1//===- ConstantRange.h - Represent a range ----------------------*- C++ -*-===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8//
9// Represent a range of possible values that may occur when the program is run
10// for an integral value. This keeps track of a lower and upper bound for the
11// constant, which MAY wrap around the end of the numeric range. To do this, it
12// keeps track of a [lower, upper) bound, which specifies an interval just like
13// STL iterators. When used with boolean values, the following are important
14// ranges: :
15//
16// [F, F) = {} = Empty set
17// [T, F) = {T}
18// [F, T) = {F}
19// [T, T) = {F, T} = Full set
20//
21// The other integral ranges use min/max values for special range values. For
22// example, for 8-bit types, it uses:
23// [0, 0) = {} = Empty set
24// [255, 255) = {0..255} = Full Set
25//
26// Note that ConstantRange can be used to represent either signed or
27// unsigned ranges.
28//
29//===----------------------------------------------------------------------===//
30
31#ifndef LLVM_IR_CONSTANTRANGE_H
32#define LLVM_IR_CONSTANTRANGE_H
33
34#include "llvm/ADT/APInt.h"
35#include "llvm/IR/InstrTypes.h"
36#include "llvm/IR/Instruction.h"
37#include "llvm/Support/Compiler.h"
38#include <cstdint>
39
40namespace llvm {
41
42class MDNode;
43class raw_ostream;
44struct KnownBits;
45
46/// This class represents a range of values.
47class LLVM_NODISCARD ConstantRange {
48 APInt Lower, Upper;
49
50 /// Create empty constant range with same bitwidth.
51 ConstantRange getEmpty() const {
52 return ConstantRange(getBitWidth(), false);
53 }
54
55 /// Create full constant range with same bitwidth.
56 ConstantRange getFull() const {
57 return ConstantRange(getBitWidth(), true);
58 }
59
60public:
61 /// Initialize a full or empty set for the specified bit width.
62 explicit ConstantRange(uint32_t BitWidth, bool isFullSet);
63
64 /// Initialize a range to hold the single specified value.
65 ConstantRange(APInt Value);
66
67 /// Initialize a range of values explicitly. This will assert out if
68 /// Lower==Upper and Lower != Min or Max value for its type. It will also
69 /// assert out if the two APInt's are not the same bit width.
70 ConstantRange(APInt Lower, APInt Upper);
71
72 /// Create empty constant range with the given bit width.
73 static ConstantRange getEmpty(uint32_t BitWidth) {
74 return ConstantRange(BitWidth, false);
75 }
76
77 /// Create full constant range with the given bit width.
78 static ConstantRange getFull(uint32_t BitWidth) {
79 return ConstantRange(BitWidth, true);
80 }
81
82 /// Create non-empty constant range with the given bounds. If Lower and
83 /// Upper are the same, a full range is returned.
84 static ConstantRange getNonEmpty(APInt Lower, APInt Upper) {
85 if (Lower == Upper)
86 return getFull(Lower.getBitWidth());
87 return ConstantRange(std::move(Lower), std::move(Upper));
88 }
89
90 /// Initialize a range based on a known bits constraint. The IsSigned flag
91 /// indicates whether the constant range should not wrap in the signed or
92 /// unsigned domain.
93 static ConstantRange fromKnownBits(const KnownBits &Known, bool IsSigned);
94
95 /// Produce the smallest range such that all values that may satisfy the given
96 /// predicate with any value contained within Other is contained in the
97 /// returned range. Formally, this returns a superset of
98 /// 'union over all y in Other . { x : icmp op x y is true }'. If the exact
99 /// answer is not representable as a ConstantRange, the return value will be a
100 /// proper superset of the above.
101 ///
102 /// Example: Pred = ult and Other = i8 [2, 5) returns Result = [0, 4)
103 static ConstantRange makeAllowedICmpRegion(CmpInst::Predicate Pred,
104 const ConstantRange &Other);
105
106 /// Produce the largest range such that all values in the returned range
107 /// satisfy the given predicate with all values contained within Other.
