1 //===-- APInt.cpp - Implement APInt class ---------------------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by Sheng Zhou and Reid Spencer and is distributed
6 // under the University of Illinois Open Source License. See LICENSE.TXT
9 //===----------------------------------------------------------------------===//
11 // This file implements a class to represent arbitrary precision integer
12 // constant values and provide a variety of arithmetic operations on them.
14 //===----------------------------------------------------------------------===//
16 #define DEBUG_TYPE "apint"
17 #include "llvm/ADT/APInt.h"
18 #include "llvm/DerivedTypes.h"
19 #include "llvm/Support/Debug.h"
20 #include "llvm/Support/MathExtras.h"
29 /// A utility function for allocating memory, checking for allocation failures,
30 /// and ensuring the contents are zeroed.
31 inline static uint64_t* getClearedMemory(uint32_t numWords) {
32 uint64_t * result = new uint64_t[numWords];
33 assert(result && "APInt memory allocation fails!");
34 memset(result, 0, numWords * sizeof(uint64_t));
38 /// A utility function for allocating memory and checking for allocation
39 /// failure. The content is not zeroed.
40 inline static uint64_t* getMemory(uint32_t numWords) {
41 uint64_t * result = new uint64_t[numWords];
42 assert(result && "APInt memory allocation fails!");
46 APInt::APInt(uint32_t numBits, uint64_t val)
47 : BitWidth(numBits), VAL(0) {
48 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small");
49 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large");
53 pVal = getClearedMemory(getNumWords());
59 APInt::APInt(uint32_t numBits, uint32_t numWords, uint64_t bigVal[])
60 : BitWidth(numBits), VAL(0) {
61 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small");
62 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large");
63 assert(bigVal && "Null pointer detected!");
67 // Get memory, cleared to 0
68 pVal = getClearedMemory(getNumWords());
69 // Calculate the number of words to copy
70 uint32_t words = std::min<uint32_t>(numWords, getNumWords());
71 // Copy the words from bigVal to pVal
72 memcpy(pVal, bigVal, words * APINT_WORD_SIZE);
74 // Make sure unused high bits are cleared
78 APInt::APInt(uint32_t numbits, const char StrStart[], uint32_t slen,
80 : BitWidth(numbits), VAL(0) {
81 fromString(numbits, StrStart, slen, radix);
84 APInt::APInt(uint32_t numbits, const std::string& Val, uint8_t radix)
85 : BitWidth(numbits), VAL(0) {
86 assert(!Val.empty() && "String empty?");
87 fromString(numbits, Val.c_str(), Val.size(), radix);
90 APInt::APInt(const APInt& that)
91 : BitWidth(that.BitWidth), VAL(0) {
95 pVal = getMemory(getNumWords());
96 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE);
101 if (!isSingleWord() && pVal)
105 APInt& APInt::operator=(const APInt& RHS) {
106 // Don't do anything for X = X
110 // If the bitwidths are the same, we can avoid mucking with memory
111 if (BitWidth == RHS.getBitWidth()) {
115 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE);
120 if (RHS.isSingleWord())
124 pVal = getMemory(RHS.getNumWords());
125 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
127 else if (getNumWords() == RHS.getNumWords())
128 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
129 else if (RHS.isSingleWord()) {
134 pVal = getMemory(RHS.getNumWords());
135 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
137 BitWidth = RHS.BitWidth;
138 return clearUnusedBits();
141 APInt& APInt::operator=(uint64_t RHS) {
146 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE);
148 return clearUnusedBits();
151 /// add_1 - This function adds a single "digit" integer, y, to the multiple
152 /// "digit" integer array, x[]. x[] is modified to reflect the addition and
153 /// 1 is returned if there is a carry out, otherwise 0 is returned.
154 /// @returns the carry of the addition.
155 static bool add_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
156 for (uint32_t i = 0; i < len; ++i) {
159 y = 1; // Carry one to next digit.
161 y = 0; // No need to carry so exit early
168 /// @brief Prefix increment operator. Increments the APInt by one.
169 APInt& APInt::operator++() {
173 add_1(pVal, pVal, getNumWords(), 1);
174 return clearUnusedBits();
177 /// sub_1 - This function subtracts a single "digit" (64-bit word), y, from
178 /// the multi-digit integer array, x[], propagating the borrowed 1 value until
179 /// no further borrowing is neeeded or it runs out of "digits" in x. The result
180 /// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted.
181 /// In other words, if y > x then this function returns 1, otherwise 0.
182 /// @returns the borrow out of the subtraction
183 static bool sub_1(uint64_t x[], uint32_t len, uint64_t y) {
184 for (uint32_t i = 0; i < len; ++i) {
188 y = 1; // We have to "borrow 1" from next "digit"
190 y = 0; // No need to borrow
191 break; // Remaining digits are unchanged so exit early
197 /// @brief Prefix decrement operator. Decrements the APInt by one.
198 APInt& APInt::operator--() {
202 sub_1(pVal, getNumWords(), 1);
203 return clearUnusedBits();
206 /// add - This function adds the integer array x to the integer array Y and
207 /// places the result in dest.
208 /// @returns the carry out from the addition
209 /// @brief General addition of 64-bit integer arrays
210 static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y,
213 for (uint32_t i = 0; i< len; ++i) {
214 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x
215 dest[i] = x[i] + y[i] + carry;
216 carry = dest[i] < limit || (carry && dest[i] == limit);
221 /// Adds the RHS APint to this APInt.
222 /// @returns this, after addition of RHS.
223 /// @brief Addition assignment operator.
224 APInt& APInt::operator+=(const APInt& RHS) {
225 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
229 add(pVal, pVal, RHS.pVal, getNumWords());
231 return clearUnusedBits();
234 /// Subtracts the integer array y from the integer array x
235 /// @returns returns the borrow out.
236 /// @brief Generalized subtraction of 64-bit integer arrays.
