Index: llvm/lib/Transforms/Scalar/LoopInterchange.cpp
===================================================================
--- llvm/lib/Transforms/Scalar/LoopInterchange.cpp
+++ llvm/lib/Transforms/Scalar/LoopInterchange.cpp
@@ -656,6 +656,65 @@
       return false;
     }
   }
+
+  // TODO: Handle triangular loops of another form.
+  // e.g. for(int i=0;i<N;i++)
+  //        for(int j=0;j<i;j++)
+  // or,
+  //      for(int i=0;i<N;i++)
+  //        for(int j=0;j*i<N;j++)
+  BasicBlock *InnerLoopLatch = InnerLoop->getLoopLatch();
+  BranchInst *InnerLoopLatchBI =
+      dyn_cast<BranchInst>(InnerLoopLatch->getTerminator());
+  if (!InnerLoopLatchBI->isConditional())
+    return false;
+  if (CmpInst *InnerLoopCmp =
+          dyn_cast<CmpInst>(InnerLoopLatchBI->getCondition())) {
+    Value *Op0 = InnerLoopCmp->getOperand(0);
+    Value *Op1 = InnerLoopCmp->getOperand(1);
+
+    // LHS and RHS of the inner loop exit condition, e.g.,
+    // in "for(int j=0;j<i;j++)", LHS is j and RHS is i.
+    Value *Left = nullptr;
+    Value *Right = nullptr;
+
+    // Check if V only involves inner loop induction variable.
+    // Return true if V is InnerInduction, or a cast from
+    // InnerInduction, or a binary operator that involves
+    // InnerInduction and a constant.
+    std::function<bool(Value *)> IsPathToIndVar;
+    IsPathToIndVar = [&InnerInduction, &IsPathToIndVar](Value *V) -> bool {
+      if (V == InnerInduction)
+        return true;
+      if (isa<Constant>(V))
+        return true;
+      Instruction *I = dyn_cast<Instruction>(V);
+      if (!I)
+        return false;
+      if (isa<CastInst>(I))
+        return IsPathToIndVar(I->getOperand(0));
+      if (isa<BinaryOperator>(I))
+        return IsPathToIndVar(I->getOperand(0)) &&
+               IsPathToIndVar(I->getOperand(1));
+      return false;
+    };
+
+    if (IsPathToIndVar(Op0) && !isa<Constant>(Op0)) {
+      Left = Op0;
+      Right = Op1;
+    } else if (IsPathToIndVar(Op1) && !isa<Constant>(Op1)) {
+      Left = Op1;
+      Right = Op0;
+    }
+
+    if (Left == nullptr)
+      return false;
+
+    const SCEV *S = SE->getSCEV(Right);
+    if (!SE->isLoopInvariant(S, OuterLoop))
+      return false;
+  }
+
   return true;
 }
 
Index: llvm/test/Transforms/LoopInterchange/inner-indvar-depend-on-outer-indvar.ll
===================================================================
--- /dev/null
+++ llvm/test/Transforms/LoopInterchange/inner-indvar-depend-on-outer-indvar.ll
@@ -0,0 +1,153 @@
+; REQUIRES: asserts
+; RUN: opt < %s -basic-aa -loop-interchange -verify-dom-info -verify-loop-info \
+; RUN:     -S -debug 2>&1 | FileCheck %s
+
+@A = common global [100 x [100 x i64]] zeroinitializer
+@N = dso_local local_unnamed_addr global i64 100, align 8
+
+
+;;  for(int i=0;i<100;i++)
+;;    for(int j=0;j<i;j++)
+;;      A[j][i] = A[j][i]+k;
+
+;; Inner loop induction variable exit condition depends on the
+;; outer loop induction variable, i.e., triangular loops.
+; CHECK: Loop structure not understood by pass
+; CHECK: Not interchanging loops. Cannot prove legality.
+
+define void @interchange_01(i64 %k) {
+entry:
+  br label %for1.header
+
+for1.header:
+  %i = phi i64 [ 0, %entry ], [ %i.next, %for1.inc10 ]
+  br label %for2
+
+for2:
+  %j = phi i64 [ %j.next, %for2 ], [ 0, %for1.header ]
+  %arrayidx5 = getelementptr inbounds [100 x [100 x i64]], [100 x [100 x i64]]* @A, i64 0, i64 %j, i64 %i
+  %lv = load i64, i64* %arrayidx5
+  %add = add nsw i64 %lv, %k
+  store i64 %add, i64* %arrayidx5
+  %j.next = add nuw nsw i64 %j, 1
+  %exitcond = icmp eq i64 %j, %i
+  br i1 %exitcond, label %for1.inc10, label %for2
+
+for1.inc10:
+  %i.next = add nuw nsw i64 %i, 1
+  %exitcond26 = icmp eq i64 %i, 99
+  br i1 %exitcond26, label %for.end12, label %for1.header
+
+for.end12:
+  ret void
+}
+
+
+;;  for(int i=0;i<100;i++)
+;;    for(int j=0;j+i<100;j++)
+;;      A[j][i] = A[j][i]+k;
+
+;; Inner loop induction variable exit condition depends on the
+;; outer loop induction variable, i.e., triangular loops.
