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());
165 return getUpper() - 1;
168 /// getUnsignedMin - Return the smallest unsigned value contained in the
171 APInt ConstantRange::getUnsignedMin() const {
172 if (isFullSet() || (isWrappedSet() && getUpper() != 0))
173 return APInt::getMinValue(getBitWidth());
178 /// getSignedMax - Return the largest signed value contained in the
181 APInt ConstantRange::getSignedMax() const {
182 APInt SignedMax(APInt::getSignedMaxValue(getBitWidth()));
183 if (!isWrappedSet()) {
184 if (getLower().sle(getUpper() - 1))
185 return getUpper() - 1;
189 if (getLower().isNegative() == getUpper().isNegative())
192 return getUpper() - 1;
196 /// getSignedMin - Return the smallest signed value contained in the
199 APInt ConstantRange::getSignedMin() const {
200 APInt SignedMin(APInt::getSignedMinValue(getBitWidth()));
201 if (!isWrappedSet()) {
202 if (getLower().sle(getUpper() - 1))
207 if ((getUpper() - 1).slt(getLower())) {
208 if (getUpper() != SignedMin)
218 /// contains - Return true if the specified value is in the set.
220 bool ConstantRange::contains(const APInt &V) const {
225 return Lower.ule(V) && V.ult(Upper);
227 return Lower.ule(V) || V.ult(Upper);
230 /// contains - Return true if the argument is a subset of this range.
231 /// Two equal sets contain each other. The empty set contained by all other
234 bool ConstantRange::contains(const ConstantRange &Other) const {
235 if (isFullSet() || Other.isEmptySet()) return true;
236 if (isEmptySet() || Other.isFullSet()) return false;
238 if (!isWrappedSet()) {
239 if (Other.isWrappedSet())
242 return Lower.ule(Other.getLower()) && Other.getUpper().ule(Upper);
245 if (!Other.isWrappedSet())
246 return Other.getUpper().ule(Upper) ||
247 Lower.ule(Other.getLower());
249 return Other.getUpper().ule(Upper) && Lower.ule(Other.getLower());
252 /// subtract - Subtract the specified constant from the endpoints of this
254 ConstantRange ConstantRange::subtract(const APInt &Val) const {
255 assert(Val.getBitWidth() == getBitWidth() && "Wrong bit width");
256 // If the set is empty or full, don't modify the endpoints.
259 return ConstantRange(Lower - Val, Upper - Val);
262 /// intersectWith - Return the range that results from the intersection of this
263 /// range with another range. The resultant range is guaranteed to include all
264 /// elements contained in both input ranges, and to have the smallest possible
265 /// set size that does so. Because there may be two intersections with the
266 /// same set size, A.intersectWith(B) might not be equal to B.intersectWith(A).
267 ConstantRange ConstantRange::intersectWith(const ConstantRange &CR) const {
268 assert(getBitWidth() == CR.getBitWidth() &&
269 "ConstantRange types don't agree!");
271 // Handle common cases.
