1 //===-- APInt.cpp - Implement APInt class ---------------------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // 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/ADT/FoldingSet.h"
18 #include "llvm/Support/Debug.h"
19 #include "llvm/Support/MathExtras.h"
28 /// This enumeration just provides for internal constants used in this
31 MIN_INT_BITS = 1, ///< Minimum number of bits that can be specified
32 ///< Note that this must remain synchronized with IntegerType::MIN_INT_BITS
33 MAX_INT_BITS = (1<<23)-1 ///< Maximum number of bits that can be specified
34 ///< Note that this must remain synchronized with IntegerType::MAX_INT_BITS
37 /// A utility function for allocating memory, checking for allocation failures,
38 /// and ensuring the contents are zeroed.
39 inline static uint64_t* getClearedMemory(uint32_t numWords) {
40 uint64_t * result = new uint64_t[numWords];
41 assert(result && "APInt memory allocation fails!");
42 memset(result, 0, numWords * sizeof(uint64_t));
46 /// A utility function for allocating memory and checking for allocation
47 /// failure. The content is not zeroed.
48 inline static uint64_t* getMemory(uint32_t numWords) {
49 uint64_t * result = new uint64_t[numWords];
50 assert(result && "APInt memory allocation fails!");
54 APInt::APInt(uint32_t numBits, uint64_t val, bool isSigned)
55 : BitWidth(numBits), VAL(0) {
56 assert(BitWidth >= MIN_INT_BITS && "bitwidth too small");
57 assert(BitWidth <= MAX_INT_BITS && "bitwidth too large");
61 pVal = getClearedMemory(getNumWords());
63 if (isSigned && int64_t(val) < 0)
64 for (unsigned i = 1; i < getNumWords(); ++i)
70 APInt::APInt(uint32_t numBits, uint32_t numWords, const uint64_t bigVal[])
71 : BitWidth(numBits), VAL(0) {
72 assert(BitWidth >= MIN_INT_BITS && "bitwidth too small");
73 assert(BitWidth <= MAX_INT_BITS && "bitwidth too large");
74 assert(bigVal && "Null pointer detected!");
78 // Get memory, cleared to 0
79 pVal = getClearedMemory(getNumWords());
80 // Calculate the number of words to copy
81 uint32_t words = std::min<uint32_t>(numWords, getNumWords());
82 // Copy the words from bigVal to pVal
83 memcpy(pVal, bigVal, words * APINT_WORD_SIZE);
85 // Make sure unused high bits are cleared
89 APInt::APInt(uint32_t numbits, const char StrStart[], uint32_t slen,
91 : BitWidth(numbits), VAL(0) {
92 assert(BitWidth >= MIN_INT_BITS && "bitwidth too small");
93 assert(BitWidth <= MAX_INT_BITS && "bitwidth too large");
94 fromString(numbits, StrStart, slen, radix);
97 APInt::APInt(uint32_t numbits, const std::string& Val, uint8_t radix)
98 : BitWidth(numbits), VAL(0) {
99 assert(BitWidth >= MIN_INT_BITS && "bitwidth too small");
100 assert(BitWidth <= MAX_INT_BITS && "bitwidth too large");
101 assert(!Val.empty() && "String empty?");
102 fromString(numbits, Val.c_str(), Val.size(), radix);
105 APInt::APInt(const APInt& that)
106 : BitWidth(that.BitWidth), VAL(0) {
107 assert(BitWidth >= MIN_INT_BITS && "bitwidth too small");
108 assert(BitWidth <= MAX_INT_BITS && "bitwidth too large");
112 pVal = getMemory(getNumWords());
113 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE);
118 if (!isSingleWord() && pVal)
122 APInt& APInt::operator=(const APInt& RHS) {
123 // Don't do anything for X = X
127 // If the bitwidths are the same, we can avoid mucking with memory
128 if (BitWidth == RHS.getBitWidth()) {
132 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE);
137 if (RHS.isSingleWord())
141 pVal = getMemory(RHS.getNumWords());
142 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
144 else if (getNumWords() == RHS.getNumWords())
145 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
146 else if (RHS.isSingleWord()) {
151 pVal = getMemory(RHS.getNumWords());
152 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE);
154 BitWidth = RHS.BitWidth;
155 return clearUnusedBits();
158 APInt& APInt::operator=(uint64_t RHS) {
163 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE);
165 return clearUnusedBits();
168 /// Profile - This method 'profiles' an APInt for use with FoldingSet.
169 void APInt::Profile(FoldingSetNodeID& ID) const {
170 ID.AddInteger(BitWidth);
172 if (isSingleWord()) {
177 uint32_t NumWords = getNumWords();
178 for (unsigned i = 0; i < NumWords; ++i)
179 ID.AddInteger(pVal[i]);
182 /// add_1 - This function adds a single "digit" integer, y, to the multiple
183 /// "digit" integer array, x[]. x[] is modified to reflect the addition and
184 /// 1 is returned if there is a carry out, otherwise 0 is returned.
185 /// @returns the carry of the addition.
186 static bool add_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
187 for (uint32_t i = 0; i < len; ++i) {
190 y = 1; // Carry one to next digit.
192 y = 0; // No need to carry so exit early
199 /// @brief Prefix increment operator. Increments the APInt by one.
200 APInt& APInt::operator++() {
204 add_1(pVal, pVal, getNumWords(), 1);
205 return clearUnusedBits();
208 /// sub_1 - This function subtracts a single "digit" (64-bit word), y, from
209 /// the multi-digit integer array, x[], propagating the borrowed 1 value until
210 /// no further borrowing is neeeded or it runs out of "digits" in x. The result
211 /// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted.
212 /// In other words, if y > x then this function returns 1, otherwise 0.
213 /// @returns the borrow out of the subtraction
214 static bool sub_1(uint64_t x[], uint32_t len, uint64_t y) {
215 for (uint32_t i = 0; i < len; ++i) {
219 y = 1; // We have to "borrow 1" from next "digit"
221 y = 0; // No need to borrow
222 break; // Remaining digits are unchanged so exit early
228 /// @brief Prefix decrement operator. Decrements the APInt by one.
229 APInt& APInt::operator--() {
233 sub_1(pVal, getNumWords(), 1);
234 return clearUnusedBits();
237 /// add - This function adds the integer array x to the integer array Y and
238 /// places the result in dest.
239 /// @returns the carry out from the addition
240 /// @brief General addition of 64-bit integer arrays
241 static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y,
244 for (uint32_t i = 0; i< len; ++i) {
245 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x
246 dest[i] = x[i] + y[i] + carry;
247 carry = dest[i] < limit || (carry && dest[i] == limit);
252 /// Adds the RHS APint to this APInt.
253 /// @returns this, after addition of RHS.
254 /// @brief Addition assignment operator.
255 APInt& APInt::operator+=(const APInt& RHS) {
256 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
260 add(pVal, pVal, RHS.pVal, getNumWords());
262 return clearUnusedBits();
265 /// Subtracts the integer array y from the integer array x
266 /// @returns returns the borrow out.
267 /// @brief Generalized subtraction of 64-bit integer arrays.
268 static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y,
271 for (uint32_t i = 0; i < len; ++i) {
272 uint64_t x_tmp = borrow ? x[i] - 1 : x[i];
273 borrow = y[i] > x_tmp || (borrow && x[i] == 0);
274 dest[i] = x_tmp - y[i];
279 /// Subtracts the RHS APInt from this APInt
280 /// @returns this, after subtraction
281 /// @brief Subtraction assignment operator.
282 APInt& APInt::operator-=(const APInt& RHS) {
283 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
287 sub(pVal, pVal, RHS.pVal, getNumWords());
288 return clearUnusedBits();
291 /// Multiplies an integer array, x by a a uint64_t integer and places the result
293 /// @returns the carry out of the multiplication.
294 /// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer.
295 static uint64_t mul_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
296 // Split y into high 32-bit part (hy) and low 32-bit part (ly)
297 uint64_t ly = y & 0xffffffffULL, hy = y >> 32;
300 // For each digit of x.
301 for (uint32_t i = 0; i < len; ++i) {
302 // Split x into high and low words
303 uint64_t lx = x[i] & 0xffffffffULL;
304 uint64_t hx = x[i] >> 32;
305 // hasCarry - A flag to indicate if there is a carry to the next digit.
306 // hasCarry == 0, no carry
307 // hasCarry == 1, has carry
308 // hasCarry == 2, no carry and the calculation result == 0.
309 uint8_t hasCarry = 0;
310 dest[i] = carry + lx * ly;
311 // Determine if the add above introduces carry.
312 hasCarry = (dest[i] < carry) ? 1 : 0;
313 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0);
314 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) +
315 // (2^32 - 1) + 2^32 = 2^64.
316 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
318 carry += (lx * hy) & 0xffffffffULL;
319 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL);
320 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) +
321 (carry >> 32) + ((lx * hy) >> 32) + hx * hy;
326 /// Multiplies integer array x by integer array y and stores the result into
327 /// the integer array dest. Note that dest's size must be >= xlen + ylen.
