1 //===-- ConstantRange.cpp - ConstantRange implementation ------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // Represent a range of possible values that may occur when the program is run
11 // for an integral value. This keeps track of a lower and upper bound for the
12 // constant, which MAY wrap around the end of the numeric range. To do this, it
13 // keeps track of a [lower, upper) bound, which specifies an interval just like
14 // STL iterators. When used with boolean values, the following are important
15 // ranges (other integral ranges use min/max values for special range values):
17 // [F, F) = {} = Empty set
20 // [T, T) = {F, T} = Full set
22 //===----------------------------------------------------------------------===//
24 #include "llvm/Support/ConstantRange.h"
25 #include "llvm/Support/raw_ostream.h"
26 #include "llvm/Instructions.h"
29 /// Initialize a full (the default) or empty set for the specified type.
31 ConstantRange::ConstantRange(uint32_t BitWidth
, bool Full
) {
33 Lower
= Upper
= APInt::getMaxValue(BitWidth
);
35 Lower
= Upper
= APInt::getMinValue(BitWidth
);
38 /// Initialize a range to hold the single specified value.
40 ConstantRange::ConstantRange(const APInt
& V
) : Lower(V
), Upper(V
+ 1) {}
42 ConstantRange::ConstantRange(const APInt
&L
, const APInt
&U
) :
44 assert(L
.getBitWidth() == U
.getBitWidth() &&
45 "ConstantRange with unequal bit widths");
46 assert((L
!= U
|| (L
.isMaxValue() || L
.isMinValue())) &&
47 "Lower == Upper, but they aren't min or max value!");
50 ConstantRange
ConstantRange::makeICmpRegion(unsigned Pred
,
51 const ConstantRange
&CR
) {
52 uint32_t W
= CR
.getBitWidth();
54 default: assert(!"Invalid ICmp predicate to makeICmpRegion()");
55 case ICmpInst::ICMP_EQ
:
57 case ICmpInst::ICMP_NE
:
58 if (CR
.isSingleElement())
59 return ConstantRange(CR
.getUpper(), CR
.getLower());
60 return ConstantRange(W
);
61 case ICmpInst::ICMP_ULT
:
62 return ConstantRange(APInt::getMinValue(W
), CR
.getUnsignedMax());
63 case ICmpInst::ICMP_SLT
:
64 return ConstantRange(APInt::getSignedMinValue(W
), CR
.getSignedMax());
65 case ICmpInst::ICMP_ULE
: {
66 APInt
UMax(CR
.getUnsignedMax());
67 if (UMax
.isMaxValue())
68 return ConstantRange(W
);
69 return ConstantRange(APInt::getMinValue(W
), UMax
+ 1);
71 case ICmpInst::ICMP_SLE
: {
72 APInt
SMax(CR
.getSignedMax());
73 if (SMax
.isMaxSignedValue() || (SMax
+1).isMaxSignedValue())
74 return ConstantRange(W
);
75 return ConstantRange(APInt::getSignedMinValue(W
), SMax
+ 1);
77 case ICmpInst::ICMP_UGT
:
78 return ConstantRange(CR
.getUnsignedMin() + 1, APInt::getNullValue(W
));
79 case ICmpInst::ICMP_SGT
:
80 return ConstantRange(CR
.getSignedMin() + 1,
81 APInt::getSignedMinValue(W
));
82 case ICmpInst::ICMP_UGE
: {
83 APInt
UMin(CR
.getUnsignedMin());
84 if (UMin
.isMinValue())
85 return ConstantRange(W
);
86 return ConstantRange(UMin
, APInt::getNullValue(W
));
88 case ICmpInst::ICMP_SGE
: {
89 APInt
SMin(CR
.getSignedMin());
90 if (SMin
.isMinSignedValue())
91 return ConstantRange(W
);
92 return ConstantRange(SMin
, APInt::getSignedMinValue(W
));
97 /// isFullSet - Return true if this set contains all of the elements possible
98 /// for this data-type
99 bool ConstantRange::isFullSet() const {
100 return Lower
== Upper
&& Lower
.isMaxValue();
103 /// isEmptySet - Return true if this set contains no members.
