1 //===-- APInt.cpp - Implement APInt class ---------------------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by Sheng Zhou and is distributed under the
6 // University of Illinois Open Source License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file implements a class to represent arbitrary precision integer
11 // constant values and provide a variety of arithmetic operations on them.
13 //===----------------------------------------------------------------------===//
15 #define DEBUG_TYPE "apint"
16 #include "llvm/ADT/APInt.h"
17 #include "llvm/DerivedTypes.h"
18 #include "llvm/Support/Debug.h"
19 #include "llvm/Support/MathExtras.h"
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) : BitWidth(numBits), VAL(0) {
47 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small");
48 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large");
52 pVal = getClearedMemory(getNumWords());
58 APInt::APInt(uint32_t numBits, uint32_t numWords, uint64_t bigVal[])
59 : BitWidth(numBits), VAL(0) {
60 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small");
61 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large");
62 assert(bigVal && "Null pointer detected!");
66 // Get memory, cleared to 0
67 pVal = getClearedMemory(getNumWords());
68 // Calculate the number of words to copy
69 uint32_t words = std::min<uint32_t>(numWords, getNumWords());
70 // Copy the words from bigVal to pVal
71 memcpy(pVal, bigVal, words * APINT_WORD_SIZE);
73 // Make sure unused high bits are cleared
77 APInt::APInt(uint32_t numbits, const char StrStart[], uint32_t slen,
79 : BitWidth(numbits), VAL(0) {
80 fromString(numbits, StrStart, slen, radix);
83 APInt::APInt(uint32_t numbits, const std::string& Val, uint8_t radix)
84 : BitWidth(numbits), VAL(0) {
85 assert(!Val.empty() && "String empty?");
86 fromString(numbits, Val.c_str(), Val.size(), radix);
89 APInt::APInt(const APInt& that)
90 : BitWidth(that.BitWidth), VAL(0) {
94 pVal = getMemory(getNumWords());
95 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE);
100 if (!isSingleWord() && pVal)
104 APInt& APInt::operator=(const APInt& RHS) {
105 // Don't do anything for X = X
109 // If the bitwidths are the same, we can avoid mucking with memory
110 if (BitWidth == RHS.getBitWidth()) {
114 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE);
119 if (RHS.isSingleWord())
123 pVal = getMemory(RHS.getNumWords());
124 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
126 else if (getNumWords() == RHS.getNumWords())
127 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
128 else if (RHS.isSingleWord()) {
133 pVal = getMemory(RHS.getNumWords());
134 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
136 BitWidth = RHS.BitWidth;
137 return clearUnusedBits();
140 APInt& APInt::operator=(uint64_t RHS) {
145 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE);
147 return clearUnusedBits();
150 /// add_1 - This function adds a single "digit" integer, y, to the multiple
151 /// "digit" integer array, x[]. x[] is modified to reflect the addition and
152 /// 1 is returned if there is a carry out, otherwise 0 is returned.
153 /// @returns the carry of the addition.
154 static bool add_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
155 for (uint32_t i = 0; i < len; ++i) {
158 y = 1; // Carry one to next digit.
160 y = 0; // No need to carry so exit early
167 /// @brief Prefix increment operator. Increments the APInt by one.
168 APInt& APInt::operator++() {
172 add_1(pVal, pVal, getNumWords(), 1);
173 return clearUnusedBits();
176 /// sub_1 - This function subtracts a single "digit" (64-bit word), y, from
177 /// the multi-digit integer array, x[], propagating the borrowed 1 value until
178 /// no further borrowing is neeeded or it runs out of "digits" in x. The result
179 /// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted.
180 /// In other words, if y > x then this function returns 1, otherwise 0.
181 /// @returns the borrow out of the subtraction
182 static bool sub_1(uint64_t x[], uint32_t len, uint64_t y) {
183 for (uint32_t i = 0; i < len; ++i) {
187 y = 1; // We have to "borrow 1" from next "digit"
189 y = 0; // No need to borrow
190 break; // Remaining digits are unchanged so exit early
196 /// @brief Prefix decrement operator. Decrements the APInt by one.
197 APInt& APInt::operator--() {
201 sub_1(pVal, getNumWords(), 1);
202 return clearUnusedBits();
205 /// add - This function adds the integer array x to the integer array Y and
206 /// places the result in dest.
207 /// @returns the carry out from the addition
208 /// @brief General addition of 64-bit integer arrays
209 static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y,
212 for (uint32_t i = 0; i< len; ++i) {
213 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x
214 dest[i] = x[i] + y[i] + carry;
215 carry = dest[i] < limit || (carry && dest[i] == limit);
220 /// Adds the RHS APint to this APInt.
221 /// @returns this, after addition of RHS.
222 /// @brief Addition assignment operator.
223 APInt& APInt::operator+=(const APInt& RHS) {
224 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
228 add(pVal, pVal, RHS.pVal, getNumWords());
230 return clearUnusedBits();
233 /// Subtracts the integer array y from the integer array x
234 /// @returns returns the borrow out.
235 /// @brief Generalized subtraction of 64-bit integer arrays.
236 static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y,
239 for (uint32_t i = 0; i < len; ++i) {
240 uint64_t x_tmp = borrow ? x[i] - 1 : x[i];
241 borrow = y[i] > x_tmp || (borrow && x[i] == 0);
242 dest[i] = x_tmp - y[i];
247 /// Subtracts the RHS APInt from this APInt
248 /// @returns this, after subtraction
249 /// @brief Subtraction assignment operator.
250 APInt& APInt::operator-=(const APInt& RHS) {
251 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
255 sub(pVal, pVal, RHS.pVal, getNumWords());
256 return clearUnusedBits();
259 /// Multiplies an integer array, x by a a uint64_t integer and places the result
261 /// @returns the carry out of the multiplication.
262 /// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer.
263 static uint64_t mul_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
264 // Split y into high 32-bit part (hy) and low 32-bit part (ly)
265 uint64_t ly = y & 0xffffffffULL, hy = y >> 32;
268 // For each digit of x.
269 for (uint32_t i = 0; i < len; ++i) {
270 // Split x into high and low words
271 uint64_t lx = x[i] & 0xffffffffULL;
272 uint64_t hx = x[i] >> 32;
273 // hasCarry - A flag to indicate if there is a carry to the next digit.
