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 for (int i = whichWord(n1 - 1); i >= 0; --i) {
544 if (pVal[i] > RHS.pVal[i])
546 if (pVal[i] < RHS.pVal[i])
552 bool APInt::slt(const APInt& RHS) const {
553 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
554 if (isSingleWord()) {
555 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
556 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth);
557 return lhsSext < rhsSext;
562 bool lhsNegative = false;
563 bool rhsNegative = false;
564 if (lhs[BitWidth-1]) {
565 // Sign bit is set so make a note of it and perform two's complement
570 if (rhs[BitWidth-1]) {
571 // Sign bit is set so make a note of it and perform two's complement
577 // Now we have unsigned values to compare so do the comparison if necessary
578 // based on the negativeness of the values.
581 return !lhs.ult(rhs);
584 else if (rhsNegative)
590 APInt& APInt::set(uint32_t bitPosition) {
592 VAL |= maskBit(bitPosition);
594 pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
598 APInt& APInt::set() {
599 if (isSingleWord()) {
601 return clearUnusedBits();
604 // Set all the bits in all the words.
605 for (uint32_t i = 0; i < getNumWords() - 1; ++i)
607 // Clear the unused ones
608 return clearUnusedBits();
611 /// Set the given bit to 0 whose position is given as "bitPosition".
612 /// @brief Set a given bit to 0.
613 APInt& APInt::clear(uint32_t bitPosition) {
615 VAL &= ~maskBit(bitPosition);
617 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
621 /// @brief Set every bit to 0.
622 APInt& APInt::clear() {
626 memset(pVal, 0, getNumWords() * APINT_WORD_SIZE);
630 /// @brief Bitwise NOT operator. Performs a bitwise logical NOT operation on
632 APInt APInt::operator~() const {
638 /// @brief Toggle every bit to its opposite value.
639 APInt& APInt::flip() {
640 if (isSingleWord()) {
642 return clearUnusedBits();
644 for (uint32_t i = 0; i < getNumWords(); ++i)
646 return clearUnusedBits();
649 /// Toggle a given bit to its opposite value whose position is given
650 /// as "bitPosition".
651 /// @brief Toggles a given bit to its opposite value.
652 APInt& APInt::flip(uint32_t bitPosition) {
653 assert(bitPosition < BitWidth && "Out of the bit-width range!");
654 if ((*this)[bitPosition]) clear(bitPosition);
655 else set(bitPosition);
659 /// getMaxValue - This function returns the largest value
660 /// for an APInt of the specified bit-width and if isSign == true,
661 /// it should be largest signed value, otherwise unsigned value.
662 APInt APInt::getMaxValue(uint32_t numBits, bool isSign) {
663 APInt Result(numBits, 0);
666 Result.clear(numBits - 1);
670 /// getMinValue - This function returns the smallest value for
671 /// an APInt of the given bit-width and if isSign == true,
672 /// it should be smallest signed value, otherwise zero.
673 APInt APInt::getMinValue(uint32_t numBits, bool isSign) {
674 APInt Result(numBits, 0);
676 Result.set(numBits - 1);
680 /// getAllOnesValue - This function returns an all-ones value for
681 /// an APInt of the specified bit-width.
682 APInt APInt::getAllOnesValue(uint32_t numBits) {
683 return getMaxValue(numBits, false);
686 /// getNullValue - This function creates an '0' value for an
687 /// APInt of the specified bit-width.
688 APInt APInt::getNullValue(uint32_t numBits) {
689 return getMinValue(numBits, false);
692 uint64_t APInt::getHashValue() const {
693 // Put the bit width into the low order bits.
694 uint64_t hash = BitWidth;
696 // Add the sum of the words to the hash.
698 hash += VAL << 6; // clear separation of up to 64 bits
700 for (uint32_t i = 0; i < getNumWords(); ++i)
701 hash += pVal[i] << 6; // clear sepration of up to 64 bits
705 /// HiBits - This function returns the high "numBits" bits of this APInt.
706 APInt APInt::getHiBits(uint32_t numBits) const {
707 return APIntOps::lshr(*this, BitWidth - numBits);
710 /// LoBits - This function returns the low "numBits" bits of this APInt.
