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) {
51 if (radix == 16 || radix == 36) {
75 void APInt::initSlowCase(unsigned numBits, uint64_t val, bool isSigned) {
76 pVal = getClearedMemory(getNumWords());
78 if (isSigned && int64_t(val) < 0)
79 for (unsigned i = 1; i < getNumWords(); ++i)
83 void APInt::initSlowCase(const APInt& that) {
84 pVal = getMemory(getNumWords());
85 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE);
88 void APInt::initFromArray(ArrayRef<uint64_t> bigVal) {
89 assert(BitWidth && "Bitwidth too small");
90 assert(bigVal.data() && "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>(bigVal.size(), getNumWords());
98 // Copy the words from bigVal to pVal
99 memcpy(pVal, bigVal.data(), words * APINT_WORD_SIZE);
101 // Make sure unused high bits are cleared
105 APInt::APInt(unsigned numBits, ArrayRef<uint64_t> bigVal)
106 : BitWidth(numBits), VAL(0) {
107 initFromArray(bigVal);
110 APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[])
111 : BitWidth(numBits), VAL(0) {
112 initFromArray(makeArrayRef(bigVal, numWords));
115 APInt::APInt(unsigned numbits, StringRef Str, uint8_t radix)
116 : BitWidth(numbits), VAL(0) {
117 assert(BitWidth && "Bitwidth too small");
118 fromString(numbits, Str, radix);
121 APInt& APInt::AssignSlowCase(const APInt& RHS) {
122 // Don't do anything for X = X
126 if (BitWidth == RHS.getBitWidth()) {
127 // assume same bit-width single-word case is already handled
128 assert(!isSingleWord());
129 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE);
133 if (isSingleWord()) {
134 // assume case where both are single words is already handled
135 assert(!RHS.isSingleWord());
137 pVal = getMemory(RHS.getNumWords());
138 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
139 } else if (getNumWords() == RHS.getNumWords())
140 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
141 else if (RHS.isSingleWord()) {
146 pVal = getMemory(RHS.getNumWords());
147 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
149 BitWidth = RHS.BitWidth;
150 return clearUnusedBits();
153 APInt& APInt::operator=(uint64_t RHS) {
158 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE);
160 return clearUnusedBits();
163 /// Profile - This method 'profiles' an APInt for use with FoldingSet.
164 void APInt::Profile(FoldingSetNodeID& ID) const {
165 ID.AddInteger(BitWidth);
167 if (isSingleWord()) {
172 unsigned NumWords = getNumWords();
173 for (unsigned i = 0; i < NumWords; ++i)
174 ID.AddInteger(pVal[i]);
177 /// add_1 - This function adds a single "digit" integer, y, to the multiple
178 /// "digit" integer array, x[]. x[] is modified to reflect the addition and
179 /// 1 is returned if there is a carry out, otherwise 0 is returned.
180 /// @returns the carry of the addition.
181 static bool add_1(uint64_t dest[], uint64_t x[], unsigned len, uint64_t y) {
182 for (unsigned i = 0; i < len; ++i) {
185 y = 1; // Carry one to next digit.
187 y = 0; // No need to carry so exit early
194 /// @brief Prefix increment operator. Increments the APInt by one.
195 APInt& APInt::operator++() {
199 add_1(pVal, pVal, getNumWords(), 1);
200 return clearUnusedBits();
203 /// sub_1 - This function subtracts a single "digit" (64-bit word), y, from
204 /// the multi-digit integer array, x[], propagating the borrowed 1 value until
205 /// no further borrowing is neeeded or it runs out of "digits" in x. The result
206 /// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted.
207 /// In other words, if y > x then this function returns 1, otherwise 0.
208 /// @returns the borrow out of the subtraction
209 static bool sub_1(uint64_t x[], unsigned len, uint64_t y) {
210 for (unsigned i = 0; i < len; ++i) {
214 y = 1; // We have to "borrow 1" from next "digit"
216 y = 0; // No need to borrow
217 break; // Remaining digits are unchanged so exit early
223 /// @brief Prefix decrement operator. Decrements the APInt by one.
224 APInt& APInt::operator--() {
228 sub_1(pVal, getNumWords(), 1);
229 return clearUnusedBits();
232 /// add - This function adds the integer array x to the integer array Y and
233 /// places the result in dest.
234 /// @returns the carry out from the addition
235 /// @brief General addition of 64-bit integer arrays
236 static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y,
239 for (unsigned i = 0; i< len; ++i) {
240 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x
241 dest[i] = x[i] + y[i] + carry;
242 carry = dest[i] < limit || (carry && dest[i] == limit);
247 /// Adds the RHS APint to this APInt.
248 /// @returns this, after addition of RHS.
249 /// @brief Addition assignment operator.
250 APInt& APInt::operator+=(const APInt& RHS) {
251 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
255 add(pVal, pVal, RHS.pVal, getNumWords());
257 return clearUnusedBits();
260 /// Subtracts the integer array y from the integer array x
261 /// @returns returns the borrow out.
262 /// @brief Generalized subtraction of 64-bit integer arrays.
263 static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y,
266 for (unsigned i = 0; i < len; ++i) {
267 uint64_t x_tmp = borrow ? x[i] - 1 : x[i];
268 borrow = y[i] > x_tmp || (borrow && x[i] == 0);
269 dest[i] = x_tmp - y[i];
274 /// Subtracts the RHS APInt from this APInt
275 /// @returns this, after subtraction
276 /// @brief Subtraction assignment operator.
277 APInt& APInt::operator-=(const APInt& RHS) {
278 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
282 sub(pVal, pVal, RHS.pVal, getNumWords());
283 return clearUnusedBits();
286 /// Multiplies an integer array, x, by a uint64_t integer and places the result
288 /// @returns the carry out of the multiplication.
289 /// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer.
290 static uint64_t mul_1(uint64_t dest[], uint64_t x[], unsigned len, uint64_t y) {
291 // Split y into high 32-bit part (hy) and low 32-bit part (ly)
292 uint64_t ly = y & 0xffffffffULL, hy = y >> 32;
295 // For each digit of x.
296 for (unsigned i = 0; i < len; ++i) {
297 // Split x into high and low words
298 uint64_t lx = x[i] & 0xffffffffULL;
299 uint64_t hx = x[i] >> 32;
300 // hasCarry - A flag to indicate if there is a carry to the next digit.
301 // hasCarry == 0, no carry
302 // hasCarry == 1, has carry
303 // hasCarry == 2, no carry and the calculation result == 0.
304 uint8_t hasCarry = 0;
305 dest[i] = carry + lx * ly;
306 // Determine if the add above introduces carry.
307 hasCarry = (dest[i] < carry) ? 1 : 0;
308 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0);
309 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) +
310 // (2^32 - 1) + 2^32 = 2^64.
311 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
313 carry += (lx * hy) & 0xffffffffULL;
314 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL);
315 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) +
316 (carry >> 32) + ((lx * hy) >> 32) + hx * hy;
321 /// Multiplies integer array x by integer array y and stores the result into
322 /// the integer array dest. Note that dest's size must be >= xlen + ylen.
323 /// @brief Generalized multiplicate of integer arrays.
324 static void mul(uint64_t dest[], uint64_t x[], unsigned xlen, uint64_t y[],
326 dest[xlen] = mul_1(dest, x, xlen, y[0]);
327 for (unsigned i = 1; i < ylen; ++i) {
328 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32;
329 uint64_t carry = 0, lx = 0, hx = 0;
330 for (unsigned j = 0; j < xlen; ++j) {
331 lx = x[j] & 0xffffffffULL;
333 // hasCarry - A flag to indicate if has carry.
334 // hasCarry == 0, no carry
335 // hasCarry == 1, has carry
336 // hasCarry == 2, no carry and the calculation result == 0.
337 uint8_t hasCarry = 0;
338 uint64_t resul = carry + lx * ly;
339 hasCarry = (resul < carry) ? 1 : 0;
340 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32);
341 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
343 carry += (lx * hy) & 0xffffffffULL;
344 resul = (carry << 32) | (resul & 0xffffffffULL);
346 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+
347 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) +
348 ((lx * hy) >> 32) + hx * hy;
350 dest[i+xlen] = carry;
354 APInt& APInt::operator*=(const APInt& RHS) {
355 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
356 if (isSingleWord()) {
362 // Get some bit facts about LHS and check for zero
363 unsigned lhsBits = getActiveBits();
364 unsigned lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1;
369 // Get some bit facts about RHS and check for zero
370 unsigned rhsBits = RHS.getActiveBits();
371 unsigned rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1;
378 // Allocate space for the result
379 unsigned destWords = rhsWords + lhsWords;
380 uint64_t *dest = getMemory(destWords);
382 // Perform the long multiply
383 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords);
385 // Copy result back into *this
387 unsigned wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords;
388 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE);
391 // delete dest array and return
396 APInt& APInt::operator&=(const APInt& RHS) {
397 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
398 if (isSingleWord()) {
402 unsigned numWords = getNumWords();
403 for (unsigned i = 0; i < numWords; ++i)
404 pVal[i] &= RHS.pVal[i];
408 APInt& APInt::operator|=(const APInt& RHS) {
409 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
410 if (isSingleWord()) {
414 unsigned numWords = getNumWords();
415 for (unsigned i = 0; i < numWords; ++i)
416 pVal[i] |= RHS.pVal[i];
420 APInt& APInt::operator^=(const APInt& RHS) {
421 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
422 if (isSingleWord()) {
424 this->clearUnusedBits();
427 unsigned numWords = getNumWords();
428 for (unsigned i = 0; i < numWords; ++i)
429 pVal[i] ^= RHS.pVal[i];
430 return clearUnusedBits();
433 APInt APInt::AndSlowCase(const APInt& RHS) const {
434 unsigned numWords = getNumWords();
435 uint64_t* val = getMemory(numWords);
436 for (unsigned i = 0; i < numWords; ++i)
437 val[i] = pVal[i] & RHS.pVal[i];
438 return APInt(val, getBitWidth());
441 APInt APInt::OrSlowCase(const APInt& RHS) const {
442 unsigned numWords = getNumWords();
443 uint64_t *val = getMemory(numWords);
444 for (unsigned i = 0; i < numWords; ++i)
445 val[i] = pVal[i] | RHS.pVal[i];
446 return APInt(val, getBitWidth());
449 APInt APInt::XorSlowCase(const APInt& RHS) const {
450 unsigned numWords = getNumWords();
451 uint64_t *val = getMemory(numWords);
452 for (unsigned i = 0; i < numWords; ++i)
453 val[i] = pVal[i] ^ RHS.pVal[i];
455 // 0^0==1 so clear the high bits in case they got set.
