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Date: Thu, 16 Jan 2014 22:28:25 +0400
From: Solar Designer <>
Subject: Re: [PHC] Using multiply (Re: [PHC] A must read...)

On Wed, Jan 15, 2014 at 09:02:46PM -0600, Steve Thomas wrote:
> > On January 15, 2014 at 11:45 AM Bill Cox <> wrote:
> >
> > [...] 32x32 -> 32 Integer multiply seems solid and
> > pervasive enough. Besides that, it's fast in our devices even
> > compared to a custom ASIC, and it's a great operation for mixing bits,
> > at least when one op is odd.
> Have you thought about doing 4 (or more) multiplies in parallel:
> 4 multiplies with SSE4.1 (PMULLD _mm_mullo_epi32)
> 8 multiplies with AVX2 (VPMULLD _mm256_mullo_epi32)
> 16 multiplies with AVX-512 (VPMULLD _mm512_mullo_epi32)

FWIW, I have usage examples of all of these in php_mt_seed:

In order to reach full speed on Intel CPUs with HT and on AMD Bulldozer,
I needed to interleave 4 instances (means 16+ concurrent 32-bit multiplies
per thread: 4 per SIMD vector, and 4 in different pipeline stages).
However, this turned out to be insufficient for Intel CPUs without HT
(e.g., as tested on a Core i5), so I had to expand to 8 interleaved
instances, which did the trick (this made those HT-lacking CPUs run
about as fast as their HT-enabled counterparts).  Of course, all of
this is with the maximum supported number of hardware threads running

When tying up memory with multiply latencies, we don't have to maximize
the number of multiplies we compute in parallel, but it's nice to do so
as well, as long as that does not reduce the minimum number of cycles
for an ASIC attacker with even more parallelism.

> You can reorder the values in any order in SSE2 with PSHUFD
> (_mm_shuffle_epi32). Reordering the values in AVX2 and AVX-512 is
> trickier and may need multiple instructions.
> SSE4.1 has been on pretty much every Intel CPU since 2008. AVX2
> just came out last year with Haswell. I think integer AVX-512 will be on
> Skylake in 2015. They could delay integer operations until the next
> iteration in 2017 like they did with AVX/AVX2. AVX-512 should probably
> be considered since this competition will end when AVX-512 is
> estimated to be available or on the horizon.

Meanwhile, we can use MIC on Xeon Phi to simulate AVX-512 for testing.
The binary encoding is different, but many (most?) of the source code
intrinsics are the same for MIC and AVX-512.

As I had mentioned before, I am happy to grant PHC submission authors
remote access to our AVX2 and Xeon Phi systems.  If interested, just
e-mail me your desired login names and SSH public keys (off-list).


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