274 // hasCarry == 0, no carry
275 // hasCarry == 1, has carry
276 // hasCarry == 2, no carry and the calculation result == 0.
277 uint8_t hasCarry = 0;
278 dest[i] = carry + lx * ly;
279 // Determine if the add above introduces carry.
280 hasCarry = (dest[i] < carry) ? 1 : 0;
281 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0);
282 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) +
283 // (2^32 - 1) + 2^32 = 2^64.
284 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
286 carry += (lx * hy) & 0xffffffffULL;
287 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL);
288 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) +
289 (carry >> 32) + ((lx * hy) >> 32) + hx * hy;
294 /// Multiplies integer array x by integer array y and stores the result into
295 /// the integer array dest. Note that dest's size must be >= xlen + ylen.
296 /// @brief Generalized multiplicate of integer arrays.
297 static void mul(uint64_t dest[], uint64_t x[], uint32_t xlen, uint64_t y[],
299 dest[xlen] = mul_1(dest, x, xlen, y[0]);
300 for (uint32_t i = 1; i < ylen; ++i) {
301 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32;
302 uint64_t carry = 0, lx = 0, hx = 0;
303 for (uint32_t j = 0; j < xlen; ++j) {
304 lx = x[j] & 0xffffffffULL;
306 // hasCarry - A flag to indicate if has carry.
307 // hasCarry == 0, no carry
308 // hasCarry == 1, has carry
309 // hasCarry == 2, no carry and the calculation result == 0.
310 uint8_t hasCarry = 0;
311 uint64_t resul = carry + lx * ly;
312 hasCarry = (resul < carry) ? 1 : 0;
313 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32);
314 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
316 carry += (lx * hy) & 0xffffffffULL;
317 resul = (carry << 32) | (resul & 0xffffffffULL);
319 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+
320 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) +
321 ((lx * hy) >> 32) + hx * hy;
323 dest[i+xlen] = carry;
327 APInt& APInt::operator*=(const APInt& RHS) {
328 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
329 if (isSingleWord()) {
335 // Get some bit facts about LHS and check for zero
336 uint32_t lhsBits = getActiveBits();
337 uint32_t lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1;
342 // Get some bit facts about RHS and check for zero
343 uint32_t rhsBits = RHS.getActiveBits();
344 uint32_t rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1;
351 // Allocate space for the result
352 uint32_t destWords = rhsWords + lhsWords;
353 uint64_t *dest = getMemory(destWords);
355 // Perform the long multiply
356 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords);
358 // Copy result back into *this
360 uint32_t wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords;
361 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE);
363 // delete dest array and return
368 APInt& APInt::operator&=(const APInt& RHS) {
369 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
370 if (isSingleWord()) {
374 uint32_t numWords = getNumWords();
375 for (uint32_t i = 0; i < numWords; ++i)
376 pVal[i] &= RHS.pVal[i];
380 APInt& APInt::operator|=(const APInt& RHS) {
381 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
382 if (isSingleWord()) {
386 uint32_t numWords = getNumWords();
387 for (uint32_t i = 0; i < numWords; ++i)
388 pVal[i] |= RHS.pVal[i];
392 APInt& APInt::operator^=(const APInt& RHS) {
393 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
394 if (isSingleWord()) {
396 this->clearUnusedBits();
399 uint32_t numWords = getNumWords();
400 for (uint32_t i = 0; i < numWords; ++i)
401 pVal[i] ^= RHS.pVal[i];
402 return clearUnusedBits();
405 APInt APInt::operator&(const APInt& RHS) const {
406 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
408 return APInt(getBitWidth(), VAL & RHS.VAL);
410 uint32_t numWords = getNumWords();
411 uint64_t* val = getMemory(numWords);
412 for (uint32_t i = 0; i < numWords; ++i)
413 val[i] = pVal[i] & RHS.pVal[i];
414 return APInt(val, getBitWidth());
417 APInt APInt::operator|(const APInt& RHS) const {
418 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
420 return APInt(getBitWidth(), VAL | RHS.VAL);
422 uint32_t numWords = getNumWords();
423 uint64_t *val = getMemory(numWords);
424 for (uint32_t i = 0; i < numWords; ++i)
425 val[i] = pVal[i] | RHS.pVal[i];
426 return APInt(val, getBitWidth());
429 APInt APInt::operator^(const APInt& RHS) const {
430 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
432 return APInt(BitWidth, VAL ^ RHS.VAL);
434 uint32_t numWords = getNumWords();
435 uint64_t *val = getMemory(numWords);
436 for (uint32_t i = 0; i < numWords; ++i)
437 val[i] = pVal[i] ^ RHS.pVal[i];
439 // 0^0==1 so clear the high bits in case they got set.
440 return APInt(val, getBitWidth()).clearUnusedBits();
443 bool APInt::operator !() const {
447 for (uint32_t i = 0; i < getNumWords(); ++i)
453 APInt APInt::operator*(const APInt& RHS) const {
454 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
456 return APInt(BitWidth, VAL * RHS.VAL);
459 return Result.clearUnusedBits();
462 APInt APInt::operator+(const APInt& RHS) const {
463 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
465 return APInt(BitWidth, VAL + RHS.VAL);
466 APInt Result(BitWidth, 0);
467 add(Result.pVal, this->pVal, RHS.pVal, getNumWords());
468 return Result.clearUnusedBits();
471 APInt APInt::operator-(const APInt& RHS) const {
472 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
474 return APInt(BitWidth, VAL - RHS.VAL);
475 APInt Result(BitWidth, 0);
476 sub(Result.pVal, this->pVal, RHS.pVal, getNumWords());
477 return Result.clearUnusedBits();
480 bool APInt::operator[](uint32_t bitPosition) const {
481 return (maskBit(bitPosition) &
482 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0;
485 bool APInt::operator==(const APInt& RHS) const {
486 assert(BitWidth == RHS.BitWidth && "Comparison requires equal bit widths");
488 return VAL == RHS.VAL;
490 // Get some facts about the number of bits used in the two operands.
491 uint32_t n1 = getActiveBits();
492 uint32_t n2 = RHS.getActiveBits();
494 // If the number of bits isn't the same, they aren't equal
498 // If the number of bits fits in a word, we only need to compare the low word.
