1 //===-- APInt.cpp - Implement APInt class ---------------------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by Sheng Zhou and is distributed under the
6 // University of Illinois Open Source 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/DerivedTypes.h"
18 #include "llvm/Support/Debug.h"
19 #include "llvm/Support/MathExtras.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(uint32_t 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(uint32_t numWords) {
42 uint64_t * result = new uint64_t[numWords];
43 assert(result && "APInt memory allocation fails!");
47 APInt::APInt(uint32_t numBits, uint64_t val, bool isSigned)
48 : BitWidth(numBits), VAL(0) {
49 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small");
50 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large");
54 pVal = getClearedMemory(getNumWords());
56 if (isSigned && int64_t(val) < 0)
57 for (unsigned i = 1; i < getNumWords(); ++i)
63 APInt::APInt(uint32_t numBits, uint32_t numWords, uint64_t bigVal[])
64 : BitWidth(numBits), VAL(0) {
65 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small");
66 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large");
67 assert(bigVal && "Null pointer detected!");
71 // Get memory, cleared to 0
72 pVal = getClearedMemory(getNumWords());
73 // Calculate the number of words to copy
74 uint32_t words = std::min<uint32_t>(numWords, getNumWords());
75 // Copy the words from bigVal to pVal
76 memcpy(pVal, bigVal, words * APINT_WORD_SIZE);
78 // Make sure unused high bits are cleared
82 APInt::APInt(uint32_t numbits, const char StrStart[], uint32_t slen,
84 : BitWidth(numbits), VAL(0) {
85 fromString(numbits, StrStart, slen, radix);
88 APInt::APInt(uint32_t numbits, const std::string& Val, uint8_t radix)
89 : BitWidth(numbits), VAL(0) {
90 assert(!Val.empty() && "String empty?");
91 fromString(numbits, Val.c_str(), Val.size(), radix);
94 APInt::APInt(const APInt& that)
95 : BitWidth(that.BitWidth), VAL(0) {
99 pVal = getMemory(getNumWords());
100 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE);
105 if (!isSingleWord() && pVal)
109 APInt& APInt::operator=(const APInt& RHS) {
110 // Don't do anything for X = X
114 // If the bitwidths are the same, we can avoid mucking with memory
115 if (BitWidth == RHS.getBitWidth()) {
119 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE);
124 if (RHS.isSingleWord())
128 pVal = getMemory(RHS.getNumWords());
129 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
131 else if (getNumWords() == RHS.getNumWords())
132 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
133 else if (RHS.isSingleWord()) {
138 pVal = getMemory(RHS.getNumWords());
139 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
141 BitWidth = RHS.BitWidth;
142 return clearUnusedBits();
145 APInt& APInt::operator=(uint64_t RHS) {
150 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE);
152 return clearUnusedBits();
155 /// add_1 - This function adds a single "digit" integer, y, to the multiple
156 /// "digit" integer array, x[]. x[] is modified to reflect the addition and
157 /// 1 is returned if there is a carry out, otherwise 0 is returned.
158 /// @returns the carry of the addition.
159 static bool add_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
160 for (uint32_t i = 0; i < len; ++i) {
163 y = 1; // Carry one to next digit.
165 y = 0; // No need to carry so exit early
172 /// @brief Prefix increment operator. Increments the APInt by one.
173 APInt& APInt::operator++() {
177 add_1(pVal, pVal, getNumWords(), 1);
178 return clearUnusedBits();
181 /// sub_1 - This function subtracts a single "digit" (64-bit word), y, from
182 /// the multi-digit integer array, x[], propagating the borrowed 1 value until
183 /// no further borrowing is neeeded or it runs out of "digits" in x. The result
184 /// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted.
185 /// In other words, if y > x then this function returns 1, otherwise 0.
186 /// @returns the borrow out of the subtraction
187 static bool sub_1(uint64_t x[], uint32_t len, uint64_t y) {
188 for (uint32_t i = 0; i < len; ++i) {
192 y = 1; // We have to "borrow 1" from next "digit"
194 y = 0; // No need to borrow
195 break; // Remaining digits are unchanged so exit early
201 /// @brief Prefix decrement operator. Decrements the APInt by one.
202 APInt& APInt::operator--() {
206 sub_1(pVal, getNumWords(), 1);
207 return clearUnusedBits();
210 /// add - This function adds the integer array x to the integer array Y and
211 /// places the result in dest.
212 /// @returns the carry out from the addition
213 /// @brief General addition of 64-bit integer arrays
214 static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y,
217 for (uint32_t i = 0; i< len; ++i) {
218 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x
219 dest[i] = x[i] + y[i] + carry;
220 carry = dest[i] < limit || (carry && dest[i] == limit);
225 /// Adds the RHS APint to this APInt.
226 /// @returns this, after addition of RHS.
227 /// @brief Addition assignment operator.
228 APInt& APInt::operator+=(const APInt& RHS) {
229 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
233 add(pVal, pVal, RHS.pVal, getNumWords());
235 return clearUnusedBits();
238 /// Subtracts the integer array y from the integer array x
239 /// @returns returns the borrow out.
240 /// @brief Generalized subtraction of 64-bit integer arrays.
241 static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y,
244 for (uint32_t i = 0; i < len; ++i) {
245 uint64_t x_tmp = borrow ? x[i] - 1 : x[i];
246 borrow = y[i] > x_tmp || (borrow && x[i] == 0);
247 dest[i] = x_tmp - y[i];
252 /// Subtracts the RHS APInt from this APInt
253 /// @returns this, after subtraction
254 /// @brief Subtraction assignment operator.
255 APInt& APInt::operator-=(const APInt& RHS) {
256 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
260 sub(pVal, pVal, RHS.pVal, getNumWords());
261 return clearUnusedBits();
264 /// Multiplies an integer array, x by a a uint64_t integer and places the result
266 /// @returns the carry out of the multiplication.
267 /// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer.
268 static uint64_t mul_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
269 // Split y into high 32-bit part (hy) and low 32-bit part (ly)
270 uint64_t ly = y & 0xffffffffULL, hy = y >> 32;
273 // For each digit of x.
274 for (uint32_t i = 0; i < len; ++i) {
275 // Split x into high and low words
276 uint64_t lx = x[i] & 0xffffffffULL;
277 uint64_t hx = x[i] >> 32;
278 // hasCarry - A flag to indicate if there is a carry to the next digit.
