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"
28 /// A utility function for allocating memory, checking for allocation failures,
29 /// and ensuring the contents are zeroed.
30 inline static uint64_t* getClearedMemory(uint32_t numWords) {
31 uint64_t * result = new uint64_t[numWords];
32 assert(result && "APInt memory allocation fails!");
33 memset(result, 0, numWords * sizeof(uint64_t));
37 /// A utility function for allocating memory and checking for allocation
38 /// failure. The content is not zeroed.
39 inline static uint64_t* getMemory(uint32_t numWords) {
40 uint64_t * result = new uint64_t[numWords];
41 assert(result && "APInt memory allocation fails!");
45 APInt::APInt(uint32_t numBits, uint64_t val) : BitWidth(numBits), VAL(0) {
46 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small");
47 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large");
51 pVal = getClearedMemory(getNumWords());
57 APInt::APInt(uint32_t numBits, uint32_t numWords, uint64_t bigVal[])
58 : BitWidth(numBits), VAL(0) {
59 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small");
60 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large");
61 assert(bigVal && "Null pointer detected!");
65 // Get memory, cleared to 0
66 pVal = getClearedMemory(getNumWords());
67 // Calculate the number of words to copy
68 uint32_t words = std::min<uint32_t>(numWords, getNumWords());
69 // Copy the words from bigVal to pVal
70 memcpy(pVal, bigVal, words * APINT_WORD_SIZE);
72 // Make sure unused high bits are cleared
76 APInt::APInt(uint32_t numbits, const char StrStart[], uint32_t slen,
78 : BitWidth(numbits), VAL(0) {
79 fromString(numbits, StrStart, slen, radix);
82 APInt::APInt(uint32_t numbits, const std::string& Val, uint8_t radix)
83 : BitWidth(numbits), VAL(0) {
84 assert(!Val.empty() && "String empty?");
85 fromString(numbits, Val.c_str(), Val.size(), radix);
88 APInt::APInt(const APInt& that)
89 : BitWidth(that.BitWidth), VAL(0) {
93 pVal = getMemory(getNumWords());
94 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE);
99 if (!isSingleWord() && pVal)
103 APInt& APInt::operator=(const APInt& RHS) {
104 // Don't do anything for X = X
108 // If the bitwidths are the same, we can avoid mucking with memory
109 if (BitWidth == RHS.getBitWidth()) {
113 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE);
118 if (RHS.isSingleWord())
122 pVal = getMemory(RHS.getNumWords());
123 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
125 else if (getNumWords() == RHS.getNumWords())
126 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
127 else if (RHS.isSingleWord()) {
132 pVal = getMemory(RHS.getNumWords());
133 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
135 BitWidth = RHS.BitWidth;
136 return clearUnusedBits();
139 APInt& APInt::operator=(uint64_t RHS) {
144 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE);
146 return clearUnusedBits();
149 /// add_1 - This function adds a single "digit" integer, y, to the multiple
150 /// "digit" integer array, x[]. x[] is modified to reflect the addition and
151 /// 1 is returned if there is a carry out, otherwise 0 is returned.
152 /// @returns the carry of the addition.
153 static bool add_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
154 for (uint32_t i = 0; i < len; ++i) {
157 y = 1; // Carry one to next digit.
159 y = 0; // No need to carry so exit early
166 /// @brief Prefix increment operator. Increments the APInt by one.
167 APInt& APInt::operator++() {
171 add_1(pVal, pVal, getNumWords(), 1);
172 return clearUnusedBits();
175 /// sub_1 - This function subtracts a single "digit" (64-bit word), y, from
176 /// the multi-digit integer array, x[], propagating the borrowed 1 value until
177 /// no further borrowing is neeeded or it runs out of "digits" in x. The result
178 /// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted.
179 /// In other words, if y > x then this function returns 1, otherwise 0.
180 /// @returns the borrow out of the subtraction
181 static bool sub_1(uint64_t x[], uint32_t len, uint64_t y) {
182 for (uint32_t i = 0; i < len; ++i) {
186 y = 1; // We have to "borrow 1" from next "digit"
188 y = 0; // No need to borrow
189 break; // Remaining digits are unchanged so exit early
195 /// @brief Prefix decrement operator. Decrements the APInt by one.
196 APInt& APInt::operator--() {
200 sub_1(pVal, getNumWords(), 1);
201 return clearUnusedBits();
204 /// add - This function adds the integer array x to the integer array Y and
205 /// places the result in dest.
206 /// @returns the carry out from the addition
207 /// @brief General addition of 64-bit integer arrays
208 static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y,
211 for (uint32_t i = 0; i< len; ++i) {
212 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x
213 dest[i] = x[i] + y[i] + carry;
214 carry = dest[i] < limit || (carry && dest[i] == limit);
219 /// Adds the RHS APint to this APInt.
220 /// @returns this, after addition of RHS.
221 /// @brief Addition assignment operator.
222 APInt& APInt::operator+=(const APInt& RHS) {
223 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
227 add(pVal, pVal, RHS.pVal, getNumWords());
229 return clearUnusedBits();
232 /// Subtracts the integer array y from the integer array x
233 /// @returns returns the borrow out.
234 /// @brief Generalized subtraction of 64-bit integer arrays.
235 static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y,
238 for (uint32_t i = 0; i < len; ++i) {
239 uint64_t x_tmp = borrow ? x[i] - 1 : x[i];
240 borrow = y[i] > x_tmp || (borrow && x[i] == 0);
241 dest[i] = x_tmp - y[i];
246 /// Subtracts the RHS APInt from this APInt
247 /// @returns this, after subtraction
248 /// @brief Subtraction assignment operator.
249 APInt& APInt::operator-=(const APInt& RHS) {
250 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
254 sub(pVal, pVal, RHS.pVal, getNumWords());
255 return clearUnusedBits();
258 /// Multiplies an integer array, x by a a uint64_t integer and places the result
260 /// @returns the carry out of the multiplication.
261 /// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer.
262 static uint64_t mul_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
263 // Split y into high 32-bit part (hy) and low 32-bit part (ly)
264 uint64_t ly = y & 0xffffffffULL, hy = y >> 32;
267 // For each digit of x.
