + r1 - nc; // update r1
1557 q1 = q1+q1; // update q1
1558 r1 = r1+r1; // update r1
1560 if ((r2 + 1).uge(d - r2)) {
1561 if (q2.uge(signedMax)) magu.a = 1;
1562 q2 = q2+q2 + 1; // update q2
1563 r2 = r2+r2 + 1 - d; // update r2
1566 if (q2.uge(signedMin)) magu.a = 1;
1567 q2 = q2+q2; // update q2
1568 r2 = r2+r2 + 1; // update r2
1571 } while (p < d.getBitWidth()*2 &&
1572 (q1.ult(delta) || (q1 == delta && r1 == 0)));
1573 magu.m = q2 + 1; // resulting magic number
1574 magu.s = p - d.getBitWidth(); // resulting shift
1578 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1579 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1580 /// variables here have the same names as in the algorithm. Comments explain
1581 /// the algorithm and any deviation from it.
1582 static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
1583 unsigned m, unsigned n) {
1584 assert(u && "Must provide dividend");
1585 assert(v && "Must provide divisor");
1586 assert(q && "Must provide quotient");
1587 assert(u != v && u != q && v != q && "Must us different memory");
1588 assert(n>1 && "n must be > 1");
1590 // Knuth uses the value b as the base of the number system. In our case b
1591 // is 2^31 so we just set it to -1u.
1592 uint64_t b = uint64_t(1) << 32;
1595 DEBUG(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n');
1596 DEBUG(dbgs() << "KnuthDiv: original:");
1597 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1598 DEBUG(dbgs() << " by");
1599 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
1600 DEBUG(dbgs() << '\n');
1602 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1603 // u and v by d. Note that we have taken Knuth's advice here to use a power
1604 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1605 // 2 allows us to shift instead of multiply and it is easy to determine the
1606 // shift amount from the leading zeros. We are basically normalizing the u
1607 // and v so that its high bits are shifted to the top of v's range without
1608 // overflow. Note that this can require an extra word in u so that u must
1609 // be of length m+n+1.
1610 unsigned shift = CountLeadingZeros_32(v[n-1]);
1611 unsigned v_carry = 0;
1612 unsigned u_carry = 0;
1614 for (unsigned i = 0; i < m+n; ++i) {
1615 unsigned u_tmp = u[i] >> (32 - shift);
1616 u[i] = (u[i] << shift) | u_carry;
1619 for (unsigned i = 0; i < n; ++i) {
1620 unsigned v_tmp = v[i] >> (32 - shift);
1621 v[i] = (v[i] << shift) | v_carry;
1627 DEBUG(dbgs() << "KnuthDiv: normal:");
1628 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1629 DEBUG(dbgs() << " by");
1630 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
1631 DEBUG(dbgs() << '\n');
1634 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1637 DEBUG(dbgs() << "KnuthDiv: quotient digit #" << j << '\n');
1638 // D3. [Calculate q'.].
1639 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1640 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1641 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1642 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1643 // on v[n-2] determines at high speed most of the cases in which the trial
1644 // value qp is one too large, and it eliminates all cases where qp is two
1646 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1647 DEBUG(dbgs() << "KnuthDiv: dividend == " << dividend << '\n');
1648 uint64_t qp = dividend / v[n-1];
1649 uint64_t rp = dividend % v[n-1];
1650 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1653 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1656 DEBUG(dbgs() << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1658 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1659 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1660 // consists of a simple multiplication by a one-place number, combined with
1663 for (unsigned i = 0; i < n; ++i) {
1664 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1665 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1666 bool borrow = subtrahend > u_tmp;
1667 DEBUG(dbgs() << "KnuthDiv: u_tmp == " << u_tmp
1668 << ", subtrahend == " << subtrahend
1669 << ", borrow = " << borrow << '\n');
1671 uint64_t result = u_tmp - subtrahend;
1673 u[k++] = (unsigned)(result & (b-1)); // subtract low word
1674 u[k++] = (unsigned)(result >> 32); // subtract high word
1675 while (borrow && k <= m+n) { // deal with borrow to the left
1681 DEBUG(dbgs() << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1684 DEBUG(dbgs() << "KnuthDiv: after subtraction:");
1685 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1686 DEBUG(dbgs() << '\n');
1687 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1688 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1689 // true value plus b**(n+1), namely as the b's complement of
1690 // the true value, and a "borrow" to the left should be remembered.
