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, 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 assert(bitPosition < getBitWidth() && "Bit position out of bounds!");
487 return (maskBit(bitPosition) &
488 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0;
491 bool APInt::EqualSlowCase(const APInt& RHS) const {
492 // Get some facts about the number of bits used in the two operands.
493 unsigned n1 = getActiveBits();
494 unsigned n2 = RHS.getActiveBits();
496 // If the number of bits isn't the same, they aren't equal
500 // If the number of bits fits in a word, we only need to compare the low word.
501 if (n1 <= APINT_BITS_PER_WORD)
502 return pVal[0] == RHS.pVal[0];
504 // Otherwise, compare everything
505 for (int i = whichWord(n1 - 1); i >= 0; --i)
506 if (pVal[i] != RHS.pVal[i])
511 bool APInt::EqualSlowCase(uint64_t Val) const {
512 unsigned n = getActiveBits();
513 if (n <= APINT_BITS_PER_WORD)
514 return pVal[0] == Val;
519 bool APInt::ult(const APInt& RHS) const {
520 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
522 return VAL < RHS.VAL;
524 // Get active bit length of both operands
525 unsigned n1 = getActiveBits();
526 unsigned n2 = RHS.getActiveBits();
528 // If magnitude of LHS is less than RHS, return true.
532 // If magnitude of RHS is greather than LHS, return false.
536 // If they bot fit in a word, just compare the low order word
537 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD)
538 return pVal[0] < RHS.pVal[0];
540 // Otherwise, compare all words
541 unsigned topWord = whichWord(std::max(n1,n2)-1);
542 for (int i = topWord; i >= 0; --i) {
543 if (pVal[i] > RHS.pVal[i])
545 if (pVal[i] < RHS.pVal[i])
551 bool APInt::slt(const APInt& RHS) const {
552 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
553 if (isSingleWord()) {
554 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
555 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth);
556 return lhsSext < rhsSext;
561 bool lhsNeg = isNegative();
562 bool rhsNeg = rhs.isNegative();
564 // Sign bit is set so perform two's complement to make it positive
569 // Sign bit is set so perform two's complement to make it positive
574 // Now we have unsigned values to compare so do the comparison if necessary
575 // based on the negativeness of the values.
587 void APInt::setBit(unsigned bitPosition) {
589 VAL |= maskBit(bitPosition);
591 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 void APInt::clearBit(unsigned bitPosition) {
598 VAL &= ~maskBit(bitPosition);
600 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
603 /// @brief Toggle every bit to its opposite value.
605 /// Toggle a given bit to its opposite value whose position is given
606 /// as "bitPosition".
607 /// @brief Toggles a given bit to its opposite value.
608 void APInt::flipBit(unsigned bitPosition) {
609 assert(bitPosition < BitWidth && "Out of the bit-width range!");
610 if ((*this)[bitPosition]) clearBit(bitPosition);
611 else setBit(bitPosition);
614 unsigned APInt::getBitsNeeded(StringRef str, uint8_t radix) {
615 assert(!str.empty() && "Invalid string length");
616 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
617 "Radix should be 2, 8, 10, or 16!");
619 size_t slen = str.size();
621 // Each computation below needs to know if it's negative.
622 StringRef::iterator p = str.begin();
623 unsigned isNegative = *p == '-';
624 if (*p == '-' || *p == '+') {
627 assert(slen && "String is only a sign, needs a value.");
630 // For radixes of power-of-two values, the bits required is accurately and
633 return slen + isNegative;
635 return slen * 3 + isNegative;
637 return slen * 4 + isNegative;
639 // This is grossly inefficient but accurate. We could probably do something
640 // with a computation of roughly slen*64/20 and then adjust by the value of
641 // the first few digits. But, I'm not sure how accurate that could be.
643 // Compute a sufficient number of bits that is always large enough but might
644 // be too large. This avoids the assertion in the constructor. This
645 // calculation doesn't work appropriately for the numbers 0-9, so just use 4
646 // bits in that case.
647 unsigned sufficient = slen == 1 ? 4 : slen * 64/18;
649 // Convert to the actual binary value.
650 APInt tmp(sufficient, StringRef(p, slen), radix);
652 // Compute how many bits are required. If the log is infinite, assume we need
654 unsigned log = tmp.logBase2();
655 if (log == (unsigned)-1) {
656 return isNegative + 1;
658 return isNegative + log + 1;
662 // From http://www.burtleburtle.net, byBob Jenkins.
663 // When targeting x86, both GCC and LLVM seem to recognize this as a
664 // rotate instruction.
665 #define rot(x,k) (((x)<<(k)) | ((x)>>(32-(k))))
667 // From http://www.burtleburtle.net, by Bob Jenkins.
670 a -= c; a ^= rot(c, 4); c += b; \
671 b -= a; b ^= rot(a, 6); a += c; \
672 c -= b; c ^= rot(b, 8); b += a; \
673 a -= c; a ^= rot(c,16); c += b; \
674 b -= a; b ^= rot(a,19); a += c; \
675 c -= b; c ^= rot(b, 4); b += a; \
678 // From http://www.burtleburtle.net, by Bob Jenkins.
679 #define final(a,b,c) \
681 c ^= b; c -= rot(b,14); \
682 a ^= c; a -= rot(c,11); \
683 b ^= a; b -= rot(a,25); \
684 c ^= b; c -= rot(b,16); \
685 a ^= c; a -= rot(c,4); \
686 b ^= a; b -= rot(a,14); \
687 c ^= b; c -= rot(b,24); \
690 // hashword() was adapted from http://www.burtleburtle.net, by Bob
691 // Jenkins. k is a pointer to an array of uint32_t values; length is
692 // the length of the key, in 32-bit chunks. This version only handles
693 // keys that are a multiple of 32 bits in size.
694 static inline uint32_t hashword(const uint64_t *k64, size_t length)
696 const uint32_t *k = reinterpret_cast<const uint32_t *>(k64);
699 /* Set up the internal state */
700 a = b = c = 0xdeadbeef + (((uint32_t)length)<<2);
702 /*------------------------------------------------- handle most of the key */
712 /*------------------------------------------- handle the last 3 uint32_t's */
713 switch (length) { /* all the case statements fall through */
718 case 0: /* case 0: nothing left to add */
721 /*------------------------------------------------------ report the result */
725 // hashword8() was adapted from http://www.burtleburtle.net, by Bob
726 // Jenkins. This computes a 32-bit hash from one 64-bit word. When
727 // targeting x86 (32 or 64 bit), both LLVM and GCC compile this
728 // function into about 35 instructions when inlined.
729 static inline uint32_t hashword8(const uint64_t k64)
732 a = b = c = 0xdeadbeef + 4;
734 a += k64 & 0xffffffff;
742 uint64_t APInt::getHashValue() const {
745 hash = hashword8(VAL);
747 hash = hashword(pVal, getNumWords()*2);
751 /// HiBits - This function returns the high "numBits" bits of this APInt.
752 APInt APInt::getHiBits(unsigned numBits) const {
753 return APIntOps::lshr(*this, BitWidth - numBits);
756 /// LoBits - This function returns the low "numBits" bits of this APInt.
757 APInt APInt::getLoBits(unsigned numBits) const {
758 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
762 unsigned APInt::countLeadingZerosSlowCase() const {
763 // Treat the most significand word differently because it might have
764 // meaningless bits set beyond the precision.
