LLVM  14.0.0git
APInt.cpp
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1 //===-- APInt.cpp - Implement APInt class ---------------------------------===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 //
9 // This file implements a class to represent arbitrary precision integer
10 // constant values and provide a variety of arithmetic operations on them.
11 //
12 //===----------------------------------------------------------------------===//
13 
14 #include "llvm/ADT/APInt.h"
15 #include "llvm/ADT/ArrayRef.h"
16 #include "llvm/ADT/FoldingSet.h"
17 #include "llvm/ADT/Hashing.h"
18 #include "llvm/ADT/Optional.h"
19 #include "llvm/ADT/SmallString.h"
20 #include "llvm/ADT/StringRef.h"
21 #include "llvm/ADT/bit.h"
22 #include "llvm/Config/llvm-config.h"
23 #include "llvm/Support/Debug.h"
27 #include <cmath>
28 #include <cstring>
29 using namespace llvm;
30 
31 #define DEBUG_TYPE "apint"
32 
33 /// A utility function for allocating memory, checking for allocation failures,
34 /// and ensuring the contents are zeroed.
35 inline static uint64_t* getClearedMemory(unsigned numWords) {
36  uint64_t *result = new uint64_t[numWords];
37  memset(result, 0, numWords * sizeof(uint64_t));
38  return result;
39 }
40 
41 /// A utility function for allocating memory and checking for allocation
42 /// failure. The content is not zeroed.
43 inline static uint64_t* getMemory(unsigned numWords) {
44  return new uint64_t[numWords];
45 }
46 
47 /// A utility function that converts a character to a digit.
48 inline static unsigned getDigit(char cdigit, uint8_t radix) {
49  unsigned r;
50 
51  if (radix == 16 || radix == 36) {
52  r = cdigit - '0';
53  if (r <= 9)
54  return r;
55 
56  r = cdigit - 'A';
57  if (r <= radix - 11U)
58  return r + 10;
59 
60  r = cdigit - 'a';
61  if (r <= radix - 11U)
62  return r + 10;
63 
64  radix = 10;
65  }
66 
67  r = cdigit - '0';
68  if (r < radix)
69  return r;
70 
71  return -1U;
72 }
73 
74 
75 void APInt::initSlowCase(uint64_t val, bool isSigned) {
76  U.pVal = getClearedMemory(getNumWords());
77  U.pVal[0] = val;
78  if (isSigned && int64_t(val) < 0)
79  for (unsigned i = 1; i < getNumWords(); ++i)
80  U.pVal[i] = WORDTYPE_MAX;
81  clearUnusedBits();
82 }
83 
84 void APInt::initSlowCase(const APInt& that) {
85  U.pVal = getMemory(getNumWords());
86  memcpy(U.pVal, that.U.pVal, getNumWords() * APINT_WORD_SIZE);
87 }
88 
89 void APInt::initFromArray(ArrayRef<uint64_t> bigVal) {
90  assert(bigVal.data() && "Null pointer detected!");
91  if (isSingleWord())
92  U.VAL = bigVal[0];
93  else {
94  // Get memory, cleared to 0
95  U.pVal = getClearedMemory(getNumWords());
96  // Calculate the number of words to copy
97  unsigned words = std::min<unsigned>(bigVal.size(), getNumWords());
98  // Copy the words from bigVal to pVal
99  memcpy(U.pVal, bigVal.data(), words * APINT_WORD_SIZE);
100  }
101  // Make sure unused high bits are cleared
102  clearUnusedBits();
103 }
104 
105 APInt::APInt(unsigned numBits, ArrayRef<uint64_t> bigVal) : BitWidth(numBits) {
106  initFromArray(bigVal);
107 }
108 
109 APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[])
110  : BitWidth(numBits) {
111  initFromArray(makeArrayRef(bigVal, numWords));
112 }
113 
114 APInt::APInt(unsigned numbits, StringRef Str, uint8_t radix)
115  : BitWidth(numbits) {
116  fromString(numbits, Str, radix);
117 }
118 
119 void APInt::reallocate(unsigned NewBitWidth) {
120  // If the number of words is the same we can just change the width and stop.
121  if (getNumWords() == getNumWords(NewBitWidth)) {
122  BitWidth = NewBitWidth;
123  return;
124  }
125 
126  // If we have an allocation, delete it.
127  if (!isSingleWord())
128  delete [] U.pVal;
129 
130  // Update BitWidth.
131  BitWidth = NewBitWidth;
132 
133  // If we are supposed to have an allocation, create it.
134  if (!isSingleWord())
135  U.pVal = getMemory(getNumWords());
136 }
137 
138 void APInt::assignSlowCase(const APInt &RHS) {
139  // Don't do anything for X = X
140  if (this == &RHS)
141  return;
142 
143  // Adjust the bit width and handle allocations as necessary.
144  reallocate(RHS.getBitWidth());
145 
146  // Copy the data.
147  if (isSingleWord())
148  U.VAL = RHS.U.VAL;
149  else
150  memcpy(U.pVal, RHS.U.pVal, getNumWords() * APINT_WORD_SIZE);
151 }
152 
153 /// This method 'profiles' an APInt for use with FoldingSet.
155  ID.AddInteger(BitWidth);
156 
157  if (isSingleWord()) {
158  ID.AddInteger(U.VAL);
159  return;
160  }
161 
162  unsigned NumWords = getNumWords();
163  for (unsigned i = 0; i < NumWords; ++i)
164  ID.AddInteger(U.pVal[i]);
165 }
166 
167 /// Prefix increment operator. Increments the APInt by one.
169  if (isSingleWord())
170  ++U.VAL;
171  else
172  tcIncrement(U.pVal, getNumWords());
173  return clearUnusedBits();
174 }
175 
176 /// Prefix decrement operator. Decrements the APInt by one.
178  if (isSingleWord())
179  --U.VAL;
180  else
181  tcDecrement(U.pVal, getNumWords());
182  return clearUnusedBits();
183 }
184 
185 /// Adds the RHS APInt to this APInt.
186 /// @returns this, after addition of RHS.
187 /// Addition assignment operator.
189  assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
190  if (isSingleWord())
191  U.VAL += RHS.U.VAL;
192  else
193  tcAdd(U.pVal, RHS.U.pVal, 0, getNumWords());
194  return clearUnusedBits();
195 }
196 
198  if (isSingleWord())
199  U.VAL += RHS;
200  else
201  tcAddPart(U.pVal, RHS, getNumWords());
202  return clearUnusedBits();
203 }
204 
205 /// Subtracts the RHS APInt from this APInt
206 /// @returns this, after subtraction
207 /// Subtraction assignment operator.
209  assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
210  if (isSingleWord())
211  U.VAL -= RHS.U.VAL;
212  else
213  tcSubtract(U.pVal, RHS.U.pVal, 0, getNumWords());
214  return clearUnusedBits();
215 }
216 
218  if (isSingleWord())
219  U.VAL -= RHS;
220  else
221  tcSubtractPart(U.pVal, RHS, getNumWords());
222  return clearUnusedBits();
223 }
224 
226  assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
227  if (isSingleWord())
228  return APInt(BitWidth, U.VAL * RHS.U.VAL);
229 
230  APInt Result(getMemory(getNumWords()), getBitWidth());
231  tcMultiply(Result.U.pVal, U.pVal, RHS.U.pVal, getNumWords());
232  Result.clearUnusedBits();
233  return Result;
234 }
235 
236 void APInt::andAssignSlowCase(const APInt &RHS) {
237  WordType *dst = U.pVal, *rhs = RHS.U.pVal;
238  for (size_t i = 0, e = getNumWords(); i != e; ++i)
239  dst[i] &= rhs[i];
240 }
241 
242 void APInt::orAssignSlowCase(const APInt &RHS) {
243  WordType *dst = U.pVal, *rhs = RHS.U.pVal;
244  for (size_t i = 0, e = getNumWords(); i != e; ++i)
245  dst[i] |= rhs[i];
246 }
247 
248 void APInt::xorAssignSlowCase(const APInt &RHS) {
249  WordType *dst = U.pVal, *rhs = RHS.U.pVal;
250  for (size_t i = 0, e = getNumWords(); i != e; ++i)
251  dst[i] ^= rhs[i];
252 }
253 
255  *this = *this * RHS;
256  return *this;
257 }
258 
260  if (isSingleWord()) {
261  U.VAL *= RHS;
262  } else {
263  unsigned NumWords = getNumWords();
264  tcMultiplyPart(U.pVal, U.pVal, RHS, 0, NumWords, NumWords, false);
265  }
266  return clearUnusedBits();
267 }
268 
269 bool APInt::equalSlowCase(const APInt &RHS) const {
270  return std::equal(U.pVal, U.pVal + getNumWords(), RHS.U.pVal);
271 }
272 
273 int APInt::compare(const APInt& RHS) const {
274  assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
275  if (isSingleWord())
276  return U.VAL < RHS.U.VAL ? -1 : U.VAL > RHS.U.VAL;
277 
278  return tcCompare(U.pVal, RHS.U.pVal, getNumWords());
279 }
280 
281 int APInt::compareSigned(const APInt& RHS) const {
282  assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison");
283  if (isSingleWord()) {
284  int64_t lhsSext = SignExtend64(U.VAL, BitWidth);
285  int64_t rhsSext = SignExtend64(RHS.U.VAL, BitWidth);
286  return lhsSext < rhsSext ? -1 : lhsSext > rhsSext;
287  }
288 
289  bool lhsNeg = isNegative();
290  bool rhsNeg = RHS.isNegative();
291 
292  // If the sign bits don't match, then (LHS < RHS) if LHS is negative
293  if (lhsNeg != rhsNeg)
294  return lhsNeg ? -1 : 1;
295 
296  // Otherwise we can just use an unsigned comparison, because even negative
297  // numbers compare correctly this way if both have the same signed-ness.
298  return tcCompare(U.pVal, RHS.U.pVal, getNumWords());
299 }
300 
301 void APInt::setBitsSlowCase(unsigned loBit, unsigned hiBit) {
302  unsigned loWord = whichWord(loBit);
303  unsigned hiWord = whichWord(hiBit);
304 
305  // Create an initial mask for the low word with zeros below loBit.
306  uint64_t loMask = WORDTYPE_MAX << whichBit(loBit);
307 
308  // If hiBit is not aligned, we need a high mask.
309  unsigned hiShiftAmt = whichBit(hiBit);
310  if (hiShiftAmt != 0) {
311  // Create a high mask with zeros above hiBit.
312  uint64_t hiMask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - hiShiftAmt);
313  // If loWord and hiWord are equal, then we combine the masks. Otherwise,
314  // set the bits in hiWord.
315  if (hiWord == loWord)
316  loMask &= hiMask;
317  else
318  U.pVal[hiWord] |= hiMask;
319  }
320  // Apply the mask to the low word.
321  U.pVal[loWord] |= loMask;
322 
323  // Fill any words between loWord and hiWord with all ones.
324  for (unsigned word = loWord + 1; word < hiWord; ++word)
325  U.pVal[word] = WORDTYPE_MAX;
326 }
327 
328 // Complement a bignum in-place.
329 static void tcComplement(APInt::WordType *dst, unsigned parts) {
330  for (unsigned i = 0; i < parts; i++)
331  dst[i] = ~dst[i];
332 }
333 
334 /// Toggle every bit to its opposite value.
335 void APInt::flipAllBitsSlowCase() {
336  tcComplement(U.pVal, getNumWords());
337  clearUnusedBits();
338 }
339 
340 /// Concatenate the bits from "NewLSB" onto the bottom of *this. This is
341 /// equivalent to:
342 /// (this->zext(NewWidth) << NewLSB.getBitWidth()) | NewLSB.zext(NewWidth)
343 /// In the slow case, we know the result is large.
344 APInt APInt::concatSlowCase(const APInt &NewLSB) const {
345  unsigned NewWidth = getBitWidth() + NewLSB.getBitWidth();
346  APInt Result = NewLSB.zextOrSelf(NewWidth);
347  Result.insertBits(*this, NewLSB.getBitWidth());
348  return Result;
349 }
350 
351 /// Toggle a given bit to its opposite value whose position is given
352 /// as "bitPosition".
353 /// Toggles a given bit to its opposite value.
354 void APInt::flipBit(unsigned bitPosition) {
355  assert(bitPosition < BitWidth && "Out of the bit-width range!");
356  setBitVal(bitPosition, !(*this)[bitPosition]);
357 }
358 
359 void APInt::insertBits(const APInt &subBits, unsigned bitPosition) {
360  unsigned subBitWidth = subBits.getBitWidth();
361  assert((subBitWidth + bitPosition) <= BitWidth && "Illegal bit insertion");
362 
363  // inserting no bits is a noop.
364  if (subBitWidth == 0)
365  return;
366 
367  // Insertion is a direct copy.
368  if (subBitWidth == BitWidth) {
369  *this = subBits;
370  return;
371  }
372 
373  // Single word result can be done as a direct bitmask.
374  if (isSingleWord()) {
375  uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - subBitWidth);
376  U.VAL &= ~(mask << bitPosition);
377  U.VAL |= (subBits.U.VAL << bitPosition);
378  return;
379  }
380 
381  unsigned loBit = whichBit(bitPosition);
382  unsigned loWord = whichWord(bitPosition);
383  unsigned hi1Word = whichWord(bitPosition + subBitWidth - 1);
384 
385  // Insertion within a single word can be done as a direct bitmask.
386  if (loWord == hi1Word) {
387  uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - subBitWidth);
388  U.pVal[loWord] &= ~(mask << loBit);
389  U.pVal[loWord] |= (subBits.U.VAL << loBit);
390  return;
391  }
392 
393  // Insert on word boundaries.
394  if (loBit == 0) {
395  // Direct copy whole words.
396  unsigned numWholeSubWords = subBitWidth / APINT_BITS_PER_WORD;
397  memcpy(U.pVal + loWord, subBits.getRawData(),
398  numWholeSubWords * APINT_WORD_SIZE);
399 
400  // Mask+insert remaining bits.
401  unsigned remainingBits = subBitWidth % APINT_BITS_PER_WORD;
402  if (remainingBits != 0) {
403  uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - remainingBits);
404  U.pVal[hi1Word] &= ~mask;
405  U.pVal[hi1Word] |= subBits.getWord(subBitWidth - 1);
406  }
407  return;
408  }
409 
410  // General case - set/clear individual bits in dst based on src.
411  // TODO - there is scope for optimization here, but at the moment this code
412  // path is barely used so prefer readability over performance.
413  for (unsigned i = 0; i != subBitWidth; ++i)
414  setBitVal(bitPosition + i, subBits[i]);
415 }
416 
417 void APInt::insertBits(uint64_t subBits, unsigned bitPosition, unsigned numBits) {
418  uint64_t maskBits = maskTrailingOnes<uint64_t>(numBits);
419  subBits &= maskBits;
420  if (isSingleWord()) {
421  U.VAL &= ~(maskBits << bitPosition);
422  U.VAL |= subBits << bitPosition;
423  return;
424  }
425 
426  unsigned loBit = whichBit(bitPosition);
427  unsigned loWord = whichWord(bitPosition);
428  unsigned hiWord = whichWord(bitPosition + numBits - 1);
429  if (loWord == hiWord) {
430  U.pVal[loWord] &= ~(maskBits << loBit);
431  U.pVal[loWord] |= subBits << loBit;
432  return;
433  }
434 
435  static_assert(8 * sizeof(WordType) <= 64, "This code assumes only two words affected");
436  unsigned wordBits = 8 * sizeof(WordType);
437  U.pVal[loWord] &= ~(maskBits << loBit);
438  U.pVal[loWord] |= subBits << loBit;
439 
440  U.pVal[hiWord] &= ~(maskBits >> (wordBits - loBit));
441  U.pVal[hiWord] |= subBits >> (wordBits - loBit);
442 }
443 
444 APInt APInt::extractBits(unsigned numBits, unsigned bitPosition) const {
445  assert(bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth &&
446  "Illegal bit extraction");
447 
448  if (isSingleWord())
449  return APInt(numBits, U.VAL >> bitPosition);
450 
451  unsigned loBit = whichBit(bitPosition);
452  unsigned loWord = whichWord(bitPosition);
453  unsigned hiWord = whichWord(bitPosition + numBits - 1);
454 
455  // Single word result extracting bits from a single word source.
456  if (loWord == hiWord)
457  return APInt(numBits, U.pVal[loWord] >> loBit);
458 
459  // Extracting bits that start on a source word boundary can be done
460  // as a fast memory copy.
461  if (loBit == 0)
462  return APInt(numBits, makeArrayRef(U.pVal + loWord, 1 + hiWord - loWord));
463 
464  // General case - shift + copy source words directly into place.
465  APInt Result(numBits, 0);
466  unsigned NumSrcWords = getNumWords();
467  unsigned NumDstWords = Result.getNumWords();
468 
469  uint64_t *DestPtr = Result.isSingleWord() ? &Result.U.VAL : Result.U.pVal;
470  for (unsigned word = 0; word < NumDstWords; ++word) {
471  uint64_t w0 = U.pVal[loWord + word];
472  uint64_t w1 =
473  (loWord + word + 1) < NumSrcWords ? U.pVal[loWord + word + 1] : 0;
474  DestPtr[word] = (w0 >> loBit) | (w1 << (APINT_BITS_PER_WORD - loBit));
475  }
476 
477  return Result.clearUnusedBits();
478 }
479 
481  unsigned bitPosition) const {
482  assert(numBits > 0 && "Can't extract zero bits");
483  assert(bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth &&
484  "Illegal bit extraction");
485  assert(numBits <= 64 && "Illegal bit extraction");
486 
487  uint64_t maskBits = maskTrailingOnes<uint64_t>(numBits);
488  if (isSingleWord())
489  return (U.VAL >> bitPosition) & maskBits;
490 
491  unsigned loBit = whichBit(bitPosition);
492  unsigned loWord = whichWord(bitPosition);
493  unsigned hiWord = whichWord(bitPosition + numBits - 1);
494  if (loWord == hiWord)
495  return (U.pVal[loWord] >> loBit) & maskBits;
496 
497  static_assert(8 * sizeof(WordType) <= 64, "This code assumes only two words affected");
498  unsigned wordBits = 8 * sizeof(WordType);
499  uint64_t retBits = U.pVal[loWord] >> loBit;
500  retBits |= U.pVal[hiWord] << (wordBits - loBit);
501  retBits &= maskBits;
502  return retBits;
503 }
504 
505 unsigned APInt::getBitsNeeded(StringRef str, uint8_t radix) {
506  assert(!str.empty() && "Invalid string length");
507  assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||
508  radix == 36) &&
509  "Radix should be 2, 8, 10, 16, or 36!");
510 
511  size_t slen = str.size();
512 
513  // Each computation below needs to know if it's negative.
514  StringRef::iterator p = str.begin();
515  unsigned isNegative = *p == '-';
516  if (*p == '-' || *p == '+') {
517  p++;
518  slen--;
519  assert(slen && "String is only a sign, needs a value.");
520  }
521 
522  // For radixes of power-of-two values, the bits required is accurately and
523  // easily computed
524  if (radix == 2)
525  return slen + isNegative;
526  if (radix == 8)
527  return slen * 3 + isNegative;
528  if (radix == 16)
529  return slen * 4 + isNegative;
530 
531  // FIXME: base 36
532 
533  // This is grossly inefficient but accurate. We could probably do something
534  // with a computation of roughly slen*64/20 and then adjust by the value of
535  // the first few digits. But, I'm not sure how accurate that could be.
536 
537  // Compute a sufficient number of bits that is always large enough but might
538  // be too large. This avoids the assertion in the constructor. This
539  // calculation doesn't work appropriately for the numbers 0-9, so just use 4
540  // bits in that case.
541  unsigned sufficient
542  = radix == 10? (slen == 1 ? 4 : slen * 64/18)
543  : (slen == 1 ? 7 : slen * 16/3);
544 
545  // Convert to the actual binary value.