1693 bool carry = true; // true because b's complement is "complement + 1"
1694 for (unsigned i = 0; i <= m+n; ++i) {
1695 u[i] = ~u[i] + carry; // b's complement
1696 carry = carry && u[i] == 0;
1699 DEBUG(dbgs() << "KnuthDiv: after complement:");
1700 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1701 DEBUG(dbgs() << '\n');
1703 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1704 // negative, go to step D6; otherwise go on to step D7.
1705 q[j] = (unsigned)qp;
1707 // D6. [Add back]. The probability that this step is necessary is very
1708 // small, on the order of only 2/b. Make sure that test data accounts for
1709 // this possibility. Decrease q[j] by 1
1711 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1712 // A carry will occur to the left of u[j+n], and it should be ignored
1713 // since it cancels with the borrow that occurred in D4.
1715 for (unsigned i = 0; i < n; i++) {
1716 unsigned limit = std::min(u[j+i],v[i]);
1717 u[j+i] += v[i] + carry;
1718 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1722 DEBUG(dbgs() << "KnuthDiv: after correction:");
1723 DEBUG(for (int i = m+n; i >=0; i--) dbgs() <<" " << u[i]);
1724 DEBUG(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n');
1726 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1729 DEBUG(dbgs() << "KnuthDiv: quotient:");
1730 DEBUG(for (int i = m; i >=0; i--) dbgs() <<" " << q[i]);
1731 DEBUG(dbgs() << '\n');
1733 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1734 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1735 // compute the remainder (urem uses this).
1737 // The value d is expressed by the "shift" value above since we avoided
1738 // multiplication by d by using a shift left. So, all we have to do is
1739 // shift right here. In order to mak
1742 DEBUG(dbgs() << "KnuthDiv: remainder:");
1743 for (int i = n-1; i >= 0; i--) {
1744 r[i] = (u[i] >> shift) | carry;
1745 carry = u[i] << (32 - shift);
1746 DEBUG(dbgs() << " " << r[i]);
1749 for (int i = n-1; i >= 0; i--) {
1751 DEBUG(dbgs() << " " << r[i]);
1754 DEBUG(dbgs() << '\n');
1757 DEBUG(dbgs() << '\n');
1761 void APInt::divide(const APInt LHS, unsigned lhsWords,
1762 const APInt &RHS, unsigned rhsWords,
1763 APInt *Quotient, APInt *Remainder)
1765 assert(lhsWords >= rhsWords && "Fractional result");
1767 // First, compose the values into an array of 32-bit words instead of
1768 // 64-bit words. This is a necessity of both the "short division" algorithm
1769 // and the Knuth "classical algorithm" which requires there to be native
1770 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1771 // can't use 64-bit operands here because we don't have native results of
1772 // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't
1773 // work on large-endian machines.
1774 uint64_t mask = ~0ull >> (sizeof(unsigned)*CHAR_BIT);
1775 unsigned n = rhsWords * 2;
1776 unsigned m = (lhsWords * 2) - n;
1778 // Allocate space for the temporary values we need either on the stack, if
1779 // it will fit, or on the heap if it won't.
1780 unsigned SPACE[128];
1785 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1788 Q = &SPACE[(m+n+1) + n];
1790 R = &SPACE[(m+n+1) + n + (m+n)];
1792 U = new unsigned[m + n + 1];
1793 V = new unsigned[n];
1794 Q = new unsigned[m+n];
1796 R = new unsigned[n];
1799 // Initialize the dividend
1800 memset(U, 0, (m+n+1)*sizeof(unsigned));
1801 for (unsigned i = 0; i < lhsWords; ++i) {
1802 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1803 U[i * 2] = (unsigned)(tmp & mask);
1804 U[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT));
1806 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1808 // Initialize the divisor
1809 memset(V, 0, (n)*sizeof(unsigned));
1810 for (unsigned i = 0; i < rhsWords; ++i) {
1811 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1812 V[i * 2] = (unsigned)(tmp & mask);
1813 V[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT));
1816 // initialize the quotient and remainder
1817 memset(Q, 0, (m+n) * sizeof(unsigned));
1819 memset(R, 0, n * sizeof(unsigned));
1821 // Now, adjust m and n for the Knuth division. n is the number of words in
1822 // the divisor. m is the number of words by which the dividend exceeds the
1823 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1824 // contain any zero words or the Knuth algorithm fails.