272 if ( isEmptySet() || CR.isFullSet()) return *this;
273 if (CR.isEmptySet() || isFullSet()) return CR;
275 if (!isWrappedSet() && CR.isWrappedSet())
276 return CR.intersectWith(*this);
278 if (!isWrappedSet() && !CR.isWrappedSet()) {
279 if (Lower.ult(CR.Lower)) {
280 if (Upper.ule(CR.Lower))
281 return ConstantRange(getBitWidth(), false);
283 if (Upper.ult(CR.Upper))
284 return ConstantRange(CR.Lower, Upper);
288 if (Upper.ult(CR.Upper))
291 if (Lower.ult(CR.Upper))
292 return ConstantRange(Lower, CR.Upper);
294 return ConstantRange(getBitWidth(), false);
298 if (isWrappedSet() && !CR.isWrappedSet()) {
299 if (CR.Lower.ult(Upper)) {
300 if (CR.Upper.ult(Upper))
303 if (CR.Upper.ult(Lower))
304 return ConstantRange(CR.Lower, Upper);
306 if (getSetSize().ult(CR.getSetSize()))
310 } else if (CR.Lower.ult(Lower)) {
311 if (CR.Upper.ule(Lower))
312 return ConstantRange(getBitWidth(), false);
314 return ConstantRange(Lower, CR.Upper);
319 if (CR.Upper.ult(Upper)) {
320 if (CR.Lower.ult(Upper)) {
321 if (getSetSize().ult(CR.getSetSize()))
327 if (CR.Lower.ult(Lower))
328 return ConstantRange(Lower, CR.Upper);
331 } else if (CR.Upper.ult(Lower)) {
332 if (CR.Lower.ult(Lower))
335 return ConstantRange(CR.Lower, Upper);
337 if (getSetSize().ult(CR.getSetSize()))
344 /// unionWith - Return the range that results from the union of this range with
345 /// another range. The resultant range is guaranteed to include the elements of
346 /// both sets, but may contain more. For example, [3, 9) union [12,15) is
347 /// [3, 15), which includes 9, 10, and 11, which were not included in either
350 ConstantRange ConstantRange::unionWith(const ConstantRange &CR) const {
351 assert(getBitWidth() == CR.getBitWidth() &&
352 "ConstantRange types don't agree!");
354 if ( isFullSet() || CR.isEmptySet()) return *this;
355 if (CR.isFullSet() || isEmptySet()) return CR;
357 if (!isWrappedSet() && CR.isWrappedSet()) return CR.unionWith(*this);
359 if (!isWrappedSet() && !CR.isWrappedSet()) {
360 if (CR.Upper.ult(Lower) || Upper.ult(CR.Lower)) {
361 // If the two ranges are disjoint, find the smaller gap and bridge it.
362 APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
364 return ConstantRange(Lower, CR.Upper);
366 return ConstantRange(CR.Lower, Upper);
369 APInt L = Lower, U = Upper;
372 if ((CR.Upper - 1).ugt(U - 1))
375 if (L == 0 && U == 0)
376 return ConstantRange(getBitWidth());
378 return ConstantRange(L, U);
381 if (!CR.isWrappedSet()) {
382 // ------U L----- and ------U L----- : this
384 if (CR.Upper.ule(Upper) || CR.Lower.uge(Lower))
387 // ------U L----- : this
389 if (CR.Lower.ule(Upper) && Lower.ule(CR.Upper))
390 return ConstantRange(getBitWidth());
392 // ----U L---- : this
395 if (Upper.ule(CR.Lower) && CR.Upper.ule(Lower)) {
396 APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
398 return ConstantRange(Lower, CR.Upper);
400 return ConstantRange(CR.Lower, Upper);
403 // ----U L----- : this
405 if (Upper.ult(CR.Lower) && Lower.ult(CR.Upper))
406 return ConstantRange(CR.Lower, Upper);
408 // ------U L---- : this
410 if (CR.Lower.ult(Upper) && CR.Upper.ult(Lower))
411 return ConstantRange(Lower, CR.Upper);
414 assert(isWrappedSet() && CR.isWrappedSet() &&
415 "ConstantRange::unionWith missed wrapped union unwrapped case");
417 // ------U L---- and ------U L---- : this
418 // -U L----------- and ------------U L : CR
419 if (CR.Lower.ule(Upper) || Lower.ule(CR.Upper))
420 return ConstantRange(getBitWidth());
422 APInt L = Lower, U = Upper;
428 return ConstantRange(L, U);
431 /// zeroExtend - Return a new range in the specified integer type, which must
432 /// be strictly larger than the current type. The returned range will
433 /// correspond to the possible range of values as if the source range had been
435 ConstantRange ConstantRange::zeroExtend(uint32_t DstTySize) const {
436 if (isEmptySet()) return ConstantRange(DstTySize, /*isFullSet=*/false);
438 unsigned SrcTySize = getBitWidth();
439 assert(SrcTySize < DstTySize && "Not a value extension");
440 if (isFullSet() || isWrappedSet())
441 // Change into [0, 1 << src bit width)
442 return ConstantRange(APInt(DstTySize,0), APInt(DstTySize,1).shl(SrcTySize));
444 return ConstantRange(Lower.zext(DstTySize), Upper.zext(DstTySize));
447 /// signExtend - Return a new range in the specified integer type, which must
448 /// be strictly larger than the current type. The returned range will
449 /// correspond to the possible range of values as if the source range had been
451 ConstantRange ConstantRange::signExtend(uint32_t DstTySize) const {
452 if (isEmptySet()) return ConstantRange(DstTySize, /*isFullSet=*/false);
454 unsigned SrcTySize = getBitWidth();
455 assert(SrcTySize < DstTySize && "Not a value extension");
456 if (isFullSet() || isSignWrappedSet()) {
457 return ConstantRange(APInt::getHighBitsSet(DstTySize,DstTySize-SrcTySize+1),
458 APInt::getLowBitsSet(DstTySize, SrcTySize-1) + 1);
461 return ConstantRange(Lower.sext(DstTySize), Upper.sext(DstTySize));
464 /// truncate - Return a new range in the specified integer type, which must be
465 /// strictly smaller than the current type. The returned range will
466 /// correspond to the possible range of values as if the source range had been
467 /// truncated to the specified type.