268 for (uint32_t i = 0; i < len; ++i) {
269 // Split x into high and low words
270 uint64_t lx = x[i] & 0xffffffffULL;
271 uint64_t hx = x[i] >> 32;
272 // hasCarry - A flag to indicate if there is a carry to the next digit.
273 // hasCarry == 0, no carry
274 // hasCarry == 1, has carry
275 // hasCarry == 2, no carry and the calculation result == 0.
276 uint8_t hasCarry = 0;
277 dest[i] = carry + lx * ly;
278 // Determine if the add above introduces carry.
279 hasCarry = (dest[i] < carry) ? 1 : 0;
280 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0);
281 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) +
282 // (2^32 - 1) + 2^32 = 2^64.
283 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
285 carry += (lx * hy) & 0xffffffffULL;
286 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL);
287 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) +
288 (carry >> 32) + ((lx * hy) >> 32) + hx * hy;
293 /// Multiplies integer array x by integer array y and stores the result into
294 /// the integer array dest. Note that dest's size must be >= xlen + ylen.
295 /// @brief Generalized multiplicate of integer arrays.
296 static void mul(uint64_t dest[], uint64_t x[], uint32_t xlen, uint64_t y[],
298 dest[xlen] = mul_1(dest, x, xlen, y[0]);
299 for (uint32_t i = 1; i < ylen; ++i) {
300 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32;
301 uint64_t carry = 0, lx = 0, hx = 0;
302 for (uint32_t j = 0; j < xlen; ++j) {
303 lx = x[j] & 0xffffffffULL;
305 // hasCarry - A flag to indicate if has carry.
306 // hasCarry == 0, no carry
307 // hasCarry == 1, has carry
308 // hasCarry == 2, no carry and the calculation result == 0.
309 uint8_t hasCarry = 0;
310 uint64_t resul = carry + lx * ly;
311 hasCarry = (resul < carry) ? 1 : 0;
312 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32);
313 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
315 carry += (lx * hy) & 0xffffffffULL;
316 resul = (carry << 32) | (resul & 0xffffffffULL);
318 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+
319 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) +
320 ((lx * hy) >> 32) + hx * hy;
322 dest[i+xlen] = carry;
326 APInt& APInt::operator*=(const APInt& RHS) {
327 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
328 if (isSingleWord()) {
334 // Get some bit facts about LHS and check for zero
335 uint32_t lhsBits = getActiveBits();
336 uint32_t lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1;
341 // Get some bit facts about RHS and check for zero
342 uint32_t rhsBits = RHS.getActiveBits();
343 uint32_t rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1;
350 // Allocate space for the result
351 uint32_t destWords = rhsWords + lhsWords;
352 uint64_t *dest = getMemory(destWords);
354 // Perform the long multiply
355 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords);
357 // Copy result back into *this
359 uint32_t wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords;
360 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE);
362 // delete dest array and return
367 APInt& APInt::operator&=(const APInt& RHS) {
368 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
369 if (isSingleWord()) {
373 uint32_t numWords = getNumWords();
374 for (uint32_t i = 0; i < numWords; ++i)
375 pVal[i] &= RHS.pVal[i];
379 APInt& APInt::operator|=(const APInt& RHS) {
380 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
381 if (isSingleWord()) {
385 uint32_t numWords = getNumWords();
386 for (uint32_t i = 0; i < numWords; ++i)
387 pVal[i] |= RHS.pVal[i];
391 APInt& APInt::operator^=(const APInt& RHS) {
392 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
393 if (isSingleWord()) {
395 this->clearUnusedBits();
398 uint32_t numWords = getNumWords();
399 for (uint32_t i = 0; i < numWords; ++i)
400 pVal[i] ^= RHS.pVal[i];
401 return clearUnusedBits();
404 APInt APInt::operator&(const APInt& RHS) const {
405 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
407 return APInt(getBitWidth(), VAL & RHS.VAL);
409 uint32_t numWords = getNumWords();
410 uint64_t* val = getMemory(numWords);
411 for (uint32_t i = 0; i < numWords; ++i)
412 val[i] = pVal[i] & RHS.pVal[i];
413 return APInt(val, getBitWidth());
416 APInt APInt::operator|(const APInt& RHS) const {
417 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
419 return APInt(getBitWidth(), VAL | RHS.VAL);
421 uint32_t numWords = getNumWords();
422 uint64_t *val = getMemory(numWords);
423 for (uint32_t i = 0; i < numWords; ++i)
424 val[i] = pVal[i] | RHS.pVal[i];
425 return APInt(val, getBitWidth());
428 APInt APInt::operator^(const APInt& RHS) const {
429 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
431 return APInt(BitWidth, VAL ^ RHS.VAL);
433 uint32_t numWords = getNumWords();
434 uint64_t *val = getMemory(numWords);
435 for (uint32_t i = 0; i < numWords; ++i)
436 val[i] = pVal[i] ^ RHS.pVal[i];
438 // 0^0==1 so clear the high bits in case they got set.
439 return APInt(val, getBitWidth()).clearUnusedBits();
442 bool APInt::operator !() const {
446 for (uint32_t i = 0; i < getNumWords(); ++i)
452 APInt APInt::operator*(const APInt& RHS) const {
453 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
455 return APInt(BitWidth, VAL * RHS.VAL);
458 return Result.clearUnusedBits();
461 APInt APInt::operator+(const APInt& RHS) const {
462 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
464 return APInt(BitWidth, VAL + RHS.VAL);
465 APInt Result(BitWidth, 0);
466 add(Result.pVal, this->pVal, RHS.pVal, getNumWords());
467 return Result.clearUnusedBits();
470 APInt APInt::operator-(const APInt& RHS) const {
471 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
473 return APInt(BitWidth, VAL - RHS.VAL);
474 APInt Result(BitWidth, 0);
475 sub(Result.pVal, this->pVal, RHS.pVal, getNumWords());
476 return Result.clearUnusedBits();
479 bool APInt::operator[](uint32_t bitPosition) const {
480 return (maskBit(bitPosition) &
481 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0;
484 bool APInt::operator==(const APInt& RHS) const {
485 assert(BitWidth == RHS.BitWidth && "Comparison requires equal bit widths");
487 return VAL == RHS.VAL;
489 // Get some facts about the number of bits used in the two operands.