765 unsigned BitsInMSW = BitWidth % APINT_BITS_PER_WORD;
767 if (BitsInMSW) MSWMask = (integerPart(1) << BitsInMSW) - 1;
769 MSWMask = ~integerPart(0);
770 BitsInMSW = APINT_BITS_PER_WORD;
773 unsigned i = getNumWords();
774 integerPart MSW = pVal[i-1] & MSWMask;
776 return CountLeadingZeros_64(MSW) - (APINT_BITS_PER_WORD - BitsInMSW);
778 unsigned Count = BitsInMSW;
779 for (--i; i > 0u; --i) {
781 Count += APINT_BITS_PER_WORD;
783 Count += CountLeadingZeros_64(pVal[i-1]);
790 static unsigned countLeadingOnes_64(uint64_t V, unsigned skip) {
794 while (V && (V & (1ULL << 63))) {
801 unsigned APInt::countLeadingOnes() const {
803 return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth);
805 unsigned highWordBits = BitWidth % APINT_BITS_PER_WORD;
808 highWordBits = APINT_BITS_PER_WORD;
811 shift = APINT_BITS_PER_WORD - highWordBits;
813 int i = getNumWords() - 1;
814 unsigned Count = countLeadingOnes_64(pVal[i], shift);
815 if (Count == highWordBits) {
816 for (i--; i >= 0; --i) {
817 if (pVal[i] == -1ULL)
818 Count += APINT_BITS_PER_WORD;
820 Count += countLeadingOnes_64(pVal[i], 0);
828 unsigned APInt::countTrailingZeros() const {
830 return std::min(unsigned(CountTrailingZeros_64(VAL)), BitWidth);
833 for (; i < getNumWords() && pVal[i] == 0; ++i)
834 Count += APINT_BITS_PER_WORD;
835 if (i < getNumWords())
836 Count += CountTrailingZeros_64(pVal[i]);
837 return std::min(Count, BitWidth);
840 unsigned APInt::countTrailingOnesSlowCase() const {
843 for (; i < getNumWords() && pVal[i] == -1ULL; ++i)
844 Count += APINT_BITS_PER_WORD;
845 if (i < getNumWords())
846 Count += CountTrailingOnes_64(pVal[i]);
847 return std::min(Count, BitWidth);
850 unsigned APInt::countPopulationSlowCase() const {
852 for (unsigned i = 0; i < getNumWords(); ++i)
853 Count += CountPopulation_64(pVal[i]);
857 APInt APInt::byteSwap() const {
858 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
860 return APInt(BitWidth, ByteSwap_16(uint16_t(VAL)));
861 else if (BitWidth == 32)
862 return APInt(BitWidth, ByteSwap_32(unsigned(VAL)));
863 else if (BitWidth == 48) {
864 unsigned Tmp1 = unsigned(VAL >> 16);
865 Tmp1 = ByteSwap_32(Tmp1);
866 uint16_t Tmp2 = uint16_t(VAL);
867 Tmp2 = ByteSwap_16(Tmp2);
868 return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1);
869 } else if (BitWidth == 64)
870 return APInt(BitWidth, ByteSwap_64(VAL));
872 APInt Result(BitWidth, 0);
873 char *pByte = (char*)Result.pVal;
874 for (unsigned i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) {
876 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i];
877 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp;
883 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
885 APInt A = API1, B = API2;
888 B = APIntOps::urem(A, B);
894 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) {
901 // Get the sign bit from the highest order bit
902 bool isNeg = T.I >> 63;
904 // Get the 11-bit exponent and adjust for the 1023 bit bias
905 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
907 // If the exponent is negative, the value is < 0 so just return 0.
909 return APInt(width, 0u);
911 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
912 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
914 // If the exponent doesn't shift all bits out of the mantissa
916 return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
917 APInt(width, mantissa >> (52 - exp));
919 // If the client didn't provide enough bits for us to shift the mantissa into
920 // then the result is undefined, just return 0
921 if (width <= exp - 52)
922 return APInt(width, 0);
924 // Otherwise, we have to shift the mantissa bits up to the right location
925 APInt Tmp(width, mantissa);
926 Tmp = Tmp.shl((unsigned)exp - 52);
927 return isNeg ? -Tmp : Tmp;
930 /// RoundToDouble - This function converts this APInt to a double.
931 /// The layout for double is as following (IEEE Standard 754):
932 /// --------------------------------------
933 /// | Sign Exponent Fraction Bias |
934 /// |-------------------------------------- |
935 /// | 1[63] 11[62-52] 52[51-00] 1023 |
936 /// --------------------------------------
937 double APInt::roundToDouble(bool isSigned) const {
939 // Handle the simple case where the value is contained in one uint64_t.
940 // It is wrong to optimize getWord(0) to VAL; there might be more than one word.
941 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
943 int64_t sext = (int64_t(getWord(0)) << (64-BitWidth)) >> (64-BitWidth);
946 return double(getWord(0));
949 // Determine if the value is negative.
950 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
952 // Construct the absolute value if we're negative.
953 APInt Tmp(isNeg ? -(*this) : (*this));
955 // Figure out how many bits we're using.
956 unsigned n = Tmp.getActiveBits();
958 // The exponent (without bias normalization) is just the number of bits
959 // we are using. Note that the sign bit is gone since we constructed the
963 // Return infinity for exponent overflow
965 if (!isSigned || !isNeg)
966 return std::numeric_limits<double>::infinity();
968 return -std::numeric_limits<double>::infinity();
970 exp += 1023; // Increment for 1023 bias
972 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
973 // extract the high 52 bits from the correct words in pVal.
975 unsigned hiWord = whichWord(n-1);
977 mantissa = Tmp.pVal[0];
979 mantissa >>= n - 52; // shift down, we want the top 52 bits.
981 assert(hiWord > 0 && "huh?");
982 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
983 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
984 mantissa = hibits | lobits;
987 // The leading bit of mantissa is implicit, so get rid of it.
988 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
993 T.I = sign | (exp << 52) | mantissa;
997 // Truncate to new width.
998 APInt &APInt::trunc(unsigned width) {
999 assert(width < BitWidth && "Invalid APInt Truncate request");
1000 assert(width && "Can't truncate to 0 bits");
1001 unsigned wordsBefore = getNumWords();
1003 unsigned wordsAfter = getNumWords();
1004 if (wordsBefore != wordsAfter) {
1005 if (wordsAfter == 1) {
1006 uint64_t *tmp = pVal;
1010 uint64_t *newVal = getClearedMemory(wordsAfter);
1011 for (unsigned i = 0; i < wordsAfter; ++i)
1012 newVal[i] = pVal[i];
1017 return clearUnusedBits();
1020 // Sign extend to a new width.
1021 APInt &APInt::sext(unsigned width) {
1022 assert(width > BitWidth && "Invalid APInt SignExtend request");
1023 // If the sign bit isn't set, this is the same as zext.
1024 if (!isNegative()) {
1029 // The sign bit is set. First, get some facts
1030 unsigned wordsBefore = getNumWords();
1031 unsigned wordBits = BitWidth % APINT_BITS_PER_WORD;
1033 unsigned wordsAfter = getNumWords();
1035 // Mask the high order word appropriately
1036 if (wordsBefore == wordsAfter) {
1037 unsigned newWordBits = width % APINT_BITS_PER_WORD;
1038 // The extension is contained to the wordsBefore-1th word.
1039 uint64_t mask = ~0ULL;
1041 mask >>= APINT_BITS_PER_WORD - newWordBits;
1043 if (wordsBefore == 1)
1046 pVal[wordsBefore-1] |= mask;
1047 return clearUnusedBits();
1050 uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits;
1051 uint64_t *newVal = getMemory(wordsAfter);
1052 if (wordsBefore == 1)
1053 newVal[0] = VAL | mask;
1055 for (unsigned i = 0; i < wordsBefore; ++i)
1056 newVal[i] = pVal[i];
1057 newVal[wordsBefore-1] |= mask;
1059 for (unsigned i = wordsBefore; i < wordsAfter; i++)
1061 if (wordsBefore != 1)
1064 return clearUnusedBits();
1067 // Zero extend to a new width.
1068 APInt &APInt::zext(unsigned width) {
1069 assert(width > BitWidth && "Invalid APInt ZeroExtend request");
1070 unsigned wordsBefore = getNumWords();
1072 unsigned wordsAfter = getNumWords();
1073 if (wordsBefore != wordsAfter) {
1074 uint64_t *newVal = getClearedMemory(wordsAfter);
1075 if (wordsBefore == 1)
1078 for (unsigned i = 0; i < wordsBefore; ++i)
1079 newVal[i] = pVal[i];
1080 if (wordsBefore != 1)
1087 APInt &APInt::zextOrTrunc(unsigned width) {
1088 if (BitWidth < width)
1090 if (BitWidth > width)
1091 return trunc(width);
1095 APInt &APInt::sextOrTrunc(unsigned width) {
1096 if (BitWidth < width)
1098 if (BitWidth > width)
1099 return trunc(width);
1103 /// Arithmetic right-shift this APInt by shiftAmt.
1104 /// @brief Arithmetic right-shift function.
1105 APInt APInt::ashr(const APInt &shiftAmt) const {
1106 return ashr((unsigned)shiftAmt.getLimitedValue(BitWidth));
1109 /// Arithmetic right-shift this APInt by shiftAmt.
1110 /// @brief Arithmetic right-shift function.