456 return APInt(val, getBitWidth()).clearUnusedBits();
459 bool APInt::operator !() const {
463 for (unsigned i = 0; i < getNumWords(); ++i)
469 APInt APInt::operator*(const APInt& RHS) const {
470 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
472 return APInt(BitWidth, VAL * RHS.VAL);
478 APInt APInt::operator+(const APInt& RHS) const {
479 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
481 return APInt(BitWidth, VAL + RHS.VAL);
482 APInt Result(BitWidth, 0);
483 add(Result.pVal, this->pVal, RHS.pVal, getNumWords());
484 return Result.clearUnusedBits();
487 APInt APInt::operator-(const APInt& RHS) const {
488 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
490 return APInt(BitWidth, VAL - RHS.VAL);
491 APInt Result(BitWidth, 0);
492 sub(Result.pVal, this->pVal, RHS.pVal, getNumWords());
493 return Result.clearUnusedBits();
496 bool APInt::operator[](unsigned bitPosition) const {
497 assert(bitPosition < getBitWidth() && "Bit position out of bounds!");
498 return (maskBit(bitPosition) &
499 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0;
502 bool APInt::EqualSlowCase(const APInt& RHS) const {
503 // Get some facts about the number of bits used in the two operands.
504 unsigned n1 = getActiveBits();
505 unsigned n2 = RHS.getActiveBits();
507 // If the number of bits isn't the same, they aren't equal
511 // If the number of bits fits in a word, we only need to compare the low word.
512 if (n1 <= APINT_BITS_PER_WORD)
513 return pVal[0] == RHS.pVal[0];
515 // Otherwise, compare everything
516 for (int i = whichWord(n1 - 1); i >= 0; --i)
517 if (pVal[i] != RHS.pVal[i])
522 bool APInt::EqualSlowCase(uint64_t Val) const {
523 unsigned n = getActiveBits();
524 if (n <= APINT_BITS_PER_WORD)
525 return pVal[0] == Val;
530 bool APInt::ult(const APInt& RHS) const {
531 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
533 return VAL < RHS.VAL;
535 // Get active bit length of both operands
536 unsigned n1 = getActiveBits();
537 unsigned n2 = RHS.getActiveBits();
539 // If magnitude of LHS is less than RHS, return true.
543 // If magnitude of RHS is greather than LHS, return false.
547 // If they bot fit in a word, just compare the low order word
548 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD)
549 return pVal[0] < RHS.pVal[0];
551 // Otherwise, compare all words
552 unsigned topWord = whichWord(std::max(n1,n2)-1);
553 for (int i = topWord; i >= 0; --i) {
554 if (pVal[i] > RHS.pVal[i])
556 if (pVal[i] < RHS.pVal[i])
562 bool APInt::slt(const APInt& RHS) const {
563 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
564 if (isSingleWord()) {
565 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
566 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth);
567 return lhsSext < rhsSext;
572 bool lhsNeg = isNegative();
573 bool rhsNeg = rhs.isNegative();
575 // Sign bit is set so perform two's complement to make it positive
580 // Sign bit is set so perform two's complement to make it positive
585 // Now we have unsigned values to compare so do the comparison if necessary
586 // based on the negativeness of the values.
598 void APInt::setBit(unsigned bitPosition) {
600 VAL |= maskBit(bitPosition);
602 pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
605 /// Set the given bit to 0 whose position is given as "bitPosition".
606 /// @brief Set a given bit to 0.
607 void APInt::clearBit(unsigned bitPosition) {
609 VAL &= ~maskBit(bitPosition);
611 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
614 /// @brief Toggle every bit to its opposite value.
616 /// Toggle a given bit to its opposite value whose position is given
617 /// as "bitPosition".
618 /// @brief Toggles a given bit to its opposite value.
619 void APInt::flipBit(unsigned bitPosition) {
620 assert(bitPosition < BitWidth && "Out of the bit-width range!");
621 if ((*this)[bitPosition]) clearBit(bitPosition);
622 else setBit(bitPosition);
625 unsigned APInt::getBitsNeeded(StringRef str, uint8_t radix) {
626 assert(!str.empty() && "Invalid string length");
627 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||
629 "Radix should be 2, 8, 10, 16, or 36!");
631 size_t slen = str.size();
633 // Each computation below needs to know if it's negative.
634 StringRef::iterator p = str.begin();
635 unsigned isNegative = *p == '-';
636 if (*p == '-' || *p == '+') {
639 assert(slen && "String is only a sign, needs a value.");
642 // For radixes of power-of-two values, the bits required is accurately and
645 return slen + isNegative;
647 return slen * 3 + isNegative;
649 return slen * 4 + isNegative;
653 // This is grossly inefficient but accurate. We could probably do something
654 // with a computation of roughly slen*64/20 and then adjust by the value of
655 // the first few digits. But, I'm not sure how accurate that could be.
657 // Compute a sufficient number of bits that is always large enough but might
658 // be too large. This avoids the assertion in the constructor. This
659 // calculation doesn't work appropriately for the numbers 0-9, so just use 4
660 // bits in that case.
662 = radix == 10? (slen == 1 ? 4 : slen * 64/18)
663 : (slen == 1 ? 7 : slen * 16/3);
665 // Convert to the actual binary value.
666 APInt tmp(sufficient, StringRef(p, slen), radix);
668 // Compute how many bits are required. If the log is infinite, assume we need
670 unsigned log = tmp.logBase2();
671 if (log == (unsigned)-1) {
672 return isNegative + 1;
674 return isNegative + log + 1;
678 // From http://www.burtleburtle.net, byBob Jenkins.
679 // When targeting x86, both GCC and LLVM seem to recognize this as a
680 // rotate instruction.
681 #define rot(x,k) (((x)<<(k)) | ((x)>>(32-(k))))
683 // From http://www.burtleburtle.net, by Bob Jenkins.
686 a -= c; a ^= rot(c, 4); c += b; \
687 b -= a; b ^= rot(a, 6); a += c; \
688 c -= b; c ^= rot(b, 8); b += a; \
689 a -= c; a ^= rot(c,16); c += b; \
690 b -= a; b ^= rot(a,19); a += c; \
691 c -= b; c ^= rot(b, 4); b += a; \
694 // From http://www.burtleburtle.net, by Bob Jenkins.
695 #define final(a,b,c) \
697 c ^= b; c -= rot(b,14); \
698 a ^= c; a -= rot(c,11); \
699 b ^= a; b -= rot(a,25); \
700 c ^= b; c -= rot(b,16); \
701 a ^= c; a -= rot(c,4); \
702 b ^= a; b -= rot(a,14); \
703 c ^= b; c -= rot(b,24); \
706 // hashword() was adapted from http://www.burtleburtle.net, by Bob
707 // Jenkins. k is a pointer to an array of uint32_t values; length is
708 // the length of the key, in 32-bit chunks. This version only handles
709 // keys that are a multiple of 32 bits in size.
710 static inline uint32_t hashword(const uint64_t *k64, size_t length)
712 const uint32_t *k = reinterpret_cast<const uint32_t *>(k64);
715 /* Set up the internal state */
716 a = b = c = 0xdeadbeef + (((uint32_t)length)<<2);
718 /*------------------------------------------------- handle most of the key */
728 /*------------------------------------------- handle the last 3 uint32_t's */
729 switch (length) { /* all the case statements fall through */
734 case 0: /* case 0: nothing left to add */
737 /*------------------------------------------------------ report the result */
741 // hashword8() was adapted from http://www.burtleburtle.net, by Bob
742 // Jenkins. This computes a 32-bit hash from one 64-bit word. When
743 // targeting x86 (32 or 64 bit), both LLVM and GCC compile this
744 // function into about 35 instructions when inlined.
745 static inline uint32_t hashword8(const uint64_t k64)
748 a = b = c = 0xdeadbeef + 4;
750 a += k64 & 0xffffffff;
758 uint64_t APInt::getHashValue() const {
761 hash = hashword8(VAL);
763 hash = hashword(pVal, getNumWords()*2);
767 /// HiBits - This function returns the high "numBits" bits of this APInt.
768 APInt APInt::getHiBits(unsigned numBits) const {
769 return APIntOps::lshr(*this, BitWidth - numBits);
772 /// LoBits - This function returns the low "numBits" bits of this APInt.
773 APInt APInt::getLoBits(unsigned numBits) const {
774 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
778 unsigned APInt::countLeadingZerosSlowCase() const {
779 // Treat the most significand word differently because it might have
780 // meaningless bits set beyond the precision.
