Index: lib/Analysis/ScalarEvolution.cpp
===================================================================
--- lib/Analysis/ScalarEvolution.cpp
+++ lib/Analysis/ScalarEvolution.cpp
@@ -77,6 +77,7 @@
 #include "llvm/IR/GlobalVariable.h"
 #include "llvm/IR/InstIterator.h"
 #include "llvm/IR/Instructions.h"
+#include "llvm/IR/Intrinsics.h"
 #include "llvm/IR/LLVMContext.h"
 #include "llvm/IR/Operator.h"
 #include "llvm/Support/CommandLine.h"
@@ -6346,6 +6347,15 @@
 
     BranchInst *LoopEntryPredicate =
       dyn_cast<BranchInst>(Pair.first->getTerminator());
+
+    if (LoopEntryPredicate)
+      for (BasicBlock::iterator I : *LoopEntryPredicate->getParent())
+        if (CallInst *CI = dyn_cast<CallInst>(I))
+          if (Function *F = CI->getCalledFunction())
+            if (F->getIntrinsicID() == Intrinsic::assume &&
+                isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
+              return true;
+
     if (!LoopEntryPredicate ||
         LoopEntryPredicate->isUnconditional())
       continue;
Index: test/Analysis/ScalarEvolution/nsw-offset-assume.ll
===================================================================
--- /dev/null
+++ test/Analysis/ScalarEvolution/nsw-offset-assume.ll
@@ -0,0 +1,83 @@
+; RUN: opt < %s -S -analyze -scalar-evolution | FileCheck %s
+
+; ScalarEvolution should be able to fold away the sign-extensions
+; on this loop with a primary induction variable incremented with
+; a nsw add of 2 (this test is derived from the nsw-offset.ll test, but uses an
+; assume instead of a preheader conditional branch to guard the loop).
+
+target datalayout = "e-p:64:64:64-i1:8:8-i8:8:8-i16:16:16-i32:32:32-i64:64:64-f32:32:32-f64:64:64-v64:64:64-v128:128:128-a0:0:64-s0:64:64-f80:128:128"
+
+define void @foo(i32 %no, double* nocapture %d, double* nocapture %q) nounwind {
+entry:
+  %n = and i32 %no, 4294967294
+  %0 = icmp sgt i32 %n, 0                         ; <i1> [#uses=1]
+  tail call void @llvm.assume(i1 %0)
+  br label %bb.nph
+
+bb.nph:                                           ; preds = %entry
+  br label %bb
+
+bb:                                               ; preds = %bb.nph, %bb1
+  %i.01 = phi i32 [ %16, %bb1 ], [ 0, %bb.nph ]   ; <i32> [#uses=5]
+
+; CHECK: %1 = sext i32 %i.01 to i64
+; CHECK: -->  {0,+,2}<nuw><nsw><%bb>
+  %1 = sext i32 %i.01 to i64                      ; <i64> [#uses=1]
+
+; CHECK: %2 = getelementptr inbounds double* %d, i64 %1
+; CHECK: -->  {%d,+,16}<nsw><%bb>
+  %2 = getelementptr inbounds double* %d, i64 %1  ; <double*> [#uses=1]
+
+  %3 = load double* %2, align 8                   ; <double> [#uses=1]
+  %4 = sext i32 %i.01 to i64                      ; <i64> [#uses=1]
+  %5 = getelementptr inbounds double* %q, i64 %4  ; <double*> [#uses=1]
+  %6 = load double* %5, align 8                   ; <double> [#uses=1]
+  %7 = or i32 %i.01, 1                            ; <i32> [#uses=1]
+
+; CHECK: %8 = sext i32 %7 to i64
+; CHECK: -->  {1,+,2}<nuw><nsw><%bb>
+  %8 = sext i32 %7 to i64                         ; <i64> [#uses=1]
+
+; CHECK: %9 = getelementptr inbounds double* %q, i64 %8
+; CHECK: {(8 + %q),+,16}<nsw><%bb>
+  %9 = getelementptr inbounds double* %q, i64 %8  ; <double*> [#uses=1]
+
+; Artificially repeat the above three instructions, this time using
+; add nsw instead of or.
+  %t7 = add nsw i32 %i.01, 1                            ; <i32> [#uses=1]
+
+; CHECK: %t8 = sext i32 %t7 to i64
+; CHECK: -->  {1,+,2}<nuw><nsw><%bb>
+  %t8 = sext i32 %t7 to i64                         ; <i64> [#uses=1]
+
+; CHECK: %t9 = getelementptr inbounds double* %q, i64 %t8
+; CHECK: {(8 + %q),+,16}<nsw><%bb>
+  %t9 = getelementptr inbounds double* %q, i64 %t8  ; <double*> [#uses=1]
+
+  %10 = load double* %9, align 8                  ; <double> [#uses=1]
+  %11 = fadd double %6, %10                       ; <double> [#uses=1]
+  %12 = fadd double %11, 3.200000e+00             ; <double> [#uses=1]
+  %13 = fmul double %3, %12                       ; <double> [#uses=1]
+  %14 = sext i32 %i.01 to i64                     ; <i64> [#uses=1]
+  %15 = getelementptr inbounds double* %d, i64 %14 ; <double*> [#uses=1]
+  store double %13, double* %15, align 8
+  %16 = add nsw i32 %i.01, 2                      ; <i32> [#uses=2]
+  br label %bb1
+
+bb1:                                              ; preds = %bb
+  %17 = icmp slt i32 %16, %n                      ; <i1> [#uses=1]
+  br i1 %17, label %bb, label %bb1.return_crit_edge
+
+bb1.return_crit_edge:                             ; preds = %bb1
+  br label %return
+
+return:                                           ; preds = %bb1.return_crit_edge, %entry
+  ret void
+}
+
+declare void @llvm.assume(i1) nounwind
+
+; Note: Without the preheader assume, there is an 'smax' in the
+; backedge-taken count expression:
+; CHECK: Loop %bb: backedge-taken count is ((-1 + (2 * (%no /u 2))) /u 2)
+; CHECK: Loop %bb: max backedge-taken count is 1073741822