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(const APInt &shiftAmt) const {
1089 return ashr(shiftAmt.getLimitedValue(BitWidth));
1092 /// Arithmetic right-shift this APInt by shiftAmt.
1093 /// @brief Arithmetic right-shift function.
1094 APInt APInt::ashr(uint32_t shiftAmt) const {
1095 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1096 // Handle a degenerate case
1100 // Handle single word shifts with built-in ashr
1101 if (isSingleWord()) {
1102 if (shiftAmt == BitWidth)
1103 return APInt(BitWidth, 0); // undefined
1105 uint32_t SignBit = APINT_BITS_PER_WORD - BitWidth;
1106 return APInt(BitWidth,
1107 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
1111 // If all the bits were shifted out, the result is, technically, undefined.
1112 // We return -1 if it was negative, 0 otherwise. We check this early to avoid
1113 // issues in the algorithm below.
1114 if (shiftAmt == BitWidth) {
1116 return APInt(BitWidth, -1ULL);
1118 return APInt(BitWidth, 0);
1121 // Create some space for the result.
1122 uint64_t * val = new uint64_t[getNumWords()];
1124 // Compute some values needed by the following shift algorithms
1125 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word
1126 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift
1127 uint32_t breakWord = getNumWords() - 1 - offset; // last word affected
1128 uint32_t bitsInWord = whichBit(BitWidth); // how many bits in last word?
1129 if (bitsInWord == 0)
1130 bitsInWord = APINT_BITS_PER_WORD;
1132 // If we are shifting whole words, just move whole words
1133 if (wordShift == 0) {
1134 // Move the words containing significant bits
1135 for (uint32_t i = 0; i <= breakWord; ++i)
1136 val[i] = pVal[i+offset]; // move whole word
1138 // Adjust the top significant word for sign bit fill, if negative
1140 if (bitsInWord < APINT_BITS_PER_WORD)
1141 val[breakWord] |= ~0ULL << bitsInWord; // set high bits
1143 // Shift the low order words
1144 for (uint32_t i = 0; i < breakWord; ++i) {
1145 // This combines the shifted corresponding word with the low bits from
1146 // the next word (shifted into this word's high bits).
1147 val[i] = (pVal[i+offset] >> wordShift) |
1148 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1151 // Shift the break word. In this case there are no bits from the next word
1152 // to include in this word.
1153 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1155 // Deal with sign extenstion in the break word, and possibly the word before
1158 if (wordShift > bitsInWord) {
1161 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord));
1162 val[breakWord] |= ~0ULL;
1164 val[breakWord] |= (~0ULL << (bitsInWord - wordShift));
1168 // Remaining words are 0 or -1, just assign them.
1169 uint64_t fillValue = (isNegative() ? -1ULL : 0);
1170 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1172 return APInt(val, BitWidth).clearUnusedBits();
1175 /// Logical right-shift this APInt by shiftAmt.
1176 /// @brief Logical right-shift function.
1177 APInt APInt::lshr(const APInt &shiftAmt) const {
1178 return ashr(shiftAmt.getLimitedValue(BitWidth));
1181 /// Logical right-shift this APInt by shiftAmt.
1182 /// @brief Logical right-shift function.
1183 APInt APInt::lshr(uint32_t shiftAmt) const {
1184 if (isSingleWord()) {
1185 if (shiftAmt == BitWidth)
1186 return APInt(BitWidth, 0);
1188 return APInt(BitWidth, this->VAL >> shiftAmt);
1191 // If all the bits were shifted out, the result is 0. This avoids issues
1192 // with shifting by the size of the integer type, which produces undefined
1193 // results. We define these "undefined results" to always be 0.
1194 if (shiftAmt == BitWidth)
1195 return APInt(BitWidth, 0);
1197 // If none of the bits are shifted out, the result is *this. This avoids
1198 // issues with shifting byt he size of the integer type, which produces
1199 // undefined results in the code below. This is also an optimization.
1203 // Create some space for the result.
1204 uint64_t * val = new uint64_t[getNumWords()];
1206 // If we are shifting less than a word, compute the shift with a simple carry
1207 if (shiftAmt < APINT_BITS_PER_WORD) {
1209 for (int i = getNumWords()-1; i >= 0; --i) {
1210 val[i] = (pVal[i] >> shiftAmt) | carry;
1211 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1213 return APInt(val, BitWidth).clearUnusedBits();
1216 // Compute some values needed by the remaining shift algorithms
1217 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1218 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1220 // If we are shifting whole words, just move whole words
1221 if (wordShift == 0) {
1222 for (uint32_t i = 0; i < getNumWords() - offset; ++i)
1223 val[i] = pVal[i+offset];
1224 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
1226 return APInt(val,BitWidth).clearUnusedBits();
1229 // Shift the low order words
1230 uint32_t breakWord = getNumWords() - offset -1;
1231 for (uint32_t i = 0; i < breakWord; ++i)
1232 val[i] = (pVal[i+offset] >> wordShift) |
1233 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift));
1234 // Shift the break word.
1235 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1237 // Remaining words are 0
1238 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1240 return APInt(val, BitWidth).clearUnusedBits();
1243 /// Left-shift this APInt by shiftAmt.
1244 /// @brief Left-shift function.
1245 APInt APInt::shl(const APInt &shiftAmt) const {
1246 // It's undefined behavior in C to shift by BitWidth or greater, but
1247 return shl(shiftAmt.getLimitedValue(BitWidth));
1250 /// Left-shift this APInt by shiftAmt.
1251 /// @brief Left-shift function.