781 unsigned BitsInMSW = BitWidth % APINT_BITS_PER_WORD;
783 if (BitsInMSW) MSWMask = (integerPart(1) << BitsInMSW) - 1;
785 MSWMask = ~integerPart(0);
786 BitsInMSW = APINT_BITS_PER_WORD;
789 unsigned i = getNumWords();
790 integerPart MSW = pVal[i-1] & MSWMask;
792 return CountLeadingZeros_64(MSW) - (APINT_BITS_PER_WORD - BitsInMSW);
794 unsigned Count = BitsInMSW;
795 for (--i; i > 0u; --i) {
797 Count += APINT_BITS_PER_WORD;
799 Count += CountLeadingZeros_64(pVal[i-1]);
806 static unsigned countLeadingOnes_64(uint64_t V, unsigned skip) {
810 while (V && (V & (1ULL << 63))) {
817 unsigned APInt::countLeadingOnes() const {
819 return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth);
821 unsigned highWordBits = BitWidth % APINT_BITS_PER_WORD;
824 highWordBits = APINT_BITS_PER_WORD;
827 shift = APINT_BITS_PER_WORD - highWordBits;
829 int i = getNumWords() - 1;
830 unsigned Count = countLeadingOnes_64(pVal[i], shift);
831 if (Count == highWordBits) {
832 for (i--; i >= 0; --i) {
833 if (pVal[i] == -1ULL)
834 Count += APINT_BITS_PER_WORD;
836 Count += countLeadingOnes_64(pVal[i], 0);
844 unsigned APInt::countTrailingZeros() const {
846 return std::min(unsigned(CountTrailingZeros_64(VAL)), BitWidth);
849 for (; i < getNumWords() && pVal[i] == 0; ++i)
850 Count += APINT_BITS_PER_WORD;
851 if (i < getNumWords())
852 Count += CountTrailingZeros_64(pVal[i]);
853 return std::min(Count, BitWidth);
856 unsigned APInt::countTrailingOnesSlowCase() const {
859 for (; i < getNumWords() && pVal[i] == -1ULL; ++i)
860 Count += APINT_BITS_PER_WORD;
861 if (i < getNumWords())
862 Count += CountTrailingOnes_64(pVal[i]);
863 return std::min(Count, BitWidth);
866 unsigned APInt::countPopulationSlowCase() const {
868 for (unsigned i = 0; i < getNumWords(); ++i)
869 Count += CountPopulation_64(pVal[i]);
873 /// Perform a logical right-shift from Src to Dst, which must be equal or
874 /// non-overlapping, of Words words, by Shift, which must be less than 64.
875 static void lshrNear(uint64_t *Dst, uint64_t *Src, unsigned Words,
878 for (int I = Words - 1; I >= 0; --I) {
879 uint64_t Tmp = Src[I];
880 Dst[I] = (Tmp >> Shift) | Carry;
881 Carry = Tmp << (64 - Shift);
885 APInt APInt::byteSwap() const {
886 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
888 return APInt(BitWidth, ByteSwap_16(uint16_t(VAL)));
890 return APInt(BitWidth, ByteSwap_32(unsigned(VAL)));
891 if (BitWidth == 48) {
892 unsigned Tmp1 = unsigned(VAL >> 16);
893 Tmp1 = ByteSwap_32(Tmp1);
894 uint16_t Tmp2 = uint16_t(VAL);
895 Tmp2 = ByteSwap_16(Tmp2);
896 return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1);
899 return APInt(BitWidth, ByteSwap_64(VAL));
901 APInt Result(getNumWords() * APINT_BITS_PER_WORD, 0);
902 for (unsigned I = 0, N = getNumWords(); I != N; ++I)
903 Result.pVal[I] = ByteSwap_64(pVal[N - I - 1]);
904 if (Result.BitWidth != BitWidth) {
905 lshrNear(Result.pVal, Result.pVal, getNumWords(),
906 Result.BitWidth - BitWidth);
907 Result.BitWidth = BitWidth;
912 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
914 APInt A = API1, B = API2;
917 B = APIntOps::urem(A, B);
923 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) {
930 // Get the sign bit from the highest order bit
931 bool isNeg = T.I >> 63;
933 // Get the 11-bit exponent and adjust for the 1023 bit bias
934 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
936 // If the exponent is negative, the value is < 0 so just return 0.
938 return APInt(width, 0u);
940 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
941 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
943 // If the exponent doesn't shift all bits out of the mantissa
945 return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
946 APInt(width, mantissa >> (52 - exp));
948 // If the client didn't provide enough bits for us to shift the mantissa into
949 // then the result is undefined, just return 0
950 if (width <= exp - 52)
951 return APInt(width, 0);
953 // Otherwise, we have to shift the mantissa bits up to the right location
954 APInt Tmp(width, mantissa);
955 Tmp = Tmp.shl((unsigned)exp - 52);
956 return isNeg ? -Tmp : Tmp;
959 /// RoundToDouble - This function converts this APInt to a double.
960 /// The layout for double is as following (IEEE Standard 754):
961 /// --------------------------------------
962 /// | Sign Exponent Fraction Bias |
963 /// |-------------------------------------- |
964 /// | 1[63] 11[62-52] 52[51-00] 1023 |
965 /// --------------------------------------
966 double APInt::roundToDouble(bool isSigned) const {
968 // Handle the simple case where the value is contained in one uint64_t.
969 // It is wrong to optimize getWord(0) to VAL; there might be more than one word.
970 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
972 int64_t sext = (int64_t(getWord(0)) << (64-BitWidth)) >> (64-BitWidth);
975 return double(getWord(0));
978 // Determine if the value is negative.
979 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
981 // Construct the absolute value if we're negative.
982 APInt Tmp(isNeg ? -(*this) : (*this));
984 // Figure out how many bits we're using.
985 unsigned n = Tmp.getActiveBits();
987 // The exponent (without bias normalization) is just the number of bits
988 // we are using. Note that the sign bit is gone since we constructed the
992 // Return infinity for exponent overflow
994 if (!isSigned || !isNeg)
995 return std::numeric_limits<double>::infinity();
997 return -std::numeric_limits<double>::infinity();
999 exp += 1023; // Increment for 1023 bias
1001 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
1002 // extract the high 52 bits from the correct words in pVal.
1004 unsigned hiWord = whichWord(n-1);
1006 mantissa = Tmp.pVal[0];
1008 mantissa >>= n - 52; // shift down, we want the top 52 bits.
1010 assert(hiWord > 0 && "huh?");
1011 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
1012 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
1013 mantissa = hibits | lobits;
1016 // The leading bit of mantissa is implicit, so get rid of it.
1017 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
1022 T.I = sign | (exp << 52) | mantissa;
1026 // Truncate to new width.
1027 APInt APInt::trunc(unsigned width) const {
1028 assert(width < BitWidth && "Invalid APInt Truncate request");
1029 assert(width && "Can't truncate to 0 bits");
1031 if (width <= APINT_BITS_PER_WORD)
1032 return APInt(width, getRawData()[0]);
1034 APInt Result(getMemory(getNumWords(width)), width);
1038 for (i = 0; i != width / APINT_BITS_PER_WORD; i++)
1039 Result.pVal[i] = pVal[i];
1041 // Truncate and copy any partial word.
1042 unsigned bits = (0 - width) % APINT_BITS_PER_WORD;
1044 Result.pVal[i] = pVal[i] << bits >> bits;
1049 // Sign extend to a new width.
1050 APInt APInt::sext(unsigned width) const {
1051 assert(width > BitWidth && "Invalid APInt SignExtend request");
1053 if (width <= APINT_BITS_PER_WORD) {
1054 uint64_t val = VAL << (APINT_BITS_PER_WORD - BitWidth);
1055 val = (int64_t)val >> (width - BitWidth);
1056 return APInt(width, val >> (APINT_BITS_PER_WORD - width));
1059 APInt Result(getMemory(getNumWords(width)), width);
1064 for (i = 0; i != BitWidth / APINT_BITS_PER_WORD; i++) {
1065 word = getRawData()[i];
1066 Result.pVal[i] = word;
1069 // Read and sign-extend any partial word.
1070 unsigned bits = (0 - BitWidth) % APINT_BITS_PER_WORD;
1072 word = (int64_t)getRawData()[i] << bits >> bits;
1074 word = (int64_t)word >> (APINT_BITS_PER_WORD - 1);
1076 // Write remaining full words.
1077 for (; i != width / APINT_BITS_PER_WORD; i++) {
1078 Result.pVal[i] = word;
1079 word = (int64_t)word >> (APINT_BITS_PER_WORD - 1);
1082 // Write any partial word.
1083 bits = (0 - width) % APINT_BITS_PER_WORD;
1085 Result.pVal[i] = word << bits >> bits;
1090 // Zero extend to a new width.
1091 APInt APInt::zext(unsigned width) const {
1092 assert(width > BitWidth && "Invalid APInt ZeroExtend request");
1094 if (width <= APINT_BITS_PER_WORD)
1095 return APInt(width, VAL);
1097 APInt Result(getMemory(getNumWords(width)), width);
1101 for (i = 0; i != getNumWords(); i++)
1102 Result.pVal[i] = getRawData()[i];
1104 // Zero remaining words.
1105 memset(&Result.pVal[i], 0, (Result.getNumWords() - i) * APINT_WORD_SIZE);
1110 APInt APInt::zextOrTrunc(unsigned width) const {
1111 if (BitWidth < width)
1113 if (BitWidth > width)
1114 return trunc(width);
1118 APInt APInt::sextOrTrunc(unsigned width) const {
1119 if (BitWidth < width)
1121 if (BitWidth > width)
1122 return trunc(width);
1126 /// Arithmetic right-shift this APInt by shiftAmt.
1127 /// @brief Arithmetic right-shift function.
1128 APInt APInt::ashr(const APInt &shiftAmt) const {
1129 return ashr((unsigned)shiftAmt.getLimitedValue(BitWidth));
1132 /// Arithmetic right-shift this APInt by shiftAmt.
1133 /// @brief Arithmetic right-shift function.
1134 APInt APInt::ashr(unsigned shiftAmt) const {
1135 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1136 // Handle a degenerate case
1140 // Handle single word shifts with built-in ashr
1141 if (isSingleWord()) {
1142 if (shiftAmt == BitWidth)
1143 return APInt(BitWidth, 0); // undefined
1145 unsigned SignBit = APINT_BITS_PER_WORD - BitWidth;
1146 return APInt(BitWidth,
1147 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1151 // If all the bits were shifted out, the result is, technically, undefined.
1152 // We return -1 if it was negative, 0 otherwise. We check this early to avoid
1153 // issues in the algorithm below.
1154 if (shiftAmt == BitWidth) {
1156 return APInt(BitWidth, -1ULL, true);
1158 return APInt(BitWidth, 0);
1161 // Create some space for the result.
1162 uint64_t * val = new uint64_t[getNumWords()];
1164 // Compute some values needed by the following shift algorithms
1165 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word
1166 unsigned offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift
1167 unsigned breakWord = getNumWords() - 1 - offset; // last word affected
1168 unsigned bitsInWord = whichBit(BitWidth); // how many bits in last word?