105 bool ConstantRange::isEmptySet() const {
106 return Lower
== Upper
&& Lower
.isMinValue();
109 /// isWrappedSet - Return true if this set wraps around the top of the range,
110 /// for example: [100, 8)
112 bool ConstantRange::isWrappedSet() const {
113 return Lower
.ugt(Upper
);
116 /// getSetSize - Return the number of elements in this set.
118 APInt
ConstantRange::getSetSize() const {
120 return APInt(getBitWidth(), 0);
121 if (getBitWidth() == 1) {
122 if (Lower
!= Upper
) // One of T or F in the set...
124 return APInt(2, 2); // Must be full set...
127 // Simply subtract the bounds...
128 return Upper
- Lower
;
131 /// getUnsignedMax - Return the largest unsigned value contained in the
134 APInt
ConstantRange::getUnsignedMax() const {
135 if (isFullSet() || isWrappedSet())
136 return APInt::getMaxValue(getBitWidth());
138 return getUpper() - 1;
141 /// getUnsignedMin - Return the smallest unsigned value contained in the
144 APInt
ConstantRange::getUnsignedMin() const {
145 if (isFullSet() || (isWrappedSet() && getUpper() != 0))
146 return APInt::getMinValue(getBitWidth());
151 /// getSignedMax - Return the largest signed value contained in the
154 APInt
ConstantRange::getSignedMax() const {
155 APInt
SignedMax(APInt::getSignedMaxValue(getBitWidth()));
156 if (!isWrappedSet()) {
157 if (getLower().sle(getUpper() - 1))
158 return getUpper() - 1;
162 if (getLower().isNegative() == getUpper().isNegative())
165 return getUpper() - 1;
169 /// getSignedMin - Return the smallest signed value contained in the
172 APInt
ConstantRange::getSignedMin() const {
173 APInt
SignedMin(APInt::getSignedMinValue(getBitWidth()));
174 if (!isWrappedSet()) {
175 if (getLower().sle(getUpper() - 1))
180 if ((getUpper() - 1).slt(getLower())) {
181 if (getUpper() != SignedMin
)
191 /// contains - Return true if the specified value is in the set.
193 bool ConstantRange::contains(const APInt
&V
) const {
198 return Lower
.ule(V
) && V
.ult(Upper
);
200 return Lower
.ule(V
) || V
.ult(Upper
);
203 /// contains - Return true if the argument is a subset of this range.
204 /// Two equal set contain each other. The empty set is considered to be
205 /// contained by all other sets.
207 bool ConstantRange::contains(const ConstantRange
&Other
) const {
208 if (isFullSet()) return true;
209 if (Other
.isFullSet()) return false;
210 if (Other
.isEmptySet()) return true;
211 if (isEmptySet()) return false;
213 if (!isWrappedSet()) {
214 if (Other
.isWrappedSet())
217 return Lower
.ule(Other
.getLower()) && Other
.getUpper().ule(Upper
);
220 if (!Other
.isWrappedSet())
221 return Other
.getUpper().ule(Upper
) ||
222 Lower
.ule(Other
.getLower());
224 return Other
.getUpper().ule(Upper
) && Lower
.ule(Other
.getLower());
227 /// subtract - Subtract the specified constant from the endpoints of this
229 ConstantRange
ConstantRange::subtract(const APInt
&Val
) const {
230 assert(Val
.getBitWidth() == getBitWidth() && "Wrong bit width");
231 // If the set is empty or full, don't modify the endpoints.
234 return ConstantRange(Lower
- Val
, Upper
- Val
);
238 // intersect1Wrapped - This helper function is used to intersect two ranges when
239 // it is known that LHS is wrapped and RHS isn't.
242 ConstantRange::intersect1Wrapped(const ConstantRange
&LHS
,
243 const ConstantRange
&RHS
) {
244 assert(LHS
.isWrappedSet() && !RHS
.isWrappedSet());
246 // Check to see if we overlap on the Left side of RHS...
248 if (RHS
.Lower
.ult(LHS
.Upper
)) {
249 // We do overlap on the left side of RHS, see if we overlap on the right of
251 if (RHS
.Upper
.ugt(LHS
.Lower
)) {
252 // Ok, the result overlaps on both the left and right sides. See if the
253 // resultant interval will be smaller if we wrap or not...