279 // hasCarry == 0, no carry
280 // hasCarry == 1, has carry
281 // hasCarry == 2, no carry and the calculation result == 0.
282 uint8_t hasCarry = 0;
283 dest[i] = carry + lx * ly;
284 // Determine if the add above introduces carry.
285 hasCarry = (dest[i] < carry) ? 1 : 0;
286 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0);
287 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) +
288 // (2^32 - 1) + 2^32 = 2^64.
289 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
291 carry += (lx * hy) & 0xffffffffULL;
292 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL);
293 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) +
294 (carry >> 32) + ((lx * hy) >> 32) + hx * hy;
299 /// Multiplies integer array x by integer array y and stores the result into
300 /// the integer array dest. Note that dest's size must be >= xlen + ylen.
301 /// @brief Generalized multiplicate of integer arrays.
302 static void mul(uint64_t dest[], uint64_t x[], uint32_t xlen, uint64_t y[],
304 dest[xlen] = mul_1(dest, x, xlen, y[0]);
305 for (uint32_t i = 1; i < ylen; ++i) {
306 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32;
307 uint64_t carry = 0, lx = 0, hx = 0;
308 for (uint32_t j = 0; j < xlen; ++j) {
309 lx = x[j] & 0xffffffffULL;
311 // hasCarry - A flag to indicate if has carry.
312 // hasCarry == 0, no carry
313 // hasCarry == 1, has carry
314 // hasCarry == 2, no carry and the calculation result == 0.
315 uint8_t hasCarry = 0;
316 uint64_t resul = carry + lx * ly;
317 hasCarry = (resul < carry) ? 1 : 0;
318 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32);
319 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
321 carry += (lx * hy) & 0xffffffffULL;
322 resul = (carry << 32) | (resul & 0xffffffffULL);
324 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+
325 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) +
326 ((lx * hy) >> 32) + hx * hy;
328 dest[i+xlen] = carry;
332 APInt& APInt::operator*=(const APInt& RHS) {
333 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
334 if (isSingleWord()) {
340 // Get some bit facts about LHS and check for zero
341 uint32_t lhsBits = getActiveBits();
342 uint32_t lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1;
347 // Get some bit facts about RHS and check for zero
348 uint32_t rhsBits = RHS.getActiveBits();
349 uint32_t rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1;
356 // Allocate space for the result
357 uint32_t destWords = rhsWords + lhsWords;
358 uint64_t *dest = getMemory(destWords);
360 // Perform the long multiply
361 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords);
363 // Copy result back into *this
365 uint32_t wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords;
366 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE);
368 // delete dest array and return
373 APInt& APInt::operator&=(const APInt& RHS) {
374 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
375 if (isSingleWord()) {
379 uint32_t numWords = getNumWords();
380 for (uint32_t i = 0; i < numWords; ++i)
381 pVal[i] &= RHS.pVal[i];
385 APInt& APInt::operator|=(const APInt& RHS) {
386 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
387 if (isSingleWord()) {
391 uint32_t numWords = getNumWords();
392 for (uint32_t 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()) {
401 this->clearUnusedBits();
404 uint32_t numWords = getNumWords();
405 for (uint32_t i = 0; i < numWords; ++i)
406 pVal[i] ^= RHS.pVal[i];
407 return clearUnusedBits();
410 APInt APInt::operator&(const APInt& RHS) const {
411 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
413 return APInt(getBitWidth(), VAL & RHS.VAL);
415 uint32_t numWords = getNumWords();
416 uint64_t* val = getMemory(numWords);
417 for (uint32_t i = 0; i < numWords; ++i)
418 val[i] = pVal[i] & RHS.pVal[i];
419 return APInt(val, getBitWidth());
422 APInt APInt::operator|(const APInt& RHS) const {
423 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
425 return APInt(getBitWidth(), VAL | RHS.VAL);
427 uint32_t numWords = getNumWords();
428 uint64_t *val = getMemory(numWords);
429 for (uint32_t i = 0; i < numWords; ++i)
430 val[i] = pVal[i] | RHS.pVal[i];
431 return APInt(val, getBitWidth());
434 APInt APInt::operator^(const APInt& RHS) const {
435 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
437 return APInt(BitWidth, VAL ^ RHS.VAL);
439 uint32_t numWords = getNumWords();
440 uint64_t *val = getMemory(numWords);
441 for (uint32_t 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 (uint32_t 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[](uint32_t bitPosition) const {
486 return (maskBit(bitPosition) &
487 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0;
490 bool APInt::operator==(const APInt& RHS) const {
491 assert(BitWidth == RHS.BitWidth && "Comparison requires equal bit widths");
493 return VAL == RHS.VAL;
495 // Get some facts about the number of bits used in the two operands.
496 uint32_t n1 = getActiveBits();
497 uint32_t n2 = RHS.getActiveBits();
499 // If the number of bits isn't the same, they aren't equal
503 // If the number of bits fits in a word, we only need to compare the low word.
504 if (n1 <= APINT_BITS_PER_WORD)
505 return pVal[0] == RHS.pVal[0];
507 // Otherwise, compare everything
508 for (int i = whichWord(n1 - 1); i >= 0; --i)
509 if (pVal[i] != RHS.pVal[i])
514 bool APInt::operator==(uint64_t Val) const {
518 uint32_t n = getActiveBits();
519 if (n <= APINT_BITS_PER_WORD)
520 return pVal[0] == Val;
525 bool APInt::ult(const APInt& RHS) const {
526 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
528 return VAL < RHS.VAL;
530 // Get active bit length of both operands
531 uint32_t n1 = getActiveBits();
532 uint32_t n2 = RHS.getActiveBits();
534 // If magnitude of LHS is less than RHS, return true.
538 // If magnitude of RHS is greather than LHS, return false.
542 // If they bot fit in a word, just compare the low order word
543 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD)
544 return pVal[0] < RHS.pVal[0];
546 // Otherwise, compare all words
547 uint32_t topWord = whichWord(std::max(n1,n2)-1);
548 for (int i = topWord; i >= 0; --i) {
549 if (pVal[i] > RHS.pVal[i])
551 if (pVal[i] < RHS.pVal[i])
557 bool APInt::slt(const APInt& RHS) const {
558 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
559 if (isSingleWord()) {
560 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
561 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth);
562 return lhsSext < rhsSext;
567 bool lhsNeg = isNegative();
568 bool rhsNeg = rhs.isNegative();
570 // Sign bit is set so perform two's complement to make it positive
575 // Sign bit is set so perform two's complement to make it positive
580 // Now we have unsigned values to compare so do the comparison if necessary
581 // based on the negativeness of the values.