1169 if (bitsInWord == 0)
1170 bitsInWord = APINT_BITS_PER_WORD;
1172 // If we are shifting whole words, just move whole words
1173 if (wordShift == 0) {
1174 // Move the words containing significant bits
1175 for (unsigned i = 0; i <= breakWord; ++i)
1176 val[i] = pVal[i+offset]; // move whole word
1178 // Adjust the top significant word for sign bit fill, if negative
1180 if (bitsInWord < APINT_BITS_PER_WORD)
1181 val[breakWord] |= ~0ULL << bitsInWord; // set high bits
1183 // Shift the low order words
1184 for (unsigned i = 0; i < breakWord; ++i) {
1185 // This combines the shifted corresponding word with the low bits from
1186 // the next word (shifted into this word's high bits).
1187 val[i] = (pVal[i+offset] >> wordShift) |
1188 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1191 // Shift the break word. In this case there are no bits from the next word
1192 // to include in this word.
1193 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1195 // Deal with sign extenstion in the break word, and possibly the word before
1198 if (wordShift > bitsInWord) {
1201 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord));
1202 val[breakWord] |= ~0ULL;
1204 val[breakWord] |= (~0ULL << (bitsInWord - wordShift));
1208 // Remaining words are 0 or -1, just assign them.
1209 uint64_t fillValue = (isNegative() ? -1ULL : 0);
1210 for (unsigned i = breakWord+1; i < getNumWords(); ++i)
1212 return APInt(val, BitWidth).clearUnusedBits();
1215 /// Logical right-shift this APInt by shiftAmt.
1216 /// @brief Logical right-shift function.
1217 APInt APInt::lshr(const APInt &shiftAmt) const {
1218 return lshr((unsigned)shiftAmt.getLimitedValue(BitWidth));
1221 /// Logical right-shift this APInt by shiftAmt.
1222 /// @brief Logical right-shift function.
1223 APInt APInt::lshr(unsigned shiftAmt) const {
1224 if (isSingleWord()) {
1225 if (shiftAmt == BitWidth)
1226 return APInt(BitWidth, 0);
1228 return APInt(BitWidth, this->VAL >> shiftAmt);
1231 // If all the bits were shifted out, the result is 0. This avoids issues
1232 // with shifting by the size of the integer type, which produces undefined
1233 // results. We define these "undefined results" to always be 0.
1234 if (shiftAmt == BitWidth)
1235 return APInt(BitWidth, 0);
1237 // If none of the bits are shifted out, the result is *this. This avoids
1238 // issues with shifting by the size of the integer type, which produces
1239 // undefined results in the code below. This is also an optimization.
1243 // Create some space for the result.
1244 uint64_t * val = new uint64_t[getNumWords()];
1246 // If we are shifting less than a word, compute the shift with a simple carry
1247 if (shiftAmt < APINT_BITS_PER_WORD) {
1248 lshrNear(val, pVal, getNumWords(), shiftAmt);
1249 return APInt(val, BitWidth).clearUnusedBits();
1252 // Compute some values needed by the remaining shift algorithms
1253 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD;
1254 unsigned offset = shiftAmt / APINT_BITS_PER_WORD;
1256 // If we are shifting whole words, just move whole words
1257 if (wordShift == 0) {
1258 for (unsigned i = 0; i < getNumWords() - offset; ++i)
1259 val[i] = pVal[i+offset];
1260 for (unsigned i = getNumWords()-offset; i < getNumWords(); i++)
1262 return APInt(val,BitWidth).clearUnusedBits();
1265 // Shift the low order words
1266 unsigned breakWord = getNumWords() - offset -1;
1267 for (unsigned i = 0; i < breakWord; ++i)
1268 val[i] = (pVal[i+offset] >> wordShift) |
1269 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1270 // Shift the break word.
1271 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1273 // Remaining words are 0
1274 for (unsigned i = breakWord+1; i < getNumWords(); ++i)
1276 return APInt(val, BitWidth).clearUnusedBits();
1279 /// Left-shift this APInt by shiftAmt.
1280 /// @brief Left-shift function.
1281 APInt APInt::shl(const APInt &shiftAmt) const {
1282 // It's undefined behavior in C to shift by BitWidth or greater.
1283 return shl((unsigned)shiftAmt.getLimitedValue(BitWidth));
1286 APInt APInt::shlSlowCase(unsigned shiftAmt) const {
1287 // If all the bits were shifted out, the result is 0. This avoids issues
1288 // with shifting by the size of the integer type, which produces undefined
1289 // results. We define these "undefined results" to always be 0.
1290 if (shiftAmt == BitWidth)
1291 return APInt(BitWidth, 0);
1293 // If none of the bits are shifted out, the result is *this. This avoids a
1294 // lshr by the words size in the loop below which can produce incorrect
1295 // results. It also avoids the expensive computation below for a common case.
1299 // Create some space for the result.
1300 uint64_t * val = new uint64_t[getNumWords()];
1302 // If we are shifting less than a word, do it the easy way
1303 if (shiftAmt < APINT_BITS_PER_WORD) {
1305 for (unsigned i = 0; i < getNumWords(); i++) {
1306 val[i] = pVal[i] << shiftAmt | carry;
1307 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1309 return APInt(val, BitWidth).clearUnusedBits();
1312 // Compute some values needed by the remaining shift algorithms
1313 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD;
1314 unsigned offset = shiftAmt / APINT_BITS_PER_WORD;
1316 // If we are shifting whole words, just move whole words
1317 if (wordShift == 0) {
1318 for (unsigned i = 0; i < offset; i++)
1320 for (unsigned i = offset; i < getNumWords(); i++)
1321 val[i] = pVal[i-offset];
1322 return APInt(val,BitWidth).clearUnusedBits();
1325 // Copy whole words from this to Result.
1326 unsigned i = getNumWords() - 1;
1327 for (; i > offset; --i)
1328 val[i] = pVal[i-offset] << wordShift |
1329 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1330 val[offset] = pVal[0] << wordShift;
1331 for (i = 0; i < offset; ++i)
1333 return APInt(val, BitWidth).clearUnusedBits();
1336 APInt APInt::rotl(const APInt &rotateAmt) const {
1337 return rotl((unsigned)rotateAmt.getLimitedValue(BitWidth));
1340 APInt APInt::rotl(unsigned rotateAmt) const {
1341 rotateAmt %= BitWidth;
1344 return shl(rotateAmt) | lshr(BitWidth - rotateAmt);
1347 APInt APInt::rotr(const APInt &rotateAmt) const {
1348 return rotr((unsigned)rotateAmt.getLimitedValue(BitWidth));
1351 APInt APInt::rotr(unsigned rotateAmt) const {
1352 rotateAmt %= BitWidth;
1355 return lshr(rotateAmt) | shl(BitWidth - rotateAmt);
1358 // Square Root - this method computes and returns the square root of "this".
1359 // Three mechanisms are used for computation. For small values (<= 5 bits),
1360 // a table lookup is done. This gets some performance for common cases. For
1361 // values using less than 52 bits, the value is converted to double and then
1362 // the libc sqrt function is called. The result is rounded and then converted
1363 // back to a uint64_t which is then used to construct the result. Finally,
1364 // the Babylonian method for computing square roots is used.
1365 APInt APInt::sqrt() const {
1367 // Determine the magnitude of the value.
1368 unsigned magnitude = getActiveBits();
1370 // Use a fast table for some small values. This also gets rid of some
1371 // rounding errors in libc sqrt for small values.
1372 if (magnitude <= 5) {
1373 static const uint8_t results[32] = {
1376 /* 3- 6 */ 2, 2, 2, 2,
1377 /* 7-12 */ 3, 3, 3, 3, 3, 3,
1378 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1379 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1382 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]);
1385 // If the magnitude of the value fits in less than 52 bits (the precision of
1386 // an IEEE double precision floating point value), then we can use the
1387 // libc sqrt function which will probably use a hardware sqrt computation.
1388 // This should be faster than the algorithm below.
1389 if (magnitude < 52) {
1391 return APInt(BitWidth,
1392 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0])))));
1394 return APInt(BitWidth,
1395 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0])) + 0.5));
1399 // Okay, all the short cuts are exhausted. We must compute it. The following
1400 // is a classical Babylonian method for computing the square root. This code
1401 // was adapted to APINt from a wikipedia article on such computations.
1402 // See http://www.wikipedia.org/ and go to the page named
1403 // Calculate_an_integer_square_root.
1404 unsigned nbits = BitWidth, i = 4;
1405 APInt testy(BitWidth, 16);
1406 APInt x_old(BitWidth, 1);
1407 APInt x_new(BitWidth, 0);
1408 APInt two(BitWidth, 2);
1410 // Select a good starting value using binary logarithms.
1411 for (;; i += 2, testy = testy.shl(2))
1412 if (i >= nbits || this->ule(testy)) {
1413 x_old = x_old.shl(i / 2);
1417 // Use the Babylonian method to arrive at the integer square root:
1419 x_new = (this->udiv(x_old) + x_old).udiv(two);
1420 if (x_old.ule(x_new))
1425 // Make sure we return the closest approximation
1426 // NOTE: The rounding calculation below is correct. It will produce an
1427 // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1428 // determined to be a rounding issue with pari/gp as it begins to use a
1429 // floating point representation after 192 bits. There are no discrepancies
1430 // between this algorithm and pari/gp for bit widths < 192 bits.
1431 APInt square(x_old * x_old);
1432 APInt nextSquare((x_old + 1) * (x_old +1));
1433 if (this->ult(square))
1435 assert(this->ule(nextSquare) && "Error in APInt::sqrt computation");
1436 APInt midpoint((nextSquare - square).udiv(two));
1437 APInt offset(*this - square);
1438 if (offset.ult(midpoint))
1443 /// Computes the multiplicative inverse of this APInt for a given modulo. The
1444 /// iterative extended Euclidean algorithm is used to solve for this value,
1445 /// however we simplify it to speed up calculating only the inverse, and take
1446 /// advantage of div+rem calculations. We also use some tricks to avoid copying
1447 /// (potentially large) APInts around.