255 if (LHS
.getSetSize().ult(RHS
.getSetSize()))
261 // No overlap on the right, just on the left.
262 return ConstantRange(RHS
.Lower
, LHS
.Upper
);
265 // We don't overlap on the left side of RHS, see if we overlap on the right
267 if (RHS
.Upper
.ugt(LHS
.Lower
)) {
269 return ConstantRange(LHS
.Lower
, RHS
.Upper
);
272 return ConstantRange(LHS
.getBitWidth(), false);
277 /// intersectWith - Return the range that results from the intersection of this
278 /// range with another range. The resultant range is guaranteed to include all
279 /// elements contained in both input ranges, and to have the smallest possible
280 /// set size that does so. Because there may be two intersections with the
281 /// same set size, A.intersectWith(B) might not be equal to B.intersectWith(A).
282 ConstantRange
ConstantRange::intersectWith(const ConstantRange
&CR
) const {
283 assert(getBitWidth() == CR
.getBitWidth() &&
284 "ConstantRange types don't agree!");
286 // Handle common cases.
287 if ( isEmptySet() || CR
.isFullSet()) return *this;
288 if (CR
.isEmptySet() || isFullSet()) return CR
;
290 if (!isWrappedSet() && CR
.isWrappedSet())
291 return CR
.intersectWith(*this);
293 if (!isWrappedSet() && !CR
.isWrappedSet()) {
294 if (Lower
.ult(CR
.Lower
)) {
295 if (Upper
.ule(CR
.Lower
))
296 return ConstantRange(getBitWidth(), false);
298 if (Upper
.ult(CR
.Upper
))
299 return ConstantRange(CR
.Lower
, Upper
);
303 if (Upper
.ult(CR
.Upper
))
306 if (Lower
.ult(CR
.Upper
))
307 return ConstantRange(Lower
, CR
.Upper
);
309 return ConstantRange(getBitWidth(), false);
313 if (isWrappedSet() && !CR
.isWrappedSet()) {
314 if (CR
.Lower
.ult(Upper
)) {
315 if (CR
.Upper
.ult(Upper
))
318 if (CR
.Upper
.ult(Lower
))
319 return ConstantRange(CR
.Lower
, Upper
);
321 if (getSetSize().ult(CR
.getSetSize()))
325 } else if (CR
.Lower
.ult(Lower
)) {
326 if (CR
.Upper
.ule(Lower
))
327 return ConstantRange(getBitWidth(), false);
329 return ConstantRange(Lower
, CR
.Upper
);
334 if (CR
.Upper
.ult(Upper
)) {
335 if (CR
.Lower
.ult(Upper
)) {
336 if (getSetSize().ult(CR
.getSetSize()))
342 if (CR
.Lower
.ult(Lower
))
343 return ConstantRange(Lower
, CR
.Upper
);
346 } else if (CR
.Upper
.ult(Lower
)) {
347 if (CR
.Lower
.ult(Lower
))
350 return ConstantRange(CR
.Lower
, Upper
);
352 if (getSetSize().ult(CR
.getSetSize()))
359 /// unionWith - Return the range that results from the union of this range with
360 /// another range. The resultant range is guaranteed to include the elements of
361 /// both sets, but may contain more. For example, [3, 9) union [12,15) is
362 /// [3, 15), which includes 9, 10, and 11, which were not included in either
365 ConstantRange
ConstantRange::unionWith(const ConstantRange
&CR
) const {
366 assert(getBitWidth() == CR
.getBitWidth() &&
367 "ConstantRange types don't agree!");
369 if ( isFullSet() || CR
.isEmptySet()) return *this;
370 if (CR
.isFullSet() || isEmptySet()) return CR
;
372 if (!isWrappedSet() && CR
.isWrappedSet()) return CR
.unionWith(*this);
374 if (!isWrappedSet() && !CR
.isWrappedSet()) {
375 if (CR
.Upper
.ult(Lower
) || Upper
.ult(CR
.Lower
)) {
376 // If the two ranges are disjoint, find the smaller gap and bridge it.
