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/InstrTypes.h"
25 #include "llvm/Support/ConstantRange.h"
26 #include "llvm/Support/Debug.h"
27 #include "llvm/Support/raw_ostream.h"
30 /// Initialize a full (the default) or empty set for the specified type.
32 ConstantRange::ConstantRange(uint32_t BitWidth, bool Full) {
34 Lower = Upper = APInt::getMaxValue(BitWidth);
36 Lower = Upper = APInt::getMinValue(BitWidth);
39 /// Initialize a range to hold the single specified value.
41 ConstantRange::ConstantRange(const APInt &V) : Lower(V), Upper(V + 1) {}
43 ConstantRange::ConstantRange(const APInt &L, const APInt &U) :
45 assert(L.getBitWidth() == U.getBitWidth() &&
46 "ConstantRange with unequal bit widths");
47 assert((L != U || (L.isMaxValue() || L.isMinValue())) &&
48 "Lower == Upper, but they aren't min or max value!");
51 ConstantRange ConstantRange::makeICmpRegion(unsigned Pred,
52 const ConstantRange &CR) {
56 uint32_t W = CR.getBitWidth();
58 default: assert(0 && "Invalid ICmp predicate to makeICmpRegion()");
59 case CmpInst::ICMP_EQ:
61 case CmpInst::ICMP_NE:
62 if (CR.isSingleElement())
63 return ConstantRange(CR.getUpper(), CR.getLower());
64 return ConstantRange(W);
65 case CmpInst::ICMP_ULT: {
66 APInt UMax(CR.getUnsignedMax());
67 if (UMax.isMinValue())
68 return ConstantRange(W, /* empty */ false);
69 return ConstantRange(APInt::getMinValue(W), UMax);
71 case CmpInst::ICMP_SLT: {
72 APInt SMax(CR.getSignedMax());
73 if (SMax.isMinSignedValue())
74 return ConstantRange(W, /* empty */ false);
75 return ConstantRange(APInt::getSignedMinValue(W), SMax);
77 case CmpInst::ICMP_ULE: {
78 APInt UMax(CR.getUnsignedMax());
79 if (UMax.isMaxValue())
80 return ConstantRange(W);
81 return ConstantRange(APInt::getMinValue(W), UMax + 1);
83 case CmpInst::ICMP_SLE: {
84 APInt SMax(CR.getSignedMax());
85 if (SMax.isMaxSignedValue())
86 return ConstantRange(W);
87 return ConstantRange(APInt::getSignedMinValue(W), SMax + 1);
89 case CmpInst::ICMP_UGT: {
90 APInt UMin(CR.getUnsignedMin());
91 if (UMin.isMaxValue())
92 return ConstantRange(W, /* empty */ false);
93 return ConstantRange(UMin + 1, APInt::getNullValue(W));
95 case CmpInst::ICMP_SGT: {
96 APInt SMin(CR.getSignedMin());
97 if (SMin.isMaxSignedValue())
98 return ConstantRange(W, /* empty */ false);
99 return ConstantRange(SMin + 1, APInt::getSignedMinValue(W));
101 case CmpInst::ICMP_UGE: {
102 APInt UMin(CR.getUnsignedMin());
103 if (UMin.isMinValue())
104 return ConstantRange(W);
105 return ConstantRange(UMin, APInt::getNullValue(W));
107 case CmpInst::ICMP_SGE: {
108 APInt SMin(CR.getSignedMin());
109 if (SMin.isMinSignedValue())
110 return ConstantRange(W);
111 return ConstantRange(SMin, APInt::getSignedMinValue(W));
116 /// isFullSet - Return true if this set contains all of the elements possible
117 /// for this data-type
118 bool ConstantRange::isFullSet() const {
119 return Lower == Upper && Lower.isMaxValue();
122 /// isEmptySet - Return true if this set contains no members.
124 bool ConstantRange::isEmptySet() const {
125 return Lower == Upper && Lower.isMinValue();
128 /// isWrappedSet - Return true if this set wraps around the top of the range,
129 /// for example: [100, 8)
131 bool ConstantRange::isWrappedSet() const {
132 return Lower.ugt(Upper);
135 /// isSignWrappedSet - Return true if this set wraps around the INT_MIN of
136 /// its bitwidth, for example: i8 [120, 140).