490 uint32_t n1 = getActiveBits();
491 uint32_t n2 = RHS.getActiveBits();
493 // If the number of bits isn't the same, they aren't equal
497 // If the number of bits fits in a word, we only need to compare the low word.
498 if (n1 <= APINT_BITS_PER_WORD)
499 return pVal[0] == RHS.pVal[0];
501 // Otherwise, compare everything
502 for (int i = whichWord(n1 - 1); i >= 0; --i)
503 if (pVal[i] != RHS.pVal[i])
508 bool APInt::operator==(uint64_t Val) const {
512 uint32_t n = getActiveBits();
513 if (n <= APINT_BITS_PER_WORD)
514 return pVal[0] == Val;
519 bool APInt::ult(const APInt& RHS) const {
520 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
522 return VAL < RHS.VAL;
524 // Get active bit length of both operands
525 uint32_t n1 = getActiveBits();
526 uint32_t n2 = RHS.getActiveBits();
528 // If magnitude of LHS is less than RHS, return true.
532 // If magnitude of RHS is greather than LHS, return false.
536 // If they bot fit in a word, just compare the low order word
537 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD)
538 return pVal[0] < RHS.pVal[0];
540 // Otherwise, compare all words
541 uint32_t topWord = whichWord(std::max(n1,n2)-1);
542 for (int i = topWord; i >= 0; --i) {
543 if (pVal[i] > RHS.pVal[i])
545 if (pVal[i] < RHS.pVal[i])
551 bool APInt::slt(const APInt& RHS) const {
552 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
553 if (isSingleWord()) {
554 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
555 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth);
556 return lhsSext < rhsSext;
561 bool lhsNeg = isNegative();
562 bool rhsNeg = rhs.isNegative();
564 // Sign bit is set so perform two's complement to make it positive
569 // Sign bit is set so perform two's complement to make it positive
574 // Now we have unsigned values to compare so do the comparison if necessary
575 // based on the negativeness of the values.
587 APInt& APInt::set(uint32_t bitPosition) {
589 VAL |= maskBit(bitPosition);
591 pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
595 APInt& APInt::set() {
596 if (isSingleWord()) {
598 return clearUnusedBits();
601 // Set all the bits in all the words.
602 for (uint32_t i = 0; i < getNumWords() - 1; ++i)
604 // Clear the unused ones
605 return clearUnusedBits();
608 /// Set the given bit to 0 whose position is given as "bitPosition".
609 /// @brief Set a given bit to 0.
610 APInt& APInt::clear(uint32_t bitPosition) {
612 VAL &= ~maskBit(bitPosition);
614 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
618 /// @brief Set every bit to 0.
619 APInt& APInt::clear() {
623 memset(pVal, 0, getNumWords() * APINT_WORD_SIZE);
627 /// @brief Bitwise NOT operator. Performs a bitwise logical NOT operation on
629 APInt APInt::operator~() const {
635 /// @brief Toggle every bit to its opposite value.
636 APInt& APInt::flip() {
637 if (isSingleWord()) {
639 return clearUnusedBits();
641 for (uint32_t i = 0; i < getNumWords(); ++i)
643 return clearUnusedBits();
646 /// Toggle a given bit to its opposite value whose position is given
647 /// as "bitPosition".
648 /// @brief Toggles a given bit to its opposite value.
649 APInt& APInt::flip(uint32_t bitPosition) {
650 assert(bitPosition < BitWidth && "Out of the bit-width range!");
651 if ((*this)[bitPosition]) clear(bitPosition);
652 else set(bitPosition);
656 uint64_t APInt::getHashValue() const {
657 // Put the bit width into the low order bits.
658 uint64_t hash = BitWidth;
660 // Add the sum of the words to the hash.
662 hash += VAL << 6; // clear separation of up to 64 bits
664 for (uint32_t i = 0; i < getNumWords(); ++i)
665 hash += pVal[i] << 6; // clear sepration of up to 64 bits
669 /// HiBits - This function returns the high "numBits" bits of this APInt.
670 APInt APInt::getHiBits(uint32_t numBits) const {
671 return APIntOps::lshr(*this, BitWidth - numBits);
674 /// LoBits - This function returns the low "numBits" bits of this APInt.
675 APInt APInt::getLoBits(uint32_t numBits) const {
676 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
680 bool APInt::isPowerOf2() const {
681 return (!!*this) && !(*this & (*this - APInt(BitWidth,1)));
684 uint32_t APInt::countLeadingZeros() const {
687 Count = CountLeadingZeros_64(VAL);
689 for (uint32_t i = getNumWords(); i > 0u; --i) {
691 Count += APINT_BITS_PER_WORD;
693 Count += CountLeadingZeros_64(pVal[i-1]);
698 uint32_t remainder = BitWidth % APINT_BITS_PER_WORD;
700 Count -= APINT_BITS_PER_WORD - remainder;
704 static uint32_t countLeadingOnes_64(uint64_t V, uint32_t skip) {
708 while (V && (V & (1ULL << 63))) {
715 uint32_t APInt::countLeadingOnes() const {
717 return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth);
719 uint32_t highWordBits = BitWidth % APINT_BITS_PER_WORD;
720 uint32_t shift = (highWordBits == 0 ? 0 : APINT_BITS_PER_WORD - highWordBits);
721 int i = getNumWords() - 1;
722 uint32_t Count = countLeadingOnes_64(pVal[i], shift);
723 if (Count == highWordBits) {
724 for (i--; i >= 0; --i) {
725 if (pVal[i] == -1ULL)
726 Count += APINT_BITS_PER_WORD;
728 Count += countLeadingOnes_64(pVal[i], 0);
736 uint32_t APInt::countTrailingZeros() const {
738 return CountTrailingZeros_64(VAL);
741 for (; i < getNumWords() && pVal[i] == 0; ++i)
742 Count += APINT_BITS_PER_WORD;
743 if (i < getNumWords())
744 Count += CountTrailingZeros_64(pVal[i]);
748 uint32_t APInt::countPopulation() const {
750 return CountPopulation_64(VAL);
752 for (uint32_t i = 0; i < getNumWords(); ++i)
753 Count += CountPopulation_64(pVal[i]);
757 APInt APInt::byteSwap() const {
758 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
760 return APInt(BitWidth, ByteSwap_16(VAL));
761 else if (BitWidth == 32)
762 return APInt(BitWidth, ByteSwap_32(VAL));
763 else if (BitWidth == 48) {
764 uint64_t Tmp1 = ((VAL >> 32) << 16) | (VAL & 0xFFFF);
765 Tmp1 = ByteSwap_32(Tmp1);
766 uint64_t Tmp2 = (VAL >> 16) & 0xFFFF;
767 Tmp2 = ByteSwap_16(Tmp2);
770 (Tmp1 & 0xff) | ((Tmp1<<16) & 0xffff00000000ULL) | (Tmp2 << 16));
771 } else if (BitWidth == 64)
772 return APInt(BitWidth, ByteSwap_64(VAL));
774 APInt Result(BitWidth, 0);
775 char *pByte = (char*)Result.pVal;
776 for (uint32_t i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) {
778 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i];
779 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp;
785 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
787 APInt A = API1, B = API2;
790 B = APIntOps::urem(A, B);
796 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, uint32_t width) {
803 // Get the sign bit from the highest order bit
804 bool isNeg = T.I >> 63;
806 // Get the 11-bit exponent and adjust for the 1023 bit bias
807 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
809 // If the exponent is negative, the value is < 0 so just return 0.