546  APInt tmp(sufficient, StringRef(p, slen), radix);
547 
548  // Compute how many bits are required. If the log is infinite, assume we need
549  // just bit. If the log is exact and value is negative, then the value is
550  // MinSignedValue with (log + 1) bits.
551  unsigned log = tmp.logBase2();
552  if (log == (unsigned)-1) {
553  return isNegative + 1;
554  } else if (isNegative && tmp.isPowerOf2()) {
555  return isNegative + log;
556  } else {
557  return isNegative + log + 1;
558  }
559 }
560 
562  if (Arg.isSingleWord())
563  return hash_combine(Arg.BitWidth, Arg.U.VAL);
564 
565  return hash_combine(
566  Arg.BitWidth,
567  hash_combine_range(Arg.U.pVal, Arg.U.pVal + Arg.getNumWords()));
568 }
569 
571  return static_cast<unsigned>(hash_value(Key));
572 }
573 
574 bool APInt::isSplat(unsigned SplatSizeInBits) const {
575  assert(getBitWidth() % SplatSizeInBits == 0 &&
576  "SplatSizeInBits must divide width!");
577  // We can check that all parts of an integer are equal by making use of a
578  // little trick: rotate and check if it's still the same value.
579  return *this == rotl(SplatSizeInBits);
580 }
581 
582 /// This function returns the high "numBits" bits of this APInt.
583 APInt APInt::getHiBits(unsigned numBits) const {
584  return this->lshr(BitWidth - numBits);
585 }
586 
587 /// This function returns the low "numBits" bits of this APInt.
588 APInt APInt::getLoBits(unsigned numBits) const {
589  APInt Result(getLowBitsSet(BitWidth, numBits));
590  Result &= *this;
591  return Result;
592 }
593 
594 /// Return a value containing V broadcasted over NewLen bits.
595 APInt APInt::getSplat(unsigned NewLen, const APInt &V) {
596  assert(NewLen >= V.getBitWidth() && "Can't splat to smaller bit width!");
597 
598  APInt Val = V.zextOrSelf(NewLen);
599  for (unsigned I = V.getBitWidth(); I < NewLen; I <<= 1)
600  Val |= Val << I;
601 
602  return Val;
603 }
604 
605 unsigned APInt::countLeadingZerosSlowCase() const {
606  unsigned Count = 0;
607  for (int i = getNumWords()-1; i >= 0; --i) {
608  uint64_t V = U.pVal[i];
609  if (V == 0)
610  Count += APINT_BITS_PER_WORD;
611  else {
612  Count += llvm::countLeadingZeros(V);
613  break;
614  }
615  }
616  // Adjust for unused bits in the most significant word (they are zero).
617  unsigned Mod = BitWidth % APINT_BITS_PER_WORD;
618  Count -= Mod > 0 ? APINT_BITS_PER_WORD - Mod : 0;
619  return Count;
620 }
621 
622 unsigned APInt::countLeadingOnesSlowCase() const {
623  unsigned highWordBits = BitWidth % APINT_BITS_PER_WORD;
624  unsigned shift;
625  if (!highWordBits) {
626  highWordBits = APINT_BITS_PER_WORD;
627  shift = 0;
628  } else {
629  shift = APINT_BITS_PER_WORD - highWordBits;
630  }
631  int i = getNumWords() - 1;
632  unsigned Count = llvm::countLeadingOnes(U.pVal[i] << shift);
633  if (Count == highWordBits) {
634  for (i--; i >= 0; --i) {
635  if (U.pVal[i] == WORDTYPE_MAX)
636  Count += APINT_BITS_PER_WORD;
637  else {
638  Count += llvm::countLeadingOnes(U.pVal[i]);
639  break;
640  }
641  }
642  }
643  return Count;
644 }
645 
646 unsigned APInt::countTrailingZerosSlowCase() const {
647  unsigned Count = 0;
648  unsigned i = 0;
649  for (; i < getNumWords() && U.pVal[i] == 0; ++i)
650  Count += APINT_BITS_PER_WORD;
651  if (i < getNumWords())
652  Count += llvm::countTrailingZeros(U.pVal[i]);
653  return std::min(Count, BitWidth);
654 }
655 
656 unsigned APInt::countTrailingOnesSlowCase() const {
657  unsigned Count = 0;
658  unsigned i = 0;
659  for (; i < getNumWords() && U.pVal[i] == WORDTYPE_MAX; ++i)
660  Count += APINT_BITS_PER_WORD;
661  if (i < getNumWords())
662  Count += llvm::countTrailingOnes(U.pVal[i]);
663  assert(Count <= BitWidth);
664  return Count;
665 }
666 
667 unsigned APInt::countPopulationSlowCase() const {
668  unsigned Count = 0;
669  for (unsigned i = 0; i < getNumWords(); ++i)
670  Count += llvm::countPopulation(U.pVal[i]);
671  return Count;
672 }
673 
674 bool APInt::intersectsSlowCase(const APInt &RHS) const {
675  for (unsigned i = 0, e = getNumWords(); i != e; ++i)
676  if ((U.pVal[i] & RHS.U.pVal[i]) != 0)
677  return true;
678 
679  return false;
680 }
681 
682 bool APInt::isSubsetOfSlowCase(const APInt &RHS) const {
683  for (unsigned i = 0, e = getNumWords(); i != e; ++i)
684  if ((U.pVal[i] & ~RHS.U.pVal[i]) != 0)
685  return false;
686 
687  return true;
688 }
689 
691  assert(BitWidth >= 16 && BitWidth % 8 == 0 && "Cannot byteswap!");
692  if (BitWidth == 16)
693  return APInt(BitWidth, ByteSwap_16(uint16_t(U.VAL)));
694  if (BitWidth == 32)
695  return APInt(BitWidth, ByteSwap_32(unsigned(U.VAL)));
696  if (BitWidth <= 64) {
697  uint64_t Tmp1 = ByteSwap_64(U.VAL);
698  Tmp1 >>= (64 - BitWidth);
699  return APInt(BitWidth, Tmp1);
700  }
701 
702  APInt Result(getNumWords() * APINT_BITS_PER_WORD, 0);
703  for (unsigned I = 0, N = getNumWords(); I != N; ++I)
704  Result.U.pVal[I] = ByteSwap_64(U.pVal[N - I - 1]);
705  if (Result.BitWidth != BitWidth) {
706  Result.lshrInPlace(Result.BitWidth - BitWidth);
707  Result.BitWidth = BitWidth;
708  }
709  return Result;
710 }
711 
713  switch (BitWidth) {
714  case 64:
715  return APInt(BitWidth, llvm::reverseBits<uint64_t>(U.VAL));
716  case 32:
717  return APInt(BitWidth, llvm::reverseBits<uint32_t>(U.VAL));
718  case 16:
719  return APInt(BitWidth, llvm::reverseBits<uint16_t>(U.VAL));
720  case 8:
721  return APInt(BitWidth, llvm::reverseBits<uint8_t>(U.VAL));
722  case 0:
723  return *this;
724  default:
725  break;
726  }
727 
728  APInt Val(*this);
729  APInt Reversed(BitWidth, 0);
730  unsigned S = BitWidth;
731 
732  for (; Val != 0; Val.lshrInPlace(1)) {
733  Reversed <<= 1;
734  Reversed |= Val[0];
735  --S;
736  }
737 
738  Reversed <<= S;
739  return Reversed;
740 }
741 
743  // Fast-path a common case.
744  if (A == B) return A;
745 
746  // Corner cases: if either operand is zero, the other is the gcd.
747  if (!A) return B;
748  if (!B) return A;
749 
750  // Count common powers of 2 and remove all other powers of 2.
751  unsigned Pow2;
752  {
753  unsigned Pow2_A = A.countTrailingZeros();
754  unsigned Pow2_B = B.countTrailingZeros();
755  if (Pow2_A > Pow2_B) {
756  A.lshrInPlace(Pow2_A - Pow2_B);
757  Pow2 = Pow2_B;
758  } else if (Pow2_B > Pow2_A) {
759  B.lshrInPlace(Pow2_B - Pow2_A);
760  Pow2 = Pow2_A;
761  } else {
762  Pow2 = Pow2_A;
763  }
764  }
765 
766  // Both operands are odd multiples of 2^Pow_2:
767  //
768  // gcd(a, b) = gcd(|a - b| / 2^i, min(a, b))
769  //
770  // This is a modified version of Stein's algorithm, taking advantage of
771  // efficient countTrailingZeros().
772  while (A != B) {
773  if (A.ugt(B)) {
774  A -= B;
775  A.lshrInPlace(A.countTrailingZeros() - Pow2);
776  } else {
777  B -= A;
778  B.lshrInPlace(B.countTrailingZeros() - Pow2);
779  }
780  }
781 
782  return A;
783 }
784 
785 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) {
786  uint64_t I = bit_cast<uint64_t>(Double);
787 
788  // Get the sign bit from the highest order bit
789  bool isNeg = I >> 63;
790 
791  // Get the 11-bit exponent and adjust for the 1023 bit bias
792  int64_t exp = ((I >> 52) & 0x7ff) - 1023;
793 
794  // If the exponent is negative, the value is < 0 so just return 0.
795  if (exp < 0)
796  return APInt(width, 0u);
797 
798  // Extract the mantissa by clearing the top 12 bits (sign + exponent).
799  uint64_t mantissa = (I & (~0ULL >> 12)) | 1ULL << 52;
800 
801  // If the exponent doesn't shift all bits out of the mantissa
802  if (exp < 52)
803  return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
804  APInt(width, mantissa >> (52 - exp));
805 
806  // If the client didn't provide enough bits for us to shift the mantissa into
807  // then the result is undefined, just return 0
808  if (width <= exp - 52)
809  return APInt(width, 0);
810 
811  // Otherwise, we have to shift the mantissa bits up to the right location
812  APInt Tmp(width, mantissa);
813  Tmp <<= (unsigned)exp - 52;
814  return isNeg ? -Tmp : Tmp;
815 }
816 
817 /// This function converts this APInt to a double.
818 /// The layout for double is as following (IEEE Standard 754):
819 /// --------------------------------------
820 /// | Sign Exponent Fraction Bias |
821 /// |-------------------------------------- |
822 /// | 1[63] 11[62-52] 52[51-00] 1023 |
823 /// --------------------------------------
824 double APInt::roundToDouble(bool isSigned) const {
825 
826  // Handle the simple case where the value is contained in one uint64_t.
827  // It is wrong to optimize getWord(0) to VAL; there might be more than one word.
829  if (isSigned) {
830  int64_t sext = SignExtend64(getWord(0), BitWidth);
831  return double(sext);
832  } else
833  return double(getWord(0));
834  }
835 
836  // Determine if the value is negative.
837  bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
838 
839  // Construct the absolute value if we're negative.
840  APInt Tmp(isNeg ? -(*this) : (*this));
841 
842  // Figure out how many bits we're using.
843  unsigned n = Tmp.getActiveBits();
844 
845  // The exponent (without bias normalization) is just the number of bits
846  // we are using. Note that the sign bit is gone since we constructed the
847  // absolute value.
848  uint64_t exp = n;
849 
850  // Return infinity for exponent overflow
851  if (exp > 1023) {
852  if (!isSigned || !isNeg)
853  return std::numeric_limits<double>::infinity();
854  else
855  return -std::numeric_limits<double>::infinity();
856  }
857  exp += 1023; // Increment for 1023 bias
858 
859  // Number of bits in mantissa is 52. To obtain the mantissa value, we must
860  // extract the high 52 bits from the correct words in pVal.
861  uint64_t mantissa;
862  unsigned hiWord = whichWord(n-1);
863  if (hiWord == 0) {
864  mantissa = Tmp.U.pVal[0];
865  if (n > 52)
866  mantissa >>= n - 52; // shift down, we want the top 52 bits.
867  } else {
868  assert(hiWord > 0 && "huh?");
869  uint64_t hibits = Tmp.U.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
870  uint64_t lobits = Tmp.U.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
871  mantissa = hibits | lobits;
872  }
873 
874  // The leading bit of mantissa is implicit, so get rid of it.
875  uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
876  uint64_t I = sign | (exp << 52) | mantissa;
877  return bit_cast<double>(I);
878 }
879 
880 // Truncate to new width.
881 APInt APInt::trunc(unsigned width) const {
882  assert(width < BitWidth && "Invalid APInt Truncate request");
883 
884  if (width <= APINT_BITS_PER_WORD)
885  return APInt(width, getRawData()[0]);
886 
887  APInt Result(getMemory(getNumWords(width)), width);
888 
889  // Copy full words.
890  unsigned i;
891  for (i = 0; i != width / APINT_BITS_PER_WORD; i++)
892  Result.U.pVal[i] = U.pVal[i];
893 
894  // Truncate and copy any partial word.
895  unsigned bits = (0 - width) % APINT_BITS_PER_WORD;
896  if (bits != 0)
897  Result.U.pVal[i] = U.pVal[i] << bits >> bits;
898 
899  return Result;
900 }
901 
902 // Truncate to new width with unsigned saturation.
903 APInt APInt::truncUSat(unsigned width) const {
904  assert(width < BitWidth && "Invalid APInt Truncate request");
905 
906  // Can we just losslessly truncate it?
907  if (isIntN(width))
908  return trunc(width);
909  // If not, then just return the new limit.
910  return APInt::getMaxValue(width);
911 }
912 
913 // Truncate to new width with signed saturation.
914 APInt APInt::truncSSat(unsigned width) const {
915  assert(width < BitWidth && "Invalid APInt Truncate request");
916 
917  // Can we just losslessly truncate it?
918  if (isSignedIntN(width))
919  return trunc(width);
920  // If not, then just return the new limits.
921  return isNegative() ? APInt::getSignedMinValue(width)
922  : APInt::getSignedMaxValue(width);
923 }
924 
925 // Sign extend to a new width.
926 APInt APInt::sext(unsigned Width) const {
927  assert(Width > BitWidth && "Invalid APInt SignExtend request");
928 
929  if (Width <= APINT_BITS_PER_WORD)
930  return APInt(Width, SignExtend64(U.VAL, BitWidth));
931 
933 
934  // Copy words.
935  std::memcpy(Result.U.pVal, getRawData(), getNumWords() * APINT_WORD_SIZE);
936 
937  // Sign extend the last word since there may be unused bits in the input.
938  Result.U.pVal[getNumWords() - 1] =
939  SignExtend64(Result.U.pVal[getNumWords() - 1],
940  ((BitWidth - 1) % APINT_BITS_PER_WORD) + 1);
941 
942  // Fill with sign bits.
943  std::memset(Result.U.pVal + getNumWords(), isNegative() ? -1 : 0,
944  (Result.getNumWords() - getNumWords()) * APINT_WORD_SIZE);
945  Result.clearUnusedBits();
946  return Result;
947 }
948 
949 // Zero extend to a new width.
950 APInt APInt::zext(unsigned width) const {
951  assert(width > BitWidth && "Invalid APInt ZeroExtend request");
952 
953  if (width <= APINT_BITS_PER_WORD)
954  return APInt(width, U.VAL);
955 
956  APInt Result(getMemory(getNumWords(width)), width);
957 
958  // Copy words.
959  std::memcpy(Result.U.pVal, getRawData(), getNumWords() * APINT_WORD_SIZE);
960 
961  // Zero remaining words.
962  std::memset(Result.U.pVal + getNumWords(), 0,
963  (Result.getNumWords() - getNumWords()) * APINT_WORD_SIZE);
964 
965  return Result;
966 }
967 
968 APInt APInt::zextOrTrunc(unsigned width) const {
969  if (BitWidth < width)
970  return zext(width);
971  if (BitWidth > width)
972  return trunc(width);
973  return *this;
974 }
975 
976 APInt APInt::sextOrTrunc(unsigned width) const {
977  if (BitWidth < width)
978  return sext(width);
979  if (BitWidth > width)
980  return trunc(width);
981  return *this;
982 }
983 
984 APInt APInt::truncOrSelf(unsigned width) const {
985  if (BitWidth > width)
986  return trunc(width);
987  return *this;
988 }
989 
990 APInt APInt::zextOrSelf(unsigned width) const {
991  if (BitWidth < width)
992  return zext(width);
993  return *this;
994 }
995 
996 APInt APInt::sextOrSelf(unsigned width) const {
997  if (BitWidth < width)
998  return sext(width);
999  return *this;
1000 }
1001 
1002 /// Arithmetic right-shift this APInt by shiftAmt.
1003 /// Arithmetic right-shift function.
1004 void APInt::ashrInPlace(const APInt &shiftAmt) {
1005  ashrInPlace((unsigned)shiftAmt.getLimitedValue(BitWidth));
1006 }
1007 
1008 /// Arithmetic right-shift this APInt by shiftAmt.
1009 /// Arithmetic right-shift function.
1010 void APInt::ashrSlowCase(unsigned ShiftAmt) {
1011  // Don't bother performing a no-op shift.
1012  if (!ShiftAmt)
1013  return;
1014 
1015  // Save the original sign bit for later.
1016  bool Negative = isNegative();
1017 
1018  // WordShift is the inter-part shift; BitShift is intra-part shift.
1019  unsigned WordShift = ShiftAmt / APINT_BITS_PER_WORD;
1020  unsigned BitShift = ShiftAmt % APINT_BITS_PER_WORD;
1021 
1022  unsigned WordsToMove = getNumWords() - WordShift;
1023  if (WordsToMove != 0) {
1024  // Sign extend the last word to fill in the unused bits.
1025  U.pVal[getNumWords() - 1] = SignExtend64(
1026  U.pVal[getNumWords() - 1], ((BitWidth - 1) % APINT_BITS_PER_WORD) + 1);
1027 
1028  // Fastpath for moving by whole words.
1029  if (BitShift == 0) {
1030  std::memmove(U.pVal, U.pVal + WordShift, WordsToMove * APINT_WORD_SIZE);
1031  } else {
1032  // Move the words containing significant bits.
1033  for (unsigned i = 0; i != WordsToMove - 1; ++i)
1034  U.pVal[i] = (U.pVal[i + WordShift] >> BitShift) |
1035  (U.pVal[i + WordShift + 1] << (APINT_BITS_PER_WORD - BitShift));
1036 
1037  // Handle the last word which has no high bits to copy.
1038  U.pVal[WordsToMove - 1] = U.pVal[WordShift + WordsToMove - 1] >> BitShift;
1039  // Sign extend one more time.
1040  U.pVal[WordsToMove - 1] =
1041  SignExtend64(U.pVal[WordsToMove - 1], APINT_BITS_PER_WORD - BitShift);
1042  }
1043  }
1044 
1045  // Fill in the remainder based on the original sign.
1046  std::memset(U.pVal + WordsToMove, Negative ? -1 : 0,
1047  WordShift * APINT_WORD_SIZE);
1048  clearUnusedBits();
1049 }
1050 
1051 /// Logical right-shift this APInt by shiftAmt.
1052 /// Logical right-shift function.
1053 void APInt::lshrInPlace(const APInt &shiftAmt) {
1054  lshrInPlace((unsigned)shiftAmt.getLimitedValue(BitWidth));
1055 }
1056 
1057 /// Logical right-shift this APInt by shiftAmt.
1058 /// Logical right-shift function.
1059 void APInt::lshrSlowCase(unsigned ShiftAmt) {
1060  tcShiftRight(U.pVal, getNumWords(), ShiftAmt);
1061 }
1062 
1063 /// Left-shift this APInt by shiftAmt.
1064 /// Left-shift function.
1065 APInt &APInt::operator<<=(const APInt &shiftAmt) {
1066  // It's undefined behavior in C to shift by BitWidth or greater.