237 static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y,
240 for (uint32_t i = 0; i < len; ++i) {
241 uint64_t x_tmp = borrow ? x[i] - 1 : x[i];
242 borrow = y[i] > x_tmp || (borrow && x[i] == 0);
243 dest[i] = x_tmp - y[i];
248 /// Subtracts the RHS APInt from this APInt
249 /// @returns this, after subtraction
250 /// @brief Subtraction assignment operator.
251 APInt& APInt::operator-=(const APInt& RHS) {
252 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
256 sub(pVal, pVal, RHS.pVal, getNumWords());
257 return clearUnusedBits();
260 /// Multiplies an integer array, x by a a uint64_t integer and places the result
262 /// @returns the carry out of the multiplication.
263 /// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer.
264 static uint64_t mul_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
265 // Split y into high 32-bit part (hy) and low 32-bit part (ly)
266 uint64_t ly = y & 0xffffffffULL, hy = y >> 32;
269 // For each digit of x.
270 for (uint32_t i = 0; i < len; ++i) {
271 // Split x into high and low words
272 uint64_t lx = x[i] & 0xffffffffULL;
273 uint64_t hx = x[i] >> 32;
274 // hasCarry - A flag to indicate if there is a carry to the next digit.
275 // hasCarry == 0, no carry
276 // hasCarry == 1, has carry
277 // hasCarry == 2, no carry and the calculation result == 0.
278 uint8_t hasCarry = 0;
279 dest[i] = carry + lx * ly;
280 // Determine if the add above introduces carry.
281 hasCarry = (dest[i] < carry) ? 1 : 0;
282 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0);
283 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) +
284 // (2^32 - 1) + 2^32 = 2^64.
285 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
287 carry += (lx * hy) & 0xffffffffULL;
288 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL);
289 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) +
290 (carry >> 32) + ((lx * hy) >> 32) + hx * hy;
295 /// Multiplies integer array x by integer array y and stores the result into
296 /// the integer array dest. Note that dest's size must be >= xlen + ylen.
297 /// @brief Generalized multiplicate of integer arrays.
298 static void mul(uint64_t dest[], uint64_t x[], uint32_t xlen, uint64_t y[],
300 dest[xlen] = mul_1(dest, x, xlen, y[0]);
301 for (uint32_t i = 1; i < ylen; ++i) {
302 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32;
303 uint64_t carry = 0, lx = 0, hx = 0;
304 for (uint32_t j = 0; j < xlen; ++j) {
305 lx = x[j] & 0xffffffffULL;
307 // hasCarry - A flag to indicate if has carry.
308 // hasCarry == 0, no carry
309 // hasCarry == 1, has carry
310 // hasCarry == 2, no carry and the calculation result == 0.
311 uint8_t hasCarry = 0;
312 uint64_t resul = carry + lx * ly;
313 hasCarry = (resul < carry) ? 1 : 0;
314 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32);
315 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
317 carry += (lx * hy) & 0xffffffffULL;
318 resul = (carry << 32) | (resul & 0xffffffffULL);
320 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+
321 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) +
322 ((lx * hy) >> 32) + hx * hy;
324 dest[i+xlen] = carry;
328 APInt& APInt::operator*=(const APInt& RHS) {
329 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
330 if (isSingleWord()) {
336 // Get some bit facts about LHS and check for zero
337 uint32_t lhsBits = getActiveBits();
338 uint32_t lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1;
343 // Get some bit facts about RHS and check for zero
344 uint32_t rhsBits = RHS.getActiveBits();
345 uint32_t rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1;
352 // Allocate space for the result
353 uint32_t destWords = rhsWords + lhsWords;
354 uint64_t *dest = getMemory(destWords);
356 // Perform the long multiply
357 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords);
359 // Copy result back into *this
361 uint32_t wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords;
362 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE);
364 // delete dest array and return
369 APInt& APInt::operator&=(const APInt& RHS) {
370 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
371 if (isSingleWord()) {
375 uint32_t numWords = getNumWords();
376 for (uint32_t i = 0; i < numWords; ++i)
377 pVal[i] &= RHS.pVal[i];
381 APInt& APInt::operator|=(const APInt& RHS) {
382 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
383 if (isSingleWord()) {
387 uint32_t numWords = getNumWords();
388 for (uint32_t i = 0; i < numWords; ++i)
389 pVal[i] |= RHS.pVal[i];
393 APInt& APInt::operator^=(const APInt& RHS) {
394 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
395 if (isSingleWord()) {
397 this->clearUnusedBits();
400 uint32_t numWords = getNumWords();
401 for (uint32_t i = 0; i < numWords; ++i)
402 pVal[i] ^= RHS.pVal[i];
403 return clearUnusedBits();
406 APInt APInt::operator&(const APInt& RHS) const {
407 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
409 return APInt(getBitWidth(), VAL & RHS.VAL);
411 uint32_t numWords = getNumWords();
412 uint64_t* val = getMemory(numWords);
413 for (uint32_t i = 0; i < numWords; ++i)
414 val[i] = pVal[i] & RHS.pVal[i];
415 return APInt(val, getBitWidth());
418 APInt APInt::operator|(const APInt& RHS) const {
419 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
421 return APInt(getBitWidth(), VAL | RHS.VAL);
423 uint32_t numWords = getNumWords();
424 uint64_t *val = getMemory(numWords);
425 for (uint32_t i = 0; i < numWords; ++i)
426 val[i] = pVal[i] | RHS.pVal[i];
427 return APInt(val, getBitWidth());
430 APInt APInt::operator^(const APInt& RHS) const {
431 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
433 return APInt(BitWidth, VAL ^ RHS.VAL);
435 uint32_t numWords = getNumWords();
436 uint64_t *val = getMemory(numWords);
437 for (uint32_t i = 0; i < numWords; ++i)
438 val[i] = pVal[i] ^ RHS.pVal[i];
440 // 0^0==1 so clear the high bits in case they got set.