377 APInt d1
= CR
.Lower
- Upper
, d2
= Lower
- CR
.Upper
;
379 return ConstantRange(Lower
, CR
.Upper
);
381 return ConstantRange(CR
.Lower
, Upper
);
384 APInt L
= Lower
, U
= Upper
;
387 if ((CR
.Upper
- 1).ugt(U
- 1))
390 if (L
== 0 && U
== 0)
391 return ConstantRange(getBitWidth());
393 return ConstantRange(L
, U
);
396 if (!CR
.isWrappedSet()) {
397 // ------U L----- and ------U L----- : this
399 if (CR
.Upper
.ule(Upper
) || CR
.Lower
.uge(Lower
))
402 // ------U L----- : this
404 if (CR
.Lower
.ule(Upper
) && Lower
.ule(CR
.Upper
))
405 return ConstantRange(getBitWidth());
407 // ----U L---- : this
410 if (Upper
.ule(CR
.Lower
) && CR
.Upper
.ule(Lower
)) {
411 APInt d1
= CR
.Lower
- Upper
, d2
= Lower
- CR
.Upper
;
413 return ConstantRange(Lower
, CR
.Upper
);
415 return ConstantRange(CR
.Lower
, Upper
);
418 // ----U L----- : this
420 if (Upper
.ult(CR
.Lower
) && Lower
.ult(CR
.Upper
))
421 return ConstantRange(CR
.Lower
, Upper
);
423 // ------U L---- : this
425 if (CR
.Lower
.ult(Upper
) && CR
.Upper
.ult(Lower
))
426 return ConstantRange(Lower
, CR
.Upper
);
429 assert(isWrappedSet() && CR
.isWrappedSet() &&
430 "ConstantRange::unionWith missed wrapped union unwrapped case");
432 // ------U L---- and ------U L---- : this
433 // -U L----------- and ------------U L : CR
434 if (CR
.Lower
.ule(Upper
) || Lower
.ule(CR
.Upper
))
435 return ConstantRange(getBitWidth());
437 APInt L
= Lower
, U
= Upper
;
443 return ConstantRange(L
, U
);
446 /// zeroExtend - Return a new range in the specified integer type, which must
447 /// be strictly larger than the current type. The returned range will
448 /// correspond to the possible range of values as if the source range had been
450 ConstantRange
ConstantRange::zeroExtend(uint32_t DstTySize
) const {
451 unsigned SrcTySize
= getBitWidth();
452 assert(SrcTySize
< DstTySize
&& "Not a value extension");
454 // Change a source full set into [0, 1 << 8*numbytes)
455 return ConstantRange(APInt(DstTySize
,0), APInt(DstTySize
,1).shl(SrcTySize
));
457 APInt L
= Lower
; L
.zext(DstTySize
);
458 APInt U
= Upper
; U
.zext(DstTySize
);
459 return ConstantRange(L
, U
);
462 /// signExtend - Return a new range in the specified integer type, which must
463 /// be strictly larger than the current type. The returned range will
464 /// correspond to the possible range of values as if the source range had been
466 ConstantRange
ConstantRange::signExtend(uint32_t DstTySize
) const {
467 unsigned SrcTySize
= getBitWidth();
468 assert(SrcTySize
< DstTySize
&& "Not a value extension");
470 return ConstantRange(APInt::getHighBitsSet(DstTySize
,DstTySize
-SrcTySize
+1),
471 APInt::getLowBitsSet(DstTySize
, SrcTySize
-1) + 1);
474 APInt L
= Lower
; L
.sext(DstTySize
);
475 APInt U
= Upper
; U
.sext(DstTySize
);
476 return ConstantRange(L
, U
);
479 /// truncate - Return a new range in the specified integer type, which must be
480 /// strictly smaller than the current type. The returned range will
481 /// correspond to the possible range of values as if the source range had been
482 /// truncated to the specified type.