711 APInt APInt::getLoBits(uint32_t numBits) const {
712 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
716 bool APInt::isPowerOf2() const {
717 return (!!*this) && !(*this & (*this - APInt(BitWidth,1)));
720 uint32_t APInt::countLeadingZeros() const {
723 Count = CountLeadingZeros_64(VAL);
725 for (uint32_t i = getNumWords(); i > 0u; --i) {
727 Count += APINT_BITS_PER_WORD;
729 Count += CountLeadingZeros_64(pVal[i-1]);
734 uint32_t remainder = BitWidth % APINT_BITS_PER_WORD;
736 Count -= APINT_BITS_PER_WORD - remainder;
740 uint32_t APInt::countTrailingZeros() const {
742 return CountTrailingZeros_64(VAL);
745 for (; i < getNumWords() && pVal[i] == 0; ++i)
746 Count += APINT_BITS_PER_WORD;
747 if (i < getNumWords())
748 Count += CountTrailingZeros_64(pVal[i]);
752 uint32_t APInt::countPopulation() const {
754 return CountPopulation_64(VAL);
756 for (uint32_t i = 0; i < getNumWords(); ++i)
757 Count += CountPopulation_64(pVal[i]);
761 APInt APInt::byteSwap() const {
762 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
764 return APInt(BitWidth, ByteSwap_16(VAL));
765 else if (BitWidth == 32)
766 return APInt(BitWidth, ByteSwap_32(VAL));
767 else if (BitWidth == 48) {
768 uint64_t Tmp1 = ((VAL >> 32) << 16) | (VAL & 0xFFFF);
769 Tmp1 = ByteSwap_32(Tmp1);
770 uint64_t Tmp2 = (VAL >> 16) & 0xFFFF;
771 Tmp2 = ByteSwap_16(Tmp2);
774 (Tmp1 & 0xff) | ((Tmp1<<16) & 0xffff00000000ULL) | (Tmp2 << 16));
775 } else if (BitWidth == 64)
776 return APInt(BitWidth, ByteSwap_64(VAL));
778 APInt Result(BitWidth, 0);
779 char *pByte = (char*)Result.pVal;
780 for (uint32_t i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) {
782 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i];
783 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp;
789 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
791 APInt A = API1, B = API2;
794 B = APIntOps::urem(A, B);
800 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double) {
807 // Get the sign bit from the highest order bit
808 bool isNeg = T.I >> 63;
810 // Get the 11-bit exponent and adjust for the 1023 bit bias
811 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
813 // If the exponent is negative, the value is < 0 so just return 0.
815 return APInt(64u, 0u);
817 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
818 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
820 // If the exponent doesn't shift all bits out of the mantissa
822 return isNeg ? -APInt(64u, mantissa >> (52 - exp)) :
823 APInt(64u, mantissa >> (52 - exp));
825 // Otherwise, we have to shift the mantissa bits up to the right location
826 APInt Tmp(exp+1, mantissa);
827 Tmp = Tmp.shl(exp - 52);
828 return isNeg ? -Tmp : Tmp;
831 /// RoundToDouble - This function convert this APInt to a double.
832 /// The layout for double is as following (IEEE Standard 754):
833 /// --------------------------------------
834 /// | Sign Exponent Fraction Bias |
835 /// |-------------------------------------- |
836 /// | 1[63] 11[62-52] 52[51-00] 1023 |
837 /// --------------------------------------
838 double APInt::roundToDouble(bool isSigned) const {
840 // Handle the simple case where the value is contained in one uint64_t.
841 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
843 int64_t sext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
849 // Determine if the value is negative.
850 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
852 // Construct the absolute value if we're negative.
853 APInt Tmp(isNeg ? -(*this) : (*this));
855 // Figure out how many bits we're using.
856 uint32_t n = Tmp.getActiveBits();
858 // The exponent (without bias normalization) is just the number of bits
859 // we are using. Note that the sign bit is gone since we constructed the
863 // Return infinity for exponent overflow
865 if (!isSigned || !isNeg)
866 return double(1.0E300 * 1.0E300); // positive infinity
868 return double(-1.0E300 * 1.0E300); // negative infinity
870 exp += 1023; // Increment for 1023 bias
872 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
873 // extract the high 52 bits from the correct words in pVal.
875 unsigned hiWord = whichWord(n-1);
877 mantissa = Tmp.pVal[0];
879 mantissa >>= n - 52; // shift down, we want the top 52 bits.