108 /// Formally, this returns a subset of
109 /// 'intersection over all y in Other . { x : icmp op x y is true }'. If the
110 /// exact answer is not representable as a ConstantRange, the return value
111 /// will be a proper subset of the above.
112 ///
113 /// Example: Pred = ult and Other = i8 [2, 5) returns [0, 2)
114 static ConstantRange makeSatisfyingICmpRegion(CmpInst::Predicate Pred,
115 const ConstantRange &Other);
116
117 /// Produce the exact range such that all values in the returned range satisfy
118 /// the given predicate with any value contained within Other. Formally, this
119 /// returns the exact answer when the superset of 'union over all y in Other
120 /// is exactly same as the subset of intersection over all y in Other.
121 /// { x : icmp op x y is true}'.
122 ///
123 /// Example: Pred = ult and Other = i8 3 returns [0, 3)
124 static ConstantRange makeExactICmpRegion(CmpInst::Predicate Pred,
125 const APInt &Other);
126
127 /// Does the predicate \p Pred hold between ranges this and \p Other?
128 /// NOTE: false does not mean that inverse predicate holds!
129 bool icmp(CmpInst::Predicate Pred, const ConstantRange &Other) const;
130
131 /// Produce the largest range containing all X such that "X BinOp Y" is
132 /// guaranteed not to wrap (overflow) for *all* Y in Other. However, there may
133 /// be *some* Y in Other for which additional X not contained in the result
134 /// also do not overflow.
135 ///
136 /// NoWrapKind must be one of OBO::NoUnsignedWrap or OBO::NoSignedWrap.
137 ///
138 /// Examples:
139 /// typedef OverflowingBinaryOperator OBO;
140 /// #define MGNR makeGuaranteedNoWrapRegion
141 /// MGNR(Add, [i8 1, 2), OBO::NoSignedWrap) == [-128, 127)
142 /// MGNR(Add, [i8 1, 2), OBO::NoUnsignedWrap) == [0, -1)
143 /// MGNR(Add, [i8 0, 1), OBO::NoUnsignedWrap) == Full Set
144 /// MGNR(Add, [i8 -1, 6), OBO::NoSignedWrap) == [INT_MIN+1, INT_MAX-4)
145 /// MGNR(Sub, [i8 1, 2), OBO::NoSignedWrap) == [-127, 128)
146 /// MGNR(Sub, [i8 1, 2), OBO::NoUnsignedWrap) == [1, 0)
147 static ConstantRange makeGuaranteedNoWrapRegion(Instruction::BinaryOps BinOp,
148 const ConstantRange &Other,
149 unsigned NoWrapKind);
150
151 /// Produce the range that contains X if and only if "X BinOp Other" does
152 /// not wrap.
153 static ConstantRange makeExactNoWrapRegion(Instruction::BinaryOps BinOp,
154 const APInt &Other,
155 unsigned NoWrapKind);
156
157 /// Returns true if ConstantRange calculations are supported for intrinsic
158 /// with \p IntrinsicID.
159 static bool isIntrinsicSupported(Intrinsic::ID IntrinsicID);
160
161 /// Compute range of intrinsic result for the given operand ranges.
162 static ConstantRange intrinsic(Intrinsic::ID IntrinsicID,
163 ArrayRef<ConstantRange> Ops);
164
165 /// Set up \p Pred and \p RHS such that
166 /// ConstantRange::makeExactICmpRegion(Pred, RHS) == *this. Return true if
167 /// successful.
168 bool getEquivalentICmp(CmpInst::Predicate &Pred, APInt &RHS) const;
169
170 /// Return the lower value for this range.
171 const APInt &getLower() const { return Lower; }
172
173 /// Return the upper value for this range.
174 const APInt &getUpper() const { return Upper; }
175
176 /// Get the bit width of this ConstantRange.
