Bug Summary

File:llvm/lib/Support/APInt.cpp
Warning:line 1427, column 22
The result of the right shift is undefined due to shifting by '32', which is greater or equal to the width of type 'uint32_t'

Annotated Source Code

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clang -cc1 -cc1 -triple x86_64-pc-linux-gnu -analyze -disable-free -clear-ast-before-backend -disable-llvm-verifier -discard-value-names -main-file-name APInt.cpp -analyzer-store=region -analyzer-opt-analyze-nested-blocks -analyzer-checker=core -analyzer-checker=apiModeling -analyzer-checker=unix -analyzer-checker=deadcode -analyzer-checker=cplusplus -analyzer-checker=security.insecureAPI.UncheckedReturn -analyzer-checker=security.insecureAPI.getpw -analyzer-checker=security.insecureAPI.gets -analyzer-checker=security.insecureAPI.mktemp -analyzer-checker=security.insecureAPI.mkstemp -analyzer-checker=security.insecureAPI.vfork -analyzer-checker=nullability.NullPassedToNonnull -analyzer-checker=nullability.NullReturnedFromNonnull -analyzer-output plist -w -setup-static-analyzer -analyzer-config-compatibility-mode=true -mrelocation-model pic -pic-level 2 -mframe-pointer=none -fmath-errno -ffp-contract=on -fno-rounding-math -mconstructor-aliases -funwind-tables=2 -target-cpu x86-64 -tune-cpu generic -debugger-tuning=gdb -ffunction-sections -fdata-sections -fcoverage-compilation-dir=/build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/build-llvm -resource-dir /usr/lib/llvm-14/lib/clang/14.0.0 -D _DEBUG -D _GNU_SOURCE -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D __STDC_LIMIT_MACROS -I lib/Support -I /build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/llvm/lib/Support -I include -I /build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/llvm/include -D _FORTIFY_SOURCE=2 -D NDEBUG -U NDEBUG -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../include/c++/10 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../include/x86_64-linux-gnu/c++/10 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../include/c++/10/backward -internal-isystem /usr/lib/llvm-14/lib/clang/14.0.0/include -internal-isystem /usr/local/include -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../x86_64-linux-gnu/include -internal-externc-isystem /usr/include/x86_64-linux-gnu -internal-externc-isystem /include -internal-externc-isystem /usr/include -fmacro-prefix-map=/build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/build-llvm=build-llvm -fmacro-prefix-map=/build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/= -fcoverage-prefix-map=/build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/build-llvm=build-llvm -fcoverage-prefix-map=/build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/= -O3 -Wno-unused-command-line-argument -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-maybe-uninitialized -Wno-class-memaccess -Wno-redundant-move -Wno-pessimizing-move -Wno-noexcept-type -Wno-comment -std=c++14 -fdeprecated-macro -fdebug-compilation-dir=/build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/build-llvm -fdebug-prefix-map=/build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/build-llvm=build-llvm -fdebug-prefix-map=/build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/= -ferror-limit 19 -fvisibility-inlines-hidden -stack-protector 2 -fgnuc-version=4.2.1 -fcolor-diagnostics -vectorize-loops -vectorize-slp -analyzer-output=html -analyzer-config stable-report-filename=true -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /tmp/scan-build-2022-01-19-134126-35450-1 -x c++ /build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/llvm/lib/Support/APInt.cpp

/build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/llvm/lib/Support/APInt.cpp

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"
24#include "llvm/Support/ErrorHandling.h"
25#include "llvm/Support/MathExtras.h"
26#include "llvm/Support/raw_ostream.h"
27#include <climits>
28#include <cmath>
29#include <cstdlib>
30#include <cstring>
31using namespace llvm;
32
33#define DEBUG_TYPE"apint" "apint"
34
35/// A utility function for allocating memory, checking for allocation failures,
36/// and ensuring the contents are zeroed.
37inline static uint64_t* getClearedMemory(unsigned numWords) {
38 uint64_t *result = new uint64_t[numWords];
39 memset(result, 0, numWords * sizeof(uint64_t));
40 return result;
41}
42
43/// A utility function for allocating memory and checking for allocation
44/// failure. The content is not zeroed.
45inline static uint64_t* getMemory(unsigned numWords) {
46 return new uint64_t[numWords];
47}
48
49/// A utility function that converts a character to a digit.
50inline static unsigned getDigit(char cdigit, uint8_t radix) {
51 unsigned r;
52
53 if (radix == 16 || radix == 36) {
54 r = cdigit - '0';
55 if (r <= 9)
56 return r;
57
58 r = cdigit - 'A';
59 if (r <= radix - 11U)
60 return r + 10;
61
62 r = cdigit - 'a';
63 if (r <= radix - 11U)
64 return r + 10;
65
66 radix = 10;
67 }
68
69 r = cdigit - '0';
70 if (r < radix)
71 return r;
72
73 return -1U;
74}
75
76
77void APInt::initSlowCase(uint64_t val, bool isSigned) {
78 U.pVal = getClearedMemory(getNumWords());
79 U.pVal[0] = val;
80 if (isSigned && int64_t(val) < 0)
81 for (unsigned i = 1; i < getNumWords(); ++i)
82 U.pVal[i] = WORDTYPE_MAX;
83 clearUnusedBits();
84}
85
86void APInt::initSlowCase(const APInt& that) {
87 U.pVal = getMemory(getNumWords());
88 memcpy(U.pVal, that.U.pVal, getNumWords() * APINT_WORD_SIZE);
89}
90
91void APInt::initFromArray(ArrayRef<uint64_t> bigVal) {
92 assert(bigVal.data() && "Null pointer detected!")(static_cast <bool> (bigVal.data() && "Null pointer detected!"
) ? void (0) : __assert_fail ("bigVal.data() && \"Null pointer detected!\""
, "llvm/lib/Support/APInt.cpp", 92, __extension__ __PRETTY_FUNCTION__
))
;
93 if (isSingleWord())
94 U.VAL = bigVal[0];
95 else {
96 // Get memory, cleared to 0
97 U.pVal = getClearedMemory(getNumWords());
98 // Calculate the number of words to copy
99 unsigned words = std::min<unsigned>(bigVal.size(), getNumWords());
100 // Copy the words from bigVal to pVal
101 memcpy(U.pVal, bigVal.data(), words * APINT_WORD_SIZE);
102 }
103 // Make sure unused high bits are cleared
104 clearUnusedBits();
105}
106
107APInt::APInt(unsigned numBits, ArrayRef<uint64_t> bigVal) : BitWidth(numBits) {
108 initFromArray(bigVal);
109}
110
111APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[])
112 : BitWidth(numBits) {
113 initFromArray(makeArrayRef(bigVal, numWords));
114}
115
116APInt::APInt(unsigned numbits, StringRef Str, uint8_t radix)
117 : BitWidth(numbits) {
118 fromString(numbits, Str, radix);
119}
120
121void APInt::reallocate(unsigned NewBitWidth) {
122 // If the number of words is the same we can just change the width and stop.
123 if (getNumWords() == getNumWords(NewBitWidth)) {
124 BitWidth = NewBitWidth;
125 return;
126 }
127
128 // If we have an allocation, delete it.
129 if (!isSingleWord())
130 delete [] U.pVal;
131
132 // Update BitWidth.
133 BitWidth = NewBitWidth;
134
135 // If we are supposed to have an allocation, create it.
136 if (!isSingleWord())
137 U.pVal = getMemory(getNumWords());
138}
139
140void APInt::assignSlowCase(const APInt &RHS) {
141 // Don't do anything for X = X
142 if (this == &RHS)
143 return;
144
145 // Adjust the bit width and handle allocations as necessary.
146 reallocate(RHS.getBitWidth());
147
148 // Copy the data.
149 if (isSingleWord())
150 U.VAL = RHS.U.VAL;
151 else
152 memcpy(U.pVal, RHS.U.pVal, getNumWords() * APINT_WORD_SIZE);
153}
154
155/// This method 'profiles' an APInt for use with FoldingSet.
156void APInt::Profile(FoldingSetNodeID& ID) const {
157 ID.AddInteger(BitWidth);
158
159 if (isSingleWord()) {
160 ID.AddInteger(U.VAL);
161 return;
162 }
163
164 unsigned NumWords = getNumWords();
165 for (unsigned i = 0; i < NumWords; ++i)
166 ID.AddInteger(U.pVal[i]);
167}
168
169/// Prefix increment operator. Increments the APInt by one.
170APInt& APInt::operator++() {
171 if (isSingleWord())
172 ++U.VAL;
173 else
174 tcIncrement(U.pVal, getNumWords());
175 return clearUnusedBits();
176}
177
178/// Prefix decrement operator. Decrements the APInt by one.
179APInt& APInt::operator--() {
180 if (isSingleWord())
181 --U.VAL;
182 else
183 tcDecrement(U.pVal, getNumWords());
184 return clearUnusedBits();
185}
186
187/// Adds the RHS APInt to this APInt.
188/// @returns this, after addition of RHS.
189/// Addition assignment operator.
190APInt& APInt::operator+=(const APInt& RHS) {
191 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same")(static_cast <bool> (BitWidth == RHS.BitWidth &&
"Bit widths must be the same") ? void (0) : __assert_fail ("BitWidth == RHS.BitWidth && \"Bit widths must be the same\""
, "llvm/lib/Support/APInt.cpp", 191, __extension__ __PRETTY_FUNCTION__
))
;
192 if (isSingleWord())
193 U.VAL += RHS.U.VAL;
194 else
195 tcAdd(U.pVal, RHS.U.pVal, 0, getNumWords());
196 return clearUnusedBits();
197}
198
199APInt& APInt::operator+=(uint64_t RHS) {
200 if (isSingleWord())
201 U.VAL += RHS;
202 else
203 tcAddPart(U.pVal, RHS, getNumWords());
204 return clearUnusedBits();
205}
206
207/// Subtracts the RHS APInt from this APInt
208/// @returns this, after subtraction
209/// Subtraction assignment operator.
210APInt& APInt::operator-=(const APInt& RHS) {
211 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same")(static_cast <bool> (BitWidth == RHS.BitWidth &&
"Bit widths must be the same") ? void (0) : __assert_fail ("BitWidth == RHS.BitWidth && \"Bit widths must be the same\""
, "llvm/lib/Support/APInt.cpp", 211, __extension__ __PRETTY_FUNCTION__
))
;
212 if (isSingleWord())
213 U.VAL -= RHS.U.VAL;
214 else
215 tcSubtract(U.pVal, RHS.U.pVal, 0, getNumWords());
216 return clearUnusedBits();
217}
218
219APInt& APInt::operator-=(uint64_t RHS) {
220 if (isSingleWord())
221 U.VAL -= RHS;
222 else
223 tcSubtractPart(U.pVal, RHS, getNumWords());
224 return clearUnusedBits();
225}
226
227APInt APInt::operator*(const APInt& RHS) const {
228 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same")(static_cast <bool> (BitWidth == RHS.BitWidth &&
"Bit widths must be the same") ? void (0) : __assert_fail ("BitWidth == RHS.BitWidth && \"Bit widths must be the same\""
, "llvm/lib/Support/APInt.cpp", 228, __extension__ __PRETTY_FUNCTION__
))
;
229 if (isSingleWord())
230 return APInt(BitWidth, U.VAL * RHS.U.VAL);
231
232 APInt Result(getMemory(getNumWords()), getBitWidth());
233 tcMultiply(Result.U.pVal, U.pVal, RHS.U.pVal, getNumWords());
234 Result.clearUnusedBits();
235 return Result;
236}
237
238void APInt::andAssignSlowCase(const APInt &RHS) {
239 WordType *dst = U.pVal, *rhs = RHS.U.pVal;
240 for (size_t i = 0, e = getNumWords(); i != e; ++i)
241 dst[i] &= rhs[i];
242}
243
244void APInt::orAssignSlowCase(const APInt &RHS) {
245 WordType *dst = U.pVal, *rhs = RHS.U.pVal;
246 for (size_t i = 0, e = getNumWords(); i != e; ++i)
247 dst[i] |= rhs[i];
248}
249
250void APInt::xorAssignSlowCase(const APInt &RHS) {
251 WordType *dst = U.pVal, *rhs = RHS.U.pVal;
252 for (size_t i = 0, e = getNumWords(); i != e; ++i)
253 dst[i] ^= rhs[i];
254}
255
256APInt &APInt::operator*=(const APInt &RHS) {
257 *this = *this * RHS;
258 return *this;
259}
260
261APInt& APInt::operator*=(uint64_t RHS) {
262 if (isSingleWord()) {
263 U.VAL *= RHS;
264 } else {
265 unsigned NumWords = getNumWords();
266 tcMultiplyPart(U.pVal, U.pVal, RHS, 0, NumWords, NumWords, false);
267 }
268 return clearUnusedBits();
269}
270
271bool APInt::equalSlowCase(const APInt &RHS) const {
272 return std::equal(U.pVal, U.pVal + getNumWords(), RHS.U.pVal);
273}
274
275int APInt::compare(const APInt& RHS) const {
276 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison")(static_cast <bool> (BitWidth == RHS.BitWidth &&
"Bit widths must be same for comparison") ? void (0) : __assert_fail
("BitWidth == RHS.BitWidth && \"Bit widths must be same for comparison\""
, "llvm/lib/Support/APInt.cpp", 276, __extension__ __PRETTY_FUNCTION__
))
;
277 if (isSingleWord())
278 return U.VAL < RHS.U.VAL ? -1 : U.VAL > RHS.U.VAL;
279
280 return tcCompare(U.pVal, RHS.U.pVal, getNumWords());
281}
282
283int APInt::compareSigned(const APInt& RHS) const {
284 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison")(static_cast <bool> (BitWidth == RHS.BitWidth &&
"Bit widths must be same for comparison") ? void (0) : __assert_fail
("BitWidth == RHS.BitWidth && \"Bit widths must be same for comparison\""
, "llvm/lib/Support/APInt.cpp", 284, __extension__ __PRETTY_FUNCTION__
))
;
285 if (isSingleWord()) {
286 int64_t lhsSext = SignExtend64(U.VAL, BitWidth);
287 int64_t rhsSext = SignExtend64(RHS.U.VAL, BitWidth);
288 return lhsSext < rhsSext ? -1 : lhsSext > rhsSext;
289 }
290
291 bool lhsNeg = isNegative();
292 bool rhsNeg = RHS.isNegative();
293
294 // If the sign bits don't match, then (LHS < RHS) if LHS is negative
295 if (lhsNeg != rhsNeg)
296 return lhsNeg ? -1 : 1;
297
298 // Otherwise we can just use an unsigned comparison, because even negative
299 // numbers compare correctly this way if both have the same signed-ness.
300 return tcCompare(U.pVal, RHS.U.pVal, getNumWords());
301}
302
303void APInt::setBitsSlowCase(unsigned loBit, unsigned hiBit) {
304 unsigned loWord = whichWord(loBit);
305 unsigned hiWord = whichWord(hiBit);
306
307 // Create an initial mask for the low word with zeros below loBit.
308 uint64_t loMask = WORDTYPE_MAX << whichBit(loBit);
309
310 // If hiBit is not aligned, we need a high mask.
311 unsigned hiShiftAmt = whichBit(hiBit);
312 if (hiShiftAmt != 0) {
313 // Create a high mask with zeros above hiBit.
314 uint64_t hiMask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - hiShiftAmt);
315 // If loWord and hiWord are equal, then we combine the masks. Otherwise,
316 // set the bits in hiWord.
317 if (hiWord == loWord)
318 loMask &= hiMask;
319 else
320 U.pVal[hiWord] |= hiMask;
321 }
322 // Apply the mask to the low word.
323 U.pVal[loWord] |= loMask;
324
325 // Fill any words between loWord and hiWord with all ones.
326 for (unsigned word = loWord + 1; word < hiWord; ++word)
327 U.pVal[word] = WORDTYPE_MAX;
328}
329
330// Complement a bignum in-place.
331static void tcComplement(APInt::WordType *dst, unsigned parts) {
332 for (unsigned i = 0; i < parts; i++)
333 dst[i] = ~dst[i];
334}
335
336/// Toggle every bit to its opposite value.
337void APInt::flipAllBitsSlowCase() {
338 tcComplement(U.pVal, getNumWords());
339 clearUnusedBits();
340}
341
342/// Concatenate the bits from "NewLSB" onto the bottom of *this. This is
343/// equivalent to:
344/// (this->zext(NewWidth) << NewLSB.getBitWidth()) | NewLSB.zext(NewWidth)
345/// In the slow case, we know the result is large.
346APInt APInt::concatSlowCase(const APInt &NewLSB) const {
347 unsigned NewWidth = getBitWidth() + NewLSB.getBitWidth();
348 APInt Result = NewLSB.zextOrSelf(NewWidth);
349 Result.insertBits(*this, NewLSB.getBitWidth());
350 return Result;
351}
352
353/// Toggle a given bit to its opposite value whose position is given
354/// as "bitPosition".
355/// Toggles a given bit to its opposite value.
356void APInt::flipBit(unsigned bitPosition) {
357 assert(bitPosition < BitWidth && "Out of the bit-width range!")(static_cast <bool> (bitPosition < BitWidth &&
"Out of the bit-width range!") ? void (0) : __assert_fail ("bitPosition < BitWidth && \"Out of the bit-width range!\""
, "llvm/lib/Support/APInt.cpp", 357, __extension__ __PRETTY_FUNCTION__
))
;
358 setBitVal(bitPosition, !(*this)[bitPosition]);
359}
360
361void APInt::insertBits(const APInt &subBits, unsigned bitPosition) {
362 unsigned subBitWidth = subBits.getBitWidth();
363 assert((subBitWidth + bitPosition) <= BitWidth && "Illegal bit insertion")(static_cast <bool> ((subBitWidth + bitPosition) <= BitWidth
&& "Illegal bit insertion") ? void (0) : __assert_fail
("(subBitWidth + bitPosition) <= BitWidth && \"Illegal bit insertion\""
, "llvm/lib/Support/APInt.cpp", 363, __extension__ __PRETTY_FUNCTION__
))
;
364
365 // inserting no bits is a noop.
366 if (subBitWidth == 0)
367 return;
368
369 // Insertion is a direct copy.
370 if (subBitWidth == BitWidth) {
371 *this = subBits;
372 return;
373 }
374
375 // Single word result can be done as a direct bitmask.
376 if (isSingleWord()) {
377 uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - subBitWidth);
378 U.VAL &= ~(mask << bitPosition);
379 U.VAL |= (subBits.U.VAL << bitPosition);
380 return;
381 }
382
383 unsigned loBit = whichBit(bitPosition);
384 unsigned loWord = whichWord(bitPosition);
385 unsigned hi1Word = whichWord(bitPosition + subBitWidth - 1);
386
387 // Insertion within a single word can be done as a direct bitmask.
388 if (loWord == hi1Word) {
389 uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - subBitWidth);
390 U.pVal[loWord] &= ~(mask << loBit);
391 U.pVal[loWord] |= (subBits.U.VAL << loBit);
392 return;
393 }
394
395 // Insert on word boundaries.
396 if (loBit == 0) {
397 // Direct copy whole words.
398 unsigned numWholeSubWords = subBitWidth / APINT_BITS_PER_WORD;
399 memcpy(U.pVal + loWord, subBits.getRawData(),
400 numWholeSubWords * APINT_WORD_SIZE);
401
402 // Mask+insert remaining bits.
403 unsigned remainingBits = subBitWidth % APINT_BITS_PER_WORD;
404 if (remainingBits != 0) {
405 uint64_t mask = WORDTYPE_MAX >> (APINT_BITS_PER_WORD - remainingBits);
406 U.pVal[hi1Word] &= ~mask;
407 U.pVal[hi1Word] |= subBits.getWord(subBitWidth - 1);
408 }
409 return;
410 }
411
412 // General case - set/clear individual bits in dst based on src.
413 // TODO - there is scope for optimization here, but at the moment this code
414 // path is barely used so prefer readability over performance.
415 for (unsigned i = 0; i != subBitWidth; ++i)
416 setBitVal(bitPosition + i, subBits[i]);
417}
418
419void APInt::insertBits(uint64_t subBits, unsigned bitPosition, unsigned numBits) {
420 uint64_t maskBits = maskTrailingOnes<uint64_t>(numBits);
421 subBits &= maskBits;
422 if (isSingleWord()) {
423 U.VAL &= ~(maskBits << bitPosition);
424 U.VAL |= subBits << bitPosition;
425 return;
426 }
427
428 unsigned loBit = whichBit(bitPosition);
429 unsigned loWord = whichWord(bitPosition);
430 unsigned hiWord = whichWord(bitPosition + numBits - 1);
431 if (loWord == hiWord) {
432 U.pVal[loWord] &= ~(maskBits << loBit);
433 U.pVal[loWord] |= subBits << loBit;
434 return;
435 }
436
437 static_assert(8 * sizeof(WordType) <= 64, "This code assumes only two words affected");
438 unsigned wordBits = 8 * sizeof(WordType);
439 U.pVal[loWord] &= ~(maskBits << loBit);
440 U.pVal[loWord] |= subBits << loBit;
441
442 U.pVal[hiWord] &= ~(maskBits >> (wordBits - loBit));
443 U.pVal[hiWord] |= subBits >> (wordBits - loBit);
444}
445
446APInt APInt::extractBits(unsigned numBits, unsigned bitPosition) const {
447 assert(bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth &&(static_cast <bool> (bitPosition < BitWidth &&
(numBits + bitPosition) <= BitWidth && "Illegal bit extraction"
) ? void (0) : __assert_fail ("bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth && \"Illegal bit extraction\""
, "llvm/lib/Support/APInt.cpp", 448, __extension__ __PRETTY_FUNCTION__
))
448 "Illegal bit extraction")(static_cast <bool> (bitPosition < BitWidth &&
(numBits + bitPosition) <= BitWidth && "Illegal bit extraction"
) ? void (0) : __assert_fail ("bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth && \"Illegal bit extraction\""
, "llvm/lib/Support/APInt.cpp", 448, __extension__ __PRETTY_FUNCTION__
))
;
449
450 if (isSingleWord())
451 return APInt(numBits, U.VAL >> bitPosition);
452
453 unsigned loBit = whichBit(bitPosition);
454 unsigned loWord = whichWord(bitPosition);
455 unsigned hiWord = whichWord(bitPosition + numBits - 1);
456
457 // Single word result extracting bits from a single word source.
458 if (loWord == hiWord)
459 return APInt(numBits, U.pVal[loWord] >> loBit);
460
461 // Extracting bits that start on a source word boundary can be done
462 // as a fast memory copy.
463 if (loBit == 0)
464 return APInt(numBits, makeArrayRef(U.pVal + loWord, 1 + hiWord - loWord));
465
466 // General case - shift + copy source words directly into place.