1825 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1829 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1832 // If we're left with only a single word for the divisor, Knuth doesn't work
1833 // so we implement the short division algorithm here. This is much simpler
1834 // and faster because we are certain that we can divide a 64-bit quantity
1835 // by a 32-bit quantity at hardware speed and short division is simply a
1836 // series of such operations. This is just like doing short division but we
1837 // are using base 2^32 instead of base 10.
1838 assert(n != 0 && "Divide by zero?");
1840 unsigned divisor = V[0];
1841 unsigned remainder = 0;
1842 for (int i = m+n-1; i >= 0; i--) {
1843 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1844 if (partial_dividend == 0) {
1847 } else if (partial_dividend < divisor) {
1849 remainder = (unsigned)partial_dividend;
1850 } else if (partial_dividend == divisor) {
1854 Q[i] = (unsigned)(partial_dividend / divisor);
1855 remainder = (unsigned)(partial_dividend - (Q[i] * divisor));
1861 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1863 KnuthDiv(U, V, Q, R, m, n);
1866 // If the caller wants the quotient
1868 // Set up the Quotient value's memory.
1869 if (Quotient->BitWidth != LHS.BitWidth) {
1870 if (Quotient->isSingleWord())
1873 delete [] Quotient->pVal;
1874 Quotient->BitWidth = LHS.BitWidth;
1875 if (!Quotient->isSingleWord())
1876 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1880 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1882 if (lhsWords == 1) {
1884 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1885 if (Quotient->isSingleWord())
1886 Quotient->VAL = tmp;
1888 Quotient->pVal[0] = tmp;
1890 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1891 for (unsigned i = 0; i < lhsWords; ++i)
1893 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1897 // If the caller wants the remainder
1899 // Set up the Remainder value's memory.
1900 if (Remainder->BitWidth != RHS.BitWidth) {
1901 if (Remainder->isSingleWord())
1904 delete [] Remainder->pVal;
1905 Remainder->BitWidth = RHS.BitWidth;
1906 if (!Remainder->isSingleWord())
1907 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1911 // The remainder is in R. Reconstitute the remainder into Remainder's low
1913 if (rhsWords == 1) {
1915 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1916 if (Remainder->isSingleWord())
1917 Remainder->VAL = tmp;
1919 Remainder->pVal[0] = tmp;
1921 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1922 for (unsigned i = 0; i < rhsWords; ++i)
1923 Remainder->pVal[i] =
1924 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1928 // Clean up the memory we allocated.
1929 if (U != &SPACE[0]) {
1937 APInt APInt::udiv(const APInt& RHS) const {
1938 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1940 // First, deal with the easy case
1941 if (isSingleWord()) {
1942 assert(RHS.VAL != 0 && "Divide by zero?");
1943 return APInt(BitWidth, VAL / RHS.VAL);
1946 // Get some facts about the LHS and RHS number of bits and words
1947 unsigned rhsBits = RHS.getActiveBits();
1948 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1949 assert(rhsWords && "Divided by zero???");
1950 unsigned lhsBits = this->getActiveBits();
1951 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1953 // Deal with some degenerate cases
1956 return APInt(BitWidth, 0);
1957 else if (lhsWords < rhsWords || this->ult(RHS)) {
1958 // X / Y ===> 0, iff X < Y
1959 return APInt(BitWidth, 0);
1960 } else if (*this == RHS) {
1962 return APInt(BitWidth, 1);
1963 } else if (lhsWords == 1 && rhsWords == 1) {
1964 // All high words are zero, just use native divide
1965 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1968 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1969 APInt Quotient(1,0); // to hold result.
