LLVM  16.0.0git
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.zext(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::getSufficientBitsNeeded(StringRef Str, uint8_t Radix) {
506  assert(!Str.empty() && "Invalid string length");
507  size_t StrLen = Str.size();
508 
509  // Each computation below needs to know if it's negative.
510  unsigned IsNegative = false;
511  if (Str[0] == '-' || Str[0] == '+') {
512  IsNegative = Str[0] == '-';
513  StrLen--;
514  assert(StrLen && "String is only a sign, needs a value.");
515  }
516 
517  // For radixes of power-of-two values, the bits required is accurately and
518  // easily computed.
519  if (Radix == 2)
520  return StrLen + IsNegative;
521  if (Radix == 8)
522  return StrLen * 3 + IsNegative;
523  if (Radix == 16)
524  return StrLen * 4 + IsNegative;
525 
526  // Compute a sufficient number of bits that is always large enough but might
527  // be too large. This avoids the assertion in the constructor. This
528  // calculation doesn't work appropriately for the numbers 0-9, so just use 4
529  // bits in that case.
530  if (Radix == 10)
531  return (StrLen == 1 ? 4 : StrLen * 64 / 18) + IsNegative;
532 
533  assert(Radix == 36);
534  return (StrLen == 1 ? 7 : StrLen * 16 / 3) + IsNegative;
535 }
536 
537 unsigned APInt::getBitsNeeded(StringRef str, uint8_t radix) {
538  // Compute a sufficient number of bits that is always large enough but might
539  // be too large.
540  unsigned sufficient = getSufficientBitsNeeded(str, radix);
541 
542  // For bases 2, 8, and 16, the sufficient number of bits is exact and we can
543  // return the value directly. For bases 10 and 36, we need to do extra work.
544  if (radix == 2 || radix == 8 || radix == 16)
545  return sufficient;
546 
547  // This is grossly inefficient but accurate. We could probably do something
548  // with a computation of roughly slen*64/20 and then adjust by the value of
549  // the first few digits. But, I'm not sure how accurate that could be.
550  size_t slen = str.size();
551 
552  // Each computation below needs to know if it's negative.
553  StringRef::iterator p = str.begin();
554  unsigned isNegative = *p == '-';
555  if (*p == '-' || *p == '+') {
556  p++;
557  slen--;
558  assert(slen && "String is only a sign, needs a value.");
559  }
560 
561 
562  // Convert to the actual binary value.
563  APInt tmp(sufficient, StringRef(p, slen), radix);
564 
565  // Compute how many bits are required. If the log is infinite, assume we need
566  // just bit. If the log is exact and value is negative, then the value is
567  // MinSignedValue with (log + 1) bits.
568  unsigned log = tmp.logBase2();
569  if (log == (unsigned)-1) {
570  return isNegative + 1;
571  } else if (isNegative && tmp.isPowerOf2()) {
572  return isNegative + log;
573  } else {
574  return isNegative + log + 1;
575  }
576 }
577 
579  if (Arg.isSingleWord())
580  return hash_combine(Arg.BitWidth, Arg.U.VAL);
581 
582  return hash_combine(
583  Arg.BitWidth,
584  hash_combine_range(Arg.U.pVal, Arg.U.pVal + Arg.getNumWords()));
585 }
586 
588  return static_cast<unsigned>(hash_value(Key));
589 }
590 
591 bool APInt::isSplat(unsigned SplatSizeInBits) const {
592  assert(getBitWidth() % SplatSizeInBits == 0 &&
593  "SplatSizeInBits must divide width!");
594  // We can check that all parts of an integer are equal by making use of a
595  // little trick: rotate and check if it's still the same value.
596  return *this == rotl(SplatSizeInBits);
597 }
598 
599 /// This function returns the high "numBits" bits of this APInt.
600 APInt APInt::getHiBits(unsigned numBits) const {
601  return this->lshr(BitWidth - numBits);
602 }
603 
604 /// This function returns the low "numBits" bits of this APInt.
605 APInt APInt::getLoBits(unsigned numBits) const {
606  APInt Result(getLowBitsSet(BitWidth, numBits));
607  Result &= *this;
608  return Result;
609 }
610 
611 /// Return a value containing V broadcasted over NewLen bits.
612 APInt APInt::getSplat(unsigned NewLen, const APInt &V) {
613  assert(NewLen >= V.getBitWidth() && "Can't splat to smaller bit width!");
614 
615  APInt Val = V.zext(NewLen);
616  for (unsigned I = V.getBitWidth(); I < NewLen; I <<= 1)
617  Val |= Val << I;
618 
619  return Val;
620 }
621 
622 unsigned APInt::countLeadingZerosSlowCase() const {
623  unsigned Count = 0;
624  for (int i = getNumWords()-1; i >= 0; --i) {
625  uint64_t V = U.pVal[i];
626  if (V == 0)
627  Count += APINT_BITS_PER_WORD;
628  else {
629  Count += llvm::countLeadingZeros(V);
630  break;
631  }
632  }
633  // Adjust for unused bits in the most significant word (they are zero).
634  unsigned Mod = BitWidth % APINT_BITS_PER_WORD;
635  Count -= Mod > 0 ? APINT_BITS_PER_WORD - Mod : 0;
636  return Count;
637 }
638 
639 unsigned APInt::countLeadingOnesSlowCase() const {
640  unsigned highWordBits = BitWidth % APINT_BITS_PER_WORD;
641  unsigned shift;
642  if (!highWordBits) {
643  highWordBits = APINT_BITS_PER_WORD;
644  shift = 0;
645  } else {
646  shift = APINT_BITS_PER_WORD - highWordBits;
647  }
648  int i = getNumWords() - 1;
649  unsigned Count = llvm::countLeadingOnes(U.pVal[i] << shift);
650  if (Count == highWordBits) {
651  for (i--; i >= 0; --i) {
652  if (U.pVal[i] == WORDTYPE_MAX)
653  Count += APINT_BITS_PER_WORD;
654  else {
655  Count += llvm::countLeadingOnes(U.pVal[i]);
656  break;
657  }
658  }
659  }
660  return Count;
661 }
662 
663 unsigned APInt::countTrailingZerosSlowCase() const {
664  unsigned Count = 0;
665  unsigned i = 0;
666  for (; i < getNumWords() && U.pVal[i] == 0; ++i)
667  Count += APINT_BITS_PER_WORD;
668  if (i < getNumWords())
669  Count += llvm::countTrailingZeros(U.pVal[i]);
670  return std::min(Count, BitWidth);
671 }
672 
673 unsigned APInt::countTrailingOnesSlowCase() const {
674  unsigned Count = 0;
675  unsigned i = 0;
676  for (; i < getNumWords() && U.pVal[i] == WORDTYPE_MAX; ++i)
677  Count += APINT_BITS_PER_WORD;
678  if (i < getNumWords())
679  Count += llvm::countTrailingOnes(U.pVal[i]);
680  assert(Count <= BitWidth);
681  return Count;
682 }
683 
684 unsigned APInt::countPopulationSlowCase() const {
685  unsigned Count = 0;
686  for (unsigned i = 0; i < getNumWords(); ++i)
687  Count += llvm::countPopulation(U.pVal[i]);
688  return Count;
689 }
690 
691 bool APInt::intersectsSlowCase(const APInt &RHS) const {
692  for (unsigned i = 0, e = getNumWords(); i != e; ++i)
693  if ((U.pVal[i] & RHS.U.pVal[i]) != 0)
694  return true;
695 
696  return false;
697 }
698 
699 bool APInt::isSubsetOfSlowCase(const APInt &RHS) const {
700  for (unsigned i = 0, e = getNumWords(); i != e; ++i)
701  if ((U.pVal[i] & ~RHS.U.pVal[i]) != 0)
702  return false;
703 
704  return true;
705 }
706 
708  assert(BitWidth >= 16 && BitWidth % 8 == 0 && "Cannot byteswap!");
709  if (BitWidth == 16)
710  return APInt(BitWidth, ByteSwap_16(uint16_t(U.VAL)));
711  if (BitWidth == 32)
712  return APInt(BitWidth, ByteSwap_32(unsigned(U.VAL)));
713  if (BitWidth <= 64) {
714  uint64_t Tmp1 = ByteSwap_64(U.VAL);
715  Tmp1 >>= (64 - BitWidth);
716  return APInt(BitWidth, Tmp1);
717  }
718 
719  APInt Result(getNumWords() * APINT_BITS_PER_WORD, 0);
720  for (unsigned I = 0, N = getNumWords(); I != N; ++I)
721  Result.U.pVal[I] = ByteSwap_64(U.pVal[N - I - 1]);
722  if (Result.BitWidth != BitWidth) {
723  Result.lshrInPlace(Result.BitWidth - BitWidth);
724  Result.BitWidth = BitWidth;
725  }
726  return Result;
727 }
728 
730  switch (BitWidth) {
731  case 64:
732  return APInt(BitWidth, llvm::reverseBits<uint64_t>(U.VAL));
733  case 32:
734  return APInt(BitWidth, llvm::reverseBits<uint32_t>(U.VAL));
735  case 16:
736  return APInt(BitWidth, llvm::reverseBits<uint16_t>(U.VAL));
737  case 8:
738  return APInt(BitWidth, llvm::reverseBits<uint8_t>(U.VAL));
739  case 0:
740  return *this;
741  default:
742  break;
743  }
744 
745  APInt Val(*this);
746  APInt Reversed(BitWidth, 0);
747  unsigned S = BitWidth;
748 
749  for (; Val != 0; Val.lshrInPlace(1)) {
750  Reversed <<= 1;
751  Reversed |= Val[0];
752  --S;
753  }
754 
755  Reversed <<= S;
756  return Reversed;
757 }
758 
760  // Fast-path a common case.
761  if (A == B) return A;
762 
763  // Corner cases: if either operand is zero, the other is the gcd.
764  if (!A) return B;
765  if (!B) return A;
766 
767  // Count common powers of 2 and remove all other powers of 2.
768  unsigned Pow2;
769  {
770  unsigned Pow2_A = A.countTrailingZeros();
771  unsigned Pow2_B = B.countTrailingZeros();
772  if (Pow2_A > Pow2_B) {
773  A.lshrInPlace(Pow2_A - Pow2_B);
774  Pow2 = Pow2_B;
775  } else if (Pow2_B > Pow2_A) {
776  B.lshrInPlace(Pow2_B - Pow2_A);
777  Pow2 = Pow2_A;
778  } else {
779  Pow2 = Pow2_A;
780  }
781  }
782 
783  // Both operands are odd multiples of 2^Pow_2:
784  //
785  // gcd(a, b) = gcd(|a - b| / 2^i, min(a, b))
786  //
787  // This is a modified version of Stein's algorithm, taking advantage of
788  // efficient countTrailingZeros().
789  while (A != B) {
790  if (A.ugt(B)) {
791  A -= B;
792  A.lshrInPlace(A.countTrailingZeros() - Pow2);
793  } else {
794  B -= A;
795  B.lshrInPlace(B.countTrailingZeros() - Pow2);
796  }
797  }
798 
799  return A;
800 }
801 
802 APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) {
803  uint64_t I = bit_cast<uint64_t>(Double);
804 
805  // Get the sign bit from the highest order bit
806  bool isNeg = I >> 63;
807 
808  // Get the 11-bit exponent and adjust for the 1023 bit bias
809  int64_t exp = ((I >> 52) & 0x7ff) - 1023;
810 
811  // If the exponent is negative, the value is < 0 so just return 0.
812  if (exp < 0)
813  return APInt(width, 0u);
814 
815  // Extract the mantissa by clearing the top 12 bits (sign + exponent).
816  uint64_t mantissa = (I & (~0ULL >> 12)) | 1ULL << 52;
817 
818  // If the exponent doesn't shift all bits out of the mantissa
819  if (exp < 52)
820  return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
821  APInt(width, mantissa >> (52 - exp));
822 
823  // If the client didn't provide enough bits for us to shift the mantissa into
824  // then the result is undefined, just return 0
825  if (width <= exp - 52)
826  return APInt(width, 0);
827 
828  // Otherwise, we have to shift the mantissa bits up to the right location
829  APInt Tmp(width, mantissa);
830  Tmp <<= (unsigned)exp - 52;
831  return isNeg ? -Tmp : Tmp;
832 }
833 
834 /// This function converts this APInt to a double.
835 /// The layout for double is as following (IEEE Standard 754):
836 /// --------------------------------------
837 /// | Sign Exponent Fraction Bias |
838 /// |-------------------------------------- |
839 /// | 1[63] 11[62-52] 52[51-00] 1023 |
840 /// --------------------------------------
841 double APInt::roundToDouble(bool isSigned) const {
842 
843  // Handle the simple case where the value is contained in one uint64_t.
844  // It is wrong to optimize getWord(0) to VAL; there might be more than one word.
846  if (isSigned) {
847  int64_t sext = SignExtend64(getWord(0), BitWidth);
848  return double(sext);
849  } else
850  return double(getWord(0));
851  }
852 
853  // Determine if the value is negative.
854  bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
855 
856  // Construct the absolute value if we're negative.
857  APInt Tmp(isNeg ? -(*this) : (*this));
858 
859  // Figure out how many bits we're using.
860  unsigned n = Tmp.getActiveBits();
861 
862  // The exponent (without bias normalization) is just the number of bits
863  // we are using. Note that the sign bit is gone since we constructed the
864  // absolute value.
865  uint64_t exp = n;
866 
867  // Return infinity for exponent overflow
868  if (exp > 1023) {
869  if (!isSigned || !isNeg)
870  return std::numeric_limits<double>::infinity();
871  else
872  return -std::numeric_limits<double>::infinity();
873  }
874  exp += 1023; // Increment for 1023 bias
875 
876  // Number of bits in mantissa is 52. To obtain the mantissa value, we must
877  // extract the high 52 bits from the correct words in pVal.
878  uint64_t mantissa;
879  unsigned hiWord = whichWord(n-1);
880  if (hiWord == 0) {
881  mantissa = Tmp.U.pVal[0];
882  if (n > 52)
883  mantissa >>= n - 52; // shift down, we want the top 52 bits.
884  } else {
885  assert(hiWord > 0 && "huh?");
886  uint64_t hibits = Tmp.U.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
887  uint64_t lobits = Tmp.U.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
888  mantissa = hibits | lobits;
889  }
890 
891  // The leading bit of mantissa is implicit, so get rid of it.