1448 APInt APInt::multiplicativeInverse(const APInt& modulo) const {
1449 assert(ult(modulo) && "This APInt must be smaller than the modulo");
1451 // Using the properties listed at the following web page (accessed 06/21/08):
1452 // http://www.numbertheory.org/php/euclid.html
1453 // (especially the properties numbered 3, 4 and 9) it can be proved that
1454 // BitWidth bits suffice for all the computations in the algorithm implemented
1455 // below. More precisely, this number of bits suffice if the multiplicative
1456 // inverse exists, but may not suffice for the general extended Euclidean
1459 APInt r[2] = { modulo, *this };
1460 APInt t[2] = { APInt(BitWidth, 0), APInt(BitWidth, 1) };
1461 APInt q(BitWidth, 0);
1464 for (i = 0; r[i^1] != 0; i ^= 1) {
1465 // An overview of the math without the confusing bit-flipping:
1466 // q = r[i-2] / r[i-1]
1467 // r[i] = r[i-2] % r[i-1]
1468 // t[i] = t[i-2] - t[i-1] * q
1469 udivrem(r[i], r[i^1], q, r[i]);
1473 // If this APInt and the modulo are not coprime, there is no multiplicative
1474 // inverse, so return 0. We check this by looking at the next-to-last
1475 // remainder, which is the gcd(*this,modulo) as calculated by the Euclidean
1478 return APInt(BitWidth, 0);
1480 // The next-to-last t is the multiplicative inverse. However, we are
1481 // interested in a positive inverse. Calcuate a positive one from a negative
1482 // one if necessary. A simple addition of the modulo suffices because
1483 // abs(t[i]) is known to be less than *this/2 (see the link above).
1484 return t[i].isNegative() ? t[i] + modulo : t[i];
1487 /// Calculate the magic numbers required to implement a signed integer division
1488 /// by a constant as a sequence of multiplies, adds and shifts. Requires that
1489 /// the divisor not be 0, 1, or -1. Taken from "Hacker's Delight", Henry S.
1490 /// Warren, Jr., chapter 10.
1491 APInt::ms APInt::magic() const {
1492 const APInt& d = *this;
1494 APInt ad, anc, delta, q1, r1, q2, r2, t;
1495 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
1499 t = signedMin + (d.lshr(d.getBitWidth() - 1));
1500 anc = t - 1 - t.urem(ad); // absolute value of nc
1501 p = d.getBitWidth() - 1; // initialize p
1502 q1 = signedMin.udiv(anc); // initialize q1 = 2p/abs(nc)
1503 r1 = signedMin - q1*anc; // initialize r1 = rem(2p,abs(nc))
1504 q2 = signedMin.udiv(ad); // initialize q2 = 2p/abs(d)
1505 r2 = signedMin - q2*ad; // initialize r2 = rem(2p,abs(d))
1508 q1 = q1<<1; // update q1 = 2p/abs(nc)
1509 r1 = r1<<1; // update r1 = rem(2p/abs(nc))
1510 if (r1.uge(anc)) { // must be unsigned comparison
1514 q2 = q2<<1; // update q2 = 2p/abs(d)
1515 r2 = r2<<1; // update r2 = rem(2p/abs(d))
1516 if (r2.uge(ad)) { // must be unsigned comparison
1521 } while (q1.ult(delta) || (q1 == delta && r1 == 0));
1524 if (d.isNegative()) mag.m = -mag.m; // resulting magic number
1525 mag.s = p - d.getBitWidth(); // resulting shift
1529 /// Calculate the magic numbers required to implement an unsigned integer
1530 /// division by a constant as a sequence of multiplies, adds and shifts.
1531 /// Requires that the divisor not be 0. Taken from "Hacker's Delight", Henry
1532 /// S. Warren, Jr., chapter 10.
1533 /// LeadingZeros can be used to simplify the calculation if the upper bits
1534 /// of the divided value are known zero.
1535 APInt::mu APInt::magicu(unsigned LeadingZeros) const {
1536 const APInt& d = *this;
1538 APInt nc, delta, q1, r1, q2, r2;
1540 magu.a = 0; // initialize "add" indicator
1541 APInt allOnes = APInt::getAllOnesValue(d.getBitWidth()).lshr(LeadingZeros);
1542 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth());
1543 APInt signedMax = APInt::getSignedMaxValue(d.getBitWidth());
1545 nc = allOnes - (-d).urem(d);
1546 p = d.getBitWidth() - 1; // initialize p
1547 q1 = signedMin.udiv(nc); // initialize q1 = 2p/nc
1548 r1 = signedMin - q1*nc; // initialize r1 = rem(2p,nc)
1549 q2 = signedMax.udiv(d); // initialize q2 = (2p-1)/d
1550 r2 = signedMax - q2*d; // initialize r2 = rem((2p-1),d)
1553 if (r1.uge(nc - r1)) {
1554 q1 = q1 + q1 + 1; // update q1
1555 r1 = r1 + r1 - nc; // update r1
1558 q1 = q1+q1; // update q1
1559 r1 = r1+r1; // update r1
1561 if ((r2 + 1).uge(d - r2)) {
1562 if (q2.uge(signedMax)) magu.a = 1;
1563 q2 = q2+q2 + 1; // update q2
1564 r2 = r2+r2 + 1 - d; // update r2
1567 if (q2.uge(signedMin)) magu.a = 1;
1568 q2 = q2+q2; // update q2
1569 r2 = r2+r2 + 1; // update r2
1572 } while (p < d.getBitWidth()*2 &&
1573 (q1.ult(delta) || (q1 == delta && r1 == 0)));
1574 magu.m = q2 + 1; // resulting magic number
1575 magu.s = p - d.getBitWidth(); // resulting shift
1579 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1580 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1581 /// variables here have the same names as in the algorithm. Comments explain
1582 /// the algorithm and any deviation from it.
1583 static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
1584 unsigned m, unsigned n) {
1585 assert(u && "Must provide dividend");
1586 assert(v && "Must provide divisor");
1587 assert(q && "Must provide quotient");
1588 assert(u != v && u != q && v != q && "Must us different memory");
1589 assert(n>1 && "n must be > 1");
1591 // Knuth uses the value b as the base of the number system. In our case b
1592 // is 2^31 so we just set it to -1u.
1593 uint64_t b = uint64_t(1) << 32;
1596 DEBUG(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n');
1597 DEBUG(dbgs() << "KnuthDiv: original:");
1598 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1599 DEBUG(dbgs() << " by");
1600 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
1601 DEBUG(dbgs() << '\n');
1603 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1604 // u and v by d. Note that we have taken Knuth's advice here to use a power
1605 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1606 // 2 allows us to shift instead of multiply and it is easy to determine the
1607 // shift amount from the leading zeros. We are basically normalizing the u
1608 // and v so that its high bits are shifted to the top of v's range without
1609 // overflow. Note that this can require an extra word in u so that u must
1610 // be of length m+n+1.
1611 unsigned shift = CountLeadingZeros_32(v[n-1]);
1612 unsigned v_carry = 0;
1613 unsigned u_carry = 0;
1615 for (unsigned i = 0; i < m+n; ++i) {
1616 unsigned u_tmp = u[i] >> (32 - shift);
1617 u[i] = (u[i] << shift) | u_carry;
1620 for (unsigned i = 0; i < n; ++i) {
1621 unsigned v_tmp = v[i] >> (32 - shift);
1622 v[i] = (v[i] << shift) | v_carry;
1628 DEBUG(dbgs() << "KnuthDiv: normal:");
1629 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1630 DEBUG(dbgs() << " by");
1631 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
1632 DEBUG(dbgs() << '\n');
1635 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1638 DEBUG(dbgs() << "KnuthDiv: quotient digit #" << j << '\n');
1639 // D3. [Calculate q'.].
1640 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1641 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1642 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1643 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1644 // on v[n-2] determines at high speed most of the cases in which the trial
1645 // value qp is one too large, and it eliminates all cases where qp is two
1647 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1648 DEBUG(dbgs() << "KnuthDiv: dividend == " << dividend << '\n');
1649 uint64_t qp = dividend / v[n-1];
1650 uint64_t rp = dividend % v[n-1];
1651 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1654 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1657 DEBUG(dbgs() << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1659 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1660 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1661 // consists of a simple multiplication by a one-place number, combined with
1664 for (unsigned i = 0; i < n; ++i) {
1665 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1666 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1667 bool borrow = subtrahend > u_tmp;
1668 DEBUG(dbgs() << "KnuthDiv: u_tmp == " << u_tmp
1669 << ", subtrahend == " << subtrahend
1670 << ", borrow = " << borrow << '\n');
1672 uint64_t result = u_tmp - subtrahend;
1674 u[k++] = (unsigned)(result & (b-1)); // subtract low word
1675 u[k++] = (unsigned)(result >> 32); // subtract high word
1676 while (borrow && k <= m+n) { // deal with borrow to the left
1682 DEBUG(dbgs() << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1685 DEBUG(dbgs() << "KnuthDiv: after subtraction:");
1686 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1687 DEBUG(dbgs() << '\n');
1688 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1689 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1690 // true value plus b**(n+1), namely as the b's complement of
1691 // the true value, and a "borrow" to the left should be remembered.
1694 bool carry = true; // true because b's complement is "complement + 1"
1695 for (unsigned i = 0; i <= m+n; ++i) {
1696 u[i] = ~u[i] + carry; // b's complement
1697 carry = carry && u[i] == 0;
1700 DEBUG(dbgs() << "KnuthDiv: after complement:");
1701 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
1702 DEBUG(dbgs() << '\n');
1704 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1705 // negative, go to step D6; otherwise go on to step D7.
1706 q[j] = (unsigned)qp;
1708 // D6. [Add back]. The probability that this step is necessary is very
1709 // small, on the order of only 2/b. Make sure that test data accounts for
1710 // this possibility. Decrease q[j] by 1
1712 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1713 // A carry will occur to the left of u[j+n], and it should be ignored
1714 // since it cancels with the borrow that occurred in D4.