881 assert(hiWord > 0 && "huh?");
882 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
883 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
884 mantissa = hibits | lobits;
887 // The leading bit of mantissa is implicit, so get rid of it.
888 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
893 T.I = sign | (exp << 52) | mantissa;
897 // Truncate to new width.
898 void APInt::trunc(uint32_t width) {
899 assert(width < BitWidth && "Invalid APInt Truncate request");
900 assert(width >= IntegerType::MIN_INT_BITS && "Can't truncate to 0 bits");
901 uint32_t wordsBefore = getNumWords();
903 uint32_t wordsAfter = getNumWords();
904 if (wordsBefore != wordsAfter) {
905 if (wordsAfter == 1) {
906 uint64_t *tmp = pVal;
910 uint64_t *newVal = getClearedMemory(wordsAfter);
911 for (uint32_t i = 0; i < wordsAfter; ++i)
920 // Sign extend to a new width.
921 void APInt::sext(uint32_t width) {
922 assert(width > BitWidth && "Invalid APInt SignExtend request");
923 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
924 // If the sign bit isn't set, this is the same as zext.
930 // The sign bit is set. First, get some facts
931 uint32_t wordsBefore = getNumWords();
932 uint32_t wordBits = BitWidth % APINT_BITS_PER_WORD;
934 uint32_t wordsAfter = getNumWords();
936 // Mask the high order word appropriately
937 if (wordsBefore == wordsAfter) {
938 uint32_t newWordBits = width % APINT_BITS_PER_WORD;
939 // The extension is contained to the wordsBefore-1th word.
940 uint64_t mask = (~0ULL >> (APINT_BITS_PER_WORD - newWordBits)) << wordBits;
941 if (wordsBefore == 1)
944 pVal[wordsBefore-1] |= mask;
949 uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits;
950 uint64_t *newVal = getMemory(wordsAfter);
951 if (wordsBefore == 1)
952 newVal[0] = VAL | mask;
954 for (uint32_t i = 0; i < wordsBefore; ++i)
956 newVal[wordsBefore-1] |= mask;
958 for (uint32_t i = wordsBefore; i < wordsAfter; i++)
960 if (wordsBefore != 1)
966 // Zero extend to a new width.
967 void APInt::zext(uint32_t width) {
968 assert(width > BitWidth && "Invalid APInt ZeroExtend request");
969 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
970 uint32_t wordsBefore = getNumWords();
972 uint32_t wordsAfter = getNumWords();
973 if (wordsBefore != wordsAfter) {
974 uint64_t *newVal = getClearedMemory(wordsAfter);
975 if (wordsBefore == 1)
978 for (uint32_t i = 0; i < wordsBefore; ++i)
980 if (wordsBefore != 1)
986 /// Arithmetic right-shift this APInt by shiftAmt.
987 /// @brief Arithmetic right-shift function.
988 APInt APInt::ashr(uint32_t shiftAmt) const {
989 assert(shiftAmt <= BitWidth && "Invalid shift amount");
990 if (isSingleWord()) {
991 if (shiftAmt == BitWidth)
992 return APInt(BitWidth, 0); // undefined
994 uint32_t SignBit = APINT_BITS_PER_WORD - BitWidth;
995 return APInt(BitWidth,
996 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1000 // If all the bits were shifted out, the result is 0 or -1. This avoids issues
1001 // with shifting by the size of the integer type, which produces undefined
1003 if (shiftAmt == BitWidth)
1005 return APInt(BitWidth, -1ULL);
1007 return APInt(BitWidth, 0);
1009 // Create some space for the result.
1010 uint64_t * val = new uint64_t[getNumWords()];
1012 // If we are shifting less than a word, compute the shift with a simple carry
1013 if (shiftAmt < APINT_BITS_PER_WORD) {
1015 for (int i = getNumWords()-1; i >= 0; --i) {
1016 val[i] = pVal[i] >> shiftAmt | carry;
1017 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1019 return APInt(val, BitWidth).clearUnusedBits();
1022 // Compute some values needed by the remaining shift algorithms
1023 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1024 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1026 // If we are shifting whole words, just move whole words
1027 if (wordShift == 0) {
1028 for (uint32_t i = 0; i < getNumWords() - offset; ++i)
1029 val[i] = pVal[i+offset];
1030 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
1031 val[i] = (isNegative() ? -1ULL : 0);
1032 return APInt(val,BitWidth).clearUnusedBits();
1035 // Shift the low order words
1036 uint32_t breakWord = getNumWords() - offset -1;
1037 for (uint32_t i = 0; i < breakWord; ++i)
1038 val[i] = pVal[i+offset] >> wordShift |
1039 pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift);
1040 // Shift the break word.
