Add more multiplicative_order() unit tests

galois/_fields/_main.py

@@ -1730,7 +1730,7 @@ def multiplicative_order(self) -> Union[np.integer, np.ndarray]:
  else:
  d = np.array(divisors(field.order - 1)) # Divisors d such that d | p^m - 1
  y = np.power.outer(x, d) # x^d -- the first divisor d for which x^d == 1 is the order of x
- idxs = np.argmin(np.abs(y.view(np.ndarray) - 1), axis=-1) # First index of divisors, which is the order of x
+ idxs = np.argmin(y, axis=-1) # First index of divisors, which is the order of x
  order = d[idxs] # The order of each element of x
 
  return order

scripts/generate_field_test_vectors.py

@@ -234,6 +234,13 @@ def make_luts(field, sub_folder, seed, sparse=False):
  d = {"X": X, "Z": Z}
  save_pickle(d, folder, "additive_order.pkl")
 
+ set_seed(seed + 11)
+ X, Z = io_1d(1, order, sparse=sparse)
+ for i in range(X.shape[0]):
+ Z[i] = int(F(X[i]).multiplicative_order())
+ d = {"X": X, "Z": Z}
+ save_pickle(d, folder, "multiplicative_order.pkl")
+
  ###############################################################################
  # Polynomial arithmetic
  ###############################################################################

tests/fields/conftest.py

@@ -279,3 +279,15 @@ def field_additive_order(field_folder):
  d["X"] = GF(d["X"])
  d["Z"] = d["Z"]
  return d
+
+
+@pytest.fixture(scope="session")
+def field_multiplicative_order(field_folder):
+ GF, folder = field_folder
+ with open(os.path.join(folder, "multiplicative_order.pkl"), "rb") as f:
+ print(f"Loading {f}...")
+ d = pickle.load(f)
+ d["GF"] = GF
+ d["X"] = GF(d["X"])
+ d["Z"] = d["Z"]
+ return d

tests/fields/test_arithmetic_methods.py

@@ -16,3 +16,21 @@ def test_additive_order(field_additive_order):
  z = x.additive_order()
  assert np.array_equal(z, Z)
  assert type(z) is np.ndarray
+
+
+def test_multiplicative_order(field_multiplicative_order):
+ GF, X, Z = field_multiplicative_order["GF"], field_multiplicative_order["X"], field_multiplicative_order["Z"]
+ if GF.dtypes[-1] == np.object_:
+ # FIXME: Skipping large fields because they're too slow
+ return
+
+ dtype = random.choice(GF.dtypes)
+ x = X.astype(dtype)
+ z = x.multiplicative_order()
+ assert np.array_equal(z, Z)
+ assert type(z) is np.ndarray
+
+ with pytest.raises(ArithmeticError):
+ GF(0).multiplicative_order()
+ with pytest.raises(ArithmeticError):
+ GF.Range(0, 2).multiplicative_order()