892  uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
893  uint64_t I = sign | (exp << 52) | mantissa;
894  return bit_cast<double>(I);
895 }
896 
897 // Truncate to new width.
898 APInt APInt::trunc(unsigned width) const {
899  assert(width <= BitWidth && "Invalid APInt Truncate request");
900 
901  if (width <= APINT_BITS_PER_WORD)
902  return APInt(width, getRawData()[0]);
903 
904  if (width == BitWidth)
905  return *this;
906 
907  APInt Result(getMemory(getNumWords(width)), width);
908 
909  // Copy full words.
910  unsigned i;
911  for (i = 0; i != width / APINT_BITS_PER_WORD; i++)
912  Result.U.pVal[i] = U.pVal[i];
913 
914  // Truncate and copy any partial word.
915  unsigned bits = (0 - width) % APINT_BITS_PER_WORD;
916  if (bits != 0)
917  Result.U.pVal[i] = U.pVal[i] << bits >> bits;
918 
919  return Result;
920 }
921 
922 // Truncate to new width with unsigned saturation.
923 APInt APInt::truncUSat(unsigned width) const {
924  assert(width <= BitWidth && "Invalid APInt Truncate request");
925 
926  // Can we just losslessly truncate it?
927  if (isIntN(width))
928  return trunc(width);
929  // If not, then just return the new limit.
930  return APInt::getMaxValue(width);
931 }
932 
933 // Truncate to new width with signed saturation.
934 APInt APInt::truncSSat(unsigned width) const {
935  assert(width <= BitWidth && "Invalid APInt Truncate request");
936 
937  // Can we just losslessly truncate it?
938  if (isSignedIntN(width))
939  return trunc(width);
940  // If not, then just return the new limits.
941  return isNegative() ? APInt::getSignedMinValue(width)
942  : APInt::getSignedMaxValue(width);
943 }
944 
945 // Sign extend to a new width.
946 APInt APInt::sext(unsigned Width) const {
947  assert(Width >= BitWidth && "Invalid APInt SignExtend request");
948 
949  if (Width <= APINT_BITS_PER_WORD)
950  return APInt(Width, SignExtend64(U.VAL, BitWidth));
951 
952  if (Width == BitWidth)
953  return *this;
954 
956 
957  // Copy words.
958  std::memcpy(Result.U.pVal, getRawData(), getNumWords() * APINT_WORD_SIZE);
959 
960  // Sign extend the last word since there may be unused bits in the input.
961  Result.U.pVal[getNumWords() - 1] =
962  SignExtend64(Result.U.pVal[getNumWords() - 1],
963  ((BitWidth - 1) % APINT_BITS_PER_WORD) + 1);
964 
965  // Fill with sign bits.
966  std::memset(Result.U.pVal + getNumWords(), isNegative() ? -1 : 0,
967  (Result.getNumWords() - getNumWords()) * APINT_WORD_SIZE);
968  Result.clearUnusedBits();
969  return Result;
970 }
971 
972 // Zero extend to a new width.
973 APInt APInt::zext(unsigned width) const {
974  assert(width >= BitWidth && "Invalid APInt ZeroExtend request");
975 
976  if (width <= APINT_BITS_PER_WORD)
977  return APInt(width, U.VAL);
978 
979  if (width == BitWidth)
980  return *this;
981 
982  APInt Result(getMemory(getNumWords(width)), width);
983 
984  // Copy words.
985  std::memcpy(Result.U.pVal, getRawData(), getNumWords() * APINT_WORD_SIZE);
986 
987  // Zero remaining words.
988  std::memset(Result.U.pVal + getNumWords(), 0,
989  (Result.getNumWords() - getNumWords()) * APINT_WORD_SIZE);
990 
991  return Result;
992 }
993 
994 APInt APInt::zextOrTrunc(unsigned width) const {
995  if (BitWidth < width)
996  return zext(width);
997  if (BitWidth > width)
998  return trunc(width);
999  return *this;
1000 }
1001 
1002 APInt APInt::sextOrTrunc(unsigned width) const {
1003  if (BitWidth < width)
1004  return sext(width);
1005  if (BitWidth > width)
1006  return trunc(width);
1007  return *this;
1008 }
1009 
1010 /// Arithmetic right-shift this APInt by shiftAmt.
1011 /// Arithmetic right-shift function.
1012 void APInt::ashrInPlace(const APInt &shiftAmt) {
1013  ashrInPlace((unsigned)shiftAmt.getLimitedValue(BitWidth));
1014 }
1015 
1016 /// Arithmetic right-shift this APInt by shiftAmt.
1017 /// Arithmetic right-shift function.
1018 void APInt::ashrSlowCase(unsigned ShiftAmt) {
1019  // Don't bother performing a no-op shift.
1020  if (!ShiftAmt)
1021  return;
1022 
1023  // Save the original sign bit for later.
1024  bool Negative = isNegative();
1025 
1026  // WordShift is the inter-part shift; BitShift is intra-part shift.
1027  unsigned WordShift = ShiftAmt / APINT_BITS_PER_WORD;
1028  unsigned BitShift = ShiftAmt % APINT_BITS_PER_WORD;
1029 
1030  unsigned WordsToMove = getNumWords() - WordShift;
1031  if (WordsToMove != 0) {
1032  // Sign extend the last word to fill in the unused bits.
1033  U.pVal[getNumWords() - 1] = SignExtend64(
1034  U.pVal[getNumWords() - 1], ((BitWidth - 1) % APINT_BITS_PER_WORD) + 1);
1035 
1036  // Fastpath for moving by whole words.
1037  if (BitShift == 0) {
1038  std::memmove(U.pVal, U.pVal + WordShift, WordsToMove * APINT_WORD_SIZE);
1039  } else {
1040  // Move the words containing significant bits.
1041  for (unsigned i = 0; i != WordsToMove - 1; ++i)
1042  U.pVal[i] = (U.pVal[i + WordShift] >> BitShift) |
1043  (U.pVal[i + WordShift + 1] << (APINT_BITS_PER_WORD - BitShift));
1044 
1045  // Handle the last word which has no high bits to copy.
1046  U.pVal[WordsToMove - 1] = U.pVal[WordShift + WordsToMove - 1] >> BitShift;
1047  // Sign extend one more time.
1048  U.pVal[WordsToMove - 1] =
1049  SignExtend64(U.pVal[WordsToMove - 1], APINT_BITS_PER_WORD - BitShift);
1050  }
1051  }
1052 
1053  // Fill in the remainder based on the original sign.
1054  std::memset(U.pVal + WordsToMove, Negative ? -1 : 0,
1055  WordShift * APINT_WORD_SIZE);
1056  clearUnusedBits();
1057 }
1058 
1059 /// Logical right-shift this APInt by shiftAmt.
1060 /// Logical right-shift function.
1061 void APInt::lshrInPlace(const APInt &shiftAmt) {
1062  lshrInPlace((unsigned)shiftAmt.getLimitedValue(BitWidth));
1063 }
1064 
1065 /// Logical right-shift this APInt by shiftAmt.
1066 /// Logical right-shift function.
1067 void APInt::lshrSlowCase(unsigned ShiftAmt) {
1068  tcShiftRight(U.pVal, getNumWords(), ShiftAmt);
1069 }
1070 
1071 /// Left-shift this APInt by shiftAmt.
1072 /// Left-shift function.
1073 APInt &APInt::operator<<=(const APInt &shiftAmt) {
1074  // It's undefined behavior in C to shift by BitWidth or greater.
1075  *this <<= (unsigned)shiftAmt.getLimitedValue(BitWidth);
1076  return *this;
1077 }
1078 
1079 void APInt::shlSlowCase(unsigned ShiftAmt) {
1080  tcShiftLeft(U.pVal, getNumWords(), ShiftAmt);
1081  clearUnusedBits();
1082 }
1083 
1084 // Calculate the rotate amount modulo the bit width.
1085 static unsigned rotateModulo(unsigned BitWidth, const APInt &rotateAmt) {
1086  if (LLVM_UNLIKELY(BitWidth == 0))
1087  return 0;
1088  unsigned rotBitWidth = rotateAmt.getBitWidth();
1089  APInt rot = rotateAmt;
1090  if (rotBitWidth < BitWidth) {
1091  // Extend the rotate APInt, so that the urem doesn't divide by 0.
1092  // e.g. APInt(1, 32) would give APInt(1, 0).
1093  rot = rotateAmt.zext(BitWidth);
1094  }
1095  rot = rot.urem(APInt(rot.getBitWidth(), BitWidth));
1096  return rot.getLimitedValue(BitWidth);
1097 }
1098 
1099 APInt APInt::rotl(const APInt &rotateAmt) const {
1100  return rotl(rotateModulo(BitWidth, rotateAmt));
1101 }
1102 
1103 APInt APInt::rotl(unsigned rotateAmt) const {
1104  if (LLVM_UNLIKELY(BitWidth == 0))
1105  return *this;
1106  rotateAmt %= BitWidth;
1107  if (rotateAmt == 0)
1108  return *this;
1109  return shl(rotateAmt) | lshr(BitWidth - rotateAmt);
1110 }
1111 
1112 APInt APInt::rotr(const APInt &rotateAmt) const {
1113  return rotr(rotateModulo(BitWidth, rotateAmt));
1114 }
1115 
1116 APInt APInt::rotr(unsigned rotateAmt) const {
1117  if (BitWidth == 0)
1118  return *this;
1119  rotateAmt %= BitWidth;
1120  if (rotateAmt == 0)
1121  return *this;
1122  return lshr(rotateAmt) | shl(BitWidth - rotateAmt);
1123 }
1124 
1125 /// \returns the nearest log base 2 of this APInt. Ties round up.
1126 ///
1127 /// NOTE: When we have a BitWidth of 1, we define:
1128 ///
1129 /// log2(0) = UINT32_MAX
1130 /// log2(1) = 0
1131 ///
1132 /// to get around any mathematical concerns resulting from
1133 /// referencing 2 in a space where 2 does no exist.
1134 unsigned APInt::nearestLogBase2() const {
1135  // Special case when we have a bitwidth of 1. If VAL is 1, then we
1136  // get 0. If VAL is 0, we get WORDTYPE_MAX which gets truncated to
1137  // UINT32_MAX.
1138  if (BitWidth == 1)
1139  return U.VAL - 1;
1140 
1141  // Handle the zero case.
1142  if (isZero())
1143  return UINT32_MAX;
1144 
1145  // The non-zero case is handled by computing:
1146  //
1147  // nearestLogBase2(x) = logBase2(x) + x[logBase2(x)-1].
1148  //
1149  // where x[i] is referring to the value of the ith bit of x.
1150  unsigned lg = logBase2();
1151  return lg + unsigned((*this)[lg - 1]);
1152 }
1153 
1154 // Square Root - this method computes and returns the square root of "this".
1155 // Three mechanisms are used for computation. For small values (<= 5 bits),
1156 // a table lookup is done. This gets some performance for common cases. For
1157 // values using less than 52 bits, the value is converted to double and then
1158 // the libc sqrt function is called. The result is rounded and then converted
1159 // back to a uint64_t which is then used to construct the result. Finally,
1160 // the Babylonian method for computing square roots is used.
1162 
1163  // Determine the magnitude of the value.
1164  unsigned magnitude = getActiveBits();
1165 
1166  // Use a fast table for some small values. This also gets rid of some
1167  // rounding errors in libc sqrt for small values.
1168  if (magnitude <= 5) {
1169  static const uint8_t results[32] = {
1170  /* 0 */ 0,
1171  /* 1- 2 */ 1, 1,
1172  /* 3- 6 */ 2, 2, 2, 2,
1173  /* 7-12 */ 3, 3, 3, 3, 3, 3,
1174  /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1175  /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1176  /* 31 */ 6
1177  };
1178  return APInt(BitWidth, results[ (isSingleWord() ? U.VAL : U.pVal[0]) ]);
1179  }
1180 
1181  // If the magnitude of the value fits in less than 52 bits (the precision of
1182  // an IEEE double precision floating point value), then we can use the
1183  // libc sqrt function which will probably use a hardware sqrt computation.
1184  // This should be faster than the algorithm below.
1185  if (magnitude < 52) {
1186  return APInt(BitWidth,
1187  uint64_t(::round(::sqrt(double(isSingleWord() ? U.VAL
1188  : U.pVal[0])))));
1189  }
1190 
1191  // Okay, all the short cuts are exhausted. We must compute it. The following
1192  // is a classical Babylonian method for computing the square root. This code
1193  // was adapted to APInt from a wikipedia article on such computations.
1194  // See http://www.wikipedia.org/ and go to the page named
1195  // Calculate_an_integer_square_root.
1196  unsigned nbits = BitWidth, i = 4;
1197  APInt testy(BitWidth, 16);
1198  APInt x_old(BitWidth, 1);
1199  APInt x_new(BitWidth, 0);
1200  APInt two(BitWidth, 2);
1201 
1202  // Select a good starting value using binary logarithms.
1203  for (;; i += 2, testy = testy.shl(2))
1204  if (i >= nbits || this->ule(testy)) {
1205  x_old = x_old.shl(i / 2);
1206  break;
1207  }
1208 
1209  // Use the Babylonian method to arrive at the integer square root:
1210  for (;;) {
1211  x_new = (this->udiv(x_old) + x_old).udiv(two);
1212  if (x_old.ule(x_new))
1213  break;
1214  x_old = x_new;
1215  }
1216 
1217  // Make sure we return the closest approximation
1218  // NOTE: The rounding calculation below is correct. It will produce an
1219  // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1220  // determined to be a rounding issue with pari/gp as it begins to use a
1221  // floating point representation after 192 bits. There are no discrepancies
1222  // between this algorithm and pari/gp for bit widths < 192 bits.
1223  APInt square(x_old * x_old);
1224  APInt nextSquare((x_old + 1) * (x_old +1));
1225  if (this->ult(square))
1226  return x_old;
1227  assert(this->ule(nextSquare) && "Error in APInt::sqrt computation");
1228  APInt midpoint((nextSquare - square).udiv(two));
1229  APInt offset(*this - square);
1230  if (offset.ult(midpoint))
1231  return x_old;
1232  return x_old + 1;
1233 }
1234 
1235 /// Computes the multiplicative inverse of this APInt for a given modulo. The
1236 /// iterative extended Euclidean algorithm is used to solve for this value,
1237 /// however we simplify it to speed up calculating only the inverse, and take
1238 /// advantage of div+rem calculations. We also use some tricks to avoid copying
1239 /// (potentially large) APInts around.