328 /// @brief Generalized multiplicate of integer arrays.
329 static void mul(uint64_t dest[], uint64_t x[], uint32_t xlen, uint64_t y[],
331 dest[xlen] = mul_1(dest, x, xlen, y[0]);
332 for (uint32_t i = 1; i < ylen; ++i) {
333 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32;
334 uint64_t carry = 0, lx = 0, hx = 0;
335 for (uint32_t j = 0; j < xlen; ++j) {
336 lx = x[j] & 0xffffffffULL;
338 // hasCarry - A flag to indicate if has carry.
339 // hasCarry == 0, no carry
340 // hasCarry == 1, has carry
341 // hasCarry == 2, no carry and the calculation result == 0.
342 uint8_t hasCarry = 0;
343 uint64_t resul = carry + lx * ly;
344 hasCarry = (resul < carry) ? 1 : 0;
345 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32);
346 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
348 carry += (lx * hy) & 0xffffffffULL;
349 resul = (carry << 32) | (resul & 0xffffffffULL);
351 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+
352 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) +
353 ((lx * hy) >> 32) + hx * hy;
355 dest[i+xlen] = carry;
359 APInt& APInt::operator*=(const APInt& RHS) {
360 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
361 if (isSingleWord()) {
367 // Get some bit facts about LHS and check for zero
368 uint32_t lhsBits = getActiveBits();
369 uint32_t lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1;
374 // Get some bit facts about RHS and check for zero
375 uint32_t rhsBits = RHS.getActiveBits();
376 uint32_t rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1;
383 // Allocate space for the result
384 uint32_t destWords = rhsWords + lhsWords;
385 uint64_t *dest = getMemory(destWords);
387 // Perform the long multiply
388 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords);
390 // Copy result back into *this
392 uint32_t wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords;
393 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE);
395 // delete dest array and return
400 APInt& APInt::operator&=(const APInt& RHS) {
401 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
402 if (isSingleWord()) {
406 uint32_t numWords = getNumWords();
407 for (uint32_t i = 0; i < numWords; ++i)
408 pVal[i] &= RHS.pVal[i];
412 APInt& APInt::operator|=(const APInt& RHS) {
413 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
414 if (isSingleWord()) {
418 uint32_t numWords = getNumWords();
419 for (uint32_t i = 0; i < numWords; ++i)
420 pVal[i] |= RHS.pVal[i];
424 APInt& APInt::operator^=(const APInt& RHS) {
425 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
426 if (isSingleWord()) {
428 this->clearUnusedBits();
431 uint32_t numWords = getNumWords();
432 for (uint32_t i = 0; i < numWords; ++i)
433 pVal[i] ^= RHS.pVal[i];
434 return clearUnusedBits();
437 APInt APInt::operator&(const APInt& RHS) const {
438 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
440 return APInt(getBitWidth(), VAL & RHS.VAL);
442 uint32_t numWords = getNumWords();
443 uint64_t* val = getMemory(numWords);
444 for (uint32_t i = 0; i < numWords; ++i)
445 val[i] = pVal[i] & RHS.pVal[i];
446 return APInt(val, getBitWidth());
449 APInt APInt::operator|(const APInt& RHS) const {
450 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
452 return APInt(getBitWidth(), VAL | RHS.VAL);
454 uint32_t numWords = getNumWords();
455 uint64_t *val = getMemory(numWords);
456 for (uint32_t i = 0; i < numWords; ++i)
457 val[i] = pVal[i] | RHS.pVal[i];
458 return APInt(val, getBitWidth());
461 APInt APInt::operator^(const APInt& RHS) const {
462 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
464 return APInt(BitWidth, VAL ^ RHS.VAL);
466 uint32_t numWords = getNumWords();
467 uint64_t *val = getMemory(numWords);
468 for (uint32_t i = 0; i < numWords; ++i)
469 val[i] = pVal[i] ^ RHS.pVal[i];
471 // 0^0==1 so clear the high bits in case they got set.
472 return APInt(val, getBitWidth()).clearUnusedBits();
475 bool APInt::operator !() const {
479 for (uint32_t i = 0; i < getNumWords(); ++i)
485 APInt APInt::operator*(const APInt& RHS) const {
486 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
488 return APInt(BitWidth, VAL * RHS.VAL);
491 return Result.clearUnusedBits();
494 APInt APInt::operator+(const APInt& RHS) const {
495 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
497 return APInt(BitWidth, VAL + RHS.VAL);
498 APInt Result(BitWidth, 0);
499 add(Result.pVal, this->pVal, RHS.pVal, getNumWords());
500 return Result.clearUnusedBits();
503 APInt APInt::operator-(const APInt& RHS) const {
504 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
506 return APInt(BitWidth, VAL - RHS.VAL);
507 APInt Result(BitWidth, 0);
508 sub(Result.pVal, this->pVal, RHS.pVal, getNumWords());
509 return Result.clearUnusedBits();
512 bool APInt::operator[](uint32_t bitPosition) const {
513 return (maskBit(bitPosition) &
514 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0;
517 bool APInt::operator==(const APInt& RHS) const {
518 assert(BitWidth == RHS.BitWidth && "Comparison requires equal bit widths");
520 return VAL == RHS.VAL;
522 // Get some facts about the number of bits used in the two operands.
523 uint32_t n1 = getActiveBits();
524 uint32_t n2 = RHS.getActiveBits();
526 // If the number of bits isn't the same, they aren't equal
530 // If the number of bits fits in a word, we only need to compare the low word.
531 if (n1 <= APINT_BITS_PER_WORD)
532 return pVal[0] == RHS.pVal[0];
534 // Otherwise, compare everything
535 for (int i = whichWord(n1 - 1); i >= 0; --i)
536 if (pVal[i] != RHS.pVal[i])
541 bool APInt::operator==(uint64_t Val) const {
545 uint32_t n = getActiveBits();
546 if (n <= APINT_BITS_PER_WORD)
547 return pVal[0] == Val;
552 bool APInt::ult(const APInt& RHS) const {
553 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
555 return VAL < RHS.VAL;
557 // Get active bit length of both operands
558 uint32_t n1 = getActiveBits();
559 uint32_t n2 = RHS.getActiveBits();
561 // If magnitude of LHS is less than RHS, return true.
565 // If magnitude of RHS is greather than LHS, return false.
569 // If they bot fit in a word, just compare the low order word
570 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD)
571 return pVal[0] < RHS.pVal[0];
573 // Otherwise, compare all words
574 uint32_t topWord = whichWord(std::max(n1,n2)-1);
575 for (int i = topWord; i >= 0; --i) {
576 if (pVal[i] > RHS.pVal[i])
578 if (pVal[i] < RHS.pVal[i])
584 bool APInt::slt(const APInt& RHS) const {
585 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
586 if (isSingleWord()) {
587 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
588 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth);
589 return lhsSext < rhsSext;
594 bool lhsNeg = isNegative();
595 bool rhsNeg = rhs.isNegative();
597 // Sign bit is set so perform two's complement to make it positive
602 // Sign bit is set so perform two's complement to make it positive
607 // Now we have unsigned values to compare so do the comparison if necessary
608 // based on the negativeness of the values.
620 APInt& APInt::set(uint32_t bitPosition) {
622 VAL |= maskBit(bitPosition);
624 pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
628 APInt& APInt::set() {
629 if (isSingleWord()) {
631 return clearUnusedBits();
634 // Set all the bits in all the words.
635 for (uint32_t i = 0; i < getNumWords(); ++i)
637 // Clear the unused ones
638 return clearUnusedBits();
641 /// Set the given bit to 0 whose position is given as "bitPosition".
642 /// @brief Set a given bit to 0.
643 APInt& APInt::clear(uint32_t bitPosition) {
645 VAL &= ~maskBit(bitPosition);
647 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
651 /// @brief Set every bit to 0.
652 APInt& APInt::clear() {
656 memset(pVal, 0, getNumWords() * APINT_WORD_SIZE);
660 /// @brief Bitwise NOT operator. Performs a bitwise logical NOT operation on
662 APInt APInt::operator~() const {
668 /// @brief Toggle every bit to its opposite value.
669 APInt& APInt::flip() {
670 if (isSingleWord()) {
672 return clearUnusedBits();
674 for (uint32_t i = 0; i < getNumWords(); ++i)
676 return clearUnusedBits();
679 /// Toggle a given bit to its opposite value whose position is given
680 /// as "bitPosition".
681 /// @brief Toggles a given bit to its opposite value.