1252 APInt APInt::shl(uint32_t shiftAmt) const {
1253 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1254 if (isSingleWord()) {
1255 if (shiftAmt == BitWidth)
1256 return APInt(BitWidth, 0); // avoid undefined shift results
1257 return APInt(BitWidth, VAL << shiftAmt);
1260 // If all the bits were shifted out, the result is 0. This avoids issues
1261 // with shifting by the size of the integer type, which produces undefined
1262 // results. We define these "undefined results" to always be 0.
1263 if (shiftAmt == BitWidth)
1264 return APInt(BitWidth, 0);
1266 // If none of the bits are shifted out, the result is *this. This avoids a
1267 // lshr by the words size in the loop below which can produce incorrect
1268 // results. It also avoids the expensive computation below for a common case.
1272 // Create some space for the result.
1273 uint64_t * val = new uint64_t[getNumWords()];
1275 // If we are shifting less than a word, do it the easy way
1276 if (shiftAmt < APINT_BITS_PER_WORD) {
1278 for (uint32_t i = 0; i < getNumWords(); i++) {
1279 val[i] = pVal[i] << shiftAmt | carry;
1280 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1282 return APInt(val, BitWidth).clearUnusedBits();
1285 // Compute some values needed by the remaining shift algorithms
1286 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1287 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1289 // If we are shifting whole words, just move whole words
1290 if (wordShift == 0) {
1291 for (uint32_t i = 0; i < offset; i++)
1293 for (uint32_t i = offset; i < getNumWords(); i++)
1294 val[i] = pVal[i-offset];
1295 return APInt(val,BitWidth).clearUnusedBits();
1298 // Copy whole words from this to Result.
1299 uint32_t i = getNumWords() - 1;
1300 for (; i > offset; --i)
1301 val[i] = pVal[i-offset] << wordShift |
1302 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1303 val[offset] = pVal[0] << wordShift;
1304 for (i = 0; i < offset; ++i)
1306 return APInt(val, BitWidth).clearUnusedBits();
1309 APInt APInt::rotl(const APInt &rotateAmt) const {
1310 return rotl(rotateAmt.getLimitedValue(BitWidth));
1313 APInt APInt::rotl(uint32_t rotateAmt) const {
1316 // Don't get too fancy, just use existing shift/or facilities
1320 lo.lshr(BitWidth - rotateAmt);
1324 APInt APInt::rotr(const APInt &rotateAmt) const {
1325 return rotr(rotateAmt.getLimitedValue(BitWidth));
1328 APInt APInt::rotr(uint32_t rotateAmt) const {
1331 // Don't get too fancy, just use existing shift/or facilities
1335 hi.shl(BitWidth - rotateAmt);
1339 // Square Root - this method computes and returns the square root of "this".
1340 // Three mechanisms are used for computation. For small values (<= 5 bits),
1341 // a table lookup is done. This gets some performance for common cases. For
1342 // values using less than 52 bits, the value is converted to double and then
1343 // the libc sqrt function is called. The result is rounded and then converted
1344 // back to a uint64_t which is then used to construct the result. Finally,
1345 // the Babylonian method for computing square roots is used.
1346 APInt APInt::sqrt() const {
1348 // Determine the magnitude of the value.
1349 uint32_t magnitude = getActiveBits();
1351 // Use a fast table for some small values. This also gets rid of some
1352 // rounding errors in libc sqrt for small values.
1353 if (magnitude <= 5) {
1354 static const uint8_t results[32] = {
1357 /* 3- 6 */ 2, 2, 2, 2,
1358 /* 7-12 */ 3, 3, 3, 3, 3, 3,
1359 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1360 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1363 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]);
1366 // If the magnitude of the value fits in less than 52 bits (the precision of
1367 // an IEEE double precision floating point value), then we can use the
1368 // libc sqrt function which will probably use a hardware sqrt computation.
1369 // This should be faster than the algorithm below.
1370 if (magnitude < 52) {
1372 // Amazingly, VC++ doesn't have round().
1373 return APInt(BitWidth,
1374 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0]))) + 0.5);
1376 return APInt(BitWidth,
1377 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0])))));
1381 // Okay, all the short cuts are exhausted. We must compute it. The following
1382 // is a classical Babylonian method for computing the square root. This code
1383 // was adapted to APINt from a wikipedia article on such computations.
1384 // See http://www.wikipedia.org/ and go to the page named
1385 // Calculate_an_integer_square_root.
1386 uint32_t nbits = BitWidth, i = 4;
1387 APInt testy(BitWidth, 16);
1388 APInt x_old(BitWidth, 1);
1389 APInt x_new(BitWidth, 0);
1390 APInt two(BitWidth, 2);
1392 // Select a good starting value using binary logarithms.
1393 for (;; i += 2, testy = testy.shl(2))
1394 if (i >= nbits || this->ule(testy)) {
1395 x_old = x_old.shl(i / 2);
1399 // Use the Babylonian method to arrive at the integer square root:
1401 x_new = (this->udiv(x_old) + x_old).udiv(two);
1402 if (x_old.ule(x_new))
1407 // Make sure we return the closest approximation
1408 // NOTE: The rounding calculation below is correct. It will produce an
1409 // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1410 // determined to be a rounding issue with pari/gp as it begins to use a
1411 // floating point representation after 192 bits. There are no discrepancies
1412 // between this algorithm and pari/gp for bit widths < 192 bits.