1041 uint32_t SignBit = APINT_BITS_PER_WORD - (BitWidth % APINT_BITS_PER_WORD);
1042 val[breakWord] = uint64_t(
1043 (((int64_t(pVal[breakWord+offset]) << SignBit) >> SignBit) >> wordShift));
1045 // Remaining words are 0 or -1
1046 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1047 val[i] = (isNegative() ? -1ULL : 0);
1048 return APInt(val, BitWidth).clearUnusedBits();
1051 /// Logical right-shift this APInt by shiftAmt.
1052 /// @brief Logical right-shift function.
1053 APInt APInt::lshr(uint32_t shiftAmt) const {
1055 if (shiftAmt == BitWidth)
1056 return APInt(BitWidth, 0);
1058 return APInt(BitWidth, this->VAL >> shiftAmt);
1060 // If all the bits were shifted out, the result is 0. This avoids issues
1061 // with shifting by the size of the integer type, which produces undefined
1062 // results. We define these "undefined results" to always be 0.
1063 if (shiftAmt == BitWidth)
1064 return APInt(BitWidth, 0);
1066 // Create some space for the result.
1067 uint64_t * val = new uint64_t[getNumWords()];
1069 // If we are shifting less than a word, compute the shift with a simple carry
1070 if (shiftAmt < APINT_BITS_PER_WORD) {
1072 for (int i = getNumWords()-1; i >= 0; --i) {
1073 val[i] = pVal[i] >> shiftAmt | carry;
1074 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1076 return APInt(val, BitWidth).clearUnusedBits();
1079 // Compute some values needed by the remaining shift algorithms
1080 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1081 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1083 // If we are shifting whole words, just move whole words
1084 if (wordShift == 0) {
1085 for (uint32_t i = 0; i < getNumWords() - offset; ++i)
1086 val[i] = pVal[i+offset];
1087 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
1089 return APInt(val,BitWidth).clearUnusedBits();
1092 // Shift the low order words
1093 uint32_t breakWord = getNumWords() - offset -1;
1094 for (uint32_t i = 0; i < breakWord; ++i)
1095 val[i] = pVal[i+offset] >> wordShift |
1096 pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift);
1097 // Shift the break word.
1098 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1100 // Remaining words are 0
1101 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1103 return APInt(val, BitWidth).clearUnusedBits();
1106 /// Left-shift this APInt by shiftAmt.
1107 /// @brief Left-shift function.
1108 APInt APInt::shl(uint32_t shiftAmt) const {
1109 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1110 if (isSingleWord()) {
1111 if (shiftAmt == BitWidth)
1112 return APInt(BitWidth, 0); // avoid undefined shift results
1113 return APInt(BitWidth, VAL << shiftAmt);
1116 // If all the bits were shifted out, the result is 0. This avoids issues
1117 // with shifting by the size of the integer type, which produces undefined
1118 // results. We define these "undefined results" to always be 0.
1119 if (shiftAmt == BitWidth)
1120 return APInt(BitWidth, 0);
1122 // Create some space for the result.
1123 uint64_t * val = new uint64_t[getNumWords()];
1125 // If we are shifting less than a word, do it the easy way
1126 if (shiftAmt < APINT_BITS_PER_WORD) {
1128 for (uint32_t i = 0; i < getNumWords(); i++) {
1129 val[i] = pVal[i] << shiftAmt | carry;
1130 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1132 return APInt(val, BitWidth).clearUnusedBits();
1135 // Compute some values needed by the remaining shift algorithms
1136 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1137 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1139 // If we are shifting whole words, just move whole words
1140 if (wordShift == 0) {
1141 for (uint32_t i = 0; i < offset; i++)
1143 for (uint32_t i = offset; i < getNumWords(); i++)
1144 val[i] = pVal[i-offset];
1145 return APInt(val,BitWidth).clearUnusedBits();
1148 // Copy whole words from this to Result.
