-
Notifications
You must be signed in to change notification settings - Fork 10.8k
/
ConstantRange.cpp
1105 lines (945 loc) · 38.6 KB
/
ConstantRange.cpp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
//===- ConstantRange.cpp - ConstantRange implementation -------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// Represent a range of possible values that may occur when the program is run
// for an integral value. This keeps track of a lower and upper bound for the
// constant, which MAY wrap around the end of the numeric range. To do this, it
// keeps track of a [lower, upper) bound, which specifies an interval just like
// STL iterators. When used with boolean values, the following are important
// ranges (other integral ranges use min/max values for special range values):
//
// [F, F) = {} = Empty set
// [T, F) = {T}
// [F, T) = {F}
// [T, T) = {F, T} = Full set
//
//===----------------------------------------------------------------------===//
#include "llvm/ADT/APInt.h"
#include "llvm/Config/llvm-config.h"
#include "llvm/IR/ConstantRange.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/InstrTypes.h"
#include "llvm/IR/Instruction.h"
#include "llvm/IR/Metadata.h"
#include "llvm/IR/Operator.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/raw_ostream.h"
#include <algorithm>
#include <cassert>
#include <cstdint>
using namespace llvm;
ConstantRange::ConstantRange(uint32_t BitWidth, bool Full)
: Lower(Full ? APInt::getMaxValue(BitWidth) : APInt::getMinValue(BitWidth)),
Upper(Lower) {}
ConstantRange::ConstantRange(APInt V)
: Lower(std::move(V)), Upper(Lower + 1) {}
ConstantRange::ConstantRange(APInt L, APInt U)
: Lower(std::move(L)), Upper(std::move(U)) {
assert(Lower.getBitWidth() == Upper.getBitWidth() &&
"ConstantRange with unequal bit widths");
assert((Lower != Upper || (Lower.isMaxValue() || Lower.isMinValue())) &&
"Lower == Upper, but they aren't min or max value!");
}
ConstantRange ConstantRange::makeAllowedICmpRegion(CmpInst::Predicate Pred,
const ConstantRange &CR) {
if (CR.isEmptySet())
return CR;
uint32_t W = CR.getBitWidth();
switch (Pred) {
default:
llvm_unreachable("Invalid ICmp predicate to makeAllowedICmpRegion()");
case CmpInst::ICMP_EQ:
return CR;
case CmpInst::ICMP_NE:
if (CR.isSingleElement())
return ConstantRange(CR.getUpper(), CR.getLower());
return ConstantRange(W);
case CmpInst::ICMP_ULT: {
APInt UMax(CR.getUnsignedMax());
if (UMax.isMinValue())
return ConstantRange(W, /* empty */ false);
return ConstantRange(APInt::getMinValue(W), std::move(UMax));
}
case CmpInst::ICMP_SLT: {
APInt SMax(CR.getSignedMax());
if (SMax.isMinSignedValue())
return ConstantRange(W, /* empty */ false);
return ConstantRange(APInt::getSignedMinValue(W), std::move(SMax));
}
case CmpInst::ICMP_ULE: {
APInt UMax(CR.getUnsignedMax());
if (UMax.isMaxValue())
return ConstantRange(W);
return ConstantRange(APInt::getMinValue(W), std::move(UMax) + 1);
}
case CmpInst::ICMP_SLE: {
APInt SMax(CR.getSignedMax());
if (SMax.isMaxSignedValue())
return ConstantRange(W);
return ConstantRange(APInt::getSignedMinValue(W), std::move(SMax) + 1);
}
case CmpInst::ICMP_UGT: {
APInt UMin(CR.getUnsignedMin());
if (UMin.isMaxValue())
return ConstantRange(W, /* empty */ false);
return ConstantRange(std::move(UMin) + 1, APInt::getNullValue(W));
}
case CmpInst::ICMP_SGT: {
APInt SMin(CR.getSignedMin());
if (SMin.isMaxSignedValue())
return ConstantRange(W, /* empty */ false);
return ConstantRange(std::move(SMin) + 1, APInt::getSignedMinValue(W));
}
case CmpInst::ICMP_UGE: {
APInt UMin(CR.getUnsignedMin());
if (UMin.isMinValue())
return ConstantRange(W);
return ConstantRange(std::move(UMin), APInt::getNullValue(W));
}
case CmpInst::ICMP_SGE: {
APInt SMin(CR.getSignedMin());
if (SMin.isMinSignedValue())
return ConstantRange(W);
return ConstantRange(std::move(SMin), APInt::getSignedMinValue(W));
}
}
}
ConstantRange ConstantRange::makeSatisfyingICmpRegion(CmpInst::Predicate Pred,
const ConstantRange &CR) {
// Follows from De-Morgan's laws:
//
// ~(~A union ~B) == A intersect B.