1240 /// WARNING: a value of '0' may be returned,
1241 /// signifying that no multiplicative inverse exists!
1243  assert(ult(modulo) && "This APInt must be smaller than the modulo");
1244 
1245  // Using the properties listed at the following web page (accessed 06/21/08):
1246  // http://www.numbertheory.org/php/euclid.html
1247  // (especially the properties numbered 3, 4 and 9) it can be proved that
1248  // BitWidth bits suffice for all the computations in the algorithm implemented
1249  // below. More precisely, this number of bits suffice if the multiplicative
1250  // inverse exists, but may not suffice for the general extended Euclidean
1251  // algorithm.
1252 
1253  APInt r[2] = { modulo, *this };
1254  APInt t[2] = { APInt(BitWidth, 0), APInt(BitWidth, 1) };
1255  APInt q(BitWidth, 0);
1256 
1257  unsigned i;
1258  for (i = 0; r[i^1] != 0; i ^= 1) {
1259  // An overview of the math without the confusing bit-flipping:
1260  // q = r[i-2] / r[i-1]
1261  // r[i] = r[i-2] % r[i-1]
1262  // t[i] = t[i-2] - t[i-1] * q
1263  udivrem(r[i], r[i^1], q, r[i]);
1264  t[i] -= t[i^1] * q;
1265  }
1266 
1267  // If this APInt and the modulo are not coprime, there is no multiplicative
1268  // inverse, so return 0. We check this by looking at the next-to-last
1269  // remainder, which is the gcd(*this,modulo) as calculated by the Euclidean
1270  // algorithm.
1271  if (r[i] != 1)
1272  return APInt(BitWidth, 0);
1273 
1274  // The next-to-last t is the multiplicative inverse. However, we are
1275  // interested in a positive inverse. Calculate a positive one from a negative
1276  // one if necessary. A simple addition of the modulo suffices because
1277  // abs(t[i]) is known to be less than *this/2 (see the link above).
1278  if (t[i].isNegative())
1279  t[i] += modulo;
1280 
1281  return std::move(t[i]);
1282 }
1283 
1284 /// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1285 /// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1286 /// variables here have the same names as in the algorithm. Comments explain
1287 /// the algorithm and any deviation from it.
1288 static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
1289  unsigned m, unsigned n) {
1290  assert(u && "Must provide dividend");
1291  assert(v && "Must provide divisor");
1292  assert(q && "Must provide quotient");
1293  assert(u != v && u != q && v != q && "Must use different memory");
1294  assert(n>1 && "n must be > 1");
1295 
1296  // b denotes the base of the number system. In our case b is 2^32.
1297  const uint64_t b = uint64_t(1) << 32;
1298 
1299 // The DEBUG macros here tend to be spam in the debug output if you're not
1300 // debugging this code. Disable them unless KNUTH_DEBUG is defined.
1301 #ifdef KNUTH_DEBUG
1302 #define DEBUG_KNUTH(X) LLVM_DEBUG(X)
1303 #else
1304 #define DEBUG_KNUTH(X) do {} while(false)
1305 #endif
1306 
1307  DEBUG_KNUTH(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n');
1308  DEBUG_KNUTH(dbgs() << "KnuthDiv: original:");
1309  DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]);
1310  DEBUG_KNUTH(dbgs() << " by");
1311  DEBUG_KNUTH(for (int i = n; i > 0; i--) dbgs() << " " << v[i - 1]);
1312  DEBUG_KNUTH(dbgs() << '\n');
1313  // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1314  // u and v by d. Note that we have taken Knuth's advice here to use a power
1315  // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1316  // 2 allows us to shift instead of multiply and it is easy to determine the
1317  // shift amount from the leading zeros. We are basically normalizing the u
1318  // and v so that its high bits are shifted to the top of v's range without
1319  // overflow. Note that this can require an extra word in u so that u must
1320  // be of length m+n+1.
1321  unsigned shift = countLeadingZeros(v[n-1]);
1322  uint32_t v_carry = 0;
1323  uint32_t u_carry = 0;
1324  if (shift) {
1325  for (unsigned i = 0; i < m+n; ++i) {
1326  uint32_t u_tmp = u[i] >> (32 - shift);
1327  u[i] = (u[i] << shift) | u_carry;
1328  u_carry = u_tmp;
1329  }
1330  for (unsigned i = 0; i < n; ++i) {
1331  uint32_t v_tmp = v[i] >> (32 - shift);
1332  v[i] = (v[i] << shift) | v_carry;
1333  v_carry = v_tmp;
1334  }
1335  }
1336  u[m+n] = u_carry;
1337 
1338  DEBUG_KNUTH(dbgs() << "KnuthDiv: normal:");
1339  DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]);
1340  DEBUG_KNUTH(dbgs() << " by");
1341  DEBUG_KNUTH(for (int i = n; i > 0; i--) dbgs() << " " << v[i - 1]);
1342  DEBUG_KNUTH(dbgs() << '\n');
1343 
1344  // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1345  int j = m;
1346  do {
1347  DEBUG_KNUTH(dbgs() << "KnuthDiv: quotient digit #" << j << '\n');
1348  // D3. [Calculate q'.].
1349  // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1350  // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1351  // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1352  // qp by 1, increase rp by v[n-1], and repeat this test if rp < b. The test
1353  // on v[n-2] determines at high speed most of the cases in which the trial
1354  // value qp is one too large, and it eliminates all cases where qp is two
1355  // too large.
1356  uint64_t dividend = Make_64(u[j+n], u[j+n-1]);
1357  DEBUG_KNUTH(dbgs() << "KnuthDiv: dividend == " << dividend << '\n');
1358  uint64_t qp = dividend / v[n-1];
1359  uint64_t rp = dividend % v[n-1];
1360  if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
1361  qp--;
1362  rp += v[n-1];
1363  if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1364  qp--;
1365  }
1366  DEBUG_KNUTH(dbgs() << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n');
1367 
1368  // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1369  // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1370  // consists of a simple multiplication by a one-place number, combined with
1371  // a subtraction.
1372  // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1373  // this step is actually negative, (u[j+n]...u[j]) should be left as the
1374  // true value plus b**(n+1), namely as the b's complement of
1375  // the true value, and a "borrow" to the left should be remembered.
1376  int64_t borrow = 0;
1377  for (unsigned i = 0; i < n; ++i) {
1378  uint64_t p = uint64_t(qp) * uint64_t(v[i]);
1379  int64_t subres = int64_t(u[j+i]) - borrow - Lo_32(p);
1380  u[j+i] = Lo_32(subres);
1381  borrow = Hi_32(p) - Hi_32(subres);
1382  DEBUG_KNUTH(dbgs() << "KnuthDiv: u[j+i] = " << u[j + i]
1383  << ", borrow = " << borrow << '\n');
1384  }
1385  bool isNeg = u[j+n] < borrow;
1386  u[j+n] -= Lo_32(borrow);
1387 
1388  DEBUG_KNUTH(dbgs() << "KnuthDiv: after subtraction:");
1389  DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]);
1390  DEBUG_KNUTH(dbgs() << '\n');
1391 
1392  // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1393  // negative, go to step D6; otherwise go on to step D7.
1394  q[j] = Lo_32(qp);
1395  if (isNeg) {
1396  // D6. [Add back]. The probability that this step is necessary is very
1397  // small, on the order of only 2/b. Make sure that test data accounts for
1398  // this possibility. Decrease q[j] by 1
1399  q[j]--;
1400  // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1401  // A carry will occur to the left of u[j+n], and it should be ignored
1402  // since it cancels with the borrow that occurred in D4.
1403  bool carry = false;
1404  for (unsigned i = 0; i < n; i++) {
1405  uint32_t limit = std::min(u[j+i],v[i]);
1406  u[j+i] += v[i] + carry;
1407  carry = u[j+i] < limit || (carry && u[j+i] == limit);
1408  }
1409  u[j+n] += carry;
1410  }
1411  DEBUG_KNUTH(dbgs() << "KnuthDiv: after correction:");
1412  DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i]);
1413  DEBUG_KNUTH(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n');
1414 
1415  // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1416  } while (--j >= 0);
1417 
1418  DEBUG_KNUTH(dbgs() << "KnuthDiv: quotient:");
1419  DEBUG_KNUTH(for (int i = m; i >= 0; i--) dbgs() << " " << q[i]);
1420  DEBUG_KNUTH(dbgs() << '\n');
1421 
1422  // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1423  // remainder may be obtained by dividing u[...] by d. If r is non-null we
1424  // compute the remainder (urem uses this).
1425  if (r) {
1426  // The value d is expressed by the "shift" value above since we avoided
1427  // multiplication by d by using a shift left. So, all we have to do is
1428  // shift right here.
1429  if (shift) {
1430  uint32_t carry = 0;
1431  DEBUG_KNUTH(dbgs() << "KnuthDiv: remainder:");
1432  for (int i = n-1; i >= 0; i--) {
1433  r[i] = (u[i] >> shift) | carry;
1434  carry = u[i] << (32 - shift);
1435  DEBUG_KNUTH(dbgs() << " " << r[i]);
1436  }
1437  } else {
1438  for (int i = n-1; i >= 0; i--) {
1439  r[i] = u[i];
1440  DEBUG_KNUTH(dbgs() << " " << r[i]);
1441  }
1442  }
1443  DEBUG_KNUTH(dbgs() << '\n');
1444  }
1445  DEBUG_KNUTH(dbgs() << '\n');
1446 }
1447 
1448 void APInt::divide(const WordType *LHS, unsigned lhsWords, const WordType *RHS,
1449  unsigned rhsWords, WordType *Quotient, WordType *Remainder) {
1450  assert(lhsWords >= rhsWords && "Fractional result");
1451 
1452  // First, compose the values into an array of 32-bit words instead of
1453  // 64-bit words. This is a necessity of both the "short division" algorithm
1454  // and the Knuth "classical algorithm" which requires there to be native
1455  // operations for +, -, and * on an m bit value with an m*2 bit result. We
1456  // can't use 64-bit operands here because we don't have native results of
1457  // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't
1458  // work on large-endian machines.
1459  unsigned n = rhsWords * 2;
1460  unsigned m = (lhsWords * 2) - n;
1461 
1462  // Allocate space for the temporary values we need either on the stack, if
1463  // it will fit, or on the heap if it won't.
1464  uint32_t SPACE[128];
1465  uint32_t *U = nullptr;
1466  uint32_t *V = nullptr;
1467  uint32_t *Q = nullptr;
1468  uint32_t *R = nullptr;
1469  if ((Remainder?4:3)*n+2*m+1 <= 128) {
1470  U = &SPACE[0];
1471  V = &SPACE[m+n+1];
1472  Q = &SPACE[(m+n+1) + n];
1473  if (Remainder)
1474  R = &SPACE[(m+n+1) + n + (m+n)];
1475  } else {
1476  U = new uint32_t[m + n + 1];
1477  V = new uint32_t[n];
1478  Q = new uint32_t[m+n];
1479  if (Remainder)
1480  R = new uint32_t[n];
1481  }
1482 
1483  // Initialize the dividend
1484  memset(U, 0, (m+n+1)*sizeof(uint32_t));
1485  for (unsigned i = 0; i < lhsWords; ++i) {
1486  uint64_t tmp = LHS[i];
1487  U[i * 2] = Lo_32(tmp);
1488  U[i * 2 + 1] = Hi_32(tmp);
1489  }
1490  U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1491 
1492  // Initialize the divisor
1493  memset(V, 0, (n)*sizeof(uint32_t));
1494  for (unsigned i = 0; i < rhsWords; ++i) {
1495  uint64_t tmp = RHS[i];
1496  V[i * 2] = Lo_32(tmp);
1497  V[i * 2 + 1] = Hi_32(tmp);
1498  }
1499 
1500  // initialize the quotient and remainder
1501  memset(Q, 0, (m+n) * sizeof(uint32_t));
1502  if (Remainder)
1503  memset(R, 0, n * sizeof(uint32_t));
1504 
1505  // Now, adjust m and n for the Knuth division. n is the number of words in
1506  // the divisor. m is the number of words by which the dividend exceeds the
1507  // divisor (i.e. m+n is the length of the dividend). These sizes must not
1508  // contain any zero words or the Knuth algorithm fails.
1509  for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1510  n--;
1511  m++;
1512  }
1513  for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1514  m--;
1515 
1516  // If we're left with only a single word for the divisor, Knuth doesn't work
1517  // so we implement the short division algorithm here. This is much simpler
1518  // and faster because we are certain that we can divide a 64-bit quantity
1519  // by a 32-bit quantity at hardware speed and short division is simply a
1520  // series of such operations. This is just like doing short division but we
1521  // are using base 2^32 instead of base 10.
1522  assert(n != 0 && "Divide by zero?");
1523  if (n == 1) {
1524  uint32_t divisor = V[0];
1525  uint32_t remainder = 0;
1526  for (int i = m; i >= 0; i--) {
1527  uint64_t partial_dividend = Make_64(remainder, U[i]);
1528  if (partial_dividend == 0) {
1529  Q[i] = 0;
1530  remainder = 0;
1531  } else if (partial_dividend < divisor) {
1532  Q[i] = 0;
1533  remainder = Lo_32(partial_dividend);
1534  } else if (partial_dividend == divisor) {
1535  Q[i] = 1;
1536  remainder = 0;
1537  } else {
1538  Q[i] = Lo_32(partial_dividend / divisor);
1539  remainder = Lo_32(partial_dividend - (Q[i] * divisor));
1540  }
1541  }
1542  if (R)
1543  R[0] = remainder;
1544  } else {
1545  // Now we're ready to invoke the Knuth classical divide algorithm. In this
1546  // case n > 1.
1547  KnuthDiv(U, V, Q, R, m, n);
1548  }
1549 
1550  // If the caller wants the quotient
1551  if (Quotient) {
1552  for (unsigned i = 0; i < lhsWords; ++i)
1553  Quotient[i] = Make_64(Q[i*2+1], Q[i*2]);
1554  }
1555 
1556  // If the caller wants the remainder
1557  if (Remainder) {
1558  for (unsigned i = 0; i < rhsWords; ++i)
1559  Remainder[i] = Make_64(R[i*2+1], R[i*2]);
1560  }
1561 
1562  // Clean up the memory we allocated.