682 APInt& APInt::flip(uint32_t bitPosition) {
683 assert(bitPosition < BitWidth && "Out of the bit-width range!");
684 if ((*this)[bitPosition]) clear(bitPosition);
685 else set(bitPosition);
689 uint32_t APInt::getBitsNeeded(const char* str, uint32_t slen, uint8_t radix) {
690 assert(str != 0 && "Invalid value string");
691 assert(slen > 0 && "Invalid string length");
693 // Each computation below needs to know if its negative
694 uint32_t isNegative = str[0] == '-';
699 // For radixes of power-of-two values, the bits required is accurately and
702 return slen + isNegative;
704 return slen * 3 + isNegative;
706 return slen * 4 + isNegative;
708 // Otherwise it must be radix == 10, the hard case
709 assert(radix == 10 && "Invalid radix");
711 // This is grossly inefficient but accurate. We could probably do something
712 // with a computation of roughly slen*64/20 and then adjust by the value of
713 // the first few digits. But, I'm not sure how accurate that could be.
715 // Compute a sufficient number of bits that is always large enough but might
716 // be too large. This avoids the assertion in the constructor.
717 uint32_t sufficient = slen*64/18;
719 // Convert to the actual binary value.
720 APInt tmp(sufficient, str, slen, radix);
722 // Compute how many bits are required.
723 return isNegative + tmp.logBase2() + 1;
726 uint64_t APInt::getHashValue() const {
727 // Put the bit width into the low order bits.
728 uint64_t hash = BitWidth;
730 // Add the sum of the words to the hash.
732 hash += VAL << 6; // clear separation of up to 64 bits
734 for (uint32_t i = 0; i < getNumWords(); ++i)
735 hash += pVal[i] << 6; // clear sepration of up to 64 bits
739 /// HiBits - This function returns the high "numBits" bits of this APInt.
740 APInt APInt::getHiBits(uint32_t numBits) const {
741 return APIntOps::lshr(*this, BitWidth - numBits);
744 /// LoBits - This function returns the low "numBits" bits of this APInt.
745 APInt APInt::getLoBits(uint32_t numBits) const {
746 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
750 bool APInt::isPowerOf2() const {
751 return (!!*this) && !(*this & (*this - APInt(BitWidth,1)));
754 uint32_t APInt::countLeadingZeros() const {
757 Count = CountLeadingZeros_64(VAL);
759 for (uint32_t i = getNumWords(); i > 0u; --i) {
761 Count += APINT_BITS_PER_WORD;
763 Count += CountLeadingZeros_64(pVal[i-1]);
768 uint32_t remainder = BitWidth % APINT_BITS_PER_WORD;
770 Count -= APINT_BITS_PER_WORD - remainder;
771 return std::min(Count, BitWidth);
774 static uint32_t countLeadingOnes_64(uint64_t V, uint32_t skip) {
778 while (V && (V & (1ULL << 63))) {
785 uint32_t APInt::countLeadingOnes() const {
787 return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth);
789 uint32_t highWordBits = BitWidth % APINT_BITS_PER_WORD;
790 uint32_t shift = (highWordBits == 0 ? 0 : APINT_BITS_PER_WORD - highWordBits);
791 int i = getNumWords() - 1;
792 uint32_t Count = countLeadingOnes_64(pVal[i], shift);
793 if (Count == highWordBits) {
794 for (i--; i >= 0; --i) {
795 if (pVal[i] == -1ULL)
796 Count += APINT_BITS_PER_WORD;
798 Count += countLeadingOnes_64(pVal[i], 0);
806 uint32_t APInt::countTrailingZeros() const {
808 return std::min(uint32_t(CountTrailingZeros_64(VAL)), BitWidth);
811 for (; i < getNumWords() && pVal[i] == 0; ++i)
812 Count += APINT_BITS_PER_WORD;
813 if (i < getNumWords())
814 Count += CountTrailingZeros_64(pVal[i]);
815 return std::min(Count, BitWidth);
818 uint32_t APInt::countTrailingOnes() const {
820 return std::min(uint32_t(CountTrailingOnes_64(VAL)), BitWidth);
823 for (; i < getNumWords() && pVal[i] == -1ULL; ++i)
824 Count += APINT_BITS_PER_WORD;
825 if (i < getNumWords())
826 Count += CountTrailingOnes_64(pVal[i]);
827 return std::min(Count, BitWidth);
830 uint32_t APInt::countPopulation() const {
832 return CountPopulation_64(VAL);
834 for (uint32_t i = 0; i < getNumWords(); ++i)
835 Count += CountPopulation_64(pVal[i]);
839 APInt APInt::byteSwap() const {
840 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
842 return APInt(BitWidth, ByteSwap_16(uint16_t(VAL)));
843 else if (BitWidth == 32)
844 return APInt(BitWidth, ByteSwap_32(uint32_t(VAL)));
845 else if (BitWidth == 48) {
846 uint32_t Tmp1 = uint32_t(VAL >> 16);
847 Tmp1 = ByteSwap_32(Tmp1);
848 uint16_t Tmp2 = uint16_t(VAL);
849 Tmp2 = ByteSwap_16(Tmp2);
850 return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1);
851 } else if (BitWidth == 64)
852 return APInt(BitWidth, ByteSwap_64(VAL));
854 APInt Result(BitWidth, 0);
855 char *pByte = (char*)Result.pVal;
856 for (uint32_t i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) {
858 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i];
859 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp;
865 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
867 APInt A = API1, B = API2;
870 B = APIntOps::urem(A, B);
876 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, uint32_t width) {
883 // Get the sign bit from the highest order bit
884 bool isNeg = T.I >> 63;
886 // Get the 11-bit exponent and adjust for the 1023 bit bias
887 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
889 // If the exponent is negative, the value is < 0 so just return 0.
891 return APInt(width, 0u);
893 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
894 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52;
896 // If the exponent doesn't shift all bits out of the mantissa
898 return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
899 APInt(width, mantissa >> (52 - exp));
901 // If the client didn't provide enough bits for us to shift the mantissa into
902 // then the result is undefined, just return 0
903 if (width <= exp - 52)
904 return APInt(width, 0);
906 // Otherwise, we have to shift the mantissa bits up to the right location
907 APInt Tmp(width, mantissa);
908 Tmp = Tmp.shl(exp - 52);
909 return isNeg ? -Tmp : Tmp;
912 /// RoundToDouble - This function convert this APInt to a double.
913 /// The layout for double is as following (IEEE Standard 754):
914 /// --------------------------------------
915 /// | Sign Exponent Fraction Bias |
916 /// |-------------------------------------- |
917 /// | 1[63] 11[62-52] 52[51-00] 1023 |
918 /// --------------------------------------
919 double APInt::roundToDouble(bool isSigned) const {
921 // Handle the simple case where the value is contained in one uint64_t.
922 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
924 int64_t sext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
930 // Determine if the value is negative.
931 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
933 // Construct the absolute value if we're negative.
934 APInt Tmp(isNeg ? -(*this) : (*this));
936 // Figure out how many bits we're using.
937 uint32_t n = Tmp.getActiveBits();
939 // The exponent (without bias normalization) is just the number of bits
940 // we are using. Note that the sign bit is gone since we constructed the
944 // Return infinity for exponent overflow
946 if (!isSigned || !isNeg)
947 return std::numeric_limits<double>::infinity();
949 return -std::numeric_limits<double>::infinity();
951 exp += 1023; // Increment for 1023 bias
953 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
954 // extract the high 52 bits from the correct words in pVal.
956 unsigned hiWord = whichWord(n-1);
958 mantissa = Tmp.pVal[0];
960 mantissa >>= n - 52; // shift down, we want the top 52 bits.
962 assert(hiWord > 0 && "huh?");
963 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
964 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
965 mantissa = hibits | lobits;
968 // The leading bit of mantissa is implicit, so get rid of it.
969 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
974 T.I = sign | (exp << 52) | mantissa;
978 // Truncate to new width.
979 APInt &APInt::trunc(uint32_t width) {
980 assert(width < BitWidth && "Invalid APInt Truncate request");
981 assert(width >= MIN_INT_BITS && "Can't truncate to 0 bits");
982 uint32_t wordsBefore = getNumWords();
984 uint32_t wordsAfter = getNumWords();
985 if (wordsBefore != wordsAfter) {
986 if (wordsAfter == 1) {
987 uint64_t *tmp = pVal;
991 uint64_t *newVal = getClearedMemory(wordsAfter);
992 for (uint32_t i = 0; i < wordsAfter; ++i)
998 return clearUnusedBits();
1001 // Sign extend to a new width.
1002 APInt &APInt::sext(uint32_t width) {
1003 assert(width > BitWidth && "Invalid APInt SignExtend request");
1004 assert(width <= MAX_INT_BITS && "Too many bits");
1005 // If the sign bit isn't set, this is the same as zext.
1006 if (!isNegative()) {
1011 // The sign bit is set. First, get some facts
1012 uint32_t wordsBefore = getNumWords();
1013 uint32_t wordBits = BitWidth % APINT_BITS_PER_WORD;
1015 uint32_t wordsAfter = getNumWords();
1017 // Mask the high order word appropriately
1018 if (wordsBefore == wordsAfter) {
1019 uint32_t newWordBits = width % APINT_BITS_PER_WORD;
1020 // The extension is contained to the wordsBefore-1th word.