811 return APInt(width, 0u);
813 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
814 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
816 // If the exponent doesn't shift all bits out of the mantissa
818 return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
819 APInt(width, mantissa >> (52 - exp));
821 // If the client didn't provide enough bits for us to shift the mantissa into
822 // then the result is undefined, just return 0
823 if (width <= exp - 52)
824 return APInt(width, 0);
826 // Otherwise, we have to shift the mantissa bits up to the right location
827 APInt Tmp(width, mantissa);
828 Tmp = Tmp.shl(exp - 52);
829 return isNeg ? -Tmp : Tmp;
832 /// RoundToDouble - This function convert this APInt to a double.
833 /// The layout for double is as following (IEEE Standard 754):
834 /// --------------------------------------
835 /// | Sign Exponent Fraction Bias |
836 /// |-------------------------------------- |
837 /// | 1[63] 11[62-52] 52[51-00] 1023 |
838 /// --------------------------------------
839 double APInt::roundToDouble(bool isSigned) const {
841 // Handle the simple case where the value is contained in one uint64_t.
842 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
844 int64_t sext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
850 // Determine if the value is negative.
851 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
853 // Construct the absolute value if we're negative.
854 APInt Tmp(isNeg ? -(*this) : (*this));
856 // Figure out how many bits we're using.
857 uint32_t n = Tmp.getActiveBits();
859 // The exponent (without bias normalization) is just the number of bits
860 // we are using. Note that the sign bit is gone since we constructed the
864 // Return infinity for exponent overflow
866 if (!isSigned || !isNeg)
867 return double(1.0E300 * 1.0E300); // positive infinity
869 return double(-1.0E300 * 1.0E300); // negative infinity
871 exp += 1023; // Increment for 1023 bias
873 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
874 // extract the high 52 bits from the correct words in pVal.
876 unsigned hiWord = whichWord(n-1);
878 mantissa = Tmp.pVal[0];
880 mantissa >>= n - 52; // shift down, we want the top 52 bits.
882 assert(hiWord > 0 && "huh?");
883 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
884 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
885 mantissa = hibits | lobits;
888 // The leading bit of mantissa is implicit, so get rid of it.
889 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
894 T.I = sign | (exp << 52) | mantissa;
898 // Truncate to new width.
899 APInt &APInt::trunc(uint32_t width) {
900 assert(width < BitWidth && "Invalid APInt Truncate request");
901 assert(width >= IntegerType::MIN_INT_BITS && "Can't truncate to 0 bits");
902 uint32_t wordsBefore = getNumWords();
904 uint32_t wordsAfter = getNumWords();
905 if (wordsBefore != wordsAfter) {
906 if (wordsAfter == 1) {
907 uint64_t *tmp = pVal;
911 uint64_t *newVal = getClearedMemory(wordsAfter);
912 for (uint32_t i = 0; i < wordsAfter; ++i)
918 return clearUnusedBits();
921 // Sign extend to a new width.
922 APInt &APInt::sext(uint32_t width) {
923 assert(width > BitWidth && "Invalid APInt SignExtend request");
924 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
925 // If the sign bit isn't set, this is the same as zext.
931 // The sign bit is set. First, get some facts
932 uint32_t wordsBefore = getNumWords();
933 uint32_t wordBits = BitWidth % APINT_BITS_PER_WORD;
935 uint32_t wordsAfter = getNumWords();
937 // Mask the high order word appropriately
938 if (wordsBefore == wordsAfter) {
939 uint32_t newWordBits = width % APINT_BITS_PER_WORD;
940 // The extension is contained to the wordsBefore-1th word.
941 uint64_t mask = (~0ULL >> (APINT_BITS_PER_WORD - newWordBits)) << wordBits;
942 if (wordsBefore == 1)
945 pVal[wordsBefore-1] |= mask;
950 uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits;
951 uint64_t *newVal = getMemory(wordsAfter);
952 if (wordsBefore == 1)
953 newVal[0] = VAL | mask;
955 for (uint32_t i = 0; i < wordsBefore; ++i)
957 newVal[wordsBefore-1] |= mask;
959 for (uint32_t i = wordsBefore; i < wordsAfter; i++)
961 if (wordsBefore != 1)
964 return clearUnusedBits();
967 // Zero extend to a new width.
968 APInt &APInt::zext(uint32_t width) {
969 assert(width > BitWidth && "Invalid APInt ZeroExtend request");
970 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
971 uint32_t wordsBefore = getNumWords();
973 uint32_t wordsAfter = getNumWords();
974 if (wordsBefore != wordsAfter) {
975 uint64_t *newVal = getClearedMemory(wordsAfter);
976 if (wordsBefore == 1)
979 for (uint32_t i = 0; i < wordsBefore; ++i)
981 if (wordsBefore != 1)
988 /// Arithmetic right-shift this APInt by shiftAmt.
989 /// @brief Arithmetic right-shift function.