1149 uint32_t i = getNumWords() - 1;
1150 for (; i > offset; --i)
1151 val[i] = pVal[i-offset] << wordShift |
1152 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1153 val[offset] = pVal[0] << wordShift;
1154 for (i = 0; i < offset; ++i)
1156 return APInt(val, BitWidth).clearUnusedBits();
1159 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1160 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1161 /// variables here have the same names as in the algorithm. Comments explain
1162 /// the algorithm and any deviation from it.
1163 static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
1164 uint32_t m, uint32_t n) {
1165 assert(u && "Must provide dividend");
1166 assert(v && "Must provide divisor");
1167 assert(q && "Must provide quotient");
1168 assert(u != v && u != q && v != q && "Must us different memory");
1169 assert(n>1 && "n must be > 1");
1171 // Knuth uses the value b as the base of the number system. In our case b
1172 // is 2^31 so we just set it to -1u.
1173 uint64_t b = uint64_t(1) << 32;
1175 DEBUG(cerr << "KnuthDiv: m=" << m << " n=" << n << '\n');
1176 DEBUG(cerr << "KnuthDiv: original:");
1177 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1178 DEBUG(cerr << " by");
1179 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1180 DEBUG(cerr << '\n');
1181 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1182 // u and v by d. Note that we have taken Knuth's advice here to use a power
1183 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1184 // 2 allows us to shift instead of multiply and it is easy to determine the
1185 // shift amount from the leading zeros. We are basically normalizing the u
1186 // and v so that its high bits are shifted to the top of v's range without
1187 // overflow. Note that this can require an extra word in u so that u must
1188 // be of length m+n+1.
1189 uint32_t shift = CountLeadingZeros_32(v[n-1]);
1190 uint32_t v_carry = 0;
1191 uint32_t u_carry = 0;
1193 for (uint32_t i = 0; i < m+n; ++i) {
1194 uint32_t u_tmp = u[i] >> (32 - shift);
1195 u[i] = (u[i] << shift) | u_carry;
1198 for (uint32_t i = 0; i < n; ++i) {
1199 uint32_t v_tmp = v[i] >> (32 - shift);
1200 v[i] = (v[i] << shift) | v_carry;
1205 DEBUG(cerr << "KnuthDiv: normal:");
1206 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1207 DEBUG(cerr << " by");
1208 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1209 DEBUG(cerr << '\n');
1211 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1214 DEBUG(cerr << "KnuthDiv: quotient digit #" << j << '\n');
1215 // D3. [Calculate q'.].
1216 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1217 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1218 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1219 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1220 // on v[n-2] determines at high speed most of the cases in which the trial
1221 // value qp is one too large, and it eliminates all cases where qp is two
1223 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1224 DEBUG(cerr << "KnuthDiv: dividend == " << dividend << '\n');
1225 uint64_t qp = dividend / v[n-1];
1226 uint64_t rp = dividend % v[n-1];
1227 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1230 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1233 DEBUG(cerr << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1235 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1236 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1237 // consists of a simple multiplication by a one-place number, combined with
1240 for (uint32_t i = 0; i < n; ++i) {
1241 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1242 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1243 bool borrow = subtrahend > u_tmp;
1244 DEBUG(cerr << "KnuthDiv: u_tmp == " << u_tmp
1245 << ", subtrahend == " << subtrahend
1246 << ", borrow = " << borrow << '\n');
1248 uint64_t result = u_tmp - subtrahend;
1250 u[k++] = result & (b-1); // subtract low word
1251 u[k++] = result >> 32; // subtract high word
1252 while (borrow && k <= m+n) { // deal with borrow to the left
1258 DEBUG(cerr << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1261 DEBUG(cerr << "KnuthDiv: after subtraction:");
1262 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1263 DEBUG(cerr << '\n');
1264 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1265 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1266 // true value plus b**(n+1), namely as the b's complement of
1267 // the true value, and a "borrow" to the left should be remembered.
1270 bool carry = true; // true because b's complement is "complement + 1"
1271 for (uint32_t i = 0; i <= m+n; ++i) {
1272 u[i] = ~u[i] + carry; // b's complement
1273 carry = carry && u[i] == 0;
1276 DEBUG(cerr << "KnuthDiv: after complement:");
1277 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1278 DEBUG(cerr << '\n');
1280 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1281 // negative, go to step D6; otherwise go on to step D7.
