Add unit tests for integer logarithms

galois/_math.py

@@ -185,7 +185,7 @@ def ilog(n: int, b: int) -> int:
  n : int
  A positive integer.
  b : int
- The logarithm base :math:`b`.
+ The logarithm base :math:`b`, must be at least 2.
 
  Returns
  -------

scripts/generate_int_test_vectors.py

@@ -11,7 +11,7 @@
 
 import sage
 import numpy as np
-from sage.all import Integer, xgcd, lcm, prod, isqrt
+from sage.all import Integer, xgcd, lcm, prod, isqrt, log
 
 PATH = os.path.join(os.path.dirname(os.path.abspath(__file__)), "..", "tests")
 FOLDER = os.path.join(PATH, "data")
@@ -108,3 +108,15 @@ def save_pickle(d, folder, name):
  Z[i] = int(z)
 d = {"X": X, "R": R, "Z": Z}
 save_pickle(d, FOLDER, "iroot.pkl")
+
+set_seed(SEED + 107)
+X = [random.randint(1, 1000) for _ in range(20)] + [random.randint(1000, 1_000_000_000) for _ in range(20)]
+B = [random.randint(2, 6) for _ in range(40)]
+Z = [0,]*len(X)
+for i in range(len(X)):
+ x = X[i]
+ b = B[i]
+ z = log(Integer(x), b)
+ Z[i] = int(z)
+d = {"X": X, "B": B, "Z": Z}
+save_pickle(d, FOLDER, "ilog.pkl")

tests/conftest.py

@@ -59,4 +59,12 @@ def iroot():
  with open(os.path.join(FOLDER, "iroot.pkl"), "rb") as f:
  print(f"Loading {f}...")
  d = pickle.load(f)
- return d
+ return d
+
+
+@pytest.fixture(scope="session")
+def ilog():
+ with open(os.path.join(FOLDER, "ilog.pkl"), "rb") as f:
+ print(f"Loading {f}...")
+ d = pickle.load(f)
+ return d

tests/test_math.py

@@ -125,3 +125,24 @@ def test_iroot(iroot):
 
  galois.iroot(10, 1) == 10
  assert galois.iroot(0, 2) == 0
+
+
+def test_ilog_exceptions():
+ with pytest.raises(TypeError):
+ galois.ilog(9.0, 2)
+ with pytest.raises(TypeError):
+ galois.ilog(9, 2.0)
+ with pytest.raises(ValueError):
+ galois.ilog(0, 2)
+ with pytest.raises(ValueError):
+ galois.ilog(-9, 2)
+ with pytest.raises(ValueError):
+ galois.ilog(9, 1)
+
+
+def test_ilog(ilog):
+ X, B, Z = ilog["X"], ilog["B"], ilog["Z"]
+ for i in range(len(X)):
+ assert galois.ilog(X[i], B[i]) == Z[i]
+
+ assert galois.ilog(10, 10) == 1

tests/test_number_theory.py

@@ -203,36 +203,3 @@ def test_is_cyclic():
  assert galois.is_cyclic(2*5*7*9) == False
 
  assert all(galois.is_cyclic(n) == (galois.euler_phi(n) == galois.carmichael_lambda(n)) for n in range(1, 100))
-
-
-###############################################################################
-# Integer arithmetic
-###############################################################################
-
-def test_ilog_exceptions():
- with pytest.raises(TypeError):
- galois.ilog(9.0, 2)
- with pytest.raises(TypeError):
- galois.ilog(9, 2.0)
- with pytest.raises(ValueError):
- galois.ilog(-9, 2)
- with pytest.raises(ValueError):
- galois.ilog(9, 1)
-
-
-# TODO: Find a way to generate test vectors with Sage
-def test_ilog():
- p = galois.mersenne_primes(2000)[-1]
- exponent = galois.ilog(p, 17)
- assert isinstance(exponent, int)
- assert 17**exponent <= p and not 17**(exponent + 1) <= p
-
- p = galois.mersenne_primes(2000)[-1] - 1
- exponent = galois.ilog(p, 17)
- assert isinstance(exponent, int)
- assert 17**exponent <= p and not 17**(exponent + 1) <= p
-
- p = galois.mersenne_primes(2000)[-1] + 1
- exponent = galois.ilog(p, 17)
- assert isinstance(exponent, int)
- assert 17**exponent <= p and not 17**(exponent + 1) <= p