//
return makeAllowedICmpRegion(CmpInst::getInversePredicate(Pred), CR)
.inverse();
}
ConstantRange ConstantRange::makeExactICmpRegion(CmpInst::Predicate Pred,
const APInt &C) {
// Computes the exact range that is equal to both the constant ranges returned
// by makeAllowedICmpRegion and makeSatisfyingICmpRegion. This is always true
// when RHS is a singleton such as an APInt and so the assert is valid.
// However for non-singleton RHS, for example ult [2,5) makeAllowedICmpRegion
// returns [0,4) but makeSatisfyICmpRegion returns [0,2).
//
assert(makeAllowedICmpRegion(Pred, C) == makeSatisfyingICmpRegion(Pred, C));
return makeAllowedICmpRegion(Pred, C);
}
bool ConstantRange::getEquivalentICmp(CmpInst::Predicate &Pred,
APInt &RHS) const {
bool Success = false;
if (isFullSet() || isEmptySet()) {
Pred = isEmptySet() ? CmpInst::ICMP_ULT : CmpInst::ICMP_UGE;
RHS = APInt(getBitWidth(), 0);
Success = true;
} else if (auto *OnlyElt = getSingleElement()) {
Pred = CmpInst::ICMP_EQ;
RHS = *OnlyElt;
Success = true;
} else if (auto *OnlyMissingElt = getSingleMissingElement()) {
Pred = CmpInst::ICMP_NE;
RHS = *OnlyMissingElt;
Success = true;
} else if (getLower().isMinSignedValue() || getLower().isMinValue()) {
Pred =
getLower().isMinSignedValue() ? CmpInst::ICMP_SLT : CmpInst::ICMP_ULT;
RHS = getUpper();
Success = true;
} else if (getUpper().isMinSignedValue() || getUpper().isMinValue()) {
Pred =
getUpper().isMinSignedValue() ? CmpInst::ICMP_SGE : CmpInst::ICMP_UGE;
RHS = getLower();
Success = true;
}
assert((!Success || ConstantRange::makeExactICmpRegion(Pred, RHS) == *this) &&
"Bad result!");
return Success;
}
ConstantRange
ConstantRange::makeGuaranteedNoWrapRegion(Instruction::BinaryOps BinOp,
const ConstantRange &Other,
unsigned NoWrapKind) {
using OBO = OverflowingBinaryOperator;
// Computes the intersection of CR0 and CR1. It is different from
// intersectWith in that the ConstantRange returned will only contain elements
// in both CR0 and CR1 (i.e. SubsetIntersect(X, Y) is a *subset*, proper or
// not, of both X and Y).
auto SubsetIntersect =
[](const ConstantRange &CR0, const ConstantRange &CR1) {
return CR0.inverse().unionWith(CR1.inverse()).inverse();
};
assert(Instruction::isBinaryOp(BinOp) && "Binary operators only!");
assert((NoWrapKind == OBO::NoSignedWrap ||
NoWrapKind == OBO::NoUnsignedWrap ||
NoWrapKind == (OBO::NoUnsignedWrap | OBO::NoSignedWrap)) &&
"NoWrapKind invalid!");
unsigned BitWidth = Other.getBitWidth();
ConstantRange Result(BitWidth);
switch (BinOp) {
default:
// Conservative answer: empty set
return ConstantRange(BitWidth, false);
case Instruction::Add:
if (auto *C = Other.getSingleElement())
if (C->isNullValue())
// Full set: nothing signed / unsigned wraps when added to 0.
return ConstantRange(BitWidth);
if (NoWrapKind & OBO::NoUnsignedWrap)
Result =
SubsetIntersect(Result, ConstantRange(APInt::getNullValue(BitWidth),
-Other.getUnsignedMax()));
if (NoWrapKind & OBO::NoSignedWrap) {
const APInt &SignedMin = Other.getSignedMin();
const APInt &SignedMax = Other.getSignedMax();
if (SignedMax.isStrictlyPositive())
Result = SubsetIntersect(
Result,
ConstantRange(APInt::getSignedMinValue(BitWidth),
APInt::getSignedMinValue(BitWidth) - SignedMax));
if (SignedMin.isNegative())
Result = SubsetIntersect(
Result,
ConstantRange(APInt::getSignedMinValue(BitWidth) - SignedMin,
APInt::getSignedMinValue(BitWidth)));
}
return Result;
case Instruction::Sub:
if (auto *C = Other.getSingleElement())
if (C->isNullValue())
// Full set: nothing signed / unsigned wraps when subtracting 0.