441 return APInt(val, getBitWidth()).clearUnusedBits();
444 bool APInt::operator !() const {
448 for (uint32_t i = 0; i < getNumWords(); ++i)
454 APInt APInt::operator*(const APInt& RHS) const {
455 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
457 return APInt(BitWidth, VAL * RHS.VAL);
460 return Result.clearUnusedBits();
463 APInt APInt::operator+(const APInt& RHS) const {
464 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
466 return APInt(BitWidth, VAL + RHS.VAL);
467 APInt Result(BitWidth, 0);
468 add(Result.pVal, this->pVal, RHS.pVal, getNumWords());
469 return Result.clearUnusedBits();
472 APInt APInt::operator-(const APInt& RHS) const {
473 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
475 return APInt(BitWidth, VAL - RHS.VAL);
476 APInt Result(BitWidth, 0);
477 sub(Result.pVal, this->pVal, RHS.pVal, getNumWords());
478 return Result.clearUnusedBits();
481 bool APInt::operator[](uint32_t bitPosition) const {
482 return (maskBit(bitPosition) &
483 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0;
486 bool APInt::operator==(const APInt& RHS) const {
487 assert(BitWidth == RHS.BitWidth && "Comparison requires equal bit widths");
489 return VAL == RHS.VAL;
491 // Get some facts about the number of bits used in the two operands.
492 uint32_t n1 = getActiveBits();
493 uint32_t n2 = RHS.getActiveBits();
495 // If the number of bits isn't the same, they aren't equal
499 // If the number of bits fits in a word, we only need to compare the low word.
500 if (n1 <= APINT_BITS_PER_WORD)
501 return pVal[0] == RHS.pVal[0];
503 // Otherwise, compare everything
504 for (int i = whichWord(n1 - 1); i >= 0; --i)
505 if (pVal[i] != RHS.pVal[i])
510 bool APInt::operator==(uint64_t Val) const {
514 uint32_t n = getActiveBits();
515 if (n <= APINT_BITS_PER_WORD)
516 return pVal[0] == Val;
521 bool APInt::ult(const APInt& RHS) const {
522 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
524 return VAL < RHS.VAL;
526 // Get active bit length of both operands
527 uint32_t n1 = getActiveBits();
528 uint32_t n2 = RHS.getActiveBits();
530 // If magnitude of LHS is less than RHS, return true.
534 // If magnitude of RHS is greather than LHS, return false.
538 // If they bot fit in a word, just compare the low order word
539 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD)
540 return pVal[0] < RHS.pVal[0];
542 // Otherwise, compare all words
543 uint32_t topWord = whichWord(std::max(n1,n2)-1);
544 for (int i = topWord; i >= 0; --i) {
545 if (pVal[i] > RHS.pVal[i])
547 if (pVal[i] < RHS.pVal[i])
553 bool APInt::slt(const APInt& RHS) const {
554 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
555 if (isSingleWord()) {
556 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
557 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth);
558 return lhsSext < rhsSext;
563 bool lhsNeg = isNegative();
564 bool rhsNeg = rhs.isNegative();
566 // Sign bit is set so perform two's complement to make it positive
571 // Sign bit is set so perform two's complement to make it positive
576 // Now we have unsigned values to compare so do the comparison if necessary
577 // based on the negativeness of the values.
589 APInt& APInt::set(uint32_t bitPosition) {
591 VAL |= maskBit(bitPosition);
593 pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
597 APInt& APInt::set() {
598 if (isSingleWord()) {
600 return clearUnusedBits();
603 // Set all the bits in all the words.
604 for (uint32_t i = 0; i < getNumWords() - 1; ++i)
606 // Clear the unused ones
607 return clearUnusedBits();
610 /// Set the given bit to 0 whose position is given as "bitPosition".
611 /// @brief Set a given bit to 0.
612 APInt& APInt::clear(uint32_t bitPosition) {
614 VAL &= ~maskBit(bitPosition);
616 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
620 /// @brief Set every bit to 0.
621 APInt& APInt::clear() {
625 memset(pVal, 0, getNumWords() * APINT_WORD_SIZE);
629 /// @brief Bitwise NOT operator. Performs a bitwise logical NOT operation on
631 APInt APInt::operator~() const {
637 /// @brief Toggle every bit to its opposite value.
638 APInt& APInt::flip() {
639 if (isSingleWord()) {
641 return clearUnusedBits();
643 for (uint32_t i = 0; i < getNumWords(); ++i)
645 return clearUnusedBits();
648 /// Toggle a given bit to its opposite value whose position is given
649 /// as "bitPosition".
650 /// @brief Toggles a given bit to its opposite value.
651 APInt& APInt::flip(uint32_t bitPosition) {
652 assert(bitPosition < BitWidth && "Out of the bit-width range!");
653 if ((*this)[bitPosition]) clear(bitPosition);
654 else set(bitPosition);
658 /// getMaxValue - This function returns the largest value
659 /// for an APInt of the specified bit-width and if isSign == true,
660 /// it should be largest signed value, otherwise unsigned value.
661 APInt APInt::getMaxValue(uint32_t numBits, bool isSign) {
662 APInt Result(numBits, 0);
665 Result.clear(numBits - 1);
669 /// getMinValue - This function returns the smallest value for
670 /// an APInt of the given bit-width and if isSign == true,
671 /// it should be smallest signed value, otherwise zero.
672 APInt APInt::getMinValue(uint32_t numBits, bool isSign) {
673 APInt Result(numBits, 0);
675 Result.set(numBits - 1);
679 /// getAllOnesValue - This function returns an all-ones value for
680 /// an APInt of the specified bit-width.
681 APInt APInt::getAllOnesValue(uint32_t numBits) {
682 return getMaxValue(numBits, false);
685 /// getNullValue - This function creates an '0' value for an
686 /// APInt of the specified bit-width.
687 APInt APInt::getNullValue(uint32_t numBits) {
688 return getMinValue(numBits, false);
691 uint64_t APInt::getHashValue() const {
692 // Put the bit width into the low order bits.
693 uint64_t hash = BitWidth;
695 // Add the sum of the words to the hash.
697 hash += VAL << 6; // clear separation of up to 64 bits
699 for (uint32_t i = 0; i < getNumWords(); ++i)
700 hash += pVal[i] << 6; // clear sepration of up to 64 bits
704 /// HiBits - This function returns the high "numBits" bits of this APInt.
