1 //===-- APInt.cpp - Implement APInt class ---------------------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by Sheng Zhou and Reid Spencer and is distributed
6 // under the // University of Illinois Open Source License. See LICENSE.TXT
9 //===----------------------------------------------------------------------===//
11 // This file implements a class to represent arbitrary precision integer
12 // constant values and provide a variety of arithmetic operations on them.
14 //===----------------------------------------------------------------------===//
16 #define DEBUG_TYPE "apint"
17 #include "llvm/ADT/APInt.h"
18 #include "llvm/DerivedTypes.h"
19 #include "llvm/Support/Debug.h"
20 #include "llvm/Support/MathExtras.h"
29 /// A utility function for allocating memory, checking for allocation failures,
30 /// and ensuring the contents are zeroed.
31 inline static uint64_t* getClearedMemory(uint32_t numWords) {
32 uint64_t * result = new uint64_t[numWords];
33 assert(result && "APInt memory allocation fails!");
34 memset(result, 0, numWords * sizeof(uint64_t));
38 /// A utility function for allocating memory and checking for allocation
39 /// failure. The content is not zeroed.
40 inline static uint64_t* getMemory(uint32_t numWords) {
41 uint64_t * result = new uint64_t[numWords];
42 assert(result && "APInt memory allocation fails!");
46 APInt::APInt(uint32_t numBits, uint64_t val)
47 : BitWidth(numBits), VAL(0) {
48 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small");
49 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large");
53 pVal = getClearedMemory(getNumWords());
59 APInt::APInt(uint32_t numBits, uint32_t numWords, uint64_t bigVal[])
60 : BitWidth(numBits), VAL(0) {
61 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small");
62 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large");
63 assert(bigVal && "Null pointer detected!");
67 // Get memory, cleared to 0
68 pVal = getClearedMemory(getNumWords());
69 // Calculate the number of words to copy
70 uint32_t words = std::min<uint32_t>(numWords, getNumWords());
71 // Copy the words from bigVal to pVal
72 memcpy(pVal, bigVal, words * APINT_WORD_SIZE);
74 // Make sure unused high bits are cleared
78 APInt::APInt(uint32_t numbits, const char StrStart[], uint32_t slen,
80 : BitWidth(numbits), VAL(0) {
81 fromString(numbits, StrStart, slen, radix);
84 APInt::APInt(uint32_t numbits, const std::string& Val, uint8_t radix)
85 : BitWidth(numbits), VAL(0) {
86 assert(!Val.empty() && "String empty?");
87 fromString(numbits, Val.c_str(), Val.size(), radix);
90 APInt::APInt(const APInt& that)
91 : BitWidth(that.BitWidth), VAL(0) {
95 pVal = getMemory(getNumWords());
96 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE);
101 if (!isSingleWord() && pVal)
105 APInt& APInt::operator=(const APInt& RHS) {
106 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
110 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE);
114 APInt& APInt::operator=(uint64_t RHS) {
119 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE);
124 /// add_1 - This function adds a single "digit" integer, y, to the multiple
125 /// "digit" integer array, x[]. x[] is modified to reflect the addition and
126 /// 1 is returned if there is a carry out, otherwise 0 is returned.
127 /// @returns the carry of the addition.
128 static bool add_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
129 for (uint32_t i = 0; i < len; ++i) {
132 y = 1; // Carry one to next digit.
134 y = 0; // No need to carry so exit early
141 /// @brief Prefix increment operator. Increments the APInt by one.
142 APInt& APInt::operator++() {
146 add_1(pVal, pVal, getNumWords(), 1);
147 return clearUnusedBits();
150 /// sub_1 - This function subtracts a single "digit" (64-bit word), y, from
151 /// the multi-digit integer array, x[], propagating the borrowed 1 value until
152 /// no further borrowing is neeeded or it runs out of "digits" in x. The result
153 /// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted.
154 /// In other words, if y > x then this function returns 1, otherwise 0.
155 /// @returns the borrow out of the subtraction
156 static bool sub_1(uint64_t x[], uint32_t len, uint64_t y) {
157 for (uint32_t i = 0; i < len; ++i) {
161 y = 1; // We have to "borrow 1" from next "digit"
163 y = 0; // No need to borrow
164 break; // Remaining digits are unchanged so exit early
170 /// @brief Prefix decrement operator. Decrements the APInt by one.
171 APInt& APInt::operator--() {
175 sub_1(pVal, getNumWords(), 1);
176 return clearUnusedBits();
179 /// add - This function adds the integer array x to the integer array Y and
180 /// places the result in dest.
181 /// @returns the carry out from the addition
182 /// @brief General addition of 64-bit integer arrays
183 static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y,
186 for (uint32_t i = 0; i< len; ++i) {
187 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x
188 dest[i] = x[i] + y[i] + carry;
189 carry = dest[i] < limit || (carry && dest[i] == limit);
194 /// Adds the RHS APint to this APInt.
195 /// @returns this, after addition of RHS.
196 /// @brief Addition assignment operator.
197 APInt& APInt::operator+=(const APInt& RHS) {
198 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
202 add(pVal, pVal, RHS.pVal, getNumWords());
204 return clearUnusedBits();
207 /// Subtracts the integer array y from the integer array x
208 /// @returns returns the borrow out.
209 /// @brief Generalized subtraction of 64-bit integer arrays.
210 static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y,
213 for (uint32_t i = 0; i < len; ++i) {
214 uint64_t x_tmp = borrow ? x[i] - 1 : x[i];
215 borrow = y[i] > x_tmp || (borrow && x[i] == 0);
216 dest[i] = x_tmp - y[i];
221 /// Subtracts the RHS APInt from this APInt
222 /// @returns this, after subtraction
223 /// @brief Subtraction assignment operator.
224 APInt& APInt::operator-=(const APInt& RHS) {
225 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
229 sub(pVal, pVal, RHS.pVal, getNumWords());
230 return clearUnusedBits();
233 /// Multiplies an integer array, x by a a uint64_t integer and places the result
235 /// @returns the carry out of the multiplication.
