Hi Robert,
I've run more experiments (and yes, the code is probably too long for
the list). The tradeoffs are platform dependent. The "nobreak" version
is slower than "break" on a corei7 (i7-3610QM), it is faster on opteron
(6282) and it is about the same on Xeon (E5-2640, E5-2670 even though
seen slower for big vectors).
It may be hard to get a universally better version. Still, a version
that performs fastest on platforms I checked, and sometimes by a lot -
about 2x faster than default - is
Rboolean hasNaN_pairsum(double *x, R_xlen_t n)
{
if ((n&1) != 0 && ISNAN(x[0]))
return TRUE;
for (int i = n&1; i < n; i += 2)
if (ISNAN(x[i]+x[i+1])) /* may also return TRUE for +-Inf */
return TRUE;
return FALSE;
}
It may also return "true" when some elements are Inf, but that is
safe/conservative for this purpose, and actually the MKL disclaimer
suggests we should be checking for Inf anyway.
This version is from pqR (except that pqR would check also the
individual arguments of the sum, it the sum is found to have NaN).
Does it perform well on Knights Landing?
Best
Tomas
On 01/16/2017 06:32 PM, Cohn, Robert S wrote:
Hi Tomas,
Can you share the full code for your benchmark, compiler options, and
performance results so that I can try to reproduce them? There are a lot of
variables that can affect the results. Private email is fine if it is too much
for the mailing list.
I am measuring on Knight's Landing (KNL) that was released in November. KNL is
not a co-processor so no offload is necessary. R executes directly on the Phi,
which looks like a multi-core machine with 64 cores.
Robert
-----Original Message-----
From: Tomas Kalibera [mailto:tomas.kalib...@gmail.com]
Sent: Monday, January 16, 2017 12:00 PM
To: Cohn, Robert S <robert.s.c...@intel.com>
Cc: r-devel@r-project.org
Subject: Re: [Rd] accelerating matrix multiply
Hi Robert,
thanks for the report and your suggestions how to make the NaN checks faster.
Based on my experiments it seems that the "break" in the loop actually can have positive impact on
performance even in the common case when we don't have NaNs. With gcc on linux (corei7), where isnan is
inlined, the "break" version uses a conditional jump while the "nobreak" version uses a
conditional move. The conditional jump is faster because it takes advantage of the branch prediction. Neither
of the two versions is vectorized (only scalar SSE instructions used).
How do you run R on Xeon Phi? Do you offload the NaN checks to the Phi coprocessor? So far I tried
without offloading to Phi, icc could vectorize the "nobreak" version, but the performance
of it was the same as "break".
For my experiments I extracted NaN checks into a function. This was the "break"
version (same performance as the current code):
static __attribute__ ((noinline)) Rboolean hasNA(double *x, int n) {
for (R_xlen_t i = 0; i < n; i++)
if (ISNAN(x[i])) return TRUE;
return FALSE;
}
And this was the "nobreak" version:
static __attribute__ ((noinline)) Rboolean hasNA(double *x, int n) {
Rboolean has = FALSE;
for (R_xlen_t i = 0; i < n; i++)
if (ISNAN(x[i])) has=TRUE;
return has;
}
Thanks,
Tomas
On 01/11/2017 02:28 PM, Cohn, Robert S wrote:
Do you have R code (including set.seed(.) if relevant) to show on how
to generate the large square matrices you've mentioned in the
beginning? So we get to some reproducible benchmarks?
Hi Martin,
Here is the program I used. I only generate 2 random numbers and reuse them to
make the benchmark run faster. Let me know if there is something I can do to
help--alternate benchmarks, tests, experiments with compilers other than icc.
MKL LAPACK behavior is undefined for NaN's so I left the check in, just made it
more efficient on a CPU with SIMD. Thanks for looking at this.
set.seed (1)
m <- 30000
n <- 30000
A <- matrix (runif(2),nrow=m,ncol=n)
B <- matrix (runif(2),nrow=m,ncol=n)
print(typeof(A[1,2]))
print(A[1,2])
# Matrix multiply
system.time (C <- B %*% A)
system.time (C <- B %*% A)
system.time (C <- B %*% A)
-----Original Message-----
From: Martin Maechler [mailto:maech...@stat.math.ethz.ch]
Sent: Tuesday, January 10, 2017 8:59 AM
To: Cohn, Robert S <robert.s.c...@intel.com>
Cc: r-devel@r-project.org
Subject: Re: [Rd] accelerating matrix multiply
Cohn, Robert S <robert.s.c...@intel.com>
on Sat, 7 Jan 2017 16:41:42 +0000 writes:
I am using R to multiply some large (30k x 30k double) matrices on a
64 core machine (xeon phi). I added some timers to src/main/array.c
to see where the time is going. All of the time is being spent in the
matprod function, most of that time is spent in dgemm. 15 seconds is
in matprod in some code that is checking if there are NaNs.
system.time (C <- B %*% A)
nancheck: wall time 15.240282s
dgemm: wall time 43.111064s
matprod: wall time 58.351572s
user system elapsed
2710.154 20.999 58.398
The NaN checking code is not being vectorized because of the early
exit when NaN is detected:
/* Don't trust the BLAS to handle NA/NaNs correctly: PR#4582
* The test is only O(n) here.
*/
for (R_xlen_t i = 0; i < NRX*ncx; i++)
if (ISNAN(x[i])) {have_na = TRUE; break;}
if (!have_na)
for (R_xlen_t i = 0; i < NRY*ncy; i++)
if (ISNAN(y[i])) {have_na = TRUE; break;}
I tried deleting the 'break'. By inspecting the asm code, I verified
that the loop was not being vectorized before, but now is vectorized.
Total time goes down:
system.time (C <- B %*% A)
nancheck: wall time 1.898667s
dgemm: wall time 43.913621s
matprod: wall time 45.812468s
user system elapsed
2727.877 20.723 45.859
The break accelerates the case when there is a NaN, at the expense of
the much more common case when there isn't a NaN. If a NaN is
detected, it doesn't call dgemm and calls its own matrix multiply,
which makes the NaN check time insignificant so I doubt the early
exit provides any benefit.
I was a little surprised that the O(n) NaN check is costly compared
to the O(n**2) dgemm that follows. I think the reason is that nan
check is single thread and not vectorized, and my machine can do 2048
floating point ops/cycle when you consider the cores/dual issue/8 way
SIMD/muladd, and the constant factor will be significant for even
large matrices.
Would you consider deleting the breaks? I can submit a patch if that
will help. Thanks.
Robert
Thank you Robert for bringing the issue up ("again", possibly).
Within R core, some have seen somewhat similar timing on some platforms (gcc)
.. but much less dramatical differences e.g. on macOS with clang.
As seen in the source code you cite above, the current implementation was
triggered by a nasty BLAS bug .. actually also showing up only on some
platforms, possibly depending on runtime libraries in addition to the compilers
used.
Do you have R code (including set.seed(.) if relevant) to show on how to
generate the large square matrices you've mentioned in the beginning? So we
get to some reproducible benchmarks?
With best regards,
Martin Maechler
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