GNFS implementation + GF2 gaussian elimination fix

test/GF2test.hs

@@ -1,43 +1,76 @@
 module GF2test (run) where
 
+import Data.Bits (xor)
+import Data.List (foldl')
 import Test.HUnit
 
 import LinearAlgebra.GF2
   ( fromBools
-  , gaussianEliminationIndices
+  , gaussianEliminationAllMasks
+  , maskToIndicesInt
   )
 
+-- XOR of the rows selected by a mask
+xorSelected :: [Integer] -> [Int] -> Integer
+xorSelected rows idxs = foldl' xor 0 [ rows !! i | i <- idxs ]
+
 run :: IO ()
 run = do
     putStrLn "GF2 Gaussian elimination test"
 
-    let rowsBools =
-          [ [True, False, True]
-          , [False, True, True]
-          , [True, True, True]
-          , [True, True, False]
-          ]
+    -- one dependency: rows 0, 1 and 3 XOR to zero
+    let rowsBits =
+          map fromBools
+            [ [True, False, True]
+            , [False, True, True]
+            , [True, True, True]
+            , [True, True, False]
+            ]
+        masks = gaussianEliminationAllMasks rowsBits
 
-        nCols = length (head rowsBools)
-        rowsBits = map fromBools rowsBools
-        maybeIndices = gaussianEliminationIndices nCols rowsBits
+    assertEqual "expected exactly one dependency" 1 (length masks)
+    assertEqual "expected rows 0,1,3" [[0,1,3]] (map maskToIndicesInt masks)
 
-    case maybeIndices of
-        Nothing   -> assertFailure "expected rows 0,1,3"
-        Just rows -> assertEqual "expected rows 0,1,3" rows [0,1,3]
+    -- no dependency case: the three rows are independent
+    let rowsBits2 =
+          map fromBools
+            [ [True, False, True]
+            , [False, True, True]
+            , [True, True, True]
+            ]
 
+    assertEqual "Expected no dependency" [] (gaussianEliminationAllMasks rowsBits2)
 
-    -- no depency case
-    let rowsBools2 =
-          [ [True, False, True]
-          , [False, True, True]
-          , [True, True, True]
-          ]
-        nCols2 = length (head rowsBools2)
-        rowsBits2 = map fromBools rowsBools2
-        maybeIndices2 = gaussianEliminationIndices nCols2 rowsBits2
+    -- several dependencies: 5 rows of rank 2 give a null space of dimension 3
+    let rowsBits3 =
+          map fromBools
+            [ [True,  False, True]    -- a
+            , [False, True,  True]    -- b
+            , [True,  True,  False]   -- a xor b
+            , [True,  False, True]    -- a again
+            , [False, False, False]   -- zero row
+            ]
+        masks3 = gaussianEliminationAllMasks rowsBits3
+        idxs3  = map maskToIndicesInt masks3
 
-    assertEqual "Expected no dependency" Nothing maybeIndices2
+    assertEqual "expected rows - rank = 3 dependencies" 3 (length masks3)
+    assertBool "every dependency must XOR to zero"
+               (all (\ix -> xorSelected rowsBits3 ix == 0) idxs3)
+    assertBool "no dependency may be empty" (all (not . null) idxs3)
+    assertBool "the zero row (index 4) must be a dependency on its own" ([4] `elem` idxs3)
+
+    -- the dependencies must be linearly independent (distinct and non-zero masks)
+    assertEqual "dependencies must be pairwise distinct" (length masks3) (length (dedup masks3))
+
+    -- a repeated row is a dependency of size two
+    let rowsBits4 = map fromBools [ [True, False], [False, True], [True, False] ]
+    assertEqual "duplicate row dependency" [[0,2]]
+                (map maskToIndicesInt (gaussianEliminationAllMasks rowsBits4))
+
+    -- empty input
+    assertEqual "no rows, no dependency" [] (gaussianEliminationAllMasks [])
 
     putStrLn "GF2 test done."
-
+  where
+    dedup []       = []
+    dedup (x : xs) = x : dedup (filter (/= x) xs)