1563  if (U != &SPACE[0]) {
1564  delete [] U;
1565  delete [] V;
1566  delete [] Q;
1567  delete [] R;
1568  }
1569 }
1570 
1571 APInt APInt::udiv(const APInt &RHS) const {
1572  assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1573 
1574  // First, deal with the easy case
1575  if (isSingleWord()) {
1576  assert(RHS.U.VAL != 0 && "Divide by zero?");
1577  return APInt(BitWidth, U.VAL / RHS.U.VAL);
1578  }
1579 
1580  // Get some facts about the LHS and RHS number of bits and words
1581  unsigned lhsWords = getNumWords(getActiveBits());
1582  unsigned rhsBits = RHS.getActiveBits();
1583  unsigned rhsWords = getNumWords(rhsBits);
1584  assert(rhsWords && "Divided by zero???");
1585 
1586  // Deal with some degenerate cases
1587  if (!lhsWords)
1588  // 0 / X ===> 0
1589  return APInt(BitWidth, 0);
1590  if (rhsBits == 1)
1591  // X / 1 ===> X
1592  return *this;
1593  if (lhsWords < rhsWords || this->ult(RHS))
1594  // X / Y ===> 0, iff X < Y
1595  return APInt(BitWidth, 0);
1596  if (*this == RHS)
1597  // X / X ===> 1
1598  return APInt(BitWidth, 1);
1599  if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1.
1600  // All high words are zero, just use native divide
1601  return APInt(BitWidth, this->U.pVal[0] / RHS.U.pVal[0]);
1602 
1603  // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1604  APInt Quotient(BitWidth, 0); // to hold result.
1605  divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal, nullptr);
1606  return Quotient;
1607 }
1608 
1610  assert(RHS != 0 && "Divide by zero?");
1611 
1612  // First, deal with the easy case
1613  if (isSingleWord())
1614  return APInt(BitWidth, U.VAL / RHS);
1615 
1616  // Get some facts about the LHS words.
1617  unsigned lhsWords = getNumWords(getActiveBits());
1618 
1619  // Deal with some degenerate cases
1620  if (!lhsWords)
1621  // 0 / X ===> 0
1622  return APInt(BitWidth, 0);
1623  if (RHS == 1)
1624  // X / 1 ===> X
1625  return *this;
1626  if (this->ult(RHS))
1627  // X / Y ===> 0, iff X < Y
1628  return APInt(BitWidth, 0);
1629  if (*this == RHS)
1630  // X / X ===> 1
1631  return APInt(BitWidth, 1);
1632  if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1.
1633  // All high words are zero, just use native divide
1634  return APInt(BitWidth, this->U.pVal[0] / RHS);
1635 
1636  // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1637  APInt Quotient(BitWidth, 0); // to hold result.
1638  divide(U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, nullptr);
1639  return Quotient;
1640 }
1641 
1642 APInt APInt::sdiv(const APInt &RHS) const {
1643  if (isNegative()) {
1644  if (RHS.isNegative())
1645  return (-(*this)).udiv(-RHS);
1646  return -((-(*this)).udiv(RHS));
1647  }
1648  if (RHS.isNegative())
1649  return -(this->udiv(-RHS));
1650  return this->udiv(RHS);
1651 }
1652 
1653 APInt APInt::sdiv(int64_t RHS) const {
1654  if (isNegative()) {
1655  if (RHS < 0)
1656  return (-(*this)).udiv(-RHS);
1657  return -((-(*this)).udiv(RHS));
1658  }
1659  if (RHS < 0)
1660  return -(this->udiv(-RHS));
1661  return this->udiv(RHS);
1662 }
1663 
1664 APInt APInt::urem(const APInt &RHS) const {
1665  assert(BitWidth == RHS.BitWidth && "Bit widths must be the same");
1666  if (isSingleWord()) {
1667  assert(RHS.U.VAL != 0 && "Remainder by zero?");
1668  return APInt(BitWidth, U.VAL % RHS.U.VAL);
1669  }
1670 
1671  // Get some facts about the LHS
1672  unsigned lhsWords = getNumWords(getActiveBits());
1673 
1674  // Get some facts about the RHS
1675  unsigned rhsBits = RHS.getActiveBits();
1676  unsigned rhsWords = getNumWords(rhsBits);
1677  assert(rhsWords && "Performing remainder operation by zero ???");
1678 
1679  // Check the degenerate cases
1680  if (lhsWords == 0)
1681  // 0 % Y ===> 0
1682  return APInt(BitWidth, 0);
1683  if (rhsBits == 1)
1684  // X % 1 ===> 0
1685  return APInt(BitWidth, 0);
1686  if (lhsWords < rhsWords || this->ult(RHS))
1687  // X % Y ===> X, iff X < Y
1688  return *this;
1689  if (*this == RHS)
1690  // X % X == 0;
1691  return APInt(BitWidth, 0);
1692  if (lhsWords == 1)
1693  // All high words are zero, just use native remainder
1694  return APInt(BitWidth, U.pVal[0] % RHS.U.pVal[0]);
1695 
1696  // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1697  APInt Remainder(BitWidth, 0);
1698  divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, nullptr, Remainder.U.pVal);
1699  return Remainder;
1700 }
1701 
1703  assert(RHS != 0 && "Remainder by zero?");
1704 
1705  if (isSingleWord())
1706  return U.VAL % RHS;
1707 
1708  // Get some facts about the LHS
1709  unsigned lhsWords = getNumWords(getActiveBits());
1710 
1711  // Check the degenerate cases
1712  if (lhsWords == 0)
1713  // 0 % Y ===> 0
1714  return 0;
1715  if (RHS == 1)
1716  // X % 1 ===> 0
1717  return 0;
1718  if (this->ult(RHS))
1719  // X % Y ===> X, iff X < Y
1720  return getZExtValue();
1721  if (*this == RHS)
1722  // X % X == 0;
1723  return 0;
1724  if (lhsWords == 1)
1725  // All high words are zero, just use native remainder
1726  return U.pVal[0] % RHS;
1727 
1728  // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1729  uint64_t Remainder;
1730  divide(U.pVal, lhsWords, &RHS, 1, nullptr, &Remainder);
1731  return Remainder;
1732 }
1733 
1734 APInt APInt::srem(const APInt &RHS) const {
1735  if (isNegative()) {
1736  if (RHS.isNegative())
1737  return -((-(*this)).urem(-RHS));
1738  return -((-(*this)).urem(RHS));
1739  }
1740  if (RHS.isNegative())
1741  return this->urem(-RHS);
1742  return this->urem(RHS);
1743 }
1744 
1745 int64_t APInt::srem(int64_t RHS) const {
1746  if (isNegative()) {
1747  if (RHS < 0)
1748  return -((-(*this)).urem(-RHS));
1749  return -((-(*this)).urem(RHS));
1750  }
1751  if (RHS < 0)
1752  return this->urem(-RHS);
1753  return this->urem(RHS);
1754 }
1755 
1756 void APInt::udivrem(const APInt &LHS, const APInt &RHS,
1757  APInt &Quotient, APInt &Remainder) {
1758  assert(LHS.BitWidth == RHS.BitWidth && "Bit widths must be the same");
1759  unsigned BitWidth = LHS.BitWidth;
1760 
1761  // First, deal with the easy case
1762  if (LHS.isSingleWord()) {
1763  assert(RHS.U.VAL != 0 && "Divide by zero?");
1764  uint64_t QuotVal = LHS.U.VAL / RHS.U.VAL;
1765  uint64_t RemVal = LHS.U.VAL % RHS.U.VAL;
1766  Quotient = APInt(BitWidth, QuotVal);
1767  Remainder = APInt(BitWidth, RemVal);
1768  return;
1769  }
1770 
1771  // Get some size facts about the dividend and divisor
1772  unsigned lhsWords = getNumWords(LHS.getActiveBits());
1773  unsigned rhsBits = RHS.getActiveBits();
1774  unsigned rhsWords = getNumWords(rhsBits);
1775  assert(rhsWords && "Performing divrem operation by zero ???");
1776 
1777  // Check the degenerate cases
1778  if (lhsWords == 0) {
1779  Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0
1780  Remainder = APInt(BitWidth, 0); // 0 % Y ===> 0
1781  return;
1782  }
1783 
1784  if (rhsBits == 1) {
1785  Quotient = LHS; // X / 1 ===> X
1786  Remainder = APInt(BitWidth, 0); // X % 1 ===> 0
1787  }
1788 
1789  if (lhsWords < rhsWords || LHS.ult(RHS)) {
1790  Remainder = LHS; // X % Y ===> X, iff X < Y
1791  Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y
1792  return;
1793  }
1794 
1795  if (LHS == RHS) {
1796  Quotient = APInt(BitWidth, 1); // X / X ===> 1
1797  Remainder = APInt(BitWidth, 0); // X % X ===> 0;
1798  return;
1799  }
1800 
1801  // Make sure there is enough space to hold the results.
1802  // NOTE: This assumes that reallocate won't affect any bits if it doesn't
1803  // change the size. This is necessary if Quotient or Remainder is aliased
1804  // with LHS or RHS.
1805  Quotient.reallocate(BitWidth);
1806  Remainder.reallocate(BitWidth);
1807 
1808  if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1.
1809  // There is only one word to consider so use the native versions.
1810  uint64_t lhsValue = LHS.U.pVal[0];
1811  uint64_t rhsValue = RHS.U.pVal[0];
1812  Quotient = lhsValue / rhsValue;
1813  Remainder = lhsValue % rhsValue;
1814  return;
1815  }
1816 
1817  // Okay, lets do it the long way
1818  divide(LHS.U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal,
1819  Remainder.U.pVal);
1820  // Clear the rest of the Quotient and Remainder.
1821  std::memset(Quotient.U.pVal + lhsWords, 0,
1822  (getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE);
1823  std::memset(Remainder.U.pVal + rhsWords, 0,
1824  (getNumWords(BitWidth) - rhsWords) * APINT_WORD_SIZE);
1825 }
1826 
1827 void APInt::udivrem(const APInt &LHS, uint64_t RHS, APInt &Quotient,
1828  uint64_t &Remainder) {
1829  assert(RHS != 0 && "Divide by zero?");
1830  unsigned BitWidth = LHS.BitWidth;
1831 
1832  // First, deal with the easy case
1833  if (LHS.isSingleWord()) {
1834  uint64_t QuotVal = LHS.U.VAL / RHS;
1835  Remainder = LHS.U.VAL % RHS;
1836  Quotient = APInt(BitWidth, QuotVal);
1837  return;
1838  }
1839 
1840  // Get some size facts about the dividend and divisor
1841  unsigned lhsWords = getNumWords(LHS.getActiveBits());
1842 
1843  // Check the degenerate cases
1844  if (lhsWords == 0) {
1845  Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0
1846  Remainder = 0; // 0 % Y ===> 0
1847  return;
1848  }
1849 
1850  if (RHS == 1) {
1851  Quotient = LHS; // X / 1 ===> X
1852  Remainder = 0; // X % 1 ===> 0
1853  return;
1854  }
1855 
1856  if (LHS.ult(RHS)) {
1857  Remainder = LHS.getZExtValue(); // X % Y ===> X, iff X < Y
1858  Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y
1859  return;
1860  }
1861 
1862  if (LHS == RHS) {
1863  Quotient = APInt(BitWidth, 1); // X / X ===> 1
1864  Remainder = 0; // X % X ===> 0;
1865  return;
1866  }
1867 
1868  // Make sure there is enough space to hold the results.
1869  // NOTE: This assumes that reallocate won't affect any bits if it doesn't
1870  // change the size. This is necessary if Quotient is aliased with LHS.
1871  Quotient.reallocate(BitWidth);
1872 
1873  if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1.
1874  // There is only one word to consider so use the native versions.
1875  uint64_t lhsValue = LHS.U.pVal[0];
1876  Quotient = lhsValue / RHS;
1877  Remainder = lhsValue % RHS;
1878  return;
1879  }
1880 
1881  // Okay, lets do it the long way
1882  divide(LHS.U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, &Remainder);
1883  // Clear the rest of the Quotient.
1884  std::memset(Quotient.U.pVal + lhsWords, 0,
1885  (getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE);
1886 }
1887 
1888 void APInt::sdivrem(const APInt &LHS, const APInt &RHS,
1889  APInt &Quotient, APInt &Remainder) {
1890  if (LHS.isNegative()) {
1891  if (RHS.isNegative())
1892  APInt::udivrem(-LHS, -RHS, Quotient, Remainder);
1893  else {
1894  APInt::udivrem(-LHS, RHS, Quotient, Remainder);
1895  Quotient.negate();
1896  }
1897  Remainder.negate();
1898  } else if (RHS.isNegative()) {
1899  APInt::udivrem(LHS, -RHS, Quotient, Remainder);
1900  Quotient.negate();
1901  } else {
1902  APInt::udivrem(LHS, RHS, Quotient, Remainder);
1903  }
1904 }
1905 
1906 void APInt::sdivrem(const APInt &LHS, int64_t RHS,
1907  APInt &Quotient, int64_t &Remainder) {
1908  uint64_t R = Remainder;
1909  if (LHS.isNegative()) {
1910  if (RHS < 0)
1911  APInt::udivrem(-LHS, -RHS, Quotient, R);
1912  else {
1913  APInt::udivrem(-LHS, RHS, Quotient, R);
1914  Quotient.negate();
1915  }
1916  R = -R;
1917  } else if (RHS < 0) {
1918  APInt::udivrem(LHS, -RHS, Quotient, R);
1919  Quotient.negate();
1920  } else {
1921  APInt::udivrem(LHS, RHS, Quotient, R);
1922  }
1923  Remainder = R;
1924 }
1925 
1926 APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const {
1927  APInt Res = *this+RHS;
1928  Overflow = isNonNegative() == RHS.isNonNegative() &&
1929  Res.isNonNegative() != isNonNegative();
1930  return Res;
1931 }
1932 
1933 APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const {
1934  APInt Res = *this+RHS;
1935  Overflow = Res.ult(RHS);
1936  return Res;
1937 }
1938 
1939 APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const {
1940  APInt Res = *this - RHS;
1941  Overflow = isNonNegative() != RHS.isNonNegative() &&
1942  Res.isNonNegative() != isNonNegative();
1943  return Res;
1944 }
1945 
1946 APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const {
1947  APInt Res = *this-RHS;
1948  Overflow = Res.ugt(*this);
1949  return Res;
1950 }
1951 
1952 APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const {
1953  // MININT/-1 --> overflow.