705 APInt APInt::getHiBits(uint32_t numBits) const {
706 return APIntOps::lshr(*this, BitWidth - numBits);
709 /// LoBits - This function returns the low "numBits" bits of this APInt.
710 APInt APInt::getLoBits(uint32_t numBits) const {
711 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
715 bool APInt::isPowerOf2() const {
716 return (!!*this) && !(*this & (*this - APInt(BitWidth,1)));
719 uint32_t APInt::countLeadingZeros() const {
722 Count = CountLeadingZeros_64(VAL);
724 for (uint32_t i = getNumWords(); i > 0u; --i) {
726 Count += APINT_BITS_PER_WORD;
728 Count += CountLeadingZeros_64(pVal[i-1]);
733 uint32_t remainder = BitWidth % APINT_BITS_PER_WORD;
735 Count -= APINT_BITS_PER_WORD - remainder;
739 uint32_t APInt::countTrailingZeros() const {
741 return CountTrailingZeros_64(VAL);
744 for (; i < getNumWords() && pVal[i] == 0; ++i)
745 Count += APINT_BITS_PER_WORD;
746 if (i < getNumWords())
747 Count += CountTrailingZeros_64(pVal[i]);
751 uint32_t APInt::countPopulation() const {
753 return CountPopulation_64(VAL);
755 for (uint32_t i = 0; i < getNumWords(); ++i)
756 Count += CountPopulation_64(pVal[i]);
760 APInt APInt::byteSwap() const {
761 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
763 return APInt(BitWidth, ByteSwap_16(VAL));
764 else if (BitWidth == 32)
765 return APInt(BitWidth, ByteSwap_32(VAL));
766 else if (BitWidth == 48) {
767 uint64_t Tmp1 = ((VAL >> 32) << 16) | (VAL & 0xFFFF);
768 Tmp1 = ByteSwap_32(Tmp1);
769 uint64_t Tmp2 = (VAL >> 16) & 0xFFFF;
770 Tmp2 = ByteSwap_16(Tmp2);
773 (Tmp1 & 0xff) | ((Tmp1<<16) & 0xffff00000000ULL) | (Tmp2 << 16));
774 } else if (BitWidth == 64)
775 return APInt(BitWidth, ByteSwap_64(VAL));
777 APInt Result(BitWidth, 0);
778 char *pByte = (char*)Result.pVal;
779 for (uint32_t i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) {
781 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i];
782 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp;
788 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
790 APInt A = API1, B = API2;
793 B = APIntOps::urem(A, B);
799 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, uint32_t width) {
806 // Get the sign bit from the highest order bit
807 bool isNeg = T.I >> 63;
809 // Get the 11-bit exponent and adjust for the 1023 bit bias
810 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
812 // If the exponent is negative, the value is < 0 so just return 0.
814 return APInt(64u, 0u);
816 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
817 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
819 // If the exponent doesn't shift all bits out of the mantissa
821 return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
822 APInt(width, mantissa >> (52 - exp));
824 // If the client didn't provide enough bits for us to shift the mantissa into
825 // then the result is undefined, just return 0
826 if (width <= exp - 52)
827 return APInt(width, 0);
829 // Otherwise, we have to shift the mantissa bits up to the right location
830 APInt Tmp(width, mantissa);
831 Tmp = Tmp.shl(exp - 52);
832 return isNeg ? -Tmp : Tmp;
835 /// RoundToDouble - This function convert this APInt to a double.
836 /// The layout for double is as following (IEEE Standard 754):
837 /// --------------------------------------
838 /// | Sign Exponent Fraction Bias |
839 /// |-------------------------------------- |
840 /// | 1[63] 11[62-52] 52[51-00] 1023 |
841 /// --------------------------------------
842 double APInt::roundToDouble(bool isSigned) const {
844 // Handle the simple case where the value is contained in one uint64_t.
845 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
847 int64_t sext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
853 // Determine if the value is negative.
854 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
856 // Construct the absolute value if we're negative.
857 APInt Tmp(isNeg ? -(*this) : (*this));
859 // Figure out how many bits we're using.
860 uint32_t n = Tmp.getActiveBits();
862 // The exponent (without bias normalization) is just the number of bits
863 // we are using. Note that the sign bit is gone since we constructed the
867 // Return infinity for exponent overflow
869 if (!isSigned || !isNeg)
870 return double(1.0E300 * 1.0E300); // positive infinity
872 return double(-1.0E300 * 1.0E300); // negative infinity
874 exp += 1023; // Increment for 1023 bias
876 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
877 // extract the high 52 bits from the correct words in pVal.
879 unsigned hiWord = whichWord(n-1);
881 mantissa = Tmp.pVal[0];
883 mantissa >>= n - 52; // shift down, we want the top 52 bits.
885 assert(hiWord > 0 && "huh?");
886 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
887 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
888 mantissa = hibits | lobits;
891 // The leading bit of mantissa is implicit, so get rid of it.
892 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
897 T.I = sign | (exp << 52) | mantissa;
901 // Truncate to new width.
902 void APInt::trunc(uint32_t width) {
903 assert(width < BitWidth && "Invalid APInt Truncate request");
904 assert(width >= IntegerType::MIN_INT_BITS && "Can't truncate to 0 bits");
905 uint32_t wordsBefore = getNumWords();
907 uint32_t wordsAfter = getNumWords();
908 if (wordsBefore != wordsAfter) {
909 if (wordsAfter == 1) {
910 uint64_t *tmp = pVal;
914 uint64_t *newVal = getClearedMemory(wordsAfter);
915 for (uint32_t i = 0; i < wordsAfter; ++i)
924 // Sign extend to a new width.
925 void APInt::sext(uint32_t width) {
926 assert(width > BitWidth && "Invalid APInt SignExtend request");
927 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
928 // If the sign bit isn't set, this is the same as zext.