593 APInt& APInt::set(uint32_t bitPosition) {
595 VAL |= maskBit(bitPosition);
597 pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
601 APInt& APInt::set() {
602 if (isSingleWord()) {
604 return clearUnusedBits();
607 // Set all the bits in all the words.
608 for (uint32_t i = 0; i < getNumWords(); ++i)
610 // Clear the unused ones
611 return clearUnusedBits();
614 /// Set the given bit to 0 whose position is given as "bitPosition".
615 /// @brief Set a given bit to 0.
616 APInt& APInt::clear(uint32_t bitPosition) {
618 VAL &= ~maskBit(bitPosition);
620 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
624 /// @brief Set every bit to 0.
625 APInt& APInt::clear() {
629 memset(pVal, 0, getNumWords() * APINT_WORD_SIZE);
633 /// @brief Bitwise NOT operator. Performs a bitwise logical NOT operation on
635 APInt APInt::operator~() const {
641 /// @brief Toggle every bit to its opposite value.
642 APInt& APInt::flip() {
643 if (isSingleWord()) {
645 return clearUnusedBits();
647 for (uint32_t i = 0; i < getNumWords(); ++i)
649 return clearUnusedBits();
652 /// Toggle a given bit to its opposite value whose position is given
653 /// as "bitPosition".
654 /// @brief Toggles a given bit to its opposite value.
655 APInt& APInt::flip(uint32_t bitPosition) {
656 assert(bitPosition < BitWidth && "Out of the bit-width range!");
657 if ((*this)[bitPosition]) clear(bitPosition);
658 else set(bitPosition);
662 uint32_t APInt::getBitsNeeded(const char* str, uint32_t slen, uint8_t radix) {
663 assert(str != 0 && "Invalid value string");
664 assert(slen > 0 && "Invalid string length");
666 // Each computation below needs to know if its negative
667 uint32_t isNegative = str[0] == '-';
672 // For radixes of power-of-two values, the bits required is accurately and
675 return slen + isNegative;
677 return slen * 3 + isNegative;
679 return slen * 4 + isNegative;
681 // Otherwise it must be radix == 10, the hard case
682 assert(radix == 10 && "Invalid radix");
684 // This is grossly inefficient but accurate. We could probably do something
685 // with a computation of roughly slen*64/20 and then adjust by the value of
686 // the first few digits. But, I'm not sure how accurate that could be.
688 // Compute a sufficient number of bits that is always large enough but might
689 // be too large. This avoids the assertion in the constructor.
690 uint32_t sufficient = slen*64/18;
692 // Convert to the actual binary value.
693 APInt tmp(sufficient, str, slen, radix);
695 // Compute how many bits are required.
696 return isNegative + tmp.logBase2();
699 uint64_t APInt::getHashValue() const {
700 // Put the bit width into the low order bits.
701 uint64_t hash = BitWidth;
703 // Add the sum of the words to the hash.
705 hash += VAL << 6; // clear separation of up to 64 bits
707 for (uint32_t i = 0; i < getNumWords(); ++i)
708 hash += pVal[i] << 6; // clear sepration of up to 64 bits
712 /// HiBits - This function returns the high "numBits" bits of this APInt.
713 APInt APInt::getHiBits(uint32_t numBits) const {
714 return APIntOps::lshr(*this, BitWidth - numBits);
717 /// LoBits - This function returns the low "numBits" bits of this APInt.
718 APInt APInt::getLoBits(uint32_t numBits) const {
719 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
723 bool APInt::isPowerOf2() const {
724 return (!!*this) && !(*this & (*this - APInt(BitWidth,1)));
727 uint32_t APInt::countLeadingZeros() const {
730 Count = CountLeadingZeros_64(VAL);
732 for (uint32_t i = getNumWords(); i > 0u; --i) {
734 Count += APINT_BITS_PER_WORD;
736 Count += CountLeadingZeros_64(pVal[i-1]);
741 uint32_t remainder = BitWidth % APINT_BITS_PER_WORD;
743 Count -= APINT_BITS_PER_WORD - remainder;
747 static uint32_t countLeadingOnes_64(uint64_t V, uint32_t skip) {
751 while (V && (V & (1ULL << 63))) {
758 uint32_t APInt::countLeadingOnes() const {
760 return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth);
762 uint32_t highWordBits = BitWidth % APINT_BITS_PER_WORD;
763 uint32_t shift = (highWordBits == 0 ? 0 : APINT_BITS_PER_WORD - highWordBits);
764 int i = getNumWords() - 1;
765 uint32_t Count = countLeadingOnes_64(pVal[i], shift);
766 if (Count == highWordBits) {
767 for (i--; i >= 0; --i) {
768 if (pVal[i] == -1ULL)
769 Count += APINT_BITS_PER_WORD;
771 Count += countLeadingOnes_64(pVal[i], 0);
779 uint32_t APInt::countTrailingZeros() const {
781 return CountTrailingZeros_64(VAL);
784 for (; i < getNumWords() && pVal[i] == 0; ++i)
785 Count += APINT_BITS_PER_WORD;
786 if (i < getNumWords())
787 Count += CountTrailingZeros_64(pVal[i]);
791 uint32_t APInt::countPopulation() const {
793 return CountPopulation_64(VAL);
795 for (uint32_t i = 0; i < getNumWords(); ++i)
796 Count += CountPopulation_64(pVal[i]);
800 APInt APInt::byteSwap() const {
801 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
803 return APInt(BitWidth, ByteSwap_16(uint16_t(VAL)));
804 else if (BitWidth == 32)
805 return APInt(BitWidth, ByteSwap_32(uint32_t(VAL)));
806 else if (BitWidth == 48) {
807 uint32_t Tmp1 = uint32_t(VAL >> 16);
808 Tmp1 = ByteSwap_32(Tmp1);
809 uint16_t Tmp2 = uint16_t(VAL);
810 Tmp2 = ByteSwap_16(Tmp2);
811 return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1);
812 } else if (BitWidth == 64)
813 return APInt(BitWidth, ByteSwap_64(VAL));
815 APInt Result(BitWidth, 0);
816 char *pByte = (char*)Result.pVal;
817 for (uint32_t i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) {
819 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i];
820 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp;
826 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
828 APInt A = API1, B = API2;
831 B = APIntOps::urem(A, B);
837 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, uint32_t width) {
844 // Get the sign bit from the highest order bit
845 bool isNeg = T.I >> 63;
847 // Get the 11-bit exponent and adjust for the 1023 bit bias
848 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
850 // If the exponent is negative, the value is < 0 so just return 0.