1954  Overflow = isMinSignedValue() && RHS.isAllOnes();
1955  return sdiv(RHS);
1956 }
1957 
1958 APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const {
1959  APInt Res = *this * RHS;
1960 
1961  if (RHS != 0)
1962  Overflow = Res.sdiv(RHS) != *this ||
1963  (isMinSignedValue() && RHS.isAllOnes());
1964  else
1965  Overflow = false;
1966  return Res;
1967 }
1968 
1969 APInt APInt::umul_ov(const APInt &RHS, bool &Overflow) const {
1970  if (countLeadingZeros() + RHS.countLeadingZeros() + 2 <= BitWidth) {
1971  Overflow = true;
1972  return *this * RHS;
1973  }
1974 
1975  APInt Res = lshr(1) * RHS;
1976  Overflow = Res.isNegative();
1977  Res <<= 1;
1978  if ((*this)[0]) {
1979  Res += RHS;
1980  if (Res.ult(RHS))
1981  Overflow = true;
1982  }
1983  return Res;
1984 }
1985 
1986 APInt APInt::sshl_ov(const APInt &ShAmt, bool &Overflow) const {
1987  Overflow = ShAmt.uge(getBitWidth());
1988  if (Overflow)
1989  return APInt(BitWidth, 0);
1990 
1991  if (isNonNegative()) // Don't allow sign change.
1992  Overflow = ShAmt.uge(countLeadingZeros());
1993  else
1994  Overflow = ShAmt.uge(countLeadingOnes());
1995 
1996  return *this << ShAmt;
1997 }
1998 
1999 APInt APInt::ushl_ov(const APInt &ShAmt, bool &Overflow) const {
2000  Overflow = ShAmt.uge(getBitWidth());
2001  if (Overflow)
2002  return APInt(BitWidth, 0);
2003 
2004  Overflow = ShAmt.ugt(countLeadingZeros());
2005 
2006  return *this << ShAmt;
2007 }
2008 
2010  bool Overflow;
2011  APInt Res = sadd_ov(RHS, Overflow);
2012  if (!Overflow)
2013  return Res;
2014 
2015  return isNegative() ? APInt::getSignedMinValue(BitWidth)
2016  : APInt::getSignedMaxValue(BitWidth);
2017 }
2018 
2020  bool Overflow;
2021  APInt Res = uadd_ov(RHS, Overflow);
2022  if (!Overflow)
2023  return Res;
2024 
2025  return APInt::getMaxValue(BitWidth);
2026 }
2027 
2029  bool Overflow;
2030  APInt Res = ssub_ov(RHS, Overflow);
2031  if (!Overflow)
2032  return Res;
2033 
2034  return isNegative() ? APInt::getSignedMinValue(BitWidth)
2035  : APInt::getSignedMaxValue(BitWidth);
2036 }
2037 
2039  bool Overflow;
2040  APInt Res = usub_ov(RHS, Overflow);
2041  if (!Overflow)
2042  return Res;
2043 
2044  return APInt(BitWidth, 0);
2045 }
2046 
2048  bool Overflow;
2049  APInt Res = smul_ov(RHS, Overflow);
2050  if (!Overflow)
2051  return Res;
2052 
2053  // The result is negative if one and only one of inputs is negative.
2054  bool ResIsNegative = isNegative() ^ RHS.isNegative();
2055 
2056  return ResIsNegative ? APInt::getSignedMinValue(BitWidth)
2057  : APInt::getSignedMaxValue(BitWidth);
2058 }
2059 
2061  bool Overflow;
2062  APInt Res = umul_ov(RHS, Overflow);
2063  if (!Overflow)
2064  return Res;
2065 
2066  return APInt::getMaxValue(BitWidth);
2067 }
2068 
2070  bool Overflow;
2071  APInt Res = sshl_ov(RHS, Overflow);
2072  if (!Overflow)
2073  return Res;
2074 
2075  return isNegative() ? APInt::getSignedMinValue(BitWidth)
2076  : APInt::getSignedMaxValue(BitWidth);
2077 }
2078 
2080  bool Overflow;
2081  APInt Res = ushl_ov(RHS, Overflow);
2082  if (!Overflow)
2083  return Res;
2084 
2085  return APInt::getMaxValue(BitWidth);
2086 }
2087 
2088 void APInt::fromString(unsigned numbits, StringRef str, uint8_t radix) {
2089  // Check our assumptions here
2090  assert(!str.empty() && "Invalid string length");
2091  assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||
2092  radix == 36) &&
2093  "Radix should be 2, 8, 10, 16, or 36!");
2094 
2095  StringRef::iterator p = str.begin();
2096  size_t slen = str.size();
2097  bool isNeg = *p == '-';
2098  if (*p == '-' || *p == '+') {
2099  p++;
2100  slen--;
2101  assert(slen && "String is only a sign, needs a value.");
2102  }
2103  assert((slen <= numbits || radix != 2) && "Insufficient bit width");
2104  assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width");
2105  assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width");
2106  assert((((slen-1)*64)/22 <= numbits || radix != 10) &&
2107  "Insufficient bit width");
2108 
2109  // Allocate memory if needed
2110  if (isSingleWord())
2111  U.VAL = 0;
2112  else
2113  U.pVal = getClearedMemory(getNumWords());
2114 
2115  // Figure out if we can shift instead of multiply
2116  unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
2117 
2118  // Enter digit traversal loop
2119  for (StringRef::iterator e = str.end(); p != e; ++p) {
2120  unsigned digit = getDigit(*p, radix);
2121  assert(digit < radix && "Invalid character in digit string");
2122 
2123  // Shift or multiply the value by the radix
2124  if (slen > 1) {
2125  if (shift)
2126  *this <<= shift;
2127  else
2128  *this *= radix;
2129  }
2130 
2131  // Add in the digit we just interpreted
2132  *this += digit;
2133  }
2134  // If its negative, put it in two's complement form
2135  if (isNeg)
2136  this->negate();
2137 }
2138 
2139 void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix,
2140  bool Signed, bool formatAsCLiteral) const {
2141  assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2 ||
2142  Radix == 36) &&
2143  "Radix should be 2, 8, 10, 16, or 36!");
2144 
2145  const char *Prefix = "";
2146  if (formatAsCLiteral) {
2147  switch (Radix) {
2148  case 2:
2149  // Binary literals are a non-standard extension added in gcc 4.3:
2150  // http://gcc.gnu.org/onlinedocs/gcc-4.3.0/gcc/Binary-constants.html
2151  Prefix = "0b";
2152  break;
2153  case 8:
2154  Prefix = "0";
2155  break;
2156  case 10:
2157  break; // No prefix
2158  case 16:
2159  Prefix = "0x";
2160  break;
2161  default:
2162  llvm_unreachable("Invalid radix!");
2163  }
2164  }
2165 
2166  // First, check for a zero value and just short circuit the logic below.
2167  if (isZero()) {
2168  while (*Prefix) {
2169  Str.push_back(*Prefix);
2170  ++Prefix;
2171  };
2172  Str.push_back('0');
2173  return;
2174  }
2175 
2176  static const char Digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
2177 
2178  if (isSingleWord()) {
2179  char Buffer[65];
2180  char *BufPtr = std::end(Buffer);
2181 
2182  uint64_t N;
2183  if (!Signed) {
2184  N = getZExtValue();
2185  } else {
2186  int64_t I = getSExtValue();
2187  if (I >= 0) {
2188  N = I;
2189  } else {
2190  Str.push_back('-');
2191  N = -(uint64_t)I;
2192  }
2193  }
2194 
2195  while (*Prefix) {
2196  Str.push_back(*Prefix);
2197  ++Prefix;
2198  };
2199 
2200  while (N) {
2201  *--BufPtr = Digits[N % Radix];
2202  N /= Radix;
2203  }
2204  Str.append(BufPtr, std::end(Buffer));
2205  return;
2206  }
2207 
2208  APInt Tmp(*this);
2209 
2210  if (Signed && isNegative()) {
2211  // They want to print the signed version and it is a negative value
2212  // Flip the bits and add one to turn it into the equivalent positive
2213  // value and put a '-' in the result.
2214  Tmp.negate();
2215  Str.push_back('-');
2216  }
2217 
2218  while (*Prefix) {
2219  Str.push_back(*Prefix);
2220  ++Prefix;
2221  };
2222 
2223  // We insert the digits backward, then reverse them to get the right order.
2224  unsigned StartDig = Str.size();
2225 
2226  // For the 2, 8 and 16 bit cases, we can just shift instead of divide
2227  // because the number of bits per digit (1, 3 and 4 respectively) divides
2228  // equally. We just shift until the value is zero.
2229  if (Radix == 2 || Radix == 8 || Radix == 16) {
2230  // Just shift tmp right for each digit width until it becomes zero
2231  unsigned ShiftAmt = (Radix == 16 ? 4 : (Radix == 8 ? 3 : 1));
2232  unsigned MaskAmt = Radix - 1;
2233 
2234  while (Tmp.getBoolValue()) {
2235  unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt;
2236  Str.push_back(Digits[Digit]);
2237  Tmp.lshrInPlace(ShiftAmt);
2238  }
2239  } else {
2240  while (Tmp.getBoolValue()) {
2241  uint64_t Digit;
2242  udivrem(Tmp, Radix, Tmp, Digit);
2243  assert(Digit < Radix && "divide failed");
2244  Str.push_back(Digits[Digit]);
2245  }
2246  }
2247 
2248  // Reverse the digits before returning.
2249  std::reverse(Str.begin()+StartDig, Str.end());
2250 }
2251 
2252 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
2254  SmallString<40> S, U;
2255  this->toStringUnsigned(U);
2256  this->toStringSigned(S);
2257  dbgs() << "APInt(" << BitWidth << "b, "
2258  << U << "u " << S << "s)\n";
2259 }
2260 #endif
2261 
2262 void APInt::print(raw_ostream &OS, bool isSigned) const {
2264  this->toString(S, 10, isSigned, /* formatAsCLiteral = */false);
2265  OS << S;
2266 }
2267 
2268 // This implements a variety of operations on a representation of
2269 // arbitrary precision, two's-complement, bignum integer values.
2270 
2271 // Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe
2272 // and unrestricting assumption.
2273 static_assert(APInt::APINT_BITS_PER_WORD % 2 == 0,
2274  "Part width must be divisible by 2!");
2275 
2276 // Returns the integer part with the least significant BITS set.
2277 // BITS cannot be zero.
2278 static inline APInt::WordType lowBitMask(unsigned bits) {
2280  return ~(APInt::WordType) 0 >> (APInt::APINT_BITS_PER_WORD - bits);
2281 }
2282 
2283 /// Returns the value of the lower half of PART.
2285  return part & lowBitMask(APInt::APINT_BITS_PER_WORD / 2);
2286 }
2287 
2288 /// Returns the value of the upper half of PART.
2290  return part >> (APInt::APINT_BITS_PER_WORD / 2);
2291 }
2292 
2293 /// Returns the bit number of the most significant set bit of a part.
2294 /// If the input number has no bits set -1U is returned.
2295 static unsigned partMSB(APInt::WordType value) {
2296  return findLastSet(value, ZB_Max);
2297 }
2298 
2299 /// Returns the bit number of the least significant set bit of a part. If the
2300 /// input number has no bits set -1U is returned.
2301 static unsigned partLSB(APInt::WordType value) {
2302  return findFirstSet(value, ZB_Max);
2303 }
2304 
2305 /// Sets the least significant part of a bignum to the input value, and zeroes
2306 /// out higher parts.
2307 void APInt::tcSet(WordType *dst, WordType part, unsigned parts) {
2308  assert(parts > 0);
2309  dst[0] = part;
2310  for (unsigned i = 1; i < parts; i++)
2311  dst[i] = 0;
2312 }
2313 
2314 /// Assign one bignum to another.
2315 void APInt::tcAssign(WordType *dst, const WordType *src, unsigned parts) {
2316  for (unsigned i = 0; i < parts; i++)
2317  dst[i] = src[i];
2318 }
2319 
2320 /// Returns true if a bignum is zero, false otherwise.
2321 bool APInt::tcIsZero(const WordType *src, unsigned parts) {
2322  for (unsigned i = 0; i < parts; i++)
2323  if (src[i])
2324  return false;
2325 
2326  return true;
2327 }
2328 
2329 /// Extract the given bit of a bignum; returns 0 or 1.
2330 int APInt::tcExtractBit(const WordType *parts, unsigned bit) {
2331  return (parts[whichWord(bit)] & maskBit(bit)) != 0;
2332 }
2333 
2334 /// Set the given bit of a bignum.
2335 void APInt::tcSetBit(WordType *parts, unsigned bit) {
2336  parts[whichWord(bit)] |= maskBit(bit);
2337 }
2338 
2339 /// Clears the given bit of a bignum.
2340 void APInt::tcClearBit(WordType *parts, unsigned bit) {
2341  parts[whichWord(bit)] &= ~maskBit(bit);
2342 }
2343 
2344 /// Returns the bit number of the least significant set bit of a number. If the
2345 /// input number has no bits set -1U is returned.
2346 unsigned APInt::tcLSB(const WordType *parts, unsigned n) {
2347  for (unsigned i = 0; i < n; i++) {
2348  if (parts[i] != 0) {
2349  unsigned lsb = partLSB(parts[i]);
2350  return lsb + i * APINT_BITS_PER_WORD;
2351  }
2352  }
2353 
2354  return -1U;
2355 }
2356 
2357 /// Returns the bit number of the most significant set bit of a number.
2358 /// If the input number has no bits set -1U is returned.
2359 unsigned APInt::tcMSB(const WordType *parts, unsigned n) {
2360  do {
2361  --n;
2362 
2363  if (parts[n] != 0) {
2364  unsigned msb = partMSB(parts[n]);
2365 
2366  return msb + n * APINT_BITS_PER_WORD;
2367  }
2368  } while (n);
2369 
2370  return -1U;
2371 }
2372 
2373 /// Copy the bit vector of width srcBITS from SRC, starting at bit srcLSB, to
2374 /// DST, of dstCOUNT parts, such that the bit srcLSB becomes the least
2375 /// significant bit of DST. All high bits above srcBITS in DST are zero-filled.