467 APInt Result(numBits, 0);
468 unsigned NumSrcWords = getNumWords();
469 unsigned NumDstWords = Result.getNumWords();
470
471 uint64_t *DestPtr = Result.isSingleWord() ? &Result.U.VAL : Result.U.pVal;
472 for (unsigned word = 0; word < NumDstWords; ++word) {
473 uint64_t w0 = U.pVal[loWord + word];
474 uint64_t w1 =
475 (loWord + word + 1) < NumSrcWords ? U.pVal[loWord + word + 1] : 0;
476 DestPtr[word] = (w0 >> loBit) | (w1 << (APINT_BITS_PER_WORD - loBit));
477 }
478
479 return Result.clearUnusedBits();
480}
481
482uint64_t APInt::extractBitsAsZExtValue(unsigned numBits,
483 unsigned bitPosition) const {
484 assert(numBits > 0 && "Can't extract zero bits")(static_cast <bool> (numBits > 0 && "Can't extract zero bits"
) ? void (0) : __assert_fail ("numBits > 0 && \"Can't extract zero bits\""
, "llvm/lib/Support/APInt.cpp", 484, __extension__ __PRETTY_FUNCTION__
))
;
485 assert(bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth &&(static_cast <bool> (bitPosition < BitWidth &&
(numBits + bitPosition) <= BitWidth && "Illegal bit extraction"
) ? void (0) : __assert_fail ("bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth && \"Illegal bit extraction\""
, "llvm/lib/Support/APInt.cpp", 486, __extension__ __PRETTY_FUNCTION__
))
486 "Illegal bit extraction")(static_cast <bool> (bitPosition < BitWidth &&
(numBits + bitPosition) <= BitWidth && "Illegal bit extraction"
) ? void (0) : __assert_fail ("bitPosition < BitWidth && (numBits + bitPosition) <= BitWidth && \"Illegal bit extraction\""
, "llvm/lib/Support/APInt.cpp", 486, __extension__ __PRETTY_FUNCTION__
))
;
487 assert(numBits <= 64 && "Illegal bit extraction")(static_cast <bool> (numBits <= 64 && "Illegal bit extraction"
) ? void (0) : __assert_fail ("numBits <= 64 && \"Illegal bit extraction\""
, "llvm/lib/Support/APInt.cpp", 487, __extension__ __PRETTY_FUNCTION__
))
;
488
489 uint64_t maskBits = maskTrailingOnes<uint64_t>(numBits);
490 if (isSingleWord())
491 return (U.VAL >> bitPosition) & maskBits;
492
493 unsigned loBit = whichBit(bitPosition);
494 unsigned loWord = whichWord(bitPosition);
495 unsigned hiWord = whichWord(bitPosition + numBits - 1);
496 if (loWord == hiWord)
497 return (U.pVal[loWord] >> loBit) & maskBits;
498
499 static_assert(8 * sizeof(WordType) <= 64, "This code assumes only two words affected");
500 unsigned wordBits = 8 * sizeof(WordType);
501 uint64_t retBits = U.pVal[loWord] >> loBit;
502 retBits |= U.pVal[hiWord] << (wordBits - loBit);
503 retBits &= maskBits;
504 return retBits;
505}
506
507unsigned APInt::getBitsNeeded(StringRef str, uint8_t radix) {
508 assert(!str.empty() && "Invalid string length")(static_cast <bool> (!str.empty() && "Invalid string length"
) ? void (0) : __assert_fail ("!str.empty() && \"Invalid string length\""
, "llvm/lib/Support/APInt.cpp", 508, __extension__ __PRETTY_FUNCTION__
))
;
509 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||(static_cast <bool> ((radix == 10 || radix == 8 || radix
== 16 || radix == 2 || radix == 36) && "Radix should be 2, 8, 10, 16, or 36!"
) ? void (0) : __assert_fail ("(radix == 10 || radix == 8 || radix == 16 || radix == 2 || radix == 36) && \"Radix should be 2, 8, 10, 16, or 36!\""
, "llvm/lib/Support/APInt.cpp", 511, __extension__ __PRETTY_FUNCTION__
))
510 radix == 36) &&(static_cast <bool> ((radix == 10 || radix == 8 || radix
== 16 || radix == 2 || radix == 36) && "Radix should be 2, 8, 10, 16, or 36!"
) ? void (0) : __assert_fail ("(radix == 10 || radix == 8 || radix == 16 || radix == 2 || radix == 36) && \"Radix should be 2, 8, 10, 16, or 36!\""
, "llvm/lib/Support/APInt.cpp", 511, __extension__ __PRETTY_FUNCTION__
))
511 "Radix should be 2, 8, 10, 16, or 36!")(static_cast <bool> ((radix == 10 || radix == 8 || radix
== 16 || radix == 2 || radix == 36) && "Radix should be 2, 8, 10, 16, or 36!"
) ? void (0) : __assert_fail ("(radix == 10 || radix == 8 || radix == 16 || radix == 2 || radix == 36) && \"Radix should be 2, 8, 10, 16, or 36!\""
, "llvm/lib/Support/APInt.cpp", 511, __extension__ __PRETTY_FUNCTION__
))
;
512
513 size_t slen = str.size();
514
515 // Each computation below needs to know if it's negative.
516 StringRef::iterator p = str.begin();
517 unsigned isNegative = *p == '-';
518 if (*p == '-' || *p == '+') {
519 p++;
520 slen--;
521 assert(slen && "String is only a sign, needs a value.")(static_cast <bool> (slen && "String is only a sign, needs a value."
) ? void (0) : __assert_fail ("slen && \"String is only a sign, needs a value.\""
, "llvm/lib/Support/APInt.cpp", 521, __extension__ __PRETTY_FUNCTION__
))
;
522 }
523
524 // For radixes of power-of-two values, the bits required is accurately and
525 // easily computed
526 if (radix == 2)
527 return slen + isNegative;
528 if (radix == 8)
529 return slen * 3 + isNegative;
530 if (radix == 16)
531 return slen * 4 + isNegative;
532
533 // FIXME: base 36
534
535 // This is grossly inefficient but accurate. We could probably do something
536 // with a computation of roughly slen*64/20 and then adjust by the value of
537 // the first few digits. But, I'm not sure how accurate that could be.
538
539 // Compute a sufficient number of bits that is always large enough but might
540 // be too large. This avoids the assertion in the constructor. This
541 // calculation doesn't work appropriately for the numbers 0-9, so just use 4
542 // bits in that case.
543 unsigned sufficient
544 = radix == 10? (slen == 1 ? 4 : slen * 64/18)
545 : (slen == 1 ? 7 : slen * 16/3);
546
547 // Convert to the actual binary value.
548 APInt tmp(sufficient, StringRef(p, slen), radix);
549
550 // Compute how many bits are required. If the log is infinite, assume we need
551 // just bit. If the log is exact and value is negative, then the value is
552 // MinSignedValue with (log + 1) bits.
553 unsigned log = tmp.logBase2();
554 if (log == (unsigned)-1) {
555 return isNegative + 1;
556 } else if (isNegative && tmp.isPowerOf2()) {
557 return isNegative + log;
558 } else {
559 return isNegative + log + 1;
560 }
561}
562
563hash_code llvm::hash_value(const APInt &Arg) {
564 if (Arg.isSingleWord())
565 return hash_combine(Arg.BitWidth, Arg.U.VAL);
566
567 return hash_combine(
568 Arg.BitWidth,
569 hash_combine_range(Arg.U.pVal, Arg.U.pVal + Arg.getNumWords()));
570}
571
572unsigned DenseMapInfo<APInt, void>::getHashValue(const APInt &Key) {
573 return static_cast<unsigned>(hash_value(Key));
574}
575
576bool APInt::isSplat(unsigned SplatSizeInBits) const {
577 assert(getBitWidth() % SplatSizeInBits == 0 &&(static_cast <bool> (getBitWidth() % SplatSizeInBits ==
0 && "SplatSizeInBits must divide width!") ? void (0
) : __assert_fail ("getBitWidth() % SplatSizeInBits == 0 && \"SplatSizeInBits must divide width!\""
, "llvm/lib/Support/APInt.cpp", 578, __extension__ __PRETTY_FUNCTION__
))
578 "SplatSizeInBits must divide width!")(static_cast <bool> (getBitWidth() % SplatSizeInBits ==
0 && "SplatSizeInBits must divide width!") ? void (0
) : __assert_fail ("getBitWidth() % SplatSizeInBits == 0 && \"SplatSizeInBits must divide width!\""
, "llvm/lib/Support/APInt.cpp", 578, __extension__ __PRETTY_FUNCTION__
))
;
579 // We can check that all parts of an integer are equal by making use of a
580 // little trick: rotate and check if it's still the same value.
581 return *this == rotl(SplatSizeInBits);
582}
583
584/// This function returns the high "numBits" bits of this APInt.
585APInt APInt::getHiBits(unsigned numBits) const {
586 return this->lshr(BitWidth - numBits);
587}
588
589/// This function returns the low "numBits" bits of this APInt.
590APInt APInt::getLoBits(unsigned numBits) const {
591 APInt Result(getLowBitsSet(BitWidth, numBits));
592 Result &= *this;
593 return Result;
594}
595
596/// Return a value containing V broadcasted over NewLen bits.
597APInt APInt::getSplat(unsigned NewLen, const APInt &V) {
598 assert(NewLen >= V.getBitWidth() && "Can't splat to smaller bit width!")(static_cast <bool> (NewLen >= V.getBitWidth() &&
"Can't splat to smaller bit width!") ? void (0) : __assert_fail
("NewLen >= V.getBitWidth() && \"Can't splat to smaller bit width!\""
, "llvm/lib/Support/APInt.cpp", 598, __extension__ __PRETTY_FUNCTION__
))
;
599
600 APInt Val = V.zextOrSelf(NewLen);
601 for (unsigned I = V.getBitWidth(); I < NewLen; I <<= 1)
602 Val |= Val << I;
603
604 return Val;
605}
606
607unsigned APInt::countLeadingZerosSlowCase() const {
608 unsigned Count = 0;
609 for (int i = getNumWords()-1; i >= 0; --i) {
610 uint64_t V = U.pVal[i];
611 if (V == 0)
612 Count += APINT_BITS_PER_WORD;
613 else {
614 Count += llvm::countLeadingZeros(V);
615 break;
616 }
617 }
618 // Adjust for unused bits in the most significant word (they are zero).
619 unsigned Mod = BitWidth % APINT_BITS_PER_WORD;
620 Count -= Mod > 0 ? APINT_BITS_PER_WORD - Mod : 0;
621 return Count;
622}
623
624unsigned APInt::countLeadingOnesSlowCase() const {
625 unsigned highWordBits = BitWidth % APINT_BITS_PER_WORD;
626 unsigned shift;
627 if (!highWordBits) {
628 highWordBits = APINT_BITS_PER_WORD;
629 shift = 0;
630 } else {
631 shift = APINT_BITS_PER_WORD - highWordBits;
632 }
633 int i = getNumWords() - 1;
634 unsigned Count = llvm::countLeadingOnes(U.pVal[i] << shift);
635 if (Count == highWordBits) {
636 for (i--; i >= 0; --i) {
637 if (U.pVal[i] == WORDTYPE_MAX)
638 Count += APINT_BITS_PER_WORD;
639 else {
640 Count += llvm::countLeadingOnes(U.pVal[i]);
641 break;
642 }
643 }
644 }
645 return Count;
646}
647
648unsigned APInt::countTrailingZerosSlowCase() const {
649 unsigned Count = 0;
650 unsigned i = 0;
651 for (; i < getNumWords() && U.pVal[i] == 0; ++i)
652 Count += APINT_BITS_PER_WORD;
653 if (i < getNumWords())
654 Count += llvm::countTrailingZeros(U.pVal[i]);
655 return std::min(Count, BitWidth);
656}
657
658unsigned APInt::countTrailingOnesSlowCase() const {
659 unsigned Count = 0;
660 unsigned i = 0;
661 for (; i < getNumWords() && U.pVal[i] == WORDTYPE_MAX; ++i)
662 Count += APINT_BITS_PER_WORD;
663 if (i < getNumWords())
664 Count += llvm::countTrailingOnes(U.pVal[i]);
665 assert(Count <= BitWidth)(static_cast <bool> (Count <= BitWidth) ? void (0) :
__assert_fail ("Count <= BitWidth", "llvm/lib/Support/APInt.cpp"
, 665, __extension__ __PRETTY_FUNCTION__))
;
666 return Count;
667}
668
669unsigned APInt::countPopulationSlowCase() const {
670 unsigned Count = 0;
671 for (unsigned i = 0; i < getNumWords(); ++i)
672 Count += llvm::countPopulation(U.pVal[i]);
673 return Count;
674}
675
676bool APInt::intersectsSlowCase(const APInt &RHS) const {
677 for (unsigned i = 0, e = getNumWords(); i != e; ++i)
678 if ((U.pVal[i] & RHS.U.pVal[i]) != 0)
679 return true;
680
681 return false;
682}
683
684bool APInt::isSubsetOfSlowCase(const APInt &RHS) const {
685 for (unsigned i = 0, e = getNumWords(); i != e; ++i)
686 if ((U.pVal[i] & ~RHS.U.pVal[i]) != 0)
687 return false;
688
689 return true;
690}
691
692APInt APInt::byteSwap() const {
693 assert(BitWidth >= 16 && BitWidth % 8 == 0 && "Cannot byteswap!")(static_cast <bool> (BitWidth >= 16 && BitWidth
% 8 == 0 && "Cannot byteswap!") ? void (0) : __assert_fail
("BitWidth >= 16 && BitWidth % 8 == 0 && \"Cannot byteswap!\""
, "llvm/lib/Support/APInt.cpp", 693, __extension__ __PRETTY_FUNCTION__
))
;
694 if (BitWidth == 16)
695 return APInt(BitWidth, ByteSwap_16(uint16_t(U.VAL)));
696 if (BitWidth == 32)
697 return APInt(BitWidth, ByteSwap_32(unsigned(U.VAL)));
698 if (BitWidth <= 64) {
699 uint64_t Tmp1 = ByteSwap_64(U.VAL);
700 Tmp1 >>= (64 - BitWidth);
701 return APInt(BitWidth, Tmp1);
702 }
703
704 APInt Result(getNumWords() * APINT_BITS_PER_WORD, 0);
705 for (unsigned I = 0, N = getNumWords(); I != N; ++I)
706 Result.U.pVal[I] = ByteSwap_64(U.pVal[N - I - 1]);
707 if (Result.BitWidth != BitWidth) {
708 Result.lshrInPlace(Result.BitWidth - BitWidth);
709 Result.BitWidth = BitWidth;
710 }
711 return Result;
712}
713
714APInt APInt::reverseBits() const {
715 switch (BitWidth) {
716 case 64:
717 return APInt(BitWidth, llvm::reverseBits<uint64_t>(U.VAL));
718 case 32:
719 return APInt(BitWidth, llvm::reverseBits<uint32_t>(U.VAL));
720 case 16:
721 return APInt(BitWidth, llvm::reverseBits<uint16_t>(U.VAL));
722 case 8:
723 return APInt(BitWidth, llvm::reverseBits<uint8_t>(U.VAL));
724 case 0:
725 return *this;
726 default:
727 break;
728 }
729
730 APInt Val(*this);
731 APInt Reversed(BitWidth, 0);
732 unsigned S = BitWidth;
733
734 for (; Val != 0; Val.lshrInPlace(1)) {
735 Reversed <<= 1;
736 Reversed |= Val[0];
737 --S;
738 }
739
740 Reversed <<= S;
741 return Reversed;
742}
743
744APInt llvm::APIntOps::GreatestCommonDivisor(APInt A, APInt B) {
745 // Fast-path a common case.
746 if (A == B) return A;
747
748 // Corner cases: if either operand is zero, the other is the gcd.
749 if (!A) return B;
750 if (!B) return A;
751
752 // Count common powers of 2 and remove all other powers of 2.
753 unsigned Pow2;
754 {
755 unsigned Pow2_A = A.countTrailingZeros();
756 unsigned Pow2_B = B.countTrailingZeros();
757 if (Pow2_A > Pow2_B) {
758 A.lshrInPlace(Pow2_A - Pow2_B);
759 Pow2 = Pow2_B;
760 } else if (Pow2_B > Pow2_A) {
761 B.lshrInPlace(Pow2_B - Pow2_A);
762 Pow2 = Pow2_A;
763 } else {
764 Pow2 = Pow2_A;
765 }
766 }
767
768 // Both operands are odd multiples of 2^Pow_2:
769 //
770 // gcd(a, b) = gcd(|a - b| / 2^i, min(a, b))
771 //
772 // This is a modified version of Stein's algorithm, taking advantage of
773 // efficient countTrailingZeros().
774 while (A != B) {
775 if (A.ugt(B)) {
776 A -= B;
777 A.lshrInPlace(A.countTrailingZeros() - Pow2);
778 } else {
779 B -= A;
780 B.lshrInPlace(B.countTrailingZeros() - Pow2);
781 }
782 }
783
784 return A;
785}
786
787APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) {
788 uint64_t I = bit_cast<uint64_t>(Double);
789
790 // Get the sign bit from the highest order bit
791 bool isNeg = I >> 63;
792
793 // Get the 11-bit exponent and adjust for the 1023 bit bias
794 int64_t exp = ((I >> 52) & 0x7ff) - 1023;
795
796 // If the exponent is negative, the value is < 0 so just return 0.
797 if (exp < 0)
798 return APInt(width, 0u);
799
800 // Extract the mantissa by clearing the top 12 bits (sign + exponent).
801 uint64_t mantissa = (I & (~0ULL >> 12)) | 1ULL << 52;
802
803 // If the exponent doesn't shift all bits out of the mantissa
804 if (exp < 52)
805 return isNeg ? -APInt(width, mantissa >> (52 - exp)) :
806 APInt(width, mantissa >> (52 - exp));
807
808 // If the client didn't provide enough bits for us to shift the mantissa into
809 // then the result is undefined, just return 0
810 if (width <= exp - 52)
811 return APInt(width, 0);
812
813 // Otherwise, we have to shift the mantissa bits up to the right location
814 APInt Tmp(width, mantissa);
815 Tmp <<= (unsigned)exp - 52;
816 return isNeg ? -Tmp : Tmp;
817}
818
819/// This function converts this APInt to a double.
820/// The layout for double is as following (IEEE Standard 754):
821/// --------------------------------------
822/// | Sign Exponent Fraction Bias |
823/// |-------------------------------------- |
824/// | 1[63] 11[62-52] 52[51-00] 1023 |
825/// --------------------------------------
826double APInt::roundToDouble(bool isSigned) const {
827
828 // Handle the simple case where the value is contained in one uint64_t.
829 // It is wrong to optimize getWord(0) to VAL; there might be more than one word.
830 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) {
831 if (isSigned) {
832 int64_t sext = SignExtend64(getWord(0), BitWidth);
833 return double(sext);
834 } else
835 return double(getWord(0));
836 }
837
838 // Determine if the value is negative.
839 bool isNeg = isSigned ? (*this)[BitWidth-1] : false;
840
841 // Construct the absolute value if we're negative.
842 APInt Tmp(isNeg ? -(*this) : (*this));
843
844 // Figure out how many bits we're using.
845 unsigned n = Tmp.getActiveBits();
846
847 // The exponent (without bias normalization) is just the number of bits
848 // we are using. Note that the sign bit is gone since we constructed the
849 // absolute value.
850 uint64_t exp = n;
851
852 // Return infinity for exponent overflow
853 if (exp > 1023) {
854 if (!isSigned || !isNeg)
855 return std::numeric_limits<double>::infinity();
856 else
857 return -std::numeric_limits<double>::infinity();
858 }
859 exp += 1023; // Increment for 1023 bias
860
861 // Number of bits in mantissa is 52. To obtain the mantissa value, we must
862 // extract the high 52 bits from the correct words in pVal.
863 uint64_t mantissa;
864 unsigned hiWord = whichWord(n-1);
865 if (hiWord == 0) {
866 mantissa = Tmp.U.pVal[0];
867 if (n > 52)
868 mantissa >>= n - 52; // shift down, we want the top 52 bits.
869 } else {
870 assert(hiWord > 0 && "huh?")(static_cast <bool> (hiWord > 0 && "huh?") ?
void (0) : __assert_fail ("hiWord > 0 && \"huh?\""
, "llvm/lib/Support/APInt.cpp", 870, __extension__ __PRETTY_FUNCTION__
))
;
871 uint64_t hibits = Tmp.U.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD);
872 uint64_t lobits = Tmp.U.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD);
873 mantissa = hibits | lobits;
874 }
875
876 // The leading bit of mantissa is implicit, so get rid of it.
877 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0;
878 uint64_t I = sign | (exp << 52) | mantissa;
879 return bit_cast<double>(I);
880}
881
882// Truncate to new width.
883APInt APInt::trunc(unsigned width) const {
884 assert(width < BitWidth && "Invalid APInt Truncate request")(static_cast <bool> (width < BitWidth && "Invalid APInt Truncate request"
) ? void (0) : __assert_fail ("width < BitWidth && \"Invalid APInt Truncate request\""
, "llvm/lib/Support/APInt.cpp", 884, __extension__ __PRETTY_FUNCTION__
))
;
885
886 if (width <= APINT_BITS_PER_WORD)
887 return APInt(width, getRawData()[0]);
888
889 APInt Result(getMemory(getNumWords(width)), width);
890
891 // Copy full words.
892 unsigned i;
893 for (i = 0; i != width / APINT_BITS_PER_WORD; i++)
894 Result.U.pVal[i] = U.pVal[i];
895
896 // Truncate and copy any partial word.
897 unsigned bits = (0 - width) % APINT_BITS_PER_WORD;
898 if (bits != 0)
899 Result.U.pVal[i] = U.pVal[i] << bits >> bits;
900
901 return Result;
902}
903
904// Truncate to new width with unsigned saturation.
905APInt APInt::truncUSat(unsigned width) const {
906 assert(width < BitWidth && "Invalid APInt Truncate request")(static_cast <bool> (width < BitWidth && "Invalid APInt Truncate request"
) ? void (0) : __assert_fail ("width < BitWidth && \"Invalid APInt Truncate request\""
, "llvm/lib/Support/APInt.cpp", 906, __extension__ __PRETTY_FUNCTION__
))
;
907
908 // Can we just losslessly truncate it?
909 if (isIntN(width))
910 return trunc(width);
911 // If not, then just return the new limit.
912 return APInt::getMaxValue(width);
913}
914
915// Truncate to new width with signed saturation.
916APInt APInt::truncSSat(unsigned width) const {
917 assert(width < BitWidth && "Invalid APInt Truncate request")(static_cast <bool> (width < BitWidth && "Invalid APInt Truncate request"
) ? void (0) : __assert_fail ("width < BitWidth && \"Invalid APInt Truncate request\""
, "llvm/lib/Support/APInt.cpp", 917, __extension__ __PRETTY_FUNCTION__
))
;
918
919 // Can we just losslessly truncate it?
920 if (isSignedIntN(width))
921 return trunc(width);
922 // If not, then just return the new limits.
923 return isNegative() ? APInt::getSignedMinValue(width)
924 : APInt::getSignedMaxValue(width);
925}
926
927// Sign extend to a new width.
928APInt APInt::sext(unsigned Width) const {
929 assert(Width > BitWidth && "Invalid APInt SignExtend request")(static_cast <bool> (Width > BitWidth && "Invalid APInt SignExtend request"
) ? void (0) : __assert_fail ("Width > BitWidth && \"Invalid APInt SignExtend request\""
, "llvm/lib/Support/APInt.cpp", 929, __extension__ __PRETTY_FUNCTION__
))
;
930
931 if (Width <= APINT_BITS_PER_WORD)
932 return APInt(Width, SignExtend64(U.VAL, BitWidth));
933
934 APInt Result(getMemory(getNumWords(Width)), Width);
935
936 // Copy words.
937 std::memcpy(Result.U.pVal, getRawData(), getNumWords() * APINT_WORD_SIZE);
938
939 // Sign extend the last word since there may be unused bits in the input.
940 Result.U.pVal[getNumWords() - 1] =
941 SignExtend64(Result.U.pVal[getNumWords() - 1],
942 ((BitWidth - 1) % APINT_BITS_PER_WORD) + 1);
943
944 // Fill with sign bits.
945 std::memset(Result.U.pVal + getNumWords(), isNegative() ? -1 : 0,
946 (Result.getNumWords() - getNumWords()) * APINT_WORD_SIZE);
947 Result.clearUnusedBits();
948 return Result;
949}
950
951// Zero extend to a new width.
952APInt APInt::zext(unsigned width) const {
953 assert(width > BitWidth && "Invalid APInt ZeroExtend request")(static_cast <bool> (width > BitWidth && "Invalid APInt ZeroExtend request"
) ? void (0) : __assert_fail ("width > BitWidth && \"Invalid APInt ZeroExtend request\""
, "llvm/lib/Support/APInt.cpp", 953, __extension__ __PRETTY_FUNCTION__
))
;
954
955 if (width <= APINT_BITS_PER_WORD)
956 return APInt(width, U.VAL);
957
958 APInt Result(getMemory(getNumWords(width)), width);
959
960 // Copy words.
961 std::memcpy(Result.U.pVal, getRawData(), getNumWords() * APINT_WORD_SIZE);
962
963 // Zero remaining words.