852 return APInt(width, 0u);
854 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
855 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
857 // If the exponent doesn't shift all bits out of the mantissa
859 return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
860 APInt(width, mantissa >> (52 - exp));
862 // If the client didn't provide enough bits for us to shift the mantissa into
863 // then the result is undefined, just return 0
864 if (width <= exp - 52)
865 return APInt(width, 0);
867 // Otherwise, we have to shift the mantissa bits up to the right location
868 APInt Tmp(width, mantissa);
869 Tmp = Tmp.shl(exp - 52);
870 return isNeg ? -Tmp : Tmp;
873 /// RoundToDouble - This function convert this APInt to a double.
874 /// The layout for double is as following (IEEE Standard 754):
875 /// --------------------------------------
876 /// | Sign Exponent Fraction Bias |
877 /// |-------------------------------------- |
878 /// | 1[63] 11[62-52] 52[51-00] 1023 |
879 /// --------------------------------------
880 double APInt::roundToDouble(bool isSigned) const {
882 // Handle the simple case where the value is contained in one uint64_t.
883 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
885 int64_t sext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
891 // Determine if the value is negative.
892 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
894 // Construct the absolute value if we're negative.
895 APInt Tmp(isNeg ? -(*this) : (*this));
897 // Figure out how many bits we're using.
898 uint32_t n = Tmp.getActiveBits();
900 // The exponent (without bias normalization) is just the number of bits
901 // we are using. Note that the sign bit is gone since we constructed the
905 // Return infinity for exponent overflow
907 if (!isSigned || !isNeg)
908 return std::numeric_limits<double>::infinity();
910 return -std::numeric_limits<double>::infinity();
912 exp += 1023; // Increment for 1023 bias
914 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
915 // extract the high 52 bits from the correct words in pVal.
917 unsigned hiWord = whichWord(n-1);
919 mantissa = Tmp.pVal[0];
921 mantissa >>= n - 52; // shift down, we want the top 52 bits.
923 assert(hiWord > 0 && "huh?");
924 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
925 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
926 mantissa = hibits | lobits;
929 // The leading bit of mantissa is implicit, so get rid of it.
930 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
935 T.I = sign | (exp << 52) | mantissa;
939 // Truncate to new width.
940 APInt &APInt::trunc(uint32_t width) {
941 assert(width < BitWidth && "Invalid APInt Truncate request");
942 assert(width >= IntegerType::MIN_INT_BITS && "Can't truncate to 0 bits");
943 uint32_t wordsBefore = getNumWords();
945 uint32_t wordsAfter = getNumWords();
946 if (wordsBefore != wordsAfter) {
947 if (wordsAfter == 1) {
948 uint64_t *tmp = pVal;
952 uint64_t *newVal = getClearedMemory(wordsAfter);
953 for (uint32_t i = 0; i < wordsAfter; ++i)
959 return clearUnusedBits();
962 // Sign extend to a new width.
963 APInt &APInt::sext(uint32_t width) {
964 assert(width > BitWidth && "Invalid APInt SignExtend request");
965 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
966 // If the sign bit isn't set, this is the same as zext.
972 // The sign bit is set. First, get some facts
973 uint32_t wordsBefore = getNumWords();
974 uint32_t wordBits = BitWidth % APINT_BITS_PER_WORD;
976 uint32_t wordsAfter = getNumWords();
978 // Mask the high order word appropriately
979 if (wordsBefore == wordsAfter) {
980 uint32_t newWordBits = width % APINT_BITS_PER_WORD;
981 // The extension is contained to the wordsBefore-1th word.
982 uint64_t mask = ~0ULL;
984 mask >>= APINT_BITS_PER_WORD - newWordBits;
986 if (wordsBefore == 1)
989 pVal[wordsBefore-1] |= mask;
990 return clearUnusedBits();
993 uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits;
994 uint64_t *newVal = getMemory(wordsAfter);
995 if (wordsBefore == 1)
996 newVal[0] = VAL | mask;
998 for (uint32_t i = 0; i < wordsBefore; ++i)
1000 newVal[wordsBefore-1] |= mask;
1002 for (uint32_t i = wordsBefore; i < wordsAfter; i++)
1004 if (wordsBefore != 1)
1007 return clearUnusedBits();
1010 // Zero extend to a new width.
1011 APInt &APInt::zext(uint32_t width) {
1012 assert(width > BitWidth && "Invalid APInt ZeroExtend request");
1013 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
1014 uint32_t wordsBefore = getNumWords();
1016 uint32_t wordsAfter = getNumWords();
1017 if (wordsBefore != wordsAfter) {
1018 uint64_t *newVal = getClearedMemory(wordsAfter);
1019 if (wordsBefore == 1)
1022 for (uint32_t i = 0; i < wordsBefore; ++i)
1023 newVal[i] = pVal[i];
1024 if (wordsBefore != 1)
1031 APInt &APInt::zextOrTrunc(uint32_t width) {
1032 if (BitWidth < width)
1034 if (BitWidth > width)
1035 return trunc(width);
1039 APInt &APInt::sextOrTrunc(uint32_t width) {
1040 if (BitWidth < width)
1042 if (BitWidth > width)
1043 return trunc(width);
1047 /// Arithmetic right-shift this APInt by shiftAmt.
1048 /// @brief Arithmetic right-shift function.
1049 APInt APInt::ashr(uint32_t shiftAmt) const {
1050 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1051 // Handle a degenerate case
1055 // Handle single word shifts with built-in ashr
1056 if (isSingleWord()) {
1057 if (shiftAmt == BitWidth)
1058 return APInt(BitWidth, 0); // undefined
1060 uint32_t SignBit = APINT_BITS_PER_WORD - BitWidth;
1061 return APInt(BitWidth,
1062 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1066 // If all the bits were shifted out, the result is, technically, undefined.
1067 // We return -1 if it was negative, 0 otherwise. We check this early to avoid
1068 // issues in the algorithm below.