990 APInt APInt::ashr(uint32_t shiftAmt) const {
991 assert(shiftAmt <= BitWidth && "Invalid shift amount");
992 if (isSingleWord()) {
993 if (shiftAmt == BitWidth)
994 return APInt(BitWidth, 0); // undefined
996 uint32_t SignBit = APINT_BITS_PER_WORD - BitWidth;
997 return APInt(BitWidth,
998 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1002 // If all the bits were shifted out, the result is 0 or -1. This avoids issues
1003 // with shifting by the size of the integer type, which produces undefined
1005 if (shiftAmt == BitWidth)
1007 return APInt(BitWidth, -1ULL);
1009 return APInt(BitWidth, 0);
1011 // Create some space for the result.
1012 uint64_t * val = new uint64_t[getNumWords()];
1014 // If we are shifting less than a word, compute the shift with a simple carry
1015 if (shiftAmt < APINT_BITS_PER_WORD) {
1017 for (int i = getNumWords()-1; i >= 0; --i) {
1018 val[i] = (pVal[i] >> shiftAmt) | carry;
1019 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1021 return APInt(val, BitWidth).clearUnusedBits();
1024 // Compute some values needed by the remaining shift algorithms
1025 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1026 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1028 // If we are shifting whole words, just move whole words
1029 if (wordShift == 0) {
1030 for (uint32_t i = 0; i < getNumWords() - offset; ++i)
1031 val[i] = pVal[i+offset];
1032 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
1033 val[i] = (isNegative() ? -1ULL : 0);
1034 return APInt(val,BitWidth).clearUnusedBits();
1037 // Shift the low order words
1038 uint32_t breakWord = getNumWords() - offset -1;
1039 for (uint32_t i = 0; i < breakWord; ++i)
1040 val[i] = (pVal[i+offset] >> wordShift) |
1041 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1042 // Shift the break word.
1043 uint32_t SignBit = APINT_BITS_PER_WORD - (BitWidth % APINT_BITS_PER_WORD);
1044 val[breakWord] = uint64_t(
1045 (((int64_t(pVal[breakWord+offset]) << SignBit) >> SignBit) >> wordShift));
1047 // Remaining words are 0 or -1
1048 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1049 val[i] = (isNegative() ? -1ULL : 0);
1050 return APInt(val, BitWidth).clearUnusedBits();
1053 /// Logical right-shift this APInt by shiftAmt.
1054 /// @brief Logical right-shift function.
1055 APInt APInt::lshr(uint32_t shiftAmt) const {
1057 if (shiftAmt == BitWidth)
1058 return APInt(BitWidth, 0);
1060 return APInt(BitWidth, this->VAL >> shiftAmt);
1062 // If all the bits were shifted out, the result is 0. This avoids issues
1063 // with shifting by the size of the integer type, which produces undefined
1064 // results. We define these "undefined results" to always be 0.
1065 if (shiftAmt == BitWidth)
1066 return APInt(BitWidth, 0);
1068 // Create some space for the result.
1069 uint64_t * val = new uint64_t[getNumWords()];
1071 // If we are shifting less than a word, compute the shift with a simple carry
1072 if (shiftAmt < APINT_BITS_PER_WORD) {
1074 for (int i = getNumWords()-1; i >= 0; --i) {
1075 val[i] = (pVal[i] >> shiftAmt) | carry;
1076 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1078 return APInt(val, BitWidth).clearUnusedBits();
1081 // Compute some values needed by the remaining shift algorithms
1082 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1083 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1085 // If we are shifting whole words, just move whole words
1086 if (wordShift == 0) {
1087 for (uint32_t i = 0; i < getNumWords() - offset; ++i)
1088 val[i] = pVal[i+offset];
1089 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
1091 return APInt(val,BitWidth).clearUnusedBits();
1094 // Shift the low order words
1095 uint32_t breakWord = getNumWords() - offset -1;
1096 for (uint32_t i = 0; i < breakWord; ++i)
1097 val[i] = (pVal[i+offset] >> wordShift) |
1098 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1099 // Shift the break word.
1100 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1102 // Remaining words are 0
1103 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1105 return APInt(val, BitWidth).clearUnusedBits();
1108 /// Left-shift this APInt by shiftAmt.
1109 /// @brief Left-shift function.
1110 APInt APInt::shl(uint32_t shiftAmt) const {
1111 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1112 if (isSingleWord()) {
1113 if (shiftAmt == BitWidth)
1114 return APInt(BitWidth, 0); // avoid undefined shift results
1115 return APInt(BitWidth, VAL << shiftAmt);
1118 // If all the bits were shifted out, the result is 0. This avoids issues
1119 // with shifting by the size of the integer type, which produces undefined
1120 // results. We define these "undefined results" to always be 0.
1121 if (shiftAmt == BitWidth)
1122 return APInt(BitWidth, 0);
1124 // Create some space for the result.
1125 uint64_t * val = new uint64_t[getNumWords()];
1127 // If we are shifting less than a word, do it the easy way
1128 if (shiftAmt < APINT_BITS_PER_WORD) {
1130 for (uint32_t i = 0; i < getNumWords(); i++) {
1131 val[i] = pVal[i] << shiftAmt | carry;
1132 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1134 return APInt(val, BitWidth).clearUnusedBits();
1137 // Compute some values needed by the remaining shift algorithms
1138 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1139 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1141 // If we are shifting whole words, just move whole words
1142 if (wordShift == 0) {
1143 for (uint32_t i = 0; i < offset; i++)
1145 for (uint32_t i = offset; i < getNumWords(); i++)
1146 val[i] = pVal[i-offset];
1147 return APInt(val,BitWidth).clearUnusedBits();
1150 // Copy whole words from this to Result.
1151 uint32_t i = getNumWords() - 1;
1152 for (; i > offset; --i)
1153 val[i] = pVal[i-offset] << wordShift |
1154 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1155 val[offset] = pVal[0] << wordShift;
1156 for (i = 0; i < offset; ++i)
1158 return APInt(val, BitWidth).clearUnusedBits();
1162 // Square Root - this method computes and returns the square root of "this".
1163 // Three mechanisms are used for computation. For small values (<= 5 bits),
1164 // a table lookup is done. This gets some performance for common cases. For
1165 // values using less than 52 bits, the value is converted to double and then
1166 // the libc sqrt function is called. The result is rounded and then converted
1167 // back to a uint64_t which is then used to construct the result. Finally,
1168 // the Babylonian method for computing square roots is used.
