Add API tests

Closes #253

Author: skirpichev

tests/test_functions.py

@@ -1,4 +1,7 @@
+import inspect
 import math
+import platform
+import sys
 
 import gmp
 import pytest
@@ -236,3 +239,13 @@ def test_interfaces():
     with pytest.raises(ValueError, match="invalid rounding mode specified"):
         _mpmath_normalize(1, mpz(111), 11, 12, 13, 1j)
     gmp._free_cache()  # just for coverage
+
+
+@pytest.mark.skipif(platform.python_implementation() != "CPython"
+                    or sys.version_info < (3, 11),
+                    reason="no way to specify a signature")
+def test_func_api():
+    for fn in ["comb", "factorial", "gcd", "isqrt", "lcm", "perm"]:
+        f = getattr(math, fn)
+        fz = getattr(gmp, fn)
+        assert inspect.signature(f) == inspect.signature(fz)

tests/test_mpz.py

@@ -1,4 +1,5 @@
 import cmath
+import inspect
 import locale
 import math
 import operator
@@ -1032,3 +1033,15 @@ def f(n):
     with ThreadPoolExecutor(max_workers=7) as tpe:
         futures = [tpe.submit(f, mpz(x)) for x in xs]
         assert all(f.result() == 1 for f in futures)
+
+
+@pytest.mark.skipif(platform.python_implementation() != "CPython"
+                    or sys.version_info < (3, 13),
+                    reason="no way to specify a signature")
+def test_int_api():
+    for meth in dir(int):
+        m = getattr(int, meth)
+        if meth.startswith("_") or not callable(m):
+            continue
+        mz = getattr(mpz, meth)
+        assert inspect.signature(m) == inspect.signature(mz)