1413 APInt square(x_old * x_old);
1414 APInt nextSquare((x_old + 1) * (x_old +1));
1415 if (this->ult(square))
1417 else if (this->ule(nextSquare)) {
1418 APInt midpoint((nextSquare - square).udiv(two));
1419 APInt offset(*this - square);
1420 if (offset.ult(midpoint))
1425 assert(0 && "Error in APInt::sqrt computation");
1429 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1430 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1431 /// variables here have the same names as in the algorithm. Comments explain
1432 /// the algorithm and any deviation from it.
1433 static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
1434 uint32_t m, uint32_t n) {
1435 assert(u && "Must provide dividend");
1436 assert(v && "Must provide divisor");
1437 assert(q && "Must provide quotient");
1438 assert(u != v && u != q && v != q && "Must us different memory");
1439 assert(n>1 && "n must be > 1");
1441 // Knuth uses the value b as the base of the number system. In our case b
1442 // is 2^31 so we just set it to -1u.
1443 uint64_t b = uint64_t(1) << 32;
1445 DEBUG(cerr << "KnuthDiv: m=" << m << " n=" << n << '\n');
1446 DEBUG(cerr << "KnuthDiv: original:");
1447 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1448 DEBUG(cerr << " by");
1449 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1450 DEBUG(cerr << '\n');
1451 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1452 // u and v by d. Note that we have taken Knuth's advice here to use a power
1453 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1454 // 2 allows us to shift instead of multiply and it is easy to determine the
1455 // shift amount from the leading zeros. We are basically normalizing the u
1456 // and v so that its high bits are shifted to the top of v's range without
1457 // overflow. Note that this can require an extra word in u so that u must
1458 // be of length m+n+1.
1459 uint32_t shift = CountLeadingZeros_32(v[n-1]);
1460 uint32_t v_carry = 0;
1461 uint32_t u_carry = 0;
1463 for (uint32_t i = 0; i < m+n; ++i) {
1464 uint32_t u_tmp = u[i] >> (32 - shift);
1465 u[i] = (u[i] << shift) | u_carry;
1468 for (uint32_t i = 0; i < n; ++i) {
1469 uint32_t v_tmp = v[i] >> (32 - shift);
1470 v[i] = (v[i] << shift) | v_carry;
1475 DEBUG(cerr << "KnuthDiv: normal:");
1476 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1477 DEBUG(cerr << " by");
1478 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1479 DEBUG(cerr << '\n');
1481 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1484 DEBUG(cerr << "KnuthDiv: quotient digit #" << j << '\n');
1485 // D3. [Calculate q'.].
1486 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1487 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1488 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1489 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1490 // on v[n-2] determines at high speed most of the cases in which the trial
1491 // value qp is one too large, and it eliminates all cases where qp is two
1493 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1494 DEBUG(cerr << "KnuthDiv: dividend == " << dividend << '\n');
1495 uint64_t qp = dividend / v[n-1];
1496 uint64_t rp = dividend % v[n-1];
1497 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1500 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1503 DEBUG(cerr << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1505 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1506 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1507 // consists of a simple multiplication by a one-place number, combined with
1510 for (uint32_t i = 0; i < n; ++i) {
1511 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1512 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1513 bool borrow = subtrahend > u_tmp;
1514 DEBUG(cerr << "KnuthDiv: u_tmp == " << u_tmp
1515 << ", subtrahend == " << subtrahend
1516 << ", borrow = " << borrow << '\n');
1518 uint64_t result = u_tmp - subtrahend;
1520 u[k++] = result & (b-1); // subtract low word
1521 u[k++] = result >> 32; // subtract high word
1522 while (borrow && k <= m+n) { // deal with borrow to the left
1528 DEBUG(cerr << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1531 DEBUG(cerr << "KnuthDiv: after subtraction:");
1532 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1533 DEBUG(cerr << '\n');
1534 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1535 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1536 // true value plus b**(n+1), namely as the b's complement of
1537 // the true value, and a "borrow" to the left should be remembered.
1540 bool carry = true; // true because b's complement is "complement + 1"
1541 for (uint32_t i = 0; i <= m+n; ++i) {
1542 u[i] = ~u[i] + carry; // b's complement
1543 carry = carry && u[i] == 0;
1546 DEBUG(cerr << "KnuthDiv: after complement:");
1547 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1548 DEBUG(cerr << '\n');
1550 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1551 // negative, go to step D6; otherwise go on to step D7.
1554 // D6. [Add back]. The probability that this step is necessary is very
1555 // small, on the order of only 2/b. Make sure that test data accounts for
1556 // this possibility. Decrease q[j] by 1
1558 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1559 // A carry will occur to the left of u[j+n], and it should be ignored
1560 // since it cancels with the borrow that occurred in D4.
1562 for (uint32_t i = 0; i < n; i++) {
1563 uint32_t limit = std::min(u[j+i],v[i]);
1564 u[j+i] += v[i] + carry;
1565 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1569 DEBUG(cerr << "KnuthDiv: after correction:");
1570 DEBUG(for (int i = m+n; i >=0; i--) cerr <<" " << u[i]);
1571 DEBUG(cerr << "\nKnuthDiv: digit result = " << q[j] << '\n');
1573 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1576 DEBUG(cerr << "KnuthDiv: quotient:");
1577 DEBUG(for (int i = m; i >=0; i--) cerr <<" " << q[i]);
1578 DEBUG(cerr << '\n');
1580 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1581 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1582 // compute the remainder (urem uses this).