1284 // D6. [Add back]. The probability that this step is necessary is very
1285 // small, on the order of only 2/b. Make sure that test data accounts for
1286 // this possibility. Decrease q[j] by 1
1288 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1289 // A carry will occur to the left of u[j+n], and it should be ignored
1290 // since it cancels with the borrow that occurred in D4.
1292 for (uint32_t i = 0; i < n; i++) {
1293 uint32_t limit = std::min(u[j+i],v[i]);
1294 u[j+i] += v[i] + carry;
1295 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1299 DEBUG(cerr << "KnuthDiv: after correction:");
1300 DEBUG(for (int i = m+n; i >=0; i--) cerr <<" " << u[i]);
1301 DEBUG(cerr << "\nKnuthDiv: digit result = " << q[j] << '\n');
1303 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1306 DEBUG(cerr << "KnuthDiv: quotient:");
1307 DEBUG(for (int i = m; i >=0; i--) cerr <<" " << q[i]);
1308 DEBUG(cerr << '\n');
1310 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1311 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1312 // compute the remainder (urem uses this).
1314 // The value d is expressed by the "shift" value above since we avoided
1315 // multiplication by d by using a shift left. So, all we have to do is
1316 // shift right here. In order to mak
1319 DEBUG(cerr << "KnuthDiv: remainder:");
1320 for (int i = n-1; i >= 0; i--) {
1321 r[i] = (u[i] >> shift) | carry;
1322 carry = u[i] << (32 - shift);
1323 DEBUG(cerr << " " << r[i]);
1326 for (int i = n-1; i >= 0; i--) {
1328 DEBUG(cerr << " " << r[i]);
1331 DEBUG(cerr << '\n');
1333 DEBUG(cerr << std::setbase(10) << '\n');
1336 void APInt::divide(const APInt LHS, uint32_t lhsWords,
1337 const APInt &RHS, uint32_t rhsWords,
1338 APInt *Quotient, APInt *Remainder)
1340 assert(lhsWords >= rhsWords && "Fractional result");
1342 // First, compose the values into an array of 32-bit words instead of
1343 // 64-bit words. This is a necessity of both the "short division" algorithm
1344 // and the the Knuth "classical algorithm" which requires there to be native
1345 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1346 // can't use 64-bit operands here because we don't have native results of
1347 // 128-bits. Furthremore, casting the 64-bit values to 32-bit values won't
1348 // work on large-endian machines.
1349 uint64_t mask = ~0ull >> (sizeof(uint32_t)*8);
1350 uint32_t n = rhsWords * 2;
1351 uint32_t m = (lhsWords * 2) - n;
1353 // Allocate space for the temporary values we need either on the stack, if
1354 // it will fit, or on the heap if it won't.
1355 uint32_t SPACE[128];
1360 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1363 Q = &SPACE[(m+n+1) + n];
1365 R = &SPACE[(m+n+1) + n + (m+n)];
1367 U = new uint32_t[m + n + 1];
1368 V = new uint32_t[n];
1369 Q = new uint32_t[m+n];
1371 R = new uint32_t[n];
1374 // Initialize the dividend
1375 memset(U, 0, (m+n+1)*sizeof(uint32_t));
1376 for (unsigned i = 0; i < lhsWords; ++i) {
1377 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1378 U[i * 2] = tmp & mask;
1379 U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1381 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1383 // Initialize the divisor
1384 memset(V, 0, (n)*sizeof(uint32_t));
1385 for (unsigned i = 0; i < rhsWords; ++i) {
1386 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1387 V[i * 2] = tmp & mask;
1388 V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1391 // initialize the quotient and remainder
1392 memset(Q, 0, (m+n) * sizeof(uint32_t));
1394 memset(R, 0, n * sizeof(uint32_t));
1396 // Now, adjust m and n for the Knuth division. n is the number of words in
1397 // the divisor. m is the number of words by which the dividend exceeds the
1398 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1399 // contain any zero words or the Knuth algorithm fails.