1067  *this <<= (unsigned)shiftAmt.getLimitedValue(BitWidth);
1068  return *this;
1069 }
1070 
1071 void APInt::shlSlowCase(unsigned ShiftAmt) {
1072  tcShiftLeft(U.pVal, getNumWords(), ShiftAmt);
1073  clearUnusedBits();
1074 }
1075 
1076 // Calculate the rotate amount modulo the bit width.
1077 static unsigned rotateModulo(unsigned BitWidth, const APInt &rotateAmt) {
1078  if (LLVM_UNLIKELY(BitWidth == 0))
1079  return 0;
1080  unsigned rotBitWidth = rotateAmt.getBitWidth();
1081  APInt rot = rotateAmt;
1082  if (rotBitWidth < BitWidth) {
1083  // Extend the rotate APInt, so that the urem doesn't divide by 0.
1084  // e.g. APInt(1, 32) would give APInt(1, 0).
1085  rot = rotateAmt.zext(BitWidth);
1086  }
1087  rot = rot.urem(APInt(rot.getBitWidth(), BitWidth));
1088  return rot.getLimitedValue(BitWidth);
1089 }
1090 
1091 APInt APInt::rotl(const APInt &rotateAmt) const {
1092  return rotl(rotateModulo(BitWidth, rotateAmt));
1093 }
1094 
1095 APInt APInt::rotl(unsigned rotateAmt) const {
1096  if (LLVM_UNLIKELY(BitWidth == 0))
1097  return *this;
1098  rotateAmt %= BitWidth;
1099  if (rotateAmt == 0)
1100  return *this;
1101  return shl(rotateAmt) | lshr(BitWidth - rotateAmt);
1102 }
1103 
1104 APInt APInt::rotr(const APInt &rotateAmt) const {
1105  return rotr(rotateModulo(BitWidth, rotateAmt));
1106 }
1107 
1108 APInt APInt::rotr(unsigned rotateAmt) const {
1109  if (BitWidth == 0)
1110  return *this;
1111  rotateAmt %= BitWidth;
1112  if (rotateAmt == 0)
1113  return *this;
1114  return lshr(rotateAmt) | shl(BitWidth - rotateAmt);
1115 }
1116 
1117 /// \returns the nearest log base 2 of this APInt. Ties round up.
1118 ///
1119 /// NOTE: When we have a BitWidth of 1, we define:
1120 ///
1121 /// log2(0) = UINT32_MAX
1122 /// log2(1) = 0
1123 ///
1124 /// to get around any mathematical concerns resulting from
1125 /// referencing 2 in a space where 2 does no exist.
1126 unsigned APInt::nearestLogBase2() const {
1127  // Special case when we have a bitwidth of 1. If VAL is 1, then we
1128  // get 0. If VAL is 0, we get WORDTYPE_MAX which gets truncated to
1129  // UINT32_MAX.
1130  if (BitWidth == 1)
1131  return U.VAL - 1;
1132 
1133  // Handle the zero case.
1134  if (isZero())
1135  return UINT32_MAX;
1136 
1137  // The non-zero case is handled by computing:
1138  //
1139  // nearestLogBase2(x) = logBase2(x) + x[logBase2(x)-1].
1140  //
1141  // where x[i] is referring to the value of the ith bit of x.
1142  unsigned lg = logBase2();
1143  return lg + unsigned((*this)[lg - 1]);
1144 }
1145 
1146 // Square Root - this method computes and returns the square root of "this".
1147 // Three mechanisms are used for computation. For small values (<= 5 bits),
1148 // a table lookup is done. This gets some performance for common cases. For
1149 // values using less than 52 bits, the value is converted to double and then
1150 // the libc sqrt function is called. The result is rounded and then converted
1151 // back to a uint64_t which is then used to construct the result. Finally,
1152 // the Babylonian method for computing square roots is used.
1154 
1155  // Determine the magnitude of the value.
1156  unsigned magnitude = getActiveBits();
1157 
1158  // Use a fast table for some small values. This also gets rid of some
1159  // rounding errors in libc sqrt for small values.
1160  if (magnitude <= 5) {
1161  static const uint8_t results[32] = {
1162  /* 0 */ 0,
1163  /* 1- 2 */ 1, 1,
1164  /* 3- 6 */ 2, 2, 2, 2,
1165  /* 7-12 */ 3, 3, 3, 3, 3, 3,
1166  /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1167  /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1168  /* 31 */ 6
1169  };
1170  return APInt(BitWidth, results[ (isSingleWord() ? U.VAL : U.pVal[0]) ]);
1171  }
1172 
1173  // If the magnitude of the value fits in less than 52 bits (the precision of
1174  // an IEEE double precision floating point value), then we can use the
1175  // libc sqrt function which will probably use a hardware sqrt computation.
1176  // This should be faster than the algorithm below.
1177  if (magnitude < 52) {
1178  return APInt(BitWidth,
1179  uint64_t(::round(::sqrt(double(isSingleWord() ? U.VAL
1180  : U.pVal[0])))));
1181  }
1182 
1183  // Okay, all the short cuts are exhausted. We must compute it. The following
1184  // is a classical Babylonian method for computing the square root. This code
1185  // was adapted to APInt from a wikipedia article on such computations.
1186  // See http://www.wikipedia.org/ and go to the page named
1187  // Calculate_an_integer_square_root.
1188  unsigned nbits = BitWidth, i = 4;
1189  APInt testy(BitWidth, 16);
1190  APInt x_old(BitWidth, 1);
1191  APInt x_new(BitWidth, 0);
1192  APInt two(BitWidth, 2);
1193 
1194  // Select a good starting value using binary logarithms.
1195  for (;; i += 2, testy = testy.shl(2))
1196  if (i >= nbits || this->ule(testy)) {
1197  x_old = x_old.shl(i / 2);
1198  break;
1199  }
1200 
1201  // Use the Babylonian method to arrive at the integer square root:
1202  for (;;) {
1203  x_new = (this->udiv(x_old) + x_old).udiv(two);
1204  if (x_old.ule(x_new))
1205  break;
1206  x_old = x_new;
1207  }
1208 
1209  // Make sure we return the closest approximation
1210  // NOTE: The rounding calculation below is correct. It will produce an
1211  // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1212  // determined to be a rounding issue with pari/gp as it begins to use a
1213  // floating point representation after 192 bits. There are no discrepancies
1214  // between this algorithm and pari/gp for bit widths < 192 bits.
1215  APInt square(x_old * x_old);
1216  APInt nextSquare((x_old + 1) * (x_old +1));
1217  if (this->ult(square))
1218  return x_old;
1219  assert(this->ule(nextSquare) && "Error in APInt::sqrt computation");
1220  APInt midpoint((nextSquare - square).udiv(two));
1221  APInt offset(*this - square);
1222  if (offset.ult(midpoint))
1223  return x_old;
1224  return x_old + 1;
1225 }
1226 
1227 /// Computes the multiplicative inverse of this APInt for a given modulo. The
1228 /// iterative extended Euclidean algorithm is used to solve for this value,
1229 /// however we simplify it to speed up calculating only the inverse, and take
1230 /// advantage of div+rem calculations. We also use some tricks to avoid copying
1231 /// (potentially large) APInts around.
1232 /// WARNING: a value of '0' may be returned,
1233 /// signifying that no multiplicative inverse exists!
1235  assert(ult(modulo) && "This APInt must be smaller than the modulo");
1236 
1237  // Using the properties listed at the following web page (accessed 06/21/08):
1238  // http://www.numbertheory.org/php/euclid.html
1239  // (especially the properties numbered 3, 4 and 9) it can be proved that
1240  // BitWidth bits suffice for all the computations in the algorithm implemented
1241  // below. More precisely, this number of bits suffice if the multiplicative
1242  // inverse exists, but may not suffice for the general extended Euclidean
1243  // algorithm.
1244 
1245  APInt r[2] = { modulo, *this };
1246  APInt t[2] = { APInt(BitWidth, 0), APInt(BitWidth, 1) };
1247  APInt q(BitWidth, 0);
1248 
1249  unsigned i;
1250  for (i = 0; r[i^1] != 0; i ^= 1) {
1251  // An overview of the math without the confusing bit-flipping:
1252  // q = r[i-2] / r[i-1]
1253  // r[i] = r[i-2] % r[i-1]
1254  // t[i] = t[i-2] - t[i-1] * q
1255  udivrem(r[i], r[i^1], q, r[i]);
1256  t[i] -= t[i^1] * q;
1257  }
1258 
1259  // If this APInt and the modulo are not coprime, there is no multiplicative
1260  // inverse, so return 0. We check this by looking at the next-to-last
1261  // remainder, which is the gcd(*this,modulo) as calculated by the Euclidean
1262  // algorithm.
1263  if (r[i] != 1)
1264  return APInt(BitWidth, 0);
1265 
1266  // The next-to-last t is the multiplicative inverse. However, we are
1267  // interested in a positive inverse. Calculate a positive one from a negative
1268  // one if necessary. A simple addition of the modulo suffices because
1269  // abs(t[i]) is known to be less than *this/2 (see the link above).
1270  if (t[i].isNegative())
1271  t[i] += modulo;
1272 
1273  return std::move(t[i]);
1274 }
1275 
1276 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1277 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1278 /// variables here have the same names as in the algorithm. Comments explain
1279 /// the algorithm and any deviation from it.
1280 static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
1281  unsigned m, unsigned n) {
1282  assert(u && "Must provide dividend");
1283  assert(v && "Must provide divisor");
1284  assert(q && "Must provide quotient");
1285  assert(u != v && u != q && v != q && "Must use different memory");
1286  assert(n>1 && "n must be > 1");
1287 
1288  // b denotes the base of the number system. In our case b is 2^32.
1289  const uint64_t b = uint64_t(1) << 32;
1290 
1291 // The DEBUG macros here tend to be spam in the debug output if you're not
1292 // debugging this code. Disable them unless KNUTH_DEBUG is defined.
1293 #ifdef KNUTH_DEBUG
1294 #define DEBUG_KNUTH(X) LLVM_DEBUG(X)
1295 #else
1296 #define DEBUG_KNUTH(X) do {} while(false)
1297 #endif
1298 
1299  DEBUG_KNUTH(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n');
1300  DEBUG_KNUTH(dbgs() << "KnuthDiv: original:");
1301  DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]);
1302  DEBUG_KNUTH(dbgs() << " by");
1303  DEBUG_KNUTH(for (int i = n; i > 0; i--) dbgs() << " " << v[i - 1]);
1304  DEBUG_KNUTH(dbgs() << '\n');
1305  // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1306  // u and v by d. Note that we have taken Knuth's advice here to use a power
1307  // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1308  // 2 allows us to shift instead of multiply and it is easy to determine the
1309  // shift amount from the leading zeros. We are basically normalizing the u
1310  // and v so that its high bits are shifted to the top of v's range without
1311  // overflow. Note that this can require an extra word in u so that u must
1312  // be of length m+n+1.
1313  unsigned shift = countLeadingZeros(v[n-1]);
1314  uint32_t v_carry = 0;
1315  uint32_t u_carry = 0;
1316  if (shift) {
1317  for (unsigned i = 0; i < m+n; ++i) {
1318  uint32_t u_tmp = u[i] >> (32 - shift);
1319  u[i] = (u[i] << shift) | u_carry;
1320  u_carry = u_tmp;
1321  }
1322  for (unsigned i = 0; i < n; ++i) {
1323  uint32_t v_tmp = v[i] >> (32 - shift);
1324  v[i] = (v[i] << shift) | v_carry;
1325  v_carry = v_tmp;
1326  }
1327  }
1328  u[m+n] = u_carry;
1329 
1330  DEBUG_KNUTH(dbgs() << "KnuthDiv: normal:");
1331  DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]);
1332  DEBUG_KNUTH(dbgs() << " by");
1333  DEBUG_KNUTH(for (int i = n; i > 0; i--) dbgs() << " " << v[i - 1]);
1334  DEBUG_KNUTH(dbgs() << '\n');
1335 
1336  // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1337  int j = m;
1338  do {
1339  DEBUG_KNUTH(dbgs() << "KnuthDiv: quotient digit #" << j << '\n');
1340  // D3. [Calculate q'.].
1341  // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1342  // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1343  // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1344  // qp by 1, increase rp by v[n-1], and repeat this test if rp < b. The test
1345  // on v[n-2] determines at high speed most of the cases in which the trial
1346  // value qp is one too large, and it eliminates all cases where qp is two
1347  // too large.
1348  uint64_t dividend = Make_64(u[j+n], u[j+n-1]);
1349  DEBUG_KNUTH(dbgs() << "KnuthDiv: dividend == " << dividend << '\n');
1350  uint64_t qp = dividend / v[n-1];
1351  uint64_t rp = dividend % v[n-1];
1352  if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1353  qp--;
1354  rp += v[n-1];
1355  if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1356  qp--;
1357  }
1358  DEBUG_KNUTH(dbgs() << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1359 
1360  // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1361  // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1362  // consists of a simple multiplication by a one-place number, combined with
1363  // a subtraction.
1364  // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1365  // this step is actually negative, (u[j+n]...u[j]) should be left as the
1366  // true value plus b**(n+1), namely as the b's complement of
1367  // the true value, and a "borrow" to the left should be remembered.
1368  int64_t borrow = 0;
1369  for (unsigned i = 0; i < n; ++i) {
1370  uint64_t p = uint64_t(qp) * uint64_t(v[i]);
1371  int64_t subres = int64_t(u[j+i]) - borrow - Lo_32(p);
1372  u[j+i] = Lo_32(subres);
1373  borrow = Hi_32(p) - Hi_32(subres);
1374  DEBUG_KNUTH(dbgs() << "KnuthDiv: u[j+i] = " << u[j + i]
1375  << ", borrow = " << borrow << '\n');
1376  }
1377  bool isNeg = u[j+n] < borrow;
1378  u[j+n] -= Lo_32(borrow);
1379 
1380  DEBUG_KNUTH(dbgs() << "KnuthDiv: after subtraction:");
1381  DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]);
1382  DEBUG_KNUTH(dbgs() << '\n');
1383 
1384  // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1385  // negative, go to step D6; otherwise go on to step D7.
1386  q[j] = Lo_32(qp);
1387  if (isNeg) {
1388  // D6. [Add back]. The probability that this step is necessary is very
1389  // small, on the order of only 2/b. Make sure that test data accounts for
1390  // this possibility. Decrease q[j] by 1
1391  q[j]--;
1392  // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1393  // A carry will occur to the left of u[j+n], and it should be ignored
1394  // since it cancels with the borrow that occurred in D4.
1395  bool carry = false;
1396  for (unsigned i = 0; i < n; i++) {
1397  uint32_t limit = std::min(u[j+i],v[i]);
1398  u[j+i] += v[i] + carry;
1399  carry = u[j+i] < limit || (carry && u[j+i] == limit);
1400  }
1401  u[j+n] += carry;
1402  }
1403  DEBUG_KNUTH(dbgs() << "KnuthDiv: after correction:");
1404  DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]);
1405  DEBUG_KNUTH(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n');
1406 
1407  // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1408  } while (--j >= 0);
1409 
1410  DEBUG_KNUTH(dbgs() << "KnuthDiv: quotient:");
1411  DEBUG_KNUTH(for (int i = m; i >= 0; i--) dbgs() << " " << q[i]);
1412  DEBUG_KNUTH(dbgs() << '\n');
1413 
1414  // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1415  // remainder may be obtained by dividing u[...] by d. If r is non-null we
1416  // compute the remainder (urem uses this).
1417  if (r) {
1418  // The value d is expressed by the "shift" value above since we avoided
1419  // multiplication by d by using a shift left. So, all we have to do is
1420  // shift right here.
1421  if (shift) {
1422  uint32_t carry = 0;
1423  DEBUG_KNUTH(dbgs() << "KnuthDiv: remainder:");
1424  for (int i = n-1; i >= 0; i--) {
1425  r[i] = (u[i] >> shift) | carry;
1426  carry = u[i] << (32 - shift);
1427  DEBUG_KNUTH(dbgs() << " " << r[i]);
1428  }
1429  } else {
1430  for (int i = n-1; i >= 0; i--) {
1431  r[i] = u[i];
1432  DEBUG_KNUTH(dbgs() << " " << r[i]);
1433  }
1434  }
1435  DEBUG_KNUTH(dbgs() << '\n');
1436  }
1437  DEBUG_KNUTH(dbgs() << '\n');
1438 }
1439 
1440 void APInt::divide(const WordType *LHS, unsigned lhsWords, const WordType *RHS,
1441  unsigned rhsWords, WordType *Quotient, WordType *Remainder) {
1442  assert(lhsWords >= rhsWords && "Fractional result");
1443 
1444  // First, compose the values into an array of 32-bit words instead of
1445  // 64-bit words. This is a necessity of both the "short division" algorithm
1446  // and the Knuth "classical algorithm" which requires there to be native
1447  // operations for +, -, and * on an m bit value with an m*2 bit result. We
1448  // can't use 64-bit operands here because we don't have native results of
1449  // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't
1450  // work on large-endian machines.
1451  unsigned n = rhsWords * 2;
1452  unsigned m = (lhsWords * 2) - n;
1453 
1454  // Allocate space for the temporary values we need either on the stack, if
1455  // it will fit, or on the heap if it won't.
1456  uint32_t SPACE[128];
1457  uint32_t *U = nullptr;
1458  uint32_t *V = nullptr;
1459  uint32_t *Q = nullptr;
1460  uint32_t *R = nullptr;
1461  if ((Remainder?4:3)*n+2*m+1 <= 128) {
1462  U = &SPACE[0];
1463  V = &SPACE[m+n+1];
1464  Q = &SPACE[(m+n+1) + n];
1465  if (Remainder)
1466  R = &SPACE[(m+n+1) + n + (m+n)];
1467  } else {
1468  U = new uint32_t[m + n + 1];
1469  V = new uint32_t[n];
1470  Q = new uint32_t[m+n];
1471  if (Remainder)
1472  R = new uint32_t[n];
1473  }
1474 
1475  // Initialize the dividend
1476  memset(U, 0, (m+n+1)*sizeof(uint32_t));
1477  for (unsigned i = 0; i < lhsWords; ++i) {
1478  uint64_t tmp = LHS[i];
1479  U[i * 2] = Lo_32(tmp);
1480  U[i * 2 + 1] = Hi_32(tmp);
1481  }
1482  U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1483 
1484  // Initialize the divisor
1485  memset(V, 0, (n)*sizeof(uint32_t));
1486  for (unsigned i = 0; i < rhsWords; ++i) {
1487  uint64_t tmp = RHS[i];
1488  V[i * 2] = Lo_32(tmp);
1489  V[i * 2 + 1] = Hi_32(tmp);
1490  }
1491 
1492  // initialize the quotient and remainder
1493  memset(Q, 0, (m+n) * sizeof(uint32_t));
1494  if (Remainder)
1495  memset(R, 0, n * sizeof(uint32_t));
1496 
1497  // Now, adjust m and n for the Knuth division. n is the number of words in
1498  // the divisor. m is the number of words by which the dividend exceeds the
1499  // divisor (i.e. m+n is the length of the dividend). These sizes must not
1500  // contain any zero words or the Knuth algorithm fails.
1501  for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1502  n--;
1503  m++;
1504  }
1505  for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1506  m--;
1507 
1508  // If we're left with only a single word for the divisor, Knuth doesn't work
1509  // so we implement the short division algorithm here. This is much simpler
1510  // and faster because we are certain that we can divide a 64-bit quantity
1511  // by a 32-bit quantity at hardware speed and short division is simply a
1512  // series of such operations. This is just like doing short division but we
1513  // are using base 2^32 instead of base 10.
