Ticket #3969: 3969-fast-matmod2-hash.patch

a/sage/matrix/matrix_mod2_dense.pyx

@@ -127 +127 @@
-    """
-    m4ri_destroy_all_codes()
-
+    
+
-cdef class Matrix_mod2_dense(matrix_dense.Matrix_dense):   # dense or sparse
-    r"""
-    Dense matrix over GF(2).
@@ -255 +257 @@
-
-    def __hash__(self):
-        """
+        The has of a matrix is computed as $\oplus i*a_i$ where the $a_i$ are 
+        the flattened entries in a matrix (by row, then by column). 
+        
-        EXAMPLE:
-            sage: B = random_matrix(GF(2),3,3)
-            sage: B.set_immutable()
@@ -262 +267 @@
-            {[0 1 0]
-            [0 1 1]
-            [0 0 0]: 0}
+            
+            sage: M = random_matrix(GF(2), 123, 321)
+            sage: M.set_immutable()
+            sage: MZ = M.change_ring(ZZ)
+            sage: MZ.set_immutable()
+            sage: hash(M) == hash(MZ)
+            True
+            sage: MS = M.sparse_matrix()
+            sage: MS.set_immutable()
+            sage: hash(M) == hash(MS)
+            True
-
-        TEST:
-            sage: A = matrix(GF(2),2,0)
@@ -269 +285 @@
-            sage: hash(A)
-            0
-        """
-
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-    cdef set_unsafe(self, Py_ssize_t i, Py_ssize_t j, value):
-        mzd_write_bit(self._entries, i, j, int(value))
-
@@ -1222 +1322 @@
-        A._entries = mzd_submatrix(A._entries, self._entries, lowr, lowc, highr, highc)
-        return A
-
+
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+
+# Used for hashing
+cdef int i, k
+cdef unsigned long parity_table[256]
+for i from 0 <= i < 256:
+    parity_table[i] = 1 & ((i) ^ (i>>1) ^ (i>>2) ^ (i>>3) ^ 
+                           (i>>4) ^ (i>>5) ^ (i>>6) ^ (i>>7))
+                           
+# gmp's ULONG_PARITY may use special 
+# assembly instructions, could be faster
+cpdef inline unsigned long parity(word a):
+    """
+    Returns the parity of the number of bits in a. 
+    
+    EXAMPLES: 
+        sage: from sage.matrix.matrix_mod2_dense import parity
+        sage: parity(1)
+        1L
+        sage: parity(3)
+        0L
+        sage: parity(0x10000101011)
+        1L
+    """
+    if sizeof(word) == 8:
+        a ^= a >> 32
+    a ^= a >> 16
+    a ^= a >> 8
+    return parity_table[a & 0xFF]
+
+cdef inline unsigned long parity_mask(word a):
+    return -parity(a)