+; CHECK: Loop structure not understood by pass
+; CHECK: Not interchanging loops. Cannot prove legality.
+
+define void @interchange_02(i64 %k) {
+entry:
+  br label %for1.header
+
+for1.header:
+  %i = phi i64 [ 0, %entry ], [ %i.next, %for1.inc10 ]
+  br label %for2
+
+for2:
+  %j = phi i64 [ %j.next, %for2 ], [ 0, %for1.header ]
+  %arrayidx5 = getelementptr inbounds [100 x [100 x i64]], [100 x [100 x i64]]* @A, i64 0, i64 %j, i64 %i
+  %lv = load i64, i64* %arrayidx5
+  %add = add nsw i64 %lv, %k
+  store i64 %add, i64* %arrayidx5
+  %0 = add nuw nsw i64 %j, %i
+  %j.next = add nuw nsw i64 %j, 1
+  %exitcond = icmp eq i64 %0, 100
+  br i1 %exitcond, label %for1.inc10, label %for2
+
+for1.inc10:
+  %i.next = add nuw nsw i64 %i, 1
+  %exitcond26 = icmp eq i64 %i, 99
+  br i1 %exitcond26, label %for.end12, label %for1.header
+
+for.end12:
+  ret void
+}
+
+;;  for(int i=0;i<100;i++)
+;;    for(int j=0;i>j;j++)
+;;      A[j][i] = A[j][i]+k;
+
+;; Inner loop induction variable exit condition depends on the
+;; outer loop induction variable, i.e., triangular loops.
+; CHECK: Loop structure not understood by pass
+; CHECK: Not interchanging loops. Cannot prove legality.
+
+define void @interchange_03(i64 %k) {
+entry:
+  br label %for1.header
+
+for1.header:
+  %i = phi i64 [ 0, %entry ], [ %i.next, %for1.inc10 ]
+  br label %for2
+
+for2:
+  %j = phi i64 [ %j.next, %for2 ], [ 0, %for1.header ]
+  %arrayidx5 = getelementptr inbounds [100 x [100 x i64]], [100 x [100 x i64]]* @A, i64 0, i64 %j, i64 %i
+  %lv = load i64, i64* %arrayidx5
+  %add = add nsw i64 %lv, %k
+  store i64 %add, i64* %arrayidx5
+  %j.next = add nuw nsw i64 %j, 1
+  %exitcond = icmp ne i64 %i, %j
+  br i1 %exitcond, label %for2, label %for1.inc10
+
+for1.inc10:
+  %i.next = add nuw nsw i64 %i, 1
+  %exitcond26 = icmp eq i64 %i, 99
+  br i1 %exitcond26, label %for.end12, label %for1.header
+
+for.end12:
+  ret void
+}
+
+;;  for(int i=0;i<100;i++)
+;;    for(int j=0;N>j;j++)
+;;      A[j][i] = A[j][i]+k;
+
+;; Inner loop induction variable exit condition depends on
+;; an outer loop invariant, can do interchange.
+; CHECK: Loops interchanged
+
+define void @interchange_04(i64 %k) {
+entry:
+  %0 = load i64, i64* @N, align 4
+  br label %for1.header
+
+for1.header:
+  %i = phi i64 [ 0, %entry ], [ %i.next, %for1.inc10 ]
+  br label %for2
+
+for2:
+  %j = phi i64 [ %j.next, %for2 ], [ 0, %for1.header ]
+  %arrayidx5 = getelementptr inbounds [100 x [100 x i64]], [100 x [100 x i64]]* @A, i64 0, i64 %j, i64 %i
+  %lv = load i64, i64* %arrayidx5
+  %add = add nsw i64 %lv, %k
+  store i64 %add, i64* %arrayidx5
+  %j.next = add nuw nsw i64 %j, 1
+  %exitcond = icmp ne i64 %0, %j
+  br i1 %exitcond, label %for2, label %for1.inc10
+
+for1.inc10:
+  %i.next = add nuw nsw i64 %i, 1
+  %exitcond26 = icmp eq i64 %i, 99
+  br i1 %exitcond26, label %for.end12, label %for1.header
+
+for.end12:
+  ret void
+}