1970 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0);
1974 APInt APInt::urem(const APInt& RHS) const {
1975 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1976 if (isSingleWord()) {
1977 assert(RHS.VAL != 0 && "Remainder by zero?");
1978 return APInt(BitWidth, VAL % RHS.VAL);
1981 // Get some facts about the LHS
1982 unsigned lhsBits = getActiveBits();
1983 unsigned lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1985 // Get some facts about the RHS
1986 unsigned rhsBits = RHS.getActiveBits();
1987 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1988 assert(rhsWords && "Performing remainder operation by zero ???");
1990 // Check the degenerate cases
1991 if (lhsWords == 0) {
1993 return APInt(BitWidth, 0);
1994 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1995 // X % Y ===> X, iff X < Y
1997 } else if (*this == RHS) {
1999 return APInt(BitWidth, 0);
2000 } else if (lhsWords == 1) {
2001 // All high words are zero, just use native remainder
2002 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
2005 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
2006 APInt Remainder(1,0);
2007 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder);
2011 void APInt::udivrem(const APInt &LHS, const APInt &RHS,
2012 APInt &Quotient, APInt &Remainder) {
2013 // Get some size facts about the dividend and divisor
2014 unsigned lhsBits = LHS.getActiveBits();
2015 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
2016 unsigned rhsBits = RHS.getActiveBits();
2017 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
2019 // Check the degenerate cases
2020 if (lhsWords == 0) {
2021 Quotient = 0; // 0 / Y ===> 0
2022 Remainder = 0; // 0 % Y ===> 0
2026 if (lhsWords < rhsWords || LHS.ult(RHS)) {
2027 Remainder = LHS; // X % Y ===> X, iff X < Y
2028 Quotient = 0; // X / Y ===> 0, iff X < Y
2033 Quotient = 1; // X / X ===> 1
2034 Remainder = 0; // X % X ===> 0;
2038 if (lhsWords == 1 && rhsWords == 1) {
2039 // There is only one word to consider so use the native versions.
2040 uint64_t lhsValue = LHS.isSingleWord() ? LHS.VAL : LHS.pVal[0];
2041 uint64_t rhsValue = RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0];
2042 Quotient = APInt(LHS.getBitWidth(), lhsValue / rhsValue);
2043 Remainder = APInt(LHS.getBitWidth(), lhsValue % rhsValue);
2047 // Okay, lets do it the long way
2048 divide(LHS, lhsWords, RHS, rhsWords, &Quotient, &Remainder);
2051 void APInt::fromString(unsigned numbits, const StringRef& str, uint8_t radix) {
2052 // Check our assumptions here
2053 assert(!str.empty() && "Invalid string length");
2054 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
2055 "Radix should be 2, 8, 10, or 16!");
2057 StringRef::iterator p = str.begin();
2058 size_t slen = str.size();
2059 bool isNeg = *p == '-';
2060 if (*p == '-' || *p == '+') {
2063 assert(slen && "String is only a sign, needs a value.");
2065 assert((slen <= numbits || radix != 2) && "Insufficient bit width");
2066 assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width");
2067 assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width");
2068 assert((((slen-1)*64)/22 <= numbits || radix != 10)
2069 && "Insufficient bit width");
2072 if (!isSingleWord())
2073 pVal = getClearedMemory(getNumWords());
2075 // Figure out if we can shift instead of multiply
2076 unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
2078 // Set up an APInt for the digit to add outside the loop so we don't
2079 // constantly construct/destruct it.
2080 APInt apdigit(getBitWidth(), 0);
2081 APInt apradix(getBitWidth(), radix);
2083 // Enter digit traversal loop
2084 for (StringRef::iterator e = str.end(); p != e; ++p) {
2085 unsigned digit = getDigit(*p, radix);
2086 assert(digit < radix && "Invalid character in digit string");
2088 // Shift or multiply the value by the radix
2096 // Add in the digit we just interpreted
2097 if (apdigit.isSingleWord())
2098 apdigit.VAL = digit;
2100 apdigit.pVal[0] = digit;
2103 // If its negative, put it in two's complement form
2110 void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix,
2111 bool Signed) const {
2112 assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2) &&
2113 "Radix should be 2, 8, 10, or 16!");
2115 // First, check for a zero value and just short circuit the logic below.