483 ConstantRange
ConstantRange::truncate(uint32_t DstTySize
) const {
484 unsigned SrcTySize
= getBitWidth();
485 assert(SrcTySize
> DstTySize
&& "Not a value truncation");
486 APInt
Size(APInt::getLowBitsSet(SrcTySize
, DstTySize
));
487 if (isFullSet() || getSetSize().ugt(Size
))
488 return ConstantRange(DstTySize
);
490 APInt L
= Lower
; L
.trunc(DstTySize
);
491 APInt U
= Upper
; U
.trunc(DstTySize
);
492 return ConstantRange(L
, U
);
496 ConstantRange::add(const ConstantRange
&Other
) const {
497 if (isEmptySet() || Other
.isEmptySet())
498 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
499 if (isFullSet() || Other
.isFullSet())
500 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
502 APInt Spread_X
= getSetSize(), Spread_Y
= Other
.getSetSize();
503 APInt NewLower
= getLower() + Other
.getLower();
504 APInt NewUpper
= getUpper() + Other
.getUpper() - 1;
505 if (NewLower
== NewUpper
)
506 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
508 ConstantRange X
= ConstantRange(NewLower
, NewUpper
);
509 if (X
.getSetSize().ult(Spread_X
) || X
.getSetSize().ult(Spread_Y
))
510 // We've wrapped, therefore, full set.
511 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
517 ConstantRange::multiply(const ConstantRange
&Other
) const {
518 if (isEmptySet() || Other
.isEmptySet())
519 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
520 if (isFullSet() || Other
.isFullSet())
521 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
523 APInt this_min
= getUnsignedMin().zext(getBitWidth() * 2);
524 APInt this_max
= getUnsignedMax().zext(getBitWidth() * 2);
525 APInt Other_min
= Other
.getUnsignedMin().zext(getBitWidth() * 2);
526 APInt Other_max
= Other
.getUnsignedMax().zext(getBitWidth() * 2);
528 ConstantRange Result_zext
= ConstantRange(this_min
* Other_min
,
529 this_max
* Other_max
+ 1);
530 return Result_zext
.truncate(getBitWidth());
534 ConstantRange::smax(const ConstantRange
&Other
) const {
535 // X smax Y is: range(smax(X_smin, Y_smin),
536 // smax(X_smax, Y_smax))
537 if (isEmptySet() || Other
.isEmptySet())
538 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
539 APInt NewL
= APIntOps::smax(getSignedMin(), Other
.getSignedMin());
540 APInt NewU
= APIntOps::smax(getSignedMax(), Other
.getSignedMax()) + 1;
542 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
543 return ConstantRange(NewL
, NewU
);
547 ConstantRange::umax(const ConstantRange
&Other
) const {
548 // X umax Y is: range(umax(X_umin, Y_umin),
549 // umax(X_umax, Y_umax))
550 if (isEmptySet() || Other
.isEmptySet())
551 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
552 APInt NewL
= APIntOps::umax(getUnsignedMin(), Other
.getUnsignedMin());
553 APInt NewU
= APIntOps::umax(getUnsignedMax(), Other
.getUnsignedMax()) + 1;
555 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
556 return ConstantRange(NewL
, NewU
);
560 ConstantRange::udiv(const ConstantRange
&RHS
) const {
561 if (isEmptySet() || RHS
.isEmptySet() || RHS
.getUnsignedMax() == 0)
562 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
564 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
566 APInt Lower
= getUnsignedMin().udiv(RHS
.getUnsignedMax());
568 APInt RHS_umin
= RHS
.getUnsignedMin();
570 // We want the lowest value in RHS excluding zero. Usually that would be 1
571 // except for a range in the form of [X, 1) in which case it would be X.
572 if (RHS
.getUpper() == 1)
573 RHS_umin
= RHS
.getLower();
575 RHS_umin
= APInt(getBitWidth(), 1);
578 APInt Upper
= getUnsignedMax().udiv(RHS_umin
) + 1;
580 // If the LHS is Full and the RHS is a wrapped interval containing 1 then
583 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
585 return ConstantRange(Lower
, Upper
);
588 /// print - Print out the bounds to a stream...
590 void ConstantRange::print(raw_ostream
&OS
) const {
591 OS
<< "[" << Lower
<< "," << Upper
<< ")";
594 /// dump - Allow printing from a debugger easily...
596 void ConstantRange::dump() const {