1514  assert(n != 0 && "Divide by zero?");
1515  if (n == 1) {
1516  uint32_t divisor = V[0];
1517  uint32_t remainder = 0;
1518  for (int i = m; i >= 0; i--) {
1519  uint64_t partial_dividend = Make_64(remainder, U[i]);
1520  if (partial_dividend == 0) {
1521  Q[i] = 0;
1522  remainder = 0;
1523  } else if (partial_dividend < divisor) {
1524  Q[i] = 0;
1525  remainder = Lo_32(partial_dividend);
1526  } else if (partial_dividend == divisor) {
1527  Q[i] = 1;
1528  remainder = 0;
1529  } else {
1530  Q[i] = Lo_32(partial_dividend / divisor);
1531  remainder = Lo_32(partial_dividend - (Q[i] * divisor));
1532  }
1533  }
1534  if (R)
1535  R[0] = remainder;
1536  } else {
1537  // Now we're ready to invoke the Knuth classical divide algorithm. In this
1538  // case n > 1.
1539  KnuthDiv(U, V, Q, R, m, n);
1540  }
1541 
1542  // If the caller wants the quotient
1543  if (Quotient) {
1544  for (unsigned i = 0; i < lhsWords; ++i)
1545  Quotient[i] = Make_64(Q[i*2+1], Q[i*2]);
1546  }
1547 
1548  // If the caller wants the remainder
1549  if (Remainder) {
1550  for (unsigned i = 0; i < rhsWords; ++i)
1551  Remainder[i] = Make_64(R[i*2+1], R[i*2]);
1552  }
1553 
1554  // Clean up the memory we allocated.
1555  if (U != &SPACE[0]) {
1556  delete [] U;
1557  delete [] V;
1558  delete [] Q;
1559  delete [] R;
1560  }
1561 }
1562 
1563 APInt APInt::udiv(const APInt &RHS) const {
1564  assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1565 
1566  // First, deal with the easy case
1567  if (isSingleWord()) {
1568  assert(RHS.U.VAL != 0 && "Divide by zero?");
1569  return APInt(BitWidth, U.VAL / RHS.U.VAL);
1570  }
1571 
1572  // Get some facts about the LHS and RHS number of bits and words
1573  unsigned lhsWords = getNumWords(getActiveBits());
1574  unsigned rhsBits = RHS.getActiveBits();
1575  unsigned rhsWords = getNumWords(rhsBits);
1576  assert(rhsWords && "Divided by zero???");
1577 
1578  // Deal with some degenerate cases
1579  if (!lhsWords)
1580  // 0 / X ===> 0
1581  return APInt(BitWidth, 0);
1582  if (rhsBits == 1)
1583  // X / 1 ===> X
1584  return *this;
1585  if (lhsWords < rhsWords || this->ult(RHS))
1586  // X / Y ===> 0, iff X < Y
1587  return APInt(BitWidth, 0);
1588  if (*this == RHS)
1589  // X / X ===> 1
1590  return APInt(BitWidth, 1);
1591  if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1.
1592  // All high words are zero, just use native divide
1593  return APInt(BitWidth, this->U.pVal[0] / RHS.U.pVal[0]);
1594 
1595  // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1596  APInt Quotient(BitWidth, 0); // to hold result.
1597  divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal, nullptr);
1598  return Quotient;
1599 }
1600 
1602  assert(RHS != 0 && "Divide by zero?");
1603 
1604  // First, deal with the easy case
1605  if (isSingleWord())
1606  return APInt(BitWidth, U.VAL / RHS);
1607 
1608  // Get some facts about the LHS words.
1609  unsigned lhsWords = getNumWords(getActiveBits());
1610 
1611  // Deal with some degenerate cases
1612  if (!lhsWords)
1613  // 0 / X ===> 0
1614  return APInt(BitWidth, 0);
1615  if (RHS == 1)
1616  // X / 1 ===> X
1617  return *this;
1618  if (this->ult(RHS))
1619  // X / Y ===> 0, iff X < Y
1620  return APInt(BitWidth, 0);
1621  if (*this == RHS)
1622  // X / X ===> 1
1623  return APInt(BitWidth, 1);
1624  if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1.
1625  // All high words are zero, just use native divide
1626  return APInt(BitWidth, this->U.pVal[0] / RHS);
1627 
1628  // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1629  APInt Quotient(BitWidth, 0); // to hold result.
1630  divide(U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, nullptr);
1631  return Quotient;
1632 }
1633 
1634 APInt APInt::sdiv(const APInt &RHS) const {
1635  if (isNegative()) {
1636  if (RHS.isNegative())
1637  return (-(*this)).udiv(-RHS);
1638  return -((-(*this)).udiv(RHS));
1639  }
1640  if (RHS.isNegative())
1641  return -(this->udiv(-RHS));
1642  return this->udiv(RHS);
1643 }
1644 
1645 APInt APInt::sdiv(int64_t RHS) const {
1646  if (isNegative()) {
1647  if (RHS < 0)
1648  return (-(*this)).udiv(-RHS);
1649  return -((-(*this)).udiv(RHS));
1650  }
1651  if (RHS < 0)
1652  return -(this->udiv(-RHS));
1653  return this->udiv(RHS);
1654 }
1655 
1656 APInt APInt::urem(const APInt &RHS) const {
1657  assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1658  if (isSingleWord()) {
1659  assert(RHS.U.VAL != 0 && "Remainder by zero?");
1660  return APInt(BitWidth, U.VAL % RHS.U.VAL);
1661  }
1662 
1663  // Get some facts about the LHS
1664  unsigned lhsWords = getNumWords(getActiveBits());
1665 
1666  // Get some facts about the RHS
1667  unsigned rhsBits = RHS.getActiveBits();
1668  unsigned rhsWords = getNumWords(rhsBits);
1669  assert(rhsWords && "Performing remainder operation by zero ???");
1670 
1671  // Check the degenerate cases
1672  if (lhsWords == 0)
1673  // 0 % Y ===> 0
1674  return APInt(BitWidth, 0);
1675  if (rhsBits == 1)
1676  // X % 1 ===> 0
1677  return APInt(BitWidth, 0);
1678  if (lhsWords < rhsWords || this->ult(RHS))
1679  // X % Y ===> X, iff X < Y
1680  return *this;
1681  if (*this == RHS)
1682  // X % X == 0;
1683  return APInt(BitWidth, 0);
1684  if (lhsWords == 1)
1685  // All high words are zero, just use native remainder
1686  return APInt(BitWidth, U.pVal[0] % RHS.U.pVal[0]);
1687 
1688  // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1689  APInt Remainder(BitWidth, 0);
1690  divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, nullptr, Remainder.U.pVal);
1691  return Remainder;
1692 }
1693 
1695  assert(RHS != 0 && "Remainder by zero?");
1696 
1697  if (isSingleWord())
1698  return U.VAL % RHS;
1699 
1700  // Get some facts about the LHS
1701  unsigned lhsWords = getNumWords(getActiveBits());
1702 
1703  // Check the degenerate cases
1704  if (lhsWords == 0)
1705  // 0 % Y ===> 0
1706  return 0;
1707  if (RHS == 1)
1708  // X % 1 ===> 0
1709  return 0;
1710  if (this->ult(RHS))
1711  // X % Y ===> X, iff X < Y
1712  return getZExtValue();
1713  if (*this == RHS)
1714  // X % X == 0;
1715  return 0;
1716  if (lhsWords == 1)
1717  // All high words are zero, just use native remainder
1718  return U.pVal[0] % RHS;
1719 
1720  // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1721  uint64_t Remainder;
1722  divide(U.pVal, lhsWords, &RHS, 1, nullptr, &Remainder);
1723  return Remainder;
1724 }
1725 
1726 APInt APInt::srem(const APInt &RHS) const {
1727  if (isNegative()) {
1728  if (RHS.isNegative())
1729  return -((-(*this)).urem(-RHS));
1730  return -((-(*this)).urem(RHS));
1731  }
1732  if (RHS.isNegative())
1733  return this->urem(-RHS);
1734  return this->urem(RHS);
1735 }
1736 
1737 int64_t APInt::srem(int64_t RHS) const {
1738  if (isNegative()) {
1739  if (RHS < 0)
1740  return -((-(*this)).urem(-RHS));
1741  return -((-(*this)).urem(RHS));
1742  }
1743  if (RHS < 0)
1744  return this->urem(-RHS);
1745  return this->urem(RHS);
1746 }
1747 
1748 void APInt::udivrem(const APInt &LHS, const APInt &RHS,
1749  APInt &Quotient, APInt &Remainder) {
1750  assert(LHS.BitWidth == RHS.BitWidth && "Bit widths must be the same");
1751  unsigned BitWidth = LHS.BitWidth;
1752 
1753  // First, deal with the easy case
1754  if (LHS.isSingleWord()) {
1755  assert(RHS.U.VAL != 0 && "Divide by zero?");
1756  uint64_t QuotVal = LHS.U.VAL / RHS.U.VAL;
1757  uint64_t RemVal = LHS.U.VAL % RHS.U.VAL;
1758  Quotient = APInt(BitWidth, QuotVal);
1759  Remainder = APInt(BitWidth, RemVal);
1760  return;
1761  }
1762 
1763  // Get some size facts about the dividend and divisor
1764  unsigned lhsWords = getNumWords(LHS.getActiveBits());
1765  unsigned rhsBits = RHS.getActiveBits();
1766  unsigned rhsWords = getNumWords(rhsBits);
1767  assert(rhsWords && "Performing divrem operation by zero ???");
1768 
1769  // Check the degenerate cases
1770  if (lhsWords == 0) {
1771  Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0
1772  Remainder = APInt(BitWidth, 0); // 0 % Y ===> 0
1773  return;
1774  }
1775 
1776  if (rhsBits == 1) {
1777  Quotient = LHS; // X / 1 ===> X
1778  Remainder = APInt(BitWidth, 0); // X % 1 ===> 0
1779  }
1780 
1781  if (lhsWords < rhsWords || LHS.ult(RHS)) {
1782  Remainder = LHS; // X % Y ===> X, iff X < Y
1783  Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y
1784  return;
1785  }
1786 
1787  if (LHS == RHS) {
1788  Quotient = APInt(BitWidth, 1); // X / X ===> 1
1789  Remainder = APInt(BitWidth, 0); // X % X ===> 0;
1790  return;
1791  }
1792 
1793  // Make sure there is enough space to hold the results.
1794  // NOTE: This assumes that reallocate won't affect any bits if it doesn't
1795  // change the size. This is necessary if Quotient or Remainder is aliased
1796  // with LHS or RHS.
1797  Quotient.reallocate(BitWidth);
1798  Remainder.reallocate(BitWidth);
1799 
1800  if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1.
1801  // There is only one word to consider so use the native versions.
1802  uint64_t lhsValue = LHS.U.pVal[0];
1803  uint64_t rhsValue = RHS.U.pVal[0];
1804  Quotient = lhsValue / rhsValue;
1805  Remainder = lhsValue % rhsValue;
1806  return;
1807  }
1808 
1809  // Okay, lets do it the long way
1810  divide(LHS.U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal,
1811  Remainder.U.pVal);
1812  // Clear the rest of the Quotient and Remainder.
1813  std::memset(Quotient.U.pVal + lhsWords, 0,
1814  (getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE);
1815  std::memset(Remainder.U.pVal + rhsWords, 0,
1816  (getNumWords(BitWidth) - rhsWords) * APINT_WORD_SIZE);
1817 }
1818 
1819 void APInt::udivrem(const APInt &LHS, uint64_t RHS, APInt &Quotient,
1820  uint64_t &Remainder) {
1821  assert(RHS != 0 && "Divide by zero?");
1822  unsigned BitWidth = LHS.BitWidth;
1823 
1824  // First, deal with the easy case
1825  if (LHS.isSingleWord()) {
1826  uint64_t QuotVal = LHS.U.VAL / RHS;
1827  Remainder = LHS.U.VAL % RHS;
1828  Quotient = APInt(BitWidth, QuotVal);
1829  return;
1830  }
1831 
1832  // Get some size facts about the dividend and divisor
1833  unsigned lhsWords = getNumWords(LHS.getActiveBits());
1834 
1835  // Check the degenerate cases
1836  if (lhsWords == 0) {
1837  Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0
1838  Remainder = 0; // 0 % Y ===> 0
1839  return;
1840  }
1841 
1842  if (RHS == 1) {
1843  Quotient = LHS; // X / 1 ===> X
1844  Remainder = 0; // X % 1 ===> 0
1845  return;
1846  }
1847 
1848  if (LHS.ult(RHS)) {
1849  Remainder = LHS.getZExtValue(); // X % Y ===> X, iff X < Y
1850  Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y
1851  return;
1852  }
1853 
1854  if (LHS == RHS) {
1855  Quotient = APInt(BitWidth, 1); // X / X ===> 1
1856  Remainder = 0; // X % X ===> 0;
1857  return;
1858  }
1859 
1860  // Make sure there is enough space to hold the results.
1861  // NOTE: This assumes that reallocate won't affect any bits if it doesn't
1862  // change the size. This is necessary if Quotient is aliased with LHS.
1863  Quotient.reallocate(BitWidth);
1864 
1865  if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1.
1866  // There is only one word to consider so use the native versions.
1867  uint64_t lhsValue = LHS.U.pVal[0];
1868  Quotient = lhsValue / RHS;
1869  Remainder = lhsValue % RHS;
1870  return;
1871  }
1872 
1873  // Okay, lets do it the long way
1874  divide(LHS.U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, &Remainder);
1875  // Clear the rest of the Quotient.
1876  std::memset(Quotient.U.pVal + lhsWords, 0,
1877  (getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE);
1878 }
1879 
1880 void APInt::sdivrem(const APInt &LHS, const APInt &RHS,
1881  APInt &Quotient, APInt &Remainder) {
1882  if (LHS.isNegative()) {
1883  if (RHS.isNegative())
1884  APInt::udivrem(-LHS, -RHS, Quotient, Remainder);
1885  else {
1886  APInt::udivrem(-LHS, RHS, Quotient, Remainder);
1887  Quotient.negate();
1888  }
1889  Remainder.negate();
1890  } else if (RHS.isNegative()) {
1891  APInt::udivrem(LHS, -RHS, Quotient, Remainder);
1892  Quotient.negate();
1893  } else {
1894  APInt::udivrem(LHS, RHS, Quotient, Remainder);
1895  }
1896 }
1897 
1898 void APInt::sdivrem(const APInt &LHS, int64_t RHS,
1899  APInt &Quotient, int64_t &Remainder) {
1900  uint64_t R = Remainder;
1901  if (LHS.isNegative()) {
1902  if (RHS < 0)
1903  APInt::udivrem(-LHS, -RHS, Quotient, R);
1904  else {
1905  APInt::udivrem(-LHS, RHS, Quotient, R);
1906  Quotient.negate();
1907  }
1908  R = -R;
1909  } else if (RHS < 0) {
1910  APInt::udivrem(LHS, -RHS, Quotient, R);
1911  Quotient.negate();
1912  } else {
1913  APInt::udivrem(LHS, RHS, Quotient, R);
1914  }
1915  Remainder = R;
1916 }
1917 
1918 APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const {
1919  APInt Res = *this+RHS;
1920  Overflow = isNonNegative() == RHS.isNonNegative() &&
1921  Res.isNonNegative() != isNonNegative();
1922  return Res;
1923 }
1924 
1925 APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const {
1926  APInt Res = *this+RHS;
1927  Overflow = Res.ult(RHS);
1928  return Res;
1929 }
1930 
1931 APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const {
1932  APInt Res = *this - RHS;
1933  Overflow = isNonNegative() != RHS.isNonNegative() &&
1934  Res.isNonNegative() != isNonNegative();
1935  return Res;
1936 }
1937 
1938 APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const {
1939  APInt Res = *this-RHS;
1940  Overflow = Res.ugt(*this);
1941  return Res;
1942 }
1943 
1944 APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const {
1945  // MININT/-1 --> overflow.
1946  Overflow = isMinSignedValue() && RHS.isAllOnes();
1947  return sdiv(RHS);
1948 }
1949 
1950 APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const {
1951  APInt Res = *this * RHS;
1952 
1953  if (RHS != 0)
1954  Overflow = Res.sdiv(RHS) != *this ||
1955  (isMinSignedValue() && RHS.isAllOnes());
1956  else
1957  Overflow = false;
1958  return Res;
1959 }
1960 
1961 APInt APInt::umul_ov(const APInt &RHS, bool &Overflow) const {
1962  if (countLeadingZeros() + RHS.countLeadingZeros() + 2 <= BitWidth) {
1963  Overflow = true;
1964  return *this * RHS;
1965  }
1966 
1967  APInt Res = lshr(1) * RHS;
1968  Overflow = Res.isNegative();
1969  Res <<= 1;
1970  if ((*this)[0]) {
1971  Res += RHS;
1972  if (Res.ult(RHS))
1973  Overflow = true;
1974  }
1975  return Res;
1976 }
1977 
1978 APInt APInt::sshl_ov(const APInt &ShAmt, bool &Overflow) const {
1979  Overflow = ShAmt.uge(getBitWidth());
1980  if (Overflow)
1981  return APInt(BitWidth, 0);
1982 
1983  if (isNonNegative()) // Don't allow sign change.
1984  Overflow = ShAmt.uge(countLeadingZeros());
1985  else
1986  Overflow = ShAmt.uge(countLeadingOnes());
1987 
1988  return *this << ShAmt;
1989 }
1990 
1991 APInt APInt::ushl_ov(const APInt &ShAmt, bool &Overflow) const {
1992  Overflow = ShAmt.uge(getBitWidth());
1993  if (Overflow)
1994  return APInt(BitWidth, 0);
1995 
1996  Overflow = ShAmt.ugt(countLeadingZeros());
1997 
1998  return *this << ShAmt;
1999 }
2000 
2002  bool Overflow;
2003  APInt Res = sadd_ov(RHS, Overflow);
2004  if (!Overflow)
2005  return Res;
2006 
2007  return isNegative() ? APInt::getSignedMinValue(BitWidth)
2008  : APInt::getSignedMaxValue(BitWidth);
2009 }
2010 
2012  bool Overflow;
2013  APInt Res = uadd_ov(RHS, Overflow);
2014  if (!Overflow)
2015  return Res;
2016 
2017  return APInt::getMaxValue(BitWidth);
2018 }
2019 
2021  bool Overflow;
2022  APInt Res = ssub_ov(RHS, Overflow);
2023  if (!Overflow)
2024  return Res;
2025 
2026  return isNegative() ? APInt::getSignedMinValue(BitWidth)
2027  : APInt::getSignedMaxValue(BitWidth);
2028 }
2029 
2031  bool Overflow;
2032  APInt Res = usub_ov(RHS, Overflow);
2033  if (!Overflow)
2034  return Res;
2035 
2036  return APInt(BitWidth, 0);
2037 }
2038 
2040  bool Overflow;
2041  APInt Res = smul_ov(RHS, Overflow);
2042  if (!Overflow)
2043  return Res;
2044 
2045  // The result is negative if one and only one of inputs is negative.