1111 APInt APInt::ashr(unsigned shiftAmt) const {
1112 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1113 // Handle a degenerate case
1117 // Handle single word shifts with built-in ashr
1118 if (isSingleWord()) {
1119 if (shiftAmt == BitWidth)
1120 return APInt(BitWidth, 0); // undefined
1122 unsigned SignBit = APINT_BITS_PER_WORD - BitWidth;
1123 return APInt(BitWidth,
1124 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1128 // If all the bits were shifted out, the result is, technically, undefined.
1129 // We return -1 if it was negative, 0 otherwise. We check this early to avoid
1130 // issues in the algorithm below.
1131 if (shiftAmt == BitWidth) {
1133 return APInt(BitWidth, -1ULL, true);
1135 return APInt(BitWidth, 0);
1138 // Create some space for the result.
1139 uint64_t * val = new uint64_t[getNumWords()];
1141 // Compute some values needed by the following shift algorithms
1142 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word
1143 unsigned offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift
1144 unsigned breakWord = getNumWords() - 1 - offset; // last word affected
1145 unsigned bitsInWord = whichBit(BitWidth); // how many bits in last word?
1146 if (bitsInWord == 0)
1147 bitsInWord = APINT_BITS_PER_WORD;
1149 // If we are shifting whole words, just move whole words
1150 if (wordShift == 0) {
1151 // Move the words containing significant bits
1152 for (unsigned i = 0; i <= breakWord; ++i)
1153 val[i] = pVal[i+offset]; // move whole word
1155 // Adjust the top significant word for sign bit fill, if negative
1157 if (bitsInWord < APINT_BITS_PER_WORD)
1158 val[breakWord] |= ~0ULL << bitsInWord; // set high bits
1160 // Shift the low order words
1161 for (unsigned i = 0; i < breakWord; ++i) {
1162 // This combines the shifted corresponding word with the low bits from
1163 // the next word (shifted into this word's high bits).
1164 val[i] = (pVal[i+offset] >> wordShift) |
1165 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1168 // Shift the break word. In this case there are no bits from the next word
1169 // to include in this word.
1170 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1172 // Deal with sign extenstion in the break word, and possibly the word before
1175 if (wordShift > bitsInWord) {
1178 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord));
1179 val[breakWord] |= ~0ULL;
1181 val[breakWord] |= (~0ULL << (bitsInWord - wordShift));
1185 // Remaining words are 0 or -1, just assign them.
1186 uint64_t fillValue = (isNegative() ? -1ULL : 0);
1187 for (unsigned i = breakWord+1; i < getNumWords(); ++i)
1189 return APInt(val, BitWidth).clearUnusedBits();
1192 /// Logical right-shift this APInt by shiftAmt.
1193 /// @brief Logical right-shift function.
1194 APInt APInt::lshr(const APInt &shiftAmt) const {
1195 return lshr((unsigned)shiftAmt.getLimitedValue(BitWidth));
1198 /// Logical right-shift this APInt by shiftAmt.
1199 /// @brief Logical right-shift function.
1200 APInt APInt::lshr(unsigned shiftAmt) const {
1201 if (isSingleWord()) {
1202 if (shiftAmt == BitWidth)
1203 return APInt(BitWidth, 0);
1205 return APInt(BitWidth, this->VAL >> shiftAmt);
1208 // If all the bits were shifted out, the result is 0. This avoids issues
1209 // with shifting by the size of the integer type, which produces undefined
1210 // results. We define these "undefined results" to always be 0.
1211 if (shiftAmt == BitWidth)
1212 return APInt(BitWidth, 0);
1214 // If none of the bits are shifted out, the result is *this. This avoids
1215 // issues with shifting by the size of the integer type, which produces
1216 // undefined results in the code below. This is also an optimization.
1220 // Create some space for the result.
1221 uint64_t * val = new uint64_t[getNumWords()];
1223 // If we are shifting less than a word, compute the shift with a simple carry
1224 if (shiftAmt < APINT_BITS_PER_WORD) {
1226 for (int i = getNumWords()-1; i >= 0; --i) {
1227 val[i] = (pVal[i] >> shiftAmt) | carry;
1228 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1230 return APInt(val, BitWidth).clearUnusedBits();
1233 // Compute some values needed by the remaining shift algorithms
1234 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD;
1235 unsigned offset = shiftAmt / APINT_BITS_PER_WORD;
1237 // If we are shifting whole words, just move whole words
1238 if (wordShift == 0) {
1239 for (unsigned i = 0; i < getNumWords() - offset; ++i)
1240 val[i] = pVal[i+offset];
1241 for (unsigned i = getNumWords()-offset; i < getNumWords(); i++)
1243 return APInt(val,BitWidth).clearUnusedBits();
1246 // Shift the low order words
1247 unsigned breakWord = getNumWords() - offset -1;
1248 for (unsigned i = 0; i < breakWord; ++i)
1249 val[i] = (pVal[i+offset] >> wordShift) |
1250 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1251 // Shift the break word.
1252 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1254 // Remaining words are 0
1255 for (unsigned i = breakWord+1; i < getNumWords(); ++i)
1257 return APInt(val, BitWidth).clearUnusedBits();
1260 /// Left-shift this APInt by shiftAmt.
1261 /// @brief Left-shift function.
1262 APInt APInt::shl(const APInt &shiftAmt) const {
1263 // It's undefined behavior in C to shift by BitWidth or greater.
1264 return shl((unsigned)shiftAmt.getLimitedValue(BitWidth));
1267 APInt APInt::shlSlowCase(unsigned shiftAmt) const {
1268 // If all the bits were shifted out, the result is 0. This avoids issues
1269 // with shifting by the size of the integer type, which produces undefined
1270 // results. We define these "undefined results" to always be 0.
1271 if (shiftAmt == BitWidth)
1272 return APInt(BitWidth, 0);
1274 // If none of the bits are shifted out, the result is *this. This avoids a
1275 // lshr by the words size in the loop below which can produce incorrect
1276 // results. It also avoids the expensive computation below for a common case.
1280 // Create some space for the result.
1281 uint64_t * val = new uint64_t[getNumWords()];
1283 // If we are shifting less than a word, do it the easy way
1284 if (shiftAmt < APINT_BITS_PER_WORD) {
1286 for (unsigned i = 0; i < getNumWords(); i++) {
1287 val[i] = pVal[i] << shiftAmt | carry;
1288 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1290 return APInt(val, BitWidth).clearUnusedBits();
1293 // Compute some values needed by the remaining shift algorithms
1294 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD;
1295 unsigned offset = shiftAmt / APINT_BITS_PER_WORD;
1297 // If we are shifting whole words, just move whole words
1298 if (wordShift == 0) {
1299 for (unsigned i = 0; i < offset; i++)
1301 for (unsigned i = offset; i < getNumWords(); i++)
1302 val[i] = pVal[i-offset];
1303 return APInt(val,BitWidth).clearUnusedBits();
1306 // Copy whole words from this to Result.
1307 unsigned i = getNumWords() - 1;
1308 for (; i > offset; --i)
1309 val[i] = pVal[i-offset] << wordShift |
1310 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1311 val[offset] = pVal[0] << wordShift;
1312 for (i = 0; i < offset; ++i)
1314 return APInt(val, BitWidth).clearUnusedBits();
1317 APInt APInt::rotl(const APInt &rotateAmt) const {
1318 return rotl((unsigned)rotateAmt.getLimitedValue(BitWidth));
1321 APInt APInt::rotl(unsigned rotateAmt) const {
1324 // Don't get too fancy, just use existing shift/or facilities
1328 lo.lshr(BitWidth - rotateAmt);
1332 APInt APInt::rotr(const APInt &rotateAmt) const {
1333 return rotr((unsigned)rotateAmt.getLimitedValue(BitWidth));
1336 APInt APInt::rotr(unsigned rotateAmt) const {
1339 // Don't get too fancy, just use existing shift/or facilities
1343 hi.shl(BitWidth - rotateAmt);
1347 // Square Root - this method computes and returns the square root of "this".
1348 // Three mechanisms are used for computation. For small values (<= 5 bits),
1349 // a table lookup is done. This gets some performance for common cases. For
1350 // values using less than 52 bits, the value is converted to double and then
1351 // the libc sqrt function is called. The result is rounded and then converted
1352 // back to a uint64_t which is then used to construct the result. Finally,
1353 // the Babylonian method for computing square roots is used.
1354 APInt APInt::sqrt() const {
1356 // Determine the magnitude of the value.
1357 unsigned magnitude = getActiveBits();
1359 // Use a fast table for some small values. This also gets rid of some
1360 // rounding errors in libc sqrt for small values.