2376 /// */
2377 void
2378 APInt::tcExtract(WordType *dst, unsigned dstCount, const WordType *src,
2379  unsigned srcBits, unsigned srcLSB) {
2380  unsigned dstParts = (srcBits + APINT_BITS_PER_WORD - 1) / APINT_BITS_PER_WORD;
2381  assert(dstParts <= dstCount);
2382 
2383  unsigned firstSrcPart = srcLSB / APINT_BITS_PER_WORD;
2384  tcAssign(dst, src + firstSrcPart, dstParts);
2385 
2386  unsigned shift = srcLSB % APINT_BITS_PER_WORD;
2387  tcShiftRight(dst, dstParts, shift);
2388 
2389  // We now have (dstParts * APINT_BITS_PER_WORD - shift) bits from SRC
2390  // in DST. If this is less that srcBits, append the rest, else
2391  // clear the high bits.
2392  unsigned n = dstParts * APINT_BITS_PER_WORD - shift;
2393  if (n < srcBits) {
2394  WordType mask = lowBitMask (srcBits - n);
2395  dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask)
2396  << n % APINT_BITS_PER_WORD);
2397  } else if (n > srcBits) {
2398  if (srcBits % APINT_BITS_PER_WORD)
2399  dst[dstParts - 1] &= lowBitMask (srcBits % APINT_BITS_PER_WORD);
2400  }
2401 
2402  // Clear high parts.
2403  while (dstParts < dstCount)
2404  dst[dstParts++] = 0;
2405 }
2406 
2407 //// DST += RHS + C where C is zero or one. Returns the carry flag.
2409  WordType c, unsigned parts) {
2410  assert(c <= 1);
2411 
2412  for (unsigned i = 0; i < parts; i++) {
2413  WordType l = dst[i];
2414  if (c) {
2415  dst[i] += rhs[i] + 1;
2416  c = (dst[i] <= l);
2417  } else {
2418  dst[i] += rhs[i];
2419  c = (dst[i] < l);
2420  }
2421  }
2422 
2423  return c;
2424 }
2425 
2426 /// This function adds a single "word" integer, src, to the multiple
2427 /// "word" integer array, dst[]. dst[] is modified to reflect the addition and
2428 /// 1 is returned if there is a carry out, otherwise 0 is returned.
2429 /// @returns the carry of the addition.
2431  unsigned parts) {
2432  for (unsigned i = 0; i < parts; ++i) {
2433  dst[i] += src;
2434  if (dst[i] >= src)
2435  return 0; // No need to carry so exit early.
2436  src = 1; // Carry one to next digit.
2437  }
2438 
2439  return 1;
2440 }
2441 
2442 /// DST -= RHS + C where C is zero or one. Returns the carry flag.
2444  WordType c, unsigned parts) {
2445  assert(c <= 1);
2446 
2447  for (unsigned i = 0; i < parts; i++) {
2448  WordType l = dst[i];
2449  if (c) {
2450  dst[i] -= rhs[i] + 1;
2451  c = (dst[i] >= l);
2452  } else {
2453  dst[i] -= rhs[i];
2454  c = (dst[i] > l);
2455  }
2456  }
2457 
2458  return c;
2459 }
2460 
2461 /// This function subtracts a single "word" (64-bit word), src, from
2462 /// the multi-word integer array, dst[], propagating the borrowed 1 value until
2463 /// no further borrowing is needed or it runs out of "words" in dst. The result
2464 /// is 1 if "borrowing" exhausted the digits in dst, or 0 if dst was not
2465 /// exhausted. In other words, if src > dst then this function returns 1,
2466 /// otherwise 0.
2467 /// @returns the borrow out of the subtraction
2469  unsigned parts) {
2470  for (unsigned i = 0; i < parts; ++i) {
2471  WordType Dst = dst[i];
2472  dst[i] -= src;
2473  if (src <= Dst)
2474  return 0; // No need to borrow so exit early.
2475  src = 1; // We have to "borrow 1" from next "word"
2476  }
2477 
2478  return 1;
2479 }
2480 
2481 /// Negate a bignum in-place.
2482 void APInt::tcNegate(WordType *dst, unsigned parts) {
2483  tcComplement(dst, parts);
2484  tcIncrement(dst, parts);
2485 }
2486 
2487 /// DST += SRC * MULTIPLIER + CARRY if add is true
2488 /// DST = SRC * MULTIPLIER + CARRY if add is false
2489 /// Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC
2490 /// they must start at the same point, i.e. DST == SRC.
2491 /// If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is
2492 /// returned. Otherwise DST is filled with the least significant
2493 /// DSTPARTS parts of the result, and if all of the omitted higher
2494 /// parts were zero return zero, otherwise overflow occurred and
2495 /// return one.
2497  WordType multiplier, WordType carry,
2498  unsigned srcParts, unsigned dstParts,
2499  bool add) {
2500  // Otherwise our writes of DST kill our later reads of SRC.
2501  assert(dst <= src || dst >= src + srcParts);
2502  assert(dstParts <= srcParts + 1);
2503 
2504  // N loops; minimum of dstParts and srcParts.
2505  unsigned n = std::min(dstParts, srcParts);
2506 
2507  for (unsigned i = 0; i < n; i++) {
2508  // [LOW, HIGH] = MULTIPLIER * SRC[i] + DST[i] + CARRY.
2509  // This cannot overflow, because:
2510  // (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1)
2511  // which is less than n^2.
2512  WordType srcPart = src[i];
2513  WordType low, mid, high;
2514  if (multiplier == 0 || srcPart == 0) {
2515  low = carry;
2516  high = 0;
2517  } else {
2518  low = lowHalf(srcPart) * lowHalf(multiplier);
2519  high = highHalf(srcPart) * highHalf(multiplier);
2520 
2521  mid = lowHalf(srcPart) * highHalf(multiplier);
2522  high += highHalf(mid);
2523  mid <<= APINT_BITS_PER_WORD / 2;
2524  if (low + mid < low)
2525  high++;
2526  low += mid;
2527 
2528  mid = highHalf(srcPart) * lowHalf(multiplier);
2529  high += highHalf(mid);
2530  mid <<= APINT_BITS_PER_WORD / 2;
2531  if (low + mid < low)
2532  high++;
2533  low += mid;
2534 
2535  // Now add carry.
2536  if (low + carry < low)
2537  high++;
2538  low += carry;
2539  }
2540 
2541  if (add) {
2542  // And now DST[i], and store the new low part there.
2543  if (low + dst[i] < low)
2544  high++;
2545  dst[i] += low;
2546  } else
2547  dst[i] = low;
2548 
2549  carry = high;
2550  }
2551 
2552  if (srcParts < dstParts) {
2553  // Full multiplication, there is no overflow.
2554  assert(srcParts + 1 == dstParts);
2555  dst[srcParts] = carry;
2556  return 0;
2557  }
2558 
2559  // We overflowed if there is carry.
2560  if (carry)
2561  return 1;
2562 
2563  // We would overflow if any significant unwritten parts would be
2564  // non-zero. This is true if any remaining src parts are non-zero
2565  // and the multiplier is non-zero.
2566  if (multiplier)
2567  for (unsigned i = dstParts; i < srcParts; i++)
2568  if (src[i])
2569  return 1;
2570 
2571  // We fitted in the narrow destination.
2572  return 0;
2573 }
2574 
2575 /// DST = LHS * RHS, where DST has the same width as the operands and
2576 /// is filled with the least significant parts of the result. Returns
2577 /// one if overflow occurred, otherwise zero. DST must be disjoint
2578 /// from both operands.
2579 int APInt::tcMultiply(WordType *dst, const WordType *lhs,
2580  const WordType *rhs, unsigned parts) {
2581  assert(dst != lhs && dst != rhs);
2582 
2583  int overflow = 0;
2584  tcSet(dst, 0, parts);
2585 
2586  for (unsigned i = 0; i < parts; i++)
2587  overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts,
2588  parts - i, true);
2589 
2590  return overflow;
2591 }
2592 
2593 /// DST = LHS * RHS, where DST has width the sum of the widths of the
2594 /// operands. No overflow occurs. DST must be disjoint from both operands.
2596  const WordType *rhs, unsigned lhsParts,
2597  unsigned rhsParts) {
2598  // Put the narrower number on the LHS for less loops below.
2599  if (lhsParts > rhsParts)
2600  return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts);
2601 
2602  assert(dst != lhs && dst != rhs);
2603 
2604  tcSet(dst, 0, rhsParts);
2605 
2606  for (unsigned i = 0; i < lhsParts; i++)
2607  tcMultiplyPart(&dst[i], rhs, lhs[i], 0, rhsParts, rhsParts + 1, true);
2608 }
2609 
2610 // If RHS is zero LHS and REMAINDER are left unchanged, return one.
2611 // Otherwise set LHS to LHS / RHS with the fractional part discarded,
2612 // set REMAINDER to the remainder, return zero. i.e.
2613 //
2614 // OLD_LHS = RHS * LHS + REMAINDER
2615 //
2616 // SCRATCH is a bignum of the same size as the operands and result for
2617 // use by the routine; its contents need not be initialized and are
2618 // destroyed. LHS, REMAINDER and SCRATCH must be distinct.
2619 int APInt::tcDivide(WordType *lhs, const WordType *rhs,
2620  WordType *remainder, WordType *srhs,
2621  unsigned parts) {
2622  assert(lhs != remainder && lhs != srhs && remainder != srhs);
2623 
2624  unsigned shiftCount = tcMSB(rhs, parts) + 1;
2625  if (shiftCount == 0)
2626  return true;
2627 
2628  shiftCount = parts * APINT_BITS_PER_WORD - shiftCount;
2629  unsigned n = shiftCount / APINT_BITS_PER_WORD;
2630  WordType mask = (WordType) 1 << (shiftCount % APINT_BITS_PER_WORD);
2631 
2632  tcAssign(srhs, rhs, parts);
2633  tcShiftLeft(srhs, parts, shiftCount);
2634  tcAssign(remainder, lhs, parts);
2635  tcSet(lhs, 0, parts);
2636 
2637  // Loop, subtracting SRHS if REMAINDER is greater and adding that to the
2638  // total.
2639  for (;;) {
2640  int compare = tcCompare(remainder, srhs, parts);
2641  if (compare >= 0) {
2642  tcSubtract(remainder, srhs, 0, parts);
2643  lhs[n] |= mask;
2644  }
2645 
2646  if (shiftCount == 0)
2647  break;
2648  shiftCount--;
2649  tcShiftRight(srhs, parts, 1);
2650  if ((mask >>= 1) == 0) {
2651  mask = (WordType) 1 << (APINT_BITS_PER_WORD - 1);
2652  n--;
2653  }
2654  }
2655 
2656  return false;
2657 }
2658 
2659 /// Shift a bignum left Cound bits in-place. Shifted in bits are zero. There are
2660 /// no restrictions on Count.
2661 void APInt::tcShiftLeft(WordType *Dst, unsigned Words, unsigned Count) {
2662  // Don't bother performing a no-op shift.
2663  if (!Count)
2664  return;
2665 
2666  // WordShift is the inter-part shift; BitShift is the intra-part shift.
2667  unsigned WordShift = std::min(Count / APINT_BITS_PER_WORD, Words);
2668  unsigned BitShift = Count % APINT_BITS_PER_WORD;
2669 
2670  // Fastpath for moving by whole words.
2671  if (BitShift == 0) {
2672  std::memmove(Dst + WordShift, Dst, (Words - WordShift) * APINT_WORD_SIZE);
2673  } else {
2674  while (Words-- > WordShift) {
2675  Dst[Words] = Dst[Words - WordShift] << BitShift;
2676  if (Words > WordShift)
2677  Dst[Words] |=
2678  Dst[Words - WordShift - 1] >> (APINT_BITS_PER_WORD - BitShift);
2679  }
2680  }
2681 
2682  // Fill in the remainder with 0s.
2683  std::memset(Dst, 0, WordShift * APINT_WORD_SIZE);
2684 }
2685 
2686 /// Shift a bignum right Count bits in-place. Shifted in bits are zero. There
2687 /// are no restrictions on Count.
2688 void APInt::tcShiftRight(WordType *Dst, unsigned Words, unsigned Count) {
2689  // Don't bother performing a no-op shift.
2690  if (!Count)
2691  return;
2692 
2693  // WordShift is the inter-part shift; BitShift is the intra-part shift.
2694  unsigned WordShift = std::min(Count / APINT_BITS_PER_WORD, Words);
2695  unsigned BitShift = Count % APINT_BITS_PER_WORD;
2696 
2697  unsigned WordsToMove = Words - WordShift;
2698  // Fastpath for moving by whole words.
2699  if (BitShift == 0) {
2700  std::memmove(Dst, Dst + WordShift, WordsToMove * APINT_WORD_SIZE);
2701  } else {
2702  for (unsigned i = 0; i != WordsToMove; ++i) {
2703  Dst[i] = Dst[i + WordShift] >> BitShift;
2704  if (i + 1 != WordsToMove)
2705  Dst[i] |= Dst[i + WordShift + 1] << (APINT_BITS_PER_WORD - BitShift);
2706  }
2707  }
2708 
2709  // Fill in the remainder with 0s.
2710  std::memset(Dst + WordsToMove, 0, WordShift * APINT_WORD_SIZE);
2711 }
2712 
2713 // Comparison (unsigned) of two bignums.
2714 int APInt::tcCompare(const WordType *lhs, const WordType *rhs,
2715  unsigned parts) {
2716  while (parts) {
2717  parts--;
2718  if (lhs[parts] != rhs[parts])
2719  return (lhs[parts] > rhs[parts]) ? 1 : -1;
2720  }
2721 
2722  return 0;
2723 }
2724 
2726  APInt::Rounding RM) {
2727  // Currently udivrem always rounds down.
2728  switch (RM) {
2729  case APInt::Rounding::DOWN:
2731  return A.udiv(B);
2732  case APInt::Rounding::UP: {
2733  APInt Quo, Rem;
2734  APInt::udivrem(A, B, Quo, Rem);
2735  if (Rem.isZero())
2736  return Quo;
2737  return Quo + 1;
2738  }
2739  }
2740  llvm_unreachable("Unknown APInt::Rounding enum");
2741 }
2742 
2744  APInt::Rounding RM) {
2745  switch (RM) {
2746  case APInt::Rounding::DOWN:
2747  case APInt::Rounding::UP: {
2748  APInt Quo, Rem;
2749  APInt::sdivrem(A, B, Quo, Rem);
2750  if (Rem.isZero())
2751  return Quo;
2752  // This algorithm deals with arbitrary rounding mode used by sdivrem.
2753  // We want to check whether the non-integer part of the mathematical value
2754  // is negative or not. If the non-integer part is negative, we need to round
2755  // down from Quo; otherwise, if it's positive or 0, we return Quo, as it's
2756  // already rounded down.
