My previous patch to optimize bits_in_digit was
rejected: http://bugs.python.org/issue29782

This leaves this issue open (mathmodule.c):

/* XXX: This routine does more or less the same thing as
 * bits_in_digit() in Objects/longobject.c.  Someday it would be nice to
 * consolidate them.  On BSD, there's a library function called fls()
 * that we could use, and GCC provides __builtin_clz().
 */

We could still deal with the code duplication without the
complexity of the optimizations in the previous patch.

New changeset c5b79003f5fe6aa28a2a028680367839ba8677db by Victor Stinner (Niklas Fiekas) in branch 'master':
bpo-31031: Unify duplicate bits_in_digit and bit_length (GH-2866)
https://github.com/python/cpython/commit/c5b79003f5fe6aa28a2a028680367839ba8677db

"On BSD, there's a library function called fls() that we could use, and GCC provides __builtin_clz()."

See also rejected bpo-29782 and GH-594.

If someone wants to experiment that, I suggest to add Include/internal/pycore_pymath.h, move _Py_bit_length() there and convert it to a static inline function.

Since the code is now unified, it makes a little bit more sense to add specialized code, *if* the code is not too complex.

I'm still not sure that GH-594 is worth it, since it was not possible to see the speedup on a microbenchmark :-(

Thanks Niklas Fiekas for merging duplicated code ;-) It should make factorial_partial_product() a little bit more efficient!