236 /// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer.
237 static uint64_t mul_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) {
238 // Split y into high 32-bit part (hy) and low 32-bit part (ly)
239 uint64_t ly = y & 0xffffffffULL, hy = y >> 32;
242 // For each digit of x.
243 for (uint32_t i = 0; i < len; ++i) {
244 // Split x into high and low words
245 uint64_t lx = x[i] & 0xffffffffULL;
246 uint64_t hx = x[i] >> 32;
247 // hasCarry - A flag to indicate if there is a carry to the next digit.
248 // hasCarry == 0, no carry
249 // hasCarry == 1, has carry
250 // hasCarry == 2, no carry and the calculation result == 0.
251 uint8_t hasCarry = 0;
252 dest[i] = carry + lx * ly;
253 // Determine if the add above introduces carry.
254 hasCarry = (dest[i] < carry) ? 1 : 0;
255 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0);
256 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) +
257 // (2^32 - 1) + 2^32 = 2^64.
258 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
260 carry += (lx * hy) & 0xffffffffULL;
261 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL);
262 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) +
263 (carry >> 32) + ((lx * hy) >> 32) + hx * hy;
268 /// Multiplies integer array x by integer array y and stores the result into
269 /// the integer array dest. Note that dest's size must be >= xlen + ylen.
270 /// @brief Generalized multiplicate of integer arrays.
271 static void mul(uint64_t dest[], uint64_t x[], uint32_t xlen, uint64_t y[],
273 dest[xlen] = mul_1(dest, x, xlen, y[0]);
274 for (uint32_t i = 1; i < ylen; ++i) {
275 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32;
276 uint64_t carry = 0, lx = 0, hx = 0;
277 for (uint32_t j = 0; j < xlen; ++j) {
278 lx = x[j] & 0xffffffffULL;
280 // hasCarry - A flag to indicate if has carry.
281 // hasCarry == 0, no carry
282 // hasCarry == 1, has carry
283 // hasCarry == 2, no carry and the calculation result == 0.
284 uint8_t hasCarry = 0;
285 uint64_t resul = carry + lx * ly;
286 hasCarry = (resul < carry) ? 1 : 0;
287 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32);
288 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0);
290 carry += (lx * hy) & 0xffffffffULL;
291 resul = (carry << 32) | (resul & 0xffffffffULL);
293 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+
294 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) +
295 ((lx * hy) >> 32) + hx * hy;
297 dest[i+xlen] = carry;
301 APInt& APInt::operator*=(const APInt& RHS) {
302 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
303 if (isSingleWord()) {
309 // Get some bit facts about LHS and check for zero
310 uint32_t lhsBits = getActiveBits();
311 uint32_t lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1;
316 // Get some bit facts about RHS and check for zero
317 uint32_t rhsBits = RHS.getActiveBits();
318 uint32_t rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1;
325 // Allocate space for the result
326 uint32_t destWords = rhsWords + lhsWords;
327 uint64_t *dest = getMemory(destWords);
329 // Perform the long multiply
330 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords);
332 // Copy result back into *this
334 uint32_t wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords;
335 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE);
337 // delete dest array and return
342 APInt& APInt::operator&=(const APInt& RHS) {
343 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
344 if (isSingleWord()) {
348 uint32_t numWords = getNumWords();
349 for (uint32_t i = 0; i < numWords; ++i)
350 pVal[i] &= RHS.pVal[i];
354 APInt& APInt::operator|=(const APInt& RHS) {
355 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
356 if (isSingleWord()) {
360 uint32_t numWords = getNumWords();
361 for (uint32_t i = 0; i < numWords; ++i)
362 pVal[i] |= RHS.pVal[i];
366 APInt& APInt::operator^=(const APInt& RHS) {
367 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
368 if (isSingleWord()) {
370 this->clearUnusedBits();
373 uint32_t numWords = getNumWords();
374 for (uint32_t i = 0; i < numWords; ++i)
375 pVal[i] ^= RHS.pVal[i];
376 return clearUnusedBits();
379 APInt APInt::operator&(const APInt& RHS) const {
380 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
382 return APInt(getBitWidth(), VAL & RHS.VAL);
384 uint32_t numWords = getNumWords();
385 uint64_t* val = getMemory(numWords);
386 for (uint32_t i = 0; i < numWords; ++i)
387 val[i] = pVal[i] & RHS.pVal[i];
388 return APInt(val, getBitWidth());
391 APInt APInt::operator|(const APInt& RHS) const {
392 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
394 return APInt(getBitWidth(), VAL | RHS.VAL);
396 uint32_t numWords = getNumWords();
397 uint64_t *val = getMemory(numWords);
398 for (uint32_t i = 0; i < numWords; ++i)
399 val[i] = pVal[i] | RHS.pVal[i];
400 return APInt(val, getBitWidth());
403 APInt APInt::operator^(const APInt& RHS) const {
404 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
406 return APInt(BitWidth, VAL ^ RHS.VAL);
408 uint32_t numWords = getNumWords();
409 uint64_t *val = getMemory(numWords);
410 for (uint32_t i = 0; i < numWords; ++i)
411 val[i] = pVal[i] ^ RHS.pVal[i];
413 // 0^0==1 so clear the high bits in case they got set.
414 return APInt(val, getBitWidth()).clearUnusedBits();
417 bool APInt::operator !() const {
421 for (uint32_t i = 0; i < getNumWords(); ++i)
427 APInt APInt::operator*(const APInt& RHS) const {
428 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
430 return APInt(BitWidth, VAL * RHS.VAL);
433 return Result.clearUnusedBits();
436 APInt APInt::operator+(const APInt& RHS) const {
437 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
439 return APInt(BitWidth, VAL + RHS.VAL);
440 APInt Result(BitWidth, 0);
441 add(Result.pVal, this->pVal, RHS.pVal, getNumWords());
442 return Result.clearUnusedBits();
445 APInt APInt::operator-(const APInt& RHS) const {
446 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
448 return APInt(BitWidth, VAL - RHS.VAL);
449 APInt Result(BitWidth, 0);
450 sub(Result.pVal, this->pVal, RHS.pVal, getNumWords());
451 return Result.clearUnusedBits();
454 bool APInt::operator[](uint32_t bitPosition) const {
455 return (maskBit(bitPosition) &
456 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0;
459 bool APInt::operator==(const APInt& RHS) const {
461 return VAL == RHS.VAL;
463 // Get some facts about the number of bits used in the two operands.