1169 APInt APInt::sqrt() const {
1171 // Determine the magnitude of the value.
1172 uint32_t magnitude = getActiveBits();
1174 // Use a fast table for some small values. This also gets rid of some
1175 // rounding errors in libc sqrt for small values.
1176 if (magnitude <= 5) {
1177 static uint8_t results[32] = {
1180 /* 3- 6 */ 2, 2, 2, 2,
1181 /* 7-12 */ 3, 3, 3, 3, 3, 3,
1182 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1183 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1186 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]);
1189 // If the magnitude of the value fits in less than 52 bits (the precision of
1190 // an IEEE double precision floating point value), then we can use the
1191 // libc sqrt function which will probably use a hardware sqrt computation.
1192 // This should be faster than the algorithm below.
1194 return APInt(BitWidth,
1195 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0])))));
1197 // Okay, all the short cuts are exhausted. We must compute it. The following
1198 // is a classical Babylonian method for computing the square root. This code
1199 // was adapted to APINt from a wikipedia article on such computations.
1200 // See http://www.wikipedia.org/ and go to the page named
1201 // Calculate_an_integer_square_root.
1202 uint32_t nbits = BitWidth, i = 4;
1203 APInt testy(BitWidth, 16);
1204 APInt x_old(BitWidth, 1);
1205 APInt x_new(BitWidth, 0);
1206 APInt two(BitWidth, 2);
1208 // Select a good starting value using binary logarithms.
1209 for (;; i += 2, testy = testy.shl(2))
1210 if (i >= nbits || this->ule(testy)) {
1211 x_old = x_old.shl(i / 2);
1215 // Use the Babylonian method to arrive at the integer square root:
1217 x_new = (this->udiv(x_old) + x_old).udiv(two);
1218 if (x_old.ule(x_new))
1223 // Make sure we return the closest approximation
1224 APInt square(x_old * x_old);
1225 APInt nextSquare((x_old + 1) * (x_old +1));
1226 if (this->ult(square))
1228 else if (this->ule(nextSquare))
1229 if ((nextSquare - *this).ult(*this - square))
1234 assert(0 && "Error in APInt::sqrt computation");
1238 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1239 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1240 /// variables here have the same names as in the algorithm. Comments explain
1241 /// the algorithm and any deviation from it.
1242 static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
1243 uint32_t m, uint32_t n) {
1244 assert(u && "Must provide dividend");
1245 assert(v && "Must provide divisor");
1246 assert(q && "Must provide quotient");
1247 assert(u != v && u != q && v != q && "Must us different memory");
1248 assert(n>1 && "n must be > 1");
1250 // Knuth uses the value b as the base of the number system. In our case b
1251 // is 2^31 so we just set it to -1u.
1252 uint64_t b = uint64_t(1) << 32;
1254 DEBUG(cerr << "KnuthDiv: m=" << m << " n=" << n << '\n');
1255 DEBUG(cerr << "KnuthDiv: original:");
1256 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1257 DEBUG(cerr << " by");
1258 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1259 DEBUG(cerr << '\n');
1260 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1261 // u and v by d. Note that we have taken Knuth's advice here to use a power
1262 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1263 // 2 allows us to shift instead of multiply and it is easy to determine the
1264 // shift amount from the leading zeros. We are basically normalizing the u
1265 // and v so that its high bits are shifted to the top of v's range without
1266 // overflow. Note that this can require an extra word in u so that u must
1267 // be of length m+n+1.
1268 uint32_t shift = CountLeadingZeros_32(v[n-1]);
1269 uint32_t v_carry = 0;
1270 uint32_t u_carry = 0;
1272 for (uint32_t i = 0; i < m+n; ++i) {
1273 uint32_t u_tmp = u[i] >> (32 - shift);
1274 u[i] = (u[i] << shift) | u_carry;
1277 for (uint32_t i = 0; i < n; ++i) {
1278 uint32_t v_tmp = v[i] >> (32 - shift);
1279 v[i] = (v[i] << shift) | v_carry;
1284 DEBUG(cerr << "KnuthDiv: normal:");
1285 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1286 DEBUG(cerr << " by");
1287 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1288 DEBUG(cerr << '\n');
1290 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1293 DEBUG(cerr << "KnuthDiv: quotient digit #" << j << '\n');
1294 // D3. [Calculate q'.].
1295 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1296 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1297 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1298 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1299 // on v[n-2] determines at high speed most of the cases in which the trial
1300 // value qp is one too large, and it eliminates all cases where qp is two
1302 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1303 DEBUG(cerr << "KnuthDiv: dividend == " << dividend << '\n');
1304 uint64_t qp = dividend / v[n-1];
1305 uint64_t rp = dividend % v[n-1];
1306 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1309 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1312 DEBUG(cerr << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1314 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1315 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1316 // consists of a simple multiplication by a one-place number, combined with
1319 for (uint32_t i = 0; i < n; ++i) {
1320 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1321 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1322 bool borrow = subtrahend > u_tmp;
1323 DEBUG(cerr << "KnuthDiv: u_tmp == " << u_tmp
1324 << ", subtrahend == " << subtrahend
1325 << ", borrow = " << borrow << '\n');
1327 uint64_t result = u_tmp - subtrahend;
1329 u[k++] = result & (b-1); // subtract low word
1330 u[k++] = result >> 32; // subtract high word
1331 while (borrow && k <= m+n) { // deal with borrow to the left
1337 DEBUG(cerr << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1340 DEBUG(cerr << "KnuthDiv: after subtraction:");
1341 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1342 DEBUG(cerr << '\n');
1343 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1344 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1345 // true value plus b**(n+1), namely as the b's complement of
1346 // the true value, and a "borrow" to the left should be remembered.
1349 bool carry = true; // true because b's complement is "complement + 1"
1350 for (uint32_t i = 0; i <= m+n; ++i) {
1351 u[i] = ~u[i] + carry; // b's complement
1352 carry = carry && u[i] == 0;
1355 DEBUG(cerr << "KnuthDiv: after complement:");
1356 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1357 DEBUG(cerr << '\n');
1359 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1360 // negative, go to step D6; otherwise go on to step D7.