177 uint32_t getBitWidth() const { return Lower.getBitWidth(); }
178
179 /// Return true if this set contains all of the elements possible
180 /// for this data-type.
181 bool isFullSet() const;
182
183 /// Return true if this set contains no members.
184 bool isEmptySet() const;
185
186 /// Return true if this set wraps around the unsigned domain. Special cases:
187 /// * Empty set: Not wrapped.
188 /// * Full set: Not wrapped.
189 /// * [X, 0) == [X, Max]: Not wrapped.
190 bool isWrappedSet() const;
191
192 /// Return true if the exclusive upper bound wraps around the unsigned
193 /// domain. Special cases:
194 /// * Empty set: Not wrapped.
195 /// * Full set: Not wrapped.
196 /// * [X, 0): Wrapped.
197 bool isUpperWrapped() const;
198
199 /// Return true if this set wraps around the signed domain. Special cases:
200 /// * Empty set: Not wrapped.
201 /// * Full set: Not wrapped.
202 /// * [X, SignedMin) == [X, SignedMax]: Not wrapped.
203 bool isSignWrappedSet() const;
204
205 /// Return true if the (exclusive) upper bound wraps around the signed
206 /// domain. Special cases:
207 /// * Empty set: Not wrapped.
208 /// * Full set: Not wrapped.
209 /// * [X, SignedMin): Wrapped.
210 bool isUpperSignWrapped() const;
211
212 /// Return true if the specified value is in the set.
213 bool contains(const APInt &Val) const;
214
215 /// Return true if the other range is a subset of this one.
216 bool contains(const ConstantRange &CR) const;
217
218 /// If this set contains a single element, return it, otherwise return null.
219 const APInt *getSingleElement() const {
220 if (Upper == Lower + 1)
221 return &Lower;
222 return nullptr;
223 }
224
225 /// If this set contains all but a single element, return it, otherwise return
226 /// null.
227 const APInt *getSingleMissingElement() const {
228 if (Lower == Upper + 1)
229 return &Upper;
230 return nullptr;
231 }
232
233 /// Return true if this set contains exactly one member.
234 bool isSingleElement() const { return getSingleElement() != nullptr; }
235
236 /// Compare set size of this range with the range CR.
237 bool isSizeStrictlySmallerThan(const ConstantRange &CR) const;
238
239 /// Compare set size of this range with Value.
240 bool isSizeLargerThan(uint64_t MaxSize) const;
241
242 /// Return true if all values in this range are negative.
243 bool isAllNegative() const;
244
245 /// Return true if all values in this range are non-negative.
246 bool isAllNonNegative() const;
247
248 /// Return the largest unsigned value contained in the ConstantRange.
249 APInt getUnsignedMax() const;
250
251 /// Return the smallest unsigned value contained in the ConstantRange.
252 APInt getUnsignedMin() const;
253
254 /// Return the largest signed value contained in the ConstantRange.
255 APInt getSignedMax() const;
256
257 /// Return the smallest signed value contained in the ConstantRange.
258 APInt getSignedMin() const;
259
260 /// Return true if this range is equal to another range.
261 bool operator==(const ConstantRange &CR) const {
262 return Lower == CR.Lower && Upper == CR.Upper;
263 }
264 bool operator!=(const ConstantRange &CR) const {
265 return !operator==(CR);
266 }
267
268 /// Compute the maximal number of active bits needed to represent every value
269 /// in this range.
270 unsigned getActiveBits() const;
271
272 /// Compute the maximal number of bits needed to represent every value
273 /// in this signed range.
274 unsigned getMinSignedBits() const;
275
276 /// Subtract the specified constant from the endpoints of this constant range.
277 ConstantRange subtract(const APInt &CI) const;
278
279 /// Subtract the specified range from this range (aka relative complement of
280 /// the sets).