1021 uint64_t mask = ~0ULL;
1023 mask >>= APINT_BITS_PER_WORD - newWordBits;
1025 if (wordsBefore == 1)
1028 pVal[wordsBefore-1] |= mask;
1029 return clearUnusedBits();
1032 uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits;
1033 uint64_t *newVal = getMemory(wordsAfter);
1034 if (wordsBefore == 1)
1035 newVal[0] = VAL | mask;
1037 for (uint32_t i = 0; i < wordsBefore; ++i)
1038 newVal[i] = pVal[i];
1039 newVal[wordsBefore-1] |= mask;
1041 for (uint32_t i = wordsBefore; i < wordsAfter; i++)
1043 if (wordsBefore != 1)
1046 return clearUnusedBits();
1049 // Zero extend to a new width.
1050 APInt &APInt::zext(uint32_t width) {
1051 assert(width > BitWidth && "Invalid APInt ZeroExtend request");
1052 assert(width <= MAX_INT_BITS && "Too many bits");
1053 uint32_t wordsBefore = getNumWords();
1055 uint32_t wordsAfter = getNumWords();
1056 if (wordsBefore != wordsAfter) {
1057 uint64_t *newVal = getClearedMemory(wordsAfter);
1058 if (wordsBefore == 1)
1061 for (uint32_t i = 0; i < wordsBefore; ++i)
1062 newVal[i] = pVal[i];
1063 if (wordsBefore != 1)
1070 APInt &APInt::zextOrTrunc(uint32_t width) {
1071 if (BitWidth < width)
1073 if (BitWidth > width)
1074 return trunc(width);
1078 APInt &APInt::sextOrTrunc(uint32_t width) {
1079 if (BitWidth < width)
1081 if (BitWidth > width)
1082 return trunc(width);
1086 /// Arithmetic right-shift this APInt by shiftAmt.
1087 /// @brief Arithmetic right-shift function.
1088 APInt APInt::ashr(uint32_t shiftAmt) const {
1089 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1090 // Handle a degenerate case
1094 // Handle single word shifts with built-in ashr
1095 if (isSingleWord()) {
1096 if (shiftAmt == BitWidth)
1097 return APInt(BitWidth, 0); // undefined
1099 uint32_t SignBit = APINT_BITS_PER_WORD - BitWidth;
1100 return APInt(BitWidth,
1101 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1105 // If all the bits were shifted out, the result is, technically, undefined.
1106 // We return -1 if it was negative, 0 otherwise. We check this early to avoid
1107 // issues in the algorithm below.
1108 if (shiftAmt == BitWidth) {
1110 return APInt(BitWidth, -1ULL);
1112 return APInt(BitWidth, 0);
1115 // Create some space for the result.
1116 uint64_t * val = new uint64_t[getNumWords()];
1118 // Compute some values needed by the following shift algorithms
1119 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word
1120 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift
1121 uint32_t breakWord = getNumWords() - 1 - offset; // last word affected
1122 uint32_t bitsInWord = whichBit(BitWidth); // how many bits in last word?
1123 if (bitsInWord == 0)
1124 bitsInWord = APINT_BITS_PER_WORD;
1126 // If we are shifting whole words, just move whole words
1127 if (wordShift == 0) {
1128 // Move the words containing significant bits
1129 for (uint32_t i = 0; i <= breakWord; ++i)
1130 val[i] = pVal[i+offset]; // move whole word
1132 // Adjust the top significant word for sign bit fill, if negative
1134 if (bitsInWord < APINT_BITS_PER_WORD)
1135 val[breakWord] |= ~0ULL << bitsInWord; // set high bits
1137 // Shift the low order words
1138 for (uint32_t i = 0; i < breakWord; ++i) {
1139 // This combines the shifted corresponding word with the low bits from
1140 // the next word (shifted into this word's high bits).
1141 val[i] = (pVal[i+offset] >> wordShift) |
1142 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1145 // Shift the break word. In this case there are no bits from the next word
1146 // to include in this word.
1147 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1149 // Deal with sign extenstion in the break word, and possibly the word before
1152 if (wordShift > bitsInWord) {
1155 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord));
1156 val[breakWord] |= ~0ULL;
1158 val[breakWord] |= (~0ULL << (bitsInWord - wordShift));
1162 // Remaining words are 0 or -1, just assign them.
1163 uint64_t fillValue = (isNegative() ? -1ULL : 0);
1164 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1166 return APInt(val, BitWidth).clearUnusedBits();
1169 /// Logical right-shift this APInt by shiftAmt.
1170 /// @brief Logical right-shift function.
1171 APInt APInt::lshr(uint32_t shiftAmt) const {
1172 if (isSingleWord()) {
1173 if (shiftAmt == BitWidth)
1174 return APInt(BitWidth, 0);
1176 return APInt(BitWidth, this->VAL >> shiftAmt);
1179 // If all the bits were shifted out, the result is 0. This avoids issues
1180 // with shifting by the size of the integer type, which produces undefined
1181 // results. We define these "undefined results" to always be 0.
1182 if (shiftAmt == BitWidth)
1183 return APInt(BitWidth, 0);
1185 // If none of the bits are shifted out, the result is *this. This avoids
1186 // issues with shifting byt he size of the integer type, which produces
1187 // undefined results in the code below. This is also an optimization.
1191 // Create some space for the result.
1192 uint64_t * val = new uint64_t[getNumWords()];
1194 // If we are shifting less than a word, compute the shift with a simple carry
1195 if (shiftAmt < APINT_BITS_PER_WORD) {
1197 for (int i = getNumWords()-1; i >= 0; --i) {
1198 val[i] = (pVal[i] >> shiftAmt) | carry;
1199 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1201 return APInt(val, BitWidth).clearUnusedBits();
1204 // Compute some values needed by the remaining shift algorithms
1205 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1206 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1208 // If we are shifting whole words, just move whole words
1209 if (wordShift == 0) {
1210 for (uint32_t i = 0; i < getNumWords() - offset; ++i)
1211 val[i] = pVal[i+offset];
1212 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
1214 return APInt(val,BitWidth).clearUnusedBits();
1217 // Shift the low order words
1218 uint32_t breakWord = getNumWords() - offset -1;
1219 for (uint32_t i = 0; i < breakWord; ++i)
1220 val[i] = (pVal[i+offset] >> wordShift) |
1221 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1222 // Shift the break word.
1223 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1225 // Remaining words are 0
1226 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1228 return APInt(val, BitWidth).clearUnusedBits();
1231 /// Left-shift this APInt by shiftAmt.
1232 /// @brief Left-shift function.
1233 APInt APInt::shl(uint32_t shiftAmt) const {
1234 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1235 if (isSingleWord()) {
1236 if (shiftAmt == BitWidth)
1237 return APInt(BitWidth, 0); // avoid undefined shift results
1238 return APInt(BitWidth, VAL << shiftAmt);
1241 // If all the bits were shifted out, the result is 0. This avoids issues
1242 // with shifting by the size of the integer type, which produces undefined
1243 // results. We define these "undefined results" to always be 0.
1244 if (shiftAmt == BitWidth)
1245 return APInt(BitWidth, 0);
1247 // If none of the bits are shifted out, the result is *this. This avoids a
1248 // lshr by the words size in the loop below which can produce incorrect
1249 // results. It also avoids the expensive computation below for a common case.
1253 // Create some space for the result.
1254 uint64_t * val = new uint64_t[getNumWords()];
1256 // If we are shifting less than a word, do it the easy way
1257 if (shiftAmt < APINT_BITS_PER_WORD) {
1259 for (uint32_t i = 0; i < getNumWords(); i++) {
1260 val[i] = pVal[i] << shiftAmt | carry;
1261 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1263 return APInt(val, BitWidth).clearUnusedBits();
1266 // Compute some values needed by the remaining shift algorithms
1267 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1268 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1270 // If we are shifting whole words, just move whole words
1271 if (wordShift == 0) {
1272 for (uint32_t i = 0; i < offset; i++)
1274 for (uint32_t i = offset; i < getNumWords(); i++)
1275 val[i] = pVal[i-offset];
1276 return APInt(val,BitWidth).clearUnusedBits();
1279 // Copy whole words from this to Result.
1280 uint32_t i = getNumWords() - 1;
1281 for (; i > offset; --i)
1282 val[i] = pVal[i-offset] << wordShift |
1283 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1284 val[offset] = pVal[0] << wordShift;
1285 for (i = 0; i < offset; ++i)
1287 return APInt(val, BitWidth).clearUnusedBits();
1290 APInt APInt::rotl(uint32_t rotateAmt) const {
1293 // Don't get too fancy, just use existing shift/or facilities
1297 lo.lshr(BitWidth - rotateAmt);
1301 APInt APInt::rotr(uint32_t rotateAmt) const {
1304 // Don't get too fancy, just use existing shift/or facilities
1308 hi.shl(BitWidth - rotateAmt);
1312 // Square Root - this method computes and returns the square root of "this".