1584 // The value d is expressed by the "shift" value above since we avoided
1585 // multiplication by d by using a shift left. So, all we have to do is
1586 // shift right here. In order to mak
1589 DEBUG(cerr << "KnuthDiv: remainder:");
1590 for (int i = n-1; i >= 0; i--) {
1591 r[i] = (u[i] >> shift) | carry;
1592 carry = u[i] << (32 - shift);
1593 DEBUG(cerr << " " << r[i]);
1596 for (int i = n-1; i >= 0; i--) {
1598 DEBUG(cerr << " " << r[i]);
1601 DEBUG(cerr << '\n');
1603 DEBUG(cerr << std::setbase(10) << '\n');
1606 void APInt::divide(const APInt LHS, uint32_t lhsWords,
1607 const APInt &RHS, uint32_t rhsWords,
1608 APInt *Quotient, APInt *Remainder)
1610 assert(lhsWords >= rhsWords && "Fractional result");
1612 // First, compose the values into an array of 32-bit words instead of
1613 // 64-bit words. This is a necessity of both the "short division" algorithm
1614 // and the the Knuth "classical algorithm" which requires there to be native
1615 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1616 // can't use 64-bit operands here because we don't have native results of
1617 // 128-bits. Furthremore, casting the 64-bit values to 32-bit values won't
1618 // work on large-endian machines.
1619 uint64_t mask = ~0ull >> (sizeof(uint32_t)*8);
1620 uint32_t n = rhsWords * 2;
1621 uint32_t m = (lhsWords * 2) - n;
1623 // Allocate space for the temporary values we need either on the stack, if
1624 // it will fit, or on the heap if it won't.
1625 uint32_t SPACE[128];
1630 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1633 Q = &SPACE[(m+n+1) + n];
1635 R = &SPACE[(m+n+1) + n + (m+n)];
1637 U = new uint32_t[m + n + 1];
1638 V = new uint32_t[n];
1639 Q = new uint32_t[m+n];
1641 R = new uint32_t[n];
1644 // Initialize the dividend
1645 memset(U, 0, (m+n+1)*sizeof(uint32_t));
1646 for (unsigned i = 0; i < lhsWords; ++i) {
1647 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1648 U[i * 2] = tmp & mask;
1649 U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1651 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1653 // Initialize the divisor
1654 memset(V, 0, (n)*sizeof(uint32_t));
1655 for (unsigned i = 0; i < rhsWords; ++i) {
1656 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1657 V[i * 2] = tmp & mask;
1658 V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1661 // initialize the quotient and remainder
1662 memset(Q, 0, (m+n) * sizeof(uint32_t));
1664 memset(R, 0, n * sizeof(uint32_t));
1666 // Now, adjust m and n for the Knuth division. n is the number of words in
1667 // the divisor. m is the number of words by which the dividend exceeds the
1668 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1669 // contain any zero words or the Knuth algorithm fails.
1670 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1674 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1677 // If we're left with only a single word for the divisor, Knuth doesn't work
1678 // so we implement the short division algorithm here. This is much simpler
1679 // and faster because we are certain that we can divide a 64-bit quantity
1680 // by a 32-bit quantity at hardware speed and short division is simply a
1681 // series of such operations. This is just like doing short division but we
1682 // are using base 2^32 instead of base 10.
1683 assert(n != 0 && "Divide by zero?");
1685 uint32_t divisor = V[0];
1686 uint32_t remainder = 0;
1687 for (int i = m+n-1; i >= 0; i--) {
1688 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1689 if (partial_dividend == 0) {
1692 } else if (partial_dividend < divisor) {
1694 remainder = partial_dividend;
1695 } else if (partial_dividend == divisor) {
1699 Q[i] = partial_dividend / divisor;
1700 remainder = partial_dividend - (Q[i] * divisor);
1706 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1708 KnuthDiv(U, V, Q, R, m, n);
1711 // If the caller wants the quotient
1713 // Set up the Quotient value's memory.
1714 if (Quotient->BitWidth != LHS.BitWidth) {
1715 if (Quotient->isSingleWord())
1718 delete [] Quotient->pVal;
1719 Quotient->BitWidth = LHS.BitWidth;
1720 if (!Quotient->isSingleWord())
1721 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1725 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1727 if (lhsWords == 1) {
1729 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1730 if (Quotient->isSingleWord())
1731 Quotient->VAL = tmp;
1733 Quotient->pVal[0] = tmp;
1735 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1736 for (unsigned i = 0; i < lhsWords; ++i)
1738 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1742 // If the caller wants the remainder
1744 // Set up the Remainder value's memory.
1745 if (Remainder->BitWidth != RHS.BitWidth) {
1746 if (Remainder->isSingleWord())
1749 delete [] Remainder->pVal;
1750 Remainder->BitWidth = RHS.BitWidth;
1751 if (!Remainder->isSingleWord())
1752 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1756 // The remainder is in R. Reconstitute the remainder into Remainder's low
1758 if (rhsWords == 1) {
1760 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1761 if (Remainder->isSingleWord())
1762 Remainder->VAL = tmp;
1764 Remainder->pVal[0] = tmp;
1766 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1767 for (unsigned i = 0; i < rhsWords; ++i)
1768 Remainder->pVal[i] =
1769 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1773 // Clean up the memory we allocated.
1774 if (U != &SPACE[0]) {
1782 APInt APInt::udiv(const APInt& RHS) const {
1783 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1785 // First, deal with the easy case
1786 if (isSingleWord()) {
1787 assert(RHS.VAL != 0 && "Divide by zero?");
1788 return APInt(BitWidth, VAL / RHS.VAL);
1791 // Get some facts about the LHS and RHS number of bits and words
1792 uint32_t rhsBits = RHS.getActiveBits();
1793 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1794 assert(rhsWords && "Divided by zero???");
1795 uint32_t lhsBits = this->getActiveBits();
1796 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1798 // Deal with some degenerate cases
1801 return APInt(BitWidth, 0);
1802 else if (lhsWords < rhsWords || this->ult(RHS)) {
1803 // X / Y ===> 0, iff X < Y
1804 return APInt(BitWidth, 0);
1805 } else if (*this == RHS) {
1807 return APInt(BitWidth, 1);
1808 } else if (lhsWords == 1 && rhsWords == 1) {
1809 // All high words are zero, just use native divide
1810 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1813 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1814 APInt Quotient(1,0); // to hold result.