2046  bool ResIsNegative = isNegative() ^ RHS.isNegative();
2047 
2048  return ResIsNegative ? APInt::getSignedMinValue(BitWidth)
2049  : APInt::getSignedMaxValue(BitWidth);
2050 }
2051 
2053  bool Overflow;
2054  APInt Res = umul_ov(RHS, Overflow);
2055  if (!Overflow)
2056  return Res;
2057 
2058  return APInt::getMaxValue(BitWidth);
2059 }
2060 
2062  bool Overflow;
2063  APInt Res = sshl_ov(RHS, Overflow);
2064  if (!Overflow)
2065  return Res;
2066 
2067  return isNegative() ? APInt::getSignedMinValue(BitWidth)
2068  : APInt::getSignedMaxValue(BitWidth);
2069 }
2070 
2072  bool Overflow;
2073  APInt Res = ushl_ov(RHS, Overflow);
2074  if (!Overflow)
2075  return Res;
2076 
2077  return APInt::getMaxValue(BitWidth);
2078 }
2079 
2080 void APInt::fromString(unsigned numbits, StringRef str, uint8_t radix) {
2081  // Check our assumptions here
2082  assert(!str.empty() && "Invalid string length");
2083  assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||
2084  radix == 36) &&
2085  "Radix should be 2, 8, 10, 16, or 36!");
2086 
2087  StringRef::iterator p = str.begin();
2088  size_t slen = str.size();
2089  bool isNeg = *p == '-';
2090  if (*p == '-' || *p == '+') {
2091  p++;
2092  slen--;
2093  assert(slen && "String is only a sign, needs a value.");
2094  }
2095  assert((slen <= numbits || radix != 2) && "Insufficient bit width");
2096  assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width");
2097  assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width");
2098  assert((((slen-1)*64)/22 <= numbits || radix != 10) &&
2099  "Insufficient bit width");
2100 
2101  // Allocate memory if needed
2102  if (isSingleWord())
2103  U.VAL = 0;
2104  else
2105  U.pVal = getClearedMemory(getNumWords());
2106 
2107  // Figure out if we can shift instead of multiply
2108  unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
2109 
2110  // Enter digit traversal loop
2111  for (StringRef::iterator e = str.end(); p != e; ++p) {
2112  unsigned digit = getDigit(*p, radix);
2113  assert(digit < radix && "Invalid character in digit string");
2114 
2115  // Shift or multiply the value by the radix
2116  if (slen > 1) {
2117  if (shift)
2118  *this <<= shift;
2119  else
2120  *this *= radix;
2121  }
2122 
2123  // Add in the digit we just interpreted
2124  *this += digit;
2125  }
2126  // If its negative, put it in two's complement form
2127  if (isNeg)
2128  this->negate();
2129 }
2130 
2131 void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix,
2132  bool Signed, bool formatAsCLiteral) const {
2133  assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2 ||
2134  Radix == 36) &&
2135  "Radix should be 2, 8, 10, 16, or 36!");
2136 
2137  const char *Prefix = "";
2138  if (formatAsCLiteral) {
2139  switch (Radix) {
2140  case 2:
2141  // Binary literals are a non-standard extension added in gcc 4.3:
2142  // http://gcc.gnu.org/onlinedocs/gcc-4.3.0/gcc/Binary-constants.html
2143  Prefix = "0b";
2144  break;
2145  case 8:
2146  Prefix = "0";
2147  break;
2148  case 10:
2149  break; // No prefix
2150  case 16:
2151  Prefix = "0x";
2152  break;
2153  default:
2154  llvm_unreachable("Invalid radix!");
2155  }
2156  }
2157 
2158  // First, check for a zero value and just short circuit the logic below.
2159  if (isZero()) {
2160  while (*Prefix) {
2161  Str.push_back(*Prefix);
2162  ++Prefix;
2163  };
2164  Str.push_back('0');
2165  return;
2166  }
2167 
2168  static const char Digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
2169 
2170  if (isSingleWord()) {
2171  char Buffer[65];
2172  char *BufPtr = std::end(Buffer);
2173 
2174  uint64_t N;
2175  if (!Signed) {
2176  N = getZExtValue();
2177  } else {
2178  int64_t I = getSExtValue();
2179  if (I >= 0) {
2180  N = I;
2181  } else {
2182  Str.push_back('-');
2183  N = -(uint64_t)I;
2184  }
2185  }
2186 
2187  while (*Prefix) {
2188  Str.push_back(*Prefix);
2189  ++Prefix;
2190  };
2191 
2192  while (N) {
2193  *--BufPtr = Digits[N % Radix];
2194  N /= Radix;
2195  }
2196  Str.append(BufPtr, std::end(Buffer));
2197  return;
2198  }
2199 
2200  APInt Tmp(*this);
2201 
2202  if (Signed && isNegative()) {
2203  // They want to print the signed version and it is a negative value
2204  // Flip the bits and add one to turn it into the equivalent positive
2205  // value and put a '-' in the result.
2206  Tmp.negate();
2207  Str.push_back('-');
2208  }
2209 
2210  while (*Prefix) {
2211  Str.push_back(*Prefix);
2212  ++Prefix;
2213  };
2214 
2215  // We insert the digits backward, then reverse them to get the right order.
2216  unsigned StartDig = Str.size();
2217 
2218  // For the 2, 8 and 16 bit cases, we can just shift instead of divide
2219  // because the number of bits per digit (1, 3 and 4 respectively) divides
2220  // equally. We just shift until the value is zero.
2221  if (Radix == 2 || Radix == 8 || Radix == 16) {
2222  // Just shift tmp right for each digit width until it becomes zero
2223  unsigned ShiftAmt = (Radix == 16 ? 4 : (Radix == 8 ? 3 : 1));
2224  unsigned MaskAmt = Radix - 1;
2225 
2226  while (Tmp.getBoolValue()) {
2227  unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt;
2228  Str.push_back(Digits[Digit]);
2229  Tmp.lshrInPlace(ShiftAmt);
2230  }
2231  } else {
2232  while (Tmp.getBoolValue()) {
2233  uint64_t Digit;
2234  udivrem(Tmp, Radix, Tmp, Digit);
2235  assert(Digit < Radix && "divide failed");
2236  Str.push_back(Digits[Digit]);
2237  }
2238  }
2239 
2240  // Reverse the digits before returning.
2241  std::reverse(Str.begin()+StartDig, Str.end());
2242 }
2243 
2244 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
2246  SmallString<40> S, U;
2247  this->toStringUnsigned(U);
2248  this->toStringSigned(S);
2249  dbgs() << "APInt(" << BitWidth << "b, "
2250  << U << "u " << S << "s)\n";
2251 }
2252 #endif
2253 
2254 void APInt::print(raw_ostream &OS, bool isSigned) const {
2256  this->toString(S, 10, isSigned, /* formatAsCLiteral = */false);
2257  OS << S;
2258 }
2259 
2260 // This implements a variety of operations on a representation of
2261 // arbitrary precision, two's-complement, bignum integer values.
2262 
2263 // Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe
2264 // and unrestricting assumption.
2265 static_assert(APInt::APINT_BITS_PER_WORD % 2 == 0,
2266  "Part width must be divisible by 2!");
2267 
2268 // Returns the integer part with the least significant BITS set.
2269 // BITS cannot be zero.
2270 static inline APInt::WordType lowBitMask(unsigned bits) {
2272  return ~(APInt::WordType) 0 >> (APInt::APINT_BITS_PER_WORD - bits);
2273 }
2274 
2275 /// Returns the value of the lower half of PART.
2277  return part & lowBitMask(APInt::APINT_BITS_PER_WORD / 2);
2278 }
2279 
2280 /// Returns the value of the upper half of PART.
2282  return part >> (APInt::APINT_BITS_PER_WORD / 2);
2283 }
2284 
2285 /// Returns the bit number of the most significant set bit of a part.
2286 /// If the input number has no bits set -1U is returned.
2287 static unsigned partMSB(APInt::WordType value) {
2288  return findLastSet(value, ZB_Max);
2289 }
2290 
2291 /// Returns the bit number of the least significant set bit of a part. If the
2292 /// input number has no bits set -1U is returned.
2293 static unsigned partLSB(APInt::WordType value) {
2294  return findFirstSet(value, ZB_Max);
2295 }
2296 
2297 /// Sets the least significant part of a bignum to the input value, and zeroes
2298 /// out higher parts.
2299 void APInt::tcSet(WordType *dst, WordType part, unsigned parts) {
2300  assert(parts > 0);
2301  dst[0] = part;
2302  for (unsigned i = 1; i < parts; i++)
2303  dst[i] = 0;
2304 }
2305 
2306 /// Assign one bignum to another.
2307 void APInt::tcAssign(WordType *dst, const WordType *src, unsigned parts) {
2308  for (unsigned i = 0; i < parts; i++)
2309  dst[i] = src[i];
2310 }
2311 
2312 /// Returns true if a bignum is zero, false otherwise.
2313 bool APInt::tcIsZero(const WordType *src, unsigned parts) {
2314  for (unsigned i = 0; i < parts; i++)
2315  if (src[i])
2316  return false;
2317 
2318  return true;
2319 }
2320 
2321 /// Extract the given bit of a bignum; returns 0 or 1.
2322 int APInt::tcExtractBit(const WordType *parts, unsigned bit) {
2323  return (parts[whichWord(bit)] & maskBit(bit)) != 0;
2324 }
2325 
2326 /// Set the given bit of a bignum.
2327 void APInt::tcSetBit(WordType *parts, unsigned bit) {
2328  parts[whichWord(bit)] |= maskBit(bit);
2329 }
2330 
2331 /// Clears the given bit of a bignum.
2332 void APInt::tcClearBit(WordType *parts, unsigned bit) {
2333  parts[whichWord(bit)] &= ~maskBit(bit);
2334 }
2335 
2336 /// Returns the bit number of the least significant set bit of a number. If the
2337 /// input number has no bits set -1U is returned.
2338 unsigned APInt::tcLSB(const WordType *parts, unsigned n) {
2339  for (unsigned i = 0; i < n; i++) {
2340  if (parts[i] != 0) {
2341  unsigned lsb = partLSB(parts[i]);
2342  return lsb + i * APINT_BITS_PER_WORD;
2343  }
2344  }
2345 
2346  return -1U;
2347 }
2348 
2349 /// Returns the bit number of the most significant set bit of a number.
2350 /// If the input number has no bits set -1U is returned.
2351 unsigned APInt::tcMSB(const WordType *parts, unsigned n) {
2352  do {
2353  --n;
2354 
2355  if (parts[n] != 0) {
2356  unsigned msb = partMSB(parts[n]);
2357 
2358  return msb + n * APINT_BITS_PER_WORD;
2359  }
2360  } while (n);
2361 
2362  return -1U;
2363 }
2364 
2365 /// Copy the bit vector of width srcBITS from SRC, starting at bit srcLSB, to
2366 /// DST, of dstCOUNT parts, such that the bit srcLSB becomes the least
2367 /// significant bit of DST. All high bits above srcBITS in DST are zero-filled.
2368 /// */
2369 void
2370 APInt::tcExtract(WordType *dst, unsigned dstCount, const WordType *src,
2371  unsigned srcBits, unsigned srcLSB) {
2372  unsigned dstParts = (srcBits + APINT_BITS_PER_WORD - 1) / APINT_BITS_PER_WORD;
2373  assert(dstParts <= dstCount);
2374 
2375  unsigned firstSrcPart = srcLSB / APINT_BITS_PER_WORD;
2376  tcAssign(dst, src + firstSrcPart, dstParts);
2377 
2378  unsigned shift = srcLSB % APINT_BITS_PER_WORD;
2379  tcShiftRight(dst, dstParts, shift);
2380 
2381  // We now have (dstParts * APINT_BITS_PER_WORD - shift) bits from SRC
2382  // in DST. If this is less that srcBits, append the rest, else
2383  // clear the high bits.
2384  unsigned n = dstParts * APINT_BITS_PER_WORD - shift;
2385  if (n < srcBits) {
2386  WordType mask = lowBitMask (srcBits - n);
2387  dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask)
2388  << n % APINT_BITS_PER_WORD);
2389  } else if (n > srcBits) {
2390  if (srcBits % APINT_BITS_PER_WORD)
2391  dst[dstParts - 1] &= lowBitMask (srcBits % APINT_BITS_PER_WORD);
2392  }
2393 
2394  // Clear high parts.
2395  while (dstParts < dstCount)
2396  dst[dstParts++] = 0;
2397 }
2398 
2399 //// DST += RHS + C where C is zero or one. Returns the carry flag.
2401  WordType c, unsigned parts) {
2402  assert(c <= 1);
2403 
2404  for (unsigned i = 0; i < parts; i++) {
2405  WordType l = dst[i];
2406  if (c) {
2407  dst[i] += rhs[i] + 1;
2408  c = (dst[i] <= l);
2409  } else {
2410  dst[i] += rhs[i];
2411  c = (dst[i] < l);
2412  }
2413  }
2414 
2415  return c;
2416 }
2417 
2418 /// This function adds a single "word" integer, src, to the multiple
2419 /// "word" integer array, dst[]. dst[] is modified to reflect the addition and
2420 /// 1 is returned if there is a carry out, otherwise 0 is returned.
2421 /// @returns the carry of the addition.
2423  unsigned parts) {
2424  for (unsigned i = 0; i < parts; ++i) {
2425  dst[i] += src;
2426  if (dst[i] >= src)
2427  return 0; // No need to carry so exit early.
2428  src = 1; // Carry one to next digit.
2429  }
2430 
2431  return 1;
2432 }
2433 
2434 /// DST -= RHS + C where C is zero or one. Returns the carry flag.
2436  WordType c, unsigned parts) {
2437  assert(c <= 1);
2438 
2439  for (unsigned i = 0; i < parts; i++) {
2440  WordType l = dst[i];
2441  if (c) {
2442  dst[i] -= rhs[i] + 1;
2443  c = (dst[i] >= l);
2444  } else {
2445  dst[i] -= rhs[i];
2446  c = (dst[i] > l);
2447  }
2448  }
2449 
2450  return c;
2451 }
2452 
2453 /// This function subtracts a single "word" (64-bit word), src, from
2454 /// the multi-word integer array, dst[], propagating the borrowed 1 value until
2455 /// no further borrowing is needed or it runs out of "words" in dst. The result
2456 /// is 1 if "borrowing" exhausted the digits in dst, or 0 if dst was not
2457 /// exhausted. In other words, if src > dst then this function returns 1,
2458 /// otherwise 0.
2459 /// @returns the borrow out of the subtraction
2461  unsigned parts) {
2462  for (unsigned i = 0; i < parts; ++i) {
2463  WordType Dst = dst[i];
2464  dst[i] -= src;
2465  if (src <= Dst)
2466  return 0; // No need to borrow so exit early.
2467  src = 1; // We have to "borrow 1" from next "word"
2468  }
2469 
2470  return 1;
2471 }
2472 
2473 /// Negate a bignum in-place.
2474 void APInt::tcNegate(WordType *dst, unsigned parts) {
2475  tcComplement(dst, parts);
2476  tcIncrement(dst, parts);
2477 }
2478 
2479 /// DST += SRC * MULTIPLIER + CARRY if add is true
2480 /// DST = SRC * MULTIPLIER + CARRY if add is false
2481 /// Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC
2482 /// they must start at the same point, i.e. DST == SRC.
2483 /// If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is
2484 /// returned. Otherwise DST is filled with the least significant
2485 /// DSTPARTS parts of the result, and if all of the omitted higher
2486 /// parts were zero return zero, otherwise overflow occurred and
2487 /// return one.
2489  WordType multiplier, WordType carry,
2490  unsigned srcParts, unsigned dstParts,
2491  bool add) {
2492  // Otherwise our writes of DST kill our later reads of SRC.
2493  assert(dst <= src || dst >= src + srcParts);
2494  assert(dstParts <= srcParts + 1);
2495 
2496  // N loops; minimum of dstParts and srcParts.
2497  unsigned n = std::min(dstParts, srcParts);
2498 
2499  for (unsigned i = 0; i < n; i++) {
2500  // [LOW, HIGH] = MULTIPLIER * SRC[i] + DST[i] + CARRY.
2501  // This cannot overflow, because:
2502  // (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1)
2503  // which is less than n^2.
2504  WordType srcPart = src[i];
2505  WordType low, mid, high;
2506  if (multiplier == 0 || srcPart == 0) {
2507  low = carry;
2508  high = 0;
2509  } else {
2510  low = lowHalf(srcPart) * lowHalf(multiplier);
2511  high = highHalf(srcPart) * highHalf(multiplier);
2512 
2513  mid = lowHalf(srcPart) * highHalf(multiplier);
2514  high += highHalf(mid);
2515  mid <<= APINT_BITS_PER_WORD / 2;
2516  if (low + mid < low)
2517  high++;
2518  low += mid;
2519 
2520  mid = highHalf(srcPart) * lowHalf(multiplier);
2521  high += highHalf(mid);
2522  mid <<= APINT_BITS_PER_WORD / 2;
2523  if (low + mid < low)
2524  high++;
2525  low += mid;
2526 
2527  // Now add carry.
2528  if (low + carry < low)
2529  high++;
2530  low += carry;
2531  }
2532 
2533  if (add) {
2534  // And now DST[i], and store the new low part there.
2535  if (low + dst[i] < low)
2536  high++;
2537  dst[i] += low;
2538  } else
2539  dst[i] = low;
2540 
2541  carry = high;
2542  }
2543 
2544  if (srcParts < dstParts) {
2545  // Full multiplication, there is no overflow.
2546  assert(srcParts + 1 == dstParts);
2547  dst[srcParts] = carry;
2548  return 0;
2549  }
2550 
2551  // We overflowed if there is carry.
2552  if (carry)
2553  return 1;
2554 
2555  // We would overflow if any significant unwritten parts would be
2556  // non-zero. This is true if any remaining src parts are non-zero
2557  // and the multiplier is non-zero.
2558  if (multiplier)
2559  for (unsigned i = dstParts; i < srcParts; i++)
2560  if (src[i])
2561  return 1;
2562 
2563  // We fitted in the narrow destination.
2564  return 0;
2565 }
2566 
2567 /// DST = LHS * RHS, where DST has the same width as the operands and
2568 /// is filled with the least significant parts of the result. Returns
2569 /// one if overflow occurred, otherwise zero. DST must be disjoint
2570 /// from both operands.
2571 int APInt::tcMultiply(WordType *dst, const WordType *lhs,
2572  const WordType *rhs, unsigned parts) {
2573  assert(dst != lhs && dst != rhs);
2574 
2575  int overflow = 0;
2576  tcSet(dst, 0, parts);
2577 
2578  for (unsigned i = 0; i < parts; i++)
2579  overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts,
2580  parts - i, true);
2581 
2582  return overflow;
2583 }
2584 
2585 /// DST = LHS * RHS, where DST has width the sum of the widths of the
2586 /// operands. No overflow occurs. DST must be disjoint from both operands.
2588  const WordType *rhs, unsigned lhsParts,
2589  unsigned rhsParts) {
2590  // Put the narrower number on the LHS for less loops below.
2591  if (lhsParts > rhsParts)
2592  return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts);
2593 
2594  assert(dst != lhs && dst != rhs);
2595 
2596  tcSet(dst, 0, rhsParts);
2597 
2598  for (unsigned i = 0; i < lhsParts; i++)
2599  tcMultiplyPart(&dst[i], rhs, lhs[i], 0, rhsParts, rhsParts + 1, true);
2600 }
2601 
2602 // If RHS is zero LHS and REMAINDER are left unchanged, return one.
2603 // Otherwise set LHS to LHS / RHS with the fractional part discarded,
2604 // set REMAINDER to the remainder, return zero. i.e.
2605 //
2606 // OLD_LHS = RHS * LHS + REMAINDER
2607 //
2608 // SCRATCH is a bignum of the same size as the operands and result for
2609 // use by the routine; its contents need not be initialized and are
2610 // destroyed. LHS, REMAINDER and SCRATCH must be distinct.
2611 int APInt::tcDivide(WordType *lhs, const WordType *rhs,
2612  WordType *remainder, WordType *srhs,
2613  unsigned parts) {
2614  assert(lhs != remainder && lhs != srhs && remainder != srhs);
2615 
2616  unsigned shiftCount = tcMSB(rhs, parts) + 1;
2617  if (shiftCount == 0)
2618  return true;
2619 
2620  shiftCount = parts * APINT_BITS_PER_WORD - shiftCount;
2621  unsigned n = shiftCount / APINT_BITS_PER_WORD;
2622  WordType mask = (WordType) 1 << (shiftCount % APINT_BITS_PER_WORD);
2623 
2624  tcAssign(srhs, rhs, parts);
2625  tcShiftLeft(srhs, parts, shiftCount);
2626  tcAssign(remainder, lhs, parts);
2627  tcSet(lhs, 0, parts);
2628 
2629  // Loop, subtracting SRHS if REMAINDER is greater and adding that to the
2630  // total.