464 uint32_t n1 = getActiveBits();
465 uint32_t n2 = RHS.getActiveBits();
467 // If the number of bits isn't the same, they aren't equal
471 // If the number of bits fits in a word, we only need to compare the low word.
472 if (n1 <= APINT_BITS_PER_WORD)
473 return pVal[0] == RHS.pVal[0];
475 // Otherwise, compare everything
476 for (int i = whichWord(n1 - 1); i >= 0; --i)
477 if (pVal[i] != RHS.pVal[i])
482 bool APInt::operator==(uint64_t Val) const {
486 uint32_t n = getActiveBits();
487 if (n <= APINT_BITS_PER_WORD)
488 return pVal[0] == Val;
493 bool APInt::ult(const APInt& RHS) const {
494 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
496 return VAL < RHS.VAL;
498 // Get active bit length of both operands
499 uint32_t n1 = getActiveBits();
500 uint32_t n2 = RHS.getActiveBits();
502 // If magnitude of LHS is less than RHS, return true.
506 // If magnitude of RHS is greather than LHS, return false.
510 // If they bot fit in a word, just compare the low order word
511 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD)
512 return pVal[0] < RHS.pVal[0];
514 // Otherwise, compare all words
515 for (int i = whichWord(n1 - 1); i >= 0; --i) {
516 if (pVal[i] > RHS.pVal[i])
518 if (pVal[i] < RHS.pVal[i])
524 bool APInt::slt(const APInt& RHS) const {
525 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
526 if (isSingleWord()) {
527 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
528 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth);
529 return lhsSext < rhsSext;
534 bool lhsNegative = false;
535 bool rhsNegative = false;
536 if (lhs[BitWidth-1]) {
537 // Sign bit is set so make a note of it and perform two's complement
542 if (rhs[BitWidth-1]) {
543 // Sign bit is set so make a note of it and perform two's complement
549 // Now we have unsigned values to compare so do the comparison if necessary
550 // based on the negativeness of the values.
553 return !lhs.ult(rhs);
556 else if (rhsNegative)
562 APInt& APInt::set(uint32_t bitPosition) {
564 VAL |= maskBit(bitPosition);
566 pVal[whichWord(bitPosition)] |= maskBit(bitPosition);
570 APInt& APInt::set() {
571 if (isSingleWord()) {
573 return clearUnusedBits();
576 // Set all the bits in all the words.
577 for (uint32_t i = 0; i < getNumWords() - 1; ++i)
579 // Clear the unused ones
580 return clearUnusedBits();
583 /// Set the given bit to 0 whose position is given as "bitPosition".
584 /// @brief Set a given bit to 0.
585 APInt& APInt::clear(uint32_t bitPosition) {
587 VAL &= ~maskBit(bitPosition);
589 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition);
593 /// @brief Set every bit to 0.
594 APInt& APInt::clear() {
598 memset(pVal, 0, getNumWords() * APINT_WORD_SIZE);
602 /// @brief Bitwise NOT operator. Performs a bitwise logical NOT operation on
604 APInt APInt::operator~() const {
610 /// @brief Toggle every bit to its opposite value.
611 APInt& APInt::flip() {
612 if (isSingleWord()) {
614 return clearUnusedBits();
616 for (uint32_t i = 0; i < getNumWords(); ++i)
618 return clearUnusedBits();
621 /// Toggle a given bit to its opposite value whose position is given
622 /// as "bitPosition".
623 /// @brief Toggles a given bit to its opposite value.
624 APInt& APInt::flip(uint32_t bitPosition) {
625 assert(bitPosition < BitWidth && "Out of the bit-width range!");
626 if ((*this)[bitPosition]) clear(bitPosition);
627 else set(bitPosition);
631 /// getMaxValue - This function returns the largest value
632 /// for an APInt of the specified bit-width and if isSign == true,
633 /// it should be largest signed value, otherwise unsigned value.
634 APInt APInt::getMaxValue(uint32_t numBits, bool isSign) {
635 APInt Result(numBits, 0);
638 Result.clear(numBits - 1);
642 /// getMinValue - This function returns the smallest value for
643 /// an APInt of the given bit-width and if isSign == true,
644 /// it should be smallest signed value, otherwise zero.
645 APInt APInt::getMinValue(uint32_t numBits, bool isSign) {
646 APInt Result(numBits, 0);
648 Result.set(numBits - 1);
652 /// getAllOnesValue - This function returns an all-ones value for
653 /// an APInt of the specified bit-width.
654 APInt APInt::getAllOnesValue(uint32_t numBits) {
655 return getMaxValue(numBits, false);
658 /// getNullValue - This function creates an '0' value for an
659 /// APInt of the specified bit-width.
660 APInt APInt::getNullValue(uint32_t numBits) {
661 return getMinValue(numBits, false);
664 uint64_t APInt::getHashValue() const {
665 // LLVM only supports bit widths up to 2^23 so shift the bitwidth into the
666 // high range. This makes the hash unique for integer values < 2^41 bits and
667 // doesn't hurt for larger values.
668 uint64_t hash = uint64_t(BitWidth) << (APINT_BITS_PER_WORD - 23);
670 // Add the sum of the words to the hash.
674 for (uint32_t i = 0; i < getNumWords(); ++i)
679 /// HiBits - This function returns the high "numBits" bits of this APInt.
680 APInt APInt::getHiBits(uint32_t numBits) const {
681 return APIntOps::lshr(*this, BitWidth - numBits);
684 /// LoBits - This function returns the low "numBits" bits of this APInt.