934 // The sign bit is set. First, get some facts
935 uint32_t wordsBefore = getNumWords();
936 uint32_t wordBits = BitWidth % APINT_BITS_PER_WORD;
938 uint32_t wordsAfter = getNumWords();
940 // Mask the high order word appropriately
941 if (wordsBefore == wordsAfter) {
942 uint32_t newWordBits = width % APINT_BITS_PER_WORD;
943 // The extension is contained to the wordsBefore-1th word.
944 uint64_t mask = (~0ULL >> (APINT_BITS_PER_WORD - newWordBits)) << wordBits;
945 if (wordsBefore == 1)
948 pVal[wordsBefore-1] |= mask;
953 uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits;
954 uint64_t *newVal = getMemory(wordsAfter);
955 if (wordsBefore == 1)
956 newVal[0] = VAL | mask;
958 for (uint32_t i = 0; i < wordsBefore; ++i)
960 newVal[wordsBefore-1] |= mask;
962 for (uint32_t i = wordsBefore; i < wordsAfter; i++)
964 if (wordsBefore != 1)
970 // Zero extend to a new width.
971 void APInt::zext(uint32_t width) {
972 assert(width > BitWidth && "Invalid APInt ZeroExtend request");
973 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
974 uint32_t wordsBefore = getNumWords();
976 uint32_t wordsAfter = getNumWords();
977 if (wordsBefore != wordsAfter) {
978 uint64_t *newVal = getClearedMemory(wordsAfter);
979 if (wordsBefore == 1)
982 for (uint32_t i = 0; i < wordsBefore; ++i)
984 if (wordsBefore != 1)
990 /// Arithmetic right-shift this APInt by shiftAmt.
991 /// @brief Arithmetic right-shift function.
992 APInt APInt::ashr(uint32_t shiftAmt) const {
993 assert(shiftAmt <= BitWidth && "Invalid shift amount");
994 if (isSingleWord()) {
995 if (shiftAmt == BitWidth)
996 return APInt(BitWidth, 0); // undefined
998 uint32_t SignBit = APINT_BITS_PER_WORD - BitWidth;
999 return APInt(BitWidth,
1000 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1004 // If all the bits were shifted out, the result is 0 or -1. This avoids issues
1005 // with shifting by the size of the integer type, which produces undefined
1007 if (shiftAmt == BitWidth)
1009 return APInt(BitWidth, -1ULL);
1011 return APInt(BitWidth, 0);
1013 // Create some space for the result.
1014 uint64_t * val = new uint64_t[getNumWords()];
1016 // If we are shifting less than a word, compute the shift with a simple carry
1017 if (shiftAmt < APINT_BITS_PER_WORD) {
1019 for (int i = getNumWords()-1; i >= 0; --i) {
1020 val[i] = pVal[i] >> shiftAmt | carry;
1021 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1023 return APInt(val, BitWidth).clearUnusedBits();
1026 // Compute some values needed by the remaining shift algorithms
1027 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1028 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1030 // If we are shifting whole words, just move whole words
1031 if (wordShift == 0) {
1032 for (uint32_t i = 0; i < getNumWords() - offset; ++i)
1033 val[i] = pVal[i+offset];
1034 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
1035 val[i] = (isNegative() ? -1ULL : 0);
1036 return APInt(val,BitWidth).clearUnusedBits();
1039 // Shift the low order words
1040 uint32_t breakWord = getNumWords() - offset -1;
1041 for (uint32_t i = 0; i < breakWord; ++i)
1042 val[i] = pVal[i+offset] >> wordShift |
1043 pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift);
1044 // Shift the break word.
1045 uint32_t SignBit = APINT_BITS_PER_WORD - (BitWidth % APINT_BITS_PER_WORD);
1046 val[breakWord] = uint64_t(
1047 (((int64_t(pVal[breakWord+offset]) << SignBit) >> SignBit) >> wordShift));
1049 // Remaining words are 0 or -1
1050 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1051 val[i] = (isNegative() ? -1ULL : 0);
1052 return APInt(val, BitWidth).clearUnusedBits();
1055 /// Logical right-shift this APInt by shiftAmt.
1056 /// @brief Logical right-shift function.
1057 APInt APInt::lshr(uint32_t shiftAmt) const {
1059 if (shiftAmt == BitWidth)
1060 return APInt(BitWidth, 0);
1062 return APInt(BitWidth, this->VAL >> shiftAmt);
1064 // If all the bits were shifted out, the result is 0. This avoids issues
1065 // with shifting by the size of the integer type, which produces undefined
1066 // results. We define these "undefined results" to always be 0.
1067 if (shiftAmt == BitWidth)
1068 return APInt(BitWidth, 0);
1070 // Create some space for the result.
1071 uint64_t * val = new uint64_t[getNumWords()];
1073 // If we are shifting less than a word, compute the shift with a simple carry
1074 if (shiftAmt < APINT_BITS_PER_WORD) {
1076 for (int i = getNumWords()-1; i >= 0; --i) {
1077 val[i] = pVal[i] >> shiftAmt | carry;
1078 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1080 return APInt(val, BitWidth).clearUnusedBits();
1083 // Compute some values needed by the remaining shift algorithms
1084 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1085 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1087 // If we are shifting whole words, just move whole words
1088 if (wordShift == 0) {
1089 for (uint32_t i = 0; i < getNumWords() - offset; ++i)
1090 val[i] = pVal[i+offset];
1091 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
1093 return APInt(val,BitWidth).clearUnusedBits();
1096 // Shift the low order words
1097 uint32_t breakWord = getNumWords() - offset -1;
1098 for (uint32_t i = 0; i < breakWord; ++i)
1099 val[i] = pVal[i+offset] >> wordShift |
1100 pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift);
1101 // Shift the break word.
1102 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1104 // Remaining words are 0
1105 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1107 return APInt(val, BitWidth).clearUnusedBits();
1110 /// Left-shift this APInt by shiftAmt.
1111 /// @brief Left-shift function.
1112 APInt APInt::shl(uint32_t shiftAmt) const {
1113 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1114 if (isSingleWord()) {
1115 if (shiftAmt == BitWidth)
1116 return APInt(BitWidth, 0); // avoid undefined shift results
1117 return APInt(BitWidth, VAL << shiftAmt);
1120 // If all the bits were shifted out, the result is 0. This avoids issues
1121 // with shifting by the size of the integer type, which produces undefined
1122 // results. We define these "undefined results" to always be 0.