1361 if (magnitude <= 5) {
1362 static const uint8_t results[32] = {
1365 /* 3- 6 */ 2, 2, 2, 2,
1366 /* 7-12 */ 3, 3, 3, 3, 3, 3,
1367 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1368 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1371 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]);
1374 // If the magnitude of the value fits in less than 52 bits (the precision of
1375 // an IEEE double precision floating point value), then we can use the
1376 // libc sqrt function which will probably use a hardware sqrt computation.
1377 // This should be faster than the algorithm below.
1378 if (magnitude < 52) {
1380 return APInt(BitWidth,
1381 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0])))));
1383 return APInt(BitWidth,
1384 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0]))) + 0.5);
1388 // Okay, all the short cuts are exhausted. We must compute it. The following
1389 // is a classical Babylonian method for computing the square root. This code
1390 // was adapted to APINt from a wikipedia article on such computations.
1391 // See http://www.wikipedia.org/ and go to the page named
1392 // Calculate_an_integer_square_root.
1393 unsigned nbits = BitWidth, i = 4;
1394 APInt testy(BitWidth, 16);
1395 APInt x_old(BitWidth, 1);
1396 APInt x_new(BitWidth, 0);
1397 APInt two(BitWidth, 2);
1399 // Select a good starting value using binary logarithms.
1400 for (;; i += 2, testy = testy.shl(2))
1401 if (i >= nbits || this->ule(testy)) {
1402 x_old = x_old.shl(i / 2);
1406 // Use the Babylonian method to arrive at the integer square root:
1408 x_new = (this->udiv(x_old) + x_old).udiv(two);
1409 if (x_old.ule(x_new))
1414 // Make sure we return the closest approximation
1415 // NOTE: The rounding calculation below is correct. It will produce an
1416 // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1417 // determined to be a rounding issue with pari/gp as it begins to use a
1418 // floating point representation after 192 bits. There are no discrepancies
1419 // between this algorithm and pari/gp for bit widths < 192 bits.
1420 APInt square(x_old * x_old);
1421 APInt nextSquare((x_old + 1) * (x_old +1));
1422 if (this->ult(square))
1424 else if (this->ule(nextSquare)) {
1425 APInt midpoint((nextSquare - square).udiv(two));
1426 APInt offset(*this - square);
1427 if (offset.ult(midpoint))
1432 llvm_unreachable("Error in APInt::sqrt computation");
1436 /// Computes the multiplicative inverse of this APInt for a given modulo. The
1437 /// iterative extended Euclidean algorithm is used to solve for this value,
1438 /// however we simplify it to speed up calculating only the inverse, and take
1439 /// advantage of div+rem calculations. We also use some tricks to avoid copying
1440 /// (potentially large) APInts around.
1441 APInt APInt::multiplicativeInverse(const APInt& modulo) const {
1442 assert(ult(modulo) && "This APInt must be smaller than the modulo");
1444 // Using the properties listed at the following web page (accessed 06/21/08):
1445 // http://www.numbertheory.org/php/euclid.html
1446 // (especially the properties numbered 3, 4 and 9) it can be proved that
1447 // BitWidth bits suffice for all the computations in the algorithm implemented
1448 // below. More precisely, this number of bits suffice if the multiplicative
1449 // inverse exists, but may not suffice for the general extended Euclidean
1452 APInt r[2] = { modulo, *this };
1453 APInt t[2] = { APInt(BitWidth, 0), APInt(BitWidth, 1) };
1454 APInt q(BitWidth, 0);
1457 for (i = 0; r[i^1] != 0; i ^= 1) {
1458 // An overview of the math without the confusing bit-flipping:
1459 // q = r[i-2] / r[i-1]
1460 // r[i] = r[i-2] % r[i-1]
1461 // t[i] = t[i-2] - t[i-1] * q
1462 udivrem(r[i], r[i^1], q, r[i]);
1466 // If this APInt and the modulo are not coprime, there is no multiplicative
1467 // inverse, so return 0. We check this by looking at the next-to-last
1468 // remainder, which is the gcd(*this,modulo) as calculated by the Euclidean
1471 return APInt(BitWidth, 0);
1473 // The next-to-last t is the multiplicative inverse. However, we are
1474 // interested in a positive inverse. Calcuate a positive one from a negative
1475 // one if necessary. A simple addition of the modulo suffices because
1476 // abs(t[i]) is known to be less than *this/2 (see the link above).
1477 return t[i].isNegative() ? t[i] + modulo : t[i];
1480 /// Calculate the magic numbers required to implement a signed integer division
1481 /// by a constant as a sequence of multiplies, adds and shifts. Requires that
1482 /// the divisor not be 0, 1, or -1. Taken from "Hacker's Delight", Henry S.
1483 /// Warren, Jr., chapter 10.
1484 APInt::ms APInt::magic() const {
1485 const APInt& d = *this;
1487 APInt ad, anc, delta, q1, r1, q2, r2, t;
1488 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
1492 t = signedMin + (d.lshr(d.getBitWidth() - 1));
1493 anc = t - 1 - t.urem(ad); // absolute value of nc
1494 p = d.getBitWidth() - 1; // initialize p
1495 q1 = signedMin.udiv(anc); // initialize q1 = 2p/abs(nc)
1496 r1 = signedMin - q1*anc; // initialize r1 = rem(2p,abs(nc))
1497 q2 = signedMin.udiv(ad); // initialize q2 = 2p/abs(d)
1498 r2 = signedMin - q2*ad; // initialize r2 = rem(2p,abs(d))
1501 q1 = q1<<1; // update q1 = 2p/abs(nc)
1502 r1 = r1<<1; // update r1 = rem(2p/abs(nc))
1503 if (r1.uge(anc)) { // must be unsigned comparison
1507 q2 = q2<<1; // update q2 = 2p/abs(d)
1508 r2 = r2<<1; // update r2 = rem(2p/abs(d))
1509 if (r2.uge(ad)) { // must be unsigned comparison
1514 } while (q1.ule(delta) || (q1 == delta && r1 == 0));
1517 if (d.isNegative()) mag.m = -mag.m; // resulting magic number
1518 mag.s = p - d.getBitWidth(); // resulting shift
1522 /// Calculate the magic numbers required to implement an unsigned integer
1523 /// division by a constant as a sequence of multiplies, adds and shifts.
1524 /// Requires that the divisor not be 0. Taken from "Hacker's Delight", Henry
1525 /// S. Warren, Jr., chapter 10.
1526 APInt::mu APInt::magicu() const {
1527 const APInt& d = *this;
1529 APInt nc, delta, q1, r1, q2, r2;
1531 magu.a = 0; // initialize "add" indicator
1532 APInt allOnes = APInt::getAllOnesValue(d.getBitWidth());
1533 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
1534 APInt signedMax = APInt::getSignedMaxValue(d.getBitWidth());
1536 nc = allOnes - (-d).urem(d);
1537 p = d.getBitWidth() - 1; // initialize p
1538 q1 = signedMin.udiv(nc); // initialize q1 = 2p/nc
1539 r1 = signedMin - q1*nc; // initialize r1 = rem(2p,nc)
1540 q2 = signedMax.udiv(d); // initialize q2 = (2p-1)/d
1541 r2 = signedMax - q2*d; // initialize r2 = rem((2p-1),d)
1544 if (r1.uge(nc - r1)) {
1545 q1 = q1 + q1 + 1; // update q1
1546 r1 = r1 + r1 - nc; // update r1
1549 q1 = q1+q1; // update q1
1550 r1 = r1+r1; // update r1
1552 if ((r2 + 1).uge(d - r2)) {
1553 if (q2.uge(signedMax)) magu.a = 1;
1554 q2 = q2+q2 + 1; // update q2
1555 r2 = r2+r2 + 1 - d; // update r2
1558 if (q2.uge(signedMin)) magu.a = 1;
1559 q2 = q2+q2; // update q2
1560 r2 = r2+r2 + 1; // update r2
1563 } while (p < d.getBitWidth()*2 &&
1564 (q1.ult(delta) || (q1 == delta && r1 == 0)));
1565 magu.m = q2 + 1; // resulting magic number
1566 magu.s = p - d.getBitWidth(); // resulting shift
1570 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1571 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1572 /// variables here have the same names as in the algorithm. Comments explain
1573 /// the algorithm and any deviation from it.