964 std::memset(Result.U.pVal + getNumWords(), 0,
965 (Result.getNumWords() - getNumWords()) * APINT_WORD_SIZE);
966
967 return Result;
968}
969
970APInt APInt::zextOrTrunc(unsigned width) const {
971 if (BitWidth < width)
972 return zext(width);
973 if (BitWidth > width)
974 return trunc(width);
975 return *this;
976}
977
978APInt APInt::sextOrTrunc(unsigned width) const {
979 if (BitWidth < width)
980 return sext(width);
981 if (BitWidth > width)
982 return trunc(width);
983 return *this;
984}
985
986APInt APInt::truncOrSelf(unsigned width) const {
987 if (BitWidth > width)
988 return trunc(width);
989 return *this;
990}
991
992APInt APInt::zextOrSelf(unsigned width) const {
993 if (BitWidth < width)
994 return zext(width);
995 return *this;
996}
997
998APInt APInt::sextOrSelf(unsigned width) const {
999 if (BitWidth < width)
1000 return sext(width);
1001 return *this;
1002}
1003
1004/// Arithmetic right-shift this APInt by shiftAmt.
1005/// Arithmetic right-shift function.
1006void APInt::ashrInPlace(const APInt &shiftAmt) {
1007 ashrInPlace((unsigned)shiftAmt.getLimitedValue(BitWidth));
1008}
1009
1010/// Arithmetic right-shift this APInt by shiftAmt.
1011/// Arithmetic right-shift function.
1012void APInt::ashrSlowCase(unsigned ShiftAmt) {
1013 // Don't bother performing a no-op shift.
1014 if (!ShiftAmt)
1015 return;
1016
1017 // Save the original sign bit for later.
1018 bool Negative = isNegative();
1019
1020 // WordShift is the inter-part shift; BitShift is intra-part shift.
1021 unsigned WordShift = ShiftAmt / APINT_BITS_PER_WORD;
1022 unsigned BitShift = ShiftAmt % APINT_BITS_PER_WORD;
1023
1024 unsigned WordsToMove = getNumWords() - WordShift;
1025 if (WordsToMove != 0) {
1026 // Sign extend the last word to fill in the unused bits.
1027 U.pVal[getNumWords() - 1] = SignExtend64(
1028 U.pVal[getNumWords() - 1], ((BitWidth - 1) % APINT_BITS_PER_WORD) + 1);
1029
1030 // Fastpath for moving by whole words.
1031 if (BitShift == 0) {
1032 std::memmove(U.pVal, U.pVal + WordShift, WordsToMove * APINT_WORD_SIZE);
1033 } else {
1034 // Move the words containing significant bits.
1035 for (unsigned i = 0; i != WordsToMove - 1; ++i)
1036 U.pVal[i] = (U.pVal[i + WordShift] >> BitShift) |
1037 (U.pVal[i + WordShift + 1] << (APINT_BITS_PER_WORD - BitShift));
1038
1039 // Handle the last word which has no high bits to copy.
1040 U.pVal[WordsToMove - 1] = U.pVal[WordShift + WordsToMove - 1] >> BitShift;
1041 // Sign extend one more time.
1042 U.pVal[WordsToMove - 1] =
1043 SignExtend64(U.pVal[WordsToMove - 1], APINT_BITS_PER_WORD - BitShift);
1044 }
1045 }
1046
1047 // Fill in the remainder based on the original sign.
1048 std::memset(U.pVal + WordsToMove, Negative ? -1 : 0,
1049 WordShift * APINT_WORD_SIZE);
1050 clearUnusedBits();
1051}
1052
1053/// Logical right-shift this APInt by shiftAmt.
1054/// Logical right-shift function.
1055void APInt::lshrInPlace(const APInt &shiftAmt) {
1056 lshrInPlace((unsigned)shiftAmt.getLimitedValue(BitWidth));
1057}
1058
1059/// Logical right-shift this APInt by shiftAmt.
1060/// Logical right-shift function.
1061void APInt::lshrSlowCase(unsigned ShiftAmt) {
1062 tcShiftRight(U.pVal, getNumWords(), ShiftAmt);
1063}
1064
1065/// Left-shift this APInt by shiftAmt.
1066/// Left-shift function.
1067APInt &APInt::operator<<=(const APInt &shiftAmt) {
1068 // It's undefined behavior in C to shift by BitWidth or greater.
1069 *this <<= (unsigned)shiftAmt.getLimitedValue(BitWidth);
1070 return *this;
1071}
1072
1073void APInt::shlSlowCase(unsigned ShiftAmt) {
1074 tcShiftLeft(U.pVal, getNumWords(), ShiftAmt);
1075 clearUnusedBits();
1076}
1077
1078// Calculate the rotate amount modulo the bit width.
1079static unsigned rotateModulo(unsigned BitWidth, const APInt &rotateAmt) {
1080 if (LLVM_UNLIKELY(BitWidth == 0)__builtin_expect((bool)(BitWidth == 0), false))
1081 return 0;
1082 unsigned rotBitWidth = rotateAmt.getBitWidth();
1083 APInt rot = rotateAmt;
1084 if (rotBitWidth < BitWidth) {
1085 // Extend the rotate APInt, so that the urem doesn't divide by 0.
1086 // e.g. APInt(1, 32) would give APInt(1, 0).
1087 rot = rotateAmt.zext(BitWidth);
1088 }
1089 rot = rot.urem(APInt(rot.getBitWidth(), BitWidth));
1090 return rot.getLimitedValue(BitWidth);
1091}
1092
1093APInt APInt::rotl(const APInt &rotateAmt) const {
1094 return rotl(rotateModulo(BitWidth, rotateAmt));
1095}
1096
1097APInt APInt::rotl(unsigned rotateAmt) const {
1098 if (LLVM_UNLIKELY(BitWidth == 0)__builtin_expect((bool)(BitWidth == 0), false))
1099 return *this;
1100 rotateAmt %= BitWidth;
1101 if (rotateAmt == 0)
1102 return *this;
1103 return shl(rotateAmt) | lshr(BitWidth - rotateAmt);
1104}
1105
1106APInt APInt::rotr(const APInt &rotateAmt) const {
1107 return rotr(rotateModulo(BitWidth, rotateAmt));
1108}
1109
1110APInt APInt::rotr(unsigned rotateAmt) const {
1111 if (BitWidth == 0)
1112 return *this;
1113 rotateAmt %= BitWidth;
1114 if (rotateAmt == 0)
1115 return *this;
1116 return lshr(rotateAmt) | shl(BitWidth - rotateAmt);
1117}
1118
1119/// \returns the nearest log base 2 of this APInt. Ties round up.
1120///
1121/// NOTE: When we have a BitWidth of 1, we define:
1122///
1123/// log2(0) = UINT32_MAX
1124/// log2(1) = 0
1125///
1126/// to get around any mathematical concerns resulting from
1127/// referencing 2 in a space where 2 does no exist.
1128unsigned APInt::nearestLogBase2() const {
1129 // Special case when we have a bitwidth of 1. If VAL is 1, then we
1130 // get 0. If VAL is 0, we get WORDTYPE_MAX which gets truncated to
1131 // UINT32_MAX.
1132 if (BitWidth == 1)
1133 return U.VAL - 1;
1134
1135 // Handle the zero case.
1136 if (isZero())
1137 return UINT32_MAX(4294967295U);
1138
1139 // The non-zero case is handled by computing:
1140 //
1141 // nearestLogBase2(x) = logBase2(x) + x[logBase2(x)-1].
1142 //
1143 // where x[i] is referring to the value of the ith bit of x.
1144 unsigned lg = logBase2();
1145 return lg + unsigned((*this)[lg - 1]);
1146}
1147
1148// Square Root - this method computes and returns the square root of "this".
1149// Three mechanisms are used for computation. For small values (<= 5 bits),
1150// a table lookup is done. This gets some performance for common cases. For
1151// values using less than 52 bits, the value is converted to double and then
1152// the libc sqrt function is called. The result is rounded and then converted
1153// back to a uint64_t which is then used to construct the result. Finally,
1154// the Babylonian method for computing square roots is used.
1155APInt APInt::sqrt() const {
1156
1157 // Determine the magnitude of the value.
1158 unsigned magnitude = getActiveBits();
1159
1160 // Use a fast table for some small values. This also gets rid of some
1161 // rounding errors in libc sqrt for small values.
1162 if (magnitude <= 5) {
1163 static const uint8_t results[32] = {
1164 /* 0 */ 0,
1165 /* 1- 2 */ 1, 1,
1166 /* 3- 6 */ 2, 2, 2, 2,
1167 /* 7-12 */ 3, 3, 3, 3, 3, 3,
1168 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4,
1169 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
1170 /* 31 */ 6
1171 };
1172 return APInt(BitWidth, results[ (isSingleWord() ? U.VAL : U.pVal[0]) ]);
1173 }
1174
1175 // If the magnitude of the value fits in less than 52 bits (the precision of
1176 // an IEEE double precision floating point value), then we can use the
1177 // libc sqrt function which will probably use a hardware sqrt computation.
1178 // This should be faster than the algorithm below.
1179 if (magnitude < 52) {
1180 return APInt(BitWidth,
1181 uint64_t(::round(::sqrt(double(isSingleWord() ? U.VAL
1182 : U.pVal[0])))));
1183 }
1184
1185 // Okay, all the short cuts are exhausted. We must compute it. The following
1186 // is a classical Babylonian method for computing the square root. This code
1187 // was adapted to APInt from a wikipedia article on such computations.
1188 // See http://www.wikipedia.org/ and go to the page named
1189 // Calculate_an_integer_square_root.
1190 unsigned nbits = BitWidth, i = 4;
1191 APInt testy(BitWidth, 16);
1192 APInt x_old(BitWidth, 1);
1193 APInt x_new(BitWidth, 0);
1194 APInt two(BitWidth, 2);
1195
1196 // Select a good starting value using binary logarithms.
1197 for (;; i += 2, testy = testy.shl(2))
1198 if (i >= nbits || this->ule(testy)) {
1199 x_old = x_old.shl(i / 2);
1200 break;
1201 }
1202
1203 // Use the Babylonian method to arrive at the integer square root:
1204 for (;;) {
1205 x_new = (this->udiv(x_old) + x_old).udiv(two);
1206 if (x_old.ule(x_new))
1207 break;
1208 x_old = x_new;
1209 }
1210
1211 // Make sure we return the closest approximation
1212 // NOTE: The rounding calculation below is correct. It will produce an
1213 // off-by-one discrepancy with results from pari/gp. That discrepancy has been
1214 // determined to be a rounding issue with pari/gp as it begins to use a
1215 // floating point representation after 192 bits. There are no discrepancies
1216 // between this algorithm and pari/gp for bit widths < 192 bits.
1217 APInt square(x_old * x_old);
1218 APInt nextSquare((x_old + 1) * (x_old +1));
1219 if (this->ult(square))
1220 return x_old;
1221 assert(this->ule(nextSquare) && "Error in APInt::sqrt computation")(static_cast <bool> (this->ule(nextSquare) &&
"Error in APInt::sqrt computation") ? void (0) : __assert_fail
("this->ule(nextSquare) && \"Error in APInt::sqrt computation\""
, "llvm/lib/Support/APInt.cpp", 1221, __extension__ __PRETTY_FUNCTION__
))
;
1222 APInt midpoint((nextSquare - square).udiv(two));
1223 APInt offset(*this - square);
1224 if (offset.ult(midpoint))
1225 return x_old;
1226 return x_old + 1;
1227}
1228
1229/// Computes the multiplicative inverse of this APInt for a given modulo. The
1230/// iterative extended Euclidean algorithm is used to solve for this value,
1231/// however we simplify it to speed up calculating only the inverse, and take
1232/// advantage of div+rem calculations. We also use some tricks to avoid copying
1233/// (potentially large) APInts around.
1234/// WARNING: a value of '0' may be returned,
1235/// signifying that no multiplicative inverse exists!
1236APInt APInt::multiplicativeInverse(const APInt& modulo) const {
1237 assert(ult(modulo) && "This APInt must be smaller than the modulo")(static_cast <bool> (ult(modulo) && "This APInt must be smaller than the modulo"
) ? void (0) : __assert_fail ("ult(modulo) && \"This APInt must be smaller than the modulo\""
, "llvm/lib/Support/APInt.cpp", 1237, __extension__ __PRETTY_FUNCTION__
))
;
1238
1239 // Using the properties listed at the following web page (accessed 06/21/08):
1240 // http://www.numbertheory.org/php/euclid.html
1241 // (especially the properties numbered 3, 4 and 9) it can be proved that
1242 // BitWidth bits suffice for all the computations in the algorithm implemented
1243 // below. More precisely, this number of bits suffice if the multiplicative
1244 // inverse exists, but may not suffice for the general extended Euclidean
1245 // algorithm.
1246
1247 APInt r[2] = { modulo, *this };
1248 APInt t[2] = { APInt(BitWidth, 0), APInt(BitWidth, 1) };
1249 APInt q(BitWidth, 0);
1250
1251 unsigned i;
1252 for (i = 0; r[i^1] != 0; i ^= 1) {
1253 // An overview of the math without the confusing bit-flipping:
1254 // q = r[i-2] / r[i-1]
1255 // r[i] = r[i-2] % r[i-1]
1256 // t[i] = t[i-2] - t[i-1] * q
1257 udivrem(r[i], r[i^1], q, r[i]);
1258 t[i] -= t[i^1] * q;
1259 }
1260
1261 // If this APInt and the modulo are not coprime, there is no multiplicative
1262 // inverse, so return 0. We check this by looking at the next-to-last
1263 // remainder, which is the gcd(*this,modulo) as calculated by the Euclidean
1264 // algorithm.
1265 if (r[i] != 1)
1266 return APInt(BitWidth, 0);
1267
1268 // The next-to-last t is the multiplicative inverse. However, we are
1269 // interested in a positive inverse. Calculate a positive one from a negative
1270 // one if necessary. A simple addition of the modulo suffices because
1271 // abs(t[i]) is known to be less than *this/2 (see the link above).
1272 if (t[i].isNegative())
1273 t[i] += modulo;
1274
1275 return std::move(t[i]);
1276}
1277
1278/// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
1279/// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
1280/// variables here have the same names as in the algorithm. Comments explain
1281/// the algorithm and any deviation from it.
1282static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
1283 unsigned m, unsigned n) {
1284 assert(u && "Must provide dividend")(static_cast <bool> (u && "Must provide dividend"
) ? void (0) : __assert_fail ("u && \"Must provide dividend\""
, "llvm/lib/Support/APInt.cpp", 1284, __extension__ __PRETTY_FUNCTION__
))
;
1
Assuming 'u' is non-null
2
'?' condition is true
1285 assert(v && "Must provide divisor")(static_cast <bool> (v && "Must provide divisor"
) ? void (0) : __assert_fail ("v && \"Must provide divisor\""
, "llvm/lib/Support/APInt.cpp", 1285, __extension__ __PRETTY_FUNCTION__
))
;
3
Assuming 'v' is non-null
4
'?' condition is true
1286 assert(q && "Must provide quotient")(static_cast <bool> (q && "Must provide quotient"
) ? void (0) : __assert_fail ("q && \"Must provide quotient\""
, "llvm/lib/Support/APInt.cpp", 1286, __extension__ __PRETTY_FUNCTION__
))
;
5
Assuming 'q' is non-null
6
'?' condition is true
1287 assert(u != v && u != q && v != q && "Must use different memory")(static_cast <bool> (u != v && u != q &&
v != q && "Must use different memory") ? void (0) : __assert_fail
("u != v && u != q && v != q && \"Must use different memory\""
, "llvm/lib/Support/APInt.cpp", 1287, __extension__ __PRETTY_FUNCTION__
))
;
7
Assuming 'u' is not equal to 'v'
8
Assuming 'u' is not equal to 'q'
9
Assuming 'v' is not equal to 'q'
10
'?' condition is true
1288 assert(n>1 && "n must be > 1")(static_cast <bool> (n>1 && "n must be > 1"
) ? void (0) : __assert_fail ("n>1 && \"n must be > 1\""
, "llvm/lib/Support/APInt.cpp", 1288, __extension__ __PRETTY_FUNCTION__
))
;
11
Assuming 'n' is > 1
12
'?' condition is true
1289
1290 // b denotes the base of the number system. In our case b is 2^32.
1291 const uint64_t b = uint64_t(1) << 32;
1292
1293// The DEBUG macros here tend to be spam in the debug output if you're not
1294// debugging this code. Disable them unless KNUTH_DEBUG is defined.
1295#ifdef KNUTH_DEBUG
1296#define DEBUG_KNUTH(X)do {} while(false) LLVM_DEBUG(X)do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("apint")) { X; } } while (false)
1297#else
1298#define DEBUG_KNUTH(X)do {} while(false) do {} while(false)
1299#endif
1300
1301 DEBUG_KNUTH(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n')do {} while(false);
13
Loop condition is false. Exiting loop
1302 DEBUG_KNUTH(dbgs() << "KnuthDiv: original:")do {} while(false);
14
Loop condition is false. Exiting loop
1303 DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i])do {} while(false);
15
Loop condition is false. Exiting loop
1304 DEBUG_KNUTH(dbgs() << " by")do {} while(false);
16
Loop condition is false. Exiting loop
1305 DEBUG_KNUTH(for (int i = n; i > 0; i--) dbgs() << " " << v[i - 1])do {} while(false);
17
Loop condition is false. Exiting loop
1306 DEBUG_KNUTH(dbgs() << '\n')do {} while(false);
18
Loop condition is false. Exiting loop
1307 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
1308 // u and v by d. Note that we have taken Knuth's advice here to use a power
1309 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
1310 // 2 allows us to shift instead of multiply and it is easy to determine the
1311 // shift amount from the leading zeros. We are basically normalizing the u
1312 // and v so that its high bits are shifted to the top of v's range without
1313 // overflow. Note that this can require an extra word in u so that u must
1314 // be of length m+n+1.
1315 unsigned shift = countLeadingZeros(v[n-1]);
19
Calling 'countLeadingZeros<unsigned int>'
28
Returning from 'countLeadingZeros<unsigned int>'
29
'shift' initialized to 32
1316 uint32_t v_carry = 0;
1317 uint32_t u_carry = 0;
1318 if (shift
29.1
'shift' is 32
29.1
'shift' is 32
) {
30
Taking true branch
1319 for (unsigned i = 0; i < m+n; ++i) {
31
Assuming the condition is false
32
Loop condition is false. Execution continues on line 1324
1320 uint32_t u_tmp = u[i] >> (32 - shift);
1321 u[i] = (u[i] << shift) | u_carry;
1322 u_carry = u_tmp;
1323 }
1324 for (unsigned i = 0; i
32.1
'i' is < 'n'
33.1
'i' is < 'n'
32.1
'i' is < 'n'
33.1
'i' is < 'n'
< n
; ++i) {
33
Loop condition is true. Entering loop body
34
Loop condition is true. Entering loop body
35
Assuming 'i' is >= 'n'
36
Loop condition is false. Execution continues on line 1330
1325 uint32_t v_tmp = v[i] >> (32 - shift);
1326 v[i] = (v[i] << shift) | v_carry;
1327 v_carry = v_tmp;
1328 }
1329 }
1330 u[m+n] = u_carry;
1331
1332 DEBUG_KNUTH(dbgs() << "KnuthDiv: normal:")do {} while(false);
37
Loop condition is false. Exiting loop
1333 DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i])do {} while(false);
38
Loop condition is false. Exiting loop
1334 DEBUG_KNUTH(dbgs() << " by")do {} while(false);
39
Loop condition is false. Exiting loop
1335 DEBUG_KNUTH(for (int i = n; i > 0; i--) dbgs() << " " << v[i - 1])do {} while(false);
40
Loop condition is false. Exiting loop
1336 DEBUG_KNUTH(dbgs() << '\n')do {} while(false);
41
Loop condition is false. Exiting loop
1337
1338 // D2. [Initialize j.] Set j to m. This is the loop counter over the places.
1339 int j = m;
1340 do {
61
Loop condition is false. Exiting loop
1341 DEBUG_KNUTH(dbgs() << "KnuthDiv: quotient digit #" << j << '\n')do {} while(false);
42
Loop condition is false. Exiting loop
1342 // D3. [Calculate q'.].
1343 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
1344 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
1345 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
1346 // qp by 1, increase rp by v[n-1], and repeat this test if rp < b. The test
1347 // on v[n-2] determines at high speed most of the cases in which the trial
1348 // value qp is one too large, and it eliminates all cases where qp is two
1349 // too large.
1350 uint64_t dividend = Make_64(u[j+n], u[j+n-1]);
1351 DEBUG_KNUTH(dbgs() << "KnuthDiv: dividend == " << dividend << '\n')do {} while(false);
43
Loop condition is false. Exiting loop
1352 uint64_t qp = dividend / v[n-1];
1353 uint64_t rp = dividend % v[n-1];
1354 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
44
Assuming 'qp' is not equal to 'b'
45
Assuming the condition is false
46
Taking false branch
1355 qp--;
1356 rp += v[n-1];
1357 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
1358 qp--;
1359 }
1360 DEBUG_KNUTH(dbgs() << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n')do {} while(false);
47
Loop condition is false. Exiting loop
1361
1362 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
1363 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
1364 // consists of a simple multiplication by a one-place number, combined with
1365 // a subtraction.
1366 // The digits (u[j+n]...u[j]) should be kept positive; if the result of
1367 // this step is actually negative, (u[j+n]...u[j]) should be left as the
1368 // true value plus b**(n+1), namely as the b's complement of
1369 // the true value, and a "borrow" to the left should be remembered.
1370 int64_t borrow = 0;
1371 for (unsigned i = 0; i < n; ++i) {
48
Loop condition is true. Entering loop body
50
Loop condition is true. Entering loop body
52
Loop condition is false. Execution continues on line 1379
1372 uint64_t p = uint64_t(qp) * uint64_t(v[i]);
1373 int64_t subres = int64_t(u[j+i]) - borrow - Lo_32(p);
1374 u[j+i] = Lo_32(subres);
1375 borrow = Hi_32(p) - Hi_32(subres);
1376 DEBUG_KNUTH(dbgs() << "KnuthDiv: u[j+i] = " << u[j + i]do {} while(false)
49
Loop condition is false. Exiting loop
51
Loop condition is false. Exiting loop
1377 << ", borrow = " << borrow << '\n')do {} while(false);
1378 }
1379 bool isNeg = u[j+n] < borrow;
53
Assuming the condition is false
1380 u[j+n] -= Lo_32(borrow);
1381
1382 DEBUG_KNUTH(dbgs() << "KnuthDiv: after subtraction:")do {} while(false);
54
Loop condition is false. Exiting loop
1383 DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i])do {} while(false);
55
Loop condition is false. Exiting loop
1384 DEBUG_KNUTH(dbgs() << '\n')do {} while(false);
56
Loop condition is false. Exiting loop
1385
1386 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
1387 // negative, go to step D6; otherwise go on to step D7.
1388 q[j] = Lo_32(qp);
1389 if (isNeg
56.1
'isNeg' is false
56.1
'isNeg' is false
) {
57
Taking false branch
1390 // D6. [Add back]. The probability that this step is necessary is very
1391 // small, on the order of only 2/b. Make sure that test data accounts for
1392 // this possibility. Decrease q[j] by 1
1393 q[j]--;
1394 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
1395 // A carry will occur to the left of u[j+n], and it should be ignored
1396 // since it cancels with the borrow that occurred in D4.
1397 bool carry = false;
1398 for (unsigned i = 0; i < n; i++) {
1399 uint32_t limit = std::min(u[j+i],v[i]);
1400 u[j+i] += v[i] + carry;
1401 carry = u[j+i] < limit || (carry && u[j+i] == limit);
1402 }
1403 u[j+n] += carry;
1404 }
1405 DEBUG_KNUTH(dbgs() << "KnuthDiv: after correction:")do {} while(false);
58
Loop condition is false. Exiting loop
1406 DEBUG_KNUTH(for (int i = m + n; i >= 0; i--) dbgs() << " " << u[i])do {} while(false);
59
Loop condition is false. Exiting loop
1407 DEBUG_KNUTH(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n')do {} while(false);
60
Loop condition is false. Exiting loop
1408
1409 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
1410 } while (--j >= 0);
1411
1412 DEBUG_KNUTH(dbgs() << "KnuthDiv: quotient:")do {} while(false);
62
Loop condition is false. Exiting loop
1413 DEBUG_KNUTH(for (int i = m; i >= 0; i--) dbgs() << " " << q[i])do {} while(false);
63
Loop condition is false. Exiting loop
1414 DEBUG_KNUTH(dbgs() << '\n')do {} while(false);
64
Loop condition is false. Exiting loop
1415
1416 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
1417 // remainder may be obtained by dividing u[...] by d. If r is non-null we
1418 // compute the remainder (urem uses this).
