diff --git a/llvm/include/llvm/Analysis/ScalarEvolution.h b/llvm/include/llvm/Analysis/ScalarEvolution.h --- a/llvm/include/llvm/Analysis/ScalarEvolution.h +++ b/llvm/include/llvm/Analysis/ScalarEvolution.h @@ -2023,11 +2023,38 @@ createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI); /// Compute the backedge taken count knowing the interval difference, and - /// the stride for an inequality. Result takes the form: - /// (Delta + (Stride - 1)) udiv Stride. - /// Caller must ensure that this expression either does not overflow or - /// that the result is undefined if it does. - const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride); + /// the stride for an inequality. + /// + /// Caller must ensure that non-negative N exists such that + /// (Start + Stride * N) >= End, and that computing "(Start + Stride * N)" + /// doesn't overflow. In other words: + /// 1. If IsSigned is true, Start <=s End. Otherwise, Start <=u End. + /// 2. If End is not equal to start and IsSigned is true, Stride >s 0. If + /// End is not equal to start and IsSigned is false, Stride >u 0. + /// 3. The index variable doesn't overflow. + /// + /// If the preconditions hold, the backedge taken count is N. + /// + /// IsSigned determines whether End, Start, and Stride are treated as + /// signed values, for the purpose of optimizing the form of the result. + /// + /// This function tries to use an optimized form: + /// ((End - Start) + (Stride - 1)) /u Stride + /// + /// If it can't prove the addition doesn't overflow in that form, it uses + /// getUDivCeilSCEV. + const SCEV *computeBECount(bool IsSigned, const SCEV *Start, const SCEV *End, + const SCEV *Stride); + + /// Compute ceil(N / D). N and D are treated as unsigned values. + /// + /// Since SCEV doesn't have native ceiling division, this generates a + /// SCEV expression of the following form: + /// + /// umin(N, 1) + floor((N - umin(N, 1)) / D) + /// + /// A denominator of zero or poison is handled the same way as getUDivExpr(). + const SCEV *getUDivCeilSCEV(const SCEV *N, const SCEV *D); /// Compute the maximum backedge count based on the range of values /// permitted by Start, End, and Stride. This is for loops of the form diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp --- a/llvm/lib/Analysis/ScalarEvolution.cpp +++ b/llvm/lib/Analysis/ScalarEvolution.cpp @@ -11497,11 +11497,108 @@ return (std::move(MinValue) + MaxStrideMinusOne).ugt(MinRHS); } -const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, - const SCEV *Step) { - const SCEV *One = getOne(Step->getType()); - Delta = getAddExpr(Delta, getMinusSCEV(Step, One)); - return getUDivExpr(Delta, Step); +const SCEV *ScalarEvolution::computeBECount(bool IsSigned, const SCEV *Start, + const SCEV *End, + const SCEV *Stride) { + // The basic formula here is ceil((End - Start) / Stride). Since SCEV + // doesn't natively have division that rounds up, we need to convert to + // floor division. + // + // MayOverflow is whether adding (End - Start) + (Stride - 1) + // can overflow if Stride is positive. It's a precondition of the + // function that "End - Start" doesn't overflow. We handle the case where + // Stride isn't positive later. + // + // In practice, the arithmetic almost never overflows, but we have to prove + // it. We have a variety of ways to come up with a proof. + const SCEV *One = getOne(Stride->getType()); + bool MayOverflow = [&] { + if (auto *StrideC = dyn_cast(Stride)) { + if (StrideC->getAPInt().isPowerOf2()) { + // Suppose Stride is a power of two, and Start/End are unsigned + // integers. Let UMAX be the largest representable unsigned + // integer. + // + // By the preconditions of this function (see comment in header), we + // know "(Start + Stride * N)" >= End, and this doesn't overflow. + // As a formula: + // + // End <= (Start + Stride * N) <= UMAX + // + // Subtracting Start from all the terms: + // + // End - Start <= Stride * N <= UMAX - Start + // + // Since Start is unsigned, UMAX - Start <= UMAX. Therefore: + // + // End - Start <= Stride * N <= UMAX + // + // Stride * N is a multiple of Stride. Therefore, + // + // End - Start <= Stride * N <= UMAX - (UMAX mod Stride) + // + // Since Stride is a power of two, UMAX + 1 is divisible by Stride. + // Therefore, UMAX mod Stride == Stride - 1. So we can write: + // + // End - Start <= Stride * N <= UMAX - Stride - 1 + // + // Dropping the middle term: + // + // End - Start <= UMAX - Stride - 1 + // + // Adding Stride - 1 to both sides: + // + // (End - Start) + (Stride - 1) <= UMAX + // + // In other words, the addition doesn't have unsigned overflow. + // + // A similar proof works if we treat Start/End as signed values. + // Just rewrite steps before "End - Start <= Stride * N <= UMAX" to + // use signed max instead of unsigned max. Note that we're trying + // to prove a lack of unsigned overflow in either case. + return false; + } + } + if (Start == Stride || Start == getMinusSCEV(Stride, One)) { + // If Start is equal to Stride, (End - Start) + (Stride - 1) == End - 1. + // If !IsSigned, 0 =s 0". + // Therefore, "0 <=s End - Start <=s INT_MAX - Start <= INT_MAX". + // IsSigned also implies "0 <=s Stride - 1 getType())); + const SCEV *NMinusOne = getMinusSCEV(N, MinNOne); + return getAddExpr(MinNOne, getUDivExpr(NMinusOne, D)); } const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start, @@ -11540,8 +11637,8 @@ APInt MaxEnd = IsSigned ? APIntOps::smin(getSignedRangeMax(End), Limit) : APIntOps::umin(getUnsignedRangeMax(End), Limit); - MaxBECount = computeBECount(getConstant(MaxEnd - MinStart) /* Delta */, - getConstant(StrideForMaxBECount) /* Step */); + MaxBECount = getUDivCeilSCEV(getConstant(MaxEnd - MinStart) /* Delta */, + getConstant(StrideForMaxBECount) /* Step */); return MaxBECount; } @@ -11699,7 +11796,7 @@ // is the LHS value of the less-than comparison the first time it is evaluated // and End is the RHS. const SCEV *BECountIfBackedgeTaken = - computeBECount(getMinusSCEV(End, Start), Stride); + computeBECount(IsSigned, Start, End, Stride); // If the loop entry is guarded by the result of the backedge test of the // first loop iteration, then we know the backedge will be taken at least // once and so the backedge taken count is as above. If not then we use the @@ -11718,7 +11815,7 @@ End = RHS; else End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start); - BECount = computeBECount(getMinusSCEV(End, Start), Stride); + BECount = computeBECount(IsSigned, Start, End, Stride); } const SCEV *MaxBECount; @@ -11804,7 +11901,7 @@ return End; } - const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride); + const SCEV *BECount = computeBECount(IsSigned, End, Start, Stride); APInt MaxStart = IsSigned ? getSignedRangeMax(Start) : getUnsignedRangeMax(Start); @@ -11825,11 +11922,8 @@ const SCEV *MaxBECount = isa(BECount) ? BECount - : computeBECount(getConstant(MaxStart - MinEnd), - getConstant(MinStride)); - - if (isa(MaxBECount)) - MaxBECount = BECount; + : getUDivCeilSCEV(getConstant(MaxStart - MinEnd), + getConstant(MinStride)); return ExitLimit(BECount, MaxBECount, false, Predicates); } diff --git a/llvm/test/Analysis/ScalarEvolution/2008-11-18-Stride1.ll b/llvm/test/Analysis/ScalarEvolution/2008-11-18-Stride1.ll --- a/llvm/test/Analysis/ScalarEvolution/2008-11-18-Stride1.ll +++ b/llvm/test/Analysis/ScalarEvolution/2008-11-18-Stride1.ll @@ -1,14 +1,9 @@ ; RUN: opt < %s -analyze -enable-new-pm=0 -scalar-evolution | FileCheck %s ; RUN: opt < %s -disable-output "-passes=print" 2>&1 | FileCheck %s -; CHECK: Loop %bb: backedge-taken count is ((-5 + %x) /u 3) +; CHECK: Loop %bb: backedge-taken count is (((-7 + (-1 * (1 umin (-7 + %x))) + %x) /u 3) + (1 umin (-7 + %x))) ; CHECK: Loop %bb: max backedge-taken count is 1431655764 - -; ScalarEvolution can't compute a trip count because it doesn't know if -; dividing by the stride will have a remainder. This could theoretically -; be teaching it how to use a more elaborate trip count computation. - define i32 @f(i32 %x) nounwind readnone { entry: %0 = icmp ugt i32 %x, 4 ; [#uses=1] diff --git a/llvm/test/Analysis/ScalarEvolution/2008-11-18-Stride2.ll