1574 static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
1575 unsigned m, unsigned n) {
1576 assert(u && "Must provide dividend");
1577 assert(v && "Must provide divisor");
1578 assert(q && "Must provide quotient");
1579 assert(u != v && u != q && v != q && "Must us different memory");
1580 assert(n>1 && "n must be > 1");
1582 // Knuth uses the value b as the base of the number system. In our case b
1583 // is 2^31 so we just set it to -1u.
1584 uint64_t b = uint64_t(1) << 32;
1587 DEBUG(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n');
1588 DEBUG(dbgs() << "KnuthDiv: original:");
1589 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1590 DEBUG(dbgs() << " by");
1591 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
1592 DEBUG(dbgs() << '\n');
1594 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1595 // u and v by d. Note that we have taken Knuth's advice here to use a power
1596 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1597 // 2 allows us to shift instead of multiply and it is easy to determine the
1598 // shift amount from the leading zeros. We are basically normalizing the u
1599 // and v so that its high bits are shifted to the top of v's range without
1600 // overflow. Note that this can require an extra word in u so that u must
1601 // be of length m+n+1.
1602 unsigned shift = CountLeadingZeros_32(v[n-1]);
1603 unsigned v_carry = 0;
1604 unsigned u_carry = 0;
1606 for (unsigned i = 0; i < m+n; ++i) {
1607 unsigned u_tmp = u[i] >> (32 - shift);
1608 u[i] = (u[i] << shift) | u_carry;
1611 for (unsigned i = 0; i < n; ++i) {
1612 unsigned v_tmp = v[i] >> (32 - shift);
1613 v[i] = (v[i] << shift) | v_carry;
1619 DEBUG(dbgs() << "KnuthDiv: normal:");
1620 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1621 DEBUG(dbgs() << " by");
1622 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
1623 DEBUG(dbgs() << '\n');
1626 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1629 DEBUG(dbgs() << "KnuthDiv: quotient digit #" << j << '\n');
1630 // D3. [Calculate q'.].
1631 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1632 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1633 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1634 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1635 // on v[n-2] determines at high speed most of the cases in which the trial
1636 // value qp is one too large, and it eliminates all cases where qp is two
1638 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1639 DEBUG(dbgs() << "KnuthDiv: dividend == " << dividend << '\n');
1640 uint64_t qp = dividend / v[n-1];
1641 uint64_t rp = dividend % v[n-1];
1642 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1645 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1648 DEBUG(dbgs() << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1650 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1651 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1652 // consists of a simple multiplication by a one-place number, combined with
1655 for (unsigned i = 0; i < n; ++i) {
1656 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1657 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1658 bool borrow = subtrahend > u_tmp;
1659 DEBUG(dbgs() << "KnuthDiv: u_tmp == " << u_tmp
1660 << ", subtrahend == " << subtrahend
1661 << ", borrow = " << borrow << '\n');
1663 uint64_t result = u_tmp - subtrahend;
1665 u[k++] = (unsigned)(result & (b-1)); // subtract low word
1666 u[k++] = (unsigned)(result >> 32); // subtract high word
1667 while (borrow && k <= m+n) { // deal with borrow to the left
1673 DEBUG(dbgs() << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1676 DEBUG(dbgs() << "KnuthDiv: after subtraction:");
1677 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1678 DEBUG(dbgs() << '\n');
1679 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1680 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1681 // true value plus b**(n+1), namely as the b's complement of
1682 // the true value, and a "borrow" to the left should be remembered.
1685 bool carry = true; // true because b's complement is "complement + 1"
1686 for (unsigned i = 0; i <= m+n; ++i) {
1687 u[i] = ~u[i] + carry; // b's complement
1688 carry = carry && u[i] == 0;
1691 DEBUG(dbgs() << "KnuthDiv: after complement:");
1692 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1693 DEBUG(dbgs() << '\n');
1695 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1696 // negative, go to step D6; otherwise go on to step D7.
1697 q[j] = (unsigned)qp;
1699 // D6. [Add back]. The probability that this step is necessary is very
1700 // small, on the order of only 2/b. Make sure that test data accounts for
1701 // this possibility. Decrease q[j] by 1
1703 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1704 // A carry will occur to the left of u[j+n], and it should be ignored
1705 // since it cancels with the borrow that occurred in D4.
1707 for (unsigned i = 0; i < n; i++) {
1708 unsigned limit = std::min(u[j+i],v[i]);
1709 u[j+i] += v[i] + carry;
1710 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1714 DEBUG(dbgs() << "KnuthDiv: after correction:");
1715 DEBUG(for (int i = m+n; i >=0; i--) dbgs() <<" " << u[i]);
1716 DEBUG(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n');
1718 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1721 DEBUG(dbgs() << "KnuthDiv: quotient:");
1722 DEBUG(for (int i = m; i >=0; i--) dbgs() <<" " << q[i]);
1723 DEBUG(dbgs() << '\n');
1725 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1726 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1727 // compute the remainder (urem uses this).
1729 // The value d is expressed by the "shift" value above since we avoided
1730 // multiplication by d by using a shift left. So, all we have to do is
1731 // shift right here. In order to mak
1734 DEBUG(dbgs() << "KnuthDiv: remainder:");
1735 for (int i = n-1; i >= 0; i--) {
1736 r[i] = (u[i] >> shift) | carry;
1737 carry = u[i] << (32 - shift);
1738 DEBUG(dbgs() << " " << r[i]);
1741 for (int i = n-1; i >= 0; i--) {
1743 DEBUG(dbgs() << " " << r[i]);
1746 DEBUG(dbgs() << '\n');
1749 DEBUG(dbgs() << '\n');
1753 void APInt::divide(const APInt LHS, unsigned lhsWords,
1754 const APInt &RHS, unsigned rhsWords,
1755 APInt *Quotient, APInt *Remainder)
1757 assert(lhsWords >= rhsWords && "Fractional result");
1759 // First, compose the values into an array of 32-bit words instead of
1760 // 64-bit words. This is a necessity of both the "short division" algorithm
1761 // and the Knuth "classical algorithm" which requires there to be native
1762 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1763 // can't use 64-bit operands here because we don't have native results of
1764 // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't
1765 // work on large-endian machines.
1766 uint64_t mask = ~0ull >> (sizeof(unsigned)*CHAR_BIT);
1767 unsigned n = rhsWords * 2;
1768 unsigned m = (lhsWords * 2) - n;
1770 // Allocate space for the temporary values we need either on the stack, if
1771 // it will fit, or on the heap if it won't.
1772 unsigned SPACE[128];
1777 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1780 Q = &SPACE[(m+n+1) + n];
1782 R = &SPACE[(m+n+1) + n + (m+n)];
1784 U = new unsigned[m + n + 1];
1785 V = new unsigned[n];
1786 Q = new unsigned[m+n];
1788 R = new unsigned[n];
1791 // Initialize the dividend
1792 memset(U, 0, (m+n+1)*sizeof(unsigned));
1793 for (unsigned i = 0; i < lhsWords; ++i) {
1794 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1795 U[i * 2] = (unsigned)(tmp & mask);
1796 U[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT));
1798 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1800 // Initialize the divisor
1801 memset(V, 0, (n)*sizeof(unsigned));
1802 for (unsigned i = 0; i < rhsWords; ++i) {
1803 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1804 V[i * 2] = (unsigned)(tmp & mask);
1805 V[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT));
1808 // initialize the quotient and remainder
1809 memset(Q, 0, (m+n) * sizeof(unsigned));
1811 memset(R, 0, n * sizeof(unsigned));
1813 // Now, adjust m and n for the Knuth division. n is the number of words in
1814 // the divisor. m is the number of words by which the dividend exceeds the
1815 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1816 // contain any zero words or the Knuth algorithm fails.
1817 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1821 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1824 // If we're left with only a single word for the divisor, Knuth doesn't work
1825 // so we implement the short division algorithm here. This is much simpler
1826 // and faster because we are certain that we can divide a 64-bit quantity
1827 // by a 32-bit quantity at hardware speed and short division is simply a
1828 // series of such operations. This is just like doing short division but we
1829 // are using base 2^32 instead of base 10.
1830 assert(n != 0 && "Divide by zero?");
1832 unsigned divisor = V[0];
1833 unsigned remainder = 0;
1834 for (int i = m+n-1; i >= 0; i--) {
1835 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1836 if (partial_dividend == 0) {
1839 } else if (partial_dividend < divisor) {
1841 remainder = (unsigned)partial_dividend;
1842 } else if (partial_dividend == divisor) {
1846 Q[i] = (unsigned)(partial_dividend / divisor);
1847 remainder = (unsigned)(partial_dividend - (Q[i] * divisor));
1853 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1855 KnuthDiv(U, V, Q, R, m, n);
1858 // If the caller wants the quotient
1860 // Set up the Quotient value's memory.