1815 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0);
1819 APInt APInt::urem(const APInt& RHS) const {
1820 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1821 if (isSingleWord()) {
1822 assert(RHS.VAL != 0 && "Remainder by zero?");
1823 return APInt(BitWidth, VAL % RHS.VAL);
1826 // Get some facts about the LHS
1827 uint32_t lhsBits = getActiveBits();
1828 uint32_t lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1830 // Get some facts about the RHS
1831 uint32_t rhsBits = RHS.getActiveBits();
1832 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1833 assert(rhsWords && "Performing remainder operation by zero ???");
1835 // Check the degenerate cases
1836 if (lhsWords == 0) {
1838 return APInt(BitWidth, 0);
1839 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1840 // X % Y ===> X, iff X < Y
1842 } else if (*this == RHS) {
1844 return APInt(BitWidth, 0);
1845 } else if (lhsWords == 1) {
1846 // All high words are zero, just use native remainder
1847 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
1850 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1851 APInt Remainder(1,0);
1852 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder);
1856 void APInt::udivrem(const APInt &LHS, const APInt &RHS,
1857 APInt &Quotient, APInt &Remainder) {
1858 // Get some size facts about the dividend and divisor
1859 uint32_t lhsBits = LHS.getActiveBits();
1860 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1861 uint32_t rhsBits = RHS.getActiveBits();
1862 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1864 // Check the degenerate cases
1865 if (lhsWords == 0) {
1866 Quotient = 0; // 0 / Y ===> 0
1867 Remainder = 0; // 0 % Y ===> 0
1871 if (lhsWords < rhsWords || LHS.ult(RHS)) {
1872 Quotient = 0; // X / Y ===> 0, iff X < Y
1873 Remainder = LHS; // X % Y ===> X, iff X < Y
1878 Quotient = 1; // X / X ===> 1
1879 Remainder = 0; // X % X ===> 0;
1883 if (lhsWords == 1 && rhsWords == 1) {
1884 // There is only one word to consider so use the native versions.
1885 if (LHS.isSingleWord()) {
1886 Quotient = APInt(LHS.getBitWidth(), LHS.VAL / RHS.VAL);
1887 Remainder = APInt(LHS.getBitWidth(), LHS.VAL % RHS.VAL);
1889 Quotient = APInt(LHS.getBitWidth(), LHS.pVal[0] / RHS.pVal[0]);
1890 Remainder = APInt(LHS.getBitWidth(), LHS.pVal[0] % RHS.pVal[0]);
1895 // Okay, lets do it the long way
1896 divide(LHS, lhsWords, RHS, rhsWords, &Quotient, &Remainder);
1899 void APInt::fromString(uint32_t numbits, const char *str, uint32_t slen,
1901 // Check our assumptions here
1902 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1903 "Radix should be 2, 8, 10, or 16!");
1904 assert(str && "String is null?");
1905 bool isNeg = str[0] == '-';
1908 assert((slen <= numbits || radix != 2) && "Insufficient bit width");
1909 assert((slen*3 <= numbits || radix != 8) && "Insufficient bit width");
1910 assert((slen*4 <= numbits || radix != 16) && "Insufficient bit width");
1911 assert(((slen*64)/22 <= numbits || radix != 10) && "Insufficient bit width");
1914 if (!isSingleWord())
1915 pVal = getClearedMemory(getNumWords());
1917 // Figure out if we can shift instead of multiply
1918 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
1920 // Set up an APInt for the digit to add outside the loop so we don't
1921 // constantly construct/destruct it.
1922 APInt apdigit(getBitWidth(), 0);
1923 APInt apradix(getBitWidth(), radix);
1925 // Enter digit traversal loop
1926 for (unsigned i = 0; i < slen; i++) {
1929 char cdigit = str[i];
1931 if (!isxdigit(cdigit))
1932 assert(0 && "Invalid hex digit in string");
1933 if (isdigit(cdigit))
1934 digit = cdigit - '0';
1935 else if (cdigit >= 'a')
1936 digit = cdigit - 'a' + 10;
1937 else if (cdigit >= 'A')
1938 digit = cdigit - 'A' + 10;
1940 assert(0 && "huh? we shouldn't get here");
1941 } else if (isdigit(cdigit)) {
1942 digit = cdigit - '0';
1944 assert(0 && "Invalid character in digit string");
1947 // Shift or multiply the value by the radix
1953 // Add in the digit we just interpreted
1954 if (apdigit.isSingleWord())
1955 apdigit.VAL = digit;
1957 apdigit.pVal[0] = digit;
1960 // If its negative, put it in two's complement form
1967 std::string APInt::toString(uint8_t radix, bool wantSigned) const {
1968 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1969 "Radix should be 2, 8, 10, or 16!");
1970 static const char *digits[] = {
1971 "0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"
1974 uint32_t bits_used = getActiveBits();
1975 if (isSingleWord()) {
1977 const char *format = (radix == 10 ? (wantSigned ? "%lld" : "%llu") :
1978 (radix == 16 ? "%llX" : (radix == 8 ? "%llo" : 0)));
1981 int64_t sextVal = (int64_t(VAL) << (APINT_BITS_PER_WORD-BitWidth)) >>
1982 (APINT_BITS_PER_WORD-BitWidth);
1983 sprintf(buf, format, sextVal);
1985 sprintf(buf, format, VAL);
1990 uint32_t bit = v & 1;
1992 buf[bits_used] = digits[bit][0];
2001 // For the 2, 8 and 16 bit cases, we can just shift instead of divide
2002 // because the number of bits per digit (1,3 and 4 respectively) divides
2003 // equaly. We just shift until there value is zero.
