make hashable, add comment about log tables, use bytes for reduction array

shamirss.py

@@ -141,7 +141,8 @@ class GF2p8:
 
 		return r
 
-	_reduce = (0, 135, 137, 14, 149, 18, 28, 155, 173, 42, 36, 163, 56, 191, 177, 54)
+	# bytes is smaller, 49 vs 168 bytes, so should fit in a cache line
+	_reduce = b'\x00\x87\x89\x0e\x95\x12\x1c\x9b\xad*$\xa38\xbf\xb16'
 
 	def __init__(self, v):
 		'''v must be in the range [ 0, 255 ].
@@ -185,6 +186,17 @@ class GF2p8:
 
 		m = o._v
 
+		# possibly use log tables:
+		# a = GF2p8(0x87)
+		# logtbl = { idx: a ** idx for idx in range(256) }
+		# invlogtbl = { v: k for k, v in logtbl.items() }
+		# len(invlogtbl)
+		# 255
+		# invlogtbl[GF2p8(6)] + invlogtbl[GF2p8(213)]
+		# 254
+		# logtbl[254]
+		# GF2p8(119)
+
 		# multiply
 		r = self._primativemul(self._v, m)
 
@@ -245,6 +257,9 @@ class GF2p8:
 	def __int__(self):
 		return self._v
 
+	def __hash__(self):
+		return hash(self._v)
+
 	def __repr__(self):
 		return '%s(%d)' % (self.__class__.__name__, self._v)
 
@@ -298,7 +313,7 @@ class TestShamirSS(unittest.TestCase):
 			self.assertEqual(val, recover_data([ a[j] for j in random.sample(range(30), 15) ], 15))
 
 	def test_gf2p8_reduce(self):
-		reduce = tuple(_makered(x, 0x87) for x in range(0, 16))
+		reduce = bytes((_makered(x, 0x87) for x in range(0, 16)))
 
 		if GF2p8._reduce != reduce: # pragma: no cover
 			print('reduce:', repr(reduce))