1123 if (shiftAmt == BitWidth)
1124 return APInt(BitWidth, 0);
1126 // Create some space for the result.
1127 uint64_t * val = new uint64_t[getNumWords()];
1129 // If we are shifting less than a word, do it the easy way
1130 if (shiftAmt < APINT_BITS_PER_WORD) {
1132 for (uint32_t i = 0; i < getNumWords(); i++) {
1133 val[i] = pVal[i] << shiftAmt | carry;
1134 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1136 return APInt(val, BitWidth).clearUnusedBits();
1139 // Compute some values needed by the remaining shift algorithms
1140 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1141 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1143 // If we are shifting whole words, just move whole words
1144 if (wordShift == 0) {
1145 for (uint32_t i = 0; i < offset; i++)
1147 for (uint32_t i = offset; i < getNumWords(); i++)
1148 val[i] = pVal[i-offset];
1149 return APInt(val,BitWidth).clearUnusedBits();
1152 // Copy whole words from this to Result.
1153 uint32_t i = getNumWords() - 1;
1154 for (; i > offset; --i)
1155 val[i] = pVal[i-offset] << wordShift |
1156 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1157 val[offset] = pVal[0] << wordShift;
1158 for (i = 0; i < offset; ++i)
1160 return APInt(val, BitWidth).clearUnusedBits();
1163 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1164 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1165 /// variables here have the same names as in the algorithm. Comments explain
1166 /// the algorithm and any deviation from it.
1167 static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
1168 uint32_t m, uint32_t n) {
1169 assert(u && "Must provide dividend");
1170 assert(v && "Must provide divisor");
1171 assert(q && "Must provide quotient");
1172 assert(u != v && u != q && v != q && "Must us different memory");
1173 assert(n>1 && "n must be > 1");
1175 // Knuth uses the value b as the base of the number system. In our case b
1176 // is 2^31 so we just set it to -1u.
1177 uint64_t b = uint64_t(1) << 32;
1179 DEBUG(cerr << "KnuthDiv: m=" << m << " n=" << n << '\n');
1180 DEBUG(cerr << "KnuthDiv: original:");
1181 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1182 DEBUG(cerr << " by");
1183 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1184 DEBUG(cerr << '\n');
1185 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1186 // u and v by d. Note that we have taken Knuth's advice here to use a power
1187 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1188 // 2 allows us to shift instead of multiply and it is easy to determine the
1189 // shift amount from the leading zeros. We are basically normalizing the u
1190 // and v so that its high bits are shifted to the top of v's range without
1191 // overflow. Note that this can require an extra word in u so that u must
1192 // be of length m+n+1.
1193 uint32_t shift = CountLeadingZeros_32(v[n-1]);
1194 uint32_t v_carry = 0;
1195 uint32_t u_carry = 0;
1197 for (uint32_t i = 0; i < m+n; ++i) {
1198 uint32_t u_tmp = u[i] >> (32 - shift);
1199 u[i] = (u[i] << shift) | u_carry;
1202 for (uint32_t i = 0; i < n; ++i) {
1203 uint32_t v_tmp = v[i] >> (32 - shift);
1204 v[i] = (v[i] << shift) | v_carry;
1209 DEBUG(cerr << "KnuthDiv: normal:");
1210 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1211 DEBUG(cerr << " by");
1212 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1213 DEBUG(cerr << '\n');
1215 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1218 DEBUG(cerr << "KnuthDiv: quotient digit #" << j << '\n');
1219 // D3. [Calculate q'.].
1220 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1221 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1222 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1223 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1224 // on v[n-2] determines at high speed most of the cases in which the trial
1225 // value qp is one too large, and it eliminates all cases where qp is two
1227 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1228 DEBUG(cerr << "KnuthDiv: dividend == " << dividend << '\n');
1229 uint64_t qp = dividend / v[n-1];
1230 uint64_t rp = dividend % v[n-1];
1231 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1234 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1237 DEBUG(cerr << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1239 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1240 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1241 // consists of a simple multiplication by a one-place number, combined with
1244 for (uint32_t i = 0; i < n; ++i) {
1245 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1246 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1247 bool borrow = subtrahend > u_tmp;
1248 DEBUG(cerr << "KnuthDiv: u_tmp == " << u_tmp
1249 << ", subtrahend == " << subtrahend
1250 << ", borrow = " << borrow << '\n');
1252 uint64_t result = u_tmp - subtrahend;
1254 u[k++] = result & (b-1); // subtract low word
1255 u[k++] = result >> 32; // subtract high word
1256 while (borrow && k <= m+n) { // deal with borrow to the left
1262 DEBUG(cerr << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1265 DEBUG(cerr << "KnuthDiv: after subtraction:");
1266 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1267 DEBUG(cerr << '\n');
1268 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1269 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1270 // true value plus b**(n+1), namely as the b's complement of
1271 // the true value, and a "borrow" to the left should be remembered.
1274 bool carry = true; // true because b's complement is "complement + 1"
1275 for (uint32_t i = 0; i <= m+n; ++i) {
1276 u[i] = ~u[i] + carry; // b's complement
1277 carry = carry && u[i] == 0;
1280 DEBUG(cerr << "KnuthDiv: after complement:");
1281 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1282 DEBUG(cerr << '\n');
1284 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1285 // negative, go to step D6; otherwise go on to step D7.
1288 // D6. [Add back]. The probability that this step is necessary is very
1289 // small, on the order of only 2/b. Make sure that test data accounts for
1290 // this possibility. Decrease q[j] by 1
1292 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1293 // A carry will occur to the left of u[j+n], and it should be ignored
1294 // since it cancels with the borrow that occurred in D4.
