lib.coding: add GrayEncoder and GrayDecoder.

Unlike the Migen ones, these are purely combinatorial.

nmigen/test/test_lib_coding.py

@@ -1,5 +1,6 @@
 from .tools import *
 from ..hdl.ast import *
+from ..hdl.dsl import *
 from ..back.pysim import *
 from ..lib.coding import *
 
@@ -79,3 +80,47 @@ class DecoderTestCase(FHDLTestCase):
 
             sim.add_process(process)
             sim.run()
+
+
+class ReversibleSpec:
+    def __init__(self, encoder_cls, decoder_cls, args):
+        self.encoder_cls = encoder_cls
+        self.decoder_cls = decoder_cls
+        self.coder_args  = args
+
+    def get_fragment(self, platform):
+        m = Module()
+        enc, dec = self.encoder_cls(*self.coder_args), self.decoder_cls(*self.coder_args)
+        m.submodules += enc, dec
+        m.d.comb += [
+            dec.i.eq(enc.o),
+            Assert(enc.i == dec.o)
+        ]
+        return m.lower(platform)
+
+
+class HammingDistanceSpec:
+    def __init__(self, distance, encoder_cls, args):
+        self.distance    = distance
+        self.encoder_cls = encoder_cls
+        self.coder_args  = args
+
+    def get_fragment(self, platform):
+        m = Module()
+        enc1, enc2 = self.encoder_cls(*self.coder_args), self.encoder_cls(*self.coder_args)
+        m.submodules += enc1, enc2
+        m.d.comb += [
+            Assume(enc1.i + 1 == enc2.i),
+            Assert(sum(enc1.o ^ enc2.o) == self.distance)
+        ]
+        return m.lower(platform)
+
+
+class GrayCoderTestCase(FHDLTestCase):
+    def test_reversible(self):
+        spec = ReversibleSpec(encoder_cls=GrayEncoder, decoder_cls=GrayDecoder, args=(16,))
+        self.assertFormal(spec, mode="prove")
+
+    def test_distance(self):
+        spec = HammingDistanceSpec(distance=1, encoder_cls=GrayEncoder, args=(16,))
+        self.assertFormal(spec, mode="prove")