1716 for (unsigned i = 0; i < n; i++) {
1717 unsigned limit = std::min(u[j+i],v[i]);
1718 u[j+i] += v[i] + carry;
1719 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1723 DEBUG(dbgs() << "KnuthDiv: after correction:");
1724 DEBUG(for (int i = m+n; i >=0; i--) dbgs() <<" " << u[i]);
1725 DEBUG(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n');
1727 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1730 DEBUG(dbgs() << "KnuthDiv: quotient:");
1731 DEBUG(for (int i = m; i >=0; i--) dbgs() <<" " << q[i]);
1732 DEBUG(dbgs() << '\n');
1734 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1735 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1736 // compute the remainder (urem uses this).
1738 // The value d is expressed by the "shift" value above since we avoided
1739 // multiplication by d by using a shift left. So, all we have to do is
1740 // shift right here. In order to mak
1743 DEBUG(dbgs() << "KnuthDiv: remainder:");
1744 for (int i = n-1; i >= 0; i--) {
1745 r[i] = (u[i] >> shift) | carry;
1746 carry = u[i] << (32 - shift);
1747 DEBUG(dbgs() << " " << r[i]);
1750 for (int i = n-1; i >= 0; i--) {
1752 DEBUG(dbgs() << " " << r[i]);
1755 DEBUG(dbgs() << '\n');
1758 DEBUG(dbgs() << '\n');
1762 void APInt::divide(const APInt LHS, unsigned lhsWords,
1763 const APInt &RHS, unsigned rhsWords,
1764 APInt *Quotient, APInt *Remainder)
1766 assert(lhsWords >= rhsWords && "Fractional result");
1768 // First, compose the values into an array of 32-bit words instead of
1769 // 64-bit words. This is a necessity of both the "short division" algorithm
1770 // and the Knuth "classical algorithm" which requires there to be native
1771 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1772 // can't use 64-bit operands here because we don't have native results of
1773 // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't
1774 // work on large-endian machines.
1775 uint64_t mask = ~0ull >> (sizeof(unsigned)*CHAR_BIT);
1776 unsigned n = rhsWords * 2;
1777 unsigned m = (lhsWords * 2) - n;
1779 // Allocate space for the temporary values we need either on the stack, if
1780 // it will fit, or on the heap if it won't.
1781 unsigned SPACE[128];
1786 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1789 Q = &SPACE[(m+n+1) + n];
1791 R = &SPACE[(m+n+1) + n + (m+n)];
1793 U = new unsigned[m + n + 1];
1794 V = new unsigned[n];
1795 Q = new unsigned[m+n];
1797 R = new unsigned[n];
1800 // Initialize the dividend
1801 memset(U, 0, (m+n+1)*sizeof(unsigned));
1802 for (unsigned i = 0; i < lhsWords; ++i) {
1803 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1804 U[i * 2] = (unsigned)(tmp & mask);
1805 U[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT));
1807 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1809 // Initialize the divisor
1810 memset(V, 0, (n)*sizeof(unsigned));
1811 for (unsigned i = 0; i < rhsWords; ++i) {
1812 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1813 V[i * 2] = (unsigned)(tmp & mask);
1814 V[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT));
1817 // initialize the quotient and remainder
1818 memset(Q, 0, (m+n) * sizeof(unsigned));
1820 memset(R, 0, n * sizeof(unsigned));
1822 // Now, adjust m and n for the Knuth division. n is the number of words in
1823 // the divisor. m is the number of words by which the dividend exceeds the
1824 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1825 // contain any zero words or the Knuth algorithm fails.
1826 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1830 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1833 // If we're left with only a single word for the divisor, Knuth doesn't work
1834 // so we implement the short division algorithm here. This is much simpler
1835 // and faster because we are certain that we can divide a 64-bit quantity
1836 // by a 32-bit quantity at hardware speed and short division is simply a
1837 // series of such operations. This is just like doing short division but we
1838 // are using base 2^32 instead of base 10.
1839 assert(n != 0 && "Divide by zero?");
1841 unsigned divisor = V[0];
1842 unsigned remainder = 0;
1843 for (int i = m+n-1; i >= 0; i--) {
1844 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1845 if (partial_dividend == 0) {
1848 } else if (partial_dividend < divisor) {
1850 remainder = (unsigned)partial_dividend;
1851 } else if (partial_dividend == divisor) {
1855 Q[i] = (unsigned)(partial_dividend / divisor);
1856 remainder = (unsigned)(partial_dividend - (Q[i] * divisor));
1862 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1864 KnuthDiv(U, V, Q, R, m, n);
1867 // If the caller wants the quotient
1869 // Set up the Quotient value's memory.
1870 if (Quotient->BitWidth != LHS.BitWidth) {
1871 if (Quotient->isSingleWord())
1874 delete [] Quotient->pVal;
1875 Quotient->BitWidth = LHS.BitWidth;
1876 if (!Quotient->isSingleWord())
1877 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1879 Quotient->clearAllBits();
1881 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1883 if (lhsWords == 1) {
1885 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1886 if (Quotient->isSingleWord())
1887 Quotient->VAL = tmp;
1889 Quotient->pVal[0] = tmp;
1891 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1892 for (unsigned i = 0; i < lhsWords; ++i)
1894 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1898 // If the caller wants the remainder
1900 // Set up the Remainder value's memory.
1901 if (Remainder->BitWidth != RHS.BitWidth) {
1902 if (Remainder->isSingleWord())
1905 delete [] Remainder->pVal;
1906 Remainder->BitWidth = RHS.BitWidth;
1907 if (!Remainder->isSingleWord())
1908 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1910 Remainder->clearAllBits();
1912 // The remainder is in R. Reconstitute the remainder into Remainder's low
1914 if (rhsWords == 1) {
1916 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1917 if (Remainder->isSingleWord())
1918 Remainder->VAL = tmp;
1920 Remainder->pVal[0] = tmp;
1922 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1923 for (unsigned i = 0; i < rhsWords; ++i)
1924 Remainder->pVal[i] =
1925 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1929 // Clean up the memory we allocated.
1930 if (U != &SPACE[0]) {
1938 APInt APInt::udiv(const APInt& RHS) const {
1939 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1941 // First, deal with the easy case
1942 if (isSingleWord()) {
1943 assert(RHS.VAL != 0 && "Divide by zero?");
1944 return APInt(BitWidth, VAL / RHS.VAL);
1947 // Get some facts about the LHS and RHS number of bits and words
1948 unsigned rhsBits = RHS.getActiveBits();
1949 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1950 assert(rhsWords && "Divided by zero???");
1951 unsigned lhsBits = this->getActiveBits();
1952 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1954 // Deal with some degenerate cases
1957 return APInt(BitWidth, 0);
1958 else if (lhsWords < rhsWords || this->ult(RHS)) {
1959 // X / Y ===> 0, iff X < Y
1960 return APInt(BitWidth, 0);
1961 } else if (*this == RHS) {
1963 return APInt(BitWidth, 1);
1964 } else if (lhsWords == 1 && rhsWords == 1) {
1965 // All high words are zero, just use native divide
1966 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1969 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1970 APInt Quotient(1,0); // to hold result.
1971 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0);
1975 APInt APInt::urem(const APInt& RHS) const {
1976 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1977 if (isSingleWord()) {
1978 assert(RHS.VAL != 0 && "Remainder by zero?");
1979 return APInt(BitWidth, VAL % RHS.VAL);
1982 // Get some facts about the LHS
1983 unsigned lhsBits = getActiveBits();
1984 unsigned lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1986 // Get some facts about the RHS
1987 unsigned rhsBits = RHS.getActiveBits();
1988 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1989 assert(rhsWords && "Performing remainder operation by zero ???");
1991 // Check the degenerate cases
1992 if (lhsWords == 0) {
1994 return APInt(BitWidth, 0);
1995 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1996 // X % Y ===> X, iff X < Y
1998 } else if (*this == RHS) {
2000 return APInt(BitWidth, 0);
2001 } else if (lhsWords == 1) {
2002 // All high words are zero, just use native remainder
2003 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
2006 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
2007 APInt Remainder(1,0);
2008 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder);
2012 void APInt::udivrem(const APInt &LHS, const APInt &RHS,
2013 APInt &Quotient, APInt &Remainder) {
2014 // Get some size facts about the dividend and divisor
2015 unsigned lhsBits = LHS.getActiveBits();
2016 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
2017 unsigned rhsBits = RHS.getActiveBits();
2018 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
2020 // Check the degenerate cases
2021 if (lhsWords == 0) {
2022 Quotient = 0; // 0 / Y ===> 0
2023 Remainder = 0; // 0 % Y ===> 0
2027 if (lhsWords < rhsWords || LHS.ult(RHS)) {
2028 Remainder = LHS; // X % Y ===> X, iff X < Y
2029 Quotient = 0; // X / Y ===> 0, iff X < Y
2034 Quotient = 1; // X / X ===> 1
2035 Remainder = 0; // X % X ===> 0;
2039 if (lhsWords == 1 && rhsWords == 1) {
2040 // There is only one word to consider so use the native versions.
2041 uint64_t lhsValue = LHS.isSingleWord() ? LHS.VAL : LHS.pVal[0];
2042 uint64_t rhsValue = RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0];
2043 Quotient = APInt(LHS.getBitWidth(), lhsValue / rhsValue);
2044 Remainder = APInt(LHS.getBitWidth(), lhsValue % rhsValue);
2048 // Okay, lets do it the long way
2049 divide(LHS, lhsWords, RHS, rhsWords, &Quotient, &Remainder);
2052 APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const {
2053 APInt Res = *this+RHS;
2054 Overflow = isNonNegative() == RHS.isNonNegative() &&
2055 Res.isNonNegative() != isNonNegative();
2059 APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const {
2060 APInt Res = *this+RHS;
2061 Overflow = Res.ult(RHS);
2065 APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const {
2066 APInt Res = *this - RHS;
2067 Overflow = isNonNegative() != RHS.isNonNegative() &&
2068 Res.isNonNegative() != isNonNegative();
2072 APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const {
2073 APInt Res = *this-RHS;
2074 Overflow = Res.ugt(*this);
2078 APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const {
2079 // MININT/-1 --> overflow.