1296 for (uint32_t i = 0; i < n; i++) {
1297 uint32_t limit = std::min(u[j+i],v[i]);
1298 u[j+i] += v[i] + carry;
1299 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1303 DEBUG(cerr << "KnuthDiv: after correction:");
1304 DEBUG(for (int i = m+n; i >=0; i--) cerr <<" " << u[i]);
1305 DEBUG(cerr << "\nKnuthDiv: digit result = " << q[j] << '\n');
1307 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1310 DEBUG(cerr << "KnuthDiv: quotient:");
1311 DEBUG(for (int i = m; i >=0; i--) cerr <<" " << q[i]);
1312 DEBUG(cerr << '\n');
1314 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1315 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1316 // compute the remainder (urem uses this).
1318 // The value d is expressed by the "shift" value above since we avoided
1319 // multiplication by d by using a shift left. So, all we have to do is
1320 // shift right here. In order to mak
1323 DEBUG(cerr << "KnuthDiv: remainder:");
1324 for (int i = n-1; i >= 0; i--) {
1325 r[i] = (u[i] >> shift) | carry;
1326 carry = u[i] << (32 - shift);
1327 DEBUG(cerr << " " << r[i]);
1330 for (int i = n-1; i >= 0; i--) {
1332 DEBUG(cerr << " " << r[i]);
1335 DEBUG(cerr << '\n');
1337 DEBUG(cerr << std::setbase(10) << '\n');
1340 void APInt::divide(const APInt LHS, uint32_t lhsWords,
1341 const APInt &RHS, uint32_t rhsWords,
1342 APInt *Quotient, APInt *Remainder)
1344 assert(lhsWords >= rhsWords && "Fractional result");
1346 // First, compose the values into an array of 32-bit words instead of
1347 // 64-bit words. This is a necessity of both the "short division" algorithm
1348 // and the the Knuth "classical algorithm" which requires there to be native
1349 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1350 // can't use 64-bit operands here because we don't have native results of
1351 // 128-bits. Furthremore, casting the 64-bit values to 32-bit values won't
1352 // work on large-endian machines.
1353 uint64_t mask = ~0ull >> (sizeof(uint32_t)*8);
1354 uint32_t n = rhsWords * 2;
1355 uint32_t m = (lhsWords * 2) - n;
1357 // Allocate space for the temporary values we need either on the stack, if
1358 // it will fit, or on the heap if it won't.
1359 uint32_t SPACE[128];
1364 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1367 Q = &SPACE[(m+n+1) + n];
1369 R = &SPACE[(m+n+1) + n + (m+n)];
1371 U = new uint32_t[m + n + 1];
1372 V = new uint32_t[n];
1373 Q = new uint32_t[m+n];
1375 R = new uint32_t[n];
1378 // Initialize the dividend
1379 memset(U, 0, (m+n+1)*sizeof(uint32_t));
1380 for (unsigned i = 0; i < lhsWords; ++i) {
1381 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1382 U[i * 2] = tmp & mask;
1383 U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1385 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1387 // Initialize the divisor
1388 memset(V, 0, (n)*sizeof(uint32_t));
1389 for (unsigned i = 0; i < rhsWords; ++i) {
1390 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1391 V[i * 2] = tmp & mask;
1392 V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1395 // initialize the quotient and remainder
1396 memset(Q, 0, (m+n) * sizeof(uint32_t));
1398 memset(R, 0, n * sizeof(uint32_t));
1400 // Now, adjust m and n for the Knuth division. n is the number of words in
1401 // the divisor. m is the number of words by which the dividend exceeds the
1402 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1403 // contain any zero words or the Knuth algorithm fails.
1404 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1408 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1411 // If we're left with only a single word for the divisor, Knuth doesn't work
1412 // so we implement the short division algorithm here. This is much simpler
1413 // and faster because we are certain that we can divide a 64-bit quantity
1414 // by a 32-bit quantity at hardware speed and short division is simply a
1415 // series of such operations. This is just like doing short division but we
1416 // are using base 2^32 instead of base 10.
1417 assert(n != 0 && "Divide by zero?");
1419 uint32_t divisor = V[0];
1420 uint32_t remainder = 0;
1421 for (int i = m+n-1; i >= 0; i--) {
1422 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1423 if (partial_dividend == 0) {
1426 } else if (partial_dividend < divisor) {
1428 remainder = partial_dividend;
1429 } else if (partial_dividend == divisor) {
1433 Q[i] = partial_dividend / divisor;
1434 remainder = partial_dividend - (Q[i] * divisor);
1440 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1442 KnuthDiv(U, V, Q, R, m, n);
1445 // If the caller wants the quotient
1447 // Set up the Quotient value's memory.
1448 if (Quotient->BitWidth != LHS.BitWidth) {
1449 if (Quotient->isSingleWord())
1452 delete [] Quotient->pVal;
1453 Quotient->BitWidth = LHS.BitWidth;
1454 if (!Quotient->isSingleWord())
1455 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1459 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1461 if (lhsWords == 1) {
1463 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1464 if (Quotient->isSingleWord())
1465 Quotient->VAL = tmp;
1467 Quotient->pVal[0] = tmp;
1469 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1470 for (unsigned i = 0; i < lhsWords; ++i)
1472 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1476 // If the caller wants the remainder
1478 // Set up the Remainder value's memory.
1479 if (Remainder->BitWidth != RHS.BitWidth) {
1480 if (Remainder->isSingleWord())
1483 delete [] Remainder->pVal;
1484 Remainder->BitWidth = RHS.BitWidth;
1485 if (!Remainder->isSingleWord())
1486 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1490 // The remainder is in R. Reconstitute the remainder into Remainder's low
1492 if (rhsWords == 1) {
1494 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1495 if (Remainder->isSingleWord())
1496 Remainder->VAL = tmp;
1498 Remainder->pVal[0] = tmp;
1500 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1501 for (unsigned i = 0; i < rhsWords; ++i)
1502 Remainder->pVal[i] =
1503 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1507 // Clean up the memory we allocated.
