Implémentation de M⁴ à l'aide de sa matrice

1 files changed, 32 insertions, 10 deletions

diff --git a/src/add_python/lilliput/multiplications.py b/src/add_python/lilliput/multiplications.py
index 65c75ab..09eaa08 100644
--- a/src/add_python/lilliput/multiplications.py
+++ b/src/add_python/lilliput/multiplications.py
@@ -23,8 +23,11 @@ from functools import reduce
 from operator import xor
 
 
+def _shl(xi, n):
+    return (xi << n) & 0xff
+
 def _Sl(n):
-    return lambda xi: (xi<<n) & 0xff
+    return lambda xi: _shl(xi, n)
 
 def _Sr(n):
     return lambda xi: xi>>n
@@ -36,16 +39,25 @@ def _0(xi):
     return 0
 
 def _M1(xi):
-    return (xi<<3 ^ xi>>3) & 0xff
+    return _shl(xi, 3) ^ xi>>3
 
 def _M2(xi):
-    return (xi<<6 ^ (xi&0b11111000) ^ xi>>6) & 0xff
+    return _shl(xi, 6) ^ xi&0b11111000 ^ xi>>6
 
 def _M3(xi):
-    return xi & 0b00011111
+    return _shl(xi>>3, 6) ^ xi>>6<<3
 
 def _M4(xi):
-    return ((xi<<2) & 0xff) >> 3
+    return _shl(xi, 2) >> 3
+
+def _M5(xi):
+    return _shl(xi, 5) ^ xi>>3<<2
+
+def _M6(xi):
+    return xi & 0b00011111
+
+def _M7(xi):
+    return _shl(xi, 2) >> 3
 
 
 M = (
@@ -81,6 +93,17 @@ M3 = (
     ( _0,     _0,    _Id,     _0,     _0,     _0,  _0,  _0),
 )
 
+M4 = (
+    ( _0,     _0, _Sl(6),    _M1,    _Id,     _0,     _0,  _0),
+    ( _0,     _0,     _0,    _M2,    _M1,    _Id,     _0,  _0),
+    ( _0, _Sl(2),     _0,    _M3,    _M2,    _M1,    _Id,  _0),
+    ( _0,    _M4, _Sl(2),     _0,     _0, _Sr(6), _Sr(3), _Id),
+    (_Id,     _0, _Sl(5), _Sl(2),     _0,     _0,     _0,  _0),
+    ( _0,    _Id,     _0,    _M5, _Sl(2),     _0,     _0,  _0),
+    ( _0,     _0,    _Id,     _0,     _0,     _0,     _0,  _0),
+    ( _0,     _0, _Sl(3),    _Id,     _0,     _0,     _0,  _0),
+)
+
 # NB: shift directions are reversed with respect to the specification
 # for powers of M_R, since the specification reverses the byte order
 # for those matrices.
@@ -99,7 +122,7 @@ MR = (
 MR2 = (
     ( _0,  _0, _Id,     _0,     _0,     _0,     _0,     _0),
     ( _0,  _0,  _0,    _Id, _Sr(3),     _0,     _0,     _0),
-    ( _0,  _0,  _0,     _0,    _Id, _Sr(3),    _M3,     _0),
+    ( _0,  _0,  _0,     _0,    _Id, _Sr(3),    _M6,     _0),
     ( _0,  _0,  _0,     _0,     _0,    _Id, _Sl(3),     _0),
     ( _0,  _0,  _0, _Sl(2),     _0,     _0,    _Id, _Sl(3)),
     ( _0,  _0,  _0,     _0, _Sl(2),     _0,     _0,    _Id),
@@ -109,8 +132,8 @@ MR2 = (
 
 MR3 = (
     (    _0,  _0,  _0,    _Id, _Sr(3),     _0,     _0,     _0),
-    (    _0,  _0,  _0,     _0,    _Id, _Sr(3),    _M3,     _0),
-    (    _0,  _0,  _0,    _M4,     _0,    _Id,    _M1,    _M3),
+    (    _0,  _0,  _0,     _0,    _Id, _Sr(3),    _M6,     _0),
+    (    _0,  _0,  _0,    _M7,     _0,    _Id,    _M1,    _M6),
     (    _0,  _0,  _0, _Sl(2),     _0,     _0,    _Id, _Sl(3)),
     (_Sl(3),  _0,  _0,     _0, _Sl(2),     _0,     _0,    _Id),
     (   _Id,  _0,  _0,     _0,     _0, _Sl(2), _Sl(5),     _0),
@@ -138,9 +161,8 @@ ALPHAS = (
     _multiplication(M),
     _multiplication(M2),
     _multiplication(M3),
+    _multiplication(M4),
     _multiplication(MR, reverse=False),
     _multiplication(MR2, reverse=False),
     _multiplication(MR3, reverse=False)
 )
-
-ALPHAS = ALPHAS[:3] + (lambda x: ALPHAS[1](ALPHAS[1](x)),) + ALPHAS[3:]