138 bool ConstantRange::isSignWrappedSet() const {
139 return contains(APInt::getSignedMaxValue(getBitWidth())) &&
140 contains(APInt::getSignedMinValue(getBitWidth()));
143 /// getSetSize - Return the number of elements in this set.
145 APInt ConstantRange::getSetSize() const {
147 return APInt(getBitWidth(), 0);
148 if (getBitWidth() == 1) {
149 if (Lower != Upper) // One of T or F in the set...
151 return APInt(2, 2); // Must be full set...
154 // Simply subtract the bounds...
155 return Upper - Lower;
158 /// getUnsignedMax - Return the largest unsigned value contained in the
161 APInt ConstantRange::getUnsignedMax() const {
162 if (isFullSet() || isWrappedSet())
163 return APInt::getMaxValue(getBitWidth());
164 return getUpper() - 1;
167 /// getUnsignedMin - Return the smallest unsigned value contained in the
170 APInt ConstantRange::getUnsignedMin() const {
171 if (isFullSet() || (isWrappedSet() && getUpper() != 0))
172 return APInt::getMinValue(getBitWidth());
176 /// getSignedMax - Return the largest signed value contained in the
179 APInt ConstantRange::getSignedMax() const {
180 APInt SignedMax(APInt::getSignedMaxValue(getBitWidth()));
181 if (!isWrappedSet()) {
182 if (getLower().sle(getUpper() - 1))
183 return getUpper() - 1;
186 if (getLower().isNegative() == getUpper().isNegative())
188 return getUpper() - 1;
191 /// getSignedMin - Return the smallest signed value contained in the
194 APInt ConstantRange::getSignedMin() const {
195 APInt SignedMin(APInt::getSignedMinValue(getBitWidth()));
196 if (!isWrappedSet()) {
197 if (getLower().sle(getUpper() - 1))
201 if ((getUpper() - 1).slt(getLower())) {
202 if (getUpper() != SignedMin)
208 /// contains - Return true if the specified value is in the set.
210 bool ConstantRange::contains(const APInt &V) const {
215 return Lower.ule(V) && V.ult(Upper);
216 return Lower.ule(V) || V.ult(Upper);
219 /// contains - Return true if the argument is a subset of this range.
220 /// Two equal sets contain each other. The empty set contained by all other
223 bool ConstantRange::contains(const ConstantRange &Other) const {
224 if (isFullSet() || Other.isEmptySet()) return true;
225 if (isEmptySet() || Other.isFullSet()) return false;
227 if (!isWrappedSet()) {
228 if (Other.isWrappedSet())
231 return Lower.ule(Other.getLower()) && Other.getUpper().ule(Upper);
234 if (!Other.isWrappedSet())
235 return Other.getUpper().ule(Upper) ||
236 Lower.ule(Other.getLower());
238 return Other.getUpper().ule(Upper) && Lower.ule(Other.getLower());
241 /// subtract - Subtract the specified constant from the endpoints of this
243 ConstantRange ConstantRange::subtract(const APInt &Val) const {
244 assert(Val.getBitWidth() == getBitWidth() && "Wrong bit width");
245 // If the set is empty or full, don't modify the endpoints.
248 return ConstantRange(Lower - Val, Upper - Val);
251 /// intersectWith - Return the range that results from the intersection of this
252 /// range with another range. The resultant range is guaranteed to include all
253 /// elements contained in both input ranges, and to have the smallest possible
254 /// set size that does so. Because there may be two intersections with the
255 /// same set size, A.intersectWith(B) might not be equal to B.intersectWith(A).
256 ConstantRange ConstantRange::intersectWith(const ConstantRange &CR) const {
257 assert(getBitWidth() == CR.getBitWidth() &&
258 "ConstantRange types don't agree!");
260 // Handle common cases.
