diff --git a/polly/lib/CodeGen/IslExprBuilder.cpp b/polly/lib/CodeGen/IslExprBuilder.cpp
index 60a46531f2e9..27c72486c7e0 100644
--- a/polly/lib/CodeGen/IslExprBuilder.cpp
+++ b/polly/lib/CodeGen/IslExprBuilder.cpp
@@ -301,6 +301,11 @@ Value *IslExprBuilder::createOpBin(__isl_take isl_ast_expr *Expr) {
     Res = Builder.CreateUDiv(LHS, RHS, "pexp.p_div_q");
     break;
   case isl_ast_op_fdiv_q: { // Round towards -infty
+    auto &Int = dyn_cast<ConstantInt>(RHS)->getValue();
+    if (Int.isPowerOf2()) {
+      Res = Builder.CreateAShr(LHS, Int.ceilLogBase2(), "polly.fdiv_q.shr");
+      break;
+    }
     // TODO: Review code and check that this calculation does not yield
     //       incorrect overflow in some bordercases.
     //
diff --git a/polly/test/Isl/CodeGen/exprModDiv.ll b/polly/test/Isl/CodeGen/exprModDiv.ll
index e471e6b1f80f..91d27fabbbc7 100644
--- a/polly/test/Isl/CodeGen/exprModDiv.ll
+++ b/polly/test/Isl/CodeGen/exprModDiv.ll
@@ -1,4 +1,5 @@
 ; RUN: opt %loadPolly -polly-import-jscop -polly-import-jscop-dir=%S -polly-codegen -S < %s | FileCheck %s
+; RUN: opt %loadPolly -polly-import-jscop -polly-import-jscop-dir=%S -polly-codegen -polly-import-jscop-postfix=pow2 -S < %s | FileCheck %s -check-prefix=POW2
 ;
 ;    void exprModDiv(float *A, float *B, float *C, long N, long p) {
 ;      for (long i = 0; i < N; i++)
@@ -12,34 +13,58 @@
 ; useful as LLVM will translate urem and udiv operations with power-of-two
 ; denominators to fast bitwise and or shift operations.
 
-; A[i % 128]
-; CHECK:  %pexp.pdiv_r = urem i64 %polly.indvar, 128
+; A[i % 127]
+; CHECK:  %pexp.pdiv_r = urem i64 %polly.indvar, 127
 ; CHECK:  %polly.access.A6 = getelementptr float, float* %A, i64 %pexp.pdiv_r
 
-; A[i / 128]
-; CHECK:  %pexp.div = sdiv i64 %polly.indvar, 128
+; A[i / 127]
+; CHECK:  %pexp.div = sdiv i64 %polly.indvar, 127
 ; CHECK:  %polly.access.B8 = getelementptr float, float* %B, i64 %pexp.div
 ;
 ; FIXME: Make isl mark this as an udiv expression.
 
 ; #define floord(n,d) ((n < 0) ? (n - d + 1) : n) / d
-; A[p + 128 * floord(-p - 1, 128) + 128]
+; A[p + 127 * floord(-p - 1, 127) + 127]
 ; CHECK:  %20 = sub nsw i64 0, %p
 ; CHECK:  %21 = sub nsw i64 %20, 1
-; CHECK:  %pexp.fdiv_q.0 = sub i64 %21, 128
+; CHECK:  %pexp.fdiv_q.0 = sub i64 %21, 127
 ; CHECK:  %pexp.fdiv_q.1 = add i64 %pexp.fdiv_q.0, 1
 ; CHECK:  %pexp.fdiv_q.2 = icmp slt i64 %21, 0
 ; CHECK:  %pexp.fdiv_q.3 = select i1 %pexp.fdiv_q.2, i64 %pexp.fdiv_q.1, i64 %21
-; CHECK:  %pexp.fdiv_q.4 = sdiv i64 %pexp.fdiv_q.3, 128
-; CHECK:  %22 = mul nsw i64 128, %pexp.fdiv_q.4
+; CHECK:  %pexp.fdiv_q.4 = sdiv i64 %pexp.fdiv_q.3, 127
+; CHECK:  %22 = mul nsw i64 127, %pexp.fdiv_q.4
 ; CHECK:  %23 = add nsw i64 %p, %22
-; CHECK:  %24 = add nsw i64 %23, 128
+; CHECK:  %24 = add nsw i64 %23, 127
 ; CHECK:  %polly.access.A10 = getelementptr float, float* %A, i64 %24
 