2121 static const char Digits[] = "0123456789ABCDEF";
2123 if (isSingleWord()) {
2125 char *BufPtr = Buffer+65;
2129 int64_t I = getSExtValue();
2140 *--BufPtr = Digits[N % Radix];
2143 Str.append(BufPtr, Buffer+65);
2149 if (Signed && isNegative()) {
2150 // They want to print the signed version and it is a negative value
2151 // Flip the bits and add one to turn it into the equivalent positive
2152 // value and put a '-' in the result.
2158 // We insert the digits backward, then reverse them to get the right order.
2159 unsigned StartDig = Str.size();
2161 // For the 2, 8 and 16 bit cases, we can just shift instead of divide
2162 // because the number of bits per digit (1, 3 and 4 respectively) divides
2163 // equaly. We just shift until the value is zero.
2165 // Just shift tmp right for each digit width until it becomes zero
2166 unsigned ShiftAmt = (Radix == 16 ? 4 : (Radix == 8 ? 3 : 1));
2167 unsigned MaskAmt = Radix - 1;
2170 unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt;
2171 Str.push_back(Digits[Digit]);
2172 Tmp = Tmp.lshr(ShiftAmt);
2175 APInt divisor(4, 10);
2177 APInt APdigit(1, 0);
2178 APInt tmp2(Tmp.getBitWidth(), 0);
2179 divide(Tmp, Tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
2181 unsigned Digit = (unsigned)APdigit.getZExtValue();
2182 assert(Digit < Radix && "divide failed");
2183 Str.push_back(Digits[Digit]);
2188 // Reverse the digits before returning.
2189 std::reverse(Str.begin()+StartDig, Str.end());
2192 /// toString - This returns the APInt as a std::string. Note that this is an
2193 /// inefficient method. It is better to pass in a SmallVector/SmallString
2194 /// to the methods above.
2195 std::string APInt::toString(unsigned Radix = 10, bool Signed = true) const {
2197 toString(S, Radix, Signed);
2202 void APInt::dump() const {
2203 SmallString<40> S, U;
2204 this->toStringUnsigned(U);
2205 this->toStringSigned(S);
2206 dbgs() << "APInt(" << BitWidth << "b, "
2207 << U.str() << "u " << S.str() << "s)";
2210 void APInt::print(raw_ostream &OS, bool isSigned) const {
2212 this->toString(S, 10, isSigned);
2216 // This implements a variety of operations on a representation of
2217 // arbitrary precision, two's-complement, bignum integer values.
2219 // Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe
2220 // and unrestricting assumption.
2221 #define COMPILE_TIME_ASSERT(cond) extern int CTAssert[(cond) ? 1 : -1]
2222 COMPILE_TIME_ASSERT(integerPartWidth % 2 == 0);
2224 /* Some handy functions local to this file. */
2227 /* Returns the integer part with the least significant BITS set.
2228 BITS cannot be zero. */
2229 static inline integerPart
2230 lowBitMask(unsigned int bits)
2232 assert (bits != 0 && bits <= integerPartWidth);
2234 return ~(integerPart) 0 >> (integerPartWidth - bits);
2237 /* Returns the value of the lower half of PART. */
2238 static inline integerPart
2239 lowHalf(integerPart part)
2241 return part & lowBitMask(integerPartWidth / 2);
2244 /* Returns the value of the upper half of PART. */
2245 static inline integerPart
2246 highHalf(integerPart part)
2248 return part >> (integerPartWidth / 2);
2251 /* Returns the bit number of the most significant set bit of a part.