1419 if (r) {
65
Assuming 'r' is non-null
66
Taking true branch
1420 // The value d is expressed by the "shift" value above since we avoided
1421 // multiplication by d by using a shift left. So, all we have to do is
1422 // shift right here.
1423 if (shift
66.1
'shift' is 32
66.1
'shift' is 32
) {
67
Taking true branch
1424 uint32_t carry = 0;
1425 DEBUG_KNUTH(dbgs() << "KnuthDiv: remainder:")do {} while(false);
68
Loop condition is false. Exiting loop
1426 for (int i = n-1; i >= 0; i--) {
69
Loop condition is true. Entering loop body
71
Loop condition is true. Entering loop body
1427 r[i] = (u[i] >> shift) | carry;
72
The result of the right shift is undefined due to shifting by '32', which is greater or equal to the width of type 'uint32_t'
1428 carry = u[i] << (32 - shift);
1429 DEBUG_KNUTH(dbgs() << " " << r[i])do {} while(false);
70
Loop condition is false. Exiting loop
1430 }
1431 } else {
1432 for (int i = n-1; i >= 0; i--) {
1433 r[i] = u[i];
1434 DEBUG_KNUTH(dbgs() << " " << r[i])do {} while(false);
1435 }
1436 }
1437 DEBUG_KNUTH(dbgs() << '\n')do {} while(false);
1438 }
1439 DEBUG_KNUTH(dbgs() << '\n')do {} while(false);
1440}
1441
1442void APInt::divide(const WordType *LHS, unsigned lhsWords, const WordType *RHS,
1443 unsigned rhsWords, WordType *Quotient, WordType *Remainder) {
1444 assert(lhsWords >= rhsWords && "Fractional result")(static_cast <bool> (lhsWords >= rhsWords &&
"Fractional result") ? void (0) : __assert_fail ("lhsWords >= rhsWords && \"Fractional result\""
, "llvm/lib/Support/APInt.cpp", 1444, __extension__ __PRETTY_FUNCTION__
))
;
1445
1446 // First, compose the values into an array of 32-bit words instead of
1447 // 64-bit words. This is a necessity of both the "short division" algorithm
1448 // and the Knuth "classical algorithm" which requires there to be native
1449 // operations for +, -, and * on an m bit value with an m*2 bit result. We
1450 // can't use 64-bit operands here because we don't have native results of
1451 // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't
1452 // work on large-endian machines.
1453 unsigned n = rhsWords * 2;
1454 unsigned m = (lhsWords * 2) - n;
1455
1456 // Allocate space for the temporary values we need either on the stack, if
1457 // it will fit, or on the heap if it won't.
1458 uint32_t SPACE[128];
1459 uint32_t *U = nullptr;
1460 uint32_t *V = nullptr;
1461 uint32_t *Q = nullptr;
1462 uint32_t *R = nullptr;
1463 if ((Remainder?4:3)*n+2*m+1 <= 128) {
1464 U = &SPACE[0];
1465 V = &SPACE[m+n+1];
1466 Q = &SPACE[(m+n+1) + n];
1467 if (Remainder)
1468 R = &SPACE[(m+n+1) + n + (m+n)];
1469 } else {
1470 U = new uint32_t[m + n + 1];
1471 V = new uint32_t[n];
1472 Q = new uint32_t[m+n];
1473 if (Remainder)
1474 R = new uint32_t[n];
1475 }
1476
1477 // Initialize the dividend
1478 memset(U, 0, (m+n+1)*sizeof(uint32_t));
1479 for (unsigned i = 0; i < lhsWords; ++i) {
1480 uint64_t tmp = LHS[i];
1481 U[i * 2] = Lo_32(tmp);
1482 U[i * 2 + 1] = Hi_32(tmp);
1483 }
1484 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
1485
1486 // Initialize the divisor
1487 memset(V, 0, (n)*sizeof(uint32_t));
1488 for (unsigned i = 0; i < rhsWords; ++i) {
1489 uint64_t tmp = RHS[i];
1490 V[i * 2] = Lo_32(tmp);
1491 V[i * 2 + 1] = Hi_32(tmp);
1492 }
1493
1494 // initialize the quotient and remainder
1495 memset(Q, 0, (m+n) * sizeof(uint32_t));
1496 if (Remainder)
1497 memset(R, 0, n * sizeof(uint32_t));
1498
1499 // Now, adjust m and n for the Knuth division. n is the number of words in
1500 // the divisor. m is the number of words by which the dividend exceeds the
1501 // divisor (i.e. m+n is the length of the dividend). These sizes must not
1502 // contain any zero words or the Knuth algorithm fails.
1503 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
1504 n--;
1505 m++;
1506 }
1507 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
1508 m--;
1509
1510 // If we're left with only a single word for the divisor, Knuth doesn't work
1511 // so we implement the short division algorithm here. This is much simpler
1512 // and faster because we are certain that we can divide a 64-bit quantity
1513 // by a 32-bit quantity at hardware speed and short division is simply a
1514 // series of such operations. This is just like doing short division but we
1515 // are using base 2^32 instead of base 10.
1516 assert(n != 0 && "Divide by zero?")(static_cast <bool> (n != 0 && "Divide by zero?"
) ? void (0) : __assert_fail ("n != 0 && \"Divide by zero?\""
, "llvm/lib/Support/APInt.cpp", 1516, __extension__ __PRETTY_FUNCTION__
))
;
1517 if (n == 1) {
1518 uint32_t divisor = V[0];
1519 uint32_t remainder = 0;
1520 for (int i = m; i >= 0; i--) {
1521 uint64_t partial_dividend = Make_64(remainder, U[i]);
1522 if (partial_dividend == 0) {
1523 Q[i] = 0;
1524 remainder = 0;
1525 } else if (partial_dividend < divisor) {
1526 Q[i] = 0;
1527 remainder = Lo_32(partial_dividend);
1528 } else if (partial_dividend == divisor) {
1529 Q[i] = 1;
1530 remainder = 0;
1531 } else {
1532 Q[i] = Lo_32(partial_dividend / divisor);
1533 remainder = Lo_32(partial_dividend - (Q[i] * divisor));
1534 }
1535 }
1536 if (R)
1537 R[0] = remainder;
1538 } else {
1539 // Now we're ready to invoke the Knuth classical divide algorithm. In this
1540 // case n > 1.
1541 KnuthDiv(U, V, Q, R, m, n);
1542 }
1543
1544 // If the caller wants the quotient
1545 if (Quotient) {
1546 for (unsigned i = 0; i < lhsWords; ++i)
1547 Quotient[i] = Make_64(Q[i*2+1], Q[i*2]);
1548 }
1549
1550 // If the caller wants the remainder
1551 if (Remainder) {
1552 for (unsigned i = 0; i < rhsWords; ++i)
1553 Remainder[i] = Make_64(R[i*2+1], R[i*2]);
1554 }
1555
1556 // Clean up the memory we allocated.
1557 if (U != &SPACE[0]) {
1558 delete [] U;
1559 delete [] V;
1560 delete [] Q;
1561 delete [] R;
1562 }
1563}
1564
1565APInt APInt::udiv(const APInt &RHS) const {
1566 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same")(static_cast <bool> (BitWidth == RHS.BitWidth &&
"Bit widths must be the same") ? void (0) : __assert_fail ("BitWidth == RHS.BitWidth && \"Bit widths must be the same\""
, "llvm/lib/Support/APInt.cpp", 1566, __extension__ __PRETTY_FUNCTION__
))
;
1567
1568 // First, deal with the easy case
1569 if (isSingleWord()) {
1570 assert(RHS.U.VAL != 0 && "Divide by zero?")(static_cast <bool> (RHS.U.VAL != 0 && "Divide by zero?"
) ? void (0) : __assert_fail ("RHS.U.VAL != 0 && \"Divide by zero?\""
, "llvm/lib/Support/APInt.cpp", 1570, __extension__ __PRETTY_FUNCTION__
))
;
1571 return APInt(BitWidth, U.VAL / RHS.U.VAL);
1572 }
1573
1574 // Get some facts about the LHS and RHS number of bits and words
1575 unsigned lhsWords = getNumWords(getActiveBits());
1576 unsigned rhsBits = RHS.getActiveBits();
1577 unsigned rhsWords = getNumWords(rhsBits);
1578 assert(rhsWords && "Divided by zero???")(static_cast <bool> (rhsWords && "Divided by zero???"
) ? void (0) : __assert_fail ("rhsWords && \"Divided by zero???\""
, "llvm/lib/Support/APInt.cpp", 1578, __extension__ __PRETTY_FUNCTION__
))
;
1579
1580 // Deal with some degenerate cases
1581 if (!lhsWords)
1582 // 0 / X ===> 0
1583 return APInt(BitWidth, 0);
1584 if (rhsBits == 1)
1585 // X / 1 ===> X
1586 return *this;
1587 if (lhsWords < rhsWords || this->ult(RHS))
1588 // X / Y ===> 0, iff X < Y
1589 return APInt(BitWidth, 0);
1590 if (*this == RHS)
1591 // X / X ===> 1
1592 return APInt(BitWidth, 1);
1593 if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1.
1594 // All high words are zero, just use native divide
1595 return APInt(BitWidth, this->U.pVal[0] / RHS.U.pVal[0]);
1596
1597 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1598 APInt Quotient(BitWidth, 0); // to hold result.
1599 divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal, nullptr);
1600 return Quotient;
1601}
1602
1603APInt APInt::udiv(uint64_t RHS) const {
1604 assert(RHS != 0 && "Divide by zero?")(static_cast <bool> (RHS != 0 && "Divide by zero?"
) ? void (0) : __assert_fail ("RHS != 0 && \"Divide by zero?\""
, "llvm/lib/Support/APInt.cpp", 1604, __extension__ __PRETTY_FUNCTION__
))
;
1605
1606 // First, deal with the easy case
1607 if (isSingleWord())
1608 return APInt(BitWidth, U.VAL / RHS);
1609
1610 // Get some facts about the LHS words.
1611 unsigned lhsWords = getNumWords(getActiveBits());
1612
1613 // Deal with some degenerate cases
1614 if (!lhsWords)
1615 // 0 / X ===> 0
1616 return APInt(BitWidth, 0);
1617 if (RHS == 1)
1618 // X / 1 ===> X
1619 return *this;
1620 if (this->ult(RHS))
1621 // X / Y ===> 0, iff X < Y
1622 return APInt(BitWidth, 0);
1623 if (*this == RHS)
1624 // X / X ===> 1
1625 return APInt(BitWidth, 1);
1626 if (lhsWords == 1) // rhsWords is 1 if lhsWords is 1.
1627 // All high words are zero, just use native divide
1628 return APInt(BitWidth, this->U.pVal[0] / RHS);
1629
1630 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1631 APInt Quotient(BitWidth, 0); // to hold result.
1632 divide(U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, nullptr);
1633 return Quotient;
1634}
1635
1636APInt APInt::sdiv(const APInt &RHS) const {
1637 if (isNegative()) {
1638 if (RHS.isNegative())
1639 return (-(*this)).udiv(-RHS);
1640 return -((-(*this)).udiv(RHS));
1641 }
1642 if (RHS.isNegative())
1643 return -(this->udiv(-RHS));
1644 return this->udiv(RHS);
1645}
1646
1647APInt APInt::sdiv(int64_t RHS) const {
1648 if (isNegative()) {
1649 if (RHS < 0)
1650 return (-(*this)).udiv(-RHS);
1651 return -((-(*this)).udiv(RHS));
1652 }
1653 if (RHS < 0)
1654 return -(this->udiv(-RHS));
1655 return this->udiv(RHS);
1656}
1657
1658APInt APInt::urem(const APInt &RHS) const {
1659 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same")(static_cast <bool> (BitWidth == RHS.BitWidth &&
"Bit widths must be the same") ? void (0) : __assert_fail ("BitWidth == RHS.BitWidth && \"Bit widths must be the same\""
, "llvm/lib/Support/APInt.cpp", 1659, __extension__ __PRETTY_FUNCTION__
))
;
1660 if (isSingleWord()) {
1661 assert(RHS.U.VAL != 0 && "Remainder by zero?")(static_cast <bool> (RHS.U.VAL != 0 && "Remainder by zero?"
) ? void (0) : __assert_fail ("RHS.U.VAL != 0 && \"Remainder by zero?\""
, "llvm/lib/Support/APInt.cpp", 1661, __extension__ __PRETTY_FUNCTION__
))
;
1662 return APInt(BitWidth, U.VAL % RHS.U.VAL);
1663 }
1664
1665 // Get some facts about the LHS
1666 unsigned lhsWords = getNumWords(getActiveBits());
1667
1668 // Get some facts about the RHS
1669 unsigned rhsBits = RHS.getActiveBits();
1670 unsigned rhsWords = getNumWords(rhsBits);
1671 assert(rhsWords && "Performing remainder operation by zero ???")(static_cast <bool> (rhsWords && "Performing remainder operation by zero ???"
) ? void (0) : __assert_fail ("rhsWords && \"Performing remainder operation by zero ???\""
, "llvm/lib/Support/APInt.cpp", 1671, __extension__ __PRETTY_FUNCTION__
))
;
1672
1673 // Check the degenerate cases
1674 if (lhsWords == 0)
1675 // 0 % Y ===> 0
1676 return APInt(BitWidth, 0);
1677 if (rhsBits == 1)
1678 // X % 1 ===> 0
1679 return APInt(BitWidth, 0);
1680 if (lhsWords < rhsWords || this->ult(RHS))
1681 // X % Y ===> X, iff X < Y
1682 return *this;
1683 if (*this == RHS)
1684 // X % X == 0;
1685 return APInt(BitWidth, 0);
1686 if (lhsWords == 1)
1687 // All high words are zero, just use native remainder
1688 return APInt(BitWidth, U.pVal[0] % RHS.U.pVal[0]);
1689
1690 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1691 APInt Remainder(BitWidth, 0);
1692 divide(U.pVal, lhsWords, RHS.U.pVal, rhsWords, nullptr, Remainder.U.pVal);
1693 return Remainder;
1694}
1695
1696uint64_t APInt::urem(uint64_t RHS) const {
1697 assert(RHS != 0 && "Remainder by zero?")(static_cast <bool> (RHS != 0 && "Remainder by zero?"
) ? void (0) : __assert_fail ("RHS != 0 && \"Remainder by zero?\""
, "llvm/lib/Support/APInt.cpp", 1697, __extension__ __PRETTY_FUNCTION__
))
;
1698
1699 if (isSingleWord())
1700 return U.VAL % RHS;
1701
1702 // Get some facts about the LHS
1703 unsigned lhsWords = getNumWords(getActiveBits());
1704
1705 // Check the degenerate cases
1706 if (lhsWords == 0)
1707 // 0 % Y ===> 0
1708 return 0;
1709 if (RHS == 1)
1710 // X % 1 ===> 0
1711 return 0;
1712 if (this->ult(RHS))
1713 // X % Y ===> X, iff X < Y
1714 return getZExtValue();
1715 if (*this == RHS)
1716 // X % X == 0;
1717 return 0;
1718 if (lhsWords == 1)
1719 // All high words are zero, just use native remainder
1720 return U.pVal[0] % RHS;
1721
1722 // We have to compute it the hard way. Invoke the Knuth divide algorithm.
1723 uint64_t Remainder;
1724 divide(U.pVal, lhsWords, &RHS, 1, nullptr, &Remainder);
1725 return Remainder;
1726}
1727
1728APInt APInt::srem(const APInt &RHS) const {
1729 if (isNegative()) {
1730 if (RHS.isNegative())
1731 return -((-(*this)).urem(-RHS));
1732 return -((-(*this)).urem(RHS));
1733 }
1734 if (RHS.isNegative())
1735 return this->urem(-RHS);
1736 return this->urem(RHS);
1737}
1738
1739int64_t APInt::srem(int64_t RHS) const {
1740 if (isNegative()) {
1741 if (RHS < 0)
1742 return -((-(*this)).urem(-RHS));
1743 return -((-(*this)).urem(RHS));
1744 }
1745 if (RHS < 0)
1746 return this->urem(-RHS);
1747 return this->urem(RHS);
1748}
1749
1750void APInt::udivrem(const APInt &LHS, const APInt &RHS,
1751 APInt &Quotient, APInt &Remainder) {
1752 assert(LHS.BitWidth == RHS.BitWidth && "Bit widths must be the same")(static_cast <bool> (LHS.BitWidth == RHS.BitWidth &&
"Bit widths must be the same") ? void (0) : __assert_fail ("LHS.BitWidth == RHS.BitWidth && \"Bit widths must be the same\""
, "llvm/lib/Support/APInt.cpp", 1752, __extension__ __PRETTY_FUNCTION__
))
;
1753 unsigned BitWidth = LHS.BitWidth;
1754
1755 // First, deal with the easy case
1756 if (LHS.isSingleWord()) {
1757 assert(RHS.U.VAL != 0 && "Divide by zero?")(static_cast <bool> (RHS.U.VAL != 0 && "Divide by zero?"
) ? void (0) : __assert_fail ("RHS.U.VAL != 0 && \"Divide by zero?\""
, "llvm/lib/Support/APInt.cpp", 1757, __extension__ __PRETTY_FUNCTION__
))
;
1758 uint64_t QuotVal = LHS.U.VAL / RHS.U.VAL;
1759 uint64_t RemVal = LHS.U.VAL % RHS.U.VAL;
1760 Quotient = APInt(BitWidth, QuotVal);
1761 Remainder = APInt(BitWidth, RemVal);
1762 return;
1763 }
1764
1765 // Get some size facts about the dividend and divisor
1766 unsigned lhsWords = getNumWords(LHS.getActiveBits());
1767 unsigned rhsBits = RHS.getActiveBits();
1768 unsigned rhsWords = getNumWords(rhsBits);
1769 assert(rhsWords && "Performing divrem operation by zero ???")(static_cast <bool> (rhsWords && "Performing divrem operation by zero ???"
) ? void (0) : __assert_fail ("rhsWords && \"Performing divrem operation by zero ???\""
, "llvm/lib/Support/APInt.cpp", 1769, __extension__ __PRETTY_FUNCTION__
))
;
1770
1771 // Check the degenerate cases
1772 if (lhsWords == 0) {
1773 Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0
1774 Remainder = APInt(BitWidth, 0); // 0 % Y ===> 0
1775 return;
1776 }
1777
1778 if (rhsBits == 1) {
1779 Quotient = LHS; // X / 1 ===> X
1780 Remainder = APInt(BitWidth, 0); // X % 1 ===> 0
1781 }
1782
1783 if (lhsWords < rhsWords || LHS.ult(RHS)) {
1784 Remainder = LHS; // X % Y ===> X, iff X < Y
1785 Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y
1786 return;
1787 }
1788
1789 if (LHS == RHS) {
1790 Quotient = APInt(BitWidth, 1); // X / X ===> 1
1791 Remainder = APInt(BitWidth, 0); // X % X ===> 0;
1792 return;
1793 }
1794
1795 // Make sure there is enough space to hold the results.
1796 // NOTE: This assumes that reallocate won't affect any bits if it doesn't
1797 // change the size. This is necessary if Quotient or Remainder is aliased
1798 // with LHS or RHS.
1799 Quotient.reallocate(BitWidth);
1800 Remainder.reallocate(BitWidth);
1801
1802 if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1.
1803 // There is only one word to consider so use the native versions.
1804 uint64_t lhsValue = LHS.U.pVal[0];
1805 uint64_t rhsValue = RHS.U.pVal[0];
1806 Quotient = lhsValue / rhsValue;
1807 Remainder = lhsValue % rhsValue;
1808 return;
1809 }
1810
1811 // Okay, lets do it the long way
1812 divide(LHS.U.pVal, lhsWords, RHS.U.pVal, rhsWords, Quotient.U.pVal,
1813 Remainder.U.pVal);
1814 // Clear the rest of the Quotient and Remainder.
1815 std::memset(Quotient.U.pVal + lhsWords, 0,
1816 (getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE);
1817 std::memset(Remainder.U.pVal + rhsWords, 0,
1818 (getNumWords(BitWidth) - rhsWords) * APINT_WORD_SIZE);
1819}
1820
1821void APInt::udivrem(const APInt &LHS, uint64_t RHS, APInt &Quotient,
1822 uint64_t &Remainder) {
1823 assert(RHS != 0 && "Divide by zero?")(static_cast <bool> (RHS != 0 && "Divide by zero?"
) ? void (0) : __assert_fail ("RHS != 0 && \"Divide by zero?\""
, "llvm/lib/Support/APInt.cpp", 1823, __extension__ __PRETTY_FUNCTION__
))
;
1824 unsigned BitWidth = LHS.BitWidth;
1825
1826 // First, deal with the easy case
1827 if (LHS.isSingleWord()) {
1828 uint64_t QuotVal = LHS.U.VAL / RHS;
1829 Remainder = LHS.U.VAL % RHS;
1830 Quotient = APInt(BitWidth, QuotVal);
1831 return;
1832 }
1833
1834 // Get some size facts about the dividend and divisor
1835 unsigned lhsWords = getNumWords(LHS.getActiveBits());
1836
1837 // Check the degenerate cases
1838 if (lhsWords == 0) {
1839 Quotient = APInt(BitWidth, 0); // 0 / Y ===> 0
1840 Remainder = 0; // 0 % Y ===> 0
1841 return;
1842 }
1843
1844 if (RHS == 1) {
1845 Quotient = LHS; // X / 1 ===> X
1846 Remainder = 0; // X % 1 ===> 0
1847 return;
1848 }
1849
1850 if (LHS.ult(RHS)) {
1851 Remainder = LHS.getZExtValue(); // X % Y ===> X, iff X < Y
1852 Quotient = APInt(BitWidth, 0); // X / Y ===> 0, iff X < Y
1853 return;
1854 }
1855
1856 if (LHS == RHS) {
1857 Quotient = APInt(BitWidth, 1); // X / X ===> 1
1858 Remainder = 0; // X % X ===> 0;
1859 return;
1860 }
1861
1862 // Make sure there is enough space to hold the results.
1863 // NOTE: This assumes that reallocate won't affect any bits if it doesn't
1864 // change the size. This is necessary if Quotient is aliased with LHS.
1865 Quotient.reallocate(BitWidth);
1866
1867 if (lhsWords == 1) { // rhsWords is 1 if lhsWords is 1.
1868 // There is only one word to consider so use the native versions.
1869 uint64_t lhsValue = LHS.U.pVal[0];
1870 Quotient = lhsValue / RHS;
1871 Remainder = lhsValue % RHS;
1872 return;
1873 }
1874
1875 // Okay, lets do it the long way
1876 divide(LHS.U.pVal, lhsWords, &RHS, 1, Quotient.U.pVal, &Remainder);
1877 // Clear the rest of the Quotient.