2757  if (RM == APInt::Rounding::DOWN) {
2758  if (Rem.isNegative() != B.isNegative())
2759  return Quo - 1;
2760  return Quo;
2761  }
2762  if (Rem.isNegative() != B.isNegative())
2763  return Quo;
2764  return Quo + 1;
2765  }
2766  // Currently sdiv rounds towards zero.
2768  return A.sdiv(B);
2769  }
2770  llvm_unreachable("Unknown APInt::Rounding enum");
2771 }
2772 
2775  unsigned RangeWidth) {
2776  unsigned CoeffWidth = A.getBitWidth();
2777  assert(CoeffWidth == B.getBitWidth() && CoeffWidth == C.getBitWidth());
2778  assert(RangeWidth <= CoeffWidth &&
2779  "Value range width should be less than coefficient width");
2780  assert(RangeWidth > 1 && "Value range bit width should be > 1");
2781 
2782  LLVM_DEBUG(dbgs() << __func__ << ": solving " << A << "x^2 + " << B
2783  << "x + " << C << ", rw:" << RangeWidth << '\n');
2784 
2785  // Identify 0 as a (non)solution immediately.
2786  if (C.sextOrTrunc(RangeWidth).isZero()) {
2787  LLVM_DEBUG(dbgs() << __func__ << ": zero solution\n");
2788  return APInt(CoeffWidth, 0);
2789  }
2790 
2791  // The result of APInt arithmetic has the same bit width as the operands,
2792  // so it can actually lose high bits. A product of two n-bit integers needs
2793  // 2n-1 bits to represent the full value.
2794  // The operation done below (on quadratic coefficients) that can produce
2795  // the largest value is the evaluation of the equation during bisection,
2796  // which needs 3 times the bitwidth of the coefficient, so the total number
2797  // of required bits is 3n.
2798  //
2799  // The purpose of this extension is to simulate the set Z of all integers,
2800  // where n+1 > n for all n in Z. In Z it makes sense to talk about positive
2801  // and negative numbers (not so much in a modulo arithmetic). The method
2802  // used to solve the equation is based on the standard formula for real
2803  // numbers, and uses the concepts of "positive" and "negative" with their
2804  // usual meanings.
2805  CoeffWidth *= 3;
2806  A = A.sext(CoeffWidth);
2807  B = B.sext(CoeffWidth);
2808  C = C.sext(CoeffWidth);
2809 
2810  // Make A > 0 for simplicity. Negate cannot overflow at this point because
2811  // the bit width has increased.
2812  if (A.isNegative()) {
2813  A.negate();
2814  B.negate();
2815  C.negate();
2816  }
2817 
2818  // Solving an equation q(x) = 0 with coefficients in modular arithmetic
2819  // is really solving a set of equations q(x) = kR for k = 0, 1, 2, ...,
2820  // and R = 2^BitWidth.
2821  // Since we're trying not only to find exact solutions, but also values
2822  // that "wrap around", such a set will always have a solution, i.e. an x
2823  // that satisfies at least one of the equations, or such that |q(x)|
2824  // exceeds kR, while |q(x-1)| for the same k does not.
2825  //
2826  // We need to find a value k, such that Ax^2 + Bx + C = kR will have a
2827  // positive solution n (in the above sense), and also such that the n
2828  // will be the least among all solutions corresponding to k = 0, 1, ...
2829  // (more precisely, the least element in the set
2830  // { n(k) | k is such that a solution n(k) exists }).
2831  //
2832  // Consider the parabola (over real numbers) that corresponds to the
2833  // quadratic equation. Since A > 0, the arms of the parabola will point
2834  // up. Picking different values of k will shift it up and down by R.
2835  //
2836  // We want to shift the parabola in such a way as to reduce the problem
2837  // of solving q(x) = kR to solving shifted_q(x) = 0.
2838  // (The interesting solutions are the ceilings of the real number
2839  // solutions.)
2840  APInt R = APInt::getOneBitSet(CoeffWidth, RangeWidth);
2841  APInt TwoA = 2 * A;
2842  APInt SqrB = B * B;
2843  bool PickLow;
2844 
2845  auto RoundUp = [] (const APInt &V, const APInt &A) -> APInt {
2846  assert(A.isStrictlyPositive());
2847  APInt T = V.abs().urem(A);
2848  if (T.isZero())
2849  return V;
2850  return V.isNegative() ? V+T : V+(A-T);
2851  };
2852 
2853  // The vertex of the parabola is at -B/2A, but since A > 0, it's negative
2854  // iff B is positive.
2855  if (B.isNonNegative()) {
2856  // If B >= 0, the vertex it at a negative location (or at 0), so in
2857  // order to have a non-negative solution we need to pick k that makes
2858  // C-kR negative. To satisfy all the requirements for the solution
2859  // that we are looking for, it needs to be closest to 0 of all k.
2860  C = C.srem(R);
2861  if (C.isStrictlyPositive())
2862  C -= R;
2863  // Pick the greater solution.
2864  PickLow = false;
2865  } else {
2866  // If B < 0, the vertex is at a positive location. For any solution
2867  // to exist, the discriminant must be non-negative. This means that
2868  // C-kR <= B^2/4A is a necessary condition for k, i.e. there is a
2869  // lower bound on values of k: kR >= C - B^2/4A.
2870  APInt LowkR = C - SqrB.udiv(2*TwoA); // udiv because all values > 0.
2871  // Round LowkR up (towards +inf) to the nearest kR.
2872  LowkR = RoundUp(LowkR, R);
2873 
2874  // If there exists k meeting the condition above, and such that
2875  // C-kR > 0, there will be two positive real number solutions of
2876  // q(x) = kR. Out of all such values of k, pick the one that makes
2877  // C-kR closest to 0, (i.e. pick maximum k such that C-kR > 0).
2878  // In other words, find maximum k such that LowkR <= kR < C.
2879  if (C.sgt(LowkR)) {
2880  // If LowkR < C, then such a k is guaranteed to exist because
2881  // LowkR itself is a multiple of R.
2882  C -= -RoundUp(-C, R); // C = C - RoundDown(C, R)
2883  // Pick the smaller solution.
2884  PickLow = true;
2885  } else {
2886  // If C-kR < 0 for all potential k's, it means that one solution
2887  // will be negative, while the other will be positive. The positive
2888  // solution will shift towards 0 if the parabola is moved up.
2889  // Pick the kR closest to the lower bound (i.e. make C-kR closest
2890  // to 0, or in other words, out of all parabolas that have solutions,
2891  // pick the one that is the farthest "up").
2892  // Since LowkR is itself a multiple of R, simply take C-LowkR.
2893  C -= LowkR;
2894  // Pick the greater solution.
2895  PickLow = false;
2896  }
2897  }
2898 
2899  LLVM_DEBUG(dbgs() << __func__ << ": updated coefficients " << A << "x^2 + "
2900  << B << "x + " << C << ", rw:" << RangeWidth << '\n');
2901 
2902  APInt D = SqrB - 4*A*C;
2903  assert(D.isNonNegative() && "Negative discriminant");
2904  APInt SQ = D.sqrt();
2905 
2906  APInt Q = SQ * SQ;
2907  bool InexactSQ = Q != D;
2908  // The calculated SQ may actually be greater than the exact (non-integer)
2909  // value. If that's the case, decrement SQ to get a value that is lower.
2910  if (Q.sgt(D))
2911  SQ -= 1;
2912 
2913  APInt X;
2914  APInt Rem;
2915 
2916  // SQ is rounded down (i.e SQ * SQ <= D), so the roots may be inexact.
2917  // When using the quadratic formula directly, the calculated low root
2918  // may be greater than the exact one, since we would be subtracting SQ.
2919  // To make sure that the calculated root is not greater than the exact
2920  // one, subtract SQ+1 when calculating the low root (for inexact value
2921  // of SQ).
2922  if (PickLow)
2923  APInt::sdivrem(-B - (SQ+InexactSQ), TwoA, X, Rem);
2924  else
2925  APInt::sdivrem(-B + SQ, TwoA, X, Rem);
2926 
2927  // The updated coefficients should be such that the (exact) solution is
2928  // positive. Since APInt division rounds towards 0, the calculated one
2929  // can be 0, but cannot be negative.
2930  assert(X.isNonNegative() && "Solution should be non-negative");
2931 
2932  if (!InexactSQ && Rem.isZero()) {
2933  LLVM_DEBUG(dbgs() << __func__ << ": solution (root): " << X << '\n');
2934  return X;
2935  }
2936 
2937  assert((SQ*SQ).sle(D) && "SQ = |_sqrt(D)_|, so SQ*SQ <= D");
2938  // The exact value of the square root of D should be between SQ and SQ+1.
2939  // This implies that the solution should be between that corresponding to
2940  // SQ (i.e. X) and that corresponding to SQ+1.
2941  //
2942  // The calculated X cannot be greater than the exact (real) solution.
2943  // Actually it must be strictly less than the exact solution, while
2944  // X+1 will be greater than or equal to it.
2945 
2946  APInt VX = (A*X + B)*X + C;
2947  APInt VY = VX + TwoA*X + A + B;
2948  bool SignChange =
2949  VX.isNegative() != VY.isNegative() || VX.isZero() != VY.isZero();
2950  // If the sign did not change between X and X+1, X is not a valid solution.
2951  // This could happen when the actual (exact) roots don't have an integer
2952  // between them, so they would both be contained between X and X+1.
2953  if (!SignChange) {
2954  LLVM_DEBUG(dbgs() << __func__ << ": no valid solution\n");
2955  return None;
2956  }
2957 
2958  X += 1;
2959  LLVM_DEBUG(dbgs() << __func__ << ": solution (wrap): " << X << '\n');
2960  return X;
2961 }
2962 
2965  assert(A.getBitWidth() == B.getBitWidth() && "Must have the same bitwidth");
2966  if (A == B)
2967  return llvm::None;
2968  return A.getBitWidth() - ((A ^ B).countLeadingZeros() + 1);
2969 }
2970 
2971 APInt llvm::APIntOps::ScaleBitMask(const APInt &A, unsigned NewBitWidth,
2972  bool MatchAllBits) {
2973  unsigned OldBitWidth = A.getBitWidth();
2974  assert((((OldBitWidth % NewBitWidth) == 0) ||
2975  ((NewBitWidth % OldBitWidth) == 0)) &&
2976  "One size should be a multiple of the other one. "
2977  "Can't do fractional scaling.");
2978 
2979  // Check for matching bitwidths.
2980  if (OldBitWidth == NewBitWidth)
2981  return A;
2982 
2983  APInt NewA = APInt::getZero(NewBitWidth);
2984 
2985  // Check for null input.
2986  if (A.isZero())
2987  return NewA;
2988 
2989  if (NewBitWidth > OldBitWidth) {
2990  // Repeat bits.
2991  unsigned Scale = NewBitWidth / OldBitWidth;
2992  for (unsigned i = 0; i != OldBitWidth; ++i)
2993  if (A[i])
2994  NewA.setBits(i * Scale, (i + 1) * Scale);
2995  } else {
2996  unsigned Scale = OldBitWidth / NewBitWidth;
2997  for (unsigned i = 0; i != NewBitWidth; ++i) {
2998  if (MatchAllBits) {
2999  if (A.extractBits(Scale, i * Scale).isAllOnes())
3000  NewA.setBit(i);
3001  } else {
3002  if (!A.extractBits(Scale, i * Scale).isZero())
3003  NewA.setBit(i);
3004  }
3005  }
3006  }
3007 
3008  return NewA;
3009 }
3010 
3011 /// StoreIntToMemory - Fills the StoreBytes bytes of memory starting from Dst
3012 /// with the integer held in IntVal.
3013 void llvm::StoreIntToMemory(const APInt &IntVal, uint8_t *Dst,
3014  unsigned StoreBytes) {
3015  assert((IntVal.getBitWidth()+7)/8 >= StoreBytes && "Integer too small!");
3016  const uint8_t *Src = (const uint8_t *)IntVal.getRawData();
3017 
3019  // Little-endian host - the source is ordered from LSB to MSB. Order the
3020  // destination from LSB to MSB: Do a straight copy.
3021  memcpy(Dst, Src, StoreBytes);
3022  } else {
3023  // Big-endian host - the source is an array of 64 bit words ordered from
3024  // LSW to MSW. Each word is ordered from MSB to LSB. Order the destination
3025  // from MSB to LSB: Reverse the word order, but not the bytes in a word.
3026  while (StoreBytes > sizeof(uint64_t)) {
3027  StoreBytes -= sizeof(uint64_t);
3028  // May not be aligned so use memcpy.
3029  memcpy(Dst + StoreBytes, Src, sizeof(uint64_t));
3030  Src += sizeof(uint64_t);
3031  }
3032 
3033  memcpy(Dst, Src + sizeof(uint64_t) - StoreBytes, StoreBytes);
3034  }
3035 }
3036 
3037 /// LoadIntFromMemory - Loads the integer stored in the LoadBytes bytes starting
3038 /// from Src into IntVal, which is assumed to be wide enough and to hold zero.
3039 void llvm::LoadIntFromMemory(APInt &IntVal, const uint8_t *Src,
3040  unsigned LoadBytes) {
3041  assert((IntVal.getBitWidth()+7)/8 >= LoadBytes && "Integer too small!");
3042  uint8_t *Dst = reinterpret_cast<uint8_t *>(
3043  const_cast<uint64_t *>(IntVal.getRawData()));
3044 
3046  // Little-endian host - the destination must be ordered from LSB to MSB.
3047  // The source is ordered from LSB to MSB: Do a straight copy.
3048  memcpy(Dst, Src, LoadBytes);
3049  else {
3050  // Big-endian - the destination is an array of 64 bit words ordered from
3051  // LSW to MSW. Each word must be ordered from MSB to LSB. The source is
3052  // ordered from MSB to LSB: Reverse the word order, but not the bytes in
3053  // a word.
3054  while (LoadBytes > sizeof(uint64_t)) {
3055  LoadBytes -= sizeof(uint64_t);
3056  // May not be aligned so use memcpy.
