mpn_mul is embarrassingly slow

[Marc Glisse]

On Fri, 20 Apr 2018, Marc Glisse wrote:

> On Fri, 20 Apr 2018, Vincent Lefevre wrote:
>
>> On 2018-04-20 04:14:15 +0200, Fredrik Johansson wrote:
>>> For operands with 1-4 limbs, that is; on my machine, mpn_mul takes up to
>>> twice as long as mpn_mul_basecase, and inline assembly for 1x1, 2x1 or 2x2
>>> multiplication is even faster. The problem is that there are three 
>>> function
>>> calls (mpn_mul -> mpn_mul_n -> mpn_mul_basecase) + branches between the
>>> user code and GMP's lightning fast assembly code.
>>> 
>>> I was reminded of this old issue when seeing this new paper on arXiv:
>>> https://arxiv.org/abs/1804.07236. Here, the author benchmarked a C++
>>> implementation of bignum arithmetic against mpn_mul for small operand 
>>> sizes
>>> and came to the conclusion that the former approach performs better than
>>> hand-optimized assembly (one wishes that compilers really were that clever
>>> about bignum code by now!).
>>> 
>>> Some advanced GMP users (including myself) know about the issue and simply
>>> avoid mpn_mul for performance-critical code with short operands. The most
>>> convenient solution is to call mpn_mul_basecase directly instead of
>>> mpn_mul. Unfortunately, mpn_mul_basecase is not public, so this is a bit
>>> iffy to rely on. One feature request would be to simply make
>>> mpn_mul_basecase / mpn_sqr_basecase public.
>> [...]
>> 
>> I'm wondering... With the current GMP code, does LTO help to avoid
>> such issues?
>
> mpn_mul and mpn_mul_n are too large to be completely inlined (unless that's 
> the only place where they are used, which could happen in a microtest, but 
> doesn't seem realistic in an application). What could happen is partial 
> inlining of the first test of each. Maybe using LTO+PGO (profile-guided 
> optimization)? Still, I am not particularly optimistic.

I just tried (LTO+PGO) on a trivial testcase, and gcc didn't manage to do 
anything clever with it. Doing it by hand to see how much potential gain 
there is, the timings are:

mpn_mul: .56
mpn_mul_n: .36
mpn_mul_basecase: .16

-- 
Marc Glisse