281 ConstantRange difference(const ConstantRange &CR) const;
282
283 /// If represented precisely, the result of some range operations may consist
284 /// of multiple disjoint ranges. As only a single range may be returned, any
285 /// range covering these disjoint ranges constitutes a valid result, but some
286 /// may be more useful than others depending on context. The preferred range
287 /// type specifies whether a range that is non-wrapping in the unsigned or
288 /// signed domain, or has the smallest size, is preferred. If a signedness is
289 /// preferred but all ranges are non-wrapping or all wrapping, then the
290 /// smallest set size is preferred. If there are multiple smallest sets, any
291 /// one of them may be returned.
292 enum PreferredRangeType { Smallest, Unsigned, Signed };
293
294 /// Return the range that results from the intersection of this range with
295 /// another range. If the intersection is disjoint, such that two results
296 /// are possible, the preferred range is determined by the PreferredRangeType.
297 ConstantRange intersectWith(const ConstantRange &CR,
298 PreferredRangeType Type = Smallest) const;
299
300 /// Return the range that results from the union of this range
301 /// with another range. The resultant range is guaranteed to include the
302 /// elements of both sets, but may contain more. For example, [3, 9) union
303 /// [12,15) is [3, 15), which includes 9, 10, and 11, which were not included
304 /// in either set before.
305 ConstantRange unionWith(const ConstantRange &CR,
306 PreferredRangeType Type = Smallest) const;
307
308 /// Return a new range representing the possible values resulting
309 /// from an application of the specified cast operator to this range. \p
310 /// BitWidth is the target bitwidth of the cast. For casts which don't
311 /// change bitwidth, it must be the same as the source bitwidth. For casts
312 /// which do change bitwidth, the bitwidth must be consistent with the
313 /// requested cast and source bitwidth.
314 ConstantRange castOp(Instruction::CastOps CastOp,
315 uint32_t BitWidth) const;
316
317 /// Return a new range in the specified integer type, which must
318 /// be strictly larger than the current type. The returned range will
319 /// correspond to the possible range of values if the source range had been
320 /// zero extended to BitWidth.
321 ConstantRange zeroExtend(uint32_t BitWidth) const;
322
323 /// Return a new range in the specified integer type, which must
324 /// be strictly larger than the current type. The returned range will
325 /// correspond to the possible range of values if the source range had been
326 /// sign extended to BitWidth.
327 ConstantRange signExtend(uint32_t BitWidth) const;
328
329 /// Return a new range in the specified integer type, which must be
330 /// strictly smaller than the current type. The returned range will
331 /// correspond to the possible range of values if the source range had been
332 /// truncated to the specified type.
333 ConstantRange truncate(uint32_t BitWidth) const;
334
335 /// Make this range have the bit width given by \p BitWidth. The
336 /// value is zero extended, truncated, or left alone to make it that width.
337 ConstantRange zextOrTrunc(uint32_t BitWidth) const;
338
339 /// Make this range have the bit width given by \p BitWidth. The
340 /// value is sign extended, truncated, or left alone to make it that width.
341 ConstantRange sextOrTrunc(uint32_t BitWidth) const;
342
343 /// Return a new range representing the possible values resulting
344 /// from an application of the specified binary operator to an left hand side
345 /// of this range and a right hand side of \p Other.
346 ConstantRange binaryOp(Instruction::BinaryOps BinOp,
347 const ConstantRange &Other) const;
348
349 /// Return a new range representing the possible values resulting
350 /// from an application of the specified overflowing binary operator to a
351 /// left hand side of this range and a right hand side of \p Other given
352 /// the provided knowledge about lack of wrapping \p NoWrapKind.
353 ConstantRange overflowingBinaryOp(Instruction::BinaryOps BinOp,
354 const ConstantRange &Other,
355 unsigned NoWrapKind) const;
356
357 /// Return a new range representing the possible values resulting
358 /// from an addition of a value in this range and a value in \p Other.
