add some more tests

tests/noisy_reduce_noise.mlir

@@ -28,3 +28,133 @@ func.func @test_insert_noise_reduction_ops_mul() -> i5 {
   %8 = noisy.decode %7 : !noisy.i32 -> i5
   return %8 : i5
 }
+
+// CHECK-LABEL: test_insert_noise_reduction_ops_add_none_needed
+// CHECK-NOT: noisy.reduce_noise
+func.func @test_insert_noise_reduction_ops_add_none_needed() -> i5 {
+  %0 = arith.constant 3 : i5
+  %1 = arith.constant 4 : i5
+  %2 = noisy.encode %0 : i5 -> !noisy.i32
+  %3 = noisy.encode %1 : i5 -> !noisy.i32
+  %4 = noisy.add %2, %3 : !noisy.i32
+  %5 = noisy.add %4, %4 : !noisy.i32
+  %6 = noisy.add %5, %5 : !noisy.i32
+  %7 = noisy.add %6, %6 : !noisy.i32
+  %8 = noisy.decode %7 : !noisy.i32 -> i5
+  return %8 : i5
+}
+
+
+// CHECK-LABEL: test_add_after_mul
+// CHECK: noisy.mul
+// CHECK: noisy.reduce_noise
+// CHECK: noisy.add
+// CHECK: noisy.add
+// CHECK: noisy.add
+// CHECK: noisy.add
+// CHECK: noisy.decode
+// CHECK: return
+func.func @test_add_after_mul() -> i5 {
+  %0 = arith.constant 3 : i5
+  %1 = arith.constant 4 : i5
+  %2 = noisy.encode %0 : i5 -> !noisy.i32
+  %3 = noisy.encode %1 : i5 -> !noisy.i32
+  // Noise: 12
+  %4 = noisy.mul %2, %3 : !noisy.i32
+  // Noise: 24
+  %5 = noisy.add %4, %3 : !noisy.i32
+  // Noise: 25
+  %6 = noisy.add %5, %5 : !noisy.i32
+  // Noise: 26
+  %7 = noisy.add %6, %6 : !noisy.i32
+  // Noise: 27
+  %8 = noisy.add %7, %7 : !noisy.i32
+  %9 = noisy.decode %8 : !noisy.i32 -> i5
+  return %9 : i5
+}
+
+// This test checks that the solver can find a single insertion point
+// for a reduce_noise op that handles two branches, each of which would
+// also need a reduce_noise op if handled separately.
+// CHECK-LABEL: test_single_insertion_branching
+// CHECK: noisy.mul
+// CHECK-NOT: noisy.add
+// CHECK-COUNT-1: noisy.reduce_noise
+// CHECK-NOT: noisy.reduce_noise
+func.func @test_single_insertion_branching() -> i5 {
+  %0 = arith.constant 3 : i5
+  %1 = arith.constant 4 : i5
+  %2 = noisy.encode %0 : i5 -> !noisy.i32
+  %3 = noisy.encode %1 : i5 -> !noisy.i32
+  // Noise: 12
+  %4 = noisy.mul %2, %3 : !noisy.i32
+  // Noise: 24
+
+  // branch 1
+  %b1 = noisy.add %4, %3 : !noisy.i32
+  // Noise: 25
+  %b2 = noisy.add %b1, %3 : !noisy.i32
+  // Noise: 25
+  %b3 = noisy.add %b2, %3 : !noisy.i32
+  // Noise: 26
+  %b4 = noisy.add %b3, %3 : !noisy.i32
+  // Noise: 27
+
+  // branch 2
+  %c1 = noisy.sub %4, %2 : !noisy.i32
+  // Noise: 25
+  %c2 = noisy.sub %c1, %3 : !noisy.i32
+  // Noise: 25
+  %c3 = noisy.sub %c2, %3 : !noisy.i32
+  // Noise: 26
+  %c4 = noisy.sub %c3, %3 : !noisy.i32
+  // Noise: 27
+
+  %x1 = noisy.decode %b4 : !noisy.i32 -> i5
+  %x2 = noisy.decode %c4 : !noisy.i32 -> i5
+  %x3 = arith.addi %x1, %x2 : i5
+  return %x3 : i5
+}
+
+// same as test_single_insertion_branching, but because the last two values
+// are multiplied, we need two reduce_noise ops, one on each branch.
+// CHECK-LABEL: test_double_insertion_branching
+// CHECK: noisy.mul
+// CHECK: noisy.add
+// CHECK-COUNT-2: noisy.reduce_noise
+// CHECK-NOT: noisy.reduce_noise
+// CHECK: noisy.mul
+func.func @test_double_insertion_branching() -> i5 {
+  %0 = arith.constant 3 : i5
+  %1 = arith.constant 4 : i5
+  %2 = noisy.encode %0 : i5 -> !noisy.i32
+  %3 = noisy.encode %1 : i5 -> !noisy.i32
+  // Noise: 12
+  %4 = noisy.mul %2, %3 : !noisy.i32
+  // Noise: 24
+
+  // branch 1
+  %b1 = noisy.add %4, %3 : !noisy.i32
+  // Noise: 25
+  %b2 = noisy.add %b1, %3 : !noisy.i32
+  // Noise: 25
+  %b3 = noisy.add %b2, %3 : !noisy.i32
+  // Noise: 26
+  %b4 = noisy.add %b3, %3 : !noisy.i32
+  // Noise: 27
+
+  // branch 2
+  %c1 = noisy.add %4, %2 : !noisy.i32
+  // Noise: 25
+  %c2 = noisy.add %c1, %3 : !noisy.i32
+  // Noise: 25
+  %c3 = noisy.add %c2, %3 : !noisy.i32
+  // Noise: 26
+  %c4 = noisy.add %c3, %3 : !noisy.i32
+  // Noise: 27
+
+  %exit = noisy.mul %b4, %c4 : !noisy.i32
+
+  %x1 = noisy.decode %exit : !noisy.i32 -> i5
+  return %x1 : i5
+}