gh-118610: Centralize power caching in _pylong.py (#118611)

A new `compute_powers()` function computes all and only the powers of the base the various base-conversion functions need, as efficiently as reasonably possible (turns out that invoking `**`is needed at most once). This typically gives a few % speedup, but the primary point is to simplify the base-conversion functions, which no longer need their own, ad hoc, and less efficient power-caching schemes.

Co-authored-by: Serhiy Storchaka <storchaka@gmail.com>

Lib/test/test_int.py

@@ -906,6 +906,18 @@ class PyLongModuleTests(unittest.TestCase):
             with self.assertRaises(RuntimeError):
                 int(big_value)
 
+    def test_pylong_roundtrip(self):
+        from random import randrange, getrandbits
+        bits = 5000
+        while bits <= 1_000_000:
+            bits += randrange(-100, 101) # break bitlength patterns
+            hibit = 1 << (bits - 1)
+            n = hibit | getrandbits(bits - 1)
+            assert n.bit_length() == bits
+            sn = str(n)
+            self.assertFalse(sn.startswith('0'))
+            self.assertEqual(n, int(sn))
+            bits <<= 1
 
 if __name__ == "__main__":
     unittest.main()