499 if (n1 <= APINT_BITS_PER_WORD)
500 return pVal[0] == RHS.pVal[0];
502 // Otherwise, compare everything
503 for (int i = whichWord(n1 - 1); i >= 0; --i)
504 if (pVal[i] != RHS.pVal[i])
509 bool APInt::operator==(uint64_t Val) const {
513 uint32_t n = getActiveBits();
514 if (n <= APINT_BITS_PER_WORD)
515 return pVal[0] == Val;
520 bool APInt::ult(const APInt& RHS) const {
521 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
523 return VAL < RHS.VAL;
525 // Get active bit length of both operands
526 uint32_t n1 = getActiveBits();
527 uint32_t n2 = RHS.getActiveBits();
529 // If magnitude of LHS is less than RHS, return true.
533 // If magnitude of RHS is greather than LHS, return false.
537 // If they bot fit in a word, just compare the low order word
538 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD)
539 return pVal[0] < RHS.pVal[0];
541 // Otherwise, compare all words
542 uint32_t topWord = whichWord(std::max(n1,n2)-1);
543 for (int i = topWord; 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 lhsNeg = isNegative();
563 bool rhsNeg = rhs.isNegative();
565 // Sign bit is set so perform two's complement to make it positive
570 // Sign bit is set so perform two's complement to make it positive
575 // Now we have unsigned values to compare so do the comparison if necessary
576 // based on the negativeness of the values.
588 APInt& APInt::set(uint32_t bitPosition) {
590 VAL |= maskBit(bitPosition);
592 pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
596 APInt& APInt::set() {
597 if (isSingleWord()) {
599 return clearUnusedBits();
602 // Set all the bits in all the words.
603 for (uint32_t i = 0; i < getNumWords() - 1; ++i)
605 // Clear the unused ones
606 return clearUnusedBits();
609 /// Set the given bit to 0 whose position is given as "bitPosition".
610 /// @brief Set a given bit to 0.
611 APInt& APInt::clear(uint32_t bitPosition) {
613 VAL &= ~maskBit(bitPosition);
615 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
619 /// @brief Set every bit to 0.
620 APInt& APInt::clear() {
624 memset(pVal, 0, getNumWords() * APINT_WORD_SIZE);
628 /// @brief Bitwise NOT operator. Performs a bitwise logical NOT operation on
630 APInt APInt::operator~() const {
636 /// @brief Toggle every bit to its opposite value.
637 APInt& APInt::flip() {
638 if (isSingleWord()) {
640 return clearUnusedBits();
642 for (uint32_t i = 0; i < getNumWords(); ++i)
644 return clearUnusedBits();
647 /// Toggle a given bit to its opposite value whose position is given
648 /// as "bitPosition".
649 /// @brief Toggles a given bit to its opposite value.
650 APInt& APInt::flip(uint32_t bitPosition) {
651 assert(bitPosition < BitWidth && "Out of the bit-width range!");
652 if ((*this)[bitPosition]) clear(bitPosition);
653 else set(bitPosition);
657 uint64_t APInt::getHashValue() const {
658 // Put the bit width into the low order bits.
659 uint64_t hash = BitWidth;
661 // Add the sum of the words to the hash.
663 hash += VAL << 6; // clear separation of up to 64 bits
665 for (uint32_t i = 0; i < getNumWords(); ++i)
666 hash += pVal[i] << 6; // clear sepration of up to 64 bits
670 /// HiBits - This function returns the high "numBits" bits of this APInt.
671 APInt APInt::getHiBits(uint32_t numBits) const {
672 return APIntOps::lshr(*this, BitWidth - numBits);
675 /// LoBits - This function returns the low "numBits" bits of this APInt.
676 APInt APInt::getLoBits(uint32_t numBits) const {
677 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
681 bool APInt::isPowerOf2() const {
682 return (!!*this) && !(*this & (*this - APInt(BitWidth,1)));
685 uint32_t APInt::countLeadingZeros() const {
688 Count = CountLeadingZeros_64(VAL);
690 for (uint32_t i = getNumWords(); i > 0u; --i) {
692 Count += APINT_BITS_PER_WORD;
694 Count += CountLeadingZeros_64(pVal[i-1]);
699 uint32_t remainder = BitWidth % APINT_BITS_PER_WORD;
701 Count -= APINT_BITS_PER_WORD - remainder;
705 static uint32_t countLeadingOnes_64(uint64_t V, uint32_t skip) {
709 while (V && (V & (1ULL << 63))) {
716 uint32_t APInt::countLeadingOnes() const {
718 return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth);
720 uint32_t highWordBits = BitWidth % APINT_BITS_PER_WORD;
721 uint32_t shift = (highWordBits == 0 ? 0 : APINT_BITS_PER_WORD - highWordBits);
722 int i = getNumWords() - 1;
723 uint32_t Count = countLeadingOnes_64(pVal[i], shift);
724 if (Count == highWordBits) {
725 for (i--; i >= 0; --i) {
726 if (pVal[i] == -1ULL)
727 Count += APINT_BITS_PER_WORD;
729 Count += countLeadingOnes_64(pVal[i], 0);
737 uint32_t APInt::countTrailingZeros() const {
739 return CountTrailingZeros_64(VAL);
742 for (; i < getNumWords() && pVal[i] == 0; ++i)
743 Count += APINT_BITS_PER_WORD;
744 if (i < getNumWords())
745 Count += CountTrailingZeros_64(pVal[i]);
749 uint32_t APInt::countPopulation() const {
751 return CountPopulation_64(VAL);
753 for (uint32_t i = 0; i < getNumWords(); ++i)
754 Count += CountPopulation_64(pVal[i]);
758 APInt APInt::byteSwap() const {
759 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
761 return APInt(BitWidth, ByteSwap_16(VAL));
762 else if (BitWidth == 32)
763 return APInt(BitWidth, ByteSwap_32(VAL));
764 else if (BitWidth == 48) {
765 uint64_t Tmp1 = ((VAL >> 32) << 16) | (VAL & 0xFFFF);
766 Tmp1 = ByteSwap_32(Tmp1);
767 uint64_t Tmp2 = (VAL >> 16) & 0xFFFF;
768 Tmp2 = ByteSwap_16(Tmp2);
771 (Tmp1 & 0xff) | ((Tmp1<<16) & 0xffff00000000ULL) | (Tmp2 << 16));
772 } else if (BitWidth == 64)
773 return APInt(BitWidth, ByteSwap_64(VAL));
775 APInt Result(BitWidth, 0);
776 char *pByte = (char*)Result.pVal;
777 for (uint32_t i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) {
779 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i];
780 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp;
786 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
788 APInt A = API1, B = API2;
791 B = APIntOps::urem(A, B);
797 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, uint32_t width) {
804 // Get the sign bit from the highest order bit
805 bool isNeg = T.I >> 63;
807 // Get the 11-bit exponent and adjust for the 1023 bit bias
808 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
810 // If the exponent is negative, the value is < 0 so just return 0.
