Index: include/polly/Support/GICHelper.h
===================================================================
--- include/polly/Support/GICHelper.h
+++ include/polly/Support/GICHelper.h
@@ -37,6 +37,36 @@
 } // namespace llvm
 
 namespace polly {
+
+/// @brief Translate an llvm::APInt to an isl_val.
+///
+/// Translate the bitsequence without sign information as provided by APInt into
+/// a signed isl_val type. Depending on the value of @p IsSigned @p Int is
+/// interpreted as unsigned value or as signed value in two's complement
+/// representation.
+///
+/// Input IsSigned                 Output
+///
+///     0        0           ->    0
+///     1        0           ->    1
+///    00        0           ->    0
+///    01        0           ->    1
+///    10        0           ->    2
+///    11        0           ->    3
+///
+///     0        1           ->    0
+///     1        1           ->   -1
+///    00        1           ->    0
+///    01        1           ->    1
+///    10        1           ->   -2
+///    11        1           ->   -1
+///
+/// @param Ctx      The isl_ctx to create the isl_val in.
+/// @param Int      The integer value to translate.
+/// @param IsSigned If the APInt should be interpreted as signed or unsigned
+///                 value.
+///
+/// @return The isl_val corresponding to @p Int.
 __isl_give isl_val *isl_valFromAPInt(isl_ctx *Ctx, const llvm::APInt Int,
                                      bool IsSigned);
 
Index: lib/Support/GICHelper.cpp
===================================================================
--- lib/Support/GICHelper.cpp
+++ lib/Support/GICHelper.cpp
@@ -30,8 +30,19 @@
   APInt Abs;
   isl_val *v;
 
+  // As isl is interpreting the input always as unsigned value, we need some
+  // additional pre and post processing to import signed values. The approach
+  // we take is to first obtain the absolute value of Int and then negate the
+  // value after it has been imported to isl.
+  //
+  // It should be noted that the smallest integer value represented in two's
+  // complement with a certain amount of bits does not have a corresponding
+  // positive representation in two's complement representation with the same
+  // number of bits. E.g. 110 (-2) does not have a corresponding value for (2).
+  // To ensure that there is always a corresponding value available we first
+  // sign-extend the input by one bit and only then take the absolute value.
   if (IsSigned)
-    Abs = Int.abs();
+    Abs = Int.sext(Int.getBitWidth() + 1).abs();
   else
     Abs = Int;
 
Index: unittests/Isl/IslTest.cpp
===================================================================
--- unittests/Isl/IslTest.cpp
+++ unittests/Isl/IslTest.cpp
@@ -20,6 +20,43 @@
   isl_ctx *IslCtx = isl_ctx_alloc();
 
   {
+    APInt APZero(1, 0, true);
+    auto *IslZero = isl_valFromAPInt(IslCtx, APZero, true);
+    EXPECT_EQ(isl_bool_true, isl_val_is_zero(IslZero));
+    isl_val_free(IslZero);
+  }
+
+  {
+    APInt APNOne(1, -1, true);
+    auto *IslNOne = isl_valFromAPInt(IslCtx, APNOne, true);
+    EXPECT_EQ(isl_bool_true, isl_val_is_negone(IslNOne));
+    isl_val_free(IslNOne);
+  }
+
+  {
+    APInt APZero(1, 0, false);
+    auto *IslZero = isl_valFromAPInt(IslCtx, APZero, false);
+    EXPECT_EQ(isl_bool_true, isl_val_is_zero(IslZero));
+    isl_val_free(IslZero);
+  }
+
+  {
+    APInt APOne(1, 1, false);
+    auto *IslOne = isl_valFromAPInt(IslCtx, APOne, false);
+    EXPECT_EQ(isl_bool_true, isl_val_is_one(IslOne));
+    isl_val_free(IslOne);
+  }
+
+  {
+    APInt APNTwo(2, -2, true);
+    auto *IslNTwo = isl_valFromAPInt(IslCtx, APNTwo, true);
+    auto *IslNTwoCmp = isl_val_int_from_si(IslCtx, -2);
+    EXPECT_EQ(isl_val_eq(IslNTwo, IslNTwoCmp), isl_bool_true);
+    isl_val_free(IslNTwo);
+    isl_val_free(IslNTwoCmp);
+  }
+
+  {
     APInt APNOne(32, -1, true);
     auto *IslNOne = isl_valFromAPInt(IslCtx, APNOne, true);
     EXPECT_EQ(isl_bool_true, isl_val_is_negone(IslNOne));
@@ -56,6 +93,17 @@
     isl_val_free(IslRef);
   }
 
+  {
+    APInt APLarge(130, 2, false);
+    APLarge = APLarge.shl(70);
+    auto *IslLarge = isl_valFromAPInt(IslCtx, APLarge, false);
+    auto *IslRef = isl_val_int_from_ui(IslCtx, 71);
+    IslRef = isl_val_2exp(IslRef);
+    EXPECT_EQ(isl_val_eq(IslLarge, IslRef), isl_bool_true);
+    isl_val_free(IslLarge);
+    isl_val_free(IslRef);
+  }
+
   isl_ctx_free(IslCtx);
 }