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Date: Thu, 27 Feb 2014 13:41:14 -0000
Subject: Re: [PHC] GPU multiplication speed?

> Are my numbers right?  My Google-fu is failing me this morning.  I
> could not find a table of NVDA or ATI GPU instruction latencies.  I
> did find one post suggesting to use 24x24 multiplication because it's
> only 4 clocks, but there was no mention of 32x32 latencies.

In older times, I did some experiments on my GPU (it was Nvidia GTX 9800+,
i.e. an older architecture, that I bought in 2009); latency for _any_
instruction (including the 24x24 multiply, but also simpler things like a
bitwise XOR) was around 22 clock cycles. Each core could issue one
instruction per cycle, but you had to intertwine at least 22 distinct
individual computations to keep the cores busy. Of course, each
computation used its own registers, and the local RAM block was shared, so
such intertwining was not necessarily easy to achieve.

Newer core architectures are supposed to have a lower latency, but 4
cycles might be overoptimistic.

A "4-cycle" delay was found in my GPU but designated something quite
different. The 128 cores were actually 32 "multicores" and each multicore
could run 8 operations in parallel, provided that operations came in
batches of 32 identical operations. I.e., once every 4 cycles (here is the
delay), an instruction was issued to the multicore, and the multicore
would execute 32 times that instruction, on 32 different sets of
registers. However, that does not mean that at the end of the 4 clock
cycles the 32 results were available. Indeed, if any of the next few
instructions tried to use the result, then stalling would occur. Stalling
would also occur for non-parallel instructions, e.g. most memory accesses.
Such stalling is automatic, but degrades performance when it occurs. With
the 22-cycle delay, you can see that you have, in general, to run 6*32 =
192 parallel computations on each multicore in order to keep all cores
busy (in practice, there appeared to be rounding issues in the instruction
scheduler, meaning that you had to go up to 8*32 = 256 per multicore, i.e.
4096 parallel computations for the whole GPU).

I think newer Nvidia chips could run 16 instructions in parallel in a
multicore, for a latency down to about 11 cycles, but I have not tried it.

In the context of password cracking, this means that if the computation
can run entirely in registers (e.g. PBKDF2 with any of the SHA-2
functions), then it is easy to use the GPU at full speed, by just running
sufficiently many instances in parallel. This would apply to use of
multiplications too; however, GPU are usually not very good at integer
multiplications (not as good as CPU); e.g. my GPU could do 24x24 in one
instruction, not 32x32.

If you want to make things awkward and difficult for GPU, good methods
include using a very large state (the number of free registers in a GPU is
large but not infinite), or to force memory usage (e.g. with accesses at
irregular addresses, like in RC4 encryption: these cannot be easily mapped
to registers; actual RAM must be used). Each multicore has access to some
"local RAM" (like 4 kB) that supports parallel access to some extent, but
all intertwined computations must share that amount: if you need to run
192 parallel instances on a multicore, then each instance only has 20 or
30 bytes to play with efficiently; everything beyond will incur accesses
to external RAM, and these won't be parallel.

All of the above is only a rough, simplistic description, and figures must
undoubtedly be modified for newer GPU.

        --Thomas Pornin

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