1878 std::memset(Quotient.U.pVal + lhsWords, 0,
1879 (getNumWords(BitWidth) - lhsWords) * APINT_WORD_SIZE);
1880}
1881
1882void APInt::sdivrem(const APInt &LHS, const APInt &RHS,
1883 APInt &Quotient, APInt &Remainder) {
1884 if (LHS.isNegative()) {
1885 if (RHS.isNegative())
1886 APInt::udivrem(-LHS, -RHS, Quotient, Remainder);
1887 else {
1888 APInt::udivrem(-LHS, RHS, Quotient, Remainder);
1889 Quotient.negate();
1890 }
1891 Remainder.negate();
1892 } else if (RHS.isNegative()) {
1893 APInt::udivrem(LHS, -RHS, Quotient, Remainder);
1894 Quotient.negate();
1895 } else {
1896 APInt::udivrem(LHS, RHS, Quotient, Remainder);
1897 }
1898}
1899
1900void APInt::sdivrem(const APInt &LHS, int64_t RHS,
1901 APInt &Quotient, int64_t &Remainder) {
1902 uint64_t R = Remainder;
1903 if (LHS.isNegative()) {
1904 if (RHS < 0)
1905 APInt::udivrem(-LHS, -RHS, Quotient, R);
1906 else {
1907 APInt::udivrem(-LHS, RHS, Quotient, R);
1908 Quotient.negate();
1909 }
1910 R = -R;
1911 } else if (RHS < 0) {
1912 APInt::udivrem(LHS, -RHS, Quotient, R);
1913 Quotient.negate();
1914 } else {
1915 APInt::udivrem(LHS, RHS, Quotient, R);
1916 }
1917 Remainder = R;
1918}
1919
1920APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const {
1921 APInt Res = *this+RHS;
1922 Overflow = isNonNegative() == RHS.isNonNegative() &&
1923 Res.isNonNegative() != isNonNegative();
1924 return Res;
1925}
1926
1927APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const {
1928 APInt Res = *this+RHS;
1929 Overflow = Res.ult(RHS);
1930 return Res;
1931}
1932
1933APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const {
1934 APInt Res = *this - RHS;
1935 Overflow = isNonNegative() != RHS.isNonNegative() &&
1936 Res.isNonNegative() != isNonNegative();
1937 return Res;
1938}
1939
1940APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const {
1941 APInt Res = *this-RHS;
1942 Overflow = Res.ugt(*this);
1943 return Res;
1944}
1945
1946APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const {
1947 // MININT/-1 --> overflow.
1948 Overflow = isMinSignedValue() && RHS.isAllOnes();
1949 return sdiv(RHS);
1950}
1951
1952APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const {
1953 APInt Res = *this * RHS;
1954
1955 if (RHS != 0)
1956 Overflow = Res.sdiv(RHS) != *this ||
1957 (isMinSignedValue() && RHS.isAllOnes());
1958 else
1959 Overflow = false;
1960 return Res;
1961}
1962
1963APInt APInt::umul_ov(const APInt &RHS, bool &Overflow) const {
1964 if (countLeadingZeros() + RHS.countLeadingZeros() + 2 <= BitWidth) {
1965 Overflow = true;
1966 return *this * RHS;
1967 }
1968
1969 APInt Res = lshr(1) * RHS;
1970 Overflow = Res.isNegative();
1971 Res <<= 1;
1972 if ((*this)[0]) {
1973 Res += RHS;
1974 if (Res.ult(RHS))
1975 Overflow = true;
1976 }
1977 return Res;
1978}
1979
1980APInt APInt::sshl_ov(const APInt &ShAmt, bool &Overflow) const {
1981 Overflow = ShAmt.uge(getBitWidth());
1982 if (Overflow)
1983 return APInt(BitWidth, 0);
1984
1985 if (isNonNegative()) // Don't allow sign change.
1986 Overflow = ShAmt.uge(countLeadingZeros());
1987 else
1988 Overflow = ShAmt.uge(countLeadingOnes());
1989
1990 return *this << ShAmt;
1991}
1992
1993APInt APInt::ushl_ov(const APInt &ShAmt, bool &Overflow) const {
1994 Overflow = ShAmt.uge(getBitWidth());
1995 if (Overflow)
1996 return APInt(BitWidth, 0);
1997
1998 Overflow = ShAmt.ugt(countLeadingZeros());
1999
2000 return *this << ShAmt;
2001}
2002
2003APInt APInt::sadd_sat(const APInt &RHS) const {
2004 bool Overflow;
2005 APInt Res = sadd_ov(RHS, Overflow);
2006 if (!Overflow)
2007 return Res;
2008
2009 return isNegative() ? APInt::getSignedMinValue(BitWidth)
2010 : APInt::getSignedMaxValue(BitWidth);
2011}
2012
2013APInt APInt::uadd_sat(const APInt &RHS) const {
2014 bool Overflow;
2015 APInt Res = uadd_ov(RHS, Overflow);
2016 if (!Overflow)
2017 return Res;
2018
2019 return APInt::getMaxValue(BitWidth);
2020}
2021
2022APInt APInt::ssub_sat(const APInt &RHS) const {
2023 bool Overflow;
2024 APInt Res = ssub_ov(RHS, Overflow);
2025 if (!Overflow)
2026 return Res;
2027
2028 return isNegative() ? APInt::getSignedMinValue(BitWidth)
2029 : APInt::getSignedMaxValue(BitWidth);
2030}
2031
2032APInt APInt::usub_sat(const APInt &RHS) const {
2033 bool Overflow;
2034 APInt Res = usub_ov(RHS, Overflow);
2035 if (!Overflow)
2036 return Res;
2037
2038 return APInt(BitWidth, 0);
2039}
2040
2041APInt APInt::smul_sat(const APInt &RHS) const {
2042 bool Overflow;
2043 APInt Res = smul_ov(RHS, Overflow);
2044 if (!Overflow)
2045 return Res;
2046
2047 // The result is negative if one and only one of inputs is negative.
2048 bool ResIsNegative = isNegative() ^ RHS.isNegative();
2049
2050 return ResIsNegative ? APInt::getSignedMinValue(BitWidth)
2051 : APInt::getSignedMaxValue(BitWidth);
2052}
2053
2054APInt APInt::umul_sat(const APInt &RHS) const {
2055 bool Overflow;
2056 APInt Res = umul_ov(RHS, Overflow);
2057 if (!Overflow)
2058 return Res;
2059
2060 return APInt::getMaxValue(BitWidth);
2061}
2062
2063APInt APInt::sshl_sat(const APInt &RHS) const {
2064 bool Overflow;
2065 APInt Res = sshl_ov(RHS, Overflow);
2066 if (!Overflow)
2067 return Res;
2068
2069 return isNegative() ? APInt::getSignedMinValue(BitWidth)
2070 : APInt::getSignedMaxValue(BitWidth);
2071}
2072
2073APInt APInt::ushl_sat(const APInt &RHS) const {
2074 bool Overflow;
2075 APInt Res = ushl_ov(RHS, Overflow);
2076 if (!Overflow)
2077 return Res;
2078
2079 return APInt::getMaxValue(BitWidth);
2080}
2081
2082void APInt::fromString(unsigned numbits, StringRef str, uint8_t radix) {
2083 // Check our assumptions here
2084 assert(!str.empty() && "Invalid string length")(static_cast <bool> (!str.empty() && "Invalid string length"
) ? void (0) : __assert_fail ("!str.empty() && \"Invalid string length\""
, "llvm/lib/Support/APInt.cpp", 2084, __extension__ __PRETTY_FUNCTION__
))
;
2085 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2 ||(static_cast <bool> ((radix == 10 || radix == 8 || radix
== 16 || radix == 2 || radix == 36) && "Radix should be 2, 8, 10, 16, or 36!"
) ? void (0) : __assert_fail ("(radix == 10 || radix == 8 || radix == 16 || radix == 2 || radix == 36) && \"Radix should be 2, 8, 10, 16, or 36!\""
, "llvm/lib/Support/APInt.cpp", 2087, __extension__ __PRETTY_FUNCTION__
))
2086 radix == 36) &&(static_cast <bool> ((radix == 10 || radix == 8 || radix
== 16 || radix == 2 || radix == 36) && "Radix should be 2, 8, 10, 16, or 36!"
) ? void (0) : __assert_fail ("(radix == 10 || radix == 8 || radix == 16 || radix == 2 || radix == 36) && \"Radix should be 2, 8, 10, 16, or 36!\""
, "llvm/lib/Support/APInt.cpp", 2087, __extension__ __PRETTY_FUNCTION__
))
2087 "Radix should be 2, 8, 10, 16, or 36!")(static_cast <bool> ((radix == 10 || radix == 8 || radix
== 16 || radix == 2 || radix == 36) && "Radix should be 2, 8, 10, 16, or 36!"
) ? void (0) : __assert_fail ("(radix == 10 || radix == 8 || radix == 16 || radix == 2 || radix == 36) && \"Radix should be 2, 8, 10, 16, or 36!\""
, "llvm/lib/Support/APInt.cpp", 2087, __extension__ __PRETTY_FUNCTION__
))
;
2088
2089 StringRef::iterator p = str.begin();
2090 size_t slen = str.size();
2091 bool isNeg = *p == '-';
2092 if (*p == '-' || *p == '+') {
2093 p++;
2094 slen--;
2095 assert(slen && "String is only a sign, needs a value.")(static_cast <bool> (slen && "String is only a sign, needs a value."
) ? void (0) : __assert_fail ("slen && \"String is only a sign, needs a value.\""
, "llvm/lib/Support/APInt.cpp", 2095, __extension__ __PRETTY_FUNCTION__
))
;
2096 }
2097 assert((slen <= numbits || radix != 2) && "Insufficient bit width")(static_cast <bool> ((slen <= numbits || radix != 2)
&& "Insufficient bit width") ? void (0) : __assert_fail
("(slen <= numbits || radix != 2) && \"Insufficient bit width\""
, "llvm/lib/Support/APInt.cpp", 2097, __extension__ __PRETTY_FUNCTION__
))
;
2098 assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width")(static_cast <bool> (((slen-1)*3 <= numbits || radix
!= 8) && "Insufficient bit width") ? void (0) : __assert_fail
("((slen-1)*3 <= numbits || radix != 8) && \"Insufficient bit width\""
, "llvm/lib/Support/APInt.cpp", 2098, __extension__ __PRETTY_FUNCTION__
))
;
2099 assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width")(static_cast <bool> (((slen-1)*4 <= numbits || radix
!= 16) && "Insufficient bit width") ? void (0) : __assert_fail
("((slen-1)*4 <= numbits || radix != 16) && \"Insufficient bit width\""
, "llvm/lib/Support/APInt.cpp", 2099, __extension__ __PRETTY_FUNCTION__
))
;
2100 assert((((slen-1)*64)/22 <= numbits || radix != 10) &&(static_cast <bool> ((((slen-1)*64)/22 <= numbits ||
radix != 10) && "Insufficient bit width") ? void (0)
: __assert_fail ("(((slen-1)*64)/22 <= numbits || radix != 10) && \"Insufficient bit width\""
, "llvm/lib/Support/APInt.cpp", 2101, __extension__ __PRETTY_FUNCTION__
))
2101 "Insufficient bit width")(static_cast <bool> ((((slen-1)*64)/22 <= numbits ||
radix != 10) && "Insufficient bit width") ? void (0)
: __assert_fail ("(((slen-1)*64)/22 <= numbits || radix != 10) && \"Insufficient bit width\""
, "llvm/lib/Support/APInt.cpp", 2101, __extension__ __PRETTY_FUNCTION__
))
;
2102
2103 // Allocate memory if needed
2104 if (isSingleWord())
2105 U.VAL = 0;
2106 else
2107 U.pVal = getClearedMemory(getNumWords());
2108
2109 // Figure out if we can shift instead of multiply
2110 unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0);
2111
2112 // Enter digit traversal loop
2113 for (StringRef::iterator e = str.end(); p != e; ++p) {
2114 unsigned digit = getDigit(*p, radix);
2115 assert(digit < radix && "Invalid character in digit string")(static_cast <bool> (digit < radix && "Invalid character in digit string"
) ? void (0) : __assert_fail ("digit < radix && \"Invalid character in digit string\""
, "llvm/lib/Support/APInt.cpp", 2115, __extension__ __PRETTY_FUNCTION__
))
;
2116
2117 // Shift or multiply the value by the radix
2118 if (slen > 1) {
2119 if (shift)
2120 *this <<= shift;
2121 else
2122 *this *= radix;
2123 }
2124
2125 // Add in the digit we just interpreted
2126 *this += digit;
2127 }
2128 // If its negative, put it in two's complement form
2129 if (isNeg)
2130 this->negate();
2131}
2132
2133void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix,
2134 bool Signed, bool formatAsCLiteral) const {
2135 assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2 ||(static_cast <bool> ((Radix == 10 || Radix == 8 || Radix
== 16 || Radix == 2 || Radix == 36) && "Radix should be 2, 8, 10, 16, or 36!"
) ? void (0) : __assert_fail ("(Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2 || Radix == 36) && \"Radix should be 2, 8, 10, 16, or 36!\""
, "llvm/lib/Support/APInt.cpp", 2137, __extension__ __PRETTY_FUNCTION__
))
2136 Radix == 36) &&(static_cast <bool> ((Radix == 10 || Radix == 8 || Radix
== 16 || Radix == 2 || Radix == 36) && "Radix should be 2, 8, 10, 16, or 36!"
) ? void (0) : __assert_fail ("(Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2 || Radix == 36) && \"Radix should be 2, 8, 10, 16, or 36!\""
, "llvm/lib/Support/APInt.cpp", 2137, __extension__ __PRETTY_FUNCTION__
))
2137 "Radix should be 2, 8, 10, 16, or 36!")(static_cast <bool> ((Radix == 10 || Radix == 8 || Radix
== 16 || Radix == 2 || Radix == 36) && "Radix should be 2, 8, 10, 16, or 36!"
) ? void (0) : __assert_fail ("(Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2 || Radix == 36) && \"Radix should be 2, 8, 10, 16, or 36!\""
, "llvm/lib/Support/APInt.cpp", 2137, __extension__ __PRETTY_FUNCTION__
))
;
2138
2139 const char *Prefix = "";
2140 if (formatAsCLiteral) {
2141 switch (Radix) {
2142 case 2:
2143 // Binary literals are a non-standard extension added in gcc 4.3:
2144 // http://gcc.gnu.org/onlinedocs/gcc-4.3.0/gcc/Binary-constants.html
2145 Prefix = "0b";
2146 break;
2147 case 8:
2148 Prefix = "0";
2149 break;
2150 case 10:
2151 break; // No prefix
2152 case 16:
2153 Prefix = "0x";
2154 break;
2155 default:
2156 llvm_unreachable("Invalid radix!")::llvm::llvm_unreachable_internal("Invalid radix!", "llvm/lib/Support/APInt.cpp"
, 2156)
;
2157 }
2158 }
2159
2160 // First, check for a zero value and just short circuit the logic below.
2161 if (isZero()) {
2162 while (*Prefix) {
2163 Str.push_back(*Prefix);
2164 ++Prefix;
2165 };
2166 Str.push_back('0');
2167 return;
2168 }
2169
2170 static const char Digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
2171
2172 if (isSingleWord()) {
2173 char Buffer[65];
2174 char *BufPtr = std::end(Buffer);
2175
2176 uint64_t N;
2177 if (!Signed) {
2178 N = getZExtValue();
2179 } else {
2180 int64_t I = getSExtValue();
2181 if (I >= 0) {
2182 N = I;
2183 } else {
2184 Str.push_back('-');
2185 N = -(uint64_t)I;
2186 }
2187 }
2188
2189 while (*Prefix) {
2190 Str.push_back(*Prefix);
2191 ++Prefix;
2192 };
2193
2194 while (N) {
2195 *--BufPtr = Digits[N % Radix];
2196 N /= Radix;
2197 }
2198 Str.append(BufPtr, std::end(Buffer));
2199 return;
2200 }
2201
2202 APInt Tmp(*this);
2203
2204 if (Signed && isNegative()) {
2205 // They want to print the signed version and it is a negative value
2206 // Flip the bits and add one to turn it into the equivalent positive
2207 // value and put a '-' in the result.
2208 Tmp.negate();
2209 Str.push_back('-');
2210 }
2211
2212 while (*Prefix) {
2213 Str.push_back(*Prefix);
2214 ++Prefix;
2215 };
2216
2217 // We insert the digits backward, then reverse them to get the right order.
2218 unsigned StartDig = Str.size();
2219
2220 // For the 2, 8 and 16 bit cases, we can just shift instead of divide
2221 // because the number of bits per digit (1, 3 and 4 respectively) divides
2222 // equally. We just shift until the value is zero.
2223 if (Radix == 2 || Radix == 8 || Radix == 16) {
2224 // Just shift tmp right for each digit width until it becomes zero
2225 unsigned ShiftAmt = (Radix == 16 ? 4 : (Radix == 8 ? 3 : 1));
2226 unsigned MaskAmt = Radix - 1;
2227
2228 while (Tmp.getBoolValue()) {
2229 unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt;
2230 Str.push_back(Digits[Digit]);
2231 Tmp.lshrInPlace(ShiftAmt);
2232 }
2233 } else {
2234 while (Tmp.getBoolValue()) {
2235 uint64_t Digit;
2236 udivrem(Tmp, Radix, Tmp, Digit);
2237 assert(Digit < Radix && "divide failed")(static_cast <bool> (Digit < Radix && "divide failed"
) ? void (0) : __assert_fail ("Digit < Radix && \"divide failed\""
, "llvm/lib/Support/APInt.cpp", 2237, __extension__ __PRETTY_FUNCTION__
))
;
2238 Str.push_back(Digits[Digit]);
2239 }
2240 }
2241
2242 // Reverse the digits before returning.
2243 std::reverse(Str.begin()+StartDig, Str.end());
2244}
2245
2246#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
2247LLVM_DUMP_METHOD__attribute__((noinline)) __attribute__((__used__)) void APInt::dump() const {
2248 SmallString<40> S, U;
2249 this->toStringUnsigned(U);
2250 this->toStringSigned(S);
2251 dbgs() << "APInt(" << BitWidth << "b, "
2252 << U << "u " << S << "s)\n";
2253}
2254#endif
2255
2256void APInt::print(raw_ostream &OS, bool isSigned) const {
2257 SmallString<40> S;
2258 this->toString(S, 10, isSigned, /* formatAsCLiteral = */false);
2259 OS << S;
2260}
2261
2262// This implements a variety of operations on a representation of
2263// arbitrary precision, two's-complement, bignum integer values.
2264
2265// Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe
2266// and unrestricting assumption.
2267static_assert(APInt::APINT_BITS_PER_WORD % 2 == 0,
2268 "Part width must be divisible by 2!");
2269
2270// Returns the integer part with the least significant BITS set.
2271// BITS cannot be zero.
2272static inline APInt::WordType lowBitMask(unsigned bits) {
2273 assert(bits != 0 && bits <= APInt::APINT_BITS_PER_WORD)(static_cast <bool> (bits != 0 && bits <= APInt
::APINT_BITS_PER_WORD) ? void (0) : __assert_fail ("bits != 0 && bits <= APInt::APINT_BITS_PER_WORD"
, "llvm/lib/Support/APInt.cpp", 2273, __extension__ __PRETTY_FUNCTION__
))
;
2274 return ~(APInt::WordType) 0 >> (APInt::APINT_BITS_PER_WORD - bits);
2275}
2276
2277/// Returns the value of the lower half of PART.
2278static inline APInt::WordType lowHalf(APInt::WordType part) {
2279 return part & lowBitMask(APInt::APINT_BITS_PER_WORD / 2);
2280}
2281
2282/// Returns the value of the upper half of PART.
2283static inline APInt::WordType highHalf(APInt::WordType part) {
2284 return part >> (APInt::APINT_BITS_PER_WORD / 2);
2285}
2286
2287/// Returns the bit number of the most significant set bit of a part.
2288/// If the input number has no bits set -1U is returned.
2289static unsigned partMSB(APInt::WordType value) {
2290 return findLastSet(value, ZB_Max);
2291}
2292
2293/// Returns the bit number of the least significant set bit of a part. If the
2294/// input number has no bits set -1U is returned.
2295static unsigned partLSB(APInt::WordType value) {
2296 return findFirstSet(value, ZB_Max);
2297}
2298
2299/// Sets the least significant part of a bignum to the input value, and zeroes
2300/// out higher parts.
2301void APInt::tcSet(WordType *dst, WordType part, unsigned parts) {
2302 assert(parts > 0)(static_cast <bool> (parts > 0) ? void (0) : __assert_fail
("parts > 0", "llvm/lib/Support/APInt.cpp", 2302, __extension__
__PRETTY_FUNCTION__))
;
2303 dst[0] = part;
2304 for (unsigned i = 1; i < parts; i++)
2305 dst[i] = 0;
2306}
2307
2308/// Assign one bignum to another.
2309void APInt::tcAssign(WordType *dst, const WordType *src, unsigned parts) {
2310 for (unsigned i = 0; i < parts; i++)
2311 dst[i] = src[i];
2312}
2313
2314/// Returns true if a bignum is zero, false otherwise.
2315bool APInt::tcIsZero(const WordType *src, unsigned parts) {
2316 for (unsigned i = 0; i < parts; i++)
2317 if (src[i])
2318 return false;
2319
2320 return true;
2321}
2322
2323/// Extract the given bit of a bignum; returns 0 or 1.
2324int APInt::tcExtractBit(const WordType *parts, unsigned bit) {
2325 return (parts[whichWord(bit)] & maskBit(bit)) != 0;
2326}
2327
2328/// Set the given bit of a bignum.
2329void APInt::tcSetBit(WordType *parts, unsigned bit) {
2330 parts[whichWord(bit)] |= maskBit(bit);
2331}
2332
2333/// Clears the given bit of a bignum.
2334void APInt::tcClearBit(WordType *parts, unsigned bit) {
2335 parts[whichWord(bit)] &= ~maskBit(bit);
2336}
2337
2338/// Returns the bit number of the least significant set bit of a number. If the
2339/// input number has no bits set -1U is returned.
2340unsigned APInt::tcLSB(const WordType *parts, unsigned n) {
2341 for (unsigned i = 0; i < n; i++) {
2342 if (parts[i] != 0) {
2343 unsigned lsb = partLSB(parts[i]);
2344 return lsb + i * APINT_BITS_PER_WORD;
2345 }
2346 }
2347
2348 return -1U;
2349}
2350
2351/// Returns the bit number of the most significant set bit of a number.
2352/// If the input number has no bits set -1U is returned.
2353unsigned APInt::tcMSB(const WordType *parts, unsigned n) {
2354 do {
2355 --n;
2356
2357 if (parts[n] != 0) {
2358 unsigned msb = partMSB(parts[n]);
2359
2360 return msb + n * APINT_BITS_PER_WORD;
2361 }
2362 } while (n);
2363
2364 return -1U;
2365}
2366
2367/// Copy the bit vector of width srcBITS from SRC, starting at bit srcLSB, to
2368/// DST, of dstCOUNT parts, such that the bit srcLSB becomes the least
2369/// significant bit of DST. All high bits above srcBITS in DST are zero-filled.
2370/// */
2371void
2372APInt::tcExtract(WordType *dst, unsigned dstCount, const WordType *src,
2373 unsigned srcBits, unsigned srcLSB) {
2374 unsigned dstParts = (srcBits + APINT_BITS_PER_WORD - 1) / APINT_BITS_PER_WORD;
2375 assert(dstParts <= dstCount)(static_cast <bool> (dstParts <= dstCount) ? void (0
) : __assert_fail ("dstParts <= dstCount", "llvm/lib/Support/APInt.cpp"
, 2375, __extension__ __PRETTY_FUNCTION__))
;
2376
2377 unsigned firstSrcPart = srcLSB / APINT_BITS_PER_WORD;
2378 tcAssign(dst, src + firstSrcPart, dstParts);
2379
2380 unsigned shift = srcLSB % APINT_BITS_PER_WORD;
2381 tcShiftRight(dst, dstParts, shift);
2382
2383 // We now have (dstParts * APINT_BITS_PER_WORD - shift) bits from SRC
2384 // in DST. If this is less that srcBits, append the rest, else
2385 // clear the high bits.
2386 unsigned n = dstParts * APINT_BITS_PER_WORD - shift;
2387 if (n < srcBits) {
2388 WordType mask = lowBitMask (srcBits - n);
2389 dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask)
2390 << n % APINT_BITS_PER_WORD);
2391 } else if (n > srcBits) {
2392 if (srcBits % APINT_BITS_PER_WORD)
2393 dst[dstParts - 1] &= lowBitMask (srcBits % APINT_BITS_PER_WORD);
2394 }
2395
2396 // Clear high parts.
2397 while (dstParts < dstCount)
2398 dst[dstParts++] = 0;
2399}
2400
2401//// DST += RHS + C where C is zero or one. Returns the carry flag.