2080 Overflow = isMinSignedValue() && RHS.isAllOnesValue();
2084 APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const {
2085 APInt Res = *this * RHS;
2087 if (*this != 0 && RHS != 0)
2088 Overflow = Res.sdiv(RHS) != *this || Res.sdiv(*this) != RHS;
2094 APInt APInt::umul_ov(const APInt &RHS, bool &Overflow) const {
2095 APInt Res = *this * RHS;
2097 if (*this != 0 && RHS != 0)
2098 Overflow = Res.udiv(RHS) != *this || Res.udiv(*this) != RHS;
2104 APInt APInt::sshl_ov(unsigned ShAmt, bool &Overflow) const {
2105 Overflow = ShAmt >= getBitWidth();
2107 ShAmt = getBitWidth()-1;
2109 if (isNonNegative()) // Don't allow sign change.
2110 Overflow = ShAmt >= countLeadingZeros();
2112 Overflow = ShAmt >= countLeadingOnes();
2114 return *this << ShAmt;
2120 void APInt::fromString(unsigned numbits, StringRef str, uint8_t radix) {
2121 // Check our assumptions here
2122 assert(!str.empty() && "Invalid string length");
2123 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||
2125 "Radix should be 2, 8, 10, 16, or 36!");
2127 StringRef::iterator p = str.begin();
2128 size_t slen = str.size();
2129 bool isNeg = *p == '-';
2130 if (*p == '-' || *p == '+') {
2133 assert(slen && "String is only a sign, needs a value.");
2135 assert((slen <= numbits || radix != 2) && "Insufficient bit width");
2136 assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width");
2137 assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width");
2138 assert((((slen-1)*64)/22 <= numbits || radix != 10) &&
2139 "Insufficient bit width");
2142 if (!isSingleWord())
2143 pVal = getClearedMemory(getNumWords());
2145 // Figure out if we can shift instead of multiply
2146 unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
2148 // Set up an APInt for the digit to add outside the loop so we don't
2149 // constantly construct/destruct it.
2150 APInt apdigit(getBitWidth(), 0);
2151 APInt apradix(getBitWidth(), radix);
2153 // Enter digit traversal loop
2154 for (StringRef::iterator e = str.end(); p != e; ++p) {
2155 unsigned digit = getDigit(*p, radix);
2156 assert(digit < radix && "Invalid character in digit string");
2158 // Shift or multiply the value by the radix
2166 // Add in the digit we just interpreted
2167 if (apdigit.isSingleWord())
2168 apdigit.VAL = digit;
2170 apdigit.pVal[0] = digit;
2173 // If its negative, put it in two's complement form
2176 this->flipAllBits();
2180 void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix,
2181 bool Signed, bool formatAsCLiteral) const {
2182 assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2 ||
2184 "Radix should be 2, 8, 10, 16, or 36!");
2186 const char *Prefix = "";
2187 if (formatAsCLiteral) {
2190 // Binary literals are a non-standard extension added in gcc 4.3:
2191 // http://gcc.gnu.org/onlinedocs/gcc-4.3.0/gcc/Binary-constants.html
2203 llvm_unreachable("Invalid radix!");
2207 // First, check for a zero value and just short circuit the logic below.
2210 Str.push_back(*Prefix);
2217 static const char Digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
2219 if (isSingleWord()) {
2221 char *BufPtr = Buffer+65;
2227 int64_t I = getSExtValue();
2237 Str.push_back(*Prefix);
2242 *--BufPtr = Digits[N % Radix];
2245 Str.append(BufPtr, Buffer+65);
2251 if (Signed && isNegative()) {
2252 // They want to print the signed version and it is a negative value
2253 // Flip the bits and add one to turn it into the equivalent positive
2254 // value and put a '-' in the result.
2261 Str.push_back(*Prefix);
2265 // We insert the digits backward, then reverse them to get the right order.
2266 unsigned StartDig = Str.size();
2268 // For the 2, 8 and 16 bit cases, we can just shift instead of divide
2269 // because the number of bits per digit (1, 3 and 4 respectively) divides
2270 // equaly. We just shift until the value is zero.
2271 if (Radix == 2 || Radix == 8 || Radix == 16) {
2272 // Just shift tmp right for each digit width until it becomes zero
2273 unsigned ShiftAmt = (Radix == 16 ? 4 : (Radix == 8 ? 3 : 1));
2274 unsigned MaskAmt = Radix - 1;
2277 unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt;
2278 Str.push_back(Digits[Digit]);
2279 Tmp = Tmp.lshr(ShiftAmt);
2282 APInt divisor(Radix == 10? 4 : 8, Radix);
2284 APInt APdigit(1, 0);
2285 APInt tmp2(Tmp.getBitWidth(), 0);
2286 divide(Tmp, Tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
2288 unsigned Digit = (unsigned)APdigit.getZExtValue();
2289 assert(Digit < Radix && "divide failed");
2290 Str.push_back(Digits[Digit]);
2295 // Reverse the digits before returning.
2296 std::reverse(Str.begin()+StartDig, Str.end());
2299 /// toString - This returns the APInt as a std::string. Note that this is an
2300 /// inefficient method. It is better to pass in a SmallVector/SmallString
2301 /// to the methods above.
2302 std::string APInt::toString(unsigned Radix = 10, bool Signed = true) const {
2304 toString(S, Radix, Signed, /* formatAsCLiteral = */false);
2309 void APInt::dump() const {
2310 SmallString<40> S, U;
2311 this->toStringUnsigned(U);
2312 this->toStringSigned(S);
2313 dbgs() << "APInt(" << BitWidth << "b, "
2314 << U.str() << "u " << S.str() << "s)";
2317 void APInt::print(raw_ostream &OS, bool isSigned) const {
2319 this->toString(S, 10, isSigned, /* formatAsCLiteral = */false);
2323 // This implements a variety of operations on a representation of
2324 // arbitrary precision, two's-complement, bignum integer values.
2326 // Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe
2327 // and unrestricting assumption.
2328 #define COMPILE_TIME_ASSERT(cond) extern int CTAssert[(cond) ? 1 : -1]
2329 COMPILE_TIME_ASSERT(integerPartWidth % 2 == 0);
2331 /* Some handy functions local to this file. */
2334 /* Returns the integer part with the least significant BITS set.
2335 BITS cannot be zero. */
2336 static inline integerPart
2337 lowBitMask(unsigned int bits)
2339 assert(bits != 0 && bits <= integerPartWidth);
2341 return ~(integerPart) 0 >> (integerPartWidth - bits);
2344 /* Returns the value of the lower half of PART. */
2345 static inline integerPart
2346 lowHalf(integerPart part)
2348 return part & lowBitMask(integerPartWidth / 2);
2351 /* Returns the value of the upper half of PART. */
2352 static inline integerPart
2353 highHalf(integerPart part)
2355 return part >> (integerPartWidth / 2);
2358 /* Returns the bit number of the most significant set bit of a part.
2359 If the input number has no bits set -1U is returned. */
2361 partMSB(integerPart value)
2363 unsigned int n, msb;
2368 n = integerPartWidth / 2;
2383 /* Returns the bit number of the least significant set bit of a
2384 part. If the input number has no bits set -1U is returned. */
2386 partLSB(integerPart value)
2388 unsigned int n, lsb;
2393 lsb = integerPartWidth - 1;
2394 n = integerPartWidth / 2;
2409 /* Sets the least significant part of a bignum to the input value, and
2410 zeroes out higher parts. */
2412 APInt::tcSet(integerPart *dst, integerPart part, unsigned int parts)
2419 for (i = 1; i < parts; i++)
2423 /* Assign one bignum to another. */
2425 APInt::tcAssign(integerPart *dst, const integerPart *src, unsigned int parts)
2429 for (i = 0; i < parts; i++)
2433 /* Returns true if a bignum is zero, false otherwise. */
2435 APInt::tcIsZero(const integerPart *src, unsigned int parts)
2439 for (i = 0; i < parts; i++)
2446 /* Extract the given bit of a bignum; returns 0 or 1. */
2448 APInt::tcExtractBit(const integerPart *parts, unsigned int bit)
2450 return (parts[bit / integerPartWidth] &
2451 ((integerPart) 1 << bit % integerPartWidth)) != 0;
2454 /* Set the given bit of a bignum. */
2456 APInt::tcSetBit(integerPart *parts, unsigned int bit)
2458 parts[bit / integerPartWidth] |= (integerPart) 1 << (bit % integerPartWidth);
2461 /* Clears the given bit of a bignum. */
2463 APInt::tcClearBit(integerPart *parts, unsigned int bit)
2465 parts[bit / integerPartWidth] &=
2466 ~((integerPart) 1 << (bit % integerPartWidth));
2469 /* Returns the bit number of the least significant set bit of a
2470 number. If the input number has no bits set -1U is returned. */
2472 APInt::tcLSB(const integerPart *parts, unsigned int n)
2474 unsigned int i, lsb;
2476 for (i = 0; i < n; i++) {
2477 if (parts[i] != 0) {
2478 lsb = partLSB(parts[i]);
2480 return lsb + i * integerPartWidth;
2487 /* Returns the bit number of the most significant set bit of a number.