685 APInt APInt::getLoBits(uint32_t numBits) const {
686 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits),
690 bool APInt::isPowerOf2() const {
691 return (!!*this) && !(*this & (*this - APInt(BitWidth,1)));
694 uint32_t APInt::countLeadingZeros() const {
697 Count = CountLeadingZeros_64(VAL);
699 for (uint32_t i = getNumWords(); i > 0u; --i) {
701 Count += APINT_BITS_PER_WORD;
703 Count += CountLeadingZeros_64(pVal[i-1]);
708 uint32_t remainder = BitWidth % APINT_BITS_PER_WORD;
710 Count -= APINT_BITS_PER_WORD - remainder;
714 uint32_t APInt::countTrailingZeros() const {
716 return CountTrailingZeros_64(VAL);
719 for (; i < getNumWords() && pVal[i] == 0; ++i)
720 Count += APINT_BITS_PER_WORD;
721 if (i < getNumWords())
722 Count += CountTrailingZeros_64(pVal[i]);
726 uint32_t APInt::countPopulation() const {
728 return CountPopulation_64(VAL);
730 for (uint32_t i = 0; i < getNumWords(); ++i)
731 Count += CountPopulation_64(pVal[i]);
735 APInt APInt::byteSwap() const {
736 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!");
738 return APInt(BitWidth, ByteSwap_16(VAL));
739 else if (BitWidth == 32)
740 return APInt(BitWidth, ByteSwap_32(VAL));
741 else if (BitWidth == 48) {
742 uint64_t Tmp1 = ((VAL >> 32) << 16) | (VAL & 0xFFFF);
743 Tmp1 = ByteSwap_32(Tmp1);
744 uint64_t Tmp2 = (VAL >> 16) & 0xFFFF;
745 Tmp2 = ByteSwap_16(Tmp2);
748 (Tmp1 & 0xff) | ((Tmp1<<16) & 0xffff00000000ULL) | (Tmp2 << 16));
749 } else if (BitWidth == 64)
750 return APInt(BitWidth, ByteSwap_64(VAL));
752 APInt Result(BitWidth, 0);
753 char *pByte = (char*)Result.pVal;
754 for (uint32_t i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) {
756 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i];
757 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp;
763 APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1,
765 APInt A = API1, B = API2;
768 B = APIntOps::urem(A, B);
774 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double) {
780 bool isNeg = T.I >> 63;
781 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023;
783 return APInt(64ull, 0u);
784 uint64_t mantissa = ((T.I << 12) >> 12) | (1ULL << 52);
786 return isNeg ? -APInt(64u, mantissa >> (52 - exp)) :
787 APInt(64u, mantissa >> (52 - exp));
788 APInt Tmp(exp + 1, mantissa);
789 Tmp = Tmp.shl(exp - 52);
790 return isNeg ? -Tmp : Tmp;
793 /// RoundToDouble - This function convert this APInt to a double.
794 /// The layout for double is as following (IEEE Standard 754):
795 /// --------------------------------------
796 /// | Sign Exponent Fraction Bias |
797 /// |-------------------------------------- |
798 /// | 1[63] 11[62-52] 52[51-00] 1023 |
799 /// --------------------------------------
800 double APInt::roundToDouble(bool isSigned) const {
802 // Handle the simple case where the value is contained in one uint64_t.
803 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
805 int64_t sext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth);
811 // Determine if the value is negative.
812 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
814 // Construct the absolute value if we're negative.
815 APInt Tmp(isNeg ? -(*this) : (*this));
817 // Figure out how many bits we're using.
818 uint32_t n = Tmp.getActiveBits();
820 // The exponent (without bias normalization) is just the number of bits
821 // we are using. Note that the sign bit is gone since we constructed the
825 // Return infinity for exponent overflow
827 if (!isSigned || !isNeg)
828 return double(1.0E300 * 1.0E300); // positive infinity
830 return double(-1.0E300 * 1.0E300); // negative infinity
832 exp += 1023; // Increment for 1023 bias
834 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
835 // extract the high 52 bits from the correct words in pVal.
837 unsigned hiWord = whichWord(n-1);
839 mantissa = Tmp.pVal[0];
841 mantissa >>= n - 52; // shift down, we want the top 52 bits.
843 assert(hiWord > 0 && "huh?");
844 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
845 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
846 mantissa = hibits | lobits;
849 // The leading bit of mantissa is implicit, so get rid of it.
850 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
855 T.I = sign | (exp << 52) | mantissa;
859 // Truncate to new width.
860 void APInt::trunc(uint32_t width) {
861 assert(width < BitWidth && "Invalid APInt Truncate request");
862 assert(width >= IntegerType::MIN_INT_BITS && "Can't truncate to 0 bits");
863 uint32_t wordsBefore = getNumWords();
865 uint32_t wordsAfter = getNumWords();
866 if (wordsBefore != wordsAfter) {
867 if (wordsAfter == 1) {
868 uint64_t *tmp = pVal;
872 uint64_t *newVal = getClearedMemory(wordsAfter);
873 for (uint32_t i = 0; i < wordsAfter; ++i)
882 // Sign extend to a new width.
883 void APInt::sext(uint32_t width) {
884 assert(width > BitWidth && "Invalid APInt SignExtend request");
885 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
886 // If the sign bit isn't set, this is the same as zext.
892 // The sign bit is set. First, get some facts
893 uint32_t wordsBefore = getNumWords();
894 uint32_t wordBits = BitWidth % APINT_BITS_PER_WORD;
896 uint32_t wordsAfter = getNumWords();
898 // Mask the high order word appropriately
899 if (wordsBefore == wordsAfter) {
900 uint32_t newWordBits = width % APINT_BITS_PER_WORD;
901 // The extension is contained to the wordsBefore-1th word.
902 uint64_t mask = (~0ULL >> (APINT_BITS_PER_WORD - newWordBits)) << wordBits;
903 if (wordsBefore == 1)
906 pVal[wordsBefore-1] |= mask;
911 uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits;
912 uint64_t *newVal = getMemory(wordsAfter);
913 if (wordsBefore == 1)
914 newVal[0] = VAL | mask;
916 for (uint32_t i = 0; i < wordsBefore; ++i)
918 newVal[wordsBefore-1] |= mask;
920 for (uint32_t i = wordsBefore; i < wordsAfter; i++)
922 if (wordsBefore != 1)
928 // Zero extend to a new width.