1861 if (Quotient->BitWidth != LHS.BitWidth) {
1862 if (Quotient->isSingleWord())
1865 delete [] Quotient->pVal;
1866 Quotient->BitWidth = LHS.BitWidth;
1867 if (!Quotient->isSingleWord())
1868 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1870 Quotient->clearAllBits();
1872 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1874 if (lhsWords == 1) {
1876 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1877 if (Quotient->isSingleWord())
1878 Quotient->VAL = tmp;
1880 Quotient->pVal[0] = tmp;
1882 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1883 for (unsigned i = 0; i < lhsWords; ++i)
1885 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1889 // If the caller wants the remainder
1891 // Set up the Remainder value's memory.
1892 if (Remainder->BitWidth != RHS.BitWidth) {
1893 if (Remainder->isSingleWord())
1896 delete [] Remainder->pVal;
1897 Remainder->BitWidth = RHS.BitWidth;
1898 if (!Remainder->isSingleWord())
1899 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1901 Remainder->clearAllBits();
1903 // The remainder is in R. Reconstitute the remainder into Remainder's low
1905 if (rhsWords == 1) {
1907 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1908 if (Remainder->isSingleWord())
1909 Remainder->VAL = tmp;
1911 Remainder->pVal[0] = tmp;
1913 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1914 for (unsigned i = 0; i < rhsWords; ++i)
1915 Remainder->pVal[i] =
1916 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1920 // Clean up the memory we allocated.
1921 if (U != &SPACE[0]) {
1929 APInt APInt::udiv(const APInt& RHS) const {
1930 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1932 // First, deal with the easy case
1933 if (isSingleWord()) {
1934 assert(RHS.VAL != 0 && "Divide by zero?");
1935 return APInt(BitWidth, VAL / RHS.VAL);
1938 // Get some facts about the LHS and RHS number of bits and words
1939 unsigned rhsBits = RHS.getActiveBits();
1940 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1941 assert(rhsWords && "Divided by zero???");
1942 unsigned lhsBits = this->getActiveBits();
1943 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1945 // Deal with some degenerate cases
1948 return APInt(BitWidth, 0);
1949 else if (lhsWords < rhsWords || this->ult(RHS)) {
1950 // X / Y ===> 0, iff X < Y
1951 return APInt(BitWidth, 0);
1952 } else if (*this == RHS) {
1954 return APInt(BitWidth, 1);
1955 } else if (lhsWords == 1 && rhsWords == 1) {
1956 // All high words are zero, just use native divide
1957 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1960 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1961 APInt Quotient(1,0); // to hold result.
1962 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0);
1966 APInt APInt::urem(const APInt& RHS) const {
1967 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1968 if (isSingleWord()) {
1969 assert(RHS.VAL != 0 && "Remainder by zero?");
1970 return APInt(BitWidth, VAL % RHS.VAL);
1973 // Get some facts about the LHS
1974 unsigned lhsBits = getActiveBits();
1975 unsigned lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1977 // Get some facts about the RHS
1978 unsigned rhsBits = RHS.getActiveBits();
1979 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1980 assert(rhsWords && "Performing remainder operation by zero ???");
1982 // Check the degenerate cases
1983 if (lhsWords == 0) {
1985 return APInt(BitWidth, 0);
1986 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1987 // X % Y ===> X, iff X < Y
1989 } else if (*this == RHS) {
1991 return APInt(BitWidth, 0);
1992 } else if (lhsWords == 1) {
1993 // All high words are zero, just use native remainder
1994 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
1997 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1998 APInt Remainder(1,0);
1999 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder);
2003 void APInt::udivrem(const APInt &LHS, const APInt &RHS,
2004 APInt &Quotient, APInt &Remainder) {
2005 // Get some size facts about the dividend and divisor
2006 unsigned lhsBits = LHS.getActiveBits();
2007 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
2008 unsigned rhsBits = RHS.getActiveBits();
2009 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
2011 // Check the degenerate cases
2012 if (lhsWords == 0) {
2013 Quotient = 0; // 0 / Y ===> 0
2014 Remainder = 0; // 0 % Y ===> 0
2018 if (lhsWords < rhsWords || LHS.ult(RHS)) {
2019 Remainder = LHS; // X % Y ===> X, iff X < Y
2020 Quotient = 0; // X / Y ===> 0, iff X < Y
2025 Quotient = 1; // X / X ===> 1
2026 Remainder = 0; // X % X ===> 0;
2030 if (lhsWords == 1 && rhsWords == 1) {
2031 // There is only one word to consider so use the native versions.
2032 uint64_t lhsValue = LHS.isSingleWord() ? LHS.VAL : LHS.pVal[0];
2033 uint64_t rhsValue = RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0];
2034 Quotient = APInt(LHS.getBitWidth(), lhsValue / rhsValue);
2035 Remainder = APInt(LHS.getBitWidth(), lhsValue % rhsValue);
2039 // Okay, lets do it the long way
2040 divide(LHS, lhsWords, RHS, rhsWords, &Quotient, &Remainder);
2043 APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const {
2044 APInt Res = *this+RHS;
2045 Overflow = isNonNegative() == RHS.isNonNegative() &&
2046 Res.isNonNegative() != isNonNegative();
2050 APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const {
2051 APInt Res = *this+RHS;
2052 Overflow = Res.ult(RHS);
2056 APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const {
2057 APInt Res = *this - RHS;
2058 Overflow = isNonNegative() != RHS.isNonNegative() &&
2059 Res.isNonNegative() != isNonNegative();
2063 APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const {
2064 APInt Res = *this-RHS;
2065 Overflow = Res.ugt(*this);
2069 APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const {
2070 // MININT/-1 --> overflow.
2071 Overflow = isMinSignedValue() && RHS.isAllOnesValue();
2075 APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const {
2076 APInt Res = *this * RHS;
2078 if (*this != 0 && RHS != 0)
2079 Overflow = Res.sdiv(RHS) != *this || Res.sdiv(*this) != RHS;
2085 APInt APInt::sshl_ov(unsigned ShAmt, bool &Overflow) const {
2086 Overflow = ShAmt >= getBitWidth();
2088 ShAmt = getBitWidth()-1;
2090 if (isNonNegative()) // Don't allow sign change.
2091 Overflow = ShAmt >= countLeadingZeros();
2093 Overflow = ShAmt >= countLeadingOnes();
2095 return *this << ShAmt;
2101 void APInt::fromString(unsigned numbits, StringRef str, uint8_t radix) {
2102 // Check our assumptions here
2103 assert(!str.empty() && "Invalid string length");
2104 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
2105 "Radix should be 2, 8, 10, or 16!");
2107 StringRef::iterator p = str.begin();
2108 size_t slen = str.size();
2109 bool isNeg = *p == '-';
2110 if (*p == '-' || *p == '+') {
2113 assert(slen && "String is only a sign, needs a value.");
2115 assert((slen <= numbits || radix != 2) && "Insufficient bit width");
2116 assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width");
2117 assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width");
2118 assert((((slen-1)*64)/22 <= numbits || radix != 10) &&
2119 "Insufficient bit width");
2122 if (!isSingleWord())
2123 pVal = getClearedMemory(getNumWords());
2125 // Figure out if we can shift instead of multiply
2126 unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
2128 // Set up an APInt for the digit to add outside the loop so we don't
2129 // constantly construct/destruct it.
2130 APInt apdigit(getBitWidth(), 0);
2131 APInt apradix(getBitWidth(), radix);
2133 // Enter digit traversal loop
2134 for (StringRef::iterator e = str.end(); p != e; ++p) {
2135 unsigned digit = getDigit(*p, radix);
2136 assert(digit < radix && "Invalid character in digit string");
2138 // Shift or multiply the value by the radix
2146 // Add in the digit we just interpreted
2147 if (apdigit.isSingleWord())
2148 apdigit.VAL = digit;
2150 apdigit.pVal[0] = digit;
2153 // If its negative, put it in two's complement form
2156 this->flipAllBits();
2160 void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix,
2161 bool Signed) const {
2162 assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2) &&
2163 "Radix should be 2, 8, 10, or 16!");
2165 // First, check for a zero value and just short circuit the logic below.