2402APInt::WordType APInt::tcAdd(WordType *dst, const WordType *rhs,
2403 WordType c, unsigned parts) {
2404 assert(c <= 1)(static_cast <bool> (c <= 1) ? void (0) : __assert_fail
("c <= 1", "llvm/lib/Support/APInt.cpp", 2404, __extension__
__PRETTY_FUNCTION__))
;
2405
2406 for (unsigned i = 0; i < parts; i++) {
2407 WordType l = dst[i];
2408 if (c) {
2409 dst[i] += rhs[i] + 1;
2410 c = (dst[i] <= l);
2411 } else {
2412 dst[i] += rhs[i];
2413 c = (dst[i] < l);
2414 }
2415 }
2416
2417 return c;
2418}
2419
2420/// This function adds a single "word" integer, src, to the multiple
2421/// "word" integer array, dst[]. dst[] is modified to reflect the addition and
2422/// 1 is returned if there is a carry out, otherwise 0 is returned.
2423/// @returns the carry of the addition.
2424APInt::WordType APInt::tcAddPart(WordType *dst, WordType src,
2425 unsigned parts) {
2426 for (unsigned i = 0; i < parts; ++i) {
2427 dst[i] += src;
2428 if (dst[i] >= src)
2429 return 0; // No need to carry so exit early.
2430 src = 1; // Carry one to next digit.
2431 }
2432
2433 return 1;
2434}
2435
2436/// DST -= RHS + C where C is zero or one. Returns the carry flag.
2437APInt::WordType APInt::tcSubtract(WordType *dst, const WordType *rhs,
2438 WordType c, unsigned parts) {
2439 assert(c <= 1)(static_cast <bool> (c <= 1) ? void (0) : __assert_fail
("c <= 1", "llvm/lib/Support/APInt.cpp", 2439, __extension__
__PRETTY_FUNCTION__))
;
2440
2441 for (unsigned i = 0; i < parts; i++) {
2442 WordType l = dst[i];
2443 if (c) {
2444 dst[i] -= rhs[i] + 1;
2445 c = (dst[i] >= l);
2446 } else {
2447 dst[i] -= rhs[i];
2448 c = (dst[i] > l);
2449 }
2450 }
2451
2452 return c;
2453}
2454
2455/// This function subtracts a single "word" (64-bit word), src, from
2456/// the multi-word integer array, dst[], propagating the borrowed 1 value until
2457/// no further borrowing is needed or it runs out of "words" in dst. The result
2458/// is 1 if "borrowing" exhausted the digits in dst, or 0 if dst was not
2459/// exhausted. In other words, if src > dst then this function returns 1,
2460/// otherwise 0.
2461/// @returns the borrow out of the subtraction
2462APInt::WordType APInt::tcSubtractPart(WordType *dst, WordType src,
2463 unsigned parts) {
2464 for (unsigned i = 0; i < parts; ++i) {
2465 WordType Dst = dst[i];
2466 dst[i] -= src;
2467 if (src <= Dst)
2468 return 0; // No need to borrow so exit early.
2469 src = 1; // We have to "borrow 1" from next "word"
2470 }
2471
2472 return 1;
2473}
2474
2475/// Negate a bignum in-place.
2476void APInt::tcNegate(WordType *dst, unsigned parts) {
2477 tcComplement(dst, parts);
2478 tcIncrement(dst, parts);
2479}
2480
2481/// DST += SRC * MULTIPLIER + CARRY if add is true
2482/// DST = SRC * MULTIPLIER + CARRY if add is false
2483/// Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC
2484/// they must start at the same point, i.e. DST == SRC.
2485/// If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is
2486/// returned. Otherwise DST is filled with the least significant
2487/// DSTPARTS parts of the result, and if all of the omitted higher
2488/// parts were zero return zero, otherwise overflow occurred and
2489/// return one.
2490int APInt::tcMultiplyPart(WordType *dst, const WordType *src,
2491 WordType multiplier, WordType carry,
2492 unsigned srcParts, unsigned dstParts,
2493 bool add) {
2494 // Otherwise our writes of DST kill our later reads of SRC.
2495 assert(dst <= src || dst >= src + srcParts)(static_cast <bool> (dst <= src || dst >= src + srcParts
) ? void (0) : __assert_fail ("dst <= src || dst >= src + srcParts"
, "llvm/lib/Support/APInt.cpp", 2495, __extension__ __PRETTY_FUNCTION__
))
;
2496 assert(dstParts <= srcParts + 1)(static_cast <bool> (dstParts <= srcParts + 1) ? void
(0) : __assert_fail ("dstParts <= srcParts + 1", "llvm/lib/Support/APInt.cpp"
, 2496, __extension__ __PRETTY_FUNCTION__))
;
2497
2498 // N loops; minimum of dstParts and srcParts.
2499 unsigned n = std::min(dstParts, srcParts);
2500
2501 for (unsigned i = 0; i < n; i++) {
2502 // [LOW, HIGH] = MULTIPLIER * SRC[i] + DST[i] + CARRY.
2503 // This cannot overflow, because:
2504 // (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1)
2505 // which is less than n^2.
2506 WordType srcPart = src[i];
2507 WordType low, mid, high;
2508 if (multiplier == 0 || srcPart == 0) {
2509 low = carry;
2510 high = 0;
2511 } else {
2512 low = lowHalf(srcPart) * lowHalf(multiplier);
2513 high = highHalf(srcPart) * highHalf(multiplier);
2514
2515 mid = lowHalf(srcPart) * highHalf(multiplier);
2516 high += highHalf(mid);
2517 mid <<= APINT_BITS_PER_WORD / 2;
2518 if (low + mid < low)
2519 high++;
2520 low += mid;
2521
2522 mid = highHalf(srcPart) * lowHalf(multiplier);
2523 high += highHalf(mid);
2524 mid <<= APINT_BITS_PER_WORD / 2;
2525 if (low + mid < low)
2526 high++;
2527 low += mid;
2528
2529 // Now add carry.
2530 if (low + carry < low)
2531 high++;
2532 low += carry;
2533 }
2534
2535 if (add) {
2536 // And now DST[i], and store the new low part there.
2537 if (low + dst[i] < low)
2538 high++;
2539 dst[i] += low;
2540 } else
2541 dst[i] = low;
2542
2543 carry = high;
2544 }
2545
2546 if (srcParts < dstParts) {
2547 // Full multiplication, there is no overflow.
2548 assert(srcParts + 1 == dstParts)(static_cast <bool> (srcParts + 1 == dstParts) ? void (
0) : __assert_fail ("srcParts + 1 == dstParts", "llvm/lib/Support/APInt.cpp"
, 2548, __extension__ __PRETTY_FUNCTION__))
;
2549 dst[srcParts] = carry;
2550 return 0;
2551 }
2552
2553 // We overflowed if there is carry.
2554 if (carry)
2555 return 1;
2556
2557 // We would overflow if any significant unwritten parts would be
2558 // non-zero. This is true if any remaining src parts are non-zero
2559 // and the multiplier is non-zero.
2560 if (multiplier)
2561 for (unsigned i = dstParts; i < srcParts; i++)
2562 if (src[i])
2563 return 1;
2564
2565 // We fitted in the narrow destination.
2566 return 0;
2567}
2568
2569/// DST = LHS * RHS, where DST has the same width as the operands and
2570/// is filled with the least significant parts of the result. Returns
2571/// one if overflow occurred, otherwise zero. DST must be disjoint
2572/// from both operands.
2573int APInt::tcMultiply(WordType *dst, const WordType *lhs,
2574 const WordType *rhs, unsigned parts) {
2575 assert(dst != lhs && dst != rhs)(static_cast <bool> (dst != lhs && dst != rhs) ?
void (0) : __assert_fail ("dst != lhs && dst != rhs"
, "llvm/lib/Support/APInt.cpp", 2575, __extension__ __PRETTY_FUNCTION__
))
;
2576
2577 int overflow = 0;
2578 tcSet(dst, 0, parts);
2579
2580 for (unsigned i = 0; i < parts; i++)
2581 overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts,
2582 parts - i, true);
2583
2584 return overflow;
2585}
2586
2587/// DST = LHS * RHS, where DST has width the sum of the widths of the
2588/// operands. No overflow occurs. DST must be disjoint from both operands.
2589void APInt::tcFullMultiply(WordType *dst, const WordType *lhs,
2590 const WordType *rhs, unsigned lhsParts,
2591 unsigned rhsParts) {
2592 // Put the narrower number on the LHS for less loops below.
2593 if (lhsParts > rhsParts)
2594 return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts);
2595
2596 assert(dst != lhs && dst != rhs)(static_cast <bool> (dst != lhs && dst != rhs) ?
void (0) : __assert_fail ("dst != lhs && dst != rhs"
, "llvm/lib/Support/APInt.cpp", 2596, __extension__ __PRETTY_FUNCTION__
))
;
2597
2598 tcSet(dst, 0, rhsParts);
2599
2600 for (unsigned i = 0; i < lhsParts; i++)
2601 tcMultiplyPart(&dst[i], rhs, lhs[i], 0, rhsParts, rhsParts + 1, true);
2602}
2603
2604// If RHS is zero LHS and REMAINDER are left unchanged, return one.
2605// Otherwise set LHS to LHS / RHS with the fractional part discarded,
2606// set REMAINDER to the remainder, return zero. i.e.
2607//
2608// OLD_LHS = RHS * LHS + REMAINDER
2609//
2610// SCRATCH is a bignum of the same size as the operands and result for
2611// use by the routine; its contents need not be initialized and are
2612// destroyed. LHS, REMAINDER and SCRATCH must be distinct.
2613int APInt::tcDivide(WordType *lhs, const WordType *rhs,
2614 WordType *remainder, WordType *srhs,
2615 unsigned parts) {
2616 assert(lhs != remainder && lhs != srhs && remainder != srhs)(static_cast <bool> (lhs != remainder && lhs !=
srhs && remainder != srhs) ? void (0) : __assert_fail
("lhs != remainder && lhs != srhs && remainder != srhs"
, "llvm/lib/Support/APInt.cpp", 2616, __extension__ __PRETTY_FUNCTION__
))
;
2617
2618 unsigned shiftCount = tcMSB(rhs, parts) + 1;
2619 if (shiftCount == 0)
2620 return true;
2621
2622 shiftCount = parts * APINT_BITS_PER_WORD - shiftCount;
2623 unsigned n = shiftCount / APINT_BITS_PER_WORD;
2624 WordType mask = (WordType) 1 << (shiftCount % APINT_BITS_PER_WORD);
2625
2626 tcAssign(srhs, rhs, parts);
2627 tcShiftLeft(srhs, parts, shiftCount);
2628 tcAssign(remainder, lhs, parts);
2629 tcSet(lhs, 0, parts);
2630
2631 // Loop, subtracting SRHS if REMAINDER is greater and adding that to the
2632 // total.
2633 for (;;) {
2634 int compare = tcCompare(remainder, srhs, parts);
2635 if (compare >= 0) {
2636 tcSubtract(remainder, srhs, 0, parts);
2637 lhs[n] |= mask;
2638 }
2639
2640 if (shiftCount == 0)
2641 break;
2642 shiftCount--;
2643 tcShiftRight(srhs, parts, 1);
2644 if ((mask >>= 1) == 0) {
2645 mask = (WordType) 1 << (APINT_BITS_PER_WORD - 1);
2646 n--;
2647 }
2648 }
2649
2650 return false;
2651}
2652
2653/// Shift a bignum left Cound bits in-place. Shifted in bits are zero. There are
2654/// no restrictions on Count.
2655void APInt::tcShiftLeft(WordType *Dst, unsigned Words, unsigned Count) {
2656 // Don't bother performing a no-op shift.
2657 if (!Count)
2658 return;
2659
2660 // WordShift is the inter-part shift; BitShift is the intra-part shift.
2661 unsigned WordShift = std::min(Count / APINT_BITS_PER_WORD, Words);
2662 unsigned BitShift = Count % APINT_BITS_PER_WORD;
2663
2664 // Fastpath for moving by whole words.
2665 if (BitShift == 0) {
2666 std::memmove(Dst + WordShift, Dst, (Words - WordShift) * APINT_WORD_SIZE);
2667 } else {
2668 while (Words-- > WordShift) {
2669 Dst[Words] = Dst[Words - WordShift] << BitShift;
2670 if (Words > WordShift)
2671 Dst[Words] |=
2672 Dst[Words - WordShift - 1] >> (APINT_BITS_PER_WORD - BitShift);
2673 }
2674 }
2675
2676 // Fill in the remainder with 0s.
2677 std::memset(Dst, 0, WordShift * APINT_WORD_SIZE);
2678}
2679
2680/// Shift a bignum right Count bits in-place. Shifted in bits are zero. There
2681/// are no restrictions on Count.
2682void APInt::tcShiftRight(WordType *Dst, unsigned Words, unsigned Count) {
2683 // Don't bother performing a no-op shift.
2684 if (!Count)
2685 return;
2686
2687 // WordShift is the inter-part shift; BitShift is the intra-part shift.
2688 unsigned WordShift = std::min(Count / APINT_BITS_PER_WORD, Words);
2689 unsigned BitShift = Count % APINT_BITS_PER_WORD;
2690
2691 unsigned WordsToMove = Words - WordShift;
2692 // Fastpath for moving by whole words.
2693 if (BitShift == 0) {
2694 std::memmove(Dst, Dst + WordShift, WordsToMove * APINT_WORD_SIZE);
2695 } else {
2696 for (unsigned i = 0; i != WordsToMove; ++i) {
2697 Dst[i] = Dst[i + WordShift] >> BitShift;
2698 if (i + 1 != WordsToMove)
2699 Dst[i] |= Dst[i + WordShift + 1] << (APINT_BITS_PER_WORD - BitShift);
2700 }
2701 }
2702
2703 // Fill in the remainder with 0s.
2704 std::memset(Dst + WordsToMove, 0, WordShift * APINT_WORD_SIZE);
2705}
2706
2707// Comparison (unsigned) of two bignums.
2708int APInt::tcCompare(const WordType *lhs, const WordType *rhs,
2709 unsigned parts) {
2710 while (parts) {
2711 parts--;
2712 if (lhs[parts] != rhs[parts])
2713 return (lhs[parts] > rhs[parts]) ? 1 : -1;
2714 }
2715
2716 return 0;
2717}
2718
2719APInt llvm::APIntOps::RoundingUDiv(const APInt &A, const APInt &B,
2720 APInt::Rounding RM) {
2721 // Currently udivrem always rounds down.
2722 switch (RM) {
2723 case APInt::Rounding::DOWN:
2724 case APInt::Rounding::TOWARD_ZERO:
2725 return A.udiv(B);
2726 case APInt::Rounding::UP: {
2727 APInt Quo, Rem;
2728 APInt::udivrem(A, B, Quo, Rem);
2729 if (Rem.isZero())
2730 return Quo;
2731 return Quo + 1;
2732 }
2733 }
2734 llvm_unreachable("Unknown APInt::Rounding enum")::llvm::llvm_unreachable_internal("Unknown APInt::Rounding enum"
, "llvm/lib/Support/APInt.cpp", 2734)
;
2735}
2736
2737APInt llvm::APIntOps::RoundingSDiv(const APInt &A, const APInt &B,
2738 APInt::Rounding RM) {
2739 switch (RM) {
2740 case APInt::Rounding::DOWN:
2741 case APInt::Rounding::UP: {
2742 APInt Quo, Rem;
2743 APInt::sdivrem(A, B, Quo, Rem);
2744 if (Rem.isZero())
2745 return Quo;
2746 // This algorithm deals with arbitrary rounding mode used by sdivrem.
2747 // We want to check whether the non-integer part of the mathematical value
2748 // is negative or not. If the non-integer part is negative, we need to round
2749 // down from Quo; otherwise, if it's positive or 0, we return Quo, as it's
2750 // already rounded down.
2751 if (RM == APInt::Rounding::DOWN) {
2752 if (Rem.isNegative() != B.isNegative())
2753 return Quo - 1;
2754 return Quo;
2755 }
2756 if (Rem.isNegative() != B.isNegative())
2757 return Quo;
2758 return Quo + 1;
2759 }
2760 // Currently sdiv rounds towards zero.
2761 case APInt::Rounding::TOWARD_ZERO:
2762 return A.sdiv(B);
2763 }
2764 llvm_unreachable("Unknown APInt::Rounding enum")::llvm::llvm_unreachable_internal("Unknown APInt::Rounding enum"
, "llvm/lib/Support/APInt.cpp", 2764)
;
2765}
2766
2767Optional<APInt>
2768llvm::APIntOps::SolveQuadraticEquationWrap(APInt A, APInt B, APInt C,
2769 unsigned RangeWidth) {
2770 unsigned CoeffWidth = A.getBitWidth();
2771 assert(CoeffWidth == B.getBitWidth() && CoeffWidth == C.getBitWidth())(static_cast <bool> (CoeffWidth == B.getBitWidth() &&
CoeffWidth == C.getBitWidth()) ? void (0) : __assert_fail ("CoeffWidth == B.getBitWidth() && CoeffWidth == C.getBitWidth()"
, "llvm/lib/Support/APInt.cpp", 2771, __extension__ __PRETTY_FUNCTION__
))
;
2772 assert(RangeWidth <= CoeffWidth &&(static_cast <bool> (RangeWidth <= CoeffWidth &&
"Value range width should be less than coefficient width") ?
void (0) : __assert_fail ("RangeWidth <= CoeffWidth && \"Value range width should be less than coefficient width\""
, "llvm/lib/Support/APInt.cpp", 2773, __extension__ __PRETTY_FUNCTION__
))
2773 "Value range width should be less than coefficient width")(static_cast <bool> (RangeWidth <= CoeffWidth &&
"Value range width should be less than coefficient width") ?
void (0) : __assert_fail ("RangeWidth <= CoeffWidth && \"Value range width should be less than coefficient width\""
, "llvm/lib/Support/APInt.cpp", 2773, __extension__ __PRETTY_FUNCTION__
))
;
2774 assert(RangeWidth > 1 && "Value range bit width should be > 1")(static_cast <bool> (RangeWidth > 1 && "Value range bit width should be > 1"
) ? void (0) : __assert_fail ("RangeWidth > 1 && \"Value range bit width should be > 1\""
, "llvm/lib/Support/APInt.cpp", 2774, __extension__ __PRETTY_FUNCTION__
))
;
2775
2776 LLVM_DEBUG(dbgs() << __func__ << ": solving " << A << "x^2 + " << Bdo { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("apint")) { dbgs() << __func__ << ": solving " <<
A << "x^2 + " << B << "x + " << C <<
", rw:" << RangeWidth << '\n'; } } while (false)
2777 << "x + " << C << ", rw:" << RangeWidth << '\n')do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("apint")) { dbgs() << __func__ << ": solving " <<
A << "x^2 + " << B << "x + " << C <<
", rw:" << RangeWidth << '\n'; } } while (false)
;
2778
2779 // Identify 0 as a (non)solution immediately.
2780 if (C.sextOrTrunc(RangeWidth).isZero()) {
2781 LLVM_DEBUG(dbgs() << __func__ << ": zero solution\n")do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("apint")) { dbgs() << __func__ << ": zero solution\n"
; } } while (false)
;
2782 return APInt(CoeffWidth, 0);
2783 }
2784
2785 // The result of APInt arithmetic has the same bit width as the operands,
2786 // so it can actually lose high bits. A product of two n-bit integers needs
2787 // 2n-1 bits to represent the full value.
2788 // The operation done below (on quadratic coefficients) that can produce
2789 // the largest value is the evaluation of the equation during bisection,
2790 // which needs 3 times the bitwidth of the coefficient, so the total number
2791 // of required bits is 3n.
2792 //
2793 // The purpose of this extension is to simulate the set Z of all integers,
2794 // where n+1 > n for all n in Z. In Z it makes sense to talk about positive
2795 // and negative numbers (not so much in a modulo arithmetic). The method
2796 // used to solve the equation is based on the standard formula for real
2797 // numbers, and uses the concepts of "positive" and "negative" with their
2798 // usual meanings.
2799 CoeffWidth *= 3;
2800 A = A.sext(CoeffWidth);
2801 B = B.sext(CoeffWidth);
2802 C = C.sext(CoeffWidth);
2803
2804 // Make A > 0 for simplicity. Negate cannot overflow at this point because
2805 // the bit width has increased.
2806 if (A.isNegative()) {
2807 A.negate();
2808 B.negate();
2809 C.negate();
2810 }
2811
2812 // Solving an equation q(x) = 0 with coefficients in modular arithmetic
2813 // is really solving a set of equations q(x) = kR for k = 0, 1, 2, ...,
2814 // and R = 2^BitWidth.
2815 // Since we're trying not only to find exact solutions, but also values
2816 // that "wrap around", such a set will always have a solution, i.e. an x
2817 // that satisfies at least one of the equations, or such that |q(x)|
2818 // exceeds kR, while |q(x-1)| for the same k does not.
2819 //
2820 // We need to find a value k, such that Ax^2 + Bx + C = kR will have a
2821 // positive solution n (in the above sense), and also such that the n
2822 // will be the least among all solutions corresponding to k = 0, 1, ...
2823 // (more precisely, the least element in the set
2824 // { n(k) | k is such that a solution n(k) exists }).
2825 //
2826 // Consider the parabola (over real numbers) that corresponds to the
2827 // quadratic equation. Since A > 0, the arms of the parabola will point
2828 // up. Picking different values of k will shift it up and down by R.
2829 //
2830 // We want to shift the parabola in such a way as to reduce the problem
2831 // of solving q(x) = kR to solving shifted_q(x) = 0.
2832 // (The interesting solutions are the ceilings of the real number
2833 // solutions.)
2834 APInt R = APInt::getOneBitSet(CoeffWidth, RangeWidth);
2835 APInt TwoA = 2 * A;
2836 APInt SqrB = B * B;
2837 bool PickLow;
2838
2839 auto RoundUp = [] (const APInt &V, const APInt &A) -> APInt {
2840 assert(A.isStrictlyPositive())(static_cast <bool> (A.isStrictlyPositive()) ? void (0)
: __assert_fail ("A.isStrictlyPositive()", "llvm/lib/Support/APInt.cpp"
, 2840, __extension__ __PRETTY_FUNCTION__))
;
2841 APInt T = V.abs().urem(A);
2842 if (T.isZero())
2843 return V;
2844 return V.isNegative() ? V+T : V+(A-T);
2845 };
2846
2847 // The vertex of the parabola is at -B/2A, but since A > 0, it's negative
2848 // iff B is positive.
2849 if (B.isNonNegative()) {
2850 // If B >= 0, the vertex it at a negative location (or at 0), so in
2851 // order to have a non-negative solution we need to pick k that makes
2852 // C-kR negative. To satisfy all the requirements for the solution
2853 // that we are looking for, it needs to be closest to 0 of all k.
2854 C = C.srem(R);
2855 if (C.isStrictlyPositive())
2856 C -= R;
2857 // Pick the greater solution.
2858 PickLow = false;
2859 } else {
2860 // If B < 0, the vertex is at a positive location. For any solution
2861 // to exist, the discriminant must be non-negative. This means that
2862 // C-kR <= B^2/4A is a necessary condition for k, i.e. there is a
2863 // lower bound on values of k: kR >= C - B^2/4A.
2864 APInt LowkR = C - SqrB.udiv(2*TwoA); // udiv because all values > 0.
2865 // Round LowkR up (towards +inf) to the nearest kR.
2866 LowkR = RoundUp(LowkR, R);
2867
2868 // If there exists k meeting the condition above, and such that
2869 // C-kR > 0, there will be two positive real number solutions of
2870 // q(x) = kR. Out of all such values of k, pick the one that makes
2871 // C-kR closest to 0, (i.e. pick maximum k such that C-kR > 0).
2872 // In other words, find maximum k such that LowkR <= kR < C.
2873 if (C.sgt(LowkR)) {
2874 // If LowkR < C, then such a k is guaranteed to exist because
2875 // LowkR itself is a multiple of R.
2876 C -= -RoundUp(-C, R); // C = C - RoundDown(C, R)
2877 // Pick the smaller solution.
2878 PickLow = true;
2879 } else {
2880 // If C-kR < 0 for all potential k's, it means that one solution
2881 // will be negative, while the other will be positive. The positive
2882 // solution will shift towards 0 if the parabola is moved up.
2883 // Pick the kR closest to the lower bound (i.e. make C-kR closest
2884 // to 0, or in other words, out of all parabolas that have solutions,
2885 // pick the one that is the farthest "up").
2886 // Since LowkR is itself a multiple of R, simply take C-LowkR.