return ConstantRange(BitWidth);
if (NoWrapKind & OBO::NoUnsignedWrap)
Result =
SubsetIntersect(Result, ConstantRange(Other.getUnsignedMax(),
APInt::getMinValue(BitWidth)));
if (NoWrapKind & OBO::NoSignedWrap) {
const APInt &SignedMin = Other.getSignedMin();
const APInt &SignedMax = Other.getSignedMax();
if (SignedMax.isStrictlyPositive())
Result = SubsetIntersect(
Result,
ConstantRange(APInt::getSignedMinValue(BitWidth) + SignedMax,
APInt::getSignedMinValue(BitWidth)));
if (SignedMin.isNegative())
Result = SubsetIntersect(
Result,
ConstantRange(APInt::getSignedMinValue(BitWidth),
APInt::getSignedMinValue(BitWidth) + SignedMin));
}
return Result;
case Instruction::Mul: {
if (NoWrapKind == (OBO::NoSignedWrap | OBO::NoUnsignedWrap)) {
return SubsetIntersect(
makeGuaranteedNoWrapRegion(BinOp, Other, OBO::NoSignedWrap),
makeGuaranteedNoWrapRegion(BinOp, Other, OBO::NoUnsignedWrap));
}
// Equivalent to calling makeGuaranteedNoWrapRegion() on [V, V+1).
const bool Unsigned = NoWrapKind == OBO::NoUnsignedWrap;
const auto makeSingleValueRegion = [Unsigned,
BitWidth](APInt V) -> ConstantRange {
// Handle special case for 0, -1 and 1. See the last for reason why we
// specialize -1 and 1.
if (V == 0 || V.isOneValue())
return ConstantRange(BitWidth, true);
APInt MinValue, MaxValue;
if (Unsigned) {
MinValue = APInt::getMinValue(BitWidth);
MaxValue = APInt::getMaxValue(BitWidth);
} else {
MinValue = APInt::getSignedMinValue(BitWidth);
MaxValue = APInt::getSignedMaxValue(BitWidth);
}
// e.g. Returning [-127, 127], represented as [-127, -128).
if (!Unsigned && V.isAllOnesValue())
return ConstantRange(-MaxValue, MinValue);
APInt Lower, Upper;
if (!Unsigned && V.isNegative()) {
Lower = APIntOps::RoundingSDiv(MaxValue, V, APInt::Rounding::UP);
Upper = APIntOps::RoundingSDiv(MinValue, V, APInt::Rounding::DOWN);
} else if (Unsigned) {
Lower = APIntOps::RoundingUDiv(MinValue, V, APInt::Rounding::UP);
Upper = APIntOps::RoundingUDiv(MaxValue, V, APInt::Rounding::DOWN);
} else {
Lower = APIntOps::RoundingSDiv(MinValue, V, APInt::Rounding::UP);
Upper = APIntOps::RoundingSDiv(MaxValue, V, APInt::Rounding::DOWN);
}
if (Unsigned) {
Lower = Lower.zextOrSelf(BitWidth);
Upper = Upper.zextOrSelf(BitWidth);
} else {
Lower = Lower.sextOrSelf(BitWidth);
Upper = Upper.sextOrSelf(BitWidth);
}
// ConstantRange ctor take a half inclusive interval [Lower, Upper + 1).
// Upper + 1 is guanranteed not to overflow, because |divisor| > 1. 0, -1,
// and 1 are already handled as special cases.
return ConstantRange(Lower, Upper + 1);
};
if (Unsigned)
return makeSingleValueRegion(Other.getUnsignedMax());
return SubsetIntersect(makeSingleValueRegion(Other.getSignedMin()),
makeSingleValueRegion(Other.getSignedMax()));
}
}
}
bool ConstantRange::isFullSet() const {
return Lower == Upper && Lower.isMaxValue();
}
bool ConstantRange::isEmptySet() const {
return Lower == Upper && Lower.isMinValue();
}
bool ConstantRange::isWrappedSet() const {
return Lower.ugt(Upper);
}
bool ConstantRange::isSignWrappedSet() const {
return contains(APInt::getSignedMaxValue(getBitWidth())) &&
contains(APInt::getSignedMinValue(getBitWidth()));
}
APInt ConstantRange::getSetSize() const {
if (isFullSet())
return APInt::getOneBitSet(getBitWidth()+1, getBitWidth());
// This is also correct for wrapped sets.
