hdl.ast: add Value.xor, mapping to $reduce_xor.

Fixes #147.

nmigen/back/pysim.py

@@ -135,6 +135,9 @@ class _RHSValueCompiler(_ValueCompiler):
                 val, = value.operands
                 mask = (1 << len(val)) - 1
                 return lambda state: normalize(arg(state) == mask, shape)
+            if value.op == "r^":
+                # Believe it or not, this is the fastest way to compute a sideways XOR in Python.
+                return lambda state: normalize(str(arg(state)).count("1") % 2, shape)
         elif len(value.operands) == 2:
             lhs, rhs = map(self, value.operands)
             if value.op == "+":

nmigen/hdl/ast.py

@@ -157,6 +157,16 @@ class Value(metaclass=ABCMeta):
         """
         return Operator("r&", [self])
 
+    def xor(self):
+        """Compute pairwise exclusive-or of every bit.
+
+        Returns
+        -------
+        Value, out
+            ``1`` if an odd number of bits are set, ``0`` if an even number of bits are set.
+        """
+        return Operator("r^", [self])
+
     def implies(premise, conclusion):
         """Implication.
 

nmigen/test/test_hdl_ast.py

@@ -259,6 +259,10 @@ class OperatorTestCase(FHDLTestCase):
         v = Const(0b101).all()
         self.assertEqual(repr(v), "(r& (const 3'd5))")
 
+    def test_xor(self):
+        v = Const(0b101).xor()
+        self.assertEqual(repr(v), "(r^ (const 3'd5))")
+
     def test_hash(self):
         with self.assertRaises(TypeError):
             hash(Const(0) + Const(0))

nmigen/test/test_sim.py

@@ -69,6 +69,12 @@ class SimulatorUnitTestCase(FHDLTestCase):
         self.assertStatement(stmt, [C(0b01, 2)], C(0))
         self.assertStatement(stmt, [C(0b11, 2)], C(1))
 
+    def test_xor(self):
+        stmt = lambda y, a: y.eq(a.xor())
+        self.assertStatement(stmt, [C(0b00, 2)], C(0))
+        self.assertStatement(stmt, [C(0b01, 2)], C(1))
+        self.assertStatement(stmt, [C(0b11, 2)], C(0))
+
     def test_add(self):
         stmt = lambda y, a, b: y.eq(a + b)
         self.assertStatement(stmt, [C(0,  4), C(1,  4)], C(1,   4))