1313 // Three mechanisms are used for computation. For small values (<= 5 bits),
1314 // a table lookup is done. This gets some performance for common cases. For
1315 // values using less than 52 bits, the value is converted to double and then
1316 // the libc sqrt function is called. The result is rounded and then converted
1317 // back to a uint64_t which is then used to construct the result. Finally,
1318 // the Babylonian method for computing square roots is used.
1319 APInt APInt::sqrt() const {
1321 // Determine the magnitude of the value.
1322 uint32_t magnitude = getActiveBits();
1324 // Use a fast table for some small values. This also gets rid of some
1325 // rounding errors in libc sqrt for small values.
1326 if (magnitude <= 5) {
1327 static const uint8_t results[32] = {
1330 /* 3- 6 */ 2, 2, 2, 2,
1331 /* 7-12 */ 3, 3, 3, 3, 3, 3,
1332 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1333 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1336 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]);
1339 // If the magnitude of the value fits in less than 52 bits (the precision of
1340 // an IEEE double precision floating point value), then we can use the
1341 // libc sqrt function which will probably use a hardware sqrt computation.
1342 // This should be faster than the algorithm below.
1343 if (magnitude < 52) {
1345 // Amazingly, VC++ doesn't have round().
1346 return APInt(BitWidth,
1347 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0]))) + 0.5);
1349 return APInt(BitWidth,
1350 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0])))));
1354 // Okay, all the short cuts are exhausted. We must compute it. The following
1355 // is a classical Babylonian method for computing the square root. This code
1356 // was adapted to APINt from a wikipedia article on such computations.
1357 // See http://www.wikipedia.org/ and go to the page named
1358 // Calculate_an_integer_square_root.
1359 uint32_t nbits = BitWidth, i = 4;
1360 APInt testy(BitWidth, 16);
1361 APInt x_old(BitWidth, 1);
1362 APInt x_new(BitWidth, 0);
1363 APInt two(BitWidth, 2);
1365 // Select a good starting value using binary logarithms.
1366 for (;; i += 2, testy = testy.shl(2))
1367 if (i >= nbits || this->ule(testy)) {
1368 x_old = x_old.shl(i / 2);
1372 // Use the Babylonian method to arrive at the integer square root:
1374 x_new = (this->udiv(x_old) + x_old).udiv(two);
1375 if (x_old.ule(x_new))
1380 // Make sure we return the closest approximation
1381 // NOTE: The rounding calculation below is correct. It will produce an
1382 // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1383 // determined to be a rounding issue with pari/gp as it begins to use a
1384 // floating point representation after 192 bits. There are no discrepancies
1385 // between this algorithm and pari/gp for bit widths < 192 bits.
1386 APInt square(x_old * x_old);
1387 APInt nextSquare((x_old + 1) * (x_old +1));
1388 if (this->ult(square))
1390 else if (this->ule(nextSquare)) {
1391 APInt midpoint((nextSquare - square).udiv(two));
1392 APInt offset(*this - square);
1393 if (offset.ult(midpoint))
1398 assert(0 && "Error in APInt::sqrt computation");
1402 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1403 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1404 /// variables here have the same names as in the algorithm. Comments explain
1405 /// the algorithm and any deviation from it.
1406 static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
1407 uint32_t m, uint32_t n) {
1408 assert(u && "Must provide dividend");
1409 assert(v && "Must provide divisor");
1410 assert(q && "Must provide quotient");
1411 assert(u != v && u != q && v != q && "Must us different memory");
1412 assert(n>1 && "n must be > 1");
1414 // Knuth uses the value b as the base of the number system. In our case b
1415 // is 2^31 so we just set it to -1u.
1416 uint64_t b = uint64_t(1) << 32;
1418 DEBUG(cerr << "KnuthDiv: m=" << m << " n=" << n << '\n');
1419 DEBUG(cerr << "KnuthDiv: original:");
1420 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1421 DEBUG(cerr << " by");
1422 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1423 DEBUG(cerr << '\n');
1424 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1425 // u and v by d. Note that we have taken Knuth's advice here to use a power
1426 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1427 // 2 allows us to shift instead of multiply and it is easy to determine the
1428 // shift amount from the leading zeros. We are basically normalizing the u
1429 // and v so that its high bits are shifted to the top of v's range without
1430 // overflow. Note that this can require an extra word in u so that u must
1431 // be of length m+n+1.
1432 uint32_t shift = CountLeadingZeros_32(v[n-1]);
1433 uint32_t v_carry = 0;
1434 uint32_t u_carry = 0;
1436 for (uint32_t i = 0; i < m+n; ++i) {
1437 uint32_t u_tmp = u[i] >> (32 - shift);
1438 u[i] = (u[i] << shift) | u_carry;
1441 for (uint32_t i = 0; i < n; ++i) {
1442 uint32_t v_tmp = v[i] >> (32 - shift);
1443 v[i] = (v[i] << shift) | v_carry;
1448 DEBUG(cerr << "KnuthDiv: normal:");
1449 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1450 DEBUG(cerr << " by");
1451 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1452 DEBUG(cerr << '\n');
1454 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1457 DEBUG(cerr << "KnuthDiv: quotient digit #" << j << '\n');
1458 // D3. [Calculate q'.].
1459 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1460 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1461 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1462 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1463 // on v[n-2] determines at high speed most of the cases in which the trial
1464 // value qp is one too large, and it eliminates all cases where qp is two
1466 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1467 DEBUG(cerr << "KnuthDiv: dividend == " << dividend << '\n');
1468 uint64_t qp = dividend / v[n-1];
1469 uint64_t rp = dividend % v[n-1];
1470 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1473 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1476 DEBUG(cerr << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1478 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1479 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1480 // consists of a simple multiplication by a one-place number, combined with
1483 for (uint32_t i = 0; i < n; ++i) {
1484 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1485 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1486 bool borrow = subtrahend > u_tmp;
1487 DEBUG(cerr << "KnuthDiv: u_tmp == " << u_tmp
1488 << ", subtrahend == " << subtrahend
1489 << ", borrow = " << borrow << '\n');
1491 uint64_t result = u_tmp - subtrahend;
1493 u[k++] = result & (b-1); // subtract low word
1494 u[k++] = result >> 32; // subtract high word
1495 while (borrow && k <= m+n) { // deal with borrow to the left
1501 DEBUG(cerr << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1504 DEBUG(cerr << "KnuthDiv: after subtraction:");
1505 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1506 DEBUG(cerr << '\n');
1507 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1508 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1509 // true value plus b**(n+1), namely as the b's complement of
1510 // the true value, and a "borrow" to the left should be remembered.
1513 bool carry = true; // true because b's complement is "complement + 1"
1514 for (uint32_t i = 0; i <= m+n; ++i) {
1515 u[i] = ~u[i] + carry; // b's complement
1516 carry = carry && u[i] == 0;
1519 DEBUG(cerr << "KnuthDiv: after complement:");
1520 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1521 DEBUG(cerr << '\n');
1523 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1524 // negative, go to step D6; otherwise go on to step D7.
1527 // D6. [Add back]. The probability that this step is necessary is very
1528 // small, on the order of only 2/b. Make sure that test data accounts for
1529 // this possibility. Decrease q[j] by 1
1531 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1532 // A carry will occur to the left of u[j+n], and it should be ignored
1533 // since it cancels with the borrow that occurred in D4.
1535 for (uint32_t i = 0; i < n; i++) {
1536 uint32_t limit = std::min(u[j+i],v[i]);
1537 u[j+i] += v[i] + carry;
1538 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1542 DEBUG(cerr << "KnuthDiv: after correction:");
1543 DEBUG(for (int i = m+n; i >=0; i--) cerr <<" " << u[i]);
1544 DEBUG(cerr << "\nKnuthDiv: digit result = " << q[j] << '\n');
1546 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1549 DEBUG(cerr << "KnuthDiv: quotient:");
1550 DEBUG(for (int i = m; i >=0; i--) cerr <<" " << q[i]);
1551 DEBUG(cerr << '\n');
1553 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1554 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1555 // compute the remainder (urem uses this).
1557 // The value d is expressed by the "shift" value above since we avoided
1558 // multiplication by d by using a shift left. So, all we have to do is
1559 // shift right here. In order to mak
1562 DEBUG(cerr << "KnuthDiv: remainder:");
1563 for (int i = n-1; i >= 0; i--) {
1564 r[i] = (u[i] >> shift) | carry;
1565 carry = u[i] << (32 - shift);
1566 DEBUG(cerr << " " << r[i]);
1569 for (int i = n-1; i >= 0; i--) {
1571 DEBUG(cerr << " " << r[i]);
1574 DEBUG(cerr << '\n');
1576 DEBUG(cerr << std::setbase(10) << '\n');
1579 void APInt::divide(const APInt LHS, uint32_t lhsWords,
1580 const APInt &RHS, uint32_t rhsWords,
1581 APInt *Quotient, APInt *Remainder)
1583 assert(lhsWords >= rhsWords && "Fractional result");
1585 // First, compose the values into an array of 32-bit words instead of
1586 // 64-bit words. This is a necessity of both the "short division" algorithm
1587 // and the the Knuth "classical algorithm" which requires there to be native
1588 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1589 // can't use 64-bit operands here because we don't have native results of
1590 // 128-bits. Furthremore, casting the 64-bit values to 32-bit values won't
1591 // work on large-endian machines.
