On Fri, 20 Apr 2018, Marc Glisse wrote:
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
Let me mention here that LLVM does manage to take advantage of LTO to get
the running time of mpn_mul down to .16 for this trivial example (only
call mpn_mul, only on 1 limb numbers).
--
Marc Glisse
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