1400 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1404 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1407 // If we're left with only a single word for the divisor, Knuth doesn't work
1408 // so we implement the short division algorithm here. This is much simpler
1409 // and faster because we are certain that we can divide a 64-bit quantity
1410 // by a 32-bit quantity at hardware speed and short division is simply a
1411 // series of such operations. This is just like doing short division but we
1412 // are using base 2^32 instead of base 10.
1413 assert(n != 0 && "Divide by zero?");
1415 uint32_t divisor = V[0];
1416 uint32_t remainder = 0;
1417 for (int i = m+n-1; i >= 0; i--) {
1418 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1419 if (partial_dividend == 0) {
1422 } else if (partial_dividend < divisor) {
1424 remainder = partial_dividend;
1425 } else if (partial_dividend == divisor) {
1429 Q[i] = partial_dividend / divisor;
1430 remainder = partial_dividend - (Q[i] * divisor);
1436 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1438 KnuthDiv(U, V, Q, R, m, n);
1441 // If the caller wants the quotient
1443 // Set up the Quotient value's memory.
1444 if (Quotient->BitWidth != LHS.BitWidth) {
1445 if (Quotient->isSingleWord())
1448 delete [] Quotient->pVal;
1449 Quotient->BitWidth = LHS.BitWidth;
1450 if (!Quotient->isSingleWord())
1451 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1455 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1457 if (lhsWords == 1) {
1459 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1460 if (Quotient->isSingleWord())
1461 Quotient->VAL = tmp;
1463 Quotient->pVal[0] = tmp;
1465 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1466 for (unsigned i = 0; i < lhsWords; ++i)
1468 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1472 // If the caller wants the remainder
1474 // Set up the Remainder value's memory.
1475 if (Remainder->BitWidth != RHS.BitWidth) {
1476 if (Remainder->isSingleWord())
1479 delete [] Remainder->pVal;
1480 Remainder->BitWidth = RHS.BitWidth;
1481 if (!Remainder->isSingleWord())
1482 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1486 // The remainder is in R. Reconstitute the remainder into Remainder's low
1488 if (rhsWords == 1) {
1490 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1491 if (Remainder->isSingleWord())
1492 Remainder->VAL = tmp;
1494 Remainder->pVal[0] = tmp;
1496 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1497 for (unsigned i = 0; i < rhsWords; ++i)
1498 Remainder->pVal[i] =
1499 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1503 // Clean up the memory we allocated.
1504 if (U != &SPACE[0]) {
1512 APInt APInt::udiv(const APInt& RHS) const {
1513 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1515 // First, deal with the easy case
1516 if (isSingleWord()) {
1517 assert(RHS.VAL != 0 && "Divide by zero?");
1518 return APInt(BitWidth, VAL / RHS.VAL);
1521 // Get some facts about the LHS and RHS number of bits and words
1522 uint32_t rhsBits = RHS.getActiveBits();
1523 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1524 assert(rhsWords && "Divided by zero???");
1525 uint32_t lhsBits = this->getActiveBits();
1526 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1528 // Deal with some degenerate cases
1531 return APInt(BitWidth, 0);
1532 else if (lhsWords < rhsWords || this->ult(RHS)) {
1533 // X / Y ===> 0, iff X < Y
1534 return APInt(BitWidth, 0);
1535 } else if (*this == RHS) {
1537 return APInt(BitWidth, 1);
1538 } else if (lhsWords == 1 && rhsWords == 1) {
1539 // All high words are zero, just use native divide
1540 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1543 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1544 APInt Quotient(1,0); // to hold result.
1545 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0);
1549 APInt APInt::urem(const APInt& RHS) const {
1550 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1551 if (isSingleWord()) {
1552 assert(RHS.VAL != 0 && "Remainder by zero?");
1553 return APInt(BitWidth, VAL % RHS.VAL);
1556 // Get some facts about the LHS
1557 uint32_t lhsBits = getActiveBits();
1558 uint32_t lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1560 // Get some facts about the RHS
1561 uint32_t rhsBits = RHS.getActiveBits();
1562 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1563 assert(rhsWords && "Performing remainder operation by zero ???");
1565 // Check the degenerate cases
1566 if (lhsWords == 0) {
1568 return APInt(BitWidth, 0);
1569 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1570 // X % Y ===> X, iff X < Y
1572 } else if (*this == RHS) {
1574 return APInt(BitWidth, 0);
1575 } else if (lhsWords == 1) {
1576 // All high words are zero, just use native remainder
1577 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
1580 // We have to compute it the hard way. Invoke the Knute divide algorithm.
