GeezerVison

Don't change it for this PR, but this shouldn't be needed, as there should only be one zero. I think this indicates a bug in the caller.
The above assert, assert(size >= 0) should then be assert(size > 0)

What is size?. The assumption is that it is size in bytes, but I think you are using size in machine words.
Also needs to be Py_ssize_t.

it's the results of sizeof(PyLongObject), that should be bytes no?

Should we move the #if WITH_FREELISTS into PyInterpreterState_FreelistFree to keep it localized?

Personally, I think we should just remove WITH_FREELISTS, but that needs a wider discussion.

Note for future PR: we should add the bulk allocate/free capability to the allocator.

Why divide by 2 and not 2 * sizeof(void *), which is the quantum of allocation for malloc and ob_malloc?
(Assuming that the size is in bytes)
Could you use the term "size class" or equivalent, instead of "freelist index" The mapping here is from sizes to classes (not all size classes get free lists).

Any reason not to make this an inline function?

Alternatively, put an assert in this function, and put a size check in the caller.

Why this formula?

You want to allocate all sizes from (n-1)*FREELIST_QUANTUM + 1 to n*FREELIST_QUANTUM (inclusive) from the same freelist.
I would expect the formula to be (size + FREELIST_QUANTUM -1)/FREELIST_QUANTUM, or (size-1)/FREELIST_QUANTUM.

And because C division rounds towards 0, not -infinity, you want to use >>LOG_BASE_2_OF_FREELIST_QUANTUM, not /FREELIST_QUANTUM.

I haven't changed this yet. I'm trying to get it to work with just ints.

There already are some macros in pycore_obmalloc.h that seem to do something like this:

/* 
 * Alignment of addresses returned to the user. 8-bytes alignment works
 * on most current architectures (with 32-bit or 64-bit address buses).
 * The alignment value is also used for grouping small requests in size
 * classes spaced ALIGNMENT bytes apart.
 *
 * You shouldn't change this unless you know what you are doing.
 */

#if SIZEOF_VOID_P > 4
#define ALIGNMENT              16               /* must be 2^N */
#define ALIGNMENT_SHIFT         4
#else
#define ALIGNMENT               8               /* must be 2^N */
#define ALIGNMENT_SHIFT         3
#endif
   
/* Return the number of bytes in size class I, as a uint. */
#define INDEX2SIZE(I) (((pymem_uint)(I) + 1) << ALIGNMENT_SHIFT)