diff --git a/polly/lib/Exchange/JSONExporter.cpp b/polly/lib/Exchange/JSONExporter.cpp
index d8392c38bf0c..d5e66f01562a 100644
--- a/polly/lib/Exchange/JSONExporter.cpp
+++ b/polly/lib/Exchange/JSONExporter.cpp
@@ -343,6 +343,28 @@ bool JSONImporter::runOnScop(Scop &S) {
         isl_map_free(newAccessMap);
         return false;
       }
+
+      auto NewAccessDomain = isl_map_domain(isl_map_copy(newAccessMap));
+      auto CurrentAccessDomain = isl_map_domain(isl_map_copy(currentAccessMap));
+
+      NewAccessDomain =
+          isl_set_intersect_params(NewAccessDomain, S.getContext());
+      CurrentAccessDomain =
+          isl_set_intersect_params(CurrentAccessDomain, S.getContext());
+
+      if (isl_set_is_subset(CurrentAccessDomain, NewAccessDomain) ==
+          isl_bool_false) {
+        errs() << "Mapping not defined for all iteration domain elements\n";
+        isl_set_free(CurrentAccessDomain);
+        isl_set_free(NewAccessDomain);
+        isl_map_free(currentAccessMap);
+        isl_map_free(newAccessMap);
+        return false;
+      }
+
+      isl_set_free(CurrentAccessDomain);
+      isl_set_free(NewAccessDomain);
+
       if (!isl_map_is_equal(newAccessMap, currentAccessMap)) {
         // Statistics.
         ++NewAccessMapFound;
diff --git a/polly/test/Isl/CodeGen/exprModDiv.ll b/polly/test/Isl/CodeGen/exprModDiv.ll
index 81a8f496c254..f3f8b9eb9472 100644
--- a/polly/test/Isl/CodeGen/exprModDiv.ll
+++ b/polly/test/Isl/CodeGen/exprModDiv.ll
@@ -17,11 +17,15 @@
 ; CHECK:  %pexp.pdiv_r = urem i64 %polly.indvar, 127
 ; CHECK:  %polly.access.A6 = getelementptr float, float* %A, i64 %pexp.pdiv_r
 
-; A[i / 127]
-; CHECK:  %pexp.div = sdiv i64 %polly.indvar, 127
-; CHECK:  %polly.access.B8 = getelementptr float, float* %B, i64 %pexp.div
+; A[floor(i / 127)]
 ;
-; FIXME: Make isl mark this as an udiv expression.
+; Note: without the floor, we would create a map i -> i/127, which only contains
+;       values of i that are divisible by 127. All other values of i would not
+;       be mapped to any value. However, to generate correct code we require
+;       each value of i to indeed be mapped to a value.
+;
+; CHECK:  %pexp.p_div_q = udiv i64 %polly.indvar, 127
+; CHECK:  %polly.access.B8 = getelementptr float, float* %B, i64 %pexp.p_div_q
 
 ; #define floord(n,d) ((n < 0) ? (n - d + 1) : n) / d
 ; A[p + 127 * floord(-p - 1, 127) + 127]
@@ -38,16 +42,16 @@
 ; CHECK:  %polly.access.A10 = getelementptr float, float* %A, i64 %24
 
 ; A[p / 127]
-; CHECK:  %pexp.div12 = sdiv i64 %p, 127
-; CHECK:  %polly.access.B13 = getelementptr float, float* %B, i64 %pexp.div12
+; CHECK:  %pexp.div = sdiv i64 %p, 127
+; CHECK:  %polly.access.B12 = getelementptr float, float* %B, i64 %pexp.div
 
 ; 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.shr = ashr i64 %polly.indvar, 7
-; POW2:  %polly.access.B8 = getelementptr float, float* %B, i64 %pexp.div
+; A[floor(i / 128)]
+; POW2:  %pexp.p_div_q = udiv i64 %polly.indvar, 128
+; POW2:  %polly.access.B8 = getelementptr float, float* %B, i64 %pexp.p_div_q
 
 ; #define floord(n,d) ((n < 0) ? (n - d + 1) : n) / d
 ; A[p + 128 * floord(-p - 1, 128) + 128]
@@ -60,8 +64,8 @@
 ; POW2:  %polly.access.A10 = getelementptr float, float* %A, i64 %24
 
 ; A[p / 128]
-; POW2:  %pexp.div.shr12 = ashr i64 %p, 7
-; POW2:  %polly.access.B13 = getelementptr float, float* %B, i64 %pexp.div.shr12
+; POW2:  %pexp.div.shr = ashr i64 %p, 7
+; POW2:  %polly.access.B12 = getelementptr float, float* %B, i64 %pexp.div.shr
 
 target datalayout = "e-m:e-i64:64-f80:128-n8:16:32:64-S128"
 
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 066c123fa888..807551373990 100644
--- a/polly/test/Isl/CodeGen/exprModDiv___%for.cond---%for.end.jscop
+++ b/polly/test/Isl/CodeGen/exprModDiv___%for.cond---%for.end.jscop
@@ -1,5 +1,5 @@
 {
-   "context" : "[N, p] -> {  : N >= -9223372036854775808 and N <= 9223372036854775807 and p >= -9223372036854775808 and p <= 9223372036854775807 }",
+   "context" : "[N, p] -> {  : N >= -9223372036854775808 and N <= 9223372036854775807 and p >= -9223372036854775808 and p <= 9223372036854775807 and (p % 127) = 0}",
    "name" : "for.cond => for.end",
    "statements" : [
       {
@@ -10,7 +10,7 @@
             },
             {
                "kind" : "read",
-               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_B[i0 / 127] }"
+               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_B[floor(i0 / 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
index 5309f8ab5772..f8c14effcce8 100644
--- a/polly/test/Isl/CodeGen/exprModDiv___%for.cond---%for.end.jscop.pow2
+++ b/polly/test/Isl/CodeGen/exprModDiv___%for.cond---%for.end.jscop.pow2
@@ -1,5 +1,5 @@
 {
-   "context" : "[N, p] -> {  : N >= -9223372036854775808 and N <= 9223372036854775807 and p >= -9223372036854775808 and p <= 9223372036854775807 }",
+   "context" : "[N, p] -> {  : N >= -9223372036854775808 and N <= 9223372036854775807 and p >= -9223372036854775808 and p <= 9223372036854775807 and p % 128 = 0}",
    "name" : "for.cond => for.end",
    "statements" : [
       {
@@ -10,7 +10,7 @@
             },
             {
                "kind" : "read",
-               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_B[i0 / 128] }"
+               "relation" : "[N, p] -> { Stmt_for_body[i0] -> MemRef_B[floor(i0 / 128)] }"
             },
             {
                "kind" : "read",