2005 // First, check for a zero value and just short circuit the logic below.
2010 size_t insert_at = 0;
2011 if (wantSigned && this->isNegative()) {
2012 // They want to print the signed version and it is a negative value
2013 // Flip the bits and add one to turn it into the equivalent positive
2014 // value and put a '-' in the result.
2020 // Just shift tmp right for each digit width until it becomes zero
2021 uint32_t shift = (radix == 16 ? 4 : (radix == 8 ? 3 : 1));
2022 uint64_t mask = radix - 1;
2023 APInt zero(tmp.getBitWidth(), 0);
2024 while (tmp.ne(zero)) {
2025 unsigned digit = (tmp.isSingleWord() ? tmp.VAL : tmp.pVal[0]) & mask;
2026 result.insert(insert_at, digits[digit]);
2027 tmp = tmp.lshr(shift);
2034 APInt divisor(4, radix);
2035 APInt zero(tmp.getBitWidth(), 0);
2036 size_t insert_at = 0;
2037 if (wantSigned && tmp[BitWidth-1]) {
2038 // They want to print the signed version and it is a negative value
2039 // Flip the bits and add one to turn it into the equivalent positive
2040 // value and put a '-' in the result.
2046 if (tmp == APInt(tmp.getBitWidth(), 0))
2048 else while (tmp.ne(zero)) {
2050 APInt tmp2(tmp.getBitWidth(), 0);
2051 divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
2053 uint32_t digit = APdigit.getZExtValue();
2054 assert(digit < radix && "divide failed");
2055 result.insert(insert_at,digits[digit]);
2062 void APInt::dump() const
2064 cerr << "APInt(" << BitWidth << ")=" << std::setbase(16);
2067 else for (unsigned i = getNumWords(); i > 0; i--) {
2068 cerr << pVal[i-1] << " ";
2070 cerr << " U(" << this->toStringUnsigned(10) << ") S("
2071 << this->toStringSigned(10) << ")" << std::setbase(10);
2074 // This implements a variety of operations on a representation of
2075 // arbitrary precision, two's-complement, bignum integer values.
2077 /* Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe
2078 and unrestricting assumption. */
2079 COMPILE_TIME_ASSERT(integerPartWidth % 2 == 0);
2081 /* Some handy functions local to this file. */
2084 /* Returns the integer part with the least significant BITS set.
2085 BITS cannot be zero. */
2087 lowBitMask(unsigned int bits)
2089 assert (bits != 0 && bits <= integerPartWidth);
2091 return ~(integerPart) 0 >> (integerPartWidth - bits);
2094 /* Returns the value of the lower half of PART. */
2096 lowHalf(integerPart part)
2098 return part & lowBitMask(integerPartWidth / 2);
2101 /* Returns the value of the upper half of PART. */
2103 highHalf(integerPart part)
2105 return part >> (integerPartWidth / 2);
2108 /* Returns the bit number of the most significant set bit of a part.
2109 If the input number has no bits set -1U is returned. */
2111 partMSB(integerPart value)
2113 unsigned int n, msb;
2118 n = integerPartWidth / 2;
2133 /* Returns the bit number of the least significant set bit of a
2134 part. If the input number has no bits set -1U is returned. */
2136 partLSB(integerPart value)
2138 unsigned int n, lsb;
2143 lsb = integerPartWidth - 1;
2144 n = integerPartWidth / 2;
2159 /* Sets the least significant part of a bignum to the input value, and
2160 zeroes out higher parts. */
2162 APInt::tcSet(integerPart *dst, integerPart part, unsigned int parts)
2169 for(i = 1; i < parts; i++)
2173 /* Assign one bignum to another. */
2175 APInt::tcAssign(integerPart *dst, const integerPart *src, unsigned int parts)
2179 for(i = 0; i < parts; i++)
2183 /* Returns true if a bignum is zero, false otherwise. */
2185 APInt::tcIsZero(const integerPart *src, unsigned int parts)
2189 for(i = 0; i < parts; i++)
2196 /* Extract the given bit of a bignum; returns 0 or 1. */
2198 APInt::tcExtractBit(const integerPart *parts, unsigned int bit)
2200 return(parts[bit / integerPartWidth]
2201 & ((integerPart) 1 << bit % integerPartWidth)) != 0;
2204 /* Set the given bit of a bignum. */
2206 APInt::tcSetBit(integerPart *parts, unsigned int bit)
2208 parts[bit / integerPartWidth] |= (integerPart) 1 << (bit % integerPartWidth);
2211 /* Returns the bit number of the least significant set bit of a
2212 number. If the input number has no bits set -1U is returned. */
2214 APInt::tcLSB(const integerPart *parts, unsigned int n)
2216 unsigned int i, lsb;
2218 for(i = 0; i < n; i++) {
2219 if (parts[i] != 0) {
2220 lsb = partLSB(parts[i]);
2222 return lsb + i * integerPartWidth;
2229 /* Returns the bit number of the most significant set bit of a number.