2252 If the input number has no bits set -1U is returned. */
2254 partMSB(integerPart value)
2256 unsigned int n, msb;
2261 n = integerPartWidth / 2;
2276 /* Returns the bit number of the least significant set bit of a
2277 part. If the input number has no bits set -1U is returned. */
2279 partLSB(integerPart value)
2281 unsigned int n, lsb;
2286 lsb = integerPartWidth - 1;
2287 n = integerPartWidth / 2;
2302 /* Sets the least significant part of a bignum to the input value, and
2303 zeroes out higher parts. */
2305 APInt::tcSet(integerPart *dst, integerPart part, unsigned int parts)
2312 for(i = 1; i < parts; i++)
2316 /* Assign one bignum to another. */
2318 APInt::tcAssign(integerPart *dst, const integerPart *src, unsigned int parts)
2322 for(i = 0; i < parts; i++)
2326 /* Returns true if a bignum is zero, false otherwise. */
2328 APInt::tcIsZero(const integerPart *src, unsigned int parts)
2332 for(i = 0; i < parts; i++)
2339 /* Extract the given bit of a bignum; returns 0 or 1. */
2341 APInt::tcExtractBit(const integerPart *parts, unsigned int bit)
2343 return(parts[bit / integerPartWidth]
2344 & ((integerPart) 1 << bit % integerPartWidth)) != 0;
2347 /* Set the given bit of a bignum. */
2349 APInt::tcSetBit(integerPart *parts, unsigned int bit)
2351 parts[bit / integerPartWidth] |= (integerPart) 1 << (bit % integerPartWidth);
2354 /* Returns the bit number of the least significant set bit of a
2355 number. If the input number has no bits set -1U is returned. */
2357 APInt::tcLSB(const integerPart *parts, unsigned int n)
2359 unsigned int i, lsb;
2361 for(i = 0; i < n; i++) {
2362 if (parts[i] != 0) {
2363 lsb = partLSB(parts[i]);
2365 return lsb + i * integerPartWidth;
2372 /* Returns the bit number of the most significant set bit of a number.
2373 If the input number has no bits set -1U is returned. */
2375 APInt::tcMSB(const integerPart *parts, unsigned int n)
2382 if (parts[n] != 0) {
2383 msb = partMSB(parts[n]);
2385 return msb + n * integerPartWidth;
2392 /* Copy the bit vector of width srcBITS from SRC, starting at bit
2393 srcLSB, to DST, of dstCOUNT parts, such that the bit srcLSB becomes
2394 the least significant bit of DST. All high bits above srcBITS in
2395 DST are zero-filled. */
2397 APInt::tcExtract(integerPart *dst, unsigned int dstCount,const integerPart *src,
2398 unsigned int srcBits, unsigned int srcLSB)
2400 unsigned int firstSrcPart, dstParts, shift, n;
2402 dstParts = (srcBits + integerPartWidth - 1) / integerPartWidth;
2403 assert (dstParts <= dstCount);
2405 firstSrcPart = srcLSB / integerPartWidth;
2406 tcAssign (dst, src + firstSrcPart, dstParts);
2408 shift = srcLSB % integerPartWidth;
2409 tcShiftRight (dst, dstParts, shift);
2411 /* We now have (dstParts * integerPartWidth - shift) bits from SRC
2412 in DST. If this is less that srcBits, append the rest, else
2413 clear the high bits. */
2414 n = dstParts * integerPartWidth - shift;
2416 integerPart mask = lowBitMask (srcBits - n);
2417 dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask)
2418 << n % integerPartWidth);
2419 } else if (n > srcBits) {
2420 if (srcBits % integerPartWidth)
2421 dst[dstParts - 1] &= lowBitMask (srcBits % integerPartWidth);
2424 /* Clear high parts. */
2425 while (dstParts < dstCount)
2426 dst[dstParts++] = 0;
2429 /* DST += RHS + C where C is zero or one. Returns the carry flag. */
2431 APInt::tcAdd(integerPart *dst, const integerPart *rhs,
2432 integerPart c, unsigned int parts)
2438 for(i = 0; i < parts; i++) {
2443 dst[i] += rhs[i] + 1;
2454 /* DST -= RHS + C where C is zero or one. Returns the carry flag. */
2456 APInt::tcSubtract(integerPart *dst, const integerPart *rhs,
2457 integerPart c, unsigned int parts)
2463 for(i = 0; i < parts; i++) {
2468 dst[i] -= rhs[i] + 1;
2479 /* Negate a bignum in-place. */
2481 APInt::tcNegate(integerPart *dst, unsigned int parts)
2483 tcComplement(dst, parts);
2484 tcIncrement(dst, parts);
2487 /* DST += SRC * MULTIPLIER + CARRY if add is true
2488 DST = SRC * MULTIPLIER + CARRY if add is false
2490 Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC
2491 they must start at the same point, i.e. DST == SRC.