1069 if (shiftAmt == BitWidth)
1071 return APInt(BitWidth, -1ULL);
1073 return APInt(BitWidth, 0);
1075 // Create some space for the result.
1076 uint64_t * val = new uint64_t[getNumWords()];
1078 // Compute some values needed by the following shift algorithms
1079 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word
1080 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift
1081 uint32_t breakWord = getNumWords() - 1 - offset; // last word affected
1082 uint32_t bitsInWord = whichBit(BitWidth); // how many bits in last word?
1083 if (bitsInWord == 0)
1084 bitsInWord = APINT_BITS_PER_WORD;
1086 // If we are shifting whole words, just move whole words
1087 if (wordShift == 0) {
1088 // Move the words containing significant bits
1089 for (uint32_t i = 0; i <= breakWord; ++i)
1090 val[i] = pVal[i+offset]; // move whole word
1092 // Adjust the top significant word for sign bit fill, if negative
1094 if (bitsInWord < APINT_BITS_PER_WORD)
1095 val[breakWord] |= ~0ULL << bitsInWord; // set high bits
1097 // Shift the low order words
1098 for (uint32_t i = 0; i < breakWord; ++i) {
1099 // This combines the shifted corresponding word with the low bits from
1100 // the next word (shifted into this word's high bits).
1101 val[i] = (pVal[i+offset] >> wordShift) |
1102 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1105 // Shift the break word. In this case there are no bits from the next word
1106 // to include in this word.
1107 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1109 // Deal with sign extenstion in the break word, and possibly the word before
1112 if (wordShift > bitsInWord) {
1115 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord));
1116 val[breakWord] |= ~0ULL;
1118 val[breakWord] |= (~0ULL << (bitsInWord - wordShift));
1121 // Remaining words are 0 or -1, just assign them.
1122 uint64_t fillValue = (isNegative() ? -1ULL : 0);
1123 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1125 return APInt(val, BitWidth).clearUnusedBits();
1128 /// Logical right-shift this APInt by shiftAmt.
1129 /// @brief Logical right-shift function.
1130 APInt APInt::lshr(uint32_t shiftAmt) const {
1132 if (shiftAmt == BitWidth)
1133 return APInt(BitWidth, 0);
1135 return APInt(BitWidth, this->VAL >> shiftAmt);
1137 // If all the bits were shifted out, the result is 0. This avoids issues
1138 // with shifting by the size of the integer type, which produces undefined
1139 // results. We define these "undefined results" to always be 0.
1140 if (shiftAmt == BitWidth)
1141 return APInt(BitWidth, 0);
1143 // Create some space for the result.
1144 uint64_t * val = new uint64_t[getNumWords()];
1146 // If we are shifting less than a word, compute the shift with a simple carry
1147 if (shiftAmt < APINT_BITS_PER_WORD) {
1149 for (int i = getNumWords()-1; i >= 0; --i) {
1150 val[i] = (pVal[i] >> shiftAmt) | carry;
1151 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1153 return APInt(val, BitWidth).clearUnusedBits();
1156 // Compute some values needed by the remaining shift algorithms
1157 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1158 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1160 // If we are shifting whole words, just move whole words
1161 if (wordShift == 0) {
1162 for (uint32_t i = 0; i < getNumWords() - offset; ++i)
1163 val[i] = pVal[i+offset];
1164 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
1166 return APInt(val,BitWidth).clearUnusedBits();
1169 // Shift the low order words
1170 uint32_t breakWord = getNumWords() - offset -1;
1171 for (uint32_t i = 0; i < breakWord; ++i)
1172 val[i] = (pVal[i+offset] >> wordShift) |
1173 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1174 // Shift the break word.
1175 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1177 // Remaining words are 0
1178 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1180 return APInt(val, BitWidth).clearUnusedBits();
1183 /// Left-shift this APInt by shiftAmt.
1184 /// @brief Left-shift function.
1185 APInt APInt::shl(uint32_t shiftAmt) const {
1186 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1187 if (isSingleWord()) {
1188 if (shiftAmt == BitWidth)
1189 return APInt(BitWidth, 0); // avoid undefined shift results
1190 return APInt(BitWidth, VAL << shiftAmt);
1193 // If all the bits were shifted out, the result is 0. This avoids issues
1194 // with shifting by the size of the integer type, which produces undefined
1195 // results. We define these "undefined results" to always be 0.
1196 if (shiftAmt == BitWidth)
1197 return APInt(BitWidth, 0);
1199 // Create some space for the result.
1200 uint64_t * val = new uint64_t[getNumWords()];
1202 // If we are shifting less than a word, do it the easy way
1203 if (shiftAmt < APINT_BITS_PER_WORD) {
1205 for (uint32_t i = 0; i < getNumWords(); i++) {
1206 val[i] = pVal[i] << shiftAmt | carry;
1207 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1209 return APInt(val, BitWidth).clearUnusedBits();
1212 // Compute some values needed by the remaining shift algorithms
1213 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1214 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1216 // If we are shifting whole words, just move whole words
1217 if (wordShift == 0) {
1218 for (uint32_t i = 0; i < offset; i++)
1220 for (uint32_t i = offset; i < getNumWords(); i++)
1221 val[i] = pVal[i-offset];
1222 return APInt(val,BitWidth).clearUnusedBits();
1225 // Copy whole words from this to Result.
1226 uint32_t i = getNumWords() - 1;
1227 for (; i > offset; --i)
1228 val[i] = pVal[i-offset] << wordShift |
1229 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1230 val[offset] = pVal[0] << wordShift;
1231 for (i = 0; i < offset; ++i)
1233 return APInt(val, BitWidth).clearUnusedBits();
1237 // Square Root - this method computes and returns the square root of "this".
1238 // Three mechanisms are used for computation. For small values (<= 5 bits),
1239 // a table lookup is done. This gets some performance for common cases. For
1240 // values using less than 52 bits, the value is converted to double and then
1241 // the libc sqrt function is called. The result is rounded and then converted
1242 // back to a uint64_t which is then used to construct the result. Finally,
1243 // the Babylonian method for computing square roots is used.
1244 APInt APInt::sqrt() const {
1246 // Determine the magnitude of the value.
1247 uint32_t magnitude = getActiveBits();
1249 // Use a fast table for some small values. This also gets rid of some
1250 // rounding errors in libc sqrt for small values.