1363 // D6. [Add back]. The probability that this step is necessary is very
1364 // small, on the order of only 2/b. Make sure that test data accounts for
1365 // this possibility. Decrease q[j] by 1
1367 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1368 // A carry will occur to the left of u[j+n], and it should be ignored
1369 // since it cancels with the borrow that occurred in D4.
1371 for (uint32_t i = 0; i < n; i++) {
1372 uint32_t limit = std::min(u[j+i],v[i]);
1373 u[j+i] += v[i] + carry;
1374 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1378 DEBUG(cerr << "KnuthDiv: after correction:");
1379 DEBUG(for (int i = m+n; i >=0; i--) cerr <<" " << u[i]);
1380 DEBUG(cerr << "\nKnuthDiv: digit result = " << q[j] << '\n');
1382 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1385 DEBUG(cerr << "KnuthDiv: quotient:");
1386 DEBUG(for (int i = m; i >=0; i--) cerr <<" " << q[i]);
1387 DEBUG(cerr << '\n');
1389 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1390 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1391 // compute the remainder (urem uses this).
1393 // The value d is expressed by the "shift" value above since we avoided
1394 // multiplication by d by using a shift left. So, all we have to do is
1395 // shift right here. In order to mak
1398 DEBUG(cerr << "KnuthDiv: remainder:");
1399 for (int i = n-1; i >= 0; i--) {
1400 r[i] = (u[i] >> shift) | carry;
1401 carry = u[i] << (32 - shift);
1402 DEBUG(cerr << " " << r[i]);
1405 for (int i = n-1; i >= 0; i--) {
1407 DEBUG(cerr << " " << r[i]);
1410 DEBUG(cerr << '\n');
1412 DEBUG(cerr << std::setbase(10) << '\n');
1415 void APInt::divide(const APInt LHS, uint32_t lhsWords,
1416 const APInt &RHS, uint32_t rhsWords,
1417 APInt *Quotient, APInt *Remainder)
1419 assert(lhsWords >= rhsWords && "Fractional result");
1421 // First, compose the values into an array of 32-bit words instead of
1422 // 64-bit words. This is a necessity of both the "short division" algorithm
1423 // and the the Knuth "classical algorithm" which requires there to be native
1424 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1425 // can't use 64-bit operands here because we don't have native results of
1426 // 128-bits. Furthremore, casting the 64-bit values to 32-bit values won't
1427 // work on large-endian machines.
1428 uint64_t mask = ~0ull >> (sizeof(uint32_t)*8);
1429 uint32_t n = rhsWords * 2;
1430 uint32_t m = (lhsWords * 2) - n;
1432 // Allocate space for the temporary values we need either on the stack, if
1433 // it will fit, or on the heap if it won't.
1434 uint32_t SPACE[128];
1439 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1442 Q = &SPACE[(m+n+1) + n];
1444 R = &SPACE[(m+n+1) + n + (m+n)];
1446 U = new uint32_t[m + n + 1];
1447 V = new uint32_t[n];
1448 Q = new uint32_t[m+n];
1450 R = new uint32_t[n];
1453 // Initialize the dividend
1454 memset(U, 0, (m+n+1)*sizeof(uint32_t));
1455 for (unsigned i = 0; i < lhsWords; ++i) {
1456 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1457 U[i * 2] = tmp & mask;
1458 U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1460 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1462 // Initialize the divisor
1463 memset(V, 0, (n)*sizeof(uint32_t));
1464 for (unsigned i = 0; i < rhsWords; ++i) {
1465 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1466 V[i * 2] = tmp & mask;
1467 V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1470 // initialize the quotient and remainder
1471 memset(Q, 0, (m+n) * sizeof(uint32_t));
1473 memset(R, 0, n * sizeof(uint32_t));
1475 // Now, adjust m and n for the Knuth division. n is the number of words in
1476 // the divisor. m is the number of words by which the dividend exceeds the
1477 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1478 // contain any zero words or the Knuth algorithm fails.
1479 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1483 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1486 // If we're left with only a single word for the divisor, Knuth doesn't work
1487 // so we implement the short division algorithm here. This is much simpler
1488 // and faster because we are certain that we can divide a 64-bit quantity
1489 // by a 32-bit quantity at hardware speed and short division is simply a
1490 // series of such operations. This is just like doing short division but we
1491 // are using base 2^32 instead of base 10.
1492 assert(n != 0 && "Divide by zero?");
1494 uint32_t divisor = V[0];
1495 uint32_t remainder = 0;
1496 for (int i = m+n-1; i >= 0; i--) {
1497 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1498 if (partial_dividend == 0) {
1501 } else if (partial_dividend < divisor) {
1503 remainder = partial_dividend;
1504 } else if (partial_dividend == divisor) {
1508 Q[i] = partial_dividend / divisor;
1509 remainder = partial_dividend - (Q[i] * divisor);
1515 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1517 KnuthDiv(U, V, Q, R, m, n);
1520 // If the caller wants the quotient
1522 // Set up the Quotient value's memory.
1523 if (Quotient->BitWidth != LHS.BitWidth) {
1524 if (Quotient->isSingleWord())
1527 delete [] Quotient->pVal;
1528 Quotient->BitWidth = LHS.BitWidth;
1529 if (!Quotient->isSingleWord())
1530 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1534 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1536 if (lhsWords == 1) {
1538 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1539 if (Quotient->isSingleWord())
1540 Quotient->VAL = tmp;
1542 Quotient->pVal[0] = tmp;
1544 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1545 for (unsigned i = 0; i < lhsWords; ++i)
1547 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1551 // If the caller wants the remainder
1553 // Set up the Remainder value's memory.
1554 if (Remainder->BitWidth != RHS.BitWidth) {
1555 if (Remainder->isSingleWord())
1558 delete [] Remainder->pVal;
1559 Remainder->BitWidth = RHS.BitWidth;
1560 if (!Remainder->isSingleWord())
1561 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1565 // The remainder is in R. Reconstitute the remainder into Remainder's low
1567 if (rhsWords == 1) {
1569 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1570 if (Remainder->isSingleWord())
1571 Remainder->VAL = tmp;
1573 Remainder->pVal[0] = tmp;
1575 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1576 for (unsigned i = 0; i < rhsWords; ++i)
1577 Remainder->pVal[i] =
1578 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1582 // Clean up the memory we allocated.
