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 40 namespace llvm { 41 42 class MDNode; 43 class raw_ostream; 44 struct KnownBits; 45 46 /// This class represents a range of values. 47 class 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 60 public: 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 }; 522 523 inline 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). 531 ConstantRange getConstantRangeFromMetadata(const MDNode &RangeMD); 532 533 } // end namespace llvm 534 535 #endif // LLVM_IR_CONSTANTRANGE_H 536