2631  for (;;) {
2632  int compare = tcCompare(remainder, srhs, parts);
2633  if (compare >= 0) {
2634  tcSubtract(remainder, srhs, 0, parts);
2635  lhs[n] |= mask;
2636  }
2637 
2638  if (shiftCount == 0)
2639  break;
2640  shiftCount--;
2641  tcShiftRight(srhs, parts, 1);
2642  if ((mask >>= 1) == 0) {
2643  mask = (WordType) 1 << (APINT_BITS_PER_WORD - 1);
2644  n--;
2645  }
2646  }
2647 
2648  return false;
2649 }
2650 
2651 /// Shift a bignum left Cound bits in-place. Shifted in bits are zero. There are
2652 /// no restrictions on Count.
2653 void APInt::tcShiftLeft(WordType *Dst, unsigned Words, unsigned Count) {
2654  // Don't bother performing a no-op shift.
2655  if (!Count)
2656  return;
2657 
2658  // WordShift is the inter-part shift; BitShift is the intra-part shift.
2659  unsigned WordShift = std::min(Count / APINT_BITS_PER_WORD, Words);
2660  unsigned BitShift = Count % APINT_BITS_PER_WORD;
2661 
2662  // Fastpath for moving by whole words.
2663  if (BitShift == 0) {
2664  std::memmove(Dst + WordShift, Dst, (Words - WordShift) * APINT_WORD_SIZE);
2665  } else {
2666  while (Words-- > WordShift) {
2667  Dst[Words] = Dst[Words - WordShift] << BitShift;
2668  if (Words > WordShift)
2669  Dst[Words] |=
2670  Dst[Words - WordShift - 1] >> (APINT_BITS_PER_WORD - BitShift);
2671  }
2672  }
2673 
2674  // Fill in the remainder with 0s.
2675  std::memset(Dst, 0, WordShift * APINT_WORD_SIZE);
2676 }
2677 
2678 /// Shift a bignum right Count bits in-place. Shifted in bits are zero. There
2679 /// are no restrictions on Count.
2680 void APInt::tcShiftRight(WordType *Dst, unsigned Words, unsigned Count) {
2681  // Don't bother performing a no-op shift.
2682  if (!Count)
2683  return;
2684 
2685  // WordShift is the inter-part shift; BitShift is the intra-part shift.
2686  unsigned WordShift = std::min(Count / APINT_BITS_PER_WORD, Words);
2687  unsigned BitShift = Count % APINT_BITS_PER_WORD;
2688 
2689  unsigned WordsToMove = Words - WordShift;
2690  // Fastpath for moving by whole words.
2691  if (BitShift == 0) {
2692  std::memmove(Dst, Dst + WordShift, WordsToMove * APINT_WORD_SIZE);
2693  } else {
2694  for (unsigned i = 0; i != WordsToMove; ++i) {
2695  Dst[i] = Dst[i + WordShift] >> BitShift;
2696  if (i + 1 != WordsToMove)
2697  Dst[i] |= Dst[i + WordShift + 1] << (APINT_BITS_PER_WORD - BitShift);
2698  }
2699  }
2700 
2701  // Fill in the remainder with 0s.
2702  std::memset(Dst + WordsToMove, 0, WordShift * APINT_WORD_SIZE);
2703 }
2704 
2705 // Comparison (unsigned) of two bignums.
2706 int APInt::tcCompare(const WordType *lhs, const WordType *rhs,
2707  unsigned parts) {
2708  while (parts) {
2709  parts--;
2710  if (lhs[parts] != rhs[parts])
2711  return (lhs[parts] > rhs[parts]) ? 1 : -1;
2712  }
2713 
2714  return 0;
2715 }
2716 
2718  APInt::Rounding RM) {
2719  // Currently udivrem always rounds down.
2720  switch (RM) {
2721  case APInt::Rounding::DOWN:
2723  return A.udiv(B);
2724  case APInt::Rounding::UP: {
2725  APInt Quo, Rem;
2726  APInt::udivrem(A, B, Quo, Rem);
2727  if (Rem.isZero())
2728  return Quo;
2729  return Quo + 1;
2730  }
2731  }
2732  llvm_unreachable("Unknown APInt::Rounding enum");
2733 }
2734 
2736  APInt::Rounding RM) {
2737  switch (RM) {
2738  case APInt::Rounding::DOWN:
2739  case APInt::Rounding::UP: {
2740  APInt Quo, Rem;
2741  APInt::sdivrem(A, B, Quo, Rem);
2742  if (Rem.isZero())
2743  return Quo;
2744  // This algorithm deals with arbitrary rounding mode used by sdivrem.
2745  // We want to check whether the non-integer part of the mathematical value
2746  // is negative or not. If the non-integer part is negative, we need to round
2747  // down from Quo; otherwise, if it's positive or 0, we return Quo, as it's
2748  // already rounded down.
2749  if (RM == APInt::Rounding::DOWN) {
2750  if (Rem.isNegative() != B.isNegative())
2751  return Quo - 1;
2752  return Quo;
2753  }
2754  if (Rem.isNegative() != B.isNegative())
2755  return Quo;
2756  return Quo + 1;
2757  }
2758  // Currently sdiv rounds towards zero.
2760  return A.sdiv(B);
2761  }
2762  llvm_unreachable("Unknown APInt::Rounding enum");
2763 }
2764 
2767  unsigned RangeWidth) {
2768  unsigned CoeffWidth = A.getBitWidth();
2769  assert(CoeffWidth == B.getBitWidth() && CoeffWidth == C.getBitWidth());
2770  assert(RangeWidth <= CoeffWidth &&
2771  "Value range width should be less than coefficient width");
2772  assert(RangeWidth > 1 && "Value range bit width should be > 1");
2773 
2774  LLVM_DEBUG(dbgs() << __func__ << ": solving " << A << "x^2 + " << B
2775  << "x + " << C << ", rw:" << RangeWidth << '\n');
2776 
2777  // Identify 0 as a (non)solution immediately.
2778  if (C.sextOrTrunc(RangeWidth).isZero()) {
2779  LLVM_DEBUG(dbgs() << __func__ << ": zero solution\n");
2780  return APInt(CoeffWidth, 0);
2781  }
2782 
2783  // The result of APInt arithmetic has the same bit width as the operands,
2784  // so it can actually lose high bits. A product of two n-bit integers needs
2785  // 2n-1 bits to represent the full value.
2786  // The operation done below (on quadratic coefficients) that can produce
2787  // the largest value is the evaluation of the equation during bisection,
2788  // which needs 3 times the bitwidth of the coefficient, so the total number
2789  // of required bits is 3n.
2790  //
2791  // The purpose of this extension is to simulate the set Z of all integers,
2792  // where n+1 > n for all n in Z. In Z it makes sense to talk about positive
2793  // and negative numbers (not so much in a modulo arithmetic). The method
2794  // used to solve the equation is based on the standard formula for real
2795  // numbers, and uses the concepts of "positive" and "negative" with their
2796  // usual meanings.
2797  CoeffWidth *= 3;
2798  A = A.sext(CoeffWidth);
2799  B = B.sext(CoeffWidth);
2800  C = C.sext(CoeffWidth);
2801 
2802  // Make A > 0 for simplicity. Negate cannot overflow at this point because
2803  // the bit width has increased.
2804  if (A.isNegative()) {
2805  A.negate();
2806  B.negate();
2807  C.negate();
2808  }
2809 
2810  // Solving an equation q(x) = 0 with coefficients in modular arithmetic
2811  // is really solving a set of equations q(x) = kR for k = 0, 1, 2, ...,
2812  // and R = 2^BitWidth.
2813  // Since we're trying not only to find exact solutions, but also values
2814  // that "wrap around", such a set will always have a solution, i.e. an x
2815  // that satisfies at least one of the equations, or such that |q(x)|
2816  // exceeds kR, while |q(x-1)| for the same k does not.
2817  //
2818  // We need to find a value k, such that Ax^2 + Bx + C = kR will have a
2819  // positive solution n (in the above sense), and also such that the n
2820  // will be the least among all solutions corresponding to k = 0, 1, ...
2821  // (more precisely, the least element in the set
2822  // { n(k) | k is such that a solution n(k) exists }).
2823  //
2824  // Consider the parabola (over real numbers) that corresponds to the
2825  // quadratic equation. Since A > 0, the arms of the parabola will point
2826  // up. Picking different values of k will shift it up and down by R.
2827  //
2828  // We want to shift the parabola in such a way as to reduce the problem
2829  // of solving q(x) = kR to solving shifted_q(x) = 0.
2830  // (The interesting solutions are the ceilings of the real number
2831  // solutions.)
2832  APInt R = APInt::getOneBitSet(CoeffWidth, RangeWidth);
2833  APInt TwoA = 2 * A;
2834  APInt SqrB = B * B;
2835  bool PickLow;
2836 
2837  auto RoundUp = [] (const APInt &V, const APInt &A) -> APInt {
2838  assert(A.isStrictlyPositive());
2839  APInt T = V.abs().urem(A);
2840  if (T.isZero())
2841  return V;
2842  return V.isNegative() ? V+T : V+(A-T);
2843  };
2844 
2845  // The vertex of the parabola is at -B/2A, but since A > 0, it's negative
2846  // iff B is positive.
2847  if (B.isNonNegative()) {
2848  // If B >= 0, the vertex it at a negative location (or at 0), so in
2849  // order to have a non-negative solution we need to pick k that makes
2850  // C-kR negative. To satisfy all the requirements for the solution
2851  // that we are looking for, it needs to be closest to 0 of all k.
2852  C = C.srem(R);
2853  if (C.isStrictlyPositive())
2854  C -= R;
2855  // Pick the greater solution.
2856  PickLow = false;
2857  } else {
2858  // If B < 0, the vertex is at a positive location. For any solution
2859  // to exist, the discriminant must be non-negative. This means that
2860  // C-kR <= B^2/4A is a necessary condition for k, i.e. there is a
2861  // lower bound on values of k: kR >= C - B^2/4A.
2862  APInt LowkR = C - SqrB.udiv(2*TwoA); // udiv because all values > 0.
2863  // Round LowkR up (towards +inf) to the nearest kR.
2864  LowkR = RoundUp(LowkR, R);
2865 
2866  // If there exists k meeting the condition above, and such that
2867  // C-kR > 0, there will be two positive real number solutions of
2868  // q(x) = kR. Out of all such values of k, pick the one that makes
2869  // C-kR closest to 0, (i.e. pick maximum k such that C-kR > 0).
2870  // In other words, find maximum k such that LowkR <= kR < C.
2871  if (C.sgt(LowkR)) {
2872  // If LowkR < C, then such a k is guaranteed to exist because
2873  // LowkR itself is a multiple of R.
2874  C -= -RoundUp(-C, R); // C = C - RoundDown(C, R)
2875  // Pick the smaller solution.
2876  PickLow = true;
2877  } else {
2878  // If C-kR < 0 for all potential k's, it means that one solution
2879  // will be negative, while the other will be positive. The positive
2880  // solution will shift towards 0 if the parabola is moved up.
2881  // Pick the kR closest to the lower bound (i.e. make C-kR closest
2882  // to 0, or in other words, out of all parabolas that have solutions,
2883  // pick the one that is the farthest "up").
2884  // Since LowkR is itself a multiple of R, simply take C-LowkR.
2885  C -= LowkR;
2886  // Pick the greater solution.
2887  PickLow = false;
2888  }
2889  }
2890 
2891  LLVM_DEBUG(dbgs() << __func__ << ": updated coefficients " << A << "x^2 + "
2892  << B << "x + " << C << ", rw:" << RangeWidth << '\n');
2893 
2894  APInt D = SqrB - 4*A*C;
2895  assert(D.isNonNegative() && "Negative discriminant");
2896  APInt SQ = D.sqrt();
2897 
2898  APInt Q = SQ * SQ;
2899  bool InexactSQ = Q != D;
2900  // The calculated SQ may actually be greater than the exact (non-integer)
2901  // value. If that's the case, decrement SQ to get a value that is lower.
2902  if (Q.sgt(D))
2903  SQ -= 1;
2904 
2905  APInt X;
2906  APInt Rem;
2907 
2908  // SQ is rounded down (i.e SQ * SQ <= D), so the roots may be inexact.
2909  // When using the quadratic formula directly, the calculated low root
2910  // may be greater than the exact one, since we would be subtracting SQ.
2911  // To make sure that the calculated root is not greater than the exact
2912  // one, subtract SQ+1 when calculating the low root (for inexact value
2913  // of SQ).
2914  if (PickLow)
2915  APInt::sdivrem(-B - (SQ+InexactSQ), TwoA, X, Rem);
2916  else
2917  APInt::sdivrem(-B + SQ, TwoA, X, Rem);
2918 
2919  // The updated coefficients should be such that the (exact) solution is
2920  // positive. Since APInt division rounds towards 0, the calculated one
2921  // can be 0, but cannot be negative.
2922  assert(X.isNonNegative() && "Solution should be non-negative");
2923 
2924  if (!InexactSQ && Rem.isZero()) {
2925  LLVM_DEBUG(dbgs() << __func__ << ": solution (root): " << X << '\n');
2926  return X;
2927  }
2928 
2929  assert((SQ*SQ).sle(D) && "SQ = |_sqrt(D)_|, so SQ*SQ <= D");
2930  // The exact value of the square root of D should be between SQ and SQ+1.
2931  // This implies that the solution should be between that corresponding to
2932  // SQ (i.e. X) and that corresponding to SQ+1.
2933  //
2934  // The calculated X cannot be greater than the exact (real) solution.
2935  // Actually it must be strictly less than the exact solution, while
2936  // X+1 will be greater than or equal to it.
2937 
2938  APInt VX = (A*X + B)*X + C;
2939  APInt VY = VX + TwoA*X + A + B;
2940  bool SignChange =
2941  VX.isNegative() != VY.isNegative() || VX.isZero() != VY.isZero();
2942  // If the sign did not change between X and X+1, X is not a valid solution.
2943  // This could happen when the actual (exact) roots don't have an integer
2944  // between them, so they would both be contained between X and X+1.
2945  if (!SignChange) {
2946  LLVM_DEBUG(dbgs() << __func__ << ": no valid solution\n");
2947  return None;
2948  }
2949 
2950  X += 1;
2951  LLVM_DEBUG(dbgs() << __func__ << ": solution (wrap): " << X << '\n');
2952  return X;
2953 }
2954 
2957  assert(A.getBitWidth() == B.getBitWidth() && "Must have the same bitwidth");
2958  if (A == B)
2959  return llvm::None;
2960  return A.getBitWidth() - ((A ^ B).countLeadingZeros() + 1);
2961 }
2962 
2963 APInt llvm::APIntOps::ScaleBitMask(const APInt &A, unsigned NewBitWidth) {
2964  unsigned OldBitWidth = A.getBitWidth();
2965  assert((((OldBitWidth % NewBitWidth) == 0) ||
2966  ((NewBitWidth % OldBitWidth) == 0)) &&
2967  "One size should be a multiple of the other one. "
2968  "Can't do fractional scaling.");
2969 
2970  // Check for matching bitwidths.
2971  if (OldBitWidth == NewBitWidth)
2972  return A;
2973 
2974  APInt NewA = APInt::getZero(NewBitWidth);
2975 
2976  // Check for null input.
2977  if (A.isZero())
2978  return NewA;
2979 
2980  if (NewBitWidth > OldBitWidth) {
2981  // Repeat bits.
2982  unsigned Scale = NewBitWidth / OldBitWidth;
2983  for (unsigned i = 0; i != OldBitWidth; ++i)
2984  if (A[i])
2985  NewA.setBits(i * Scale, (i + 1) * Scale);
2986  } else {
2987  // Merge bits - if any old bit is set, then set scale equivalent new bit.
2988  unsigned Scale = OldBitWidth / NewBitWidth;
2989  for (unsigned i = 0; i != NewBitWidth; ++i)
2990  if (!A.extractBits(Scale, i * Scale).isZero())
2991  NewA.setBit(i);
2992  }
2993 
2994  return NewA;
2995 }
2996 
2997 /// StoreIntToMemory - Fills the StoreBytes bytes of memory starting from Dst
2998 /// with the integer held in IntVal.
2999 void llvm::StoreIntToMemory(const APInt &IntVal, uint8_t *Dst,
3000  unsigned StoreBytes) {
3001  assert((IntVal.getBitWidth()+7)/8 >= StoreBytes && "Integer too small!");
3002  const uint8_t *Src = (const uint8_t *)IntVal.getRawData();
3003 
3005  // Little-endian host - the source is ordered from LSB to MSB. Order the
3006  // destination from LSB to MSB: Do a straight copy.
3007  memcpy(Dst, Src, StoreBytes);
3008  } else {
3009  // Big-endian host - the source is an array of 64 bit words ordered from
3010  // LSW to MSW. Each word is ordered from MSB to LSB. Order the destination
3011  // from MSB to LSB: Reverse the word order, but not the bytes in a word.
3012  while (StoreBytes > sizeof(uint64_t)) {
3013  StoreBytes -= sizeof(uint64_t);
3014  // May not be aligned so use memcpy.
3015  memcpy(Dst + StoreBytes, Src, sizeof(uint64_t));
3016  Src += sizeof(uint64_t);
3017  }
3018 
3019  memcpy(Dst, Src + sizeof(uint64_t) - StoreBytes, StoreBytes);
3020  }
3021 }
3022 
3023 /// LoadIntFromMemory - Loads the integer stored in the LoadBytes bytes starting
3024 /// from Src into IntVal, which is assumed to be wide enough and to hold zero.
3025 void llvm::LoadIntFromMemory(APInt &IntVal, const uint8_t *Src,
3026  unsigned LoadBytes) {
3027  assert((IntVal.getBitWidth()+7)/8 >= LoadBytes && "Integer too small!");
3028  uint8_t *Dst = reinterpret_cast<uint8_t *>(
3029  const_cast<uint64_t *>(IntVal.getRawData()));
3030 
3032  // Little-endian host - the destination must be ordered from LSB to MSB.
3033  // The source is ordered from LSB to MSB: Do a straight copy.
3034  memcpy(Dst, Src, LoadBytes);
3035  else {
3036  // Big-endian - the destination is an array of 64 bit words ordered from
3037  // LSW to MSW. Each word must be ordered from MSB to LSB. The source is
3038  // ordered from MSB to LSB: Reverse the word order, but not the bytes in
3039  // a word.
3040  while (LoadBytes > sizeof(uint64_t)) {
3041  LoadBytes -= sizeof(uint64_t);
3042  // May not be aligned so use memcpy.
3043  memcpy(Dst, Src + LoadBytes, sizeof(uint64_t));
3044  Dst += sizeof(uint64_t);
3045  }
3046 
3047  memcpy(Dst + sizeof(uint64_t) - LoadBytes, Src, LoadBytes);
3048  }
3049 }
i
i
Definition: README.txt:29
llvm::APInt::reverseBits
APInt reverseBits() const
Definition: APInt.cpp:712
llvm::findFirstSet
T findFirstSet(T Val, ZeroBehavior ZB=ZB_Max)
Get the index of the first set bit starting from the least significant bit.
Definition: MathExtras.h:239
Signed
@ Signed
Definition: NVPTXISelLowering.cpp:4645
LLVM_DUMP_METHOD
#define LLVM_DUMP_METHOD
Mark debug helper function definitions like dump() that should not be stripped from debug builds.
Definition: Compiler.h:507
MathExtras.h
llvm::APInt::sadd_ov
APInt sadd_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1918
llvm
This is an optimization pass for GlobalISel generic memory operations.
Definition: AllocatorList.h:22
llvm::APInt::VAL
uint64_t VAL
Used to store the <= 64 bits integer value.
Definition: APInt.h:1819
llvm::APInt::insertBits
void insertBits(const APInt &SubBits, unsigned bitPosition)
Insert the bits from a smaller APInt starting at bitPosition.