2493 If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is
2494 returned. Otherwise DST is filled with the least significant
2495 DSTPARTS parts of the result, and if all of the omitted higher
2496 parts were zero return zero, otherwise overflow occurred and
2499 APInt::tcMultiplyPart(integerPart *dst, const integerPart *src,
2500 integerPart multiplier, integerPart carry,
2501 unsigned int srcParts, unsigned int dstParts,
2506 /* Otherwise our writes of DST kill our later reads of SRC. */
2507 assert(dst <= src || dst >= src + srcParts);
2508 assert(dstParts <= srcParts + 1);
2510 /* N loops; minimum of dstParts and srcParts. */
2511 n = dstParts < srcParts ? dstParts: srcParts;
2513 for(i = 0; i < n; i++) {
2514 integerPart low, mid, high, srcPart;
2516 /* [ LOW, HIGH ] = MULTIPLIER * SRC[i] + DST[i] + CARRY.
2518 This cannot overflow, because
2520 (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1)
2522 which is less than n^2. */
2526 if (multiplier == 0 || srcPart == 0) {
2530 low = lowHalf(srcPart) * lowHalf(multiplier);
2531 high = highHalf(srcPart) * highHalf(multiplier);
2533 mid = lowHalf(srcPart) * highHalf(multiplier);
2534 high += highHalf(mid);
2535 mid <<= integerPartWidth / 2;
2536 if (low + mid < low)
2540 mid = highHalf(srcPart) * lowHalf(multiplier);
2541 high += highHalf(mid);
2542 mid <<= integerPartWidth / 2;
2543 if (low + mid < low)
2547 /* Now add carry. */
2548 if (low + carry < low)
2554 /* And now DST[i], and store the new low part there. */
2555 if (low + dst[i] < low)
2565 /* Full multiplication, there is no overflow. */
2566 assert(i + 1 == dstParts);
2570 /* We overflowed if there is carry. */
2574 /* We would overflow if any significant unwritten parts would be
2575 non-zero. This is true if any remaining src parts are non-zero
2576 and the multiplier is non-zero. */
2578 for(; i < srcParts; i++)
2582 /* We fitted in the narrow destination. */
2587 /* DST = LHS * RHS, where DST has the same width as the operands and
2588 is filled with the least significant parts of the result. Returns
2589 one if overflow occurred, otherwise zero. DST must be disjoint
2590 from both operands. */
2592 APInt::tcMultiply(integerPart *dst, const integerPart *lhs,
2593 const integerPart *rhs, unsigned int parts)
2598 assert(dst != lhs && dst != rhs);
2601 tcSet(dst, 0, parts);
2603 for(i = 0; i < parts; i++)
2604 overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts,
2610 /* DST = LHS * RHS, where DST has width the sum of the widths of the
2611 operands. No overflow occurs. DST must be disjoint from both
2612 operands. Returns the number of parts required to hold the
2615 APInt::tcFullMultiply(integerPart *dst, const integerPart *lhs,
2616 const integerPart *rhs, unsigned int lhsParts,
2617 unsigned int rhsParts)
2619 /* Put the narrower number on the LHS for less loops below. */
2620 if (lhsParts > rhsParts) {
2621 return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts);
2625 assert(dst != lhs && dst != rhs);
2627 tcSet(dst, 0, rhsParts);
2629 for(n = 0; n < lhsParts; n++)
2630 tcMultiplyPart(&dst[n], rhs, lhs[n], 0, rhsParts, rhsParts + 1, true);
2632 n = lhsParts + rhsParts;
2634 return n - (dst[n - 1] == 0);
2638 /* If RHS is zero LHS and REMAINDER are left unchanged, return one.
2639 Otherwise set LHS to LHS / RHS with the fractional part discarded,
2640 set REMAINDER to the remainder, return zero. i.e.
2642 OLD_LHS = RHS * LHS + REMAINDER
2644 SCRATCH is a bignum of the same size as the operands and result for
2645 use by the routine; its contents need not be initialized and are
2646 destroyed. LHS, REMAINDER and SCRATCH must be distinct.
