diff --git a/galois.py b/galois.py
index ff9460e..e2298c3 100755
--- a/galois.py
+++ b/galois.py
@@ -37,7 +37,7 @@ class GaloisNumber:
         the field with which the GaloisNumber instance was defined.
         '''
         if v > self.field.size:
-            raise GaloisException ("Value {0} is outside field".format (value))
+            raise GaloisException ("Value {0} is outside field".format (v))
         self.value = v
 
     def __add__ (self, other):
@@ -171,9 +171,9 @@ class GaloisFieldDirect:
     There only needs to be one instantiation of the field for a given set of parameters,
     but elements from different field instances with the same parameters may be mixed.
     '''
-    field_widths = (4, 8, 12, 16)
-    poly_defaults = {4: 0x13, 8: 0x11d, 12:0x1053, 16: 0x1100b}
-    multiply_test_size = 10000
+    field_widths = (4, 8, 12, 16, 32)
+    poly_defaults = {4: 0x13, 8: 0x11d, 12:0x1053, 16: 0x1100b, 32: 0x1000000c5}
+    max_test_size = 5000
     def __init__ (self, bits, primitive_polynomial = None, repr_prefix = 'G', alpha = 1):
         '''
         Create a Galois field using direct arithmetic.  No log tables or inverses to
@@ -241,14 +241,15 @@ class GaloisFieldDirect:
         v = GaloisNumber (self)
         g_0 = GaloisNumber (self, 0)
         g_1 = GaloisNumber (self, 1)
-        for i in range (self.size):
-            v.assign (i)
-            if i == 0: continue
+        small_field = self.size < self.max_test_size
+        n_tests = (self.size - 1) if small_field else self.max_test_size
+        for i in range (0, n_tests):
+            v.assign ((i if small_field else random.randint (0, self.size - 2)) + 1)
             assert v * ~v == mul_identity, "Multiplicative inverse failed at {}".format (i)
             assert g_0 - v == -v, "Additive inverse failed at {}".format (i)
             assert v * g_1 == v, "Multiplicative identity failed at {}".format (i)
         vb = GaloisNumber (self)
-        for a in range (1, self.multiply_test_size):
+        for a in range (1, self.max_test_size):
             v.assign (random.randint (1, self.size - 1))
             vb.assign (random.randint (1, self.size - 1))
             product = v * vb
@@ -257,17 +258,19 @@ class GaloisFieldDirect:
         return True
 
 if __name__ == '__main__':
+    print '\nTesting direct fields...........'
     for width in GaloisFieldDirect.field_widths:
         field = GaloisFieldDirect (width)
-        g0 = GaloisNumber (field, 5)
+        g0 = GaloisNumber (field, 2)
         g1 = GaloisNumber (field, 7)
-        print g0 + g1
+        print '{0} + {1} = {2}'.format (g0, g1, g0 + g1)
         if field.self_test ():
             print "{0} bit field (direct) passed!".format (width)
+    print '\nTesting log fields...........'
     for width in GaloisFieldLog.field_widths:
         field = GaloisFieldLog (width)
+        g0 = GaloisNumber (field, 2)
+        g1 = GaloisNumber (field, 7)
+        print '{0} + {1} = {2}'.format (g0, g1, g0 + g1)
         if field.self_test ():
             print "{0} bit field (log) passed!".format (width)
-        g0 = GaloisNumber (field, 5)
-        g1 = GaloisNumber (field, 7)
-        print g0 + g1