1581 APInt Remainder(1,0);
1582 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder);
1586 void APInt::fromString(uint32_t numbits, const char *str, uint32_t slen,
1588 // Check our assumptions here
1589 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1590 "Radix should be 2, 8, 10, or 16!");
1591 assert(str && "String is null?");
1592 bool isNeg = str[0] == '-';
1595 assert(slen <= numbits || radix != 2 && "Insufficient bit width");
1596 assert(slen*3 <= numbits || radix != 8 && "Insufficient bit width");
1597 assert(slen*4 <= numbits || radix != 16 && "Insufficient bit width");
1598 assert((slen*64)/20 <= numbits || radix != 10 && "Insufficient bit width");
1601 if (!isSingleWord())
1602 pVal = getClearedMemory(getNumWords());
1604 // Figure out if we can shift instead of multiply
1605 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
1607 // Set up an APInt for the digit to add outside the loop so we don't
1608 // constantly construct/destruct it.
1609 APInt apdigit(getBitWidth(), 0);
1610 APInt apradix(getBitWidth(), radix);
1612 // Enter digit traversal loop
1613 for (unsigned i = 0; i < slen; i++) {
1616 char cdigit = str[i];
1617 if (isdigit(cdigit))
1618 digit = cdigit - '0';
1619 else if (isxdigit(cdigit))
1621 digit = cdigit - 'a' + 10;
1622 else if (cdigit >= 'A')
1623 digit = cdigit - 'A' + 10;
1625 assert(0 && "huh?");
1627 assert(0 && "Invalid character in digit string");
1629 // Shift or multiple the value by the radix
1635 // Add in the digit we just interpreted
1636 if (apdigit.isSingleWord())
1637 apdigit.VAL = digit;
1639 apdigit.pVal[0] = digit;
1642 // If its negative, put it in two's complement form
1649 std::string APInt::toString(uint8_t radix, bool wantSigned) const {
1650 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1651 "Radix should be 2, 8, 10, or 16!");
1652 static const char *digits[] = {
1653 "0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"
1656 uint32_t bits_used = getActiveBits();
1657 if (isSingleWord()) {
1659 const char *format = (radix == 10 ? (wantSigned ? "%lld" : "%llu") :
1660 (radix == 16 ? "%llX" : (radix == 8 ? "%llo" : 0)));
1663 int64_t sextVal = (int64_t(VAL) << (APINT_BITS_PER_WORD-BitWidth)) >>
1664 (APINT_BITS_PER_WORD-BitWidth);
1665 sprintf(buf, format, sextVal);
1667 sprintf(buf, format, VAL);
1672 uint32_t bit = v & 1;
1674 buf[bits_used] = digits[bit][0];
1683 uint64_t mask = radix - 1;
1684 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : 1);
1685 uint32_t nibbles = APINT_BITS_PER_WORD / shift;
1686 for (uint32_t i = 0; i < getNumWords(); ++i) {
1687 uint64_t value = pVal[i];
1688 for (uint32_t j = 0; j < nibbles; ++j) {
1689 result.insert(0, digits[ value & mask ]);
1697 APInt divisor(4, radix);
1698 APInt zero(tmp.getBitWidth(), 0);
1699 size_t insert_at = 0;
1700 if (wantSigned && tmp[BitWidth-1]) {
1701 // They want to print the signed version and it is a negative value
1702 // Flip the bits and add one to turn it into the equivalent positive
1703 // value and put a '-' in the result.
1709 if (tmp == APInt(tmp.getBitWidth(), 0))
1711 else while (tmp.ne(zero)) {
1713 APInt tmp2(tmp.getBitWidth(), 0);
1714 divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
1716 uint32_t digit = APdigit.getZExtValue();
1717 assert(digit < radix && "divide failed");
1718 result.insert(insert_at,digits[digit]);
1726 void APInt::dump() const
1728 cerr << "APInt(" << BitWidth << ")=" << std::setbase(16);
1731 else for (unsigned i = getNumWords(); i > 0; i--) {
1732 cerr << pVal[i-1] << " ";
1734 cerr << " (" << this->toString(10, false) << ")\n" << std::setbase(10);