return (Upper - Lower).zext(getBitWidth()+1);
}
bool
ConstantRange::isSizeStrictlySmallerThan(const ConstantRange &Other) const {
assert(getBitWidth() == Other.getBitWidth());
if (isFullSet())
return false;
if (Other.isFullSet())
return true;
return (Upper - Lower).ult(Other.Upper - Other.Lower);
}
bool
ConstantRange::isSizeLargerThan(uint64_t MaxSize) const {
assert(MaxSize && "MaxSize can't be 0.");
// If this a full set, we need special handling to avoid needing an extra bit
// to represent the size.
if (isFullSet())
return APInt::getMaxValue(getBitWidth()).ugt(MaxSize - 1);
return (Upper - Lower).ugt(MaxSize);
}
APInt ConstantRange::getUnsignedMax() const {
if (isFullSet() || isWrappedSet())
return APInt::getMaxValue(getBitWidth());
return getUpper() - 1;
}
APInt ConstantRange::getUnsignedMin() const {
if (isFullSet() || (isWrappedSet() && !getUpper().isNullValue()))
return APInt::getMinValue(getBitWidth());
return getLower();
}
APInt ConstantRange::getSignedMax() const {
if (isFullSet() || Lower.sgt(Upper))
return APInt::getSignedMaxValue(getBitWidth());
return getUpper() - 1;
}
APInt ConstantRange::getSignedMin() const {
if (isFullSet() || (Lower.sgt(Upper) && !getUpper().isMinSignedValue()))
return APInt::getSignedMinValue(getBitWidth());
return getLower();
}
bool ConstantRange::contains(const APInt &V) const {
if (Lower == Upper)
return isFullSet();
if (!isWrappedSet())
return Lower.ule(V) && V.ult(Upper);
return Lower.ule(V) || V.ult(Upper);
}
bool ConstantRange::contains(const ConstantRange &Other) const {
if (isFullSet() || Other.isEmptySet()) return true;
if (isEmptySet() || Other.isFullSet()) return false;
if (!isWrappedSet()) {
if (Other.isWrappedSet())
return false;
return Lower.ule(Other.getLower()) && Other.getUpper().ule(Upper);
}
if (!Other.isWrappedSet())
return Other.getUpper().ule(Upper) ||
Lower.ule(Other.getLower());
return Other.getUpper().ule(Upper) && Lower.ule(Other.getLower());
}
ConstantRange ConstantRange::subtract(const APInt &Val) const {
assert(Val.getBitWidth() == getBitWidth() && "Wrong bit width");
// If the set is empty or full, don't modify the endpoints.
if (Lower == Upper)
return *this;
return ConstantRange(Lower - Val, Upper - Val);
}
ConstantRange ConstantRange::difference(const ConstantRange &CR) const {
return intersectWith(CR.inverse());
}
ConstantRange ConstantRange::intersectWith(const ConstantRange &CR) const {
assert(getBitWidth() == CR.getBitWidth() &&
"ConstantRange types don't agree!");
// Handle common cases.
if ( isEmptySet() || CR.isFullSet()) return *this;
if (CR.isEmptySet() || isFullSet()) return CR;
if (!isWrappedSet() && CR.isWrappedSet())
return CR.intersectWith(*this);
if (!isWrappedSet() && !CR.isWrappedSet()) {
if (Lower.ult(CR.Lower)) {
if (Upper.ule(CR.Lower))
return ConstantRange(getBitWidth(), false);
if (Upper.ult(CR.Upper))
return ConstantRange(CR.Lower, Upper);
return CR;
}
if (Upper.ult(CR.Upper))
return *this;
if (Lower.ult(CR.Upper))
return ConstantRange(Lower, CR.Upper);
return ConstantRange(getBitWidth(), false);
}
if (isWrappedSet() && !CR.isWrappedSet()) {
if (CR.Lower.ult(Upper)) {
if (CR.Upper.ult(Upper))
return CR;
if (CR.Upper.ule(Lower))
return ConstantRange(CR.Lower, Upper);
if (isSizeStrictlySmallerThan(CR))
return *this;
return CR;
}
if (CR.Lower.ult(Lower)) {
if (CR.Upper.ule(Lower))
return ConstantRange(getBitWidth(), false);
return ConstantRange(Lower, CR.Upper);
}
return CR;
}
if (CR.Upper.ult(Upper)) {
if (CR.Lower.ult(Upper)) {
if (isSizeStrictlySmallerThan(CR))
return *this;
return CR;
}
if (CR.Lower.ult(Lower))
return ConstantRange(Lower, CR.Upper);
return CR;
}
if (CR.Upper.ule(Lower)) {
if (CR.Lower.ult(Lower))
return *this;
return ConstantRange(CR.Lower, Upper);
}
if (isSizeStrictlySmallerThan(CR))
return *this;
return CR;
}
ConstantRange ConstantRange::unionWith(const ConstantRange &CR) const {
assert(getBitWidth() == CR.getBitWidth() &&
"ConstantRange types don't agree!");
if ( isFullSet() || CR.isEmptySet()) return *this;
if (CR.isFullSet() || isEmptySet()) return CR;
if (!isWrappedSet() && CR.isWrappedSet()) return CR.unionWith(*this);
if (!isWrappedSet() && !CR.isWrappedSet()) {
if (CR.Upper.ult(Lower) || Upper.ult(CR.Lower)) {
// If the two ranges are disjoint, find the smaller gap and bridge it.
APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
if (d1.ult(d2))
return ConstantRange(Lower, CR.Upper);
return ConstantRange(CR.Lower, Upper);
}
APInt L = CR.Lower.ult(Lower) ? CR.Lower : Lower;
APInt U = (CR.Upper - 1).ugt(Upper - 1) ? CR.Upper : Upper;
if (L.isNullValue() && U.isNullValue())
return ConstantRange(getBitWidth());
return ConstantRange(std::move(L), std::move(U));
}
if (!CR.isWrappedSet()) {
// ------U L----- and ------U L----- : this
// L--U L--U : CR
if (CR.Upper.ule(Upper) || CR.Lower.uge(Lower))
return *this;
// ------U L----- : this
// L---------U : CR
if (CR.Lower.ule(Upper) && Lower.ule(CR.Upper))
return ConstantRange(getBitWidth());
// ----U L---- : this
// L---U : CR
// <d1> <d2>
if (Upper.ule(CR.Lower) && CR.Upper.ule(Lower)) {
APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
if (d1.ult(d2))
return ConstantRange(Lower, CR.Upper);
return ConstantRange(CR.Lower, Upper);
}
// ----U L----- : this
// L----U : CR
if (Upper.ult(CR.Lower) && Lower.ult(CR.Upper))
return ConstantRange(CR.Lower, Upper);
// ------U L---- : this
// L-----U : CR
assert(CR.Lower.ult(Upper) && CR.Upper.ult(Lower) &&
"ConstantRange::unionWith missed a case with one range wrapped");
return ConstantRange(Lower, CR.Upper);
}
// ------U L---- and ------U L---- : this
// -U L----------- and ------------U L : CR
if (CR.Lower.ule(Upper) || Lower.ule(CR.Upper))
return ConstantRange(getBitWidth());
APInt L = CR.Lower.ult(Lower) ? CR.Lower : Lower;
APInt U = CR.Upper.ugt(Upper) ? CR.Upper : Upper;
return ConstantRange(std::move(L), std::move(U));
}
ConstantRange ConstantRange::castOp(Instruction::CastOps CastOp,
uint32_t ResultBitWidth) const {
switch (CastOp) {
default:
llvm_unreachable("unsupported cast type");
case Instruction::Trunc:
return truncate(ResultBitWidth);
case Instruction::SExt:
return signExtend(ResultBitWidth);
case Instruction::ZExt:
return zeroExtend(ResultBitWidth);
case Instruction::BitCast:
return *this;
case Instruction::FPToUI:
case Instruction::FPToSI:
if (getBitWidth() == ResultBitWidth)
return *this;
else
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
case Instruction::UIToFP: {
// TODO: use input range if available
auto BW = getBitWidth();
APInt Min = APInt::getMinValue(BW).zextOrSelf(ResultBitWidth);
APInt Max = APInt::getMaxValue(BW).zextOrSelf(ResultBitWidth);
return ConstantRange(std::move(Min), std::move(Max));
}
case Instruction::SIToFP: {
// TODO: use input range if available
auto BW = getBitWidth();
APInt SMin = APInt::getSignedMinValue(BW).sextOrSelf(ResultBitWidth);
APInt SMax = APInt::getSignedMaxValue(BW).sextOrSelf(ResultBitWidth);
return ConstantRange(std::move(SMin), std::move(SMax));
}
case Instruction::FPTrunc:
case Instruction::FPExt:
case Instruction::IntToPtr:
case Instruction::PtrToInt:
case Instruction::AddrSpaceCast:
// Conservatively return full set.