1592 uint64_t mask = ~0ull >> (sizeof(uint32_t)*8);
1593 uint32_t n = rhsWords * 2;
1594 uint32_t m = (lhsWords * 2) - n;
1596 // Allocate space for the temporary values we need either on the stack, if
1597 // it will fit, or on the heap if it won't.
1598 uint32_t SPACE[128];
1603 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1606 Q = &SPACE[(m+n+1) + n];
1608 R = &SPACE[(m+n+1) + n + (m+n)];
1610 U = new uint32_t[m + n + 1];
1611 V = new uint32_t[n];
1612 Q = new uint32_t[m+n];
1614 R = new uint32_t[n];
1617 // Initialize the dividend
1618 memset(U, 0, (m+n+1)*sizeof(uint32_t));
1619 for (unsigned i = 0; i < lhsWords; ++i) {
1620 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1621 U[i * 2] = tmp & mask;
1622 U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1624 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1626 // Initialize the divisor
1627 memset(V, 0, (n)*sizeof(uint32_t));
1628 for (unsigned i = 0; i < rhsWords; ++i) {
1629 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1630 V[i * 2] = tmp & mask;
1631 V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1634 // initialize the quotient and remainder
1635 memset(Q, 0, (m+n) * sizeof(uint32_t));
1637 memset(R, 0, n * sizeof(uint32_t));
1639 // Now, adjust m and n for the Knuth division. n is the number of words in
1640 // the divisor. m is the number of words by which the dividend exceeds the
1641 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1642 // contain any zero words or the Knuth algorithm fails.
1643 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1647 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1650 // If we're left with only a single word for the divisor, Knuth doesn't work
1651 // so we implement the short division algorithm here. This is much simpler
1652 // and faster because we are certain that we can divide a 64-bit quantity
1653 // by a 32-bit quantity at hardware speed and short division is simply a
1654 // series of such operations. This is just like doing short division but we
1655 // are using base 2^32 instead of base 10.
1656 assert(n != 0 && "Divide by zero?");
1658 uint32_t divisor = V[0];
1659 uint32_t remainder = 0;
1660 for (int i = m+n-1; i >= 0; i--) {
1661 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1662 if (partial_dividend == 0) {
1665 } else if (partial_dividend < divisor) {
1667 remainder = partial_dividend;
1668 } else if (partial_dividend == divisor) {
1672 Q[i] = partial_dividend / divisor;
1673 remainder = partial_dividend - (Q[i] * divisor);
1679 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1681 KnuthDiv(U, V, Q, R, m, n);
1684 // If the caller wants the quotient
1686 // Set up the Quotient value's memory.
1687 if (Quotient->BitWidth != LHS.BitWidth) {
1688 if (Quotient->isSingleWord())
1691 delete [] Quotient->pVal;
1692 Quotient->BitWidth = LHS.BitWidth;
1693 if (!Quotient->isSingleWord())
1694 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1698 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1700 if (lhsWords == 1) {
1702 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1703 if (Quotient->isSingleWord())
1704 Quotient->VAL = tmp;
1706 Quotient->pVal[0] = tmp;
1708 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1709 for (unsigned i = 0; i < lhsWords; ++i)
1711 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1715 // If the caller wants the remainder
1717 // Set up the Remainder value's memory.
1718 if (Remainder->BitWidth != RHS.BitWidth) {
1719 if (Remainder->isSingleWord())
1722 delete [] Remainder->pVal;
1723 Remainder->BitWidth = RHS.BitWidth;
1724 if (!Remainder->isSingleWord())
1725 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1729 // The remainder is in R. Reconstitute the remainder into Remainder's low
1731 if (rhsWords == 1) {
1733 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1734 if (Remainder->isSingleWord())
1735 Remainder->VAL = tmp;
1737 Remainder->pVal[0] = tmp;
1739 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1740 for (unsigned i = 0; i < rhsWords; ++i)
1741 Remainder->pVal[i] =
1742 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1746 // Clean up the memory we allocated.
1747 if (U != &SPACE[0]) {
1755 APInt APInt::udiv(const APInt& RHS) const {
1756 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1758 // First, deal with the easy case
1759 if (isSingleWord()) {
1760 assert(RHS.VAL != 0 && "Divide by zero?");
1761 return APInt(BitWidth, VAL / RHS.VAL);
1764 // Get some facts about the LHS and RHS number of bits and words
1765 uint32_t rhsBits = RHS.getActiveBits();
1766 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1767 assert(rhsWords && "Divided by zero???");
1768 uint32_t lhsBits = this->getActiveBits();
1769 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1771 // Deal with some degenerate cases
1774 return APInt(BitWidth, 0);
1775 else if (lhsWords < rhsWords || this->ult(RHS)) {
1776 // X / Y ===> 0, iff X < Y
1777 return APInt(BitWidth, 0);
1778 } else if (*this == RHS) {
1780 return APInt(BitWidth, 1);
1781 } else if (lhsWords == 1 && rhsWords == 1) {
1782 // All high words are zero, just use native divide
1783 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1786 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1787 APInt Quotient(1,0); // to hold result.
1788 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0);
1792 APInt APInt::urem(const APInt& RHS) const {
1793 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1794 if (isSingleWord()) {
1795 assert(RHS.VAL != 0 && "Remainder by zero?");
1796 return APInt(BitWidth, VAL % RHS.VAL);
1799 // Get some facts about the LHS
1800 uint32_t lhsBits = getActiveBits();
1801 uint32_t lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1803 // Get some facts about the RHS
1804 uint32_t rhsBits = RHS.getActiveBits();
1805 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1806 assert(rhsWords && "Performing remainder operation by zero ???");
1808 // Check the degenerate cases
1809 if (lhsWords == 0) {
1811 return APInt(BitWidth, 0);
1812 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1813 // X % Y ===> X, iff X < Y
1815 } else if (*this == RHS) {
1817 return APInt(BitWidth, 0);
1818 } else if (lhsWords == 1) {
1819 // All high words are zero, just use native remainder
1820 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
1823 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1824 APInt Remainder(1,0);
1825 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder);
1829 void APInt::udivrem(const APInt &LHS, const APInt &RHS,
1830 APInt &Quotient, APInt &Remainder) {
1831 // Get some size facts about the dividend and divisor
1832 uint32_t lhsBits = LHS.getActiveBits();
1833 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1834 uint32_t rhsBits = RHS.getActiveBits();
1835 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1837 // Check the degenerate cases
1838 if (lhsWords == 0) {
1839 Quotient = 0; // 0 / Y ===> 0
1840 Remainder = 0; // 0 % Y ===> 0
1844 if (lhsWords < rhsWords || LHS.ult(RHS)) {
1845 Quotient = 0; // X / Y ===> 0, iff X < Y
1846 Remainder = LHS; // X % Y ===> X, iff X < Y
1851 Quotient = 1; // X / X ===> 1
1852 Remainder = 0; // X % X ===> 0;
1856 if (lhsWords == 1 && rhsWords == 1) {
1857 // There is only one word to consider so use the native versions.
1858 if (LHS.isSingleWord()) {
1859 Quotient = APInt(LHS.getBitWidth(), LHS.VAL / RHS.VAL);
1860 Remainder = APInt(LHS.getBitWidth(), LHS.VAL % RHS.VAL);
1862 Quotient = APInt(LHS.getBitWidth(), LHS.pVal[0] / RHS.pVal[0]);
1863 Remainder = APInt(LHS.getBitWidth(), LHS.pVal[0] % RHS.pVal[0]);
1868 // Okay, lets do it the long way
1869 divide(LHS, lhsWords, RHS, rhsWords, &Quotient, &Remainder);
1872 void APInt::fromString(uint32_t numbits, const char *str, uint32_t slen,
1874 // Check our assumptions here
1875 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1876 "Radix should be 2, 8, 10, or 16!");
1877 assert(str && "String is null?");
1878 bool isNeg = str[0] == '-';
1881 assert((slen <= numbits || radix != 2) && "Insufficient bit width");
1882 assert((slen*3 <= numbits || radix != 8) && "Insufficient bit width");
1883 assert((slen*4 <= numbits || radix != 16) && "Insufficient bit width");
1884 assert(((slen*64)/22 <= numbits || radix != 10) && "Insufficient bit width");
1887 if (!isSingleWord())
1888 pVal = getClearedMemory(getNumWords());
1890 // Figure out if we can shift instead of multiply
1891 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
1893 // Set up an APInt for the digit to add outside the loop so we don't
1894 // constantly construct/destruct it.