1251 if (magnitude <= 5) {
1252 static const uint8_t results[32] = {
1255 /* 3- 6 */ 2, 2, 2, 2,
1256 /* 7-12 */ 3, 3, 3, 3, 3, 3,
1257 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1258 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1261 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]);
1264 // If the magnitude of the value fits in less than 52 bits (the precision of
1265 // an IEEE double precision floating point value), then we can use the
1266 // libc sqrt function which will probably use a hardware sqrt computation.
1267 // This should be faster than the algorithm below.
1268 if (magnitude < 52) {
1270 // Amazingly, VC++ doesn't have round().
1271 return APInt(BitWidth,
1272 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0]))) + 0.5);
1274 return APInt(BitWidth,
1275 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0])))));
1279 // Okay, all the short cuts are exhausted. We must compute it. The following
1280 // is a classical Babylonian method for computing the square root. This code
1281 // was adapted to APINt from a wikipedia article on such computations.
1282 // See http://www.wikipedia.org/ and go to the page named
1283 // Calculate_an_integer_square_root.
1284 uint32_t nbits = BitWidth, i = 4;
1285 APInt testy(BitWidth, 16);
1286 APInt x_old(BitWidth, 1);
1287 APInt x_new(BitWidth, 0);
1288 APInt two(BitWidth, 2);
1290 // Select a good starting value using binary logarithms.
1291 for (;; i += 2, testy = testy.shl(2))
1292 if (i >= nbits || this->ule(testy)) {
1293 x_old = x_old.shl(i / 2);
1297 // Use the Babylonian method to arrive at the integer square root:
1299 x_new = (this->udiv(x_old) + x_old).udiv(two);
1300 if (x_old.ule(x_new))
1305 // Make sure we return the closest approximation
1306 // NOTE: The rounding calculation below is correct. It will produce an
1307 // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1308 // determined to be a rounding issue with pari/gp as it begins to use a
1309 // floating point representation after 192 bits. There are no discrepancies
1310 // between this algorithm and pari/gp for bit widths < 192 bits.
1311 APInt square(x_old * x_old);
1312 APInt nextSquare((x_old + 1) * (x_old +1));
1313 if (this->ult(square))
1315 else if (this->ule(nextSquare)) {
1316 APInt midpoint((nextSquare - square).udiv(two));
1317 APInt offset(*this - square);
1318 if (offset.ult(midpoint))
1323 assert(0 && "Error in APInt::sqrt computation");
1327 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1328 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1329 /// variables here have the same names as in the algorithm. Comments explain
1330 /// the algorithm and any deviation from it.
1331 static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
1332 uint32_t m, uint32_t n) {
1333 assert(u && "Must provide dividend");
1334 assert(v && "Must provide divisor");
1335 assert(q && "Must provide quotient");
1336 assert(u != v && u != q && v != q && "Must us different memory");
1337 assert(n>1 && "n must be > 1");
1339 // Knuth uses the value b as the base of the number system. In our case b
1340 // is 2^31 so we just set it to -1u.
1341 uint64_t b = uint64_t(1) << 32;
1343 DEBUG(cerr << "KnuthDiv: m=" << m << " n=" << n << '\n');
1344 DEBUG(cerr << "KnuthDiv: original:");
1345 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1346 DEBUG(cerr << " by");
1347 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1348 DEBUG(cerr << '\n');
1349 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1350 // u and v by d. Note that we have taken Knuth's advice here to use a power
1351 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1352 // 2 allows us to shift instead of multiply and it is easy to determine the
1353 // shift amount from the leading zeros. We are basically normalizing the u
1354 // and v so that its high bits are shifted to the top of v's range without
1355 // overflow. Note that this can require an extra word in u so that u must
1356 // be of length m+n+1.
1357 uint32_t shift = CountLeadingZeros_32(v[n-1]);
1358 uint32_t v_carry = 0;
1359 uint32_t u_carry = 0;
1361 for (uint32_t i = 0; i < m+n; ++i) {
1362 uint32_t u_tmp = u[i] >> (32 - shift);
1363 u[i] = (u[i] << shift) | u_carry;
1366 for (uint32_t i = 0; i < n; ++i) {
1367 uint32_t v_tmp = v[i] >> (32 - shift);
1368 v[i] = (v[i] << shift) | v_carry;
1373 DEBUG(cerr << "KnuthDiv: normal:");
1374 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1375 DEBUG(cerr << " by");
1376 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1377 DEBUG(cerr << '\n');
1379 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1382 DEBUG(cerr << "KnuthDiv: quotient digit #" << j << '\n');
1383 // D3. [Calculate q'.].
1384 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1385 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1386 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1387 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1388 // on v[n-2] determines at high speed most of the cases in which the trial
1389 // value qp is one too large, and it eliminates all cases where qp is two
1391 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1392 DEBUG(cerr << "KnuthDiv: dividend == " << dividend << '\n');
1393 uint64_t qp = dividend / v[n-1];
1394 uint64_t rp = dividend % v[n-1];
1395 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1398 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1401 DEBUG(cerr << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1403 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1404 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1405 // consists of a simple multiplication by a one-place number, combined with
1408 for (uint32_t i = 0; i < n; ++i) {
1409 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1410 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1411 bool borrow = subtrahend > u_tmp;
1412 DEBUG(cerr << "KnuthDiv: u_tmp == " << u_tmp
1413 << ", subtrahend == " << subtrahend
1414 << ", borrow = " << borrow << '\n');
1416 uint64_t result = u_tmp - subtrahend;
1418 u[k++] = result & (b-1); // subtract low word
1419 u[k++] = result >> 32; // subtract high word
1420 while (borrow && k <= m+n) { // deal with borrow to the left
1426 DEBUG(cerr << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1429 DEBUG(cerr << "KnuthDiv: after subtraction:");
1430 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1431 DEBUG(cerr << '\n');
1432 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1433 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1434 // true value plus b**(n+1), namely as the b's complement of
1435 // the true value, and a "borrow" to the left should be remembered.
1438 bool carry = true; // true because b's complement is "complement + 1"
1439 for (uint32_t i = 0; i <= m+n; ++i) {
1440 u[i] = ~u[i] + carry; // b's complement
1441 carry = carry && u[i] == 0;
1444 DEBUG(cerr << "KnuthDiv: after complement:");
1445 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1446 DEBUG(cerr << '\n');
1448 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1449 // negative, go to step D6; otherwise go on to step D7.