2887 C -= LowkR;
2888 // Pick the greater solution.
2889 PickLow = false;
2890 }
2891 }
2892
2893 LLVM_DEBUG(dbgs() << __func__ << ": updated coefficients " << A << "x^2 + "do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("apint")) { dbgs() << __func__ << ": updated coefficients "
<< A << "x^2 + " << B << "x + " <<
C << ", rw:" << RangeWidth << '\n'; } } while
(false)
2894 << B << "x + " << C << ", rw:" << RangeWidth << '\n')do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("apint")) { dbgs() << __func__ << ": updated coefficients "
<< A << "x^2 + " << B << "x + " <<
C << ", rw:" << RangeWidth << '\n'; } } while
(false)
;
2895
2896 APInt D = SqrB - 4*A*C;
2897 assert(D.isNonNegative() && "Negative discriminant")(static_cast <bool> (D.isNonNegative() && "Negative discriminant"
) ? void (0) : __assert_fail ("D.isNonNegative() && \"Negative discriminant\""
, "llvm/lib/Support/APInt.cpp", 2897, __extension__ __PRETTY_FUNCTION__
))
;
2898 APInt SQ = D.sqrt();
2899
2900 APInt Q = SQ * SQ;
2901 bool InexactSQ = Q != D;
2902 // The calculated SQ may actually be greater than the exact (non-integer)
2903 // value. If that's the case, decrement SQ to get a value that is lower.
2904 if (Q.sgt(D))
2905 SQ -= 1;
2906
2907 APInt X;
2908 APInt Rem;
2909
2910 // SQ is rounded down (i.e SQ * SQ <= D), so the roots may be inexact.
2911 // When using the quadratic formula directly, the calculated low root
2912 // may be greater than the exact one, since we would be subtracting SQ.
2913 // To make sure that the calculated root is not greater than the exact
2914 // one, subtract SQ+1 when calculating the low root (for inexact value
2915 // of SQ).
2916 if (PickLow)
2917 APInt::sdivrem(-B - (SQ+InexactSQ), TwoA, X, Rem);
2918 else
2919 APInt::sdivrem(-B + SQ, TwoA, X, Rem);
2920
2921 // The updated coefficients should be such that the (exact) solution is
2922 // positive. Since APInt division rounds towards 0, the calculated one
2923 // can be 0, but cannot be negative.
2924 assert(X.isNonNegative() && "Solution should be non-negative")(static_cast <bool> (X.isNonNegative() && "Solution should be non-negative"
) ? void (0) : __assert_fail ("X.isNonNegative() && \"Solution should be non-negative\""
, "llvm/lib/Support/APInt.cpp", 2924, __extension__ __PRETTY_FUNCTION__
))
;
2925
2926 if (!InexactSQ && Rem.isZero()) {
2927 LLVM_DEBUG(dbgs() << __func__ << ": solution (root): " << X << '\n')do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("apint")) { dbgs() << __func__ << ": solution (root): "
<< X << '\n'; } } while (false)
;
2928 return X;
2929 }
2930
2931 assert((SQ*SQ).sle(D) && "SQ = |_sqrt(D)_|, so SQ*SQ <= D")(static_cast <bool> ((SQ*SQ).sle(D) && "SQ = |_sqrt(D)_|, so SQ*SQ <= D"
) ? void (0) : __assert_fail ("(SQ*SQ).sle(D) && \"SQ = |_sqrt(D)_|, so SQ*SQ <= D\""
, "llvm/lib/Support/APInt.cpp", 2931, __extension__ __PRETTY_FUNCTION__
))
;
2932 // The exact value of the square root of D should be between SQ and SQ+1.
2933 // This implies that the solution should be between that corresponding to
2934 // SQ (i.e. X) and that corresponding to SQ+1.
2935 //
2936 // The calculated X cannot be greater than the exact (real) solution.
2937 // Actually it must be strictly less than the exact solution, while
2938 // X+1 will be greater than or equal to it.
2939
2940 APInt VX = (A*X + B)*X + C;
2941 APInt VY = VX + TwoA*X + A + B;
2942 bool SignChange =
2943 VX.isNegative() != VY.isNegative() || VX.isZero() != VY.isZero();
2944 // If the sign did not change between X and X+1, X is not a valid solution.
2945 // This could happen when the actual (exact) roots don't have an integer
2946 // between them, so they would both be contained between X and X+1.
2947 if (!SignChange) {
2948 LLVM_DEBUG(dbgs() << __func__ << ": no valid solution\n")do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("apint")) { dbgs() << __func__ << ": no valid solution\n"
; } } while (false)
;
2949 return None;
2950 }
2951
2952 X += 1;
2953 LLVM_DEBUG(dbgs() << __func__ << ": solution (wrap): " << X << '\n')do { if (::llvm::DebugFlag && ::llvm::isCurrentDebugType
("apint")) { dbgs() << __func__ << ": solution (wrap): "
<< X << '\n'; } } while (false)
;
2954 return X;
2955}
2956
2957Optional<unsigned>
2958llvm::APIntOps::GetMostSignificantDifferentBit(const APInt &A, const APInt &B) {
2959 assert(A.getBitWidth() == B.getBitWidth() && "Must have the same bitwidth")(static_cast <bool> (A.getBitWidth() == B.getBitWidth()
&& "Must have the same bitwidth") ? void (0) : __assert_fail
("A.getBitWidth() == B.getBitWidth() && \"Must have the same bitwidth\""
, "llvm/lib/Support/APInt.cpp", 2959, __extension__ __PRETTY_FUNCTION__
))
;
2960 if (A == B)
2961 return llvm::None;
2962 return A.getBitWidth() - ((A ^ B).countLeadingZeros() + 1);
2963}
2964
2965APInt llvm::APIntOps::ScaleBitMask(const APInt &A, unsigned NewBitWidth) {
2966 unsigned OldBitWidth = A.getBitWidth();
2967 assert((((OldBitWidth % NewBitWidth) == 0) ||(static_cast <bool> ((((OldBitWidth % NewBitWidth) == 0
) || ((NewBitWidth % OldBitWidth) == 0)) && "One size should be a multiple of the other one. "
"Can't do fractional scaling.") ? void (0) : __assert_fail (
"(((OldBitWidth % NewBitWidth) == 0) || ((NewBitWidth % OldBitWidth) == 0)) && \"One size should be a multiple of the other one. \" \"Can't do fractional scaling.\""
, "llvm/lib/Support/APInt.cpp", 2970, __extension__ __PRETTY_FUNCTION__
))
2968 ((NewBitWidth % OldBitWidth) == 0)) &&(static_cast <bool> ((((OldBitWidth % NewBitWidth) == 0
) || ((NewBitWidth % OldBitWidth) == 0)) && "One size should be a multiple of the other one. "
"Can't do fractional scaling.") ? void (0) : __assert_fail (
"(((OldBitWidth % NewBitWidth) == 0) || ((NewBitWidth % OldBitWidth) == 0)) && \"One size should be a multiple of the other one. \" \"Can't do fractional scaling.\""
, "llvm/lib/Support/APInt.cpp", 2970, __extension__ __PRETTY_FUNCTION__
))
2969 "One size should be a multiple of the other one. "(static_cast <bool> ((((OldBitWidth % NewBitWidth) == 0
) || ((NewBitWidth % OldBitWidth) == 0)) && "One size should be a multiple of the other one. "
"Can't do fractional scaling.") ? void (0) : __assert_fail (
"(((OldBitWidth % NewBitWidth) == 0) || ((NewBitWidth % OldBitWidth) == 0)) && \"One size should be a multiple of the other one. \" \"Can't do fractional scaling.\""
, "llvm/lib/Support/APInt.cpp", 2970, __extension__ __PRETTY_FUNCTION__
))
2970 "Can't do fractional scaling.")(static_cast <bool> ((((OldBitWidth % NewBitWidth) == 0
) || ((NewBitWidth % OldBitWidth) == 0)) && "One size should be a multiple of the other one. "
"Can't do fractional scaling.") ? void (0) : __assert_fail (
"(((OldBitWidth % NewBitWidth) == 0) || ((NewBitWidth % OldBitWidth) == 0)) && \"One size should be a multiple of the other one. \" \"Can't do fractional scaling.\""
, "llvm/lib/Support/APInt.cpp", 2970, __extension__ __PRETTY_FUNCTION__
))
;
2971
2972 // Check for matching bitwidths.
2973 if (OldBitWidth == NewBitWidth)
2974 return A;
2975
2976 APInt NewA = APInt::getZero(NewBitWidth);
2977
2978 // Check for null input.
2979 if (A.isZero())
2980 return NewA;
2981
2982 if (NewBitWidth > OldBitWidth) {
2983 // Repeat bits.
2984 unsigned Scale = NewBitWidth / OldBitWidth;
2985 for (unsigned i = 0; i != OldBitWidth; ++i)
2986 if (A[i])
2987 NewA.setBits(i * Scale, (i + 1) * Scale);
2988 } else {
2989 // Merge bits - if any old bit is set, then set scale equivalent new bit.
2990 unsigned Scale = OldBitWidth / NewBitWidth;
2991 for (unsigned i = 0; i != NewBitWidth; ++i)
2992 if (!A.extractBits(Scale, i * Scale).isZero())
2993 NewA.setBit(i);
2994 }
2995
2996 return NewA;
2997}
2998
2999/// StoreIntToMemory - Fills the StoreBytes bytes of memory starting from Dst
3000/// with the integer held in IntVal.
3001void llvm::StoreIntToMemory(const APInt &IntVal, uint8_t *Dst,
3002 unsigned StoreBytes) {
3003 assert((IntVal.getBitWidth()+7)/8 >= StoreBytes && "Integer too small!")(static_cast <bool> ((IntVal.getBitWidth()+7)/8 >= StoreBytes
&& "Integer too small!") ? void (0) : __assert_fail (
"(IntVal.getBitWidth()+7)/8 >= StoreBytes && \"Integer too small!\""
, "llvm/lib/Support/APInt.cpp", 3003, __extension__ __PRETTY_FUNCTION__
))
;
3004 const uint8_t *Src = (const uint8_t *)IntVal.getRawData();
3005
3006 if (sys::IsLittleEndianHost) {
3007 // Little-endian host - the source is ordered from LSB to MSB. Order the
3008 // destination from LSB to MSB: Do a straight copy.
3009 memcpy(Dst, Src, StoreBytes);
3010 } else {
3011 // Big-endian host - the source is an array of 64 bit words ordered from
3012 // LSW to MSW. Each word is ordered from MSB to LSB. Order the destination
3013 // from MSB to LSB: Reverse the word order, but not the bytes in a word.
3014 while (StoreBytes > sizeof(uint64_t)) {
3015 StoreBytes -= sizeof(uint64_t);
3016 // May not be aligned so use memcpy.
3017 memcpy(Dst + StoreBytes, Src, sizeof(uint64_t));
3018 Src += sizeof(uint64_t);
3019 }
3020
3021 memcpy(Dst, Src + sizeof(uint64_t) - StoreBytes, StoreBytes);
3022 }
3023}
3024
3025/// LoadIntFromMemory - Loads the integer stored in the LoadBytes bytes starting
3026/// from Src into IntVal, which is assumed to be wide enough and to hold zero.
3027void llvm::LoadIntFromMemory(APInt &IntVal, const uint8_t *Src,
3028 unsigned LoadBytes) {
3029 assert((IntVal.getBitWidth()+7)/8 >= LoadBytes && "Integer too small!")(static_cast <bool> ((IntVal.getBitWidth()+7)/8 >= LoadBytes
&& "Integer too small!") ? void (0) : __assert_fail (
"(IntVal.getBitWidth()+7)/8 >= LoadBytes && \"Integer too small!\""
, "llvm/lib/Support/APInt.cpp", 3029, __extension__ __PRETTY_FUNCTION__
))
;
3030 uint8_t *Dst = reinterpret_cast<uint8_t *>(
3031 const_cast<uint64_t *>(IntVal.getRawData()));
3032
3033 if (sys::IsLittleEndianHost)
3034 // Little-endian host - the destination must be ordered from LSB to MSB.
3035 // The source is ordered from LSB to MSB: Do a straight copy.
3036 memcpy(Dst, Src, LoadBytes);
3037 else {
3038 // Big-endian - the destination is an array of 64 bit words ordered from
3039 // LSW to MSW. Each word must be ordered from MSB to LSB. The source is
3040 // ordered from MSB to LSB: Reverse the word order, but not the bytes in
3041 // a word.
3042 while (LoadBytes > sizeof(uint64_t)) {
3043 LoadBytes -= sizeof(uint64_t);
3044 // May not be aligned so use memcpy.
3045 memcpy(Dst, Src + LoadBytes, sizeof(uint64_t));
3046 Dst += sizeof(uint64_t);
3047 }
3048
3049 memcpy(Dst + sizeof(uint64_t) - LoadBytes, Src, LoadBytes);
3050 }
3051}

/build/llvm-toolchain-snapshot-14~++20220119111520+da61cb019eb2/llvm/include/llvm/Support/MathExtras.h

1//===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
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 contains some functions that are useful for math stuff.
10//
11//===----------------------------------------------------------------------===//
12
13#ifndef LLVM_SUPPORT_MATHEXTRAS_H
14#define LLVM_SUPPORT_MATHEXTRAS_H
15
16#include "llvm/Support/Compiler.h"
17#include <cassert>
18#include <climits>
19#include <cmath>
20#include <cstdint>
21#include <cstring>
22#include <limits>
23#include <type_traits>
24
25#ifdef __ANDROID_NDK__
26#include <android/api-level.h>
27#endif
28
29#ifdef _MSC_VER
30// Declare these intrinsics manually rather including intrin.h. It's very
31// expensive, and MathExtras.h is popular.
32// #include <intrin.h>
33extern "C" {
34unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask);
35unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask);
36unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask);
37unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask);
38}
39#endif
40
41namespace llvm {
42
43/// The behavior an operation has on an input of 0.
44enum ZeroBehavior {
45 /// The returned value is undefined.
46 ZB_Undefined,
47 /// The returned value is numeric_limits<T>::max()
48 ZB_Max,
49 /// The returned value is numeric_limits<T>::digits
50 ZB_Width
51};
52
53/// Mathematical constants.
54namespace numbers {
55// TODO: Track C++20 std::numbers.
56// TODO: Favor using the hexadecimal FP constants (requires C++17).
57constexpr double e = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113
58 egamma = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620
59 ln2 = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162
60 ln10 = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392
61 log2e = 1.4426950408889634074, // (0x1.71547652b82feP+0)
62 log10e = .43429448190325182765, // (0x1.bcb7b1526e50eP-2)
63 pi = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796
64 inv_pi = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541
65 sqrtpi = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161
66 inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197
67 sqrt2 = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219
68 inv_sqrt2 = .70710678118654752440, // (0x1.6a09e667f3bcdP-1)
69 sqrt3 = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194
70 inv_sqrt3 = .57735026918962576451, // (0x1.279a74590331cP-1)
71 phi = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622
72constexpr float ef = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113
73 egammaf = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620
74 ln2f = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162
75 ln10f = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392
76 log2ef = 1.44269504F, // (0x1.715476P+0)
77 log10ef = .434294482F, // (0x1.bcb7b2P-2)
78 pif = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796
79 inv_pif = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541
80 sqrtpif = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161
81 inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197
82 sqrt2f = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193
83 inv_sqrt2f = .707106781F, // (0x1.6a09e6P-1)
84 sqrt3f = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194
85 inv_sqrt3f = .577350269F, // (0x1.279a74P-1)
86 phif = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622
87} // namespace numbers
88
89namespace detail {
90template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
91 static unsigned count(T Val, ZeroBehavior) {
92 if (!Val)
93 return std::numeric_limits<T>::digits;
94 if (Val & 0x1)
95 return 0;
96
97 // Bisection method.
98 unsigned ZeroBits = 0;
99 T Shift = std::numeric_limits<T>::digits >> 1;
100 T Mask = std::numeric_limits<T>::max() >> Shift;
101 while (Shift) {
102 if ((Val & Mask) == 0) {
103 Val >>= Shift;
104 ZeroBits |= Shift;
105 }
106 Shift >>= 1;
107 Mask >>= Shift;
108 }
109 return ZeroBits;
110 }
111};
112
113#if defined(__GNUC__4) || defined(_MSC_VER)
114template <typename T> struct TrailingZerosCounter<T, 4> {
115 static unsigned count(T Val, ZeroBehavior ZB) {
116 if (ZB != ZB_Undefined && Val == 0)
117 return 32;
118
119#if __has_builtin(__builtin_ctz)1 || defined(__GNUC__4)
120 return __builtin_ctz(Val);
121#elif defined(_MSC_VER)
122 unsigned long Index;
123 _BitScanForward(&Index, Val);
124 return Index;
125#endif
126 }
127};
128
129#if !defined(_MSC_VER) || defined(_M_X64)
130template <typename T> struct TrailingZerosCounter<T, 8> {
131 static unsigned count(T Val, ZeroBehavior ZB) {
132 if (ZB != ZB_Undefined && Val == 0)
133 return 64;
134
135#if __has_builtin(__builtin_ctzll)1 || defined(__GNUC__4)
136 return __builtin_ctzll(Val);
137#elif defined(_MSC_VER)
138 unsigned long Index;
139 _BitScanForward64(&Index, Val);
140 return Index;
141#endif
142 }
143};
144#endif
145#endif
146} // namespace detail
147
148/// Count number of 0's from the least significant bit to the most
149/// stopping at the first 1.
150///
151/// Only unsigned integral types are allowed.
152///
153/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
154/// valid arguments.
155template <typename T>
156unsigned countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
157 static_assert(std::numeric_limits<T>::is_integer &&
158 !std::numeric_limits<T>::is_signed,
159 "Only unsigned integral types are allowed.");
160 return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB);
161}
162
163namespace detail {
164template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
165 static unsigned count(T Val, ZeroBehavior) {
166 if (!Val)
167 return std::numeric_limits<T>::digits;
168
169 // Bisection method.
170 unsigned ZeroBits = 0;
171 for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
172 T Tmp = Val >> Shift;
173 if (Tmp)
174 Val = Tmp;
175 else
176 ZeroBits |= Shift;
177 }
178 return ZeroBits;
179 }
180};
181
182#if defined(__GNUC__4) || defined(_MSC_VER)
183template <typename T> struct LeadingZerosCounter<T, 4> {
184 static unsigned count(T Val, ZeroBehavior ZB) {
185 if (ZB
20.1
'ZB' is not equal to ZB_Undefined
20.1
'ZB' is not equal to ZB_Undefined
!= ZB_Undefined && Val == 0)
21
Assuming 'Val' is equal to 0
22
Taking true branch
186 return 32;
23
Returning the value 32, which participates in a condition later
24
Returning the value 32
187
188#if __has_builtin(__builtin_clz)1 || defined(__GNUC__4)
189 return __builtin_clz(Val);
190#elif defined(_MSC_VER)
191 unsigned long Index;
192 _BitScanReverse(&Index, Val);
193 return Index ^ 31;
194#endif
195 }
196};
197
198#if !defined(_MSC_VER) || defined(_M_X64)
199template <typename T> struct LeadingZerosCounter<T, 8> {
200 static unsigned count(T Val, ZeroBehavior ZB) {
201 if (ZB != ZB_Undefined && Val == 0)
202 return 64;
203
204#if __has_builtin(__builtin_clzll)1 || defined(__GNUC__4)
205 return __builtin_clzll(Val);
206#elif defined(_MSC_VER)
207 unsigned long Index;
208 _BitScanReverse64(&Index, Val);
209 return Index ^ 63;
210#endif
211 }
212};
213#endif
214#endif
215} // namespace detail
216
217/// Count number of 0's from the most significant bit to the least
218/// stopping at the first 1.
219///
220/// Only unsigned integral types are allowed.
221///
222/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
223/// valid arguments.
224template <typename T>
225unsigned countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
226 static_assert(std::numeric_limits<T>::is_integer &&
227 !std::numeric_limits<T>::is_signed,
228 "Only unsigned integral types are allowed.");
229 return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
20
Calling 'LeadingZerosCounter::count'
25
Returning from 'LeadingZerosCounter::count'
26
Returning the value 32, which participates in a condition later
27
Returning the value 32
230}
231
232/// Get the index of the first set bit starting from the least
233/// significant bit.
234///
235/// Only unsigned integral types are allowed.
236///
237/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
238/// valid arguments.
239template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
240 if (ZB == ZB_Max && Val == 0)
241 return std::numeric_limits<T>::max();
242
243 return countTrailingZeros(Val, ZB_Undefined);
244}
245
246/// Create a bitmask with the N right-most bits set to 1, and all other
247/// bits set to 0. Only unsigned types are allowed.
248template <typename T> T maskTrailingOnes(unsigned N) {
249 static_assert(std::is_unsigned<T>::value, "Invalid type!");
250 const unsigned Bits = CHAR_BIT8 * sizeof(T);
251 assert(N <= Bits && "Invalid bit index")(static_cast <bool> (N <= Bits && "Invalid bit index"
) ? void (0) : __assert_fail ("N <= Bits && \"Invalid bit index\""
, "llvm/include/llvm/Support/MathExtras.h", 251, __extension__
__PRETTY_FUNCTION__))
;
252 return N == 0 ? 0 : (T(-1) >> (Bits - N));
253}
254
255/// Create a bitmask with the N left-most bits set to 1, and all other
256/// bits set to 0. Only unsigned types are allowed.
257template <typename T> T maskLeadingOnes(unsigned N) {
258 return ~maskTrailingOnes<T>(CHAR_BIT8 * sizeof(T) - N);
259}
260
261/// Create a bitmask with the N right-most bits set to 0, and all other
262/// bits set to 1. Only unsigned types are allowed.
263template <typename T> T maskTrailingZeros(unsigned N) {
264 return maskLeadingOnes<T>(CHAR_BIT8 * sizeof(T) - N);
265}
266
267/// Create a bitmask with the N left-most bits set to 0, and all other
268/// bits set to 1. Only unsigned types are allowed.
269template <typename T> T maskLeadingZeros(unsigned N) {
270 return maskTrailingOnes<T>(CHAR_BIT8 * sizeof(T) - N);
271}
272
273/// Get the index of the last set bit starting from the least
274/// significant bit.
275///
276/// Only unsigned integral types are allowed.
277///
278/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
279/// valid arguments.
280template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
281 if (ZB == ZB_Max && Val == 0)
282 return std::numeric_limits<T>::max();
283
284 // Use ^ instead of - because both gcc and llvm can remove the associated ^
285 // in the __builtin_clz intrinsic on x86.
286 return countLeadingZeros(Val, ZB_Undefined) ^
287 (std::numeric_limits<T>::digits - 1);
288}
289
290/// Macro compressed bit reversal table for 256 bits.
291///
292/// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
293static const unsigned char BitReverseTable256[256] = {
294#define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
295#define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
296#define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
297 R6(0), R6(2), R6(1), R6(3)
298#undef R2
299#undef R4
300#undef R6
301};
302
303/// Reverse the bits in \p Val.
304template <typename T>
305T reverseBits(T Val) {
306 unsigned char in[sizeof(Val)];
307 unsigned char out[sizeof(Val)];
308 std::memcpy(in, &Val, sizeof(Val));
309 for (unsigned i = 0; i < sizeof(Val); ++i)
310 out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
311 std::memcpy(&Val, out, sizeof(Val));
312 return Val;
313}
314
315#if __has_builtin(__builtin_bitreverse8)1
316template<>
317inline uint8_t reverseBits<uint8_t>(uint8_t Val) {
318 return __builtin_bitreverse8(Val);
319}
320#endif
321
322#if __has_builtin(__builtin_bitreverse16)1
323template<>
324inline uint16_t reverseBits<uint16_t>(uint16_t Val) {
325 return __builtin_bitreverse16(Val);
326}
327#endif
328
329#if __has_builtin(__builtin_bitreverse32)1
330template<>
331inline uint32_t reverseBits<uint32_t>(uint32_t Val) {
332 return __builtin_bitreverse32(Val);
333}
334#endif
335
336#if __has_builtin(__builtin_bitreverse64)1
337template<>
338inline uint64_t reverseBits<uint64_t>(uint64_t Val) {
339 return __builtin_bitreverse64(Val);
340}
341#endif
342
343// NOTE: The following support functions use the _32/_64 extensions instead of
344// type overloading so that signed and unsigned integers can be used without
345// ambiguity.