812 return APInt(width, 0u);
814 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
815 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
817 // If the exponent doesn't shift all bits out of the mantissa
819 return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
820 APInt(width, mantissa >> (52 - exp));
822 // If the client didn't provide enough bits for us to shift the mantissa into
823 // then the result is undefined, just return 0
824 if (width <= exp - 52)
825 return APInt(width, 0);
827 // Otherwise, we have to shift the mantissa bits up to the right location
828 APInt Tmp(width, mantissa);
829 Tmp = Tmp.shl(exp - 52);
830 return isNeg ? -Tmp : Tmp;
833 /// RoundToDouble - This function convert this APInt to a double.
834 /// The layout for double is as following (IEEE Standard 754):
835 /// --------------------------------------
836 /// | Sign Exponent Fraction Bias |
837 /// |-------------------------------------- |
838 /// | 1[63] 11[62-52] 52[51-00] 1023 |
839 /// --------------------------------------
840 double APInt::roundToDouble(bool isSigned) const {
842 // Handle the simple case where the value is contained in one uint64_t.
843 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
845 int64_t sext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
851 // Determine if the value is negative.
852 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
854 // Construct the absolute value if we're negative.
855 APInt Tmp(isNeg ? -(*this) : (*this));
857 // Figure out how many bits we're using.
858 uint32_t n = Tmp.getActiveBits();
860 // The exponent (without bias normalization) is just the number of bits
861 // we are using. Note that the sign bit is gone since we constructed the
865 // Return infinity for exponent overflow
867 if (!isSigned || !isNeg)
868 return double(1.0E300 * 1.0E300); // positive infinity
870 return double(-1.0E300 * 1.0E300); // negative infinity
872 exp += 1023; // Increment for 1023 bias
874 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
875 // extract the high 52 bits from the correct words in pVal.
877 unsigned hiWord = whichWord(n-1);
879 mantissa = Tmp.pVal[0];
881 mantissa >>= n - 52; // shift down, we want the top 52 bits.
883 assert(hiWord > 0 && "huh?");
884 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
885 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
886 mantissa = hibits | lobits;
889 // The leading bit of mantissa is implicit, so get rid of it.
890 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
895 T.I = sign | (exp << 52) | mantissa;
899 // Truncate to new width.
900 APInt &APInt::trunc(uint32_t width) {
901 assert(width < BitWidth && "Invalid APInt Truncate request");
902 assert(width >= IntegerType::MIN_INT_BITS && "Can't truncate to 0 bits");
903 uint32_t wordsBefore = getNumWords();
905 uint32_t wordsAfter = getNumWords();
906 if (wordsBefore != wordsAfter) {
907 if (wordsAfter == 1) {
908 uint64_t *tmp = pVal;
912 uint64_t *newVal = getClearedMemory(wordsAfter);
913 for (uint32_t i = 0; i < wordsAfter; ++i)
919 return clearUnusedBits();
922 // Sign extend to a new width.
923 APInt &APInt::sext(uint32_t width) {
924 assert(width > BitWidth && "Invalid APInt SignExtend request");
925 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
926 // If the sign bit isn't set, this is the same as zext.
932 // The sign bit is set. First, get some facts
933 uint32_t wordsBefore = getNumWords();
934 uint32_t wordBits = BitWidth % APINT_BITS_PER_WORD;
936 uint32_t wordsAfter = getNumWords();
938 // Mask the high order word appropriately
939 if (wordsBefore == wordsAfter) {
940 uint32_t newWordBits = width % APINT_BITS_PER_WORD;
941 // The extension is contained to the wordsBefore-1th word.
942 uint64_t mask = ~0ULL;
944 mask >>= APINT_BITS_PER_WORD - newWordBits;
946 if (wordsBefore == 1)
949 pVal[wordsBefore-1] |= mask;
950 return clearUnusedBits();
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)
967 return clearUnusedBits();
970 // Zero extend to a new width.
971 APInt &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)
991 APInt &APInt::zextOrTrunc(uint32_t width) {
992 if (BitWidth < width)
994 if (BitWidth > width)
999 APInt &APInt::sextOrTrunc(uint32_t width) {
1000 if (BitWidth < width)
1002 if (BitWidth > width)
1003 return trunc(width);
1007 /// Arithmetic right-shift this APInt by shiftAmt.
1008 /// @brief Arithmetic right-shift function.
1009 APInt APInt::ashr(uint32_t shiftAmt) const {
1010 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1011 // Handle a degenerate case
1015 // Handle single word shifts with built-in ashr
1016 if (isSingleWord()) {
1017 if (shiftAmt == BitWidth)
1018 return APInt(BitWidth, 0); // undefined
1020 uint32_t SignBit = APINT_BITS_PER_WORD - BitWidth;
1021 return APInt(BitWidth,
1022 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1026 // If all the bits were shifted out, the result is, technically, undefined.
1027 // We return -1 if it was negative, 0 otherwise. We check this early to avoid
1028 // issues in the algorithm below.
1029 if (shiftAmt == BitWidth)
1031 return APInt(BitWidth, -1ULL);
1033 return APInt(BitWidth, 0);
1035 // Create some space for the result.
1036 uint64_t * val = new uint64_t[getNumWords()];
1038 // Compute some values needed by the following shift algorithms
1039 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word
1040 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift
1041 uint32_t breakWord = getNumWords() - 1 - offset; // last word affected
1042 uint32_t bitsInWord = whichBit(BitWidth); // how many bits in last word?