929 void APInt::zext(uint32_t width) {
930 assert(width > BitWidth && "Invalid APInt ZeroExtend request");
931 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits");
932 uint32_t wordsBefore = getNumWords();
934 uint32_t wordsAfter = getNumWords();
935 if (wordsBefore != wordsAfter) {
936 uint64_t *newVal = getClearedMemory(wordsAfter);
937 if (wordsBefore == 1)
940 for (uint32_t i = 0; i < wordsBefore; ++i)
942 if (wordsBefore != 1)
948 /// Arithmetic right-shift this APInt by shiftAmt.
949 /// @brief Arithmetic right-shift function.
950 APInt APInt::ashr(uint32_t shiftAmt) const {
951 assert(shiftAmt <= BitWidth && "Invalid shift amount");
952 if (isSingleWord()) {
953 if (shiftAmt == BitWidth)
954 return APInt(BitWidth, 0); // undefined
956 uint32_t SignBit = APINT_BITS_PER_WORD - BitWidth;
957 return APInt(BitWidth,
958 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt));
962 // If all the bits were shifted out, the result is 0 or -1. This avoids issues
963 // with shifting by the size of the integer type, which produces undefined
965 if (shiftAmt == BitWidth)
967 return APInt(BitWidth, -1ULL);
969 return APInt(BitWidth, 0);
971 // Create some space for the result.
972 uint64_t * val = new uint64_t[getNumWords()];
974 // If we are shifting less than a word, compute the shift with a simple carry
975 if (shiftAmt < APINT_BITS_PER_WORD) {
977 for (int i = getNumWords()-1; i >= 0; --i) {
978 val[i] = pVal[i] >> shiftAmt | carry;
979 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
981 return APInt(val, BitWidth).clearUnusedBits();
984 // Compute some values needed by the remaining shift algorithms
985 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
986 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
988 // If we are shifting whole words, just move whole words
989 if (wordShift == 0) {
990 for (uint32_t i = 0; i < getNumWords() - offset; ++i)
991 val[i] = pVal[i+offset];
992 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
993 val[i] = (isNegative() ? -1ULL : 0);
994 return APInt(val,BitWidth).clearUnusedBits();
997 // Shift the low order words
998 uint32_t breakWord = getNumWords() - offset -1;
999 for (uint32_t i = 0; i < breakWord; ++i)
1000 val[i] = pVal[i+offset] >> wordShift |
1001 pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift);
1002 // Shift the break word.
1003 uint32_t SignBit = APINT_BITS_PER_WORD - (BitWidth % APINT_BITS_PER_WORD);
1004 val[breakWord] = uint64_t(
1005 (((int64_t(pVal[breakWord+offset]) << SignBit) >> SignBit) >> wordShift));
1007 // Remaining words are 0 or -1
1008 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1009 val[i] = (isNegative() ? -1ULL : 0);
1010 return APInt(val, BitWidth).clearUnusedBits();
1013 /// Logical right-shift this APInt by shiftAmt.
1014 /// @brief Logical right-shift function.
1015 APInt APInt::lshr(uint32_t shiftAmt) const {
1017 if (shiftAmt == BitWidth)
1018 return APInt(BitWidth, 0);
1020 return APInt(BitWidth, this->VAL >> shiftAmt);
1022 // If all the bits were shifted out, the result is 0. This avoids issues
1023 // with shifting by the size of the integer type, which produces undefined
1024 // results. We define these "undefined results" to always be 0.
1025 if (shiftAmt == BitWidth)
1026 return APInt(BitWidth, 0);
1028 // Create some space for the result.
1029 uint64_t * val = new uint64_t[getNumWords()];
1031 // If we are shifting less than a word, compute the shift with a simple carry
1032 if (shiftAmt < APINT_BITS_PER_WORD) {
1034 for (int i = getNumWords()-1; i >= 0; --i) {
1035 val[i] = pVal[i] >> shiftAmt | carry;
1036 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt);
1038 return APInt(val, BitWidth).clearUnusedBits();
1041 // Compute some values needed by the remaining shift algorithms
1042 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1043 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1045 // If we are shifting whole words, just move whole words
1046 if (wordShift == 0) {
1047 for (uint32_t i = 0; i < getNumWords() - offset; ++i)
1048 val[i] = pVal[i+offset];
1049 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++)
1051 return APInt(val,BitWidth).clearUnusedBits();
1054 // Shift the low order words
1055 uint32_t breakWord = getNumWords() - offset -1;
1056 for (uint32_t i = 0; i < breakWord; ++i)
1057 val[i] = pVal[i+offset] >> wordShift |
1058 pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift);
1059 // Shift the break word.
1060 val[breakWord] = pVal[breakWord+offset] >> wordShift;
1062 // Remaining words are 0
1063 for (uint32_t i = breakWord+1; i < getNumWords(); ++i)
1065 return APInt(val, BitWidth).clearUnusedBits();
1068 /// Left-shift this APInt by shiftAmt.
1069 /// @brief Left-shift function.
1070 APInt APInt::shl(uint32_t shiftAmt) const {
1071 assert(shiftAmt <= BitWidth && "Invalid shift amount");
1072 if (isSingleWord()) {
1073 if (shiftAmt == BitWidth)
1074 return APInt(BitWidth, 0); // avoid undefined shift results
1075 return APInt(BitWidth, VAL << shiftAmt);
1078 // If all the bits were shifted out, the result is 0. This avoids issues
1079 // with shifting by the size of the integer type, which produces undefined
1080 // results. We define these "undefined results" to always be 0.
1081 if (shiftAmt == BitWidth)
1082 return APInt(BitWidth, 0);
1084 // Create some space for the result.