261 if ( isEmptySet() || CR.isFullSet()) return *this;
262 if (CR.isEmptySet() || isFullSet()) return CR;
264 if (!isWrappedSet() && CR.isWrappedSet())
265 return CR.intersectWith(*this);
267 if (!isWrappedSet() && !CR.isWrappedSet()) {
268 if (Lower.ult(CR.Lower)) {
269 if (Upper.ule(CR.Lower))
270 return ConstantRange(getBitWidth(), false);
272 if (Upper.ult(CR.Upper))
273 return ConstantRange(CR.Lower, Upper);
277 if (Upper.ult(CR.Upper))
280 if (Lower.ult(CR.Upper))
281 return ConstantRange(Lower, CR.Upper);
283 return ConstantRange(getBitWidth(), false);
286 if (isWrappedSet() && !CR.isWrappedSet()) {
287 if (CR.Lower.ult(Upper)) {
288 if (CR.Upper.ult(Upper))
291 if (CR.Upper.ult(Lower))
292 return ConstantRange(CR.Lower, Upper);
294 if (getSetSize().ult(CR.getSetSize()))
298 if (CR.Lower.ult(Lower)) {
299 if (CR.Upper.ule(Lower))
300 return ConstantRange(getBitWidth(), false);
302 return ConstantRange(Lower, CR.Upper);
307 if (CR.Upper.ult(Upper)) {
308 if (CR.Lower.ult(Upper)) {
309 if (getSetSize().ult(CR.getSetSize()))
314 if (CR.Lower.ult(Lower))
315 return ConstantRange(Lower, CR.Upper);
319 if (CR.Upper.ult(Lower)) {
320 if (CR.Lower.ult(Lower))
323 return ConstantRange(CR.Lower, Upper);
325 if (getSetSize().ult(CR.getSetSize()))
331 /// unionWith - Return the range that results from the union of this range with
332 /// another range. The resultant range is guaranteed to include the elements of
333 /// both sets, but may contain more. For example, [3, 9) union [12,15) is
334 /// [3, 15), which includes 9, 10, and 11, which were not included in either
337 ConstantRange ConstantRange::unionWith(const ConstantRange &CR) const {
338 assert(getBitWidth() == CR.getBitWidth() &&
339 "ConstantRange types don't agree!");
341 if ( isFullSet() || CR.isEmptySet()) return *this;
342 if (CR.isFullSet() || isEmptySet()) return CR;
344 if (!isWrappedSet() && CR.isWrappedSet()) return CR.unionWith(*this);
346 if (!isWrappedSet() && !CR.isWrappedSet()) {
347 if (CR.Upper.ult(Lower) || Upper.ult(CR.Lower)) {
348 // If the two ranges are disjoint, find the smaller gap and bridge it.
349 APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
351 return ConstantRange(Lower, CR.Upper);
352 return ConstantRange(CR.Lower, Upper);
355 APInt L = Lower, U = Upper;
358 if ((CR.Upper - 1).ugt(U - 1))
361 if (L == 0 && U == 0)
362 return ConstantRange(getBitWidth());
364 return ConstantRange(L, U);
367 if (!CR.isWrappedSet()) {
368 // ------U L----- and ------U L----- : this
370 if (CR.Upper.ule(Upper) || CR.Lower.uge(Lower))
373 // ------U L----- : this
375 if (CR.Lower.ule(Upper) && Lower.ule(CR.Upper))
376 return ConstantRange(getBitWidth());
378 // ----U L---- : this
381 if (Upper.ule(CR.Lower) && CR.Upper.ule(Lower)) {
382 APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
384 return ConstantRange(Lower, CR.Upper);
385 return ConstantRange(CR.Lower, Upper);
388 // ----U L----- : this
390 if (Upper.ult(CR.Lower) && Lower.ult(CR.Upper))
391 return ConstantRange(CR.Lower, Upper);
393 // ------U L---- : this
395 assert(CR.Lower.ult(Upper) && CR.Upper.ult(Lower) &&
396 "ConstantRange::unionWith missed a case with one range wrapped");
397 return ConstantRange(Lower, CR.Upper);
400 // ------U L---- and ------U L---- : this
401 // -U L----------- and ------------U L : CR
402 if (CR.Lower.ule(Upper) || Lower.ule(CR.Upper))
403 return ConstantRange(getBitWidth());
405 APInt L = Lower, U = Upper;
411 return ConstantRange(L, U);
414 /// zeroExtend - Return a new range in the specified integer type, which must
415 /// be strictly larger than the current type. The returned range will
416 /// correspond to the possible range of values as if the source range had been
418 ConstantRange ConstantRange::zeroExtend(uint32_t DstTySize) const {
419 if (isEmptySet()) return ConstantRange(DstTySize, /*isFullSet=*/false);
421 unsigned SrcTySize = getBitWidth();
422 assert(SrcTySize < DstTySize && "Not a value extension");
423 if (isFullSet() || isWrappedSet())
424 // Change into [0, 1 << src bit width)
425 return ConstantRange(APInt(DstTySize,0), APInt(DstTySize,1).shl(SrcTySize));
427 return ConstantRange(Lower.zext(DstTySize), Upper.zext(DstTySize));
430 /// signExtend - Return a new range in the specified integer type, which must
431 /// be strictly larger than the current type. The returned range will
432 /// correspond to the possible range of values as if the source range had been
434 ConstantRange ConstantRange::signExtend(uint32_t DstTySize) const {
435 if (isEmptySet()) return ConstantRange(DstTySize, /*isFullSet=*/false);
437 unsigned SrcTySize = getBitWidth();
438 assert(SrcTySize < DstTySize && "Not a value extension");
439 if (isFullSet() || isSignWrappedSet()) {
440 return ConstantRange(APInt::getHighBitsSet(DstTySize,DstTySize-SrcTySize+1),
441 APInt::getLowBitsSet(DstTySize, SrcTySize-1) + 1);
444 return ConstantRange(Lower.sext(DstTySize), Upper.sext(DstTySize));
447 /// truncate - Return a new range in the specified integer type, which must be
448 /// strictly smaller than the current type. The returned range will
449 /// correspond to the possible range of values as if the source range had been
450 /// truncated to the specified type.