b/llvm/test/Analysis/ScalarEvolution/2008-11-18-Stride2.ll --- a/llvm/test/Analysis/ScalarEvolution/2008-11-18-Stride2.ll +++ b/llvm/test/Analysis/ScalarEvolution/2008-11-18-Stride2.ll @@ -1,12 +1,10 @@ ; RUN: opt < %s -analyze -enable-new-pm=0 -scalar-evolution 2>&1 | FileCheck %s ; RUN: opt < %s -disable-output "-passes=print" 2>&1 2>&1 | FileCheck %s -; CHECK: Loop %bb: backedge-taken count is ((999 + (-1 * %x)) /u 3) +; CHECK: Loop %bb: backedge-taken count is (((997 + (-1 * (1 umin (997 + (-1 * %x)))) + (-1 * %x)) /u 3) + (1 umin (997 + (-1 * %x)))) ; CHECK: Loop %bb: max backedge-taken count is 334 - -; This is a tricky testcase for unsigned wrap detection which ScalarEvolution -; doesn't yet know how to do. +; This is a tricky testcase for unsigned wrap detection. define i32 @f(i32 %x) nounwind readnone { entry: diff --git a/llvm/test/Analysis/ScalarEvolution/trip-count-unknown-stride.ll b/llvm/test/Analysis/ScalarEvolution/trip-count-unknown-stride.ll --- a/llvm/test/Analysis/ScalarEvolution/trip-count-unknown-stride.ll +++ b/llvm/test/Analysis/ScalarEvolution/trip-count-unknown-stride.ll @@ -4,8 +4,8 @@ ; ScalarEvolution should be able to compute trip count of the loop by proving ; that this is not an infinite loop with side effects. -; CHECK: Determining loop execution counts for: @foo1 -; CHECK: backedge-taken count is ((-1 + %n) /u %s) +; CHECK-LABEL: Determining loop execution counts for: @foo1 +; CHECK: backedge-taken count is ((-1 + (-1 * %s) + (1 umax %s) + %n) /u (1 umax %s)) ; We should have a conservative estimate for the max backedge taken count for ; loops with unknown stride. @@ -34,8 +34,8 @@ ; Check that we are able to compute trip count of a loop without an entry guard. -; CHECK: Determining loop execution counts for: @foo2 -; CHECK: backedge-taken count is ((-1 + (%n smax %s)) /u %s) +; CHECK-LABEL: Determining loop execution counts for: @foo2 +; CHECK: backedge-taken count is ((-1 + (-1 * %s) + (1 umax %s) + (%n smax %s)) /u (1 umax %s)) ; We should have a conservative estimate for the max backedge taken count for ; loops with unknown stride. @@ -61,7 +61,7 @@ ; Check that without mustprogress we don't make assumptions about infinite ; loops being UB. -; CHECK: Determining loop execution counts for: @foo3 +; CHECK-LABEL: Determining loop execution counts for: @foo3 ; CHECK: Loop %for.body: Unpredictable backedge-taken count. ; CHECK: Loop %for.body: Unpredictable max backedge-taken count. @@ -84,8 +84,8 @@ } ; Same as foo2, but with mustprogress on loop, not function -; CHECK: Determining loop execution counts for: @foo4 -; CHECK: backedge-taken count is ((-1 + (%n smax %s)) /u %s) +; CHECK-LABEL: Determining loop execution counts for: @foo4 +; CHECK: backedge-taken count is ((-1 + (-1 * %s) + (1 umax %s) + (%n smax %s)) /u (1 umax %s)) ; CHECK: max backedge-taken count is -1 define void @foo4(i32* nocapture %A, i32 %n, i32 %s) { @@ -106,5 +106,31 @@ ret void } +; A more complex case with pre-increment compare instead of post-increment. +; CHECK-LABEL: Determining loop execution counts for: @foo5 +; CHECK: Loop %for.body: backedge-taken count is ((((-1 * (1 umin ((-1 * %start) + (%n smax %start)))) + (-1 * %start) + (%n smax %start)) /u (1 umax %s)) + (1 umin ((-1 * %start) + (%n smax %start)))) + +; We should have a conservative estimate for the max backedge taken count for +; loops with unknown stride. +; CHECK: max backedge-taken count is -1 + +define void @foo5(i32* nocapture %A, i32 %n, i32 %s, i32 %start) mustprogress { +entry: + br label %for.body + +for.body: ; preds = %entry, %for.body + %i.05 = phi i32 [ %add, %for.body ], [ %start, %entry ] + %arrayidx = getelementptr inbounds i32, i32* %A, i32 %i.05 + %0 = load i32, i32* %arrayidx, align 4 + %inc = add nsw i32 %0, 1 + store i32 %inc, i32* %arrayidx, align 4 + %add = add nsw i32 %i.05, %s + %cmp = icmp slt i32 %i.05, %n + br i1 %cmp, label %for.body, label %for.end + +for.end: ; preds = %for.body, %entry + ret void +} + !8 = distinct !{!8, !9} !9 = !{!"llvm.loop.mustprogress"}