468 ConstantRange ConstantRange::truncate(uint32_t DstTySize) const {
469 unsigned SrcTySize = getBitWidth();
470 assert(SrcTySize > DstTySize && "Not a value truncation");
471 APInt Size(APInt::getLowBitsSet(SrcTySize, DstTySize));
472 if (isFullSet() || getSetSize().ugt(Size))
473 return ConstantRange(DstTySize, /*isFullSet=*/true);
475 return ConstantRange(Lower.trunc(DstTySize), Upper.trunc(DstTySize));
478 /// zextOrTrunc - make this range have the bit width given by \p DstTySize. The
479 /// value is zero extended, truncated, or left alone to make it that width.
480 ConstantRange ConstantRange::zextOrTrunc(uint32_t DstTySize) const {
481 unsigned SrcTySize = getBitWidth();
482 if (SrcTySize > DstTySize)
483 return truncate(DstTySize);
484 else if (SrcTySize < DstTySize)
485 return zeroExtend(DstTySize);
490 /// sextOrTrunc - make this range have the bit width given by \p DstTySize. The
491 /// value is sign extended, truncated, or left alone to make it that width.
492 ConstantRange ConstantRange::sextOrTrunc(uint32_t DstTySize) const {
493 unsigned SrcTySize = getBitWidth();
494 if (SrcTySize > DstTySize)
495 return truncate(DstTySize);
496 else if (SrcTySize < DstTySize)
497 return signExtend(DstTySize);
503 ConstantRange::add(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.getLower();
511 APInt NewUpper = getUpper() + Other.getUpper() - 1;
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::sub(const ConstantRange &Other) const {
525 if (isEmptySet() || Other.isEmptySet())
526 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
527 if (isFullSet() || Other.isFullSet())
528 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
530 APInt Spread_X = getSetSize(), Spread_Y = Other.getSetSize();
531 APInt NewLower = getLower() - Other.getUpper() + 1;
532 APInt NewUpper = getUpper() - Other.getLower();
533 if (NewLower == NewUpper)
534 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
536 ConstantRange X = ConstantRange(NewLower, NewUpper);
537 if (X.getSetSize().ult(Spread_X) || X.getSetSize().ult(Spread_Y))
538 // We've wrapped, therefore, full set.
539 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
545 ConstantRange::multiply(const ConstantRange &Other) const {
546 // TODO: If either operand is a single element and the multiply is known to
547 // be non-wrapping, round the result min and max value to the appropriate
548 // multiple of that element. If wrapping is possible, at least adjust the
549 // range according to the greatest power-of-two factor of the single element.