3057  memcpy(Dst, Src + LoadBytes, sizeof(uint64_t));
3058  Dst += sizeof(uint64_t);
3059  }
3060 
3061  memcpy(Dst + sizeof(uint64_t) - LoadBytes, Src, LoadBytes);
3062  }
3063 }
i
i
Definition: README.txt:29
llvm::APInt::reverseBits
APInt reverseBits() const
Definition: APInt.cpp:729
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:234
Signed
@ Signed
Definition: NVPTXISelLowering.cpp:4709
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:492
MathExtras.h
llvm::APInt::sadd_ov
APInt sadd_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1926
llvm
This is an optimization pass for GlobalISel generic memory operations.
Definition: AddressRanges.h:18
llvm::APInt::VAL
uint64_t VAL
Used to store the <= 64 bits integer value.
Definition: APInt.h:1823
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:1756
Optional.h
llvm::APInt::tcAssign
static void tcAssign(WordType *, const WordType *, unsigned)
Assign one bignum to another.
Definition: APInt.cpp:2315
llvm::APInt::byteSwap
APInt byteSwap() const
Definition: APInt.cpp:707
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:1800
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:160
T
llvm::APInt::getNumWords
unsigned getNumWords() const
Get the number of words.
Definition: APInt.h:1418
llvm::APInt::setBits
void setBits(unsigned loBit, unsigned hiBit)
Set the bits from loBit (inclusive) to hiBit (exclusive) to 1.
Definition: APInt.h:1317
llvm::APInt::ule
bool ule(const APInt &RHS) const
Unsigned less or equal comparison.
Definition: APInt.h:1100
llvm::APInt::rotr
APInt rotr(unsigned rotateAmt) const
Rotate right by rotateAmt.
Definition: APInt.cpp:1116
StringRef.h
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:1986
DEBUG_KNUTH
#define DEBUG_KNUTH(X)
llvm::APInt::roundToDouble
double roundToDouble() const
Converts this unsigned APInt to a double value.
Definition: APInt.h:1610
llvm::APInt::tcSetBit
static void tcSetBit(WordType *, unsigned bit)
Set the given bit of a bignum. Zero-based.
Definition: APInt.cpp:2335
llvm::APInt::getSExtValue
int64_t getSExtValue() const
Get sign extended value.
Definition: APInt.h:1478
llvm::APInt::tcDecrement
static WordType tcDecrement(WordType *dst, unsigned parts)
Decrement a bignum in-place. Return the borrow flag.
Definition: APInt.h:1805
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:1824
llvm::APInt::zextOrTrunc
APInt zextOrTrunc(unsigned width) const
Zero extend or truncate to width.
Definition: APInt.cpp:994
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:2307
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:2289
llvm::APInt::getBitWidth
unsigned getBitWidth() const
Return the number of bits in the APInt.
Definition: APInt.h:1411
llvm::sys::path::end
const_iterator end(StringRef path)
Get end iterator over path.
Definition: Path.cpp:235
llvm::APInt::ugt
bool ugt(const APInt &RHS) const
Unsigned greater than comparison.
Definition: APInt.h:1132
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:2619
Hashing.h
llvm::APInt::lshr
APInt lshr(unsigned shiftAmt) const
Logical right-shift function.
Definition: APInt.h:832
RHS
Value * RHS
Definition: X86PartialReduction.cpp:76
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:477
llvm::Lo_32
constexpr uint32_t Lo_32(uint64_t Value)
Return the low 32 bits of a 64 bit value.
Definition: MathExtras.h:336
llvm::hash_value
hash_code hash_value(const APFloat &Arg)
See friend declarations above.
Definition: APFloat.cpp:4828
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:2964
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:2378
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:161
llvm::RISCVFenceField::R
@ R
Definition: RISCVBaseInfo.h:265
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:1103
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:186
llvm::APInt::umul_ov
APInt umul_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1969
llvm::APInt::uge
bool uge(const APInt &RHS) const
Unsigned greater or equal comparison.
Definition: APInt.h:1171
LHS
Value * LHS
Definition: X86PartialReduction.cpp:75
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:2278
llvm::APInt::setBit
void setBit(unsigned BitPosition)
Set the given bit to 1 whose position is given as "bitPosition".
Definition: APInt.h:1280
llvm::APInt::lshrInPlace
void lshrInPlace(unsigned ShiftAmt)
Logical right-shift this APInt by ShiftAmt in place.
Definition: APInt.h:839
bits
demanded bits
Definition: DemandedBits.cpp:57
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:2443
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:2359
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:2038
round
static uint64_t round(uint64_t Acc, uint64_t Input)
Definition: xxhash.cpp:56
llvm::APInt::getHiBits
APInt getHiBits(unsigned numBits) const
Compute an APInt containing numBits highbits from this APInt.
Definition: APInt.cpp:600
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:54
llvm::AMDGPU::PALMD::Key
Key
PAL metadata keys.
Definition: AMDGPUMetadata.h:486
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:2253
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:1466
llvm::raw_ostream
This class implements an extremely fast bulk output stream that can only output to a stream.
Definition: raw_ostream.h:52
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:2284
llvm::APInt::tcClearBit
static void tcClearBit(WordType *, unsigned bit)
Clear the given bit of a bignum. Zero-based.
Definition: APInt.cpp:2340
llvm::APInt::smul_sat
APInt smul_sat(const APInt &RHS) const
Definition: APInt.cpp:2047
rotateModulo
static unsigned rotateModulo(unsigned BitWidth, const APInt &rotateAmt)
Definition: APInt.cpp:1085
llvm::APInt::usub_ov
APInt usub_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1946
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:24
RoundUp
static size_t RoundUp(size_t size, size_t align)
Definition: InstrProfReader.cpp:576
llvm::CallingConv::ID
unsigned ID
LLVM IR allows to use arbitrary numbers as calling convention identifiers.
Definition: CallingConv.h:24
llvm::APInt::sqrt
APInt sqrt() const
Compute the square root.
Definition: APInt.cpp:1161
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:2346
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:2661
llvm::APInt::srem
APInt srem(const APInt &RHS) const
Function for signed remainder operation.
Definition: APInt.cpp:1734
llvm::SmallString
SmallString - A SmallString is just a SmallVector with methods and accessors that make it work better...
Definition: SmallString.h:26
llvm::Hi_32
constexpr uint32_t Hi_32(uint64_t Value)
Return the high 32 bits of a 64 bit value.
Definition: MathExtras.h:331
llvm::APInt::print
void print(raw_ostream &OS, bool isSigned) const
Definition: APInt.cpp:2262
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::StringRef::empty
constexpr bool empty() const
empty - Check if the string is empty.
Definition: StringRef.h:134
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:341
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:502
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:2330
llvm::APInt::operator<<=
APInt & operator<<=(unsigned ShiftAmt)
Left-shift assignment function.
Definition: APInt.h:766
llvm::APInt::sdiv
APInt sdiv(const APInt &RHS) const
Signed division function for APInt.
Definition: APInt.cpp:1642
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:3013
llvm::APIntOps::ScaleBitMask
APInt ScaleBitMask(const APInt &A, unsigned NewBitWidth, bool MatchAllBits=false)
Splat/Merge neighboring bits to widen/narrow the bitmask represented by.
Definition: APInt.cpp:2971
llvm::APInt::getRawData
const uint64_t * getRawData() const
This function returns a pointer to the internal storage of the APInt.
Definition: APInt.h:550
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:2774
llvm::StringRef::end
iterator end() const
Definition: StringRef.h:113
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:2139
llvm::APInt::sdivrem
static void sdivrem(const APInt &LHS, const APInt &RHS, APInt &Quotient, APInt &Remainder)
Definition: APInt.cpp:1888
llvm::APInt::logBase2
unsigned logBase2() const
Definition: APInt.h:1652
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:54
partLSB
static unsigned partLSB(APInt::WordType value)
Returns the bit number of the least significant set bit of a part.
Definition: APInt.cpp:2301
llvm::APInt::negate
void negate()
Negate this APInt in place.
Definition: APInt.h:1393
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:45
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:492
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:2408
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:1293
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:923
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:275
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:1589
llvm::APInt::urem
APInt urem(const APInt &RHS) const
Unsigned remainder operation.
Definition: APInt.cpp:1664
llvm::APInt
Class for arbitrary precision integers.
Definition: APInt.h:75
llvm::AArch64::RM
@ RM
Definition: AArch64ISelLowering.h:478
llvm::ArrayRef< uint64_t >
llvm::APInt::ssub_ov
APInt ssub_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1939
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:153
llvm::StringRef
StringRef - Represent a constant reference to a string, i.e.
Definition: StringRef.h:50
llvm::APInt::sshl_sat
APInt sshl_sat(const APInt &RHS) const
Definition: APInt.cpp:2069
llvm_unreachable
#define llvm_unreachable(msg)
Marks that the current location is not supposed to be reachable.
Definition: ErrorHandling.h:143
uint32_t
llvm::APInt::tcShiftRight
static void tcShiftRight(WordType *, unsigned Words, unsigned Count)
Shift a bignum right Count bits.
Definition: APInt.cpp:2688
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:2079
llvm::FoldingSetNodeID
FoldingSetNodeID - This class is used to gather all the unique data bits of a node.
Definition: FoldingSet.h:318
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:2743
llvm::APInt::tcIsZero
static bool tcIsZero(const WordType *, unsigned)
Returns true if a bignum is zero, false otherwise.
Definition: APInt.cpp:2321
llvm::APInt::umul_sat
APInt umul_sat(const APInt &RHS) const
Definition: APInt.cpp:2060
llvm::APInt::ult
bool ult(const APInt &RHS) const
Unsigned less than comparison.
Definition: APInt.h:1061
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:719
llvm::APInt::udiv
APInt udiv(const APInt &RHS) const
Unsigned division operation.
Definition: APInt.cpp:1571
FoldingSet.h
llvm::APInt::zext
APInt zext(unsigned width) const
Zero extend to a new width.
Definition: APInt.cpp:973
llvm::APInt::uadd_ov
APInt uadd_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1933
llvm::APInt::Rounding::DOWN
@ DOWN
llvm::StringRef::size
constexpr size_t size() const
size - Get the string size.
Definition: StringRef.h:137
llvm::APInt::ssub_sat
APInt ssub_sat(const APInt &RHS) const
Definition: APInt.cpp:2028
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:2579
j
return j(j<< 16)
llvm::tgtok::IntVal
@ IntVal
Definition: TGLexer.h:65
llvm::APInt::countLeadingZeros
unsigned countLeadingZeros() const
The APInt version of the countLeadingZeros functions in MathExtras.h.
Definition: APInt.h:1504
llvm::APInt::tcCompare
static int tcCompare(const WordType *, const WordType *, unsigned)
Comparison (unsigned) of two bignums.
Definition: APInt.cpp:2714
llvm::APInt::uadd_sat
APInt uadd_sat(const APInt &RHS) const
Definition: APInt.cpp:2019
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:1242
llvm::APInt::tcSubtractPart
static WordType tcSubtractPart(WordType *, WordType, unsigned)
DST -= RHS. Returns the carry flag.
Definition: APInt.cpp:2468
llvm::APInt::trunc
APInt trunc(unsigned width) const
Truncate to new width.
Definition: APInt.cpp:898
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:934
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:2496
bit.h
llvm::APInt::sextOrTrunc
APInt sextOrTrunc(unsigned width) const
Sign extend or truncate to width.
Definition: APInt.cpp:1002
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:1958
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:3039
llvm::APInt::getLoBits
APInt getLoBits(unsigned numBits) const
Compute an APInt containing numBits lowbits from this APInt.
Definition: APInt.cpp:605
llvm::APInt::getSplat
static APInt getSplat(unsigned NewLen, const APInt &V)
Return a value containing V broadcasted over NewLen bits.
Definition: APInt.cpp:612
llvm::APIntOps::RoundDoubleToAPInt
APInt RoundDoubleToAPInt(double Double, unsigned width)
Converts the given double value into a APInt.
Definition: APInt.cpp:802
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:221
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:439
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:946
llvm::makeArrayRef
ArrayRef< T > makeArrayRef(const T &OneElt)
Construct an ArrayRef from a single element.
Definition: ArrayRef.h:475
llvm::APInt::abs
APInt abs() const
Get the absolute value.
Definition: APInt.h:1686
llvm::APInt::sdiv_ov
APInt sdiv_ov(const APInt &RHS, bool &Overflow) const
Definition: APInt.cpp:1952
isSigned
static bool isSigned(unsigned int Opcode)
Definition: ExpandLargeDivRem.cpp:52
llvm::APInt::getBitsNeeded
static unsigned getBitsNeeded(StringRef str, uint8_t radix)
Get bits required for string value.
Definition: APInt.cpp:537
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:2295
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:2430
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:759
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:2595
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::getSufficientBitsNeeded
static unsigned getSufficientBitsNeeded(StringRef Str, uint8_t Radix)
Get the bits that are sufficient to represent the string value.
Definition: APInt.cpp:505
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:164
llvm::APInt::getActiveBits
unsigned getActiveBits() const
Compute the number of active bits in the value.
Definition: APInt.h:1435
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:1595
llvm::APInt::WordType
uint64_t WordType
Definition: APInt.h:77
llvm::SmallVectorImpl< char >
llvm::reverse
auto reverse(ContainerTy &&C)
Definition: STLExtras.h:365
llvm::APInt::sgt
bool sgt(const APInt &RHS) const
Signed greater than comparison.
Definition: APInt.h:1151
llvm::APInt::sadd_sat
APInt sadd_sat(const APInt &RHS) const
Definition: APInt.cpp:2009
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:2725
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:854
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:1288
LLVM_UNLIKELY
#define LLVM_UNLIKELY(EXPR)
Definition: Compiler.h:210
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:815
llvm::APInt::isSplat
bool isSplat(unsigned SplatSizeInBits) const
Check if the APInt consists of a repeated bit pattern.
Definition: APInt.cpp:591
llvm::APInt::countLeadingOnes
unsigned countLeadingOnes() const
Count the number of leading one bits.
Definition: APInt.h:1520
llvm::StringRef::begin
iterator begin() const
Definition: StringRef.h:111
llvm::APInt::nearestLogBase2
unsigned nearestLogBase2() const
Definition: APInt.cpp:1134
llvm::APInt::ushl_ov
APInt ushl_ov(const APInt &Amt, bool &Overflow) const
Definition: APInt.cpp:1999
Debug.h
llvm::APInt::tcNegate
static void tcNegate(WordType *, unsigned)
Negate a bignum in-place.
Definition: APInt.cpp:2482
llvm::APInt::Rounding
Rounding
Definition: APInt.h:87
llvm::hash_code
An opaque object representing a hash code.
Definition: Hashing.h:73