1452 // D6. [Add back]. The probability that this step is necessary is very
1453 // small, on the order of only 2/b. Make sure that test data accounts for
1454 // this possibility. Decrease q[j] by 1
1456 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1457 // A carry will occur to the left of u[j+n], and it should be ignored
1458 // since it cancels with the borrow that occurred in D4.
1460 for (uint32_t i = 0; i < n; i++) {
1461 uint32_t limit = std::min(u[j+i],v[i]);
1462 u[j+i] += v[i] + carry;
1463 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1467 DEBUG(cerr << "KnuthDiv: after correction:");
1468 DEBUG(for (int i = m+n; i >=0; i--) cerr <<" " << u[i]);
1469 DEBUG(cerr << "\nKnuthDiv: digit result = " << q[j] << '\n');
1471 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1474 DEBUG(cerr << "KnuthDiv: quotient:");
1475 DEBUG(for (int i = m; i >=0; i--) cerr <<" " << q[i]);
1476 DEBUG(cerr << '\n');
1478 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1479 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1480 // compute the remainder (urem uses this).
1482 // The value d is expressed by the "shift" value above since we avoided
1483 // multiplication by d by using a shift left. So, all we have to do is
1484 // shift right here. In order to mak
1487 DEBUG(cerr << "KnuthDiv: remainder:");
1488 for (int i = n-1; i >= 0; i--) {
1489 r[i] = (u[i] >> shift) | carry;
1490 carry = u[i] << (32 - shift);
1491 DEBUG(cerr << " " << r[i]);
1494 for (int i = n-1; i >= 0; i--) {
1496 DEBUG(cerr << " " << r[i]);
1499 DEBUG(cerr << '\n');
1501 DEBUG(cerr << std::setbase(10) << '\n');
1504 void APInt::divide(const APInt LHS, uint32_t lhsWords,
1505 const APInt &RHS, uint32_t rhsWords,
1506 APInt *Quotient, APInt *Remainder)
1508 assert(lhsWords >= rhsWords && "Fractional result");
1510 // First, compose the values into an array of 32-bit words instead of
1511 // 64-bit words. This is a necessity of both the "short division" algorithm
1512 // and the the Knuth "classical algorithm" which requires there to be native
1513 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1514 // can't use 64-bit operands here because we don't have native results of
1515 // 128-bits. Furthremore, casting the 64-bit values to 32-bit values won't
1516 // work on large-endian machines.
1517 uint64_t mask = ~0ull >> (sizeof(uint32_t)*8);
1518 uint32_t n = rhsWords * 2;
1519 uint32_t m = (lhsWords * 2) - n;
1521 // Allocate space for the temporary values we need either on the stack, if
1522 // it will fit, or on the heap if it won't.
1523 uint32_t SPACE[128];
1528 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1531 Q = &SPACE[(m+n+1) + n];
1533 R = &SPACE[(m+n+1) + n + (m+n)];
1535 U = new uint32_t[m + n + 1];
1536 V = new uint32_t[n];
1537 Q = new uint32_t[m+n];
1539 R = new uint32_t[n];
1542 // Initialize the dividend
1543 memset(U, 0, (m+n+1)*sizeof(uint32_t));
1544 for (unsigned i = 0; i < lhsWords; ++i) {
1545 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1546 U[i * 2] = tmp & mask;
1547 U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1549 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1551 // Initialize the divisor
1552 memset(V, 0, (n)*sizeof(uint32_t));
1553 for (unsigned i = 0; i < rhsWords; ++i) {
1554 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1555 V[i * 2] = tmp & mask;
1556 V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1559 // initialize the quotient and remainder
1560 memset(Q, 0, (m+n) * sizeof(uint32_t));
1562 memset(R, 0, n * sizeof(uint32_t));
1564 // Now, adjust m and n for the Knuth division. n is the number of words in
1565 // the divisor. m is the number of words by which the dividend exceeds the
1566 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1567 // contain any zero words or the Knuth algorithm fails.
1568 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1572 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1575 // If we're left with only a single word for the divisor, Knuth doesn't work
1576 // so we implement the short division algorithm here. This is much simpler
1577 // and faster because we are certain that we can divide a 64-bit quantity
1578 // by a 32-bit quantity at hardware speed and short division is simply a
1579 // series of such operations. This is just like doing short division but we
1580 // are using base 2^32 instead of base 10.
1581 assert(n != 0 && "Divide by zero?");
1583 uint32_t divisor = V[0];
1584 uint32_t remainder = 0;
1585 for (int i = m+n-1; i >= 0; i--) {
1586 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1587 if (partial_dividend == 0) {
1590 } else if (partial_dividend < divisor) {
1592 remainder = partial_dividend;
1593 } else if (partial_dividend == divisor) {
1597 Q[i] = partial_dividend / divisor;
1598 remainder = partial_dividend - (Q[i] * divisor);
1604 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1606 KnuthDiv(U, V, Q, R, m, n);
1609 // If the caller wants the quotient
1611 // Set up the Quotient value's memory.
1612 if (Quotient->BitWidth != LHS.BitWidth) {
1613 if (Quotient->isSingleWord())
1616 delete [] Quotient->pVal;
1617 Quotient->BitWidth = LHS.BitWidth;
1618 if (!Quotient->isSingleWord())
1619 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1623 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1625 if (lhsWords == 1) {
1627 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1628 if (Quotient->isSingleWord())
1629 Quotient->VAL = tmp;
1631 Quotient->pVal[0] = tmp;
1633 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1634 for (unsigned i = 0; i < lhsWords; ++i)
1636 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1640 // If the caller wants the remainder
1642 // Set up the Remainder value's memory.
1643 if (Remainder->BitWidth != RHS.BitWidth) {
1644 if (Remainder->isSingleWord())
1647 delete [] Remainder->pVal;
1648 Remainder->BitWidth = RHS.BitWidth;
1649 if (!Remainder->isSingleWord())
1650 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1654 // The remainder is in R. Reconstitute the remainder into Remainder's low
1656 if (rhsWords == 1) {
1658 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1659 if (Remainder->isSingleWord())
1660 Remainder->VAL = tmp;
1662 Remainder->pVal[0] = tmp;
1664 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1665 for (unsigned i = 0; i < rhsWords; ++i)
1666 Remainder->pVal[i] =
1667 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1671 // Clean up the memory we allocated.