1043 if (bitsInWord == 0)
1044 bitsInWord = APINT_BITS_PER_WORD;
1046 // If we are shifting whole words, just move whole words
1047 if (wordShift == 0) {
1048 // Move the words containing significant bits
1049 for (uint32_t i = 0; i <= breakWord; ++i)
1050 val[i] = pVal[i+offset]; // move whole word
1052 // Adjust the top significant word for sign bit fill, if negative
1054 if (bitsInWord < APINT_BITS_PER_WORD)
1055 val[breakWord] |= ~0ULL << bitsInWord; // set high bits
1057 // Shift the low order words
1058 for (uint32_t i = 0; i < breakWord; ++i) {
1059 // This combines the shifted corresponding word with the low bits from
1060 // the next word (shifted into this word's high bits).
1061 val[i] = (pVal[i+offset] >> wordShift) |
1062 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1065 // Shift the break word. In this case there are no bits from the next word
1066 // to include in this word.
1067 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1069 // Deal with sign extenstion in the break word, and possibly the word before
1072 if (wordShift > bitsInWord) {
1075 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord));
1076 val[breakWord] |= ~0ULL;
1078 val[breakWord] |= (~0ULL << (bitsInWord - wordShift));
1081 // Remaining words are 0 or -1, just assign them.
1082 uint64_t fillValue = (isNegative() ? -1ULL : 0);
1083 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1085 return APInt(val, BitWidth).clearUnusedBits();
1088 /// Logical right-shift this APInt by shiftAmt.
1089 /// @brief Logical right-shift function.
1090 APInt APInt::lshr(uint32_t shiftAmt) const {
1092 if (shiftAmt == BitWidth)
1093 return APInt(BitWidth, 0);
1095 return APInt(BitWidth, this->VAL >> shiftAmt);
1097 // If all the bits were shifted out, the result is 0. This avoids issues
1098 // with shifting by the size of the integer type, which produces undefined
1099 // results. We define these "undefined results" to always be 0.
1100 if (shiftAmt == BitWidth)
1101 return APInt(BitWidth, 0);
1103 // Create some space for the result.
1104 uint64_t * val = new uint64_t[getNumWords()];
1106 // If we are shifting less than a word, compute the shift with a simple carry
1107 if (shiftAmt < APINT_BITS_PER_WORD) {
1109 for (int i = getNumWords()-1; i >= 0; --i) {
1110 val[i] = (pVal[i] >> shiftAmt) | carry;
1111 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1113 return APInt(val, BitWidth).clearUnusedBits();
1116 // Compute some values needed by the remaining shift algorithms
1117 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1118 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1120 // If we are shifting whole words, just move whole words
1121 if (wordShift == 0) {
1122 for (uint32_t i = 0; i < getNumWords() - offset; ++i)
1123 val[i] = pVal[i+offset];
1124 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
1126 return APInt(val,BitWidth).clearUnusedBits();
1129 // Shift the low order words
1130 uint32_t breakWord = getNumWords() - offset -1;
1131 for (uint32_t i = 0; i < breakWord; ++i)
1132 val[i] = (pVal[i+offset] >> wordShift) |
1133 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1134 // Shift the break word.
1135 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1137 // Remaining words are 0
1138 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1140 return APInt(val, BitWidth).clearUnusedBits();
1143 /// Left-shift this APInt by shiftAmt.
1144 /// @brief Left-shift function.
1145 APInt APInt::shl(uint32_t shiftAmt) const {
1146 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1147 if (isSingleWord()) {
1148 if (shiftAmt == BitWidth)
1149 return APInt(BitWidth, 0); // avoid undefined shift results
1150 return APInt(BitWidth, VAL << shiftAmt);
1153 // If all the bits were shifted out, the result is 0. This avoids issues
1154 // with shifting by the size of the integer type, which produces undefined
1155 // results. We define these "undefined results" to always be 0.
1156 if (shiftAmt == BitWidth)
1157 return APInt(BitWidth, 0);
1159 // Create some space for the result.
1160 uint64_t * val = new uint64_t[getNumWords()];
1162 // If we are shifting less than a word, do it the easy way
1163 if (shiftAmt < APINT_BITS_PER_WORD) {
1165 for (uint32_t i = 0; i < getNumWords(); i++) {
1166 val[i] = pVal[i] << shiftAmt | carry;
1167 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1169 return APInt(val, BitWidth).clearUnusedBits();
1172 // Compute some values needed by the remaining shift algorithms
1173 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1174 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1176 // If we are shifting whole words, just move whole words
1177 if (wordShift == 0) {
1178 for (uint32_t i = 0; i < offset; i++)
1180 for (uint32_t i = offset; i < getNumWords(); i++)
1181 val[i] = pVal[i-offset];
1182 return APInt(val,BitWidth).clearUnusedBits();
1185 // Copy whole words from this to Result.
1186 uint32_t i = getNumWords() - 1;
1187 for (; i > offset; --i)
1188 val[i] = pVal[i-offset] << wordShift |
1189 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1190 val[offset] = pVal[0] << wordShift;
1191 for (i = 0; i < offset; ++i)
1193 return APInt(val, BitWidth).clearUnusedBits();
1197 // Square Root - this method computes and returns the square root of "this".
1198 // Three mechanisms are used for computation. For small values (<= 5 bits),
1199 // a table lookup is done. This gets some performance for common cases. For
1200 // values using less than 52 bits, the value is converted to double and then
1201 // the libc sqrt function is called. The result is rounded and then converted
1202 // back to a uint64_t which is then used to construct the result. Finally,
1203 // the Babylonian method for computing square roots is used.
1204 APInt APInt::sqrt() const {
1206 // Determine the magnitude of the value.
1207 uint32_t magnitude = getActiveBits();
1209 // Use a fast table for some small values. This also gets rid of some
1210 // rounding errors in libc sqrt for small values.
1211 if (magnitude <= 5) {
1212 static const uint8_t results[32] = {
1215 /* 3- 6 */ 2, 2, 2, 2,
1216 /* 7-12 */ 3, 3, 3, 3, 3, 3,
1217 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1218 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1221 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]);
1224 // If the magnitude of the value fits in less than 52 bits (the precision of
1225 // an IEEE double precision floating point value), then we can use the
1226 // libc sqrt function which will probably use a hardware sqrt computation.