2649 APInt::tcDivide(integerPart *lhs, const integerPart *rhs,
2650 integerPart *remainder, integerPart *srhs,
2653 unsigned int n, shiftCount;
2656 assert(lhs != remainder && lhs != srhs && remainder != srhs);
2658 shiftCount = tcMSB(rhs, parts) + 1;
2659 if (shiftCount == 0)
2662 shiftCount = parts * integerPartWidth - shiftCount;
2663 n = shiftCount / integerPartWidth;
2664 mask = (integerPart) 1 << (shiftCount % integerPartWidth);
2666 tcAssign(srhs, rhs, parts);
2667 tcShiftLeft(srhs, parts, shiftCount);
2668 tcAssign(remainder, lhs, parts);
2669 tcSet(lhs, 0, parts);
2671 /* Loop, subtracting SRHS if REMAINDER is greater and adding that to
2676 compare = tcCompare(remainder, srhs, parts);
2678 tcSubtract(remainder, srhs, 0, parts);
2682 if (shiftCount == 0)
2685 tcShiftRight(srhs, parts, 1);
2686 if ((mask >>= 1) == 0)
2687 mask = (integerPart) 1 << (integerPartWidth - 1), n--;
2693 /* Shift a bignum left COUNT bits in-place. Shifted in bits are zero.
2694 There are no restrictions on COUNT. */
2696 APInt::tcShiftLeft(integerPart *dst, unsigned int parts, unsigned int count)
2699 unsigned int jump, shift;
2701 /* Jump is the inter-part jump; shift is is intra-part shift. */
2702 jump = count / integerPartWidth;
2703 shift = count % integerPartWidth;
2705 while (parts > jump) {
2710 /* dst[i] comes from the two parts src[i - jump] and, if we have
2711 an intra-part shift, src[i - jump - 1]. */
2712 part = dst[parts - jump];
2715 if (parts >= jump + 1)
2716 part |= dst[parts - jump - 1] >> (integerPartWidth - shift);
2727 /* Shift a bignum right COUNT bits in-place. Shifted in bits are
2728 zero. There are no restrictions on COUNT. */
2730 APInt::tcShiftRight(integerPart *dst, unsigned int parts, unsigned int count)
2733 unsigned int i, jump, shift;
2735 /* Jump is the inter-part jump; shift is is intra-part shift. */
2736 jump = count / integerPartWidth;
2737 shift = count % integerPartWidth;
2739 /* Perform the shift. This leaves the most significant COUNT bits
2740 of the result at zero. */
2741 for(i = 0; i < parts; i++) {
2744 if (i + jump >= parts) {
2747 part = dst[i + jump];
2750 if (i + jump + 1 < parts)
2751 part |= dst[i + jump + 1] << (integerPartWidth - shift);
2760 /* Bitwise and of two bignums. */
2762 APInt::tcAnd(integerPart *dst, const integerPart *rhs, unsigned int parts)
2766 for(i = 0; i < parts; i++)
2770 /* Bitwise inclusive or of two bignums. */
2772 APInt::tcOr(integerPart *dst, const integerPart *rhs, unsigned int parts)
2776 for(i = 0; i < parts; i++)
2780 /* Bitwise exclusive or of two bignums. */
2782 APInt::tcXor(integerPart *dst, const integerPart *rhs, unsigned int parts)
2786 for(i = 0; i < parts; i++)
2790 /* Complement a bignum in-place. */
2792 APInt::tcComplement(integerPart *dst, unsigned int parts)
2796 for(i = 0; i < parts; i++)
2800 /* Comparison (unsigned) of two bignums. */
2802 APInt::tcCompare(const integerPart *lhs, const integerPart *rhs,
2807 if (lhs[parts] == rhs[parts])
2810 if (lhs[parts] > rhs[parts])
2819 /* Increment a bignum in-place, return the carry flag. */
2821 APInt::tcIncrement(integerPart *dst, unsigned int parts)
2825 for(i = 0; i < parts; i++)
2832 /* Set the least significant BITS bits of a bignum, clear the
2835 APInt::tcSetLeastSignificantBits(integerPart *dst, unsigned int parts,
2841 while (bits > integerPartWidth) {
2842 dst[i++] = ~(integerPart) 0;
2843 bits -= integerPartWidth;
2847 dst[i++] = ~(integerPart) 0 >> (integerPartWidth - bits);