2230 If the input number has no bits set -1U is returned. */
2232 APInt::tcMSB(const integerPart *parts, unsigned int n)
2239 if (parts[n] != 0) {
2240 msb = partMSB(parts[n]);
2242 return msb + n * integerPartWidth;
2249 /* Copy the bit vector of width srcBITS from SRC, starting at bit
2250 srcLSB, to DST, of dstCOUNT parts, such that the bit srcLSB becomes
2251 the least significant bit of DST. All high bits above srcBITS in
2252 DST are zero-filled. */
2254 APInt::tcExtract(integerPart *dst, unsigned int dstCount, const integerPart *src,
2255 unsigned int srcBits, unsigned int srcLSB)
2257 unsigned int firstSrcPart, dstParts, shift, n;
2259 dstParts = (srcBits + integerPartWidth - 1) / integerPartWidth;
2260 assert (dstParts <= dstCount);
2262 firstSrcPart = srcLSB / integerPartWidth;
2263 tcAssign (dst, src + firstSrcPart, dstParts);
2265 shift = srcLSB % integerPartWidth;
2266 tcShiftRight (dst, dstParts, shift);
2268 /* We now have (dstParts * integerPartWidth - shift) bits from SRC
2269 in DST. If this is less that srcBits, append the rest, else
2270 clear the high bits. */
2271 n = dstParts * integerPartWidth - shift;
2273 integerPart mask = lowBitMask (srcBits - n);
2274 dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask)
2275 << n % integerPartWidth);
2276 } else if (n > srcBits) {
2277 if (srcBits % integerPartWidth)
2278 dst[dstParts - 1] &= lowBitMask (srcBits % integerPartWidth);
2281 /* Clear high parts. */
2282 while (dstParts < dstCount)
2283 dst[dstParts++] = 0;
2286 /* DST += RHS + C where C is zero or one. Returns the carry flag. */
2288 APInt::tcAdd(integerPart *dst, const integerPart *rhs,
2289 integerPart c, unsigned int parts)
2295 for(i = 0; i < parts; i++) {
2300 dst[i] += rhs[i] + 1;
2311 /* DST -= RHS + C where C is zero or one. Returns the carry flag. */
2313 APInt::tcSubtract(integerPart *dst, const integerPart *rhs,
2314 integerPart c, unsigned int parts)
2320 for(i = 0; i < parts; i++) {
2325 dst[i] -= rhs[i] + 1;
2336 /* Negate a bignum in-place. */
2338 APInt::tcNegate(integerPart *dst, unsigned int parts)
2340 tcComplement(dst, parts);
2341 tcIncrement(dst, parts);
2344 /* DST += SRC * MULTIPLIER + CARRY if add is true
2345 DST = SRC * MULTIPLIER + CARRY if add is false
2347 Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC
2348 they must start at the same point, i.e. DST == SRC.
2350 If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is
2351 returned. Otherwise DST is filled with the least significant
2352 DSTPARTS parts of the result, and if all of the omitted higher
2353 parts were zero return zero, otherwise overflow occurred and
2356 APInt::tcMultiplyPart(integerPart *dst, const integerPart *src,
2357 integerPart multiplier, integerPart carry,
2358 unsigned int srcParts, unsigned int dstParts,
2363 /* Otherwise our writes of DST kill our later reads of SRC. */
2364 assert(dst <= src || dst >= src + srcParts);
2365 assert(dstParts <= srcParts + 1);
2367 /* N loops; minimum of dstParts and srcParts. */
2368 n = dstParts < srcParts ? dstParts: srcParts;
2370 for(i = 0; i < n; i++) {
2371 integerPart low, mid, high, srcPart;
2373 /* [ LOW, HIGH ] = MULTIPLIER * SRC[i] + DST[i] + CARRY.
2375 This cannot overflow, because
2377 (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1)
2379 which is less than n^2. */
2383 if (multiplier == 0 || srcPart == 0) {
2387 low = lowHalf(srcPart) * lowHalf(multiplier);
2388 high = highHalf(srcPart) * highHalf(multiplier);
2390 mid = lowHalf(srcPart) * highHalf(multiplier);
2391 high += highHalf(mid);
2392 mid <<= integerPartWidth / 2;
2393 if (low + mid < low)
2397 mid = highHalf(srcPart) * lowHalf(multiplier);
2398 high += highHalf(mid);
2399 mid <<= integerPartWidth / 2;
2400 if (low + mid < low)
2404 /* Now add carry. */
2405 if (low + carry < low)
2411 /* And now DST[i], and store the new low part there. */
2412 if (low + dst[i] < low)
2422 /* Full multiplication, there is no overflow. */
2423 assert(i + 1 == dstParts);
2427 /* We overflowed if there is carry. */
2431 /* We would overflow if any significant unwritten parts would be
2432 non-zero. This is true if any remaining src parts are non-zero
2433 and the multiplier is non-zero. */
2435 for(; i < srcParts; i++)
2439 /* We fitted in the narrow destination. */
2444 /* DST = LHS * RHS, where DST has the same width as the operands and
2445 is filled with the least significant parts of the result. Returns
2446 one if overflow occurred, otherwise zero. DST must be disjoint
2447 from both operands. */
2449 APInt::tcMultiply(integerPart *dst, const integerPart *lhs,
2450 const integerPart *rhs, unsigned int parts)
2455 assert(dst != lhs && dst != rhs);
2458 tcSet(dst, 0, parts);
2460 for(i = 0; i < parts; i++)
2461 overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts,
2467 /* DST = LHS * RHS, where DST has width the sum of the widths of the
2468 operands. No overflow occurs. DST must be disjoint from both
2469 operands. Returns the number of parts required to hold the
2472 APInt::tcFullMultiply(integerPart *dst, const integerPart *lhs,
2473 const integerPart *rhs, unsigned int lhsParts,
2474 unsigned int rhsParts)
2476 /* Put the narrower number on the LHS for less loops below. */
2477 if (lhsParts > rhsParts) {
2478 return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts);
2482 assert(dst != lhs && dst != rhs);
2484 tcSet(dst, 0, rhsParts);
2486 for(n = 0; n < lhsParts; n++)
2487 tcMultiplyPart(&dst[n], rhs, lhs[n], 0, rhsParts, rhsParts + 1, true);
2489 n = lhsParts + rhsParts;
2491 return n - (dst[n - 1] == 0);
2495 /* If RHS is zero LHS and REMAINDER are left unchanged, return one.