1508 if (U != &SPACE[0]) {
1516 APInt APInt::udiv(const APInt& RHS) const {
1517 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1519 // First, deal with the easy case
1520 if (isSingleWord()) {
1521 assert(RHS.VAL != 0 && "Divide by zero?");
1522 return APInt(BitWidth, VAL / RHS.VAL);
1525 // Get some facts about the LHS and RHS number of bits and words
1526 uint32_t rhsBits = RHS.getActiveBits();
1527 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1528 assert(rhsWords && "Divided by zero???");
1529 uint32_t lhsBits = this->getActiveBits();
1530 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1532 // Deal with some degenerate cases
1535 return APInt(BitWidth, 0);
1536 else if (lhsWords < rhsWords || this->ult(RHS)) {
1537 // X / Y ===> 0, iff X < Y
1538 return APInt(BitWidth, 0);
1539 } else if (*this == RHS) {
1541 return APInt(BitWidth, 1);
1542 } else if (lhsWords == 1 && rhsWords == 1) {
1543 // All high words are zero, just use native divide
1544 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1547 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1548 APInt Quotient(1,0); // to hold result.
1549 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0);
1553 APInt APInt::urem(const APInt& RHS) const {
1554 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1555 if (isSingleWord()) {
1556 assert(RHS.VAL != 0 && "Remainder by zero?");
1557 return APInt(BitWidth, VAL % RHS.VAL);
1560 // Get some facts about the LHS
1561 uint32_t lhsBits = getActiveBits();
1562 uint32_t lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1564 // Get some facts about the RHS
1565 uint32_t rhsBits = RHS.getActiveBits();
1566 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1567 assert(rhsWords && "Performing remainder operation by zero ???");
1569 // Check the degenerate cases
1570 if (lhsWords == 0) {
1572 return APInt(BitWidth, 0);
1573 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1574 // X % Y ===> X, iff X < Y
1576 } else if (*this == RHS) {
1578 return APInt(BitWidth, 0);
1579 } else if (lhsWords == 1) {
1580 // All high words are zero, just use native remainder
1581 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
1584 // We have to compute it the hard way. Invoke the Knute divide algorithm.
1585 APInt Remainder(1,0);
1586 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder);
1590 void APInt::fromString(uint32_t numbits, const char *str, uint32_t slen,
1592 // Check our assumptions here
1593 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1594 "Radix should be 2, 8, 10, or 16!");
1595 assert(str && "String is null?");
1596 bool isNeg = str[0] == '-';
1599 assert(slen <= numbits || radix != 2 && "Insufficient bit width");
1600 assert(slen*3 <= numbits || radix != 8 && "Insufficient bit width");
1601 assert(slen*4 <= numbits || radix != 16 && "Insufficient bit width");
1602 assert((slen*64)/20 <= numbits || radix != 10 && "Insufficient bit width");
1605 if (!isSingleWord())
1606 pVal = getClearedMemory(getNumWords());
1608 // Figure out if we can shift instead of multiply
1609 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
1611 // Set up an APInt for the digit to add outside the loop so we don't
1612 // constantly construct/destruct it.
1613 APInt apdigit(getBitWidth(), 0);
1614 APInt apradix(getBitWidth(), radix);
1616 // Enter digit traversal loop
1617 for (unsigned i = 0; i < slen; i++) {
1620 char cdigit = str[i];
1621 if (isdigit(cdigit))
1622 digit = cdigit - '0';
1623 else if (isxdigit(cdigit))
1625 digit = cdigit - 'a' + 10;
1626 else if (cdigit >= 'A')
1627 digit = cdigit - 'A' + 10;
1629 assert(0 && "huh?");
1631 assert(0 && "Invalid character in digit string");
1633 // Shift or multiple the value by the radix
1639 // Add in the digit we just interpreted
1640 if (apdigit.isSingleWord())
1641 apdigit.VAL = digit;
1643 apdigit.pVal[0] = digit;
1646 // If its negative, put it in two's complement form
1653 std::string APInt::toString(uint8_t radix, bool wantSigned) const {
1654 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1655 "Radix should be 2, 8, 10, or 16!");
1656 static const char *digits[] = {
1657 "0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"
1660 uint32_t bits_used = getActiveBits();
1661 if (isSingleWord()) {
1663 const char *format = (radix == 10 ? (wantSigned ? "%lld" : "%llu") :
1664 (radix == 16 ? "%llX" : (radix == 8 ? "%llo" : 0)));
1667 int64_t sextVal = (int64_t(VAL) << (APINT_BITS_PER_WORD-BitWidth)) >>
1668 (APINT_BITS_PER_WORD-BitWidth);
1669 sprintf(buf, format, sextVal);
1671 sprintf(buf, format, VAL);
1676 uint32_t bit = v & 1;
1678 buf[bits_used] = digits[bit][0];
1687 uint64_t mask = radix - 1;
1688 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : 1);
1689 uint32_t nibbles = APINT_BITS_PER_WORD / shift;
1690 for (uint32_t i = 0; i < getNumWords(); ++i) {
1691 uint64_t value = pVal[i];
1692 for (uint32_t j = 0; j < nibbles; ++j) {
1693 result.insert(0, digits[ value & mask ]);
1701 APInt divisor(4, radix);
1702 APInt zero(tmp.getBitWidth(), 0);
1703 size_t insert_at = 0;
1704 if (wantSigned && tmp[BitWidth-1]) {
1705 // They want to print the signed version and it is a negative value
1706 // Flip the bits and add one to turn it into the equivalent positive
1707 // value and put a '-' in the result.
1713 if (tmp == APInt(tmp.getBitWidth(), 0))
1715 else while (tmp.ne(zero)) {
1717 APInt tmp2(tmp.getBitWidth(), 0);
1718 divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
1720 uint32_t digit = APdigit.getZExtValue();
1721 assert(digit < radix && "divide failed");
1722 result.insert(insert_at,digits[digit]);
1730 void APInt::dump() const
1732 cerr << "APInt(" << BitWidth << ")=" << std::setbase(16);
1735 else for (unsigned i = getNumWords(); i > 0; i--) {
1736 cerr << pVal[i-1] << " ";
1738 cerr << " (" << this->toString(10, false) << ")\n" << std::setbase(10);