2171 static const char Digits[] = "0123456789ABCDEF";
2173 if (isSingleWord()) {
2175 char *BufPtr = Buffer+65;
2181 int64_t I = getSExtValue();
2191 *--BufPtr = Digits[N % Radix];
2194 Str.append(BufPtr, Buffer+65);
2200 if (Signed && isNegative()) {
2201 // They want to print the signed version and it is a negative value
2202 // Flip the bits and add one to turn it into the equivalent positive
2203 // value and put a '-' in the result.
2209 // We insert the digits backward, then reverse them to get the right order.
2210 unsigned StartDig = Str.size();
2212 // For the 2, 8 and 16 bit cases, we can just shift instead of divide
2213 // because the number of bits per digit (1, 3 and 4 respectively) divides
2214 // equaly. We just shift until the value is zero.
2216 // Just shift tmp right for each digit width until it becomes zero
2217 unsigned ShiftAmt = (Radix == 16 ? 4 : (Radix == 8 ? 3 : 1));
2218 unsigned MaskAmt = Radix - 1;
2221 unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt;
2222 Str.push_back(Digits[Digit]);
2223 Tmp = Tmp.lshr(ShiftAmt);
2226 APInt divisor(4, 10);
2228 APInt APdigit(1, 0);
2229 APInt tmp2(Tmp.getBitWidth(), 0);
2230 divide(Tmp, Tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
2232 unsigned Digit = (unsigned)APdigit.getZExtValue();
2233 assert(Digit < Radix && "divide failed");
2234 Str.push_back(Digits[Digit]);
2239 // Reverse the digits before returning.
2240 std::reverse(Str.begin()+StartDig, Str.end());
2243 /// toString - This returns the APInt as a std::string. Note that this is an
2244 /// inefficient method. It is better to pass in a SmallVector/SmallString
2245 /// to the methods above.
2246 std::string APInt::toString(unsigned Radix = 10, bool Signed = true) const {
2248 toString(S, Radix, Signed);
2253 void APInt::dump() const {
2254 SmallString<40> S, U;
2255 this->toStringUnsigned(U);
2256 this->toStringSigned(S);
2257 dbgs() << "APInt(" << BitWidth << "b, "
2258 << U.str() << "u " << S.str() << "s)";
2261 void APInt::print(raw_ostream &OS, bool isSigned) const {
2263 this->toString(S, 10, isSigned);
2267 // This implements a variety of operations on a representation of
2268 // arbitrary precision, two's-complement, bignum integer values.
2270 // Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe
2271 // and unrestricting assumption.
2272 #define COMPILE_TIME_ASSERT(cond) extern int CTAssert[(cond) ? 1 : -1]
2273 COMPILE_TIME_ASSERT(integerPartWidth % 2 == 0);
2275 /* Some handy functions local to this file. */
2278 /* Returns the integer part with the least significant BITS set.
2279 BITS cannot be zero. */
2280 static inline integerPart
2281 lowBitMask(unsigned int bits)
2283 assert(bits != 0 && bits <= integerPartWidth);
2285 return ~(integerPart) 0 >> (integerPartWidth - bits);
2288 /* Returns the value of the lower half of PART. */
2289 static inline integerPart
2290 lowHalf(integerPart part)
2292 return part & lowBitMask(integerPartWidth / 2);
2295 /* Returns the value of the upper half of PART. */
2296 static inline integerPart
2297 highHalf(integerPart part)
2299 return part >> (integerPartWidth / 2);
2302 /* Returns the bit number of the most significant set bit of a part.
2303 If the input number has no bits set -1U is returned. */
2305 partMSB(integerPart value)
2307 unsigned int n, msb;
2312 n = integerPartWidth / 2;
2327 /* Returns the bit number of the least significant set bit of a
2328 part. If the input number has no bits set -1U is returned. */
2330 partLSB(integerPart value)
2332 unsigned int n, lsb;
2337 lsb = integerPartWidth - 1;
2338 n = integerPartWidth / 2;
2353 /* Sets the least significant part of a bignum to the input value, and
2354 zeroes out higher parts. */
2356 APInt::tcSet(integerPart *dst, integerPart part, unsigned int parts)
2363 for (i = 1; i < parts; i++)
2367 /* Assign one bignum to another. */
2369 APInt::tcAssign(integerPart *dst, const integerPart *src, unsigned int parts)
2373 for (i = 0; i < parts; i++)
2377 /* Returns true if a bignum is zero, false otherwise. */
2379 APInt::tcIsZero(const integerPart *src, unsigned int parts)
2383 for (i = 0; i < parts; i++)
2390 /* Extract the given bit of a bignum; returns 0 or 1. */
2392 APInt::tcExtractBit(const integerPart *parts, unsigned int bit)
2394 return (parts[bit / integerPartWidth] &
2395 ((integerPart) 1 << bit % integerPartWidth)) != 0;
2398 /* Set the given bit of a bignum. */
2400 APInt::tcSetBit(integerPart *parts, unsigned int bit)
2402 parts[bit / integerPartWidth] |= (integerPart) 1 << (bit % integerPartWidth);
2405 /* Clears the given bit of a bignum. */
2407 APInt::tcClearBit(integerPart *parts, unsigned int bit)
2409 parts[bit / integerPartWidth] &=
2410 ~((integerPart) 1 << (bit % integerPartWidth));
2413 /* Returns the bit number of the least significant set bit of a
2414 number. If the input number has no bits set -1U is returned. */
2416 APInt::tcLSB(const integerPart *parts, unsigned int n)
2418 unsigned int i, lsb;
2420 for (i = 0; i < n; i++) {
2421 if (parts[i] != 0) {
2422 lsb = partLSB(parts[i]);
2424 return lsb + i * integerPartWidth;
2431 /* Returns the bit number of the most significant set bit of a number.
2432 If the input number has no bits set -1U is returned. */
2434 APInt::tcMSB(const integerPart *parts, unsigned int n)
2441 if (parts[n] != 0) {
2442 msb = partMSB(parts[n]);
2444 return msb + n * integerPartWidth;
2451 /* Copy the bit vector of width srcBITS from SRC, starting at bit
2452 srcLSB, to DST, of dstCOUNT parts, such that the bit srcLSB becomes
2453 the least significant bit of DST. All high bits above srcBITS in
2454 DST are zero-filled. */
2456 APInt::tcExtract(integerPart *dst, unsigned int dstCount,const integerPart *src,
2457 unsigned int srcBits, unsigned int srcLSB)
2459 unsigned int firstSrcPart, dstParts, shift, n;
2461 dstParts = (srcBits + integerPartWidth - 1) / integerPartWidth;
2462 assert(dstParts <= dstCount);
2464 firstSrcPart = srcLSB / integerPartWidth;
2465 tcAssign (dst, src + firstSrcPart, dstParts);
2467 shift = srcLSB % integerPartWidth;
2468 tcShiftRight (dst, dstParts, shift);
2470 /* We now have (dstParts * integerPartWidth - shift) bits from SRC
2471 in DST. If this is less that srcBits, append the rest, else
2472 clear the high bits. */
2473 n = dstParts * integerPartWidth - shift;
2475 integerPart mask = lowBitMask (srcBits - n);
2476 dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask)
2477 << n % integerPartWidth);
2478 } else if (n > srcBits) {
2479 if (srcBits % integerPartWidth)
2480 dst[dstParts - 1] &= lowBitMask (srcBits % integerPartWidth);
2483 /* Clear high parts. */
2484 while (dstParts < dstCount)
2485 dst[dstParts++] = 0;
2488 /* DST += RHS + C where C is zero or one. Returns the carry flag. */
2490 APInt::tcAdd(integerPart *dst, const integerPart *rhs,
2491 integerPart c, unsigned int parts)
2497 for (i = 0; i < parts; i++) {
2502 dst[i] += rhs[i] + 1;
2513 /* DST -= RHS + C where C is zero or one. Returns the carry flag. */
2515 APInt::tcSubtract(integerPart *dst, const integerPart *rhs,
2516 integerPart c, unsigned int parts)
2522 for (i = 0; i < parts; i++) {
2527 dst[i] -= rhs[i] + 1;
2538 /* Negate a bignum in-place. */
2540 APInt::tcNegate(integerPart *dst, unsigned int parts)
2542 tcComplement(dst, parts);
2543 tcIncrement(dst, parts);
2546 /* DST += SRC * MULTIPLIER + CARRY if add is true
2547 DST = SRC * MULTIPLIER + CARRY if add is false
2549 Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC
2550 they must start at the same point, i.e. DST == SRC.