1895 APInt apdigit(getBitWidth(), 0);
1896 APInt apradix(getBitWidth(), radix);
1898 // Enter digit traversal loop
1899 for (unsigned i = 0; i < slen; i++) {
1902 char cdigit = str[i];
1904 if (!isxdigit(cdigit))
1905 assert(0 && "Invalid hex digit in string");
1906 if (isdigit(cdigit))
1907 digit = cdigit - '0';
1908 else if (cdigit >= 'a')
1909 digit = cdigit - 'a' + 10;
1910 else if (cdigit >= 'A')
1911 digit = cdigit - 'A' + 10;
1913 assert(0 && "huh? we shouldn't get here");
1914 } else if (isdigit(cdigit)) {
1915 digit = cdigit - '0';
1917 assert(0 && "Invalid character in digit string");
1920 // Shift or multiply the value by the radix
1926 // Add in the digit we just interpreted
1927 if (apdigit.isSingleWord())
1928 apdigit.VAL = digit;
1930 apdigit.pVal[0] = digit;
1933 // If its negative, put it in two's complement form
1940 std::string APInt::toString(uint8_t radix, bool wantSigned) const {
1941 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1942 "Radix should be 2, 8, 10, or 16!");
1943 static const char *digits[] = {
1944 "0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"
1947 uint32_t bits_used = getActiveBits();
1948 if (isSingleWord()) {
1950 const char *format = (radix == 10 ? (wantSigned ? "%lld" : "%llu") :
1951 (radix == 16 ? "%llX" : (radix == 8 ? "%llo" : 0)));
1954 int64_t sextVal = (int64_t(VAL) << (APINT_BITS_PER_WORD-BitWidth)) >>
1955 (APINT_BITS_PER_WORD-BitWidth);
1956 sprintf(buf, format, sextVal);
1958 sprintf(buf, format, VAL);
1963 uint32_t bit = v & 1;
1965 buf[bits_used] = digits[bit][0];
1974 // For the 2, 8 and 16 bit cases, we can just shift instead of divide
1975 // because the number of bits per digit (1,3 and 4 respectively) divides
1976 // equaly. We just shift until there value is zero.
1978 // First, check for a zero value and just short circuit the logic below.
1983 size_t insert_at = 0;
1984 if (wantSigned && this->isNegative()) {
1985 // They want to print the signed version and it is a negative value
1986 // Flip the bits and add one to turn it into the equivalent positive
1987 // value and put a '-' in the result.
1993 // Just shift tmp right for each digit width until it becomes zero
1994 uint32_t shift = (radix == 16 ? 4 : (radix == 8 ? 3 : 1));
1995 uint64_t mask = radix - 1;
1996 APInt zero(tmp.getBitWidth(), 0);
1997 while (tmp.ne(zero)) {
1998 unsigned digit = (tmp.isSingleWord() ? tmp.VAL : tmp.pVal[0]) & mask;
1999 result.insert(insert_at, digits[digit]);
2000 tmp = tmp.lshr(shift);
2007 APInt divisor(4, radix);
2008 APInt zero(tmp.getBitWidth(), 0);
2009 size_t insert_at = 0;
2010 if (wantSigned && tmp[BitWidth-1]) {
2011 // They want to print the signed version and it is a negative value
2012 // Flip the bits and add one to turn it into the equivalent positive
2013 // value and put a '-' in the result.
2019 if (tmp == APInt(tmp.getBitWidth(), 0))
2021 else while (tmp.ne(zero)) {
2023 APInt tmp2(tmp.getBitWidth(), 0);
2024 divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
2026 uint32_t digit = APdigit.getZExtValue();
2027 assert(digit < radix && "divide failed");
2028 result.insert(insert_at,digits[digit]);
2035 void APInt::dump() const
2037 cerr << "APInt(" << BitWidth << ")=" << std::setbase(16);
2040 else for (unsigned i = getNumWords(); i > 0; i--) {
2041 cerr << pVal[i-1] << " ";
2043 cerr << " U(" << this->toStringUnsigned(10) << ") S("
2044 << this->toStringSigned(10) << ")" << std::setbase(10);
2047 // This implements a variety of operations on a representation of
2048 // arbitrary precision, two's-complement, bignum integer values.
2050 /* Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe
2051 and unrestricting assumption. */
2052 COMPILE_TIME_ASSERT(integerPartWidth % 2 == 0);
2054 /* Some handy functions local to this file. */
2057 /* Returns the integer part with the least significant BITS set.
2058 BITS cannot be zero. */
2060 lowBitMask(unsigned int bits)
2062 assert (bits != 0 && bits <= integerPartWidth);
2064 return ~(integerPart) 0 >> (integerPartWidth - bits);
2067 /* Returns the value of the lower half of PART. */
2069 lowHalf(integerPart part)
2071 return part & lowBitMask(integerPartWidth / 2);
2074 /* Returns the value of the upper half of PART. */
2076 highHalf(integerPart part)
2078 return part >> (integerPartWidth / 2);
2081 /* Returns the bit number of the most significant set bit of a part.
2082 If the input number has no bits set -1U is returned. */
2084 partMSB(integerPart value)
2086 unsigned int n, msb;
2091 n = integerPartWidth / 2;
2106 /* Returns the bit number of the least significant set bit of a
2107 part. If the input number has no bits set -1U is returned. */
2109 partLSB(integerPart value)
2111 unsigned int n, lsb;
2116 lsb = integerPartWidth - 1;
2117 n = integerPartWidth / 2;
2132 /* Sets the least significant part of a bignum to the input value, and
2133 zeroes out higher parts. */
2135 APInt::tcSet(integerPart *dst, integerPart part, unsigned int parts)
2142 for(i = 1; i < parts; i++)
2146 /* Assign one bignum to another. */
2148 APInt::tcAssign(integerPart *dst, const integerPart *src, unsigned int parts)
2152 for(i = 0; i < parts; i++)
2156 /* Returns true if a bignum is zero, false otherwise. */
2158 APInt::tcIsZero(const integerPart *src, unsigned int parts)
2162 for(i = 0; i < parts; i++)
2169 /* Extract the given bit of a bignum; returns 0 or 1. */
2171 APInt::tcExtractBit(const integerPart *parts, unsigned int bit)
2173 return(parts[bit / integerPartWidth]
2174 & ((integerPart) 1 << bit % integerPartWidth)) != 0;
2177 /* Set the given bit of a bignum. */
2179 APInt::tcSetBit(integerPart *parts, unsigned int bit)
2181 parts[bit / integerPartWidth] |= (integerPart) 1 << (bit % integerPartWidth);
2184 /* Returns the bit number of the least significant set bit of a
2185 number. If the input number has no bits set -1U is returned. */
2187 APInt::tcLSB(const integerPart *parts, unsigned int n)
2189 unsigned int i, lsb;
2191 for(i = 0; i < n; i++) {
2192 if (parts[i] != 0) {
2193 lsb = partLSB(parts[i]);
2195 return lsb + i * integerPartWidth;
2202 /* Returns the bit number of the most significant set bit of a number.
2203 If the input number has no bits set -1U is returned. */
2205 APInt::tcMSB(const integerPart *parts, unsigned int n)
2212 if (parts[n] != 0) {
2213 msb = partMSB(parts[n]);
2215 return msb + n * integerPartWidth;
2222 /* Copy the bit vector of width srcBITS from SRC, starting at bit
2223 srcLSB, to DST, of dstCOUNT parts, such that the bit srcLSB becomes
2224 the least significant bit of DST. All high bits above srcBITS in
2225 DST are zero-filled. */
2227 APInt::tcExtract(integerPart *dst, unsigned int dstCount, const integerPart *src,
2228 unsigned int srcBits, unsigned int srcLSB)
2230 unsigned int firstSrcPart, dstParts, shift, n;
2232 dstParts = (srcBits + integerPartWidth - 1) / integerPartWidth;
2233 assert (dstParts <= dstCount);
2235 firstSrcPart = srcLSB / integerPartWidth;
2236 tcAssign (dst, src + firstSrcPart, dstParts);
2238 shift = srcLSB % integerPartWidth;
2239 tcShiftRight (dst, dstParts, shift);
2241 /* We now have (dstParts * integerPartWidth - shift) bits from SRC
2242 in DST. If this is less that srcBits, append the rest, else
2243 clear the high bits. */
2244 n = dstParts * integerPartWidth - shift;
2246 integerPart mask = lowBitMask (srcBits - n);
2247 dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask)
2248 << n % integerPartWidth);
2249 } else if (n > srcBits) {
2250 if (srcBits % integerPartWidth)
2251 dst[dstParts - 1] &= lowBitMask (srcBits % integerPartWidth);
2254 /* Clear high parts. */
2255 while (dstParts < dstCount)
2256 dst[dstParts++] = 0;
2259 /* DST += RHS + C where C is zero or one. Returns the carry flag. */
2261 APInt::tcAdd(integerPart *dst, const integerPart *rhs,
2262 integerPart c, unsigned int parts)
2268 for(i = 0; i < parts; i++) {
2273 dst[i] += rhs[i] + 1;
2284 /* DST -= RHS + C where C is zero or one. Returns the carry flag. */
2286 APInt::tcSubtract(integerPart *dst, const integerPart *rhs,
2287 integerPart c, unsigned int parts)
2293 for(i = 0; i < parts; i++) {
2298 dst[i] -= rhs[i] + 1;
2309 /* Negate a bignum in-place. */
2311 APInt::tcNegate(integerPart *dst, unsigned int parts)
2313 tcComplement(dst, parts);
2314 tcIncrement(dst, parts);
2317 /* DST += SRC * MULTIPLIER + CARRY if add is true
2318 DST = SRC * MULTIPLIER + CARRY if add is false
2320 Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC
2321 they must start at the same point, i.e. DST == SRC.