-; A[p / 128]
-; CHECK:  %pexp.div12 = sdiv i64 %p, 128
+; A[p / 127]
+; CHECK:  %pexp.div12 = sdiv i64 %p, 127
 ; CHECK:  %polly.access.B13 = getelementptr float, float* %B, i64 %pexp.div12
 
+; A[i % 128]
+; POW2:  %pexp.pdiv_r = urem i64 %polly.indvar, 128
+; POW2:  %polly.access.A6 = getelementptr float, float* %A, i64 %pexp.pdiv_r
+
+; A[i / 128]
+; POW2:  %pexp.div = sdiv i64 %polly.indvar, 128
+; POW2:  %polly.access.B8 = getelementptr float, float* %B, i64 %pexp.div
+;
+; FIXME: Make isl mark this as an udiv expression.
+
+; #define floord(n,d) ((n < 0) ? (n - d + 1) : n) / d
+; A[p + 128 * floord(-p - 1, 128) + 128]
+; POW2:  %20 = sub nsw i64 0, %p
+; POW2:  %21 = sub nsw i64 %20, 1
+; POW2:  %polly.fdiv_q.shr = ashr i64 %21, 7
+; POW2:  %22 = mul nsw i64 128, %polly.fdiv_q.shr
+; POW2:  %23 = add nsw i64 %p, %22
+; POW2:  %24 = add nsw i64 %23, 128
+; POW2:  %polly.access.A10 = getelementptr float, float* %A, i64 %24
+
+; A[p / 128]
+; POW2:  %pexp.div12 = sdiv i64 %p, 128
+; POW2:  %polly.access.B13 = getelementptr float, float* %B, i64 %pexp.div12
+
 target datalayout = "e-m:e-i64:64-f80:128-n8:16:32:64-S128"
 
 define void @exprModDiv(float* %A, float* %B, float* %C, i64 %N, i64 %p) {
diff --git a/polly/test/Isl/CodeGen/exprModDiv___%for.cond---%for.end.jscop b/polly/test/Isl/CodeGen/exprModDiv___%for.cond---%for.end.jscop
index 5309f8ab5772..066c123fa888 100644
--- a/polly/test/Isl/CodeGen/exprModDiv___%for.cond---%for.end.jscop
+++ b/polly/test/Isl/CodeGen/exprModDiv___%for.cond---%for.end.jscop
@@ -6,19 +6,19 @@
          "accesses" : [
             {
                "kind" : "read",
-               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_A[i0 % 128] }"
+               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_A[i0 % 127] }"
             },
             {
                "kind" : "read",
-               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_B[i0 / 128] }"
+               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_B[i0 / 127] }"
             },
             {
                "kind" : "read",
-               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_A[p % 128] }"
+               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_A[p % 127] }"
             },
             {
                "kind" : "read",
-               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_B[p / 128] }"
+               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_B[p / 127] }"
             },
             {
                "kind" : "read",
diff --git a/polly/test/Isl/CodeGen/exprModDiv___%for.cond---%for.end.jscop.pow2 b/polly/test/Isl/CodeGen/exprModDiv___%for.cond---%for.end.jscop.pow2
new file mode 100644
index 000000000000..5309f8ab5772
--- /dev/null
+++ b/polly/test/Isl/CodeGen/exprModDiv___%for.cond---%for.end.jscop.pow2
@@ -0,0 +1,37 @@
+{
+   "context" : "[N, p] -> {  : N >= -9223372036854775808 and N <= 9223372036854775807 and p >= -9223372036854775808 and p <= 9223372036854775807 }",
+   "name" : "for.cond => for.end",
+   "statements" : [
+      {
+         "accesses" : [
+            {
+               "kind" : "read",
+               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_A[i0 % 128] }"
+            },
+            {
+               "kind" : "read",
+               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_B[i0 / 128] }"
+            },
+            {
+               "kind" : "read",
+               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_A[p % 128] }"
+            },
+            {
+               "kind" : "read",
+               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_B[p / 128] }"
+            },
+            {
+               "kind" : "read",
+               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_C[i0] }"
+            },
+            {
+               "kind" : "write",
+               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_C[i0] }"
+            }
+         ],
+         "domain" : "[N, p] -> { Stmt_for_body[i0] : i0 >= 0 and N >= 1 and i0 <= -1 + N }",
+         "name" : "Stmt_for_body",
+         "schedule" : "[N, p] -> { Stmt_for_body[i0] -> [i0] }"
+      }
+   ]
+}