1085 uint64_t * val = new uint64_t[getNumWords()];
1087 // If we are shifting less than a word, do it the easy way
1088 if (shiftAmt < APINT_BITS_PER_WORD) {
1090 for (uint32_t i = 0; i < getNumWords(); i++) {
1091 val[i] = pVal[i] << shiftAmt | carry;
1092 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt);
1094 return APInt(val, BitWidth).clearUnusedBits();
1097 // Compute some values needed by the remaining shift algorithms
1098 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD;
1099 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD;
1101 // If we are shifting whole words, just move whole words
1102 if (wordShift == 0) {
1103 for (uint32_t i = 0; i < offset; i++)
1105 for (uint32_t i = offset; i < getNumWords(); i++)
1106 val[i] = pVal[i-offset];
1107 return APInt(val,BitWidth).clearUnusedBits();
1110 // Copy whole words from this to Result.
1111 uint32_t i = getNumWords() - 1;
1112 for (; i > offset; --i)
1113 val[i] = pVal[i-offset] << wordShift |
1114 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift);
1115 val[offset] = pVal[0] << wordShift;
1116 for (i = 0; i < offset; ++i)
1118 return APInt(val, BitWidth).clearUnusedBits();
1121 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1122 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1123 /// variables here have the same names as in the algorithm. Comments explain
1124 /// the algorithm and any deviation from it.
1125 static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
1126 uint32_t m, uint32_t n) {
1127 assert(u && "Must provide dividend");
1128 assert(v && "Must provide divisor");
1129 assert(q && "Must provide quotient");
1130 assert(u != v && u != q && v != q && "Must us different memory");
1131 assert(n>1 && "n must be > 1");
1133 // Knuth uses the value b as the base of the number system. In our case b
1134 // is 2^31 so we just set it to -1u.
1135 uint64_t b = uint64_t(1) << 32;
1137 DEBUG(cerr << "KnuthDiv: m=" << m << " n=" << n << '\n');
1138 DEBUG(cerr << "KnuthDiv: original:");
1139 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1140 DEBUG(cerr << " by");
1141 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1142 DEBUG(cerr << '\n');
1143 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1144 // u and v by d. Note that we have taken Knuth's advice here to use a power
1145 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1146 // 2 allows us to shift instead of multiply and it is easy to determine the
1147 // shift amount from the leading zeros. We are basically normalizing the u
1148 // and v so that its high bits are shifted to the top of v's range without
1149 // overflow. Note that this can require an extra word in u so that u must
1150 // be of length m+n+1.
1151 uint32_t shift = CountLeadingZeros_32(v[n-1]);
1152 uint32_t v_carry = 0;
1153 uint32_t u_carry = 0;
1155 for (uint32_t i = 0; i < m+n; ++i) {
1156 uint32_t u_tmp = u[i] >> (32 - shift);
1157 u[i] = (u[i] << shift) | u_carry;
1160 for (uint32_t i = 0; i < n; ++i) {
1161 uint32_t v_tmp = v[i] >> (32 - shift);
1162 v[i] = (v[i] << shift) | v_carry;
1167 DEBUG(cerr << "KnuthDiv: normal:");
1168 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]);
1169 DEBUG(cerr << " by");
1170 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]);
1171 DEBUG(cerr << '\n');
1173 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1176 DEBUG(cerr << "KnuthDiv: quotient digit #" << j << '\n');
1177 // D3. [Calculate q'.].
1178 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1179 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1180 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1181 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test
1182 // on v[n-2] determines at high speed most of the cases in which the trial
1183 // value qp is one too large, and it eliminates all cases where qp is two
1185 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]);
1186 DEBUG(cerr << "KnuthDiv: dividend == " << dividend << '\n');
1187 uint64_t qp = dividend / v[n-1];
1188 uint64_t rp = dividend % v[n-1];
1189 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1192 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1195 DEBUG(cerr << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1197 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1198 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1199 // consists of a simple multiplication by a one-place number, combined with
1202 for (uint32_t i = 0; i < n; ++i) {
1203 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
1204 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
1205 bool borrow = subtrahend > u_tmp;
1206 DEBUG(cerr << "KnuthDiv: u_tmp == " << u_tmp
1207 << ", subtrahend == " << subtrahend
1208 << ", borrow = " << borrow << '\n');
1210 uint64_t result = u_tmp - subtrahend;
1212 u[k++] = result & (b-1); // subtract low word
1213 u[k++] = result >> 32; // subtract high word
1214 while (borrow && k <= m+n) { // deal with borrow to the left
1220 DEBUG(cerr << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " <<
1223 DEBUG(cerr << "KnuthDiv: after subtraction:");
1224 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1225 DEBUG(cerr << '\n');
1226 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1227 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1228 // true value plus b**(n+1), namely as the b's complement of
1229 // the true value, and a "borrow" to the left should be remembered.
1232 bool carry = true; // true because b's complement is "complement + 1"
1233 for (uint32_t i = 0; i <= m+n; ++i) {
1234 u[i] = ~u[i] + carry; // b's complement
1235 carry = carry && u[i] == 0;
1238 DEBUG(cerr << "KnuthDiv: after complement:");
1239 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]);
1240 DEBUG(cerr << '\n');
1242 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1243 // negative, go to step D6; otherwise go on to step D7.
1246 // D6. [Add back]. The probability that this step is necessary is very
1247 // small, on the order of only 2/b. Make sure that test data accounts for
1248 // this possibility. Decrease q[j] by 1
1250 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1251 // A carry will occur to the left of u[j+n], and it should be ignored
1252 // since it cancels with the borrow that occurred in D4.
1254 for (uint32_t i = 0; i < n; i++) {
1255 uint32_t limit = std::min(u[j+i],v[i]);
1256 u[j+i] += v[i] + carry;
1257 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1261 DEBUG(cerr << "KnuthDiv: after correction:");
1262 DEBUG(for (int i = m+n; i >=0; i--) cerr <<" " << u[i]);
1263 DEBUG(cerr << "\nKnuthDiv: digit result = " << q[j] << '\n');
1265 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1268 DEBUG(cerr << "KnuthDiv: quotient:");
1269 DEBUG(for (int i = m; i >=0; i--) cerr <<" " << q[i]);
1270 DEBUG(cerr << '\n');
1272 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1273 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1274 // compute the remainder (urem uses this).