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
};
}
ConstantRange ConstantRange::zeroExtend(uint32_t DstTySize) const {
if (isEmptySet()) return ConstantRange(DstTySize, /*isFullSet=*/false);
unsigned SrcTySize = getBitWidth();
assert(SrcTySize < DstTySize && "Not a value extension");
if (isFullSet() || isWrappedSet()) {
// Change into [0, 1 << src bit width)
APInt LowerExt(DstTySize, 0);
if (!Upper) // special case: [X, 0) -- not really wrapping around
LowerExt = Lower.zext(DstTySize);
return ConstantRange(std::move(LowerExt),
APInt::getOneBitSet(DstTySize, SrcTySize));
}
return ConstantRange(Lower.zext(DstTySize), Upper.zext(DstTySize));
}
ConstantRange ConstantRange::signExtend(uint32_t DstTySize) const {
if (isEmptySet()) return ConstantRange(DstTySize, /*isFullSet=*/false);
unsigned SrcTySize = getBitWidth();
assert(SrcTySize < DstTySize && "Not a value extension");
// special case: [X, INT_MIN) -- not really wrapping around
if (Upper.isMinSignedValue())
return ConstantRange(Lower.sext(DstTySize), Upper.zext(DstTySize));
if (isFullSet() || isSignWrappedSet()) {
return ConstantRange(APInt::getHighBitsSet(DstTySize,DstTySize-SrcTySize+1),
APInt::getLowBitsSet(DstTySize, SrcTySize-1) + 1);
}
return ConstantRange(Lower.sext(DstTySize), Upper.sext(DstTySize));
}
ConstantRange ConstantRange::truncate(uint32_t DstTySize) const {
assert(getBitWidth() > DstTySize && "Not a value truncation");
if (isEmptySet())
return ConstantRange(DstTySize, /*isFullSet=*/false);
if (isFullSet())
return ConstantRange(DstTySize, /*isFullSet=*/true);
APInt LowerDiv(Lower), UpperDiv(Upper);
ConstantRange Union(DstTySize, /*isFullSet=*/false);
// Analyze wrapped sets in their two parts: [0, Upper) \/ [Lower, MaxValue]
// We use the non-wrapped set code to analyze the [Lower, MaxValue) part, and
// then we do the union with [MaxValue, Upper)
if (isWrappedSet()) {
// If Upper is greater than or equal to MaxValue(DstTy), it covers the whole
// truncated range.
if (Upper.getActiveBits() > DstTySize ||
Upper.countTrailingOnes() == DstTySize)
return ConstantRange(DstTySize, /*isFullSet=*/true);
Union = ConstantRange(APInt::getMaxValue(DstTySize),Upper.trunc(DstTySize));
UpperDiv.setAllBits();
// Union covers the MaxValue case, so return if the remaining range is just
// MaxValue(DstTy).
if (LowerDiv == UpperDiv)
return Union;
}
// Chop off the most significant bits that are past the destination bitwidth.
if (LowerDiv.getActiveBits() > DstTySize) {
// Mask to just the signficant bits and subtract from LowerDiv/UpperDiv.
APInt Adjust = LowerDiv & APInt::getBitsSetFrom(getBitWidth(), DstTySize);
LowerDiv -= Adjust;
UpperDiv -= Adjust;
}
unsigned UpperDivWidth = UpperDiv.getActiveBits();
if (UpperDivWidth <= DstTySize)
return ConstantRange(LowerDiv.trunc(DstTySize),
UpperDiv.trunc(DstTySize)).unionWith(Union);
// The truncated value wraps around. Check if we can do better than fullset.
if (UpperDivWidth == DstTySize + 1) {
// Clear the MSB so that UpperDiv wraps around.