451 ConstantRange ConstantRange::truncate(uint32_t DstTySize) const {
452 assert(getBitWidth() > DstTySize && "Not a value truncation");
453 if (isFullSet() || getSetSize().getActiveBits() > DstTySize)
454 return ConstantRange(DstTySize, /*isFullSet=*/true);
456 return ConstantRange(Lower.trunc(DstTySize), Upper.trunc(DstTySize));
459 /// zextOrTrunc - make this range have the bit width given by \p DstTySize. The
460 /// value is zero extended, truncated, or left alone to make it that width.
461 ConstantRange ConstantRange::zextOrTrunc(uint32_t DstTySize) const {
462 unsigned SrcTySize = getBitWidth();
463 if (SrcTySize > DstTySize)
464 return truncate(DstTySize);
465 if (SrcTySize < DstTySize)
466 return zeroExtend(DstTySize);
470 /// sextOrTrunc - make this range have the bit width given by \p DstTySize. The
471 /// value is sign extended, truncated, or left alone to make it that width.
472 ConstantRange ConstantRange::sextOrTrunc(uint32_t DstTySize) const {
473 unsigned SrcTySize = getBitWidth();
474 if (SrcTySize > DstTySize)
475 return truncate(DstTySize);
476 if (SrcTySize < DstTySize)
477 return signExtend(DstTySize);
482 ConstantRange::add(const ConstantRange &Other) const {
483 if (isEmptySet() || Other.isEmptySet())
484 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
485 if (isFullSet() || Other.isFullSet())
486 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
488 APInt Spread_X = getSetSize(), Spread_Y = Other.getSetSize();
489 APInt NewLower = getLower() + Other.getLower();
490 APInt NewUpper = getUpper() + Other.getUpper() - 1;
491 if (NewLower == NewUpper)
492 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
494 ConstantRange X = ConstantRange(NewLower, NewUpper);
495 if (X.getSetSize().ult(Spread_X) || X.getSetSize().ult(Spread_Y))
496 // We've wrapped, therefore, full set.
497 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
503 ConstantRange::sub(const ConstantRange &Other) const {
504 if (isEmptySet() || Other.isEmptySet())
505 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
506 if (isFullSet() || Other.isFullSet())
507 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
509 APInt Spread_X = getSetSize(), Spread_Y = Other.getSetSize();
510 APInt NewLower = getLower() - Other.getUpper() + 1;
511 APInt NewUpper = getUpper() - Other.getLower();
512 if (NewLower == NewUpper)
513 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
515 ConstantRange X = ConstantRange(NewLower, NewUpper);
516 if (X.getSetSize().ult(Spread_X) || X.getSetSize().ult(Spread_Y))
517 // We've wrapped, therefore, full set.
518 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
524 ConstantRange::multiply(const ConstantRange &Other) const {
525 // TODO: If either operand is a single element and the multiply is known to
526 // be non-wrapping, round the result min and max value to the appropriate
527 // multiple of that element. If wrapping is possible, at least adjust the
528 // range according to the greatest power-of-two factor of the single element.