2323 If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is
2324 returned. Otherwise DST is filled with the least significant
2325 DSTPARTS parts of the result, and if all of the omitted higher
2326 parts were zero return zero, otherwise overflow occurred and
2329 APInt::tcMultiplyPart(integerPart *dst, const integerPart *src,
2330 integerPart multiplier, integerPart carry,
2331 unsigned int srcParts, unsigned int dstParts,
2336 /* Otherwise our writes of DST kill our later reads of SRC. */
2337 assert(dst <= src || dst >= src + srcParts);
2338 assert(dstParts <= srcParts + 1);
2340 /* N loops; minimum of dstParts and srcParts. */
2341 n = dstParts < srcParts ? dstParts: srcParts;
2343 for(i = 0; i < n; i++) {
2344 integerPart low, mid, high, srcPart;
2346 /* [ LOW, HIGH ] = MULTIPLIER * SRC[i] + DST[i] + CARRY.
2348 This cannot overflow, because
2350 (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1)
2352 which is less than n^2. */
2356 if (multiplier == 0 || srcPart == 0) {
2360 low = lowHalf(srcPart) * lowHalf(multiplier);
2361 high = highHalf(srcPart) * highHalf(multiplier);
2363 mid = lowHalf(srcPart) * highHalf(multiplier);
2364 high += highHalf(mid);
2365 mid <<= integerPartWidth / 2;
2366 if (low + mid < low)
2370 mid = highHalf(srcPart) * lowHalf(multiplier);
2371 high += highHalf(mid);
2372 mid <<= integerPartWidth / 2;
2373 if (low + mid < low)
2377 /* Now add carry. */
2378 if (low + carry < low)
2384 /* And now DST[i], and store the new low part there. */
2385 if (low + dst[i] < low)
2395 /* Full multiplication, there is no overflow. */
2396 assert(i + 1 == dstParts);
2400 /* We overflowed if there is carry. */
2404 /* We would overflow if any significant unwritten parts would be
2405 non-zero. This is true if any remaining src parts are non-zero
2406 and the multiplier is non-zero. */
2408 for(; i < srcParts; i++)
2412 /* We fitted in the narrow destination. */
2417 /* DST = LHS * RHS, where DST has the same width as the operands and
2418 is filled with the least significant parts of the result. Returns
2419 one if overflow occurred, otherwise zero. DST must be disjoint
2420 from both operands. */
2422 APInt::tcMultiply(integerPart *dst, const integerPart *lhs,
2423 const integerPart *rhs, unsigned int parts)
2428 assert(dst != lhs && dst != rhs);
2431 tcSet(dst, 0, parts);
2433 for(i = 0; i < parts; i++)
2434 overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts,
2440 /* DST = LHS * RHS, where DST has width the sum of the widths of the
2441 operands. No overflow occurs. DST must be disjoint from both
2442 operands. Returns the number of parts required to hold the
2445 APInt::tcFullMultiply(integerPart *dst, const integerPart *lhs,
2446 const integerPart *rhs, unsigned int lhsParts,
2447 unsigned int rhsParts)
2449 /* Put the narrower number on the LHS for less loops below. */
2450 if (lhsParts > rhsParts) {
2451 return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts);
2455 assert(dst != lhs && dst != rhs);
2457 tcSet(dst, 0, rhsParts);
2459 for(n = 0; n < lhsParts; n++)
2460 tcMultiplyPart(&dst[n], rhs, lhs[n], 0, rhsParts, rhsParts + 1, true);
2462 n = lhsParts + rhsParts;
2464 return n - (dst[n - 1] == 0);
2468 /* If RHS is zero LHS and REMAINDER are left unchanged, return one.
2469 Otherwise set LHS to LHS / RHS with the fractional part discarded,
2470 set REMAINDER to the remainder, return zero. i.e.
2472 OLD_LHS = RHS * LHS + REMAINDER
2474 SCRATCH is a bignum of the same size as the operands and result for
2475 use by the routine; its contents need not be initialized and are
2476 destroyed. LHS, REMAINDER and SCRATCH must be distinct.
2479 APInt::tcDivide(integerPart *lhs, const integerPart *rhs,
2480 integerPart *remainder, integerPart *srhs,
2483 unsigned int n, shiftCount;
2486 assert(lhs != remainder && lhs != srhs && remainder != srhs);
2488 shiftCount = tcMSB(rhs, parts) + 1;
2489 if (shiftCount == 0)
2492 shiftCount = parts * integerPartWidth - shiftCount;
2493 n = shiftCount / integerPartWidth;
2494 mask = (integerPart) 1 << (shiftCount % integerPartWidth);
2496 tcAssign(srhs, rhs, parts);
2497 tcShiftLeft(srhs, parts, shiftCount);
2498 tcAssign(remainder, lhs, parts);
2499 tcSet(lhs, 0, parts);
2501 /* Loop, subtracting SRHS if REMAINDER is greater and adding that to
2506 compare = tcCompare(remainder, srhs, parts);
2508 tcSubtract(remainder, srhs, 0, parts);
2512 if (shiftCount == 0)
2515 tcShiftRight(srhs, parts, 1);
2516 if ((mask >>= 1) == 0)
2517 mask = (integerPart) 1 << (integerPartWidth - 1), n--;
2523 /* Shift a bignum left COUNT bits in-place. Shifted in bits are zero.
2524 There are no restrictions on COUNT. */
2526 APInt::tcShiftLeft(integerPart *dst, unsigned int parts, unsigned int count)
2529 unsigned int jump, shift;
2531 /* Jump is the inter-part jump; shift is is intra-part shift. */
2532 jump = count / integerPartWidth;
2533 shift = count % integerPartWidth;
2535 while (parts > jump) {
2540 /* dst[i] comes from the two parts src[i - jump] and, if we have
2541 an intra-part shift, src[i - jump - 1]. */
2542 part = dst[parts - jump];
2545 if (parts >= jump + 1)
2546 part |= dst[parts - jump - 1] >> (integerPartWidth - shift);
2557 /* Shift a bignum right COUNT bits in-place. Shifted in bits are
2558 zero. There are no restrictions on COUNT. */
2560 APInt::tcShiftRight(integerPart *dst, unsigned int parts, unsigned int count)
2563 unsigned int i, jump, shift;
2565 /* Jump is the inter-part jump; shift is is intra-part shift. */
2566 jump = count / integerPartWidth;
2567 shift = count % integerPartWidth;
2569 /* Perform the shift. This leaves the most significant COUNT bits
2570 of the result at zero. */
2571 for(i = 0; i < parts; i++) {
2574 if (i + jump >= parts) {
2577 part = dst[i + jump];
2580 if (i + jump + 1 < parts)
2581 part |= dst[i + jump + 1] << (integerPartWidth - shift);
2590 /* Bitwise and of two bignums. */
2592 APInt::tcAnd(integerPart *dst, const integerPart *rhs, unsigned int parts)
2596 for(i = 0; i < parts; i++)
2600 /* Bitwise inclusive or of two bignums. */
2602 APInt::tcOr(integerPart *dst, const integerPart *rhs, unsigned int parts)
2606 for(i = 0; i < parts; i++)
2610 /* Bitwise exclusive or of two bignums. */
2612 APInt::tcXor(integerPart *dst, const integerPart *rhs, unsigned int parts)
2616 for(i = 0; i < parts; i++)
2620 /* Complement a bignum in-place. */
2622 APInt::tcComplement(integerPart *dst, unsigned int parts)
2626 for(i = 0; i < parts; i++)
2630 /* Comparison (unsigned) of two bignums. */
2632 APInt::tcCompare(const integerPart *lhs, const integerPart *rhs,
2637 if (lhs[parts] == rhs[parts])
2640 if (lhs[parts] > rhs[parts])
2649 /* Increment a bignum in-place, return the carry flag. */
2651 APInt::tcIncrement(integerPart *dst, unsigned int parts)
2655 for(i = 0; i < parts; i++)
2662 /* Set the least significant BITS bits of a bignum, clear the
2665 APInt::tcSetLeastSignificantBits(integerPart *dst, unsigned int parts,
2671 while (bits > integerPartWidth) {
2672 dst[i++] = ~(integerPart) 0;
2673 bits -= integerPartWidth;
2677 dst[i++] = ~(integerPart) 0 >> (integerPartWidth - bits);