From d68f5376fe2160e300ac6b64c8a6db29c1419355 Mon Sep 17 00:00:00 2001
From: mhostetter <matthostetter@gmail.com>
Date: Fri, 4 Feb 2022 11:16:28 -0500
Subject: [PATCH] Add unit tests for integer logarithms

---
 galois/_math.py                      |   2 +-
 scripts/generate_int_test_vectors.py |  14 +++++++++++-
 tests/conftest.py                    |  10 +++++++-
 tests/data/ilog.pkl                  | Bin 0 -> 355 bytes
 tests/test_math.py                   |  21 +++++++++++++++++
 tests/test_number_theory.py          |  33 ---------------------------
 6 files changed, 44 insertions(+), 36 deletions(-)
 create mode 100644 tests/data/ilog.pkl

diff --git a/galois/_math.py b/galois/_math.py
index 79dc47033..bfff7a685 100644
--- a/galois/_math.py
+++ b/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
     -------
diff --git a/scripts/generate_int_test_vectors.py b/scripts/generate_int_test_vectors.py
index 25f51e037..e2ece2e12 100644
--- a/scripts/generate_int_test_vectors.py
+++ b/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")
diff --git a/tests/conftest.py b/tests/conftest.py
index b48e8aad8..f31d687ae 100644
--- a/tests/conftest.py
+++ b/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
\ No newline at end of file
+    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
diff --git a/tests/data/ilog.pkl b/tests/data/ilog.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..8715d270fe22c647ba1e0e5ecf36c513b9cd57dc
GIT binary patch
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diff --git a/tests/test_math.py b/tests/test_math.py
index 39d0520fa..a0de6351e 100644
--- a/tests/test_math.py
+++ b/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
diff --git a/tests/test_number_theory.py b/tests/test_number_theory.py
index 33f8e4207..4b8fad839 100644
--- a/tests/test_number_theory.py
+++ b/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