1276 // The value d is expressed by the "shift" value above since we avoided
1277 // multiplication by d by using a shift left. So, all we have to do is
1278 // shift right here. In order to mak
1281 DEBUG(cerr << "KnuthDiv: remainder:");
1282 for (int i = n-1; i >= 0; i--) {
1283 r[i] = (u[i] >> shift) | carry;
1284 carry = u[i] << (32 - shift);
1285 DEBUG(cerr << " " << r[i]);
1288 for (int i = n-1; i >= 0; i--) {
1290 DEBUG(cerr << " " << r[i]);
1293 DEBUG(cerr << '\n');
1295 DEBUG(cerr << std::setbase(10) << '\n');
1298 void APInt::divide(const APInt LHS, uint32_t lhsWords,
1299 const APInt &RHS, uint32_t rhsWords,
1300 APInt *Quotient, APInt *Remainder)
1302 assert(lhsWords >= rhsWords && "Fractional result");
1304 // First, compose the values into an array of 32-bit words instead of
1305 // 64-bit words. This is a necessity of both the "short division" algorithm
1306 // and the the Knuth "classical algorithm" which requires there to be native
1307 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1308 // can't use 64-bit operands here because we don't have native results of
1309 // 128-bits. Furthremore, casting the 64-bit values to 32-bit values won't
1310 // work on large-endian machines.
1311 uint64_t mask = ~0ull >> (sizeof(uint32_t)*8);
1312 uint32_t n = rhsWords * 2;
1313 uint32_t m = (lhsWords * 2) - n;
1315 // Allocate space for the temporary values we need either on the stack, if
1316 // it will fit, or on the heap if it won't.
1317 uint32_t SPACE[128];
1322 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1325 Q = &SPACE[(m+n+1) + n];
1327 R = &SPACE[(m+n+1) + n + (m+n)];
1329 U = new uint32_t[m + n + 1];
1330 V = new uint32_t[n];
1331 Q = new uint32_t[m+n];
1333 R = new uint32_t[n];
1336 // Initialize the dividend
1337 memset(U, 0, (m+n+1)*sizeof(uint32_t));
1338 for (unsigned i = 0; i < lhsWords; ++i) {
1339 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]);
1340 U[i * 2] = tmp & mask;
1341 U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1343 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1345 // Initialize the divisor
1346 memset(V, 0, (n)*sizeof(uint32_t));
1347 for (unsigned i = 0; i < rhsWords; ++i) {
1348 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]);
1349 V[i * 2] = tmp & mask;
1350 V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8);
1353 // initialize the quotient and remainder
1354 memset(Q, 0, (m+n) * sizeof(uint32_t));
1356 memset(R, 0, n * sizeof(uint32_t));
1358 // Now, adjust m and n for the Knuth division. n is the number of words in
1359 // the divisor. m is the number of words by which the dividend exceeds the
1360 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1361 // contain any zero words or the Knuth algorithm fails.
1362 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1366 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1369 // If we're left with only a single word for the divisor, Knuth doesn't work
1370 // so we implement the short division algorithm here. This is much simpler
1371 // and faster because we are certain that we can divide a 64-bit quantity
1372 // by a 32-bit quantity at hardware speed and short division is simply a
1373 // series of such operations. This is just like doing short division but we
1374 // are using base 2^32 instead of base 10.
1375 assert(n != 0 && "Divide by zero?");
1377 uint32_t divisor = V[0];
1378 uint32_t remainder = 0;
1379 for (int i = m+n-1; i >= 0; i--) {
1380 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i];
1381 if (partial_dividend == 0) {
1384 } else if (partial_dividend < divisor) {
1386 remainder = partial_dividend;
1387 } else if (partial_dividend == divisor) {
1391 Q[i] = partial_dividend / divisor;
1392 remainder = partial_dividend - (Q[i] * divisor);
1398 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1400 KnuthDiv(U, V, Q, R, m, n);
1403 // If the caller wants the quotient
1405 // Set up the Quotient value's memory.
1406 if (Quotient->BitWidth != LHS.BitWidth) {
1407 if (Quotient->isSingleWord())
1410 delete Quotient->pVal;
1411 Quotient->BitWidth = LHS.BitWidth;
1412 if (!Quotient->isSingleWord())
1413 Quotient->pVal = getClearedMemory(Quotient->getNumWords());
1417 // The quotient is in Q. Reconstitute the quotient into Quotient's low
1419 if (lhsWords == 1) {
1421 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
1422 if (Quotient->isSingleWord())
1423 Quotient->VAL = tmp;
1425 Quotient->pVal[0] = tmp;
1427 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough");
1428 for (unsigned i = 0; i < lhsWords; ++i)
1430 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1434 // If the caller wants the remainder
1436 // Set up the Remainder value's memory.
1437 if (Remainder->BitWidth != RHS.BitWidth) {
1438 if (Remainder->isSingleWord())
1441 delete Remainder->pVal;
1442 Remainder->BitWidth = RHS.BitWidth;
1443 if (!Remainder->isSingleWord())
1444 Remainder->pVal = getClearedMemory(Remainder->getNumWords());
1448 // The remainder is in R. Reconstitute the remainder into Remainder's low
1450 if (rhsWords == 1) {
1452 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2));
1453 if (Remainder->isSingleWord())
1454 Remainder->VAL = tmp;
1456 Remainder->pVal[0] = tmp;
1458 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough");
1459 for (unsigned i = 0; i < rhsWords; ++i)
1460 Remainder->pVal[i] =
1461 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2));
1465 // Clean up the memory we allocated.