551 if (isEmptySet() || Other.isEmptySet())
552 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
553 if (isFullSet() || Other.isFullSet())
554 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
556 APInt this_min = getUnsignedMin().zext(getBitWidth() * 2);
557 APInt this_max = getUnsignedMax().zext(getBitWidth() * 2);
558 APInt Other_min = Other.getUnsignedMin().zext(getBitWidth() * 2);
559 APInt Other_max = Other.getUnsignedMax().zext(getBitWidth() * 2);
561 ConstantRange Result_zext = ConstantRange(this_min * Other_min,
562 this_max * Other_max + 1);
563 return Result_zext.truncate(getBitWidth());
567 ConstantRange::smax(const ConstantRange &Other) const {
568 // X smax Y is: range(smax(X_smin, Y_smin),
569 // smax(X_smax, Y_smax))
570 if (isEmptySet() || Other.isEmptySet())
571 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
572 APInt NewL = APIntOps::smax(getSignedMin(), Other.getSignedMin());
573 APInt NewU = APIntOps::smax(getSignedMax(), Other.getSignedMax()) + 1;
575 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
576 return ConstantRange(NewL, NewU);
580 ConstantRange::umax(const ConstantRange &Other) const {
581 // X umax Y is: range(umax(X_umin, Y_umin),
582 // umax(X_umax, Y_umax))
583 if (isEmptySet() || Other.isEmptySet())
584 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
585 APInt NewL = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
586 APInt NewU = APIntOps::umax(getUnsignedMax(), Other.getUnsignedMax()) + 1;
588 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
589 return ConstantRange(NewL, NewU);
593 ConstantRange::udiv(const ConstantRange &RHS) const {
594 if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax() == 0)
595 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
597 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
599 APInt Lower = getUnsignedMin().udiv(RHS.getUnsignedMax());
601 APInt RHS_umin = RHS.getUnsignedMin();
603 // We want the lowest value in RHS excluding zero. Usually that would be 1
604 // except for a range in the form of [X, 1) in which case it would be X.
605 if (RHS.getUpper() == 1)
606 RHS_umin = RHS.getLower();
608 RHS_umin = APInt(getBitWidth(), 1);
611 APInt Upper = getUnsignedMax().udiv(RHS_umin) + 1;
613 // If the LHS is Full and the RHS is a wrapped interval containing 1 then
616 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
618 return ConstantRange(Lower, Upper);
622 ConstantRange::binaryAnd(const ConstantRange &Other) const {
623 if (isEmptySet() || Other.isEmptySet())
624 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
626 // TODO: replace this with something less conservative
628 APInt umin = APIntOps::umin(Other.getUnsignedMax(), getUnsignedMax());
629 if (umin.isAllOnesValue())
630 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
631 return ConstantRange(APInt::getNullValue(getBitWidth()), umin + 1);
635 ConstantRange::binaryOr(const ConstantRange &Other) const {
636 if (isEmptySet() || Other.isEmptySet())
637 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
639 // TODO: replace this with something less conservative
641 APInt umax = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
642 if (umax.isMinValue())
643 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
644 return ConstantRange(umax, APInt::getNullValue(getBitWidth()));
648 ConstantRange::shl(const ConstantRange &Other) const {
649 if (isEmptySet() || Other.isEmptySet())
650 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
652 APInt min = getUnsignedMin().shl(Other.getUnsignedMin());
653 APInt max = getUnsignedMax().shl(Other.getUnsignedMax());
655 // there's no overflow!
656 APInt Zeros(getBitWidth(), getUnsignedMax().countLeadingZeros());
657 if (Zeros.ugt(Other.getUnsignedMax()))
658 return ConstantRange(min, max + 1);
660 // FIXME: implement the other tricky cases
661 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
665 ConstantRange::lshr(const ConstantRange &Other) const {
666 if (isEmptySet() || Other.isEmptySet())
667 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
669 APInt max = getUnsignedMax().lshr(Other.getUnsignedMin());
670 APInt min = getUnsignedMin().lshr(Other.getUnsignedMax());
672 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
674 return ConstantRange(min, max + 1);
677 ConstantRange ConstantRange::inverse() const {
679 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
680 } else if (isEmptySet()) {
681 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
683 return ConstantRange(Upper, Lower);
686 /// print - Print out the bounds to a stream...
688 void ConstantRange::print(raw_ostream &OS) const {
691 else if (isEmptySet())
694 OS << "[" << Lower << "," << Upper << ")";
697 /// dump - Allow printing from a debugger easily...
699 void ConstantRange::dump() const {