359 ConstantRange add(const ConstantRange &Other) const;
360
361 /// Return a new range representing the possible values resulting
362 /// from an addition with wrap type \p NoWrapKind of a value in this
363 /// range and a value in \p Other.
364 /// If the result range is disjoint, the preferred range is determined by the
365 /// \p PreferredRangeType.
366 ConstantRange addWithNoWrap(const ConstantRange &Other, unsigned NoWrapKind,
367 PreferredRangeType RangeType = Smallest) const;
368
369 /// Return a new range representing the possible values resulting
370 /// from a subtraction of a value in this range and a value in \p Other.
371 ConstantRange sub(const ConstantRange &Other) const;
372
373 /// Return a new range representing the possible values resulting
374 /// from an subtraction with wrap type \p NoWrapKind of a value in this
375 /// range and a value in \p Other.
376 /// If the result range is disjoint, the preferred range is determined by the
377 /// \p PreferredRangeType.
378 ConstantRange subWithNoWrap(const ConstantRange &Other, unsigned NoWrapKind,
379 PreferredRangeType RangeType = Smallest) const;
380
381 /// Return a new range representing the possible values resulting
382 /// from a multiplication of a value in this range and a value in \p Other,
383 /// treating both this and \p Other as unsigned ranges.
384 ConstantRange multiply(const ConstantRange &Other) const;
385
386 /// Return a new range representing the possible values resulting
387 /// from a signed maximum of a value in this range and a value in \p Other.
388 ConstantRange smax(const ConstantRange &Other) const;
389
390 /// Return a new range representing the possible values resulting
391 /// from an unsigned maximum of a value in this range and a value in \p Other.
392 ConstantRange umax(const ConstantRange &Other) const;
393
394 /// Return a new range representing the possible values resulting
395 /// from a signed minimum of a value in this range and a value in \p Other.
396 ConstantRange smin(const ConstantRange &Other) const;
397
398 /// Return a new range representing the possible values resulting
399 /// from an unsigned minimum of a value in this range and a value in \p Other.
400 ConstantRange umin(const ConstantRange &Other) const;
401
402 /// Return a new range representing the possible values resulting
403 /// from an unsigned division of a value in this range and a value in
404 /// \p Other.
405 ConstantRange udiv(const ConstantRange &Other) const;
406
407 /// Return a new range representing the possible values resulting
408 /// from a signed division of a value in this range and a value in
409 /// \p Other. Division by zero and division of SignedMin by -1 are considered
410 /// undefined behavior, in line with IR, and do not contribute towards the
411 /// result.
412 ConstantRange sdiv(const ConstantRange &Other) const;
413
414 /// Return a new range representing the possible values resulting
415 /// from an unsigned remainder operation of a value in this range and a
416 /// value in \p Other.
417 ConstantRange urem(const ConstantRange &Other) const;
418
419 /// Return a new range representing the possible values resulting
420 /// from a signed remainder operation of a value in this range and a
421 /// value in \p Other.
422 ConstantRange srem(const ConstantRange &Other) const;
423
424 /// Return a new range representing the possible values resulting from
425 /// a binary-xor of a value in this range by an all-one value,
426 /// aka bitwise complement operation.
427 ConstantRange binaryNot() const;
428
429 /// Return a new range representing the possible values resulting
430 /// from a binary-and of a value in this range by a value in \p Other.
431 ConstantRange binaryAnd(const ConstantRange &Other) const;
432
433 /// Return a new range representing the possible values resulting
434 /// from a binary-or of a value in this range by a value in \p Other.
435 ConstantRange binaryOr(const ConstantRange &Other) const;
436
437 /// Return a new range representing the possible values resulting
438 /// from a binary-xor of a value in this range by a value in \p Other.
439 ConstantRange binaryXor(const ConstantRange &Other) const;
440
441 /// Return a new range representing the possible values resulting
442 /// from a left shift of a value in this range by a value in \p Other.
443 /// TODO: This isn't fully implemented yet.