1227 // This should be faster than the algorithm below.
1228 if (magnitude < 52) {
1230 // Amazingly, VC++ doesn't have round().
1231 return APInt(BitWidth,
1232 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0]))) + 0.5);
1234 return APInt(BitWidth,
1235 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0])))));
1239 // Okay, all the short cuts are exhausted. We must compute it. The following
1240 // is a classical Babylonian method for computing the square root. This code
1241 // was adapted to APINt from a wikipedia article on such computations.
1242 // See http://www.wikipedia.org/ and go to the page named
1243 // Calculate_an_integer_square_root.
1244 uint32_t nbits = BitWidth, i = 4;
1245 APInt testy(BitWidth, 16);
1246 APInt x_old(BitWidth, 1);
1247 APInt x_new(BitWidth, 0);
1248 APInt two(BitWidth, 2);
1250 // Select a good starting value using binary logarithms.
1251 for (;; i += 2, testy = testy.shl(2))
1252 if (i >= nbits || this->ule(testy)) {
1253 x_old = x_old.shl(i / 2);
1257 // Use the Babylonian method to arrive at the integer square root:
1259 x_new = (this->udiv(x_old) + x_old).udiv(two);
1260 if (x_old.ule(x_new))
1265 // Make sure we return the closest approximation
1266 // NOTE: The rounding calculation below is correct. It will produce an
1267 // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1268 // determined to be a rounding issue with pari/gp as it begins to use a
1269 // floating point representation after 192 bits. There are no discrepancies
1270 // between this algorithm and pari/gp for bit widths < 192 bits.
1271 APInt square(x_old * x_old);
1272 APInt nextSquare((x_old + 1) * (x_old +1));
1273 if (this->ult(square))
1275 else if (this->ule(nextSquare)) {
1276 APInt midpoint((nextSquare - square).udiv(two));
1277 APInt offset(*this - square);
1278 if (offset.ult(midpoint))
1283 assert(0 && "Error in APInt::sqrt computation");
1287 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1288 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1289 /// variables here have the same names as in the algorithm. Comments explain
1290 /// the algorithm and any deviation from it.
1291 static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
1292 uint32_t m, uint32_t n) {
1293 assert(u && "Must provide dividend");
1294 assert(v && "Must provide divisor");
1295 assert(q && "Must provide quotient");
1296 assert(u != v && u != q && v != q && "Must us different memory");
1297 assert(n>1 && "n must be > 1");
1299 // Knuth uses the value b as the base of the number system. In our case b
1300 // is 2^31 so we just set it to -1u.
1301 uint64_t b = uint64_t(1) << 32;
1303 DEBUG(cerr << "KnuthDiv: m=" << m << " n=" << n << '\n');
1304 DEBUG(cerr << "KnuthDiv: original:");
1305 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1306 DEBUG(cerr << " by");
1307 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1308 DEBUG(cerr << '\n');
1309 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1310 // u and v by d. Note that we have taken Knuth's advice here to use a power
1311 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1312 // 2 allows us to shift instead of multiply and it is easy to determine the
1313 // shift amount from the leading zeros. We are basically normalizing the u
1314 // and v so that its high bits are shifted to the top of v's range without
1315 // overflow. Note that this can require an extra word in u so that u must
1316 // be of length m+n+1.
1317 uint32_t shift = CountLeadingZeros_32(v[n-1]);
1318 uint32_t v_carry = 0;
1319 uint32_t u_carry = 0;
1321 for (uint32_t i = 0; i < m+n; ++i) {
1322 uint32_t u_tmp = u[i] >> (32 - shift);
1323 u[i] = (u[i] << shift) | u_carry;
1326 for (uint32_t i = 0; i < n; ++i) {
1327 uint32_t v_tmp = v[i] >> (32 - shift);
1328 v[i] = (v[i] << shift) | v_carry;
1333 DEBUG(cerr << "KnuthDiv: normal:");
1334 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1335 DEBUG(cerr << " by");
1336 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1337 DEBUG(cerr << '\n');
1339 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1342 DEBUG(cerr << "KnuthDiv: quotient digit #" << j << '\n');
1343 // D3. [Calculate q'.].
1344 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1345 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1346 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1347 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1348 // on v[n-2] determines at high speed most of the cases in which the trial
1349 // value qp is one too large, and it eliminates all cases where qp is two
1351 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1352 DEBUG(cerr << "KnuthDiv: dividend == " << dividend << '\n');
1353 uint64_t qp = dividend / v[n-1];
1354 uint64_t rp = dividend % v[n-1];
1355 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1358 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1361 DEBUG(cerr << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1363 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1364 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1365 // consists of a simple multiplication by a one-place number, combined with
1368 for (uint32_t i = 0; i < n; ++i) {
1369 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1370 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1371 bool borrow = subtrahend > u_tmp;
1372 DEBUG(cerr << "KnuthDiv: u_tmp == " << u_tmp
1373 << ", subtrahend == " << subtrahend
1374 << ", borrow = " << borrow << '\n');
1376 uint64_t result = u_tmp - subtrahend;
1378 u[k++] = result & (b-1); // subtract low word
1379 u[k++] = result >> 32; // subtract high word
1380 while (borrow && k <= m+n) { // deal with borrow to the left
1386 DEBUG(cerr << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1389 DEBUG(cerr << "KnuthDiv: after subtraction:");
1390 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1391 DEBUG(cerr << '\n');
1392 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1393 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1394 // true value plus b**(n+1), namely as the b's complement of
1395 // the true value, and a "borrow" to the left should be remembered.
1398 bool carry = true; // true because b's complement is "complement + 1"
1399 for (uint32_t i = 0; i <= m+n; ++i) {
1400 u[i] = ~u[i] + carry; // b's complement
1401 carry = carry && u[i] == 0;
1404 DEBUG(cerr << "KnuthDiv: after complement:");
1405 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1406 DEBUG(cerr << '\n');
1408 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1409 // negative, go to step D6; otherwise go on to step D7.