1672 if (U != &SPACE[0]) {
1680 APInt APInt::udiv(const APInt& RHS) const {
1681 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1683 // First, deal with the easy case
1684 if (isSingleWord()) {
1685 assert(RHS.VAL != 0 && "Divide by zero?");
1686 return APInt(BitWidth, VAL / RHS.VAL);
1689 // Get some facts about the LHS and RHS number of bits and words
1690 uint32_t rhsBits = RHS.getActiveBits();
1691 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1692 assert(rhsWords && "Divided by zero???");
1693 uint32_t lhsBits = this->getActiveBits();
1694 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1696 // Deal with some degenerate cases
1699 return APInt(BitWidth, 0);
1700 else if (lhsWords < rhsWords || this->ult(RHS)) {
1701 // X / Y ===> 0, iff X < Y
1702 return APInt(BitWidth, 0);
1703 } else if (*this == RHS) {
1705 return APInt(BitWidth, 1);
1706 } else if (lhsWords == 1 && rhsWords == 1) {
1707 // All high words are zero, just use native divide
1708 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1711 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1712 APInt Quotient(1,0); // to hold result.
1713 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0);
1717 APInt APInt::urem(const APInt& RHS) const {
1718 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1719 if (isSingleWord()) {
1720 assert(RHS.VAL != 0 && "Remainder by zero?");
1721 return APInt(BitWidth, VAL % RHS.VAL);
1724 // Get some facts about the LHS
1725 uint32_t lhsBits = getActiveBits();
1726 uint32_t lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1728 // Get some facts about the RHS
1729 uint32_t rhsBits = RHS.getActiveBits();
1730 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1731 assert(rhsWords && "Performing remainder operation by zero ???");
1733 // Check the degenerate cases
1734 if (lhsWords == 0) {
1736 return APInt(BitWidth, 0);
1737 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1738 // X % Y ===> X, iff X < Y
1740 } else if (*this == RHS) {
1742 return APInt(BitWidth, 0);
1743 } else if (lhsWords == 1) {
1744 // All high words are zero, just use native remainder
1745 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
1748 // We have to compute it the hard way. Invoke the Knute divide algorithm.
1749 APInt Remainder(1,0);
1750 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder);
1754 void APInt::fromString(uint32_t numbits, const char *str, uint32_t slen,
1756 // Check our assumptions here
1757 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1758 "Radix should be 2, 8, 10, or 16!");
1759 assert(str && "String is null?");
1760 bool isNeg = str[0] == '-';
1763 assert(slen <= numbits || radix != 2 && "Insufficient bit width");
1764 assert(slen*3 <= numbits || radix != 8 && "Insufficient bit width");
1765 assert(slen*4 <= numbits || radix != 16 && "Insufficient bit width");
1766 assert((slen*64)/22 <= numbits || radix != 10 && "Insufficient bit width");
1769 if (!isSingleWord())
1770 pVal = getClearedMemory(getNumWords());
1772 // Figure out if we can shift instead of multiply
1773 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
1775 // Set up an APInt for the digit to add outside the loop so we don't
1776 // constantly construct/destruct it.
1777 APInt apdigit(getBitWidth(), 0);
1778 APInt apradix(getBitWidth(), radix);
1780 // Enter digit traversal loop
1781 for (unsigned i = 0; i < slen; i++) {
1784 char cdigit = str[i];
1785 if (isdigit(cdigit))
1786 digit = cdigit - '0';
1787 else if (isxdigit(cdigit))
1789 digit = cdigit - 'a' + 10;
1790 else if (cdigit >= 'A')
1791 digit = cdigit - 'A' + 10;
1793 assert(0 && "huh?");
1795 assert(0 && "Invalid character in digit string");
1797 // Shift or multiple the value by the radix
1803 // Add in the digit we just interpreted
1804 if (apdigit.isSingleWord())
1805 apdigit.VAL = digit;
1807 apdigit.pVal[0] = digit;
1810 // If its negative, put it in two's complement form
1817 std::string APInt::toString(uint8_t radix, bool wantSigned) const {
1818 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1819 "Radix should be 2, 8, 10, or 16!");
1820 static const char *digits[] = {
1821 "0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"
1824 uint32_t bits_used = getActiveBits();
1825 if (isSingleWord()) {
1827 const char *format = (radix == 10 ? (wantSigned ? "%lld" : "%llu") :
1828 (radix == 16 ? "%llX" : (radix == 8 ? "%llo" : 0)));
1831 int64_t sextVal = (int64_t(VAL) << (APINT_BITS_PER_WORD-BitWidth)) >>
1832 (APINT_BITS_PER_WORD-BitWidth);
1833 sprintf(buf, format, sextVal);
1835 sprintf(buf, format, VAL);
1840 uint32_t bit = v & 1;
1842 buf[bits_used] = digits[bit][0];
1851 uint64_t mask = radix - 1;
1852 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : 1);
1853 uint32_t nibbles = APINT_BITS_PER_WORD / shift;
1854 for (uint32_t i = 0; i < getNumWords(); ++i) {
1855 uint64_t value = pVal[i];
1856 for (uint32_t j = 0; j < nibbles; ++j) {
1857 result.insert(0, digits[ value & mask ]);
1865 APInt divisor(4, radix);
1866 APInt zero(tmp.getBitWidth(), 0);
1867 size_t insert_at = 0;
1868 if (wantSigned && tmp[BitWidth-1]) {
1869 // They want to print the signed version and it is a negative value
1870 // Flip the bits and add one to turn it into the equivalent positive
1871 // value and put a '-' in the result.
1877 if (tmp == APInt(tmp.getBitWidth(), 0))
1879 else while (tmp.ne(zero)) {
1881 APInt tmp2(tmp.getBitWidth(), 0);
1882 divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
1884 uint32_t digit = APdigit.getZExtValue();
1885 assert(digit < radix && "divide failed");
1886 result.insert(insert_at,digits[digit]);
1894 void APInt::dump() const
1896 cerr << "APInt(" << BitWidth << ")=" << std::setbase(16);
1899 else for (unsigned i = getNumWords(); i > 0; i--) {
1900 cerr << pVal[i-1] << " ";
1902 cerr << " U(" << this->toString(10) << ") S(" << this->toStringSigned(10)
1903 << ")\n" << std::setbase(10);