UpperDiv.clearBit(DstTySize);
if (UpperDiv.ult(LowerDiv))
return ConstantRange(LowerDiv.trunc(DstTySize),
UpperDiv.trunc(DstTySize)).unionWith(Union);
}
return ConstantRange(DstTySize, /*isFullSet=*/true);
}
ConstantRange ConstantRange::zextOrTrunc(uint32_t DstTySize) const {
unsigned SrcTySize = getBitWidth();
if (SrcTySize > DstTySize)
return truncate(DstTySize);
if (SrcTySize < DstTySize)
return zeroExtend(DstTySize);
return *this;
}
ConstantRange ConstantRange::sextOrTrunc(uint32_t DstTySize) const {
unsigned SrcTySize = getBitWidth();
if (SrcTySize > DstTySize)
return truncate(DstTySize);
if (SrcTySize < DstTySize)
return signExtend(DstTySize);
return *this;
}
ConstantRange ConstantRange::binaryOp(Instruction::BinaryOps BinOp,
const ConstantRange &Other) const {
assert(Instruction::isBinaryOp(BinOp) && "Binary operators only!");
switch (BinOp) {
case Instruction::Add:
return add(Other);
case Instruction::Sub:
return sub(Other);
case Instruction::Mul:
return multiply(Other);
case Instruction::UDiv:
return udiv(Other);
case Instruction::Shl:
return shl(Other);
case Instruction::LShr:
return lshr(Other);
case Instruction::AShr:
return ashr(Other);
case Instruction::And:
return binaryAnd(Other);
case Instruction::Or:
return binaryOr(Other);
// Note: floating point operations applied to abstract ranges are just
// ideal integer operations with a lossy representation
case Instruction::FAdd:
return add(Other);
case Instruction::FSub:
return sub(Other);
case Instruction::FMul:
return multiply(Other);
default:
// Conservatively return full set.
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
}
}
ConstantRange
ConstantRange::add(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
if (isFullSet() || Other.isFullSet())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
APInt NewLower = getLower() + Other.getLower();
APInt NewUpper = getUpper() + Other.getUpper() - 1;
if (NewLower == NewUpper)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
ConstantRange X = ConstantRange(std::move(NewLower), std::move(NewUpper));
if (X.isSizeStrictlySmallerThan(*this) ||
X.isSizeStrictlySmallerThan(Other))
// We've wrapped, therefore, full set.
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return X;
}
ConstantRange ConstantRange::addWithNoSignedWrap(const APInt &Other) const {
// Calculate the subset of this range such that "X + Other" is
// guaranteed not to wrap (overflow) for all X in this subset.
// makeGuaranteedNoWrapRegion will produce an exact NSW range since we are
// passing a single element range.
auto NSWRange = ConstantRange::makeGuaranteedNoWrapRegion(BinaryOperator::Add,
ConstantRange(Other),
OverflowingBinaryOperator::NoSignedWrap);
auto NSWConstrainedRange = intersectWith(NSWRange);
return NSWConstrainedRange.add(ConstantRange(Other));
}
ConstantRange
ConstantRange::sub(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
if (isFullSet() || Other.isFullSet())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
APInt NewLower = getLower() - Other.getUpper() + 1;
APInt NewUpper = getUpper() - Other.getLower();
if (NewLower == NewUpper)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
ConstantRange X = ConstantRange(std::move(NewLower), std::move(NewUpper));
if (X.isSizeStrictlySmallerThan(*this) ||
X.isSizeStrictlySmallerThan(Other))
// We've wrapped, therefore, full set.
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return X;
}
ConstantRange
ConstantRange::multiply(const ConstantRange &Other) const {
// TODO: If either operand is a single element and the multiply is known to
// be non-wrapping, round the result min and max value to the appropriate
// multiple of that element. If wrapping is possible, at least adjust the
// range according to the greatest power-of-two factor of the single element.
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
// Multiplication is signedness-independent. However different ranges can be
// obtained depending on how the input ranges are treated. These different
// ranges are all conservatively correct, but one might be better than the
// other. We calculate two ranges; one treating the inputs as unsigned
// and the other signed, then return the smallest of these ranges.
// Unsigned range first.
APInt this_min = getUnsignedMin().zext(getBitWidth() * 2);
APInt this_max = getUnsignedMax().zext(getBitWidth() * 2);
APInt Other_min = Other.getUnsignedMin().zext(getBitWidth() * 2);
APInt Other_max = Other.getUnsignedMax().zext(getBitWidth() * 2);
ConstantRange Result_zext = ConstantRange(this_min * Other_min,
this_max * Other_max + 1);
ConstantRange UR = Result_zext.truncate(getBitWidth());
// If the unsigned range doesn't wrap, and isn't negative then it's a range
// from one positive number to another which is as good as we can generate.
// In this case, skip the extra work of generating signed ranges which aren't
// going to be better than this range.
if (!UR.isWrappedSet() &&
(UR.getUpper().isNonNegative() || UR.getUpper().isMinSignedValue()))
return UR;
// Now the signed range. Because we could be dealing with negative numbers
// here, the lower bound is the smallest of the cartesian product of the
// lower and upper ranges; for example:
// [-1,4) * [-2,3) = min(-1*-2, -1*2, 3*-2, 3*2) = -6.