1412 // D6. [Add back]. The probability that this step is necessary is very
1413 // small, on the order of only 2/b. Make sure that test data accounts for
1414 // this possibility. Decrease q[j] by 1
1416 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1417 // A carry will occur to the left of u[j+n], and it should be ignored
1418 // since it cancels with the borrow that occurred in D4.
1420 for (uint32_t i = 0; i < n; i++) {
1421 uint32_t limit = std::min(u[j+i],v[i]);
1422 u[j+i] += v[i] + carry;
1423 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1427 DEBUG(cerr << "KnuthDiv: after correction:");
1428 DEBUG(for (int i = m+n; i >=0; i--) cerr <<" " << u[i]);
1429 DEBUG(cerr << "\nKnuthDiv: digit result = " << q[j] << '\n');
1431 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1434 DEBUG(cerr << "KnuthDiv: quotient:");
1435 DEBUG(for (int i = m; i >=0; i--) cerr <<" " << q[i]);
1436 DEBUG(cerr << '\n');
1438 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1439 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1440 // compute the remainder (urem uses this).
1442 // The value d is expressed by the "shift" value above since we avoided
1443 // multiplication by d by using a shift left. So, all we have to do is
1444 // shift right here. In order to mak
1447 DEBUG(cerr << "KnuthDiv: remainder:");
1448 for (int i = n-1; i >= 0; i--) {
1449 r[i] = (u[i] >> shift) | carry;
1450 carry = u[i] << (32 - shift);
1451 DEBUG(cerr << " " << r[i]);
1454 for (int i = n-1; i >= 0; i--) {
1456 DEBUG(cerr << " " << r[i]);
1459 DEBUG(cerr << '\n');
1461 DEBUG(cerr << std::setbase(10) << '\n');
1464 void APInt::divide(const APInt LHS, uint32_t lhsWords,
1465 const APInt &RHS, uint32_t rhsWords,
1466 APInt *Quotient, APInt *Remainder)
1468 assert(lhsWords >= rhsWords && "Fractional result");
1470 // First, compose the values into an array of 32-bit words instead of
1471 // 64-bit words. This is a necessity of both the "short division" algorithm
1472 // and the the Knuth "classical algorithm" which requires there to be native
1473 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1474 // can't use 64-bit operands here because we don't have native results of
1475 // 128-bits. Furthremore, casting the 64-bit values to 32-bit values won't
1476 // work on large-endian machines.
1477 uint64_t mask = ~0ull >> (sizeof(uint32_t)*8);
1478 uint32_t n = rhsWords * 2;
1479 uint32_t m = (lhsWords * 2) - n;
1481 // Allocate space for the temporary values we need either on the stack, if
1482 // it will fit, or on the heap if it won't.
1483 uint32_t SPACE[128];
1488 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1491 Q = &SPACE[(m+n+1) + n];
1493 R = &SPACE[(m+n+1) + n + (m+n)];
1495 U = new uint32_t[m + n + 1];
1496 V = new uint32_t[n];
1497 Q = new uint32_t[m+n];
1499 R = new uint32_t[n];
1502 // Initialize the dividend
1503 memset(U, 0, (m+n+1)*sizeof(uint32_t));
1504 for (unsigned i = 0; i < lhsWords; ++i) {
1505 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1506 U[i * 2] = tmp & mask;
1507 U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1509 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1511 // Initialize the divisor
1512 memset(V, 0, (n)*sizeof(uint32_t));
1513 for (unsigned i = 0; i < rhsWords; ++i) {
1514 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1515 V[i * 2] = tmp & mask;
1516 V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1519 // initialize the quotient and remainder
1520 memset(Q, 0, (m+n) * sizeof(uint32_t));
1522 memset(R, 0, n * sizeof(uint32_t));
1524 // Now, adjust m and n for the Knuth division. n is the number of words in
1525 // the divisor. m is the number of words by which the dividend exceeds the
1526 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1527 // contain any zero words or the Knuth algorithm fails.
1528 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1532 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1535 // If we're left with only a single word for the divisor, Knuth doesn't work
1536 // so we implement the short division algorithm here. This is much simpler
1537 // and faster because we are certain that we can divide a 64-bit quantity
1538 // by a 32-bit quantity at hardware speed and short division is simply a
1539 // series of such operations. This is just like doing short division but we
1540 // are using base 2^32 instead of base 10.
1541 assert(n != 0 && "Divide by zero?");
1543 uint32_t divisor = V[0];
1544 uint32_t remainder = 0;
1545 for (int i = m+n-1; i >= 0; i--) {
1546 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1547 if (partial_dividend == 0) {
1550 } else if (partial_dividend < divisor) {
1552 remainder = partial_dividend;
1553 } else if (partial_dividend == divisor) {
1557 Q[i] = partial_dividend / divisor;
1558 remainder = partial_dividend - (Q[i] * divisor);
1564 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1566 KnuthDiv(U, V, Q, R, m, n);
1569 // If the caller wants the quotient
1571 // Set up the Quotient value's memory.
1572 if (Quotient->BitWidth != LHS.BitWidth) {
1573 if (Quotient->isSingleWord())
1576 delete [] Quotient->pVal;
1577 Quotient->BitWidth = LHS.BitWidth;
1578 if (!Quotient->isSingleWord())
1579 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1583 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1585 if (lhsWords == 1) {
1587 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1588 if (Quotient->isSingleWord())
1589 Quotient->VAL = tmp;
1591 Quotient->pVal[0] = tmp;
1593 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1594 for (unsigned i = 0; i < lhsWords; ++i)
1596 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1600 // If the caller wants the remainder
1602 // Set up the Remainder value's memory.
1603 if (Remainder->BitWidth != RHS.BitWidth) {
1604 if (Remainder->isSingleWord())
1607 delete [] Remainder->pVal;
1608 Remainder->BitWidth = RHS.BitWidth;
1609 if (!Remainder->isSingleWord())
1610 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1614 // The remainder is in R. Reconstitute the remainder into Remainder's low
1616 if (rhsWords == 1) {
1618 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1619 if (Remainder->isSingleWord())
1620 Remainder->VAL = tmp;
1622 Remainder->pVal[0] = tmp;
1624 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1625 for (unsigned i = 0; i < rhsWords; ++i)
1626 Remainder->pVal[i] =
1627 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1631 // Clean up the memory we allocated.
