[SCEV] Introduce a guarded backedge taken count and use it in LAA and LV

Summary:
When the backedge taken codition is computed from an icmp, SCEV can
deduce the backedge taken count only if one of the sides of the icmp
is an AddRecExpr. However, due to sign/zero extensions, we sometimes
end up with something that is not an AddRecExpr.

However, we can use SCEV predicates to produce a 'guarded' expression.
This change adds a method to SCEV to get this expression, and the
SCEV predicate associated with it.

In HowManyGreaterThans and HowManyLessThans we will now add a SCEV
predicate associated with the guarded backedge taken count when the
analyzed SCEV expression is not an AddRecExpr. Note that we only do
this as an alternative to returning a 'CouldNotCompute'.

We use new feature in Loop Access Analysis and LoopVectorize to analyze
and transform more loops.

Reviewers: anemet, mzolotukhin, hfinkel, sanjoy

Subscribers: flyingforyou, mcrosier, atrick, mssimpso, sanjoy, mzolotukhin, llvm-commits

Differential Revision: http://reviews.llvm.org/D17201

llvm-svn: 265535

1 files changed, 109 insertions, 0 deletions

diff --git a/llvm/test/Analysis/ScalarEvolution/predicated-trip-count.ll b/llvm/test/Analysis/ScalarEvolution/predicated-trip-count.ll
new file mode 100644
index 00000000000..2db0a8b5777
--- /dev/null
+++ b/llvm/test/Analysis/ScalarEvolution/predicated-trip-count.ll
@@ -0,0 +1,109 @@
+; RUN: opt < %s -analyze -scalar-evolution | FileCheck %s
+
+target datalayout = "e-m:e-i64:64-f80:128-n8:16:32:64-S128"
+
+@A = weak global [1000 x i32] zeroinitializer, align 32
+
+; The resulting predicate is i16 {0,+,1} <nssw>, meanining
+; that the resulting backedge expression will be valid for:
+;   (1 + (-1 smax %M)) <= MAX_INT16
+;
+; At the limit condition for M (MAX_INT16 - 1) we have in the
+; last iteration:
+;    i0 <- MAX_INT16
+;    i0.ext <- MAX_INT16
+;
+; and therefore no wrapping happend for i0 or i0.ext
+; throughout the execution of the loop. The resulting predicated
+; backedge taken count is correct.
+
+; CHECK: Classifying expressions for: @test1
+; CHECK: %i.0.ext = sext i16 %i.0 to i32
+; CHECK-NEXT:  -->  (sext i16 {0,+,1}<%bb3> to i32)
+; CHECK:      Loop %bb3: Unpredictable backedge-taken count.
+; CHECK-NEXT: Loop %bb3: Unpredictable max backedge-taken count.
+; CHECK-NEXT: Loop %bb3: Predicated backedge-taken count is (1 + (-1 smax %M))
+; CHECK-NEXT: Predicates:
+; CHECK-NEXT:    {0,+,1}<%bb3> Added Flags: <nssw>
+define void @test1(i32 %N, i32 %M) {
+entry:
+        br label %bb3
+
+bb:             ; preds = %bb3
+        %tmp = getelementptr [1000 x i32], [1000 x i32]* @A, i32 0, i16 %i.0          ; <i32*> [#uses=1]
+        store i32 123, i32* %tmp
+        %tmp2 = add i16 %i.0, 1         ; <i32> [#uses=1]
+        br label %bb3
+
+bb3:            ; preds = %bb, %entry
+        %i.0 = phi i16 [ 0, %entry ], [ %tmp2, %bb ]            ; <i32> [#uses=3]
+        %i.0.ext = sext i16 %i.0 to i32
+        %tmp3 = icmp sle i32 %i.0.ext, %M          ; <i1> [#uses=1]
+        br i1 %tmp3, label %bb, label %bb5
+
+bb5:            ; preds = %bb3
+        br label %return
+
+return:         ; preds = %bb5
+        ret void
+}
+
+; The predicated backedge taken count is:
+;    (2 + (zext i16 %Start to i32) + ((-2 + (-1 * (sext i16 %Start to i32)))
+;                                     smax (-1 + (-1 * %M)))
+;    )
+
+; -1 + (-1 * %M) <= (-2 + (-1 * (sext i16 %Start to i32))
+; The predicated backedge taken count is 0.
+; From the IR, this is correct since we will bail out at the
+; first iteration.
+
+
+; * -1 + (-1 * %M) > (-2 + (-1 * (sext i16 %Start to i32))
+; or: %M < 1 + (sext i16 %Start to i32)
+;
+; The predicated backedge taken count is 1 + (zext i16 %Start to i32) - %M
+;
+; If %M >= MIN_INT + 1, this predicated backedge taken count would be correct (even
+; without predicates). However, for %M < MIN_INT this would be an infinite loop.
+; In these cases, the {%Start,+,-1} <nusw> predicate would be false, as the
+; final value of the expression {%Start,+,-1} expression (%M - 1) would not be
+; representable as an i16.
+
+; There is also a limit case here where the value of %M is MIN_INT. In this case
+; we still have an infinite loop, since icmp sge %x, MIN_INT will always return
+; true.
+
+; CHECK: Classifying expressions for: @test2
+
+; CHECK:      %i.0.ext = sext i16 %i.0 to i32
+; CHECK-NEXT:    -->  (sext i16 {%Start,+,-1}<%bb3> to i32)
+; CHECK:       Loop %bb3: Unpredictable backedge-taken count.
+; CHECK-NEXT:  Loop %bb3: Unpredictable max backedge-taken count.
+; CHECK-NEXT:  Loop %bb3: Predicated backedge-taken count is (2 + (sext i16 %Start to i32) + ((-2 + (-1 * (sext i16 %Start to i32))) smax (-1 + (-1 * %M))))
+; CHECK-NEXT:  Predicates:
+; CHECK-NEXT:    {%Start,+,-1}<%bb3> Added Flags: <nssw>
+
+define void @test2(i32 %N, i32 %M, i16 %Start) {
+entry:
+        br label %bb3
+
+bb:             ; preds = %bb3
+        %tmp = getelementptr [1000 x i32], [1000 x i32]* @A, i32 0, i16 %i.0          ; <i32*> [#uses=1]
+        store i32 123, i32* %tmp
+        %tmp2 = sub i16 %i.0, 1         ; <i32> [#uses=1]
+        br label %bb3
+
+bb3:            ; preds = %bb, %entry
+        %i.0 = phi i16 [ %Start, %entry ], [ %tmp2, %bb ]            ; <i32> [#uses=3]
+        %i.0.ext = sext i16 %i.0 to i32
+        %tmp3 = icmp sge i32 %i.0.ext, %M          ; <i1> [#uses=1]
+        br i1 %tmp3, label %bb, label %bb5
+
+bb5:            ; preds = %bb3
+        br label %return
+
+return:         ; preds = %bb5
+        ret void
+}
+