// Similarly for the upper bound, swapping min for max.
this_min = getSignedMin().sext(getBitWidth() * 2);
this_max = getSignedMax().sext(getBitWidth() * 2);
Other_min = Other.getSignedMin().sext(getBitWidth() * 2);
Other_max = Other.getSignedMax().sext(getBitWidth() * 2);
auto L = {this_min * Other_min, this_min * Other_max,
this_max * Other_min, this_max * Other_max};
auto Compare = [](const APInt &A, const APInt &B) { return A.slt(B); };
ConstantRange Result_sext(std::min(L, Compare), std::max(L, Compare) + 1);
ConstantRange SR = Result_sext.truncate(getBitWidth());
return UR.isSizeStrictlySmallerThan(SR) ? UR : SR;
}
ConstantRange
ConstantRange::smax(const ConstantRange &Other) const {
// X smax Y is: range(smax(X_smin, Y_smin),
// smax(X_smax, Y_smax))
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt NewL = APIntOps::smax(getSignedMin(), Other.getSignedMin());
APInt NewU = APIntOps::smax(getSignedMax(), Other.getSignedMax()) + 1;
if (NewU == NewL)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(std::move(NewL), std::move(NewU));
}
ConstantRange
ConstantRange::umax(const ConstantRange &Other) const {
// X umax Y is: range(umax(X_umin, Y_umin),
// umax(X_umax, Y_umax))
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt NewL = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
APInt NewU = APIntOps::umax(getUnsignedMax(), Other.getUnsignedMax()) + 1;
if (NewU == NewL)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(std::move(NewL), std::move(NewU));
}
ConstantRange
ConstantRange::smin(const ConstantRange &Other) const {
// X smin Y is: range(smin(X_smin, Y_smin),
// smin(X_smax, Y_smax))
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt NewL = APIntOps::smin(getSignedMin(), Other.getSignedMin());
APInt NewU = APIntOps::smin(getSignedMax(), Other.getSignedMax()) + 1;
if (NewU == NewL)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(std::move(NewL), std::move(NewU));
}
ConstantRange
ConstantRange::umin(const ConstantRange &Other) const {
// X umin Y is: range(umin(X_umin, Y_umin),
// umin(X_umax, Y_umax))
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt NewL = APIntOps::umin(getUnsignedMin(), Other.getUnsignedMin());
APInt NewU = APIntOps::umin(getUnsignedMax(), Other.getUnsignedMax()) + 1;
if (NewU == NewL)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(std::move(NewL), std::move(NewU));
}
ConstantRange
ConstantRange::udiv(const ConstantRange &RHS) const {
if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax().isNullValue())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
if (RHS.isFullSet())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
APInt Lower = getUnsignedMin().udiv(RHS.getUnsignedMax());
APInt RHS_umin = RHS.getUnsignedMin();
if (RHS_umin.isNullValue()) {
// We want the lowest value in RHS excluding zero. Usually that would be 1
// except for a range in the form of [X, 1) in which case it would be X.
if (RHS.getUpper() == 1)
RHS_umin = RHS.getLower();
else
RHS_umin = 1;
}
APInt Upper = getUnsignedMax().udiv(RHS_umin) + 1;
// If the LHS is Full and the RHS is a wrapped interval containing 1 then
// this could occur.
if (Lower == Upper)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(std::move(Lower), std::move(Upper));
}
ConstantRange
ConstantRange::binaryAnd(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
// TODO: replace this with something less conservative
APInt umin = APIntOps::umin(Other.getUnsignedMax(), getUnsignedMax());
if (umin.isAllOnesValue())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(APInt::getNullValue(getBitWidth()), std::move(umin) + 1);
}
ConstantRange
ConstantRange::binaryOr(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
// TODO: replace this with something less conservative
APInt umax = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
if (umax.isNullValue())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(std::move(umax), APInt::getNullValue(getBitWidth()));
}
ConstantRange
ConstantRange::shl(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt max = getUnsignedMax();
APInt Other_umax = Other.getUnsignedMax();
// there's overflow!
if (Other_umax.uge(max.countLeadingZeros()))
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
// FIXME: implement the other tricky cases
APInt min = getUnsignedMin();
min <<= Other.getUnsignedMin();
max <<= Other_umax;
return ConstantRange(std::move(min), std::move(max) + 1);
}
ConstantRange
ConstantRange::lshr(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt max = getUnsignedMax().lshr(Other.getUnsignedMin()) + 1;