2552 If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is
2553 returned. Otherwise DST is filled with the least significant
2554 DSTPARTS parts of the result, and if all of the omitted higher
2555 parts were zero return zero, otherwise overflow occurred and
2558 APInt::tcMultiplyPart(integerPart *dst, const integerPart *src,
2559 integerPart multiplier, integerPart carry,
2560 unsigned int srcParts, unsigned int dstParts,
2565 /* Otherwise our writes of DST kill our later reads of SRC. */
2566 assert(dst <= src || dst >= src + srcParts);
2567 assert(dstParts <= srcParts + 1);
2569 /* N loops; minimum of dstParts and srcParts. */
2570 n = dstParts < srcParts ? dstParts: srcParts;
2572 for (i = 0; i < n; i++) {
2573 integerPart low, mid, high, srcPart;
2575 /* [ LOW, HIGH ] = MULTIPLIER * SRC[i] + DST[i] + CARRY.
2577 This cannot overflow, because
2579 (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1)
2581 which is less than n^2. */
2585 if (multiplier == 0 || srcPart == 0) {
2589 low = lowHalf(srcPart) * lowHalf(multiplier);
2590 high = highHalf(srcPart) * highHalf(multiplier);
2592 mid = lowHalf(srcPart) * highHalf(multiplier);
2593 high += highHalf(mid);
2594 mid <<= integerPartWidth / 2;
2595 if (low + mid < low)
2599 mid = highHalf(srcPart) * lowHalf(multiplier);
2600 high += highHalf(mid);
2601 mid <<= integerPartWidth / 2;
2602 if (low + mid < low)
2606 /* Now add carry. */
2607 if (low + carry < low)
2613 /* And now DST[i], and store the new low part there. */
2614 if (low + dst[i] < low)
2624 /* Full multiplication, there is no overflow. */
2625 assert(i + 1 == dstParts);
2629 /* We overflowed if there is carry. */
2633 /* We would overflow if any significant unwritten parts would be
2634 non-zero. This is true if any remaining src parts are non-zero
2635 and the multiplier is non-zero. */
2637 for (; i < srcParts; i++)
2641 /* We fitted in the narrow destination. */
2646 /* DST = LHS * RHS, where DST has the same width as the operands and
2647 is filled with the least significant parts of the result. Returns
2648 one if overflow occurred, otherwise zero. DST must be disjoint
2649 from both operands. */
2651 APInt::tcMultiply(integerPart *dst, const integerPart *lhs,
2652 const integerPart *rhs, unsigned int parts)
2657 assert(dst != lhs && dst != rhs);
2660 tcSet(dst, 0, parts);
2662 for (i = 0; i < parts; i++)
2663 overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts,
2669 /* DST = LHS * RHS, where DST has width the sum of the widths of the
2670 operands. No overflow occurs. DST must be disjoint from both
2671 operands. Returns the number of parts required to hold the
2674 APInt::tcFullMultiply(integerPart *dst, const integerPart *lhs,
2675 const integerPart *rhs, unsigned int lhsParts,
2676 unsigned int rhsParts)
2678 /* Put the narrower number on the LHS for less loops below. */
2679 if (lhsParts > rhsParts) {
2680 return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts);
2684 assert(dst != lhs && dst != rhs);
2686 tcSet(dst, 0, rhsParts);
2688 for (n = 0; n < lhsParts; n++)
2689 tcMultiplyPart(&dst[n], rhs, lhs[n], 0, rhsParts, rhsParts + 1, true);
2691 n = lhsParts + rhsParts;
2693 return n - (dst[n - 1] == 0);
2697 /* If RHS is zero LHS and REMAINDER are left unchanged, return one.
2698 Otherwise set LHS to LHS / RHS with the fractional part discarded,
2699 set REMAINDER to the remainder, return zero. i.e.
2701 OLD_LHS = RHS * LHS + REMAINDER
2703 SCRATCH is a bignum of the same size as the operands and result for
2704 use by the routine; its contents need not be initialized and are
2705 destroyed. LHS, REMAINDER and SCRATCH must be distinct.
2708 APInt::tcDivide(integerPart *lhs, const integerPart *rhs,
2709 integerPart *remainder, integerPart *srhs,
2712 unsigned int n, shiftCount;
2715 assert(lhs != remainder && lhs != srhs && remainder != srhs);
2717 shiftCount = tcMSB(rhs, parts) + 1;
2718 if (shiftCount == 0)
2721 shiftCount = parts * integerPartWidth - shiftCount;
2722 n = shiftCount / integerPartWidth;
2723 mask = (integerPart) 1 << (shiftCount % integerPartWidth);
2725 tcAssign(srhs, rhs, parts);
2726 tcShiftLeft(srhs, parts, shiftCount);
2727 tcAssign(remainder, lhs, parts);
2728 tcSet(lhs, 0, parts);
2730 /* Loop, subtracting SRHS if REMAINDER is greater and adding that to
2735 compare = tcCompare(remainder, srhs, parts);
2737 tcSubtract(remainder, srhs, 0, parts);
2741 if (shiftCount == 0)
2744 tcShiftRight(srhs, parts, 1);
2745 if ((mask >>= 1) == 0)
2746 mask = (integerPart) 1 << (integerPartWidth - 1), n--;
2752 /* Shift a bignum left COUNT bits in-place. Shifted in bits are zero.
2753 There are no restrictions on COUNT. */
2755 APInt::tcShiftLeft(integerPart *dst, unsigned int parts, unsigned int count)
2758 unsigned int jump, shift;
2760 /* Jump is the inter-part jump; shift is is intra-part shift. */
2761 jump = count / integerPartWidth;
2762 shift = count % integerPartWidth;
2764 while (parts > jump) {
2769 /* dst[i] comes from the two parts src[i - jump] and, if we have
2770 an intra-part shift, src[i - jump - 1]. */
2771 part = dst[parts - jump];
2774 if (parts >= jump + 1)
2775 part |= dst[parts - jump - 1] >> (integerPartWidth - shift);
2786 /* Shift a bignum right COUNT bits in-place. Shifted in bits are
2787 zero. There are no restrictions on COUNT. */
2789 APInt::tcShiftRight(integerPart *dst, unsigned int parts, unsigned int count)
2792 unsigned int i, jump, shift;
2794 /* Jump is the inter-part jump; shift is is intra-part shift. */
2795 jump = count / integerPartWidth;
2796 shift = count % integerPartWidth;
2798 /* Perform the shift. This leaves the most significant COUNT bits
2799 of the result at zero. */
2800 for (i = 0; i < parts; i++) {
2803 if (i + jump >= parts) {
2806 part = dst[i + jump];
2809 if (i + jump + 1 < parts)
2810 part |= dst[i + jump + 1] << (integerPartWidth - shift);
2819 /* Bitwise and of two bignums. */
2821 APInt::tcAnd(integerPart *dst, const integerPart *rhs, unsigned int parts)
2825 for (i = 0; i < parts; i++)
2829 /* Bitwise inclusive or of two bignums. */
2831 APInt::tcOr(integerPart *dst, const integerPart *rhs, unsigned int parts)
2835 for (i = 0; i < parts; i++)
2839 /* Bitwise exclusive or of two bignums. */
2841 APInt::tcXor(integerPart *dst, const integerPart *rhs, unsigned int parts)
2845 for (i = 0; i < parts; i++)
2849 /* Complement a bignum in-place. */
2851 APInt::tcComplement(integerPart *dst, unsigned int parts)
2855 for (i = 0; i < parts; i++)
2859 /* Comparison (unsigned) of two bignums. */
2861 APInt::tcCompare(const integerPart *lhs, const integerPart *rhs,
2866 if (lhs[parts] == rhs[parts])
2869 if (lhs[parts] > rhs[parts])
2878 /* Increment a bignum in-place, return the carry flag. */
2880 APInt::tcIncrement(integerPart *dst, unsigned int parts)
2884 for (i = 0; i < parts; i++)
2891 /* Set the least significant BITS bits of a bignum, clear the
2894 APInt::tcSetLeastSignificantBits(integerPart *dst, unsigned int parts,
2900 while (bits > integerPartWidth) {
2901 dst[i++] = ~(integerPart) 0;
2902 bits -= integerPartWidth;
2906 dst[i++] = ~(integerPart) 0 >> (integerPartWidth - bits);