530 if (isEmptySet() || Other.isEmptySet())
531 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
532 if (isFullSet() || Other.isFullSet())
533 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
535 APInt this_min = getUnsignedMin().zext(getBitWidth() * 2);
536 APInt this_max = getUnsignedMax().zext(getBitWidth() * 2);
537 APInt Other_min = Other.getUnsignedMin().zext(getBitWidth() * 2);
538 APInt Other_max = Other.getUnsignedMax().zext(getBitWidth() * 2);
540 ConstantRange Result_zext = ConstantRange(this_min * Other_min,
541 this_max * Other_max + 1);
542 return Result_zext.truncate(getBitWidth());
546 ConstantRange::smax(const ConstantRange &Other) const {
547 // X smax Y is: range(smax(X_smin, Y_smin),
548 // smax(X_smax, Y_smax))
549 if (isEmptySet() || Other.isEmptySet())
550 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
551 APInt NewL = APIntOps::smax(getSignedMin(), Other.getSignedMin());
552 APInt NewU = APIntOps::smax(getSignedMax(), Other.getSignedMax()) + 1;
554 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
555 return ConstantRange(NewL, NewU);
559 ConstantRange::umax(const ConstantRange &Other) const {
560 // X umax Y is: range(umax(X_umin, Y_umin),
561 // umax(X_umax, Y_umax))
562 if (isEmptySet() || Other.isEmptySet())
563 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
564 APInt NewL = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
565 APInt NewU = APIntOps::umax(getUnsignedMax(), Other.getUnsignedMax()) + 1;
567 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
568 return ConstantRange(NewL, NewU);
572 ConstantRange::udiv(const ConstantRange &RHS) const {
573 if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax() == 0)
574 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
576 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
578 APInt Lower = getUnsignedMin().udiv(RHS.getUnsignedMax());
580 APInt RHS_umin = RHS.getUnsignedMin();
582 // We want the lowest value in RHS excluding zero. Usually that would be 1
583 // except for a range in the form of [X, 1) in which case it would be X.
584 if (RHS.getUpper() == 1)
585 RHS_umin = RHS.getLower();
587 RHS_umin = APInt(getBitWidth(), 1);
590 APInt Upper = getUnsignedMax().udiv(RHS_umin) + 1;
592 // If the LHS is Full and the RHS is a wrapped interval containing 1 then
595 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
597 return ConstantRange(Lower, Upper);
601 ConstantRange::binaryAnd(const ConstantRange &Other) const {
602 if (isEmptySet() || Other.isEmptySet())
603 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
605 // TODO: replace this with something less conservative
607 APInt umin = APIntOps::umin(Other.getUnsignedMax(), getUnsignedMax());
608 if (umin.isAllOnesValue())
609 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
610 return ConstantRange(APInt::getNullValue(getBitWidth()), umin + 1);
614 ConstantRange::binaryOr(const ConstantRange &Other) const {
615 if (isEmptySet() || Other.isEmptySet())
616 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
618 // TODO: replace this with something less conservative
620 APInt umax = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
621 if (umax.isMinValue())
622 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
623 return ConstantRange(umax, APInt::getNullValue(getBitWidth()));
627 ConstantRange::shl(const ConstantRange &Other) const {
628 if (isEmptySet() || Other.isEmptySet())
629 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
631 APInt min = getUnsignedMin().shl(Other.getUnsignedMin());
632 APInt max = getUnsignedMax().shl(Other.getUnsignedMax());
634 // there's no overflow!
635 APInt Zeros(getBitWidth(), getUnsignedMax().countLeadingZeros());
636 if (Zeros.ugt(Other.getUnsignedMax()))
637 return ConstantRange(min, max + 1);
639 // FIXME: implement the other tricky cases
640 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
644 ConstantRange::lshr(const ConstantRange &Other) const {
645 if (isEmptySet() || Other.isEmptySet())
646 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
648 APInt max = getUnsignedMax().lshr(Other.getUnsignedMin());
649 APInt min = getUnsignedMin().lshr(Other.getUnsignedMax());
651 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
653 return ConstantRange(min, max + 1);
656 ConstantRange ConstantRange::inverse() const {
658 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
660 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
661 return ConstantRange(Upper, Lower);
664 /// print - Print out the bounds to a stream...
666 void ConstantRange::print(raw_ostream &OS) const {
669 else if (isEmptySet())
672 OS << "[" << Lower << "," << Upper << ")";
675 /// dump - Allow printing from a debugger easily...
677 void ConstantRange::dump() const {