Index: lib/Target/NVPTX/NVPTXISelLowering.h
===================================================================
--- lib/Target/NVPTX/NVPTXISelLowering.h
+++ lib/Target/NVPTX/NVPTXISelLowering.h
@@ -459,6 +459,14 @@
   bool isLegalAddressingMode(const DataLayout &DL, const AddrMode &AM, Type *Ty,
                              unsigned AS) const override;
 
+  bool isTruncateFree(Type *SrcTy, Type *DstTy) const override {
+    // Truncating 64-bit to 32-bit is free in SASS.
+    if (!SrcTy->isIntegerTy() || !DstTy->isIntegerTy())
+      return false;
+    return SrcTy->getPrimitiveSizeInBits() == 64 &&
+           DstTy->getPrimitiveSizeInBits() == 32;
+  }
+
   /// getFunctionAlignment - Return the Log2 alignment of this function.
   unsigned getFunctionAlignment(const Function *F) const;
 
Index: test/Transforms/LoopStrengthReduce/NVPTX/lit.local.cfg
===================================================================
--- /dev/null
+++ test/Transforms/LoopStrengthReduce/NVPTX/lit.local.cfg
@@ -0,0 +1,2 @@
+if not 'NVPTX' in config.root.targets:
+    config.unsupported = True
Index: test/Transforms/LoopStrengthReduce/NVPTX/trunc.ll
===================================================================
--- /dev/null
+++ test/Transforms/LoopStrengthReduce/NVPTX/trunc.ll
@@ -0,0 +1,45 @@
+; RUN: opt < %s -loop-reduce -S | FileCheck %s
+
+target datalayout = "e-i64:64-v16:16-v32:32-n16:32:64"
+target triple = "nvptx64-nvidia-cuda"
+
+; This confirms that NVPTXTTI considers a 64-to-32 integer trunc free. If such
+; truncs were not considered free, LSR would promote (int)i as a separate
+; induction variable in the following example.
+;
+;   for (long i = begin; i != end; i += stride)
+;     use((int)i);
+;
+; That would be worthless, because "i" is simulated by two 32-bit registers and
+; truncating it to 32-bit is as simple as directly using the register that
+; contains the low bits.
+define void @trunc_is_free(i64 %begin, i64 %stride, i64 %end) {
+; CHECK-LABEL: @trunc_is_free(
+entry:
+  %cmp.4 = icmp eq i64 %begin, %end
+  br i1 %cmp.4, label %for.cond.cleanup, label %for.body.preheader
+
+for.body.preheader:                               ; preds = %entry
+  br label %for.body
+
+for.cond.cleanup.loopexit:                        ; preds = %for.body
+  br label %for.cond.cleanup
+
+for.cond.cleanup:                                 ; preds = %for.cond.cleanup.loopexit, %entry
+  ret void
+
+for.body:                                         ; preds = %for.body.preheader, %for.body
+; CHECK: for.body:
+  %i.05 = phi i64 [ %add, %for.body ], [ %begin, %for.body.preheader ]
+  %conv = trunc i64 %i.05 to i32
+; CHECK: trunc i64 %{{[^ ]+}} to i32
+  tail call void @_Z3usei(i32 %conv) #2
+  %add = add nsw i64 %i.05, %stride
+  %cmp = icmp eq i64 %add, %end
+  br i1 %cmp, label %for.cond.cleanup.loopexit, label %for.body
+}
+
+declare void @_Z3usei(i32)
+
+!nvvm.annotations = !{!0}
+!0 = !{void (i64, i64, i64)* @trunc_is_free, !"kernel", i32 1}