1466 if (U != &SPACE[0]) {
1474 APInt APInt::udiv(const APInt& RHS) const {
1475 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1477 // First, deal with the easy case
1478 if (isSingleWord()) {
1479 assert(RHS.VAL != 0 && "Divide by zero?");
1480 return APInt(BitWidth, VAL / RHS.VAL);
1483 // Get some facts about the LHS and RHS number of bits and words
1484 uint32_t rhsBits = RHS.getActiveBits();
1485 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1486 assert(rhsWords && "Divided by zero???");
1487 uint32_t lhsBits = this->getActiveBits();
1488 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1);
1490 // Deal with some degenerate cases
1493 return APInt(BitWidth, 0);
1494 else if (lhsWords < rhsWords || this->ult(RHS)) {
1495 // X / Y ===> 0, iff X < Y
1496 return APInt(BitWidth, 0);
1497 } else if (*this == RHS) {
1499 return APInt(BitWidth, 1);
1500 } else if (lhsWords == 1 && rhsWords == 1) {
1501 // All high words are zero, just use native divide
1502 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]);
1505 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1506 APInt Quotient(1,0); // to hold result.
1507 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0);
1511 APInt APInt::urem(const APInt& RHS) const {
1512 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1513 if (isSingleWord()) {
1514 assert(RHS.VAL != 0 && "Remainder by zero?");
1515 return APInt(BitWidth, VAL % RHS.VAL);
1518 // Get some facts about the LHS
1519 uint32_t lhsBits = getActiveBits();
1520 uint32_t lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1);
1522 // Get some facts about the RHS
1523 uint32_t rhsBits = RHS.getActiveBits();
1524 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1);
1525 assert(rhsWords && "Performing remainder operation by zero ???");
1527 // Check the degenerate cases
1528 if (lhsWords == 0) {
1530 return APInt(BitWidth, 0);
1531 } else if (lhsWords < rhsWords || this->ult(RHS)) {
1532 // X % Y ===> X, iff X < Y
1534 } else if (*this == RHS) {
1536 return APInt(BitWidth, 0);
1537 } else if (lhsWords == 1) {
1538 // All high words are zero, just use native remainder
1539 return APInt(BitWidth, pVal[0] % RHS.pVal[0]);
1542 // We have to compute it the hard way. Invoke the Knute divide algorithm.
1543 APInt Remainder(1,0);
1544 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder);
1548 void APInt::fromString(uint32_t numbits, const char *str, uint32_t slen,
1550 // Check our assumptions here
1551 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1552 "Radix should be 2, 8, 10, or 16!");
1553 assert(str && "String is null?");
1554 bool isNeg = str[0] == '-';
1557 assert(slen <= numbits || radix != 2 && "Insufficient bit width");
1558 assert(slen*3 <= numbits || radix != 8 && "Insufficient bit width");
1559 assert(slen*4 <= numbits || radix != 16 && "Insufficient bit width");
1560 assert((slen*64)/20 <= numbits || radix != 10 && "Insufficient bit width");
1563 if (!isSingleWord())
1564 pVal = getClearedMemory(getNumWords());
1566 // Figure out if we can shift instead of multiply
1567 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
1569 // Set up an APInt for the digit to add outside the loop so we don't
1570 // constantly construct/destruct it.
1571 APInt apdigit(getBitWidth(), 0);
1572 APInt apradix(getBitWidth(), radix);
1574 // Enter digit traversal loop
1575 for (unsigned i = 0; i < slen; i++) {
1578 char cdigit = str[i];
1579 if (isdigit(cdigit))
1580 digit = cdigit - '0';
1581 else if (isxdigit(cdigit))
1583 digit = cdigit - 'a' + 10;
1584 else if (cdigit >= 'A')
1585 digit = cdigit - 'A' + 10;
1587 assert(0 && "huh?");
1589 assert(0 && "Invalid character in digit string");
1591 // Shift or multiple the value by the radix
1597 // Add in the digit we just interpreted
1598 if (apdigit.isSingleWord())
1599 apdigit.VAL = digit;
1601 apdigit.pVal[0] = digit;
1604 // If its negative, put it in two's complement form
1611 std::string APInt::toString(uint8_t radix, bool wantSigned) const {
1612 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) &&
1613 "Radix should be 2, 8, 10, or 16!");
1614 static const char *digits[] = {
1615 "0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"
1618 uint32_t bits_used = getActiveBits();
1619 if (isSingleWord()) {
1621 const char *format = (radix == 10 ? (wantSigned ? "%lld" : "%llu") :
1622 (radix == 16 ? "%llX" : (radix == 8 ? "%llo" : 0)));
1625 int64_t sextVal = (int64_t(VAL) << (APINT_BITS_PER_WORD-BitWidth)) >>
1626 (APINT_BITS_PER_WORD-BitWidth);
1627 sprintf(buf, format, sextVal);
1629 sprintf(buf, format, VAL);
1634 uint32_t bit = v & 1;
1636 buf[bits_used] = digits[bit][0];
1645 uint64_t mask = radix - 1;
1646 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : 1);
1647 uint32_t nibbles = APINT_BITS_PER_WORD / shift;
1648 for (uint32_t i = 0; i < getNumWords(); ++i) {
1649 uint64_t value = pVal[i];
1650 for (uint32_t j = 0; j < nibbles; ++j) {
1651 result.insert(0, digits[ value & mask ]);
1659 APInt divisor(4, radix);
1660 APInt zero(tmp.getBitWidth(), 0);
1661 size_t insert_at = 0;
1662 if (wantSigned && tmp[BitWidth-1]) {
1663 // They want to print the signed version and it is a negative value
1664 // Flip the bits and add one to turn it into the equivalent positive
1665 // value and put a '-' in the result.
1671 if (tmp == APInt(tmp.getBitWidth(), 0))
1673 else while (tmp.ne(zero)) {
1675 APInt tmp2(tmp.getBitWidth(), 0);
1676 divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2,
1678 uint32_t digit = APdigit.getZExtValue();
1679 assert(digit < radix && "divide failed");
1680 result.insert(insert_at,digits[digit]);
1688 void APInt::dump() const
1690 cerr << "APInt(" << BitWidth << ")=" << std::setbase(16);
1693 else for (unsigned i = getNumWords(); i > 0; i--) {
1694 cerr << pVal[i-1] << " ";
1696 cerr << " (" << this->toString(10, false) << ")\n" << std::setbase(10);