From 401fd928088f51e90e391377c9d696b162d1878f Mon Sep 17 00:00:00 2001
From: Kévin Le Gouguec <kevin.legouguec@airbus.com>
Date: Tue, 2 Jul 2019 15:30:01 +0200
Subject: Réécriture de M et M² en Python
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Pour que le lien avec la spec saute aux yeux.
---
 src/add_python/lilliput/multiplications.py | 73 ++++++++++++++++++------------
 1 file changed, 45 insertions(+), 28 deletions(-)

(limited to 'src/add_python/lilliput/multiplications.py')

diff --git a/src/add_python/lilliput/multiplications.py b/src/add_python/lilliput/multiplications.py
index 2dea948..3b50987 100644
--- a/src/add_python/lilliput/multiplications.py
+++ b/src/add_python/lilliput/multiplications.py
@@ -19,40 +19,57 @@ from ALPHAS[0] = α₀ = I to ALPHAS[6] = α₆ = M_R³.
 """
 
 
-def _multiply_M(lane):
-    multiplied_lane = [lane[(byte-1) % 8] for byte in range(0, 8)]
+from functools import reduce
+from operator import xor
 
-    multiplied_lane[2] ^= ((lane[6] << 2) & 0xff)
-    multiplied_lane[4] ^= ((lane[4] >> 3) & 0xff)
-    multiplied_lane[5] ^= ((lane[5] << 3) & 0xff)
 
-    return multiplied_lane
+def _Sl(n):
+    return lambda xi: (xi<<n) & 0xff
 
+def _Sr(n):
+    return lambda xi: xi>>n
 
-def _multiply_M2(lane):
-    multiplied_lane = [lane[(byte-2) % 8] for byte in range(0, 8)]
+def _Id(xi):
+    return xi
 
-    multiplied_lane[2] ^= ((lane[5] << 2) & 0xff)
-    multiplied_lane[3] ^= ((lane[6] << 2) & 0xff)
-    multiplied_lane[4] ^= ((lane[3] >> 3) & 0xff) ^ ((lane[4] >> 6) & 0xff)
-    multiplied_lane[5] ^= ((lane[5] << 6) & 0xff)
-    multiplied_lane[6] ^= ((lane[5] << 3) & 0xff)
+def _0(xi):
+    return 0
 
-    # binary matrix M1
-    multi_mat_l4_m1 = 0
-    l4 = lane[4]
-    multi_mat_l4_m1 ^= ((l4 & 0x8) >> 3)
-    multi_mat_l4_m1 ^= ((l4 & 0x10) >> 3)
-    multi_mat_l4_m1 ^= ((l4 & 0x20) >> 3)
-    multi_mat_l4_m1 ^= ((l4 & 0x40) >> 3) ^ ((l4 & 0x1) << 3)
-    multi_mat_l4_m1 ^= ((l4 & 0x80) >> 3) ^ ((l4 & 0x2) << 3)
-    multi_mat_l4_m1 ^= ((l4 & 0x04) << 3)
-    multi_mat_l4_m1 ^= ((l4 & 0x08) << 3)
-    multi_mat_l4_m1 ^= ((l4 & 0x10) << 3)
+def _M1(xi):
+    return (xi<<3 ^ xi>>3) & 0xff
 
-    multiplied_lane[5] ^= multi_mat_l4_m1
 
-    return multiplied_lane
+M = (
+    ( _0,    _Id,     _0,     _0,  _0,  _0,  _0,  _0),
+    ( _0,     _0,    _Id,     _0,  _0,  _0,  _0,  _0),
+    ( _0,     _0, _Sl(3),    _Id,  _0,  _0,  _0,  _0),
+    ( _0,     _0,     _0, _Sr(3), _Id,  _0,  _0,  _0),
+    ( _0,     _0,     _0,     _0,  _0, _Id,  _0,  _0),
+    ( _0, _Sl(2),     _0,     _0,  _0,  _0, _Id,  _0),
+    ( _0,     _0,     _0,     _0,  _0,  _0,  _0, _Id),
+    (_Id,     _0,     _0,     _0,  _0,  _0,  _0,  _0),
+)
+
+M2 = (
+    ( _0,     _0,    _Id,     _0,     _0,  _0,  _0,  _0),
+    ( _0,     _0, _Sl(3),    _Id,     _0,  _0,  _0,  _0),
+    ( _0,     _0, _Sl(6),    _M1,    _Id,  _0,  _0,  _0),
+    ( _0,     _0,     _0, _Sr(6), _Sr(3), _Id,  _0,  _0),
+    ( _0, _Sl(2),     _0,     _0,     _0,  _0, _Id,  _0),
+    ( _0,     _0, _Sl(2),     _0,     _0,  _0,  _0, _Id),
+    (_Id,     _0,     _0,     _0,     _0,  _0,  _0,  _0),
+    ( _0,    _Id,     _0,     _0,     _0,  _0,  _0,  _0),
+)
+
+
+def _multiplication(m):
+    def _multiply(x):
+        return list(reversed([
+            reduce(xor, (mj[i](xi) for i, xi in enumerate(reversed(x))))
+            for mj in m
+        ]))
+
+    return _multiply
 
 
 def _multiply_M3(lane):
@@ -198,8 +215,8 @@ def _multiply_MR3(lane):
 
 ALPHAS = (
     list,                       # Identity.
-    _multiply_M,
-    _multiply_M2,
+    _multiplication(M),
+    _multiplication(M2),
     _multiply_M3,
     _multiply_MR,
     _multiply_MR2,
-- 
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