1583 if (U != &SPACE[0]) {
1591 APInt APInt::udiv(const APInt& RHS) const {
1592 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1594 // First, deal with the easy case
1595 if (isSingleWord()) {
1596 assert(RHS.VAL != 0 && "Divide by zero?");
1597 return APInt(BitWidth, VAL / RHS.VAL);
1600 // Get some facts about the LHS and RHS number of bits and words
1601 uint32_t rhsBits = RHS.getActiveBits();
1602 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1603 assert(rhsWords && "Divided by zero???");
1604 uint32_t lhsBits = this->getActiveBits();
1605 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1607 // Deal with some degenerate cases
1610 return APInt(BitWidth, 0);
1611 else if (lhsWords < rhsWords || this->ult(RHS)) {
1612 // X / Y ===> 0, iff X < Y
1613 return APInt(BitWidth, 0);
1614 } else if (*this == RHS) {
1616 return APInt(BitWidth, 1);
1617 } else if (lhsWords == 1 && rhsWords == 1) {
1618 // All high words are zero, just use native divide
1619 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1622 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1623 APInt Quotient(1,0); // to hold result.
1624 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0);
1628 APInt APInt::urem(const APInt& RHS) const {
1629 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1630 if (isSingleWord()) {
1631 assert(RHS.VAL != 0 && "Remainder by zero?");
1632 return APInt(BitWidth, VAL % RHS.VAL);
1635 // Get some facts about the LHS
1636 uint32_t lhsBits = getActiveBits();
1637 uint32_t lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1639 // Get some facts about the RHS
1640 uint32_t rhsBits = RHS.getActiveBits();
1641 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1642 assert(rhsWords && "Performing remainder operation by zero ???");
1644 // Check the degenerate cases
1645 if (lhsWords == 0) {
1647 return APInt(BitWidth, 0);
1648 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1649 // X % Y ===> X, iff X < Y
1651 } else if (*this == RHS) {
1653 return APInt(BitWidth, 0);
1654 } else if (lhsWords == 1) {
1655 // All high words are zero, just use native remainder
1656 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
1659 // We have to compute it the hard way. Invoke the Knute divide algorithm.
1660 APInt Remainder(1,0);
1661 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder);
1665 void APInt::fromString(uint32_t numbits, const char *str, uint32_t slen,
1667 // Check our assumptions here
1668 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1669 "Radix should be 2, 8, 10, or 16!");
1670 assert(str && "String is null?");
1671 bool isNeg = str[0] == '-';
1674 assert(slen <= numbits || radix != 2 && "Insufficient bit width");
1675 assert(slen*3 <= numbits || radix != 8 && "Insufficient bit width");
1676 assert(slen*4 <= numbits || radix != 16 && "Insufficient bit width");
1677 assert((slen*64)/20 <= numbits || radix != 10 && "Insufficient bit width");
1680 if (!isSingleWord())
1681 pVal = getClearedMemory(getNumWords());
1683 // Figure out if we can shift instead of multiply
1684 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
1686 // Set up an APInt for the digit to add outside the loop so we don't
1687 // constantly construct/destruct it.
1688 APInt apdigit(getBitWidth(), 0);
1689 APInt apradix(getBitWidth(), radix);
1691 // Enter digit traversal loop
1692 for (unsigned i = 0; i < slen; i++) {
1695 char cdigit = str[i];
1696 if (isdigit(cdigit))
1697 digit = cdigit - '0';
1698 else if (isxdigit(cdigit))
1700 digit = cdigit - 'a' + 10;
1701 else if (cdigit >= 'A')
1702 digit = cdigit - 'A' + 10;
1704 assert(0 && "huh?");
1706 assert(0 && "Invalid character in digit string");
1708 // Shift or multiple the value by the radix
1714 // Add in the digit we just interpreted
1715 if (apdigit.isSingleWord())
1716 apdigit.VAL = digit;
1718 apdigit.pVal[0] = digit;
1721 // If its negative, put it in two's complement form
1728 std::string APInt::toString(uint8_t radix, bool wantSigned) const {
1729 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1730 "Radix should be 2, 8, 10, or 16!");
1731 static const char *digits[] = {
1732 "0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"
1735 uint32_t bits_used = getActiveBits();
1736 if (isSingleWord()) {
1738 const char *format = (radix == 10 ? (wantSigned ? "%lld" : "%llu") :
1739 (radix == 16 ? "%llX" : (radix == 8 ? "%llo" : 0)));
1742 int64_t sextVal = (int64_t(VAL) << (APINT_BITS_PER_WORD-BitWidth)) >>
1743 (APINT_BITS_PER_WORD-BitWidth);
1744 sprintf(buf, format, sextVal);
1746 sprintf(buf, format, VAL);
1751 uint32_t bit = v & 1;
1753 buf[bits_used] = digits[bit][0];
1762 uint64_t mask = radix - 1;
1763 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : 1);
1764 uint32_t nibbles = APINT_BITS_PER_WORD / shift;
1765 for (uint32_t i = 0; i < getNumWords(); ++i) {
1766 uint64_t value = pVal[i];
1767 for (uint32_t j = 0; j < nibbles; ++j) {
1768 result.insert(0, digits[ value & mask ]);
1776 APInt divisor(4, radix);
1777 APInt zero(tmp.getBitWidth(), 0);
1778 size_t insert_at = 0;
1779 if (wantSigned && tmp[BitWidth-1]) {
1780 // They want to print the signed version and it is a negative value
1781 // Flip the bits and add one to turn it into the equivalent positive
1782 // value and put a '-' in the result.
1788 if (tmp == APInt(tmp.getBitWidth(), 0))
1790 else while (tmp.ne(zero)) {
1792 APInt tmp2(tmp.getBitWidth(), 0);
1793 divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
1795 uint32_t digit = APdigit.getZExtValue();
1796 assert(digit < radix && "divide failed");
1797 result.insert(insert_at,digits[digit]);
1805 void APInt::dump() const
1807 cerr << "APInt(" << BitWidth << ")=" << std::setbase(16);
1810 else for (unsigned i = getNumWords(); i > 0; i--) {
1811 cerr << pVal[i-1] << " ";
1813 cerr << " U(" << this->toString(10) << ") S(" << this->toStringSigned(10)
1814 << ")\n" << std::setbase(10);