Definition: APInt.cpp:359
llvm::APInt::udivrem
static void udivrem(const APInt &LHS, const APInt &RHS, APInt &Quotient, APInt &Remainder)
Dual division/remainder interface.
Definition: APInt.cpp:1748
Optional.h
llvm::APInt::tcAssign
static void tcAssign(WordType *, const WordType *, unsigned)
Assign one bignum to another.
Definition: APInt.cpp:2307
llvm::APInt::byteSwap
APInt byteSwap() const
Definition: APInt.cpp:690
getMemory
static uint64_t * getMemory(unsigned numWords)
A utility function for allocating memory and checking for allocation failure.
Definition: APInt.cpp:43
llvm::APInt::tcIncrement
static WordType tcIncrement(WordType *dst, unsigned parts)
Increment a bignum in-place. Return the carry flag.
Definition: APInt.h:1796
llvm::APInt::operator*=
APInt & operator*=(const APInt &RHS)
Multiplication assignment operator.
Definition: APInt.cpp:254
llvm::APInt::isSignedIntN
bool isSignedIntN(unsigned N) const
Check if this APInt has an N-bits signed integer value.
Definition: APInt.h:420
llvm::cl::Prefix
@ Prefix
Definition: CommandLine.h:164
T
llvm::APInt::getNumWords
unsigned getNumWords() const
Get the number of words.
Definition: APInt.h:1419
llvm::APInt::setBits
void setBits(unsigned loBit, unsigned hiBit)
Set the bits from loBit (inclusive) to hiBit (exclusive) to 1.
Definition: APInt.h:1318
llvm::APInt::ule
bool ule(const APInt &RHS) const
Unsigned less or equal comparison.
Definition: APInt.h:1083
llvm::APInt::rotr
APInt rotr(unsigned rotateAmt) const
Rotate right by rotateAmt.
Definition: APInt.cpp:1108
StringRef.h
llvm::APInt::truncOrSelf
APInt truncOrSelf(unsigned width) const
Truncate to width.
Definition: APInt.cpp:984
double
into xmm2 addss xmm2 xmm1 xmm3 addss xmm3 movaps xmm0 unpcklps xmm0 ret seems silly when it could just be one addps Expand libm rounding functions main should enable SSE DAZ mode and other fast SSE modes Think about doing i64 math in SSE regs on x86 This testcase should have no SSE instructions in and only one load from a constant double
Definition: README-SSE.txt:85
llvm::APInt::sshl_ov
APInt sshl_ov(const APInt &Amt, bool &Overflow) const
Definition: APInt.cpp:1978
DEBUG_KNUTH
#define DEBUG_KNUTH(X)
llvm::APInt::roundToDouble
double roundToDouble() const
Converts this unsigned APInt to a double value.
Definition: APInt.h:1606
llvm::APInt::tcSetBit
static void tcSetBit(WordType *, unsigned bit)
Set the given bit of a bignum. Zero-based.
Definition: APInt.cpp:2327
llvm::APInt::getSExtValue
int64_t getSExtValue() const
Get sign extended value.
Definition: APInt.h:1479
llvm::APInt::tcDecrement
static WordType tcDecrement(WordType *dst, unsigned parts)
Decrement a bignum in-place. Return the borrow flag.
Definition: APInt.h:1801
ErrorHandling.h
getDigit
static unsigned getDigit(char cdigit, uint8_t radix)
A utility function that converts a character to a digit.
Definition: APInt.cpp:48
llvm::APInt::getMaxValue
static APInt getMaxValue(unsigned numBits)
Gets maximum unsigned value of APInt for specific bit width.
Definition: APInt.h:186
llvm::APInt::pVal
uint64_t * pVal
Used to store the >64 bits integer value.
Definition: APInt.h:1820
llvm::APInt::zextOrTrunc
APInt zextOrTrunc(unsigned width) const
Zero extend or truncate to width.
Definition: APInt.cpp:968
llvm::APIntOps::ScaleBitMask
APInt ScaleBitMask(const APInt &A, unsigned NewBitWidth)
Splat/Merge neighboring bits to widen/narrow the bitmask represented by.
Definition: APInt.cpp:2963
APInt.h
llvm::APInt::tcSet
static void tcSet(WordType *, WordType, unsigned)
Sets the least significant part of a bignum to the input value, and zeroes out higher parts.
Definition: APInt.cpp:2299
llvm::APInt::operator-=
APInt & operator-=(const APInt &RHS)
Subtraction assignment operator.
Definition: APInt.cpp:208
llvm::APInt::getSignedMaxValue
static APInt getSignedMaxValue(unsigned numBits)
Gets maximum signed value of APInt for a specific bit width.
Definition: APInt.h:189
highHalf
static APInt::WordType highHalf(APInt::WordType part)
Returns the value of the upper half of PART.
Definition: APInt.cpp:2281
llvm::APInt::getBitWidth
unsigned getBitWidth() const
Return the number of bits in the APInt.
Definition: APInt.h:1412
llvm::reverse
auto reverse(ContainerTy &&C, std::enable_if_t< has_rbegin< ContainerTy >::value > *=nullptr)
Definition: STLExtras.h:357
llvm::sys::path::end
const_iterator end(StringRef path)
Get end iterator over path.
Definition: Path.cpp:236
llvm::APInt::ugt
bool ugt(const APInt &RHS) const
Unsigned greater than comparison.
Definition: APInt.h:1115
llvm::Optional
Definition: APInt.h:33
llvm::APInt::tcDivide
static int tcDivide(WordType *lhs, const WordType *rhs, WordType *remainder, WordType *scratch, unsigned parts)
If RHS is zero LHS and REMAINDER are left unchanged, return one.
Definition: APInt.cpp:2611
Hashing.h
llvm::APInt::lshr
APInt lshr(unsigned shiftAmt) const
Logical right-shift function.
Definition: APInt.h:815
RHS
Value * RHS
Definition: X86PartialReduction.cpp:74
that
we should consider alternate ways to model stack dependencies Lots of things could be done in WebAssemblyTargetTransformInfo cpp there are numerous optimization related hooks that can be overridden in WebAssemblyTargetLowering Instead of the OptimizeReturned which should consider preserving the returned attribute through to MachineInstrs and extending the MemIntrinsicResults pass to do this optimization on calls too That would also let the WebAssemblyPeephole pass clean up dead defs for such as it does for stores Consider implementing and or getMachineCombinerPatterns Find a clean way to fix the problem which leads to the Shrink Wrapping pass being run after the WebAssembly PEI pass When setting multiple variables to the same we currently get code like const It could be done with a smaller encoding like local tee $pop5 local $pop6 WebAssembly registers are implicitly initialized to zero Explicit zeroing is therefore often redundant and could be optimized away Small indices may use smaller encodings than large indices WebAssemblyRegColoring and or WebAssemblyRegRenumbering should sort registers according to their usage frequency to maximize the usage of smaller encodings Many cases of irreducible control flow could be transformed more optimally than via the transform in WebAssemblyFixIrreducibleControlFlow cpp It may also be worthwhile to do transforms before register particularly when duplicating to allow register coloring to be aware of the duplication WebAssemblyRegStackify could use AliasAnalysis to reorder loads and stores more aggressively WebAssemblyRegStackify is currently a greedy algorithm This means that
Definition: README.txt:130
tmp
alloca< 16 x float >, align 16 %tmp2=alloca< 16 x float >, align 16 store< 16 x float > %A,< 16 x float > *%tmp %s=bitcast< 16 x float > *%tmp to i8 *%s2=bitcast< 16 x float > *%tmp2 to i8 *call void @llvm.memcpy.i64(i8 *%s, i8 *%s2, i64 64, i32 16) %R=load< 16 x float > *%tmp2 ret< 16 x float > %R } declare void @llvm.memcpy.i64(i8 *nocapture, i8 *nocapture, i64, i32) nounwind which compiles to:_foo:subl $140, %esp movaps %xmm3, 112(%esp) movaps %xmm2, 96(%esp) movaps %xmm1, 80(%esp) movaps %xmm0, 64(%esp) movl 60(%esp), %eax movl %eax, 124(%esp) movl 56(%esp), %eax movl %eax, 120(%esp) movl 52(%esp), %eax< many many more 32-bit copies > movaps(%esp), %xmm0 movaps 16(%esp), %xmm1 movaps 32(%esp), %xmm2 movaps 48(%esp), %xmm3 addl $140, %esp ret On Nehalem, it may even be cheaper to just use movups when unaligned than to fall back to lower-granularity chunks. Implement processor-specific optimizations for parity with GCC on these processors. GCC does two optimizations:1. ix86_pad_returns inserts a noop before ret instructions if immediately preceded by a conditional branch or is the target of a jump. 2. ix86_avoid_jump_misspredicts inserts noops in cases where a 16-byte block of code contains more than 3 branches. The first one is done for all AMDs, Core2, and "Generic" The second one is done for:Atom, Pentium Pro, all AMDs, Pentium 4, Nocona, Core 2, and "Generic" Testcase:int x(int a) { return(a &0xf0)> >4 tmp
Definition: README.txt:1347
llvm::countLeadingOnes
unsigned countLeadingOnes(T Value, ZeroBehavior ZB=ZB_Width)
Count the number of ones from the most significant bit to the first zero bit.
Definition: MathExtras.h:509
llvm::Lo_32
constexpr uint32_t Lo_32(uint64_t Value)
Return the low 32 bits of a 64 bit value.
Definition: MathExtras.h:353
llvm::hash_value
hash_code hash_value(const APFloat &Arg)
See friend declarations above.
Definition: APFloat.cpp:4821
llvm::APIntOps::GetMostSignificantDifferentBit
Optional< unsigned > GetMostSignificantDifferentBit(const APInt &A, const APInt &B)
Compare two values, and if they are different, return the position of the most significant bit that i...
Definition: APInt.cpp:2956
llvm::APInt::tcExtract
static void tcExtract(WordType *, unsigned dstCount, const WordType *, unsigned srcBits, unsigned srcLSB)
Copy the bit vector of width srcBITS from SRC, starting at bit srcLSB, to DST, of dstCOUNT parts,...
Definition: APInt.cpp:2370
llvm::APInt::Rounding::UP
@ UP
p
the resulting code requires compare and branches when and if * p
Definition: README.txt:396
llvm::APInt::getZero
static APInt getZero(unsigned numBits)
Get the '0' value for the specified bit-width.
Definition: APInt.h:177
LLVM_DEBUG
#define LLVM_DEBUG(X)
Definition: Debug.h:101
llvm::ArrayRef::data
const T * data() const
Definition: ArrayRef.h:160
llvm::RISCVFenceField::R
@ R
Definition: RISCVBaseInfo.h:208
llvm::lltok::equal
@ equal
Definition: LLToken.h:25
remainder
div rem Hoist decompose integer division and remainder
Definition: DivRemPairs.cpp:427
llvm::APInt::rotl
APInt rotl(unsigned rotateAmt) const
Rotate left by rotateAmt.
Definition: APInt.cpp:1095
result
It looks like we only need to define PPCfmarto for these because according to these instructions perform RTO on fma s result
Definition: README_P9.txt:256
llvm::dbgs
raw_ostream & dbgs()
dbgs() - This returns a reference to a raw_ostream for debugging messages.
Definition: Debug.cpp:163
Arg
amdgpu Simplify well known AMD library false FunctionCallee Value * Arg
Definition: AMDGPULibCalls.cpp:185
llvm::APInt::umul_ov
APInt umul_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1961
llvm::APInt::uge
bool uge(const APInt &RHS) const
Unsigned greater or equal comparison.
Definition: APInt.h:1154
LHS
Value * LHS
Definition: X86PartialReduction.cpp:73
llvm::DenseMapInfo
An information struct used to provide DenseMap with the various necessary components for a given valu...
Definition: APInt.h:34
llvm::APInt::isNonNegative
bool isNonNegative() const
Determine if this APInt Value is non-negative (>= 0)
Definition: APInt.h:317
llvm::APInt::isNegative
bool isNegative() const
Determine sign of this APInt.
Definition: APInt.h:312
lowBitMask
static APInt::WordType lowBitMask(unsigned bits)
Definition: APInt.cpp:2270
llvm::APInt::setBit
void setBit(unsigned BitPosition)
Set the given bit to 1 whose position is given as "bitPosition".
Definition: APInt.h:1281
llvm::APInt::lshrInPlace
void lshrInPlace(unsigned ShiftAmt)
Logical right-shift this APInt by ShiftAmt in place.
Definition: APInt.h:822
bits
demanded bits
Definition: DemandedBits.cpp:63
llvm::APInt::tcSubtract
static WordType tcSubtract(WordType *, const WordType *, WordType carry, unsigned)
DST -= RHS + CARRY where CARRY is zero or one. Returns the carry flag.
Definition: APInt.cpp:2435
llvm::APInt::tcMSB
static unsigned tcMSB(const WordType *parts, unsigned n)
Returns the bit number of the most significant set bit of a number.
Definition: APInt.cpp:2351
llvm::APInt::isZero
bool isZero() const
Determine if this value is zero, i.e. all bits are clear.
Definition: APInt.h:359
SmallString.h
tcComplement
static void tcComplement(APInt::WordType *dst, unsigned parts)
Definition: APInt.cpp:329
C
(vector float) vec_cmpeq(*A, *B) C
Definition: README_ALTIVEC.txt:86
llvm::APInt::usub_sat
APInt usub_sat(const APInt &RHS) const
Definition: APInt.cpp:2030
round
static uint64_t round(uint64_t Acc, uint64_t Input)
Definition: xxhash.cpp:57
llvm::APInt::getHiBits
APInt getHiBits(unsigned numBits) const
Compute an APInt containing numBits highbits from this APInt.
Definition: APInt.cpp:583
llvm::APInt::isSingleWord
bool isSingleWord() const
Determine if this APInt just has one word to store value.
Definition: APInt.h:305
llvm::APInt::operator--
APInt & operator--()
Prefix decrement operator.
Definition: APInt.cpp:177
t
bitcast float %x to i32 %s=and i32 %t, 2147483647 %d=bitcast i32 %s to float ret float %d } declare float @fabsf(float %n) define float @bar(float %x) nounwind { %d=call float @fabsf(float %x) ret float %d } This IR(from PR6194):target datalayout="e-p:64:64:64-i1:8:8-i8:8:8-i16:16:16-i32:32:32-i64:64:64-f32:32:32-f64:64:64-v64:64:64-v128:128:128-a0:0:64-s0:64:64-f80:128:128-n8:16:32:64-S128" target triple="x86_64-apple-darwin10.0.0" %0=type { double, double } %struct.float3=type { float, float, float } define void @test(%0, %struct.float3 *nocapture %res) nounwind noinline ssp { entry:%tmp18=extractvalue %0 %0, 0 t
Definition: README-SSE.txt:788
b
the resulting code requires compare and branches when and if the revised code is with conditional branches instead of More there is a byte word extend before each where there should be only and the condition codes are not remembered when the same two values are compared twice More LSR enhancements i8 and i32 load store addressing modes are identical int b
Definition: README.txt:418
llvm::ms_demangle::QualifierMangleMode::Result
@ Result
llvm::StringRef::iterator
const char * iterator
Definition: StringRef.h:62
llvm::AMDGPU::PALMD::Key
Key
PAL metadata keys.
Definition: AMDGPUMetadata.h:481
llvm::APInt::getLimitedValue
uint64_t getLimitedValue(uint64_t Limit=UINT64_MAX) const
If this value is smaller than the specified limit, return it, otherwise return the limit value.
Definition: APInt.h:456
llvm::APInt::dump
void dump() const
debug method
Definition: APInt.cpp:2245
l
This requires reassociating to forms of expressions that are already something that reassoc doesn t think about yet These two functions should generate the same code on big endian int * l
Definition: README.txt:100
getClearedMemory
static uint64_t * getClearedMemory(unsigned numWords)
A utility function for allocating memory, checking for allocation failures, and ensuring the contents...
Definition: APInt.cpp:35
llvm::ByteSwap_64
uint64_t ByteSwap_64(uint64_t value)
This function returns a byte-swapped representation of the 64-bit argument.
Definition: SwapByteOrder.h:81
B
static GCRegistry::Add< OcamlGC > B("ocaml", "ocaml 3.10-compatible GC")
llvm::APInt::extractBitsAsZExtValue
uint64_t extractBitsAsZExtValue(unsigned numBits, unsigned bitPosition) const
Definition: APInt.cpp:480
llvm::APInt::getZExtValue
uint64_t getZExtValue() const
Get zero extended value.
Definition: APInt.h:1467
llvm::raw_ostream
This class implements an extremely fast bulk output stream that can only output to a stream.
Definition: raw_ostream.h:54
llvm::APInt::isIntN
bool isIntN(unsigned N) const
Check if this APInt has an N-bits unsigned integer value.
Definition: APInt.h:417
lowHalf
static APInt::WordType lowHalf(APInt::WordType part)
Returns the value of the lower half of PART.
Definition: APInt.cpp:2276
llvm::APInt::tcClearBit
static void tcClearBit(WordType *, unsigned bit)
Clear the given bit of a bignum. Zero-based.
Definition: APInt.cpp:2332
llvm::APInt::smul_sat
APInt smul_sat(const APInt &RHS) const
Definition: APInt.cpp:2039
rotateModulo
static unsigned rotateModulo(unsigned BitWidth, const APInt &rotateAmt)
Definition: APInt.cpp:1077
llvm::APInt::usub_ov
APInt usub_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1938
llvm::APInt::operator++
APInt & operator++()
Prefix increment operator.
Definition: APInt.cpp:168
c
the resulting code requires compare and branches when and if the revised code is with conditional branches instead of More there is a byte word extend before each where there should be only and the condition codes are not remembered when the same two values are compared twice More LSR enhancements i8 and i32 load store addressing modes are identical int int c
Definition: README.txt:418
llvm::None
const NoneType None
Definition: None.h:23
RoundUp
static size_t RoundUp(size_t size, size_t align)
Definition: InstrProfReader.cpp:553
llvm::APInt::sqrt
APInt sqrt() const
Compute the square root.
Definition: APInt.cpp:1153
llvm::APInt::tcLSB
static unsigned tcLSB(const WordType *, unsigned n)
Returns the bit number of the least or most significant set bit of a number.
Definition: APInt.cpp:2338
X
static GCMetadataPrinterRegistry::Add< ErlangGCPrinter > X("erlang", "erlang-compatible garbage collector")
llvm::APInt::tcShiftLeft
static void tcShiftLeft(WordType *, unsigned Words, unsigned Count)
Shift a bignum left Count bits.
Definition: APInt.cpp:2653
llvm::APInt::srem
APInt srem(const APInt &RHS) const
Function for signed remainder operation.
Definition: APInt.cpp:1726
llvm::SmallString
SmallString - A SmallString is just a SmallVector with methods and accessors that make it work better...
Definition: SmallString.h:25
llvm::Hi_32
constexpr uint32_t Hi_32(uint64_t Value)
Return the high 32 bits of a 64 bit value.
Definition: MathExtras.h:348
llvm::APInt::print
void print(raw_ostream &OS, bool isSigned) const
Definition: APInt.cpp:2254
llvm::ByteSwap_16
uint16_t ByteSwap_16(uint16_t value)
ByteSwap_16 - This function returns a byte-swapped representation of the 16-bit argument.
Definition: SwapByteOrder.h:53
llvm::APInt::flipBit
void flipBit(unsigned bitPosition)
Toggles a given bit to its opposite value.
Definition: APInt.cpp:354
llvm::APInt::getOneBitSet
static APInt getOneBitSet(unsigned numBits, unsigned BitNo)
Return an APInt with exactly one bit set in the result.
Definition: APInt.h:222
llvm::APInt::operator+=
APInt & operator+=(const APInt &RHS)
Addition assignment operator.