346
347/// Return the high 32 bits of a 64 bit value.
348constexpr inline uint32_t Hi_32(uint64_t Value) {
349 return static_cast<uint32_t>(Value >> 32);
350}
351
352/// Return the low 32 bits of a 64 bit value.
353constexpr inline uint32_t Lo_32(uint64_t Value) {
354 return static_cast<uint32_t>(Value);
355}
356
357/// Make a 64-bit integer from a high / low pair of 32-bit integers.
358constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
359 return ((uint64_t)High << 32) | (uint64_t)Low;
360}
361
362/// Checks if an integer fits into the given bit width.
363template <unsigned N> constexpr inline bool isInt(int64_t x) {
364 return N >= 64 || (-(INT64_C(1)1L<<(N-1)) <= x && x < (INT64_C(1)1L<<(N-1)));
365}
366// Template specializations to get better code for common cases.
367template <> constexpr inline bool isInt<8>(int64_t x) {
368 return static_cast<int8_t>(x) == x;
369}
370template <> constexpr inline bool isInt<16>(int64_t x) {
371 return static_cast<int16_t>(x) == x;
372}
373template <> constexpr inline bool isInt<32>(int64_t x) {
374 return static_cast<int32_t>(x) == x;
375}
376
377/// Checks if a signed integer is an N bit number shifted left by S.
378template <unsigned N, unsigned S>
379constexpr inline bool isShiftedInt(int64_t x) {
380 static_assert(
381 N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
382 static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
383 return isInt<N + S>(x) && (x % (UINT64_C(1)1UL << S) == 0);
384}
385
386/// Checks if an unsigned integer fits into the given bit width.
387///
388/// This is written as two functions rather than as simply
389///
390/// return N >= 64 || X < (UINT64_C(1) << N);
391///
392/// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
393/// left too many places.
394template <unsigned N>
395constexpr inline std::enable_if_t<(N < 64), bool> isUInt(uint64_t X) {
396 static_assert(N > 0, "isUInt<0> doesn't make sense");
397 return X < (UINT64_C(1)1UL << (N));
398}
399template <unsigned N>
400constexpr inline std::enable_if_t<N >= 64, bool> isUInt(uint64_t) {
401 return true;
402}
403
404// Template specializations to get better code for common cases.
405template <> constexpr inline bool isUInt<8>(uint64_t x) {
406 return static_cast<uint8_t>(x) == x;
407}
408template <> constexpr inline bool isUInt<16>(uint64_t x) {
409 return static_cast<uint16_t>(x) == x;
410}
411template <> constexpr inline bool isUInt<32>(uint64_t x) {
412 return static_cast<uint32_t>(x) == x;
413}
414
415/// Checks if a unsigned integer is an N bit number shifted left by S.
416template <unsigned N, unsigned S>
417constexpr inline bool isShiftedUInt(uint64_t x) {
418 static_assert(
419 N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
420 static_assert(N + S <= 64,
421 "isShiftedUInt<N, S> with N + S > 64 is too wide.");
422 // Per the two static_asserts above, S must be strictly less than 64. So
423 // 1 << S is not undefined behavior.
424 return isUInt<N + S>(x) && (x % (UINT64_C(1)1UL << S) == 0);
425}
426
427/// Gets the maximum value for a N-bit unsigned integer.
428inline uint64_t maxUIntN(uint64_t N) {
429 assert(N > 0 && N <= 64 && "integer width out of range")(static_cast <bool> (N > 0 && N <= 64 &&
"integer width out of range") ? void (0) : __assert_fail ("N > 0 && N <= 64 && \"integer width out of range\""
, "llvm/include/llvm/Support/MathExtras.h", 429, __extension__
__PRETTY_FUNCTION__))
;
430
431 // uint64_t(1) << 64 is undefined behavior, so we can't do
432 // (uint64_t(1) << N) - 1
433 // without checking first that N != 64. But this works and doesn't have a
434 // branch.
435 return UINT64_MAX(18446744073709551615UL) >> (64 - N);
436}
437
438/// Gets the minimum value for a N-bit signed integer.
439inline int64_t minIntN(int64_t N) {
440 assert(N > 0 && N <= 64 && "integer width out of range")(static_cast <bool> (N > 0 && N <= 64 &&
"integer width out of range") ? void (0) : __assert_fail ("N > 0 && N <= 64 && \"integer width out of range\""
, "llvm/include/llvm/Support/MathExtras.h", 440, __extension__
__PRETTY_FUNCTION__))
;
441
442 return UINT64_C(1)1UL + ~(UINT64_C(1)1UL << (N - 1));
443}
444
445/// Gets the maximum value for a N-bit signed integer.
446inline int64_t maxIntN(int64_t N) {
447 assert(N > 0 && N <= 64 && "integer width out of range")(static_cast <bool> (N > 0 && N <= 64 &&
"integer width out of range") ? void (0) : __assert_fail ("N > 0 && N <= 64 && \"integer width out of range\""
, "llvm/include/llvm/Support/MathExtras.h", 447, __extension__
__PRETTY_FUNCTION__))
;
448
449 // This relies on two's complement wraparound when N == 64, so we convert to
450 // int64_t only at the very end to avoid UB.
451 return (UINT64_C(1)1UL << (N - 1)) - 1;
452}
453
454/// Checks if an unsigned integer fits into the given (dynamic) bit width.
455inline bool isUIntN(unsigned N, uint64_t x) {
456 return N >= 64 || x <= maxUIntN(N);
457}
458
459/// Checks if an signed integer fits into the given (dynamic) bit width.
460inline bool isIntN(unsigned N, int64_t x) {
461 return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
462}
463
464/// Return true if the argument is a non-empty sequence of ones starting at the
465/// least significant bit with the remainder zero (32 bit version).
466/// Ex. isMask_32(0x0000FFFFU) == true.
467constexpr inline bool isMask_32(uint32_t Value) {
468 return Value && ((Value + 1) & Value) == 0;
469}
470
471/// Return true if the argument is a non-empty sequence of ones starting at the
472/// least significant bit with the remainder zero (64 bit version).
473constexpr inline bool isMask_64(uint64_t Value) {
474 return Value && ((Value + 1) & Value) == 0;
475}
476
477/// Return true if the argument contains a non-empty sequence of ones with the
478/// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
479constexpr inline bool isShiftedMask_32(uint32_t Value) {
480 return Value && isMask_32((Value - 1) | Value);
481}
482
483/// Return true if the argument contains a non-empty sequence of ones with the
484/// remainder zero (64 bit version.)
485constexpr inline bool isShiftedMask_64(uint64_t Value) {
486 return Value && isMask_64((Value - 1) | Value);
487}
488
489/// Return true if the argument is a power of two > 0.
490/// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
491constexpr inline bool isPowerOf2_32(uint32_t Value) {
492 return Value && !(Value & (Value - 1));
493}
494
495/// Return true if the argument is a power of two > 0 (64 bit edition.)
496constexpr inline bool isPowerOf2_64(uint64_t Value) {
497 return Value && !(Value & (Value - 1));
498}
499
500/// Count the number of ones from the most significant bit to the first
501/// zero bit.
502///
503/// Ex. countLeadingOnes(0xFF0FFF00) == 8.
504/// Only unsigned integral types are allowed.
505///
506/// \param ZB the behavior on an input of all ones. Only ZB_Width and
507/// ZB_Undefined are valid arguments.
508template <typename T>
509unsigned countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
510 static_assert(std::numeric_limits<T>::is_integer &&
511 !std::numeric_limits<T>::is_signed,
512 "Only unsigned integral types are allowed.");
513 return countLeadingZeros<T>(~Value, ZB);
514}
515
516/// Count the number of ones from the least significant bit to the first
517/// zero bit.
518///
519/// Ex. countTrailingOnes(0x00FF00FF) == 8.
520/// Only unsigned integral types are allowed.
521///
522/// \param ZB the behavior on an input of all ones. Only ZB_Width and
523/// ZB_Undefined are valid arguments.
524template <typename T>
525unsigned countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
526 static_assert(std::numeric_limits<T>::is_integer &&
527 !std::numeric_limits<T>::is_signed,
528 "Only unsigned integral types are allowed.");
529 return countTrailingZeros<T>(~Value, ZB);
530}
531
532namespace detail {
533template <typename T, std::size_t SizeOfT> struct PopulationCounter {
534 static unsigned count(T Value) {
535 // Generic version, forward to 32 bits.
536 static_assert(SizeOfT <= 4, "Not implemented!");
537#if defined(__GNUC__4)
538 return __builtin_popcount(Value);
539#else
540 uint32_t v = Value;
541 v = v - ((v >> 1) & 0x55555555);
542 v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
543 return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
544#endif
545 }
546};
547
548template <typename T> struct PopulationCounter<T, 8> {
549 static unsigned count(T Value) {
550#if defined(__GNUC__4)
551 return __builtin_popcountll(Value);
552#else
553 uint64_t v = Value;
554 v = v - ((v >> 1) & 0x5555555555555555ULL);
555 v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
556 v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
557 return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
558#endif
559 }
560};
561} // namespace detail
562
563/// Count the number of set bits in a value.
564/// Ex. countPopulation(0xF000F000) = 8
565/// Returns 0 if the word is zero.
566template <typename T>
567inline unsigned countPopulation(T Value) {
568 static_assert(std::numeric_limits<T>::is_integer &&
569 !std::numeric_limits<T>::is_signed,
570 "Only unsigned integral types are allowed.");
571 return detail::PopulationCounter<T, sizeof(T)>::count(Value);
572}
573
574/// Compile time Log2.
575/// Valid only for positive powers of two.
576template <size_t kValue> constexpr inline size_t CTLog2() {
577 static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue),
578 "Value is not a valid power of 2");
579 return 1 + CTLog2<kValue / 2>();
580}
581
582template <> constexpr inline size_t CTLog2<1>() { return 0; }
583
584/// Return the log base 2 of the specified value.
585inline double Log2(double Value) {
586#if defined(__ANDROID_API__) && __ANDROID_API__ < 18
587 return __builtin_log(Value) / __builtin_log(2.0);
588#else
589 return log2(Value);
590#endif
591}
592
593/// Return the floor log base 2 of the specified value, -1 if the value is zero.
594/// (32 bit edition.)
595/// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
596inline unsigned Log2_32(uint32_t Value) {
597 return 31 - countLeadingZeros(Value);
598}
599
600/// Return the floor log base 2 of the specified value, -1 if the value is zero.
601/// (64 bit edition.)
602inline unsigned Log2_64(uint64_t Value) {
603 return 63 - countLeadingZeros(Value);
604}
605
606/// Return the ceil log base 2 of the specified value, 32 if the value is zero.
607/// (32 bit edition).
608/// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
609inline unsigned Log2_32_Ceil(uint32_t Value) {
610 return 32 - countLeadingZeros(Value - 1);
611}
612
613/// Return the ceil log base 2 of the specified value, 64 if the value is zero.
614/// (64 bit edition.)
615inline unsigned Log2_64_Ceil(uint64_t Value) {
616 return 64 - countLeadingZeros(Value - 1);
617}
618
619/// Return the greatest common divisor of the values using Euclid's algorithm.
620template <typename T>
621inline T greatestCommonDivisor(T A, T B) {
622 while (B) {
623 T Tmp = B;
624 B = A % B;
625 A = Tmp;
626 }
627 return A;
628}
629
630inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
631 return greatestCommonDivisor<uint64_t>(A, B);
632}
633
634/// This function takes a 64-bit integer and returns the bit equivalent double.
635inline double BitsToDouble(uint64_t Bits) {
636 double D;
637 static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
638 memcpy(&D, &Bits, sizeof(Bits));
639 return D;
640}
641
642/// This function takes a 32-bit integer and returns the bit equivalent float.
643inline float BitsToFloat(uint32_t Bits) {
644 float F;
645 static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
646 memcpy(&F, &Bits, sizeof(Bits));
647 return F;
648}
649
650/// This function takes a double and returns the bit equivalent 64-bit integer.
651/// Note that copying doubles around changes the bits of NaNs on some hosts,
652/// notably x86, so this routine cannot be used if these bits are needed.
653inline uint64_t DoubleToBits(double Double) {
654 uint64_t Bits;
655 static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
656 memcpy(&Bits, &Double, sizeof(Double));
657 return Bits;
658}
659
660/// This function takes a float and returns the bit equivalent 32-bit integer.
661/// Note that copying floats around changes the bits of NaNs on some hosts,
662/// notably x86, so this routine cannot be used if these bits are needed.
663inline uint32_t FloatToBits(float Float) {
664 uint32_t Bits;
665 static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
666 memcpy(&Bits, &Float, sizeof(Float));
667 return Bits;
668}
669
670/// A and B are either alignments or offsets. Return the minimum alignment that
671/// may be assumed after adding the two together.
672constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
673 // The largest power of 2 that divides both A and B.
674 //
675 // Replace "-Value" by "1+~Value" in the following commented code to avoid
676 // MSVC warning C4146
677 // return (A | B) & -(A | B);
678 return (A | B) & (1 + ~(A | B));
679}
680
681/// Returns the next power of two (in 64-bits) that is strictly greater than A.
682/// Returns zero on overflow.
683inline uint64_t NextPowerOf2(uint64_t A) {
684 A |= (A >> 1);
685 A |= (A >> 2);
686 A |= (A >> 4);
687 A |= (A >> 8);
688 A |= (A >> 16);
689 A |= (A >> 32);
690 return A + 1;
691}
692
693/// Returns the power of two which is less than or equal to the given value.
694/// Essentially, it is a floor operation across the domain of powers of two.
695inline uint64_t PowerOf2Floor(uint64_t A) {
696 if (!A) return 0;
697 return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
698}
699
700/// Returns the power of two which is greater than or equal to the given value.
701/// Essentially, it is a ceil operation across the domain of powers of two.
702inline uint64_t PowerOf2Ceil(uint64_t A) {
703 if (!A)
704 return 0;
705 return NextPowerOf2(A - 1);
706}
707
708/// Returns the next integer (mod 2**64) that is greater than or equal to
709/// \p Value and is a multiple of \p Align. \p Align must be non-zero.
710///
711/// If non-zero \p Skew is specified, the return value will be a minimal
712/// integer that is greater than or equal to \p Value and equal to
713/// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
714/// \p Align, its value is adjusted to '\p Skew mod \p Align'.
715///
716/// Examples:
717/// \code
718/// alignTo(5, 8) = 8
719/// alignTo(17, 8) = 24
720/// alignTo(~0LL, 8) = 0
721/// alignTo(321, 255) = 510
722///
723/// alignTo(5, 8, 7) = 7
724/// alignTo(17, 8, 1) = 17
725/// alignTo(~0LL, 8, 3) = 3
726/// alignTo(321, 255, 42) = 552
727/// \endcode
728inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
729 assert(Align != 0u && "Align can't be 0.")(static_cast <bool> (Align != 0u && "Align can't be 0."
) ? void (0) : __assert_fail ("Align != 0u && \"Align can't be 0.\""
, "llvm/include/llvm/Support/MathExtras.h", 729, __extension__
__PRETTY_FUNCTION__))
;
730 Skew %= Align;
731 return (Value + Align - 1 - Skew) / Align * Align + Skew;
732}
733
734/// Returns the next integer (mod 2**64) that is greater than or equal to
735/// \p Value and is a multiple of \c Align. \c Align must be non-zero.
736template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
737 static_assert(Align != 0u, "Align must be non-zero");
738 return (Value + Align - 1) / Align * Align;
739}
740
741/// Returns the integer ceil(Numerator / Denominator).
742inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
743 return alignTo(Numerator, Denominator) / Denominator;
744}
745
746/// Returns the integer nearest(Numerator / Denominator).
747inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) {
748 return (Numerator + (Denominator / 2)) / Denominator;
749}
750
751/// Returns the largest uint64_t less than or equal to \p Value and is
752/// \p Skew mod \p Align. \p Align must be non-zero
753inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
754 assert(Align != 0u && "Align can't be 0.")(static_cast <bool> (Align != 0u && "Align can't be 0."
) ? void (0) : __assert_fail ("Align != 0u && \"Align can't be 0.\""
, "llvm/include/llvm/Support/MathExtras.h", 754, __extension__
__PRETTY_FUNCTION__))
;
755 Skew %= Align;
756 return (Value - Skew) / Align * Align + Skew;
757}
758
759/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
760/// Requires 0 < B <= 32.
761template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
762 static_assert(B > 0, "Bit width can't be 0.");
763 static_assert(B <= 32, "Bit width out of range.");
764 return int32_t(X << (32 - B)) >> (32 - B);
765}
766
767/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
768/// Requires 0 < B <= 32.
769inline int32_t SignExtend32(uint32_t X, unsigned B) {
770 assert(B > 0 && "Bit width can't be 0.")(static_cast <bool> (B > 0 && "Bit width can't be 0."
) ? void (0) : __assert_fail ("B > 0 && \"Bit width can't be 0.\""
, "llvm/include/llvm/Support/MathExtras.h", 770, __extension__
__PRETTY_FUNCTION__))
;
771 assert(B <= 32 && "Bit width out of range.")(static_cast <bool> (B <= 32 && "Bit width out of range."
) ? void (0) : __assert_fail ("B <= 32 && \"Bit width out of range.\""
, "llvm/include/llvm/Support/MathExtras.h", 771, __extension__
__PRETTY_FUNCTION__))
;
772 return int32_t(X << (32 - B)) >> (32 - B);
773}
774
775/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
776/// Requires 0 < B <= 64.
777template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
778 static_assert(B > 0, "Bit width can't be 0.");
779 static_assert(B <= 64, "Bit width out of range.");
780 return int64_t(x << (64 - B)) >> (64 - B);
781}
782
783/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
784/// Requires 0 < B <= 64.
785inline int64_t SignExtend64(uint64_t X, unsigned B) {
786 assert(B > 0 && "Bit width can't be 0.")(static_cast <bool> (B > 0 && "Bit width can't be 0."
) ? void (0) : __assert_fail ("B > 0 && \"Bit width can't be 0.\""
, "llvm/include/llvm/Support/MathExtras.h", 786, __extension__
__PRETTY_FUNCTION__))
;
787 assert(B <= 64 && "Bit width out of range.")(static_cast <bool> (B <= 64 && "Bit width out of range."
) ? void (0) : __assert_fail ("B <= 64 && \"Bit width out of range.\""
, "llvm/include/llvm/Support/MathExtras.h", 787, __extension__
__PRETTY_FUNCTION__))
;
788 return int64_t(X << (64 - B)) >> (64 - B);
789}
790
791/// Subtract two unsigned integers, X and Y, of type T and return the absolute
792/// value of the result.
793template <typename T>
794std::enable_if_t<std::is_unsigned<T>::value, T> AbsoluteDifference(T X, T Y) {
795 return X > Y ? (X - Y) : (Y - X);
796}
797
798/// Add two unsigned integers, X and Y, of type T. Clamp the result to the
799/// maximum representable value of T on overflow. ResultOverflowed indicates if
800/// the result is larger than the maximum representable value of type T.
801template <typename T>
802std::enable_if_t<std::is_unsigned<T>::value, T>
803SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
804 bool Dummy;
805 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
806 // Hacker's Delight, p. 29
807 T Z = X + Y;
808 Overflowed = (Z < X || Z < Y);
809 if (Overflowed)
810 return std::numeric_limits<T>::max();
811 else
812 return Z;
813}
814
815/// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the
816/// maximum representable value of T on overflow. ResultOverflowed indicates if
817/// the result is larger than the maximum representable value of type T.
818template <typename T>
819std::enable_if_t<std::is_unsigned<T>::value, T>
820SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
821 bool Dummy;
822 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
823
824 // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
825 // because it fails for uint16_t (where multiplication can have undefined
826 // behavior due to promotion to int), and requires a division in addition
827 // to the multiplication.
828
829 Overflowed = false;
830
831 // Log2(Z) would be either Log2Z or Log2Z + 1.
832 // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
833 // will necessarily be less than Log2Max as desired.
834 int Log2Z = Log2_64(X) + Log2_64(Y);
835 const T Max = std::numeric_limits<T>::max();
836 int Log2Max = Log2_64(Max);
837 if (Log2Z < Log2Max) {
838 return X * Y;
839 }
840 if (Log2Z > Log2Max) {
841 Overflowed = true;
842 return Max;
843 }
844
845 // We're going to use the top bit, and maybe overflow one
846 // bit past it. Multiply all but the bottom bit then add
847 // that on at the end.
848 T Z = (X >> 1) * Y;
849 if (Z & ~(Max >> 1)) {
850 Overflowed = true;
851 return Max;
852 }
853 Z <<= 1;
854 if (X & 1)
855 return SaturatingAdd(Z, Y, ResultOverflowed);
856
857 return Z;
858}
859
860/// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
861/// the product. Clamp the result to the maximum representable value of T on
862/// overflow. ResultOverflowed indicates if the result is larger than the
863/// maximum representable value of type T.
864template <typename T>
865std::enable_if_t<std::is_unsigned<T>::value, T>
866SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
867 bool Dummy;
868 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
869
870 T Product = SaturatingMultiply(X, Y, &Overflowed);
871 if (Overflowed)
872 return Product;
873
874 return SaturatingAdd(A, Product, &Overflowed);
875}
876
877/// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
878extern const float huge_valf;
879
880
881/// Add two signed integers, computing the two's complement truncated result,
882/// returning true if overflow occured.
883template <typename T>
884std::enable_if_t<std::is_signed<T>::value, T> AddOverflow(T X, T Y, T &Result) {
885#if __has_builtin(__builtin_add_overflow)1
886 return __builtin_add_overflow(X, Y, &Result);
887#else
888 // Perform the unsigned addition.
889 using U = std::make_unsigned_t<T>;
890 const U UX = static_cast<U>(X);
891 const U UY = static_cast<U>(Y);
892 const U UResult = UX + UY;
893
894 // Convert to signed.
895 Result = static_cast<T>(UResult);
896
897 // Adding two positive numbers should result in a positive number.
898 if (X > 0 && Y > 0)
899 return Result <= 0;
900 // Adding two negatives should result in a negative number.
901 if (X < 0 && Y < 0)
902 return Result >= 0;
903 return false;
904#endif
905}
906
907/// Subtract two signed integers, computing the two's complement truncated
908/// result, returning true if an overflow ocurred.
909template <typename T>
910std::enable_if_t<std::is_signed<T>::value, T> SubOverflow(T X, T Y, T &Result) {
911#if __has_builtin(__builtin_sub_overflow)1
912 return __builtin_sub_overflow(X, Y, &Result);
913#else
914 // Perform the unsigned addition.
915 using U = std::make_unsigned_t<T>;
916 const U UX = static_cast<U>(X);
917 const U UY = static_cast<U>(Y);
918 const U UResult = UX - UY;
919
920 // Convert to signed.
921 Result = static_cast<T>(UResult);
922
923 // Subtracting a positive number from a negative results in a negative number.
924 if (X <= 0 && Y > 0)
925 return Result >= 0;
926 // Subtracting a negative number from a positive results in a positive number.
927 if (X >= 0 && Y < 0)
928 return Result <= 0;
929 return false;
930#endif
931}
932
933/// Multiply two signed integers, computing the two's complement truncated
934/// result, returning true if an overflow ocurred.
935template <typename T>
936std::enable_if_t<std::is_signed<T>::value, T> MulOverflow(T X, T Y, T &Result) {
937 // Perform the unsigned multiplication on absolute values.
938 using U = std::make_unsigned_t<T>;
939 const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X);
940 const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y);
941 const U UResult = UX * UY;
942
943 // Convert to signed.
944 const bool IsNegative = (X < 0) ^ (Y < 0);
945 Result = IsNegative ? (0 - UResult) : UResult;
946
947 // If any of the args was 0, result is 0 and no overflow occurs.
948 if (UX == 0 || UY == 0)
949 return false;
950
951 // UX and UY are in [1, 2^n], where n is the number of digits.
952 // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for
953 // positive) divided by an argument compares to the other.
954 if (IsNegative)
955 return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY;
956 else
957 return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY;
958}
959
960} // End llvm namespace
961
962#endif