1632 if (U != &SPACE[0]) {
1640 APInt APInt::udiv(const APInt& RHS) const {
1641 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1643 // First, deal with the easy case
1644 if (isSingleWord()) {
1645 assert(RHS.VAL != 0 && "Divide by zero?");
1646 return APInt(BitWidth, VAL / RHS.VAL);
1649 // Get some facts about the LHS and RHS number of bits and words
1650 uint32_t rhsBits = RHS.getActiveBits();
1651 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1652 assert(rhsWords && "Divided by zero???");
1653 uint32_t lhsBits = this->getActiveBits();
1654 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1656 // Deal with some degenerate cases
1659 return APInt(BitWidth, 0);
1660 else if (lhsWords < rhsWords || this->ult(RHS)) {
1661 // X / Y ===> 0, iff X < Y
1662 return APInt(BitWidth, 0);
1663 } else if (*this == RHS) {
1665 return APInt(BitWidth, 1);
1666 } else if (lhsWords == 1 && rhsWords == 1) {
1667 // All high words are zero, just use native divide
1668 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1671 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1672 APInt Quotient(1,0); // to hold result.
1673 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0);
1677 APInt APInt::urem(const APInt& RHS) const {
1678 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1679 if (isSingleWord()) {
1680 assert(RHS.VAL != 0 && "Remainder by zero?");
1681 return APInt(BitWidth, VAL % RHS.VAL);
1684 // Get some facts about the LHS
1685 uint32_t lhsBits = getActiveBits();
1686 uint32_t lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1688 // Get some facts about the RHS
1689 uint32_t rhsBits = RHS.getActiveBits();
1690 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1691 assert(rhsWords && "Performing remainder operation by zero ???");
1693 // Check the degenerate cases
1694 if (lhsWords == 0) {
1696 return APInt(BitWidth, 0);
1697 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1698 // X % Y ===> X, iff X < Y
1700 } else if (*this == RHS) {
1702 return APInt(BitWidth, 0);
1703 } else if (lhsWords == 1) {
1704 // All high words are zero, just use native remainder
1705 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
1708 // We have to compute it the hard way. Invoke the Knute divide algorithm.
1709 APInt Remainder(1,0);
1710 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder);
1714 void APInt::fromString(uint32_t numbits, const char *str, uint32_t slen,
1716 // Check our assumptions here
1717 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1718 "Radix should be 2, 8, 10, or 16!");
1719 assert(str && "String is null?");
1720 bool isNeg = str[0] == '-';
1723 assert(slen <= numbits || radix != 2 && "Insufficient bit width");
1724 assert(slen*3 <= numbits || radix != 8 && "Insufficient bit width");
1725 assert(slen*4 <= numbits || radix != 16 && "Insufficient bit width");
1726 assert((slen*64)/20 <= numbits || radix != 10 && "Insufficient bit width");
1729 if (!isSingleWord())
1730 pVal = getClearedMemory(getNumWords());
1732 // Figure out if we can shift instead of multiply
1733 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
1735 // Set up an APInt for the digit to add outside the loop so we don't
1736 // constantly construct/destruct it.
1737 APInt apdigit(getBitWidth(), 0);
1738 APInt apradix(getBitWidth(), radix);
1740 // Enter digit traversal loop
1741 for (unsigned i = 0; i < slen; i++) {
1744 char cdigit = str[i];
1745 if (isdigit(cdigit))
1746 digit = cdigit - '0';
1747 else if (isxdigit(cdigit))
1749 digit = cdigit - 'a' + 10;
1750 else if (cdigit >= 'A')
1751 digit = cdigit - 'A' + 10;
1753 assert(0 && "huh?");
1755 assert(0 && "Invalid character in digit string");
1757 // Shift or multiple the value by the radix
1763 // Add in the digit we just interpreted
1764 if (apdigit.isSingleWord())
1765 apdigit.VAL = digit;
1767 apdigit.pVal[0] = digit;
1770 // If its negative, put it in two's complement form
1777 std::string APInt::toString(uint8_t radix, bool wantSigned) const {
1778 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1779 "Radix should be 2, 8, 10, or 16!");
1780 static const char *digits[] = {
1781 "0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"
1784 uint32_t bits_used = getActiveBits();
1785 if (isSingleWord()) {
1787 const char *format = (radix == 10 ? (wantSigned ? "%lld" : "%llu") :
1788 (radix == 16 ? "%llX" : (radix == 8 ? "%llo" : 0)));
1791 int64_t sextVal = (int64_t(VAL) << (APINT_BITS_PER_WORD-BitWidth)) >>
1792 (APINT_BITS_PER_WORD-BitWidth);
1793 sprintf(buf, format, sextVal);
1795 sprintf(buf, format, VAL);
1800 uint32_t bit = v & 1;
1802 buf[bits_used] = digits[bit][0];
1811 uint64_t mask = radix - 1;
1812 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : 1);
1813 uint32_t nibbles = APINT_BITS_PER_WORD / shift;
1814 for (uint32_t i = 0; i < getNumWords(); ++i) {
1815 uint64_t value = pVal[i];
1816 for (uint32_t j = 0; j < nibbles; ++j) {
1817 result.insert(0, digits[ value & mask ]);
1825 APInt divisor(4, radix);
1826 APInt zero(tmp.getBitWidth(), 0);
1827 size_t insert_at = 0;
1828 if (wantSigned && tmp[BitWidth-1]) {
1829 // They want to print the signed version and it is a negative value
1830 // Flip the bits and add one to turn it into the equivalent positive
1831 // value and put a '-' in the result.
1837 if (tmp == APInt(tmp.getBitWidth(), 0))
1839 else while (tmp.ne(zero)) {
1841 APInt tmp2(tmp.getBitWidth(), 0);
1842 divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
1844 uint32_t digit = APdigit.getZExtValue();
1845 assert(digit < radix && "divide failed");
1846 result.insert(insert_at,digits[digit]);
1854 void APInt::dump() const
1856 cerr << "APInt(" << BitWidth << ")=" << std::setbase(16);
1859 else for (unsigned i = getNumWords(); i > 0; i--) {
1860 cerr << pVal[i-1] << " ";
1862 cerr << " U(" << this->toString(10) << ") S(" << this->toStringSigned(10)
1863 << ")\n" << std::setbase(10);