2488 If the input number has no bits set -1U is returned. */
2490 APInt::tcMSB(const integerPart *parts, unsigned int n)
2497 if (parts[n] != 0) {
2498 msb = partMSB(parts[n]);
2500 return msb + n * integerPartWidth;
2507 /* Copy the bit vector of width srcBITS from SRC, starting at bit
2508 srcLSB, to DST, of dstCOUNT parts, such that the bit srcLSB becomes
2509 the least significant bit of DST. All high bits above srcBITS in
2510 DST are zero-filled. */
2512 APInt::tcExtract(integerPart *dst, unsigned int dstCount,const integerPart *src,
2513 unsigned int srcBits, unsigned int srcLSB)
2515 unsigned int firstSrcPart, dstParts, shift, n;
2517 dstParts = (srcBits + integerPartWidth - 1) / integerPartWidth;
2518 assert(dstParts <= dstCount);
2520 firstSrcPart = srcLSB / integerPartWidth;
2521 tcAssign (dst, src + firstSrcPart, dstParts);
2523 shift = srcLSB % integerPartWidth;
2524 tcShiftRight (dst, dstParts, shift);
2526 /* We now have (dstParts * integerPartWidth - shift) bits from SRC
2527 in DST. If this is less that srcBits, append the rest, else
2528 clear the high bits. */
2529 n = dstParts * integerPartWidth - shift;
2531 integerPart mask = lowBitMask (srcBits - n);
2532 dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask)
2533 << n % integerPartWidth);
2534 } else if (n > srcBits) {
2535 if (srcBits % integerPartWidth)
2536 dst[dstParts - 1] &= lowBitMask (srcBits % integerPartWidth);
2539 /* Clear high parts. */
2540 while (dstParts < dstCount)
2541 dst[dstParts++] = 0;
2544 /* DST += RHS + C where C is zero or one. Returns the carry flag. */
2546 APInt::tcAdd(integerPart *dst, const integerPart *rhs,
2547 integerPart c, unsigned int parts)
2553 for (i = 0; i < parts; i++) {
2558 dst[i] += rhs[i] + 1;
2569 /* DST -= RHS + C where C is zero or one. Returns the carry flag. */
2571 APInt::tcSubtract(integerPart *dst, const integerPart *rhs,
2572 integerPart c, unsigned int parts)
2578 for (i = 0; i < parts; i++) {
2583 dst[i] -= rhs[i] + 1;
2594 /* Negate a bignum in-place. */
2596 APInt::tcNegate(integerPart *dst, unsigned int parts)
2598 tcComplement(dst, parts);
2599 tcIncrement(dst, parts);
2602 /* DST += SRC * MULTIPLIER + CARRY if add is true
2603 DST = SRC * MULTIPLIER + CARRY if add is false
2605 Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC
2606 they must start at the same point, i.e. DST == SRC.
2608 If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is
2609 returned. Otherwise DST is filled with the least significant
2610 DSTPARTS parts of the result, and if all of the omitted higher
2611 parts were zero return zero, otherwise overflow occurred and
2614 APInt::tcMultiplyPart(integerPart *dst, const integerPart *src,
2615 integerPart multiplier, integerPart carry,
2616 unsigned int srcParts, unsigned int dstParts,
2621 /* Otherwise our writes of DST kill our later reads of SRC. */
2622 assert(dst <= src || dst >= src + srcParts);
2623 assert(dstParts <= srcParts + 1);
2625 /* N loops; minimum of dstParts and srcParts. */
2626 n = dstParts < srcParts ? dstParts: srcParts;
2628 for (i = 0; i < n; i++) {
2629 integerPart low, mid, high, srcPart;
2631 /* [ LOW, HIGH ] = MULTIPLIER * SRC[i] + DST[i] + CARRY.
2633 This cannot overflow, because
2635 (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1)
2637 which is less than n^2. */
2641 if (multiplier == 0 || srcPart == 0) {
2645 low = lowHalf(srcPart) * lowHalf(multiplier);
2646 high = highHalf(srcPart) * highHalf(multiplier);
2648 mid = lowHalf(srcPart) * highHalf(multiplier);
2649 high += highHalf(mid);
2650 mid <<= integerPartWidth / 2;
2651 if (low + mid < low)
2655 mid = highHalf(srcPart) * lowHalf(multiplier);
2656 high += highHalf(mid);
2657 mid <<= integerPartWidth / 2;
2658 if (low + mid < low)
2662 /* Now add carry. */
2663 if (low + carry < low)
2669 /* And now DST[i], and store the new low part there. */
2670 if (low + dst[i] < low)
2680 /* Full multiplication, there is no overflow. */
2681 assert(i + 1 == dstParts);
2685 /* We overflowed if there is carry. */
2689 /* We would overflow if any significant unwritten parts would be
2690 non-zero. This is true if any remaining src parts are non-zero
2691 and the multiplier is non-zero. */
2693 for (; i < srcParts; i++)
2697 /* We fitted in the narrow destination. */
2702 /* DST = LHS * RHS, where DST has the same width as the operands and
2703 is filled with the least significant parts of the result. Returns
2704 one if overflow occurred, otherwise zero. DST must be disjoint
2705 from both operands. */
2707 APInt::tcMultiply(integerPart *dst, const integerPart *lhs,
2708 const integerPart *rhs, unsigned int parts)
2713 assert(dst != lhs && dst != rhs);
2716 tcSet(dst, 0, parts);
2718 for (i = 0; i < parts; i++)
2719 overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts,
2725 /* DST = LHS * RHS, where DST has width the sum of the widths of the
2726 operands. No overflow occurs. DST must be disjoint from both
2727 operands. Returns the number of parts required to hold the
2730 APInt::tcFullMultiply(integerPart *dst, const integerPart *lhs,
2731 const integerPart *rhs, unsigned int lhsParts,
2732 unsigned int rhsParts)
2734 /* Put the narrower number on the LHS for less loops below. */
2735 if (lhsParts > rhsParts) {
2736 return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts);
2740 assert(dst != lhs && dst != rhs);
2742 tcSet(dst, 0, rhsParts);
2744 for (n = 0; n < lhsParts; n++)
2745 tcMultiplyPart(&dst[n], rhs, lhs[n], 0, rhsParts, rhsParts + 1, true);
2747 n = lhsParts + rhsParts;
2749 return n - (dst[n - 1] == 0);
2753 /* If RHS is zero LHS and REMAINDER are left unchanged, return one.
2754 Otherwise set LHS to LHS / RHS with the fractional part discarded,
2755 set REMAINDER to the remainder, return zero. i.e.
2757 OLD_LHS = RHS * LHS + REMAINDER
2759 SCRATCH is a bignum of the same size as the operands and result for
2760 use by the routine; its contents need not be initialized and are
2761 destroyed. LHS, REMAINDER and SCRATCH must be distinct.
2764 APInt::tcDivide(integerPart *lhs, const integerPart *rhs,
2765 integerPart *remainder, integerPart *srhs,
2768 unsigned int n, shiftCount;
2771 assert(lhs != remainder && lhs != srhs && remainder != srhs);
2773 shiftCount = tcMSB(rhs, parts) + 1;
2774 if (shiftCount == 0)
2777 shiftCount = parts * integerPartWidth - shiftCount;
2778 n = shiftCount / integerPartWidth;
2779 mask = (integerPart) 1 << (shiftCount % integerPartWidth);
2781 tcAssign(srhs, rhs, parts);
2782 tcShiftLeft(srhs, parts, shiftCount);
2783 tcAssign(remainder, lhs, parts);
2784 tcSet(lhs, 0, parts);
2786 /* Loop, subtracting SRHS if REMAINDER is greater and adding that to
2791 compare = tcCompare(remainder, srhs, parts);
2793 tcSubtract(remainder, srhs, 0, parts);
2797 if (shiftCount == 0)
2800 tcShiftRight(srhs, parts, 1);
2801 if ((mask >>= 1) == 0)
2802 mask = (integerPart) 1 << (integerPartWidth - 1), n--;
2808 /* Shift a bignum left COUNT bits in-place. Shifted in bits are zero.
2809 There are no restrictions on COUNT. */
2811 APInt::tcShiftLeft(integerPart *dst, unsigned int parts, unsigned int count)
2814 unsigned int jump, shift;
2816 /* Jump is the inter-part jump; shift is is intra-part shift. */
2817 jump = count / integerPartWidth;
2818 shift = count % integerPartWidth;
2820 while (parts > jump) {
2825 /* dst[i] comes from the two parts src[i - jump] and, if we have
2826 an intra-part shift, src[i - jump - 1]. */
2827 part = dst[parts - jump];
2830 if (parts >= jump + 1)
2831 part |= dst[parts - jump - 1] >> (integerPartWidth - shift);
2842 /* Shift a bignum right COUNT bits in-place. Shifted in bits are
2843 zero. There are no restrictions on COUNT. */
2845 APInt::tcShiftRight(integerPart *dst, unsigned int parts, unsigned int count)
2848 unsigned int i, jump, shift;
2850 /* Jump is the inter-part jump; shift is is intra-part shift. */
2851 jump = count / integerPartWidth;
2852 shift = count % integerPartWidth;
2854 /* Perform the shift. This leaves the most significant COUNT bits
2855 of the result at zero. */
2856 for (i = 0; i < parts; i++) {
2859 if (i + jump >= parts) {
2862 part = dst[i + jump];
2865 if (i + jump + 1 < parts)
2866 part |= dst[i + jump + 1] << (integerPartWidth - shift);
2875 /* Bitwise and of two bignums. */
2877 APInt::tcAnd(integerPart *dst, const integerPart *rhs, unsigned int parts)
2881 for (i = 0; i < parts; i++)
2885 /* Bitwise inclusive or of two bignums. */
2887 APInt::tcOr(integerPart *dst, const integerPart *rhs, unsigned int parts)
2891 for (i = 0; i < parts; i++)
2895 /* Bitwise exclusive or of two bignums. */
2897 APInt::tcXor(integerPart *dst, const integerPart *rhs, unsigned int parts)
2901 for (i = 0; i < parts; i++)
2905 /* Complement a bignum in-place. */
2907 APInt::tcComplement(integerPart *dst, unsigned int parts)
2911 for (i = 0; i < parts; i++)
2915 /* Comparison (unsigned) of two bignums. */
2917 APInt::tcCompare(const integerPart *lhs, const integerPart *rhs,
2922 if (lhs[parts] == rhs[parts])
2925 if (lhs[parts] > rhs[parts])
2934 /* Increment a bignum in-place, return the carry flag. */
2936 APInt::tcIncrement(integerPart *dst, unsigned int parts)
2940 for (i = 0; i < parts; i++)
2947 /* Set the least significant BITS bits of a bignum, clear the
2950 APInt::tcSetLeastSignificantBits(integerPart *dst, unsigned int parts,
2956 while (bits > integerPartWidth) {
2957 dst[i++] = ~(integerPart) 0;
2958 bits -= integerPartWidth;
2962 dst[i++] = ~(integerPart) 0 >> (integerPartWidth - bits);