444 ConstantRange shl(const ConstantRange &Other) const;
445
446 /// Return a new range representing the possible values resulting from a
447 /// logical right shift of a value in this range and a value in \p Other.
448 ConstantRange lshr(const ConstantRange &Other) const;
449
450 /// Return a new range representing the possible values resulting from a
451 /// arithmetic right shift of a value in this range and a value in \p Other.
452 ConstantRange ashr(const ConstantRange &Other) const;
453
454 /// Perform an unsigned saturating addition of two constant ranges.
455 ConstantRange uadd_sat(const ConstantRange &Other) const;
456
457 /// Perform a signed saturating addition of two constant ranges.
458 ConstantRange sadd_sat(const ConstantRange &Other) const;
459
460 /// Perform an unsigned saturating subtraction of two constant ranges.
461 ConstantRange usub_sat(const ConstantRange &Other) const;
462
463 /// Perform a signed saturating subtraction of two constant ranges.
464 ConstantRange ssub_sat(const ConstantRange &Other) const;
465
466 /// Perform an unsigned saturating multiplication of two constant ranges.
467 ConstantRange umul_sat(const ConstantRange &Other) const;
468
469 /// Perform a signed saturating multiplication of two constant ranges.
470 ConstantRange smul_sat(const ConstantRange &Other) const;
471
472 /// Perform an unsigned saturating left shift of this constant range by a
473 /// value in \p Other.
474 ConstantRange ushl_sat(const ConstantRange &Other) const;
475
476 /// Perform a signed saturating left shift of this constant range by a
477 /// value in \p Other.
478 ConstantRange sshl_sat(const ConstantRange &Other) const;
479
480 /// Return a new range that is the logical not of the current set.
481 ConstantRange inverse() const;
482
483 /// Calculate absolute value range. If the original range contains signed
484 /// min, then the resulting range will contain signed min if and only if
485 /// \p IntMinIsPoison is false.
486 ConstantRange abs(bool IntMinIsPoison = false) const;
487
488 /// Represents whether an operation on the given constant range is known to
489 /// always or never overflow.
490 enum class OverflowResult {
491 /// Always overflows in the direction of signed/unsigned min value.
492 AlwaysOverflowsLow,
493 /// Always overflows in the direction of signed/unsigned max value.
494 AlwaysOverflowsHigh,
495 /// May or may not overflow.
496 MayOverflow,
497 /// Never overflows.
498 NeverOverflows,
499 };
500
501 /// Return whether unsigned add of the two ranges always/never overflows.
502 OverflowResult unsignedAddMayOverflow(const ConstantRange &Other) const;
503
504 /// Return whether signed add of the two ranges always/never overflows.
505 OverflowResult signedAddMayOverflow(const ConstantRange &Other) const;
506
507 /// Return whether unsigned sub of the two ranges always/never overflows.
508 OverflowResult unsignedSubMayOverflow(const ConstantRange &Other) const;
509
510 /// Return whether signed sub of the two ranges always/never overflows.
511 OverflowResult signedSubMayOverflow(const ConstantRange &Other) const;
512
513 /// Return whether unsigned mul of the two ranges always/never overflows.
514 OverflowResult unsignedMulMayOverflow(const ConstantRange &Other) const;
515
516 /// Print out the bounds to a stream.
517 void print(raw_ostream &OS) const;
518
519 /// Allow printing from a debugger easily.
520 void dump() const;
521};
522
523inline raw_ostream &operator<<(raw_ostream &OS, const ConstantRange &CR) {
524 CR.print(OS);
525 return OS;
526}
527
528/// Parse out a conservative ConstantRange from !range metadata.
529///
530/// E.g. if RangeMD is !{i32 0, i32 10, i32 15, i32 20} then return [0, 20).
531ConstantRange getConstantRangeFromMetadata(const MDNode &RangeMD);
532
533} // end namespace llvm
534
535#endif // LLVM_IR_CONSTANTRANGE_H
536