Definition: APInt.cpp:188
llvm::Make_64
constexpr uint64_t Make_64(uint32_t High, uint32_t Low)
Make a 64-bit integer from a high / low pair of 32-bit integers.
Definition: MathExtras.h:358
val
The initial backend is deliberately restricted to z10 We should add support for later architectures at some point If an asm ties an i32 r result to an i64 the input will be treated as an leaving the upper bits uninitialised For i64 store i32 val
Definition: README.txt:15
llvm::APInt::WORDTYPE_MAX
static constexpr WordType WORDTYPE_MAX
Definition: APInt.h:93
llvm::countPopulation
unsigned countPopulation(T Value)
Count the number of set bits in a value.
Definition: MathExtras.h:567
llvm::APInt::tcExtractBit
static int tcExtractBit(const WordType *, unsigned bit)
Extract the given bit of a bignum; returns 0 or 1. Zero-based.
Definition: APInt.cpp:2322
llvm::APInt::operator<<=
APInt & operator<<=(unsigned ShiftAmt)
Left-shift assignment function.
Definition: APInt.h:749
llvm::StringRef::empty
constexpr LLVM_NODISCARD bool empty() const
empty - Check if the string is empty.
Definition: StringRef.h:153
llvm::APInt::sdiv
APInt sdiv(const APInt &RHS) const
Signed division function for APInt.
Definition: APInt.cpp:1634
uint64_t
llvm::StoreIntToMemory
void StoreIntToMemory(const APInt &IntVal, uint8_t *Dst, unsigned StoreBytes)
StoreIntToMemory - Fills the StoreBytes bytes of memory starting from Dst with the integer held in In...
Definition: APInt.cpp:2999
llvm::APInt::getRawData
const uint64_t * getRawData() const
This function returns a pointer to the internal storage of the APInt.
Definition: APInt.h:533
D
static GCRegistry::Add< StatepointGC > D("statepoint-example", "an example strategy for statepoint")
llvm::APIntOps::SolveQuadraticEquationWrap
Optional< APInt > SolveQuadraticEquationWrap(APInt A, APInt B, APInt C, unsigned RangeWidth)
Let q(n) = An^2 + Bn + C, and BW = bit width of the value range (e.g.
Definition: APInt.cpp:2766
llvm::StringRef::end
iterator end() const
Definition: StringRef.h:130
llvm::APInt::toString
void toString(SmallVectorImpl< char > &Str, unsigned Radix, bool Signed, bool formatAsCLiteral=false) const
Converts an APInt to a string and append it to Str.
Definition: APInt.cpp:2131
llvm::APInt::sdivrem
static void sdivrem(const APInt &LHS, const APInt &RHS, APInt &Quotient, APInt &Remainder)
Definition: APInt.cpp:1880
llvm::APInt::logBase2
unsigned logBase2() const
Definition: APInt.h:1648
llvm::ARM_AM::add
@ add
Definition: ARMAddressingModes.h:39
move
compiles ldr LCPI1_0 ldr ldr mov lsr tst moveq r1 ldr LCPI1_1 and r0 bx lr It would be better to do something like to fold the shift into the conditional move
Definition: README.txt:546
llvm::numbers::e
constexpr double e
Definition: MathExtras.h:57
partLSB
static unsigned partLSB(APInt::WordType value)
Returns the bit number of the least significant set bit of a part.
Definition: APInt.cpp:2293
llvm::APInt::negate
void negate()
Negate this APInt in place.
Definition: APInt.h:1394
I
#define I(x, y, z)
Definition: MD5.cpp:58
llvm::ZB_Max
@ ZB_Max
The returned value is numeric_limits<T>::max()
Definition: MathExtras.h:48
llvm::countTrailingOnes
unsigned countTrailingOnes(T Value, ZeroBehavior ZB=ZB_Width)
Count the number of ones from the least significant bit to the first zero bit.
Definition: MathExtras.h:525
llvm::APInt::sextOrSelf
APInt sextOrSelf(unsigned width) const
Sign extend or truncate to width.
Definition: APInt.cpp:996
llvm::APInt::tcAdd
static WordType tcAdd(WordType *, const WordType *, WordType carry, unsigned)
DST += RHS + CARRY where CARRY is zero or one. Returns the carry flag.
Definition: APInt.cpp:2400
ArrayRef.h
llvm::APInt::getBoolValue
bool getBoolValue() const
Convert APInt to a boolean value.
Definition: APInt.h:452
llvm::APInt::setBitVal
void setBitVal(unsigned BitPosition, bool BitValue)
Set a given bit to a given value.
Definition: APInt.h:1294
assert
assert(ImpDefSCC.getReg()==AMDGPU::SCC &&ImpDefSCC.isDef())
llvm::APInt::truncUSat
APInt truncUSat(unsigned width) const
Truncate to new width with unsigned saturation.
Definition: APInt.cpp:903
memcpy
<%struct.s * > cast struct s *S to sbyte *< sbyte * > sbyte uint cast struct s *agg result to sbyte *< sbyte * > sbyte uint cast struct s *memtmp to sbyte *< sbyte * > sbyte uint ret void llc ends up issuing two memcpy or custom lower memcpy(of small size) to be ldmia/stmia. I think option 2 is better but the current register allocator cannot allocate a chunk of registers at a time. A feasible temporary solution is to use specific physical registers at the lowering time for small(<
llvm::APInt::extractBits
APInt extractBits(unsigned numBits, unsigned bitPosition) const
Return an APInt with the extracted bits [bitPosition,bitPosition+numBits).
Definition: APInt.cpp:444
llvm::findLastSet
T findLastSet(T Val, ZeroBehavior ZB=ZB_Max)
Get the index of the last set bit starting from the least significant bit.
Definition: MathExtras.h:280
llvm::APInt::toStringUnsigned
void toStringUnsigned(SmallVectorImpl< char > &Str, unsigned Radix=10) const
Considers the APInt to be unsigned and converts it into a string in the radix given.
Definition: APInt.h:1585
llvm::APInt::urem
APInt urem(const APInt &RHS) const
Unsigned remainder operation.
Definition: APInt.cpp:1656
llvm::APInt
Class for arbitrary precision integers.
Definition: APInt.h:75
llvm::AArch64::RM
@ RM
Definition: AArch64ISelLowering.h:482
llvm::ArrayRef< uint64_t >
llvm::APInt::ssub_ov
APInt ssub_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1931
llvm::min
Expected< ExpressionValue > min(const ExpressionValue &Lhs, const ExpressionValue &Rhs)
Definition: FileCheck.cpp:357
llvm::countTrailingZeros
unsigned countTrailingZeros(T Val, ZeroBehavior ZB=ZB_Width)
Count number of 0's from the least significant bit to the most stopping at the first 1.
Definition: MathExtras.h:156
llvm::StringRef
StringRef - Represent a constant reference to a string, i.e.
Definition: StringRef.h:58
llvm::APInt::zextOrSelf
APInt zextOrSelf(unsigned width) const
Zero extend or truncate to width.
Definition: APInt.cpp:990
llvm::APInt::sshl_sat
APInt sshl_sat(const APInt &RHS) const
Definition: APInt.cpp:2061
llvm_unreachable
#define llvm_unreachable(msg)
Marks that the current location is not supposed to be reachable.
Definition: ErrorHandling.h:134
uint32_t
llvm::APInt::tcShiftRight
static void tcShiftRight(WordType *, unsigned Words, unsigned Count)
Shift a bignum right Count bits.
Definition: APInt.cpp:2680
llvm::APInt::operator*
APInt operator*(const APInt &RHS) const
Multiplication operator.
Definition: APInt.cpp:225
llvm::APInt::ushl_sat
APInt ushl_sat(const APInt &RHS) const
Definition: APInt.cpp:2071
llvm::FoldingSetNodeID
FoldingSetNodeID - This class is used to gather all the unique data bits of a node.
Definition: FoldingSet.h:313
S
add sub stmia L5 ldr r0 bl L_printf $stub Instead of a and a wouldn t it be better to do three moves *Return an aggregate type is even return S
Definition: README.txt:210
llvm::APIntOps::RoundingSDiv
APInt RoundingSDiv(const APInt &A, const APInt &B, APInt::Rounding RM)
Return A sign-divided by B, rounded by the given rounding mode.
Definition: APInt.cpp:2735
llvm::APInt::tcIsZero
static bool tcIsZero(const WordType *, unsigned)
Returns true if a bignum is zero, false otherwise.
Definition: APInt.cpp:2313
llvm::APInt::umul_sat
APInt umul_sat(const APInt &RHS) const
Definition: APInt.cpp:2052
llvm::APInt::ult
bool ult(const APInt &RHS) const
Unsigned less than comparison.
Definition: APInt.h:1044
llvm::SignExtend64
constexpr int64_t SignExtend64(uint64_t x)
Sign-extend the number in the bottom B bits of X to a 64-bit integer.
Definition: MathExtras.h:777
llvm::APInt::udiv
APInt udiv(const APInt &RHS) const
Unsigned division operation.
Definition: APInt.cpp:1563
FoldingSet.h
llvm::APInt::zext
APInt zext(unsigned width) const
Zero extend to a new width.
Definition: APInt.cpp:950
llvm::APInt::uadd_ov
APInt uadd_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1925
llvm::APInt::Rounding::DOWN
@ DOWN
llvm::APInt::ssub_sat
APInt ssub_sat(const APInt &RHS) const
Definition: APInt.cpp:2020
llvm::APInt::tcMultiply
static int tcMultiply(WordType *, const WordType *, const WordType *, unsigned)
DST = LHS * RHS, where DST has the same width as the operands and is filled with the least significan...
Definition: APInt.cpp:2571
llvm::StringRef::size
constexpr LLVM_NODISCARD size_t size() const
size - Get the string size.
Definition: StringRef.h:157
j
return j(j<< 16)
llvm::tgtok::IntVal
@ IntVal
Definition: TGLexer.h:64
llvm::APInt::countLeadingZeros
unsigned countLeadingZeros() const
The APInt version of the countLeadingZeros functions in MathExtras.h.
Definition: APInt.h:1500
llvm::APInt::tcCompare
static int tcCompare(const WordType *, const WordType *, unsigned)
Comparison (unsigned) of two bignums.
Definition: APInt.cpp:2706
llvm::APInt::uadd_sat
APInt uadd_sat(const APInt &RHS) const
Definition: APInt.cpp:2011
llvm::APInt::APINT_WORD_SIZE
@ APINT_WORD_SIZE
Byte size of a word.
Definition: APInt.h:82
llvm::APInt::multiplicativeInverse
APInt multiplicativeInverse(const APInt &modulo) const
Computes the multiplicative inverse of this APInt for a given modulo.
Definition: APInt.cpp:1234
llvm::APInt::tcSubtractPart
static WordType tcSubtractPart(WordType *, WordType, unsigned)
DST -= RHS. Returns the carry flag.
Definition: APInt.cpp:2460
llvm::APInt::trunc
APInt trunc(unsigned width) const
Truncate to new width.
Definition: APInt.cpp:881
bit
compiles ldr LCPI1_0 ldr ldr mov lsr tst moveq r1 ldr LCPI1_1 and r0 bx lr It would be better to do something like to fold the shift into the conditional ldr LCPI1_0 ldr ldr tst movne lsr ldr LCPI1_1 and r0 bx lr it saves an instruction and a register It might be profitable to cse MOVi16 if there are lots of bit immediates with the same bottom half Robert Muth started working on an alternate jump table implementation that does not put the tables in line in the text This is more like the llvm default jump table implementation This might be useful sometime Several revisions of patches are on the mailing beginning while CMP sets them like a subtract Therefore to be able to use CMN for comparisons other than the Z bit
Definition: README.txt:584
llvm::APInt::isMinSignedValue
bool isMinSignedValue() const
Determine if this is the smallest signed value.
Definition: APInt.h:408
llvm::APInt::truncSSat
APInt truncSSat(unsigned width) const
Truncate to new width with signed saturation.
Definition: APInt.cpp:914
uint16_t
llvm::APInt::tcMultiplyPart
static int tcMultiplyPart(WordType *dst, const WordType *src, WordType multiplier, WordType carry, unsigned srcParts, unsigned dstParts, bool add)
DST += SRC * MULTIPLIER + PART if add is true DST = SRC * MULTIPLIER + PART if add is false.
Definition: APInt.cpp:2488
bit.h
llvm::APInt::sextOrTrunc
APInt sextOrTrunc(unsigned width) const
Sign extend or truncate to width.
Definition: APInt.cpp:976
llvm::APInt::Rounding::TOWARD_ZERO
@ TOWARD_ZERO
llvm::BitWidth
constexpr unsigned BitWidth
Definition: BitmaskEnum.h:147
llvm::APInt::smul_ov
APInt smul_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1950
llvm::LoadIntFromMemory
void LoadIntFromMemory(APInt &IntVal, const uint8_t *Src, unsigned LoadBytes)
LoadIntFromMemory - Loads the integer stored in the LoadBytes bytes starting from Src into IntVal,...
Definition: APInt.cpp:3025
llvm::APInt::getLoBits
APInt getLoBits(unsigned numBits) const
Compute an APInt containing numBits lowbits from this APInt.
Definition: APInt.cpp:588
llvm::APInt::getSplat
static APInt getSplat(unsigned NewLen, const APInt &V)
Return a value containing V broadcasted over NewLen bits.
Definition: APInt.cpp:595
llvm::APIntOps::RoundDoubleToAPInt
APInt RoundDoubleToAPInt(double Double, unsigned width)
Converts the given double value into a APInt.
Definition: APInt.cpp:785
llvm::countLeadingZeros
unsigned countLeadingZeros(T Val, ZeroBehavior ZB=ZB_Width)
Count number of 0's from the most significant bit to the least stopping at the first 1.
Definition: MathExtras.h:225
llvm::APInt::getSignedMinValue
static APInt getSignedMinValue(unsigned numBits)
Gets minimum signed value of APInt for a specific bit width.
Definition: APInt.h:199
llvm::AMDGPU::Hwreg::Width
Width
Definition: SIDefines.h:416
llvm::APInt::Profile
void Profile(FoldingSetNodeID &id) const
Used to insert APInt objects, or objects that contain APInt objects, into FoldingSets.
Definition: APInt.cpp:154
llvm::APInt::sext
APInt sext(unsigned width) const
Sign extend to a new width.
Definition: APInt.cpp:926
llvm::makeArrayRef
ArrayRef< T > makeArrayRef(const T &OneElt)
Construct an ArrayRef from a single element.
Definition: ArrayRef.h:474
llvm::APInt::abs
APInt abs() const
Get the absolute value.
Definition: APInt.h:1682
llvm::APInt::sdiv_ov
APInt sdiv_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1944
llvm::APInt::getBitsNeeded
static unsigned getBitsNeeded(StringRef str, uint8_t radix)
Get bits required for string value.
Definition: APInt.cpp:505
llvm::APInt::APINT_BITS_PER_WORD
@ APINT_BITS_PER_WORD
Bits in a word.
Definition: APInt.h:84
partMSB
static unsigned partMSB(APInt::WordType value)
Returns the bit number of the most significant set bit of a part.
Definition: APInt.cpp:2287
llvm::hash_combine
hash_code hash_combine(const Ts &...args)
Combine values into a single hash_code.
Definition: Hashing.h:605
llvm::APInt::tcAddPart
static WordType tcAddPart(WordType *, WordType, unsigned)
DST += RHS. Returns the carry flag.
Definition: APInt.cpp:2422
llvm::sys::IsLittleEndianHost
static const bool IsLittleEndianHost
Definition: SwapByteOrder.h:101
llvm::APIntOps::GreatestCommonDivisor
APInt GreatestCommonDivisor(APInt A, APInt B)
Compute GCD of two unsigned APInt values.
Definition: APInt.cpp:742
llvm::APInt::tcFullMultiply
static void tcFullMultiply(WordType *, const WordType *, const WordType *, unsigned, unsigned)
DST = LHS * RHS, where DST has width the sum of the widths of the operands.
Definition: APInt.cpp:2587
N
#define N
llvm::hash_combine_range
hash_code hash_combine_range(InputIteratorT first, InputIteratorT last)
Compute a hash_code for a sequence of values.
Definition: Hashing.h:483
llvm::APInt::APInt
APInt()
Default constructor that creates an APInt with a 1-bit zero value.
Definition: APInt.h:150
llvm::ArrayRef::size
size_t size() const
size - Get the array size.
Definition: ArrayRef.h:163
llvm::APInt::getActiveBits
unsigned getActiveBits() const
Compute the number of active bits in the value.
Definition: APInt.h:1436
shift
http eax xorl edx cl sete al setne dl sall eax sall edx But that requires good bit subreg support this might be better It s an extra shift
Definition: README.txt:30
llvm::APInt::toStringSigned
void toStringSigned(SmallVectorImpl< char > &Str, unsigned Radix=10) const
Considers the APInt to be signed and converts it into a string in the radix given.
Definition: APInt.h:1591
llvm::APInt::WordType
uint64_t WordType
Definition: APInt.h:77
llvm::SmallVectorImpl< char >
llvm::APInt::sgt
bool sgt(const APInt &RHS) const
Signed greater than comparison.
Definition: APInt.h:1134
llvm::APInt::sadd_sat
APInt sadd_sat(const APInt &RHS) const
Definition: APInt.cpp:2001
llvm::APIntOps::RoundingUDiv
APInt RoundingUDiv(const APInt &A, const APInt &B, APInt::Rounding RM)
Return A unsign-divided by B, rounded by the given rounding mode.
Definition: APInt.cpp:2717
llvm::APInt::getLowBitsSet
static APInt getLowBitsSet(unsigned numBits, unsigned loBitsSet)
Constructs an APInt value that has the bottom loBitsSet bits set.
Definition: APInt.h:289
llvm::ByteSwap_32
uint32_t ByteSwap_32(uint32_t value)
This function returns a byte-swapped representation of the 32-bit argument.
Definition: SwapByteOrder.h:66
llvm::APInt::shl
APInt shl(unsigned shiftAmt) const
Left-shift function.
Definition: APInt.h:837
Mod
Module * Mod
Definition: PassBuilderBindings.cpp:54
KnuthDiv
static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t *r, unsigned m, unsigned n)
Implementation of Knuth's Algorithm D (Division of nonnegative integers) from "Art of Computer Progra...
Definition: APInt.cpp:1280
LLVM_UNLIKELY
#define LLVM_UNLIKELY(EXPR)
Definition: Compiler.h:227
raw_ostream.h
n
The same transformation can work with an even modulo with the addition of a and shrink the compare RHS by the same amount Unless the target supports that transformation probably isn t worthwhile The transformation can also easily be made to work with non zero equality for n
Definition: README.txt:685
llvm::APInt::ashrInPlace
void ashrInPlace(unsigned ShiftAmt)
Arithmetic right-shift this APInt by ShiftAmt in place.
Definition: APInt.h:798
llvm::APInt::isSplat
bool isSplat(unsigned SplatSizeInBits) const
Check if the APInt consists of a repeated bit pattern.
Definition: APInt.cpp:574
llvm::APInt::countLeadingOnes
unsigned countLeadingOnes() const
Count the number of leading one bits.
Definition: APInt.h:1516
llvm::StringRef::begin
iterator begin() const
Definition: StringRef.h:128
llvm::APInt::nearestLogBase2
unsigned nearestLogBase2() const
Definition: APInt.cpp:1126
llvm::APInt::ushl_ov
APInt ushl_ov(const APInt &Amt, bool &Overflow) const
Definition: APInt.cpp:1991
Debug.h
llvm::APInt::tcNegate
static void tcNegate(WordType *, unsigned)
Negate a bignum in-place.
Definition: APInt.cpp:2474
llvm::APInt::Rounding
Rounding
Definition: APInt.h:87
llvm::Intrinsic::ID
unsigned ID
Definition: TargetTransformInfo.h:38
llvm::hash_code
An opaque object representing a hash code.
Definition: Hashing.h:73