[mlir][test] Add unittests for getInversePermutation

The only way to test `getInversePermutation` is through unit tests. The
concept of "inverse permutations" is tricky to document and these tests
are a good source documentation of the expected/intended behavoiur.
Hence these additional unit tests.

This is a follon-on #114775 for in which I added tests for
`isProjectedPermutation`.

Author: banach-space

mlir/unittests/IR/AffineMapTest.cpp

@@ -76,3 +76,39 @@ TEST(AffineMapTest, isProjectedPermutation) {
   AffineMap map10 = AffineMap::get(6, 0, {d5, d3, d2, d4}, &ctx);
   EXPECT_TRUE(map10.isProjectedPermutation());
 }
+
+TEST(AffineMapTest, getInversePermutation) {
+  MLIRContext ctx;
+  OpBuilder b(&ctx);
+
+  // 0. Empty map
+  AffineMap map0 = AffineMap::get(0, 0, {}, &ctx);
+  AffineMap inverseMap0 = inversePermutation(map0);
+  EXPECT_TRUE(inverseMap0.isEmpty());
+
+  auto d0 = b.getAffineDimExpr(0);
+  auto d1 = b.getAffineDimExpr(1);
+  auto d2 = b.getAffineDimExpr(2);
+
+  // 1.   (d0, d1, d2) -> (d1, d1, d0, d2, d1, d2, d1, d0)
+  AffineMap map1 = AffineMap::get(3, 0, {d1, d1, d0, d2, d1, d2, d1, d0}, &ctx);
+  //      (d0, d1, d2, d3, d4, d5, d6, d7) -> (d2, d0, d3)
+  AffineMap inverseMap1 = inversePermutation(map1);
+  auto resultsInv1 = inverseMap1.getResults();
+  EXPECT_EQ(resultsInv1.size(), 3UL);
+  EXPECT_TRUE(resultsInv1[0].isFunctionOfDim(2));
+  EXPECT_TRUE(resultsInv1[1].isFunctionOfDim(0));
+  EXPECT_TRUE(resultsInv1[2].isFunctionOfDim(3));
+
+  // 2.   (d0, d1, d2) -> (d1, d0 + d1, d0, d2, d1, d2, d1, d0)
+  auto sum = d0 + d1;
+  AffineMap map2 =
+      AffineMap::get(3, 0, {d1, sum, d0, d2, d1, d2, d1, d0}, &ctx);
+  //      (d0, d1, d2, d3, d4, d5, d6, d7) -> (d2, d0, d3)
+  AffineMap inverseMap2 = inversePermutation(map2);
+  auto resultsInv2 = inverseMap2.getResults();
+  EXPECT_EQ(resultsInv2.size(), 3UL);
+  EXPECT_TRUE(resultsInv1[0].isFunctionOfDim(2));
+  EXPECT_TRUE(resultsInv1[1].isFunctionOfDim(0));
+  EXPECT_TRUE(resultsInv1[2].isFunctionOfDim(3));
+}