2496 Otherwise set LHS to LHS / RHS with the fractional part discarded,
2497 set REMAINDER to the remainder, return zero. i.e.
2499 OLD_LHS = RHS * LHS + REMAINDER
2501 SCRATCH is a bignum of the same size as the operands and result for
2502 use by the routine; its contents need not be initialized and are
2503 destroyed. LHS, REMAINDER and SCRATCH must be distinct.
2506 APInt::tcDivide(integerPart *lhs, const integerPart *rhs,
2507 integerPart *remainder, integerPart *srhs,
2510 unsigned int n, shiftCount;
2513 assert(lhs != remainder && lhs != srhs && remainder != srhs);
2515 shiftCount = tcMSB(rhs, parts) + 1;
2516 if (shiftCount == 0)
2519 shiftCount = parts * integerPartWidth - shiftCount;
2520 n = shiftCount / integerPartWidth;
2521 mask = (integerPart) 1 << (shiftCount % integerPartWidth);
2523 tcAssign(srhs, rhs, parts);
2524 tcShiftLeft(srhs, parts, shiftCount);
2525 tcAssign(remainder, lhs, parts);
2526 tcSet(lhs, 0, parts);
2528 /* Loop, subtracting SRHS if REMAINDER is greater and adding that to
2533 compare = tcCompare(remainder, srhs, parts);
2535 tcSubtract(remainder, srhs, 0, parts);
2539 if (shiftCount == 0)
2542 tcShiftRight(srhs, parts, 1);
2543 if ((mask >>= 1) == 0)
2544 mask = (integerPart) 1 << (integerPartWidth - 1), n--;
2550 /* Shift a bignum left COUNT bits in-place. Shifted in bits are zero.
2551 There are no restrictions on COUNT. */
2553 APInt::tcShiftLeft(integerPart *dst, unsigned int parts, unsigned int count)
2556 unsigned int jump, shift;
2558 /* Jump is the inter-part jump; shift is is intra-part shift. */
2559 jump = count / integerPartWidth;
2560 shift = count % integerPartWidth;
2562 while (parts > jump) {
2567 /* dst[i] comes from the two parts src[i - jump] and, if we have
2568 an intra-part shift, src[i - jump - 1]. */
2569 part = dst[parts - jump];
2572 if (parts >= jump + 1)
2573 part |= dst[parts - jump - 1] >> (integerPartWidth - shift);
2584 /* Shift a bignum right COUNT bits in-place. Shifted in bits are
2585 zero. There are no restrictions on COUNT. */
2587 APInt::tcShiftRight(integerPart *dst, unsigned int parts, unsigned int count)
2590 unsigned int i, jump, shift;
2592 /* Jump is the inter-part jump; shift is is intra-part shift. */
2593 jump = count / integerPartWidth;
2594 shift = count % integerPartWidth;
2596 /* Perform the shift. This leaves the most significant COUNT bits
2597 of the result at zero. */
2598 for(i = 0; i < parts; i++) {
2601 if (i + jump >= parts) {
2604 part = dst[i + jump];
2607 if (i + jump + 1 < parts)
2608 part |= dst[i + jump + 1] << (integerPartWidth - shift);
2617 /* Bitwise and of two bignums. */
2619 APInt::tcAnd(integerPart *dst, const integerPart *rhs, unsigned int parts)
2623 for(i = 0; i < parts; i++)
2627 /* Bitwise inclusive or of two bignums. */
2629 APInt::tcOr(integerPart *dst, const integerPart *rhs, unsigned int parts)
2633 for(i = 0; i < parts; i++)
2637 /* Bitwise exclusive or of two bignums. */
2639 APInt::tcXor(integerPart *dst, const integerPart *rhs, unsigned int parts)
2643 for(i = 0; i < parts; i++)
2647 /* Complement a bignum in-place. */
2649 APInt::tcComplement(integerPart *dst, unsigned int parts)
2653 for(i = 0; i < parts; i++)
2657 /* Comparison (unsigned) of two bignums. */
2659 APInt::tcCompare(const integerPart *lhs, const integerPart *rhs,
2664 if (lhs[parts] == rhs[parts])
2667 if (lhs[parts] > rhs[parts])
2676 /* Increment a bignum in-place, return the carry flag. */
2678 APInt::tcIncrement(integerPart *dst, unsigned int parts)
2682 for(i = 0; i < parts; i++)
2689 /* Set the least significant BITS bits of a bignum, clear the
2692 APInt::tcSetLeastSignificantBits(integerPart *dst, unsigned int parts,
2698 while (bits > integerPartWidth) {
2699 dst[i++] = ~(integerPart) 0;
2700 bits -= integerPartWidth;
2704 dst[i++] = ~(integerPart) 0 >> (integerPartWidth - bits);