How about this for a careful (nonreckless) matmul (or other BLAS):
Spend O(n^2) to check the inputs for NaNs (and perhaps infinities)
... cheap
If (a NaN appears) ... very unlikely
use a version of matmul that we know will propagate them correctly
... could be slower matmul, or we could just fill in
selected rows and
... columns of product with NaNs depending on where NaNs
appeared in the input
else
use your favorite performance tuned (reckless) version,
including Strassen etc.
end if
How to do this of course depends on how we decide to treat the cases
alpha=0, beta=0.
A less portable version might use some kind of exceptions flags at the
end (of course
the usual ones will not be set by quiet NaNs) to see if a NaN appeared,
and recomputation
is necessary (so slow with low probability). This would of course not
fix the problem identified
in Julien's email, where the NaN may not be touched at all.
Jim
On 7/10/14, 8:34 AM, Julien Langou wrote:
Hi all,
1) Below is an email that we just received from some R & redhat folks
about NaN propagation in the BLAS. Please read the email discussion
between them and I.
I summarized their request in my reply to them. (So you can just read
my answer.)
2) Please see as well my question to them. Starting with: "A related
question. How do you feel about the other of IF statements if DGEMM??
(I do not have an answer yet from them.)
3) Please see as well:
http://icl.cs.utk.edu/lapackforum/viewtopic.php?f=5&t=4499
4) Please see as well email from Jim (Demmel) to Penny Andrerson
(MathWorks) "[LAPACKDEV] NaNs and consistent exception handling" from
DEC142012.
So basically this is the recurring of issue of NaN propagation.
1) I think we will apply the patch of these guys. Reason: I am OK with
keeping the nonpropagation of NaNs when ALPHA and BETA have special
values (for now), but this nonpropagation here is really weird. It is
specific to the JLI variant of DGEMM, it applies when an entry of B is
ZERO, pfff . . . Oh my. I just have a headache to think what the
output would look like. There would be NaN at some places in C, no NaN
at other places. A mess. I am OK with keeping the nonpropagation of
NaNs when ALPHA and BETA have special values (for now), but not based
on values of the entries of the matrices A and B.
(Does this make sense?)
2) We can rethink the NaN propagation in DGEMM (and BLAS in general)
for values of ALPHA and BETA. (???) So bottom line: do we want the
reference DGEMM to just be three loops and propagate everything? I
think this is more a question for users, superusers, etc. Jim might
have some answers with his related projects.
3) Note: Strassen version of DGEMM will not propagate NaN correctly.
Too many NaNs will be created. (Just a random comment, I was just
thinking about this.)
Cheers,
Julien.
Begin forwarded message:
*From: *Julien Langou <julien.langou@Domain.Removed
<mailto:julien.langou@Domain.Removed>>
*Subject: **Re: [Lapack] Issue with BLAS causing regression test
failure in R*
*Date: *July 10, 2014 at 9:12:10 AM MDT
*To: *Tom Callaway <tcallawa@Domain.Removed <mailto:tcallawa@Domain.Removed>>
*Cc: *Martyn Plummer <plummerm@Domain.Removed
<mailto:plummerm@Domain.Removed>>,
"peljasz@Domain.Removed <mailto:peljasz@Domain.Removed>"
<peljasz@Domain.Removed <mailto:peljasz@Domain.Removed>>, julie langou
<julie@Domain.Removed <mailto:julie@Domain.Removed>>
Hi Tom, Hi Martyn, Hi Lejeczek,
Thanks for pointing this, just to let you know that we (LAPACK folks)
are discussing this.
So just taking DGEMM as an example, if you use notation:
C(I,J) = C(I,J) + alpha * A(I,L) * B(L,J),
the reference BLAS DGEMM is using the JLI version of matrix matrix
multiply and is checking for each J (from 1 to N) and each L (from 1
to K), whether B(L,J) is zero (or not) to save (or not) the 2M
following operations.
The snippets of code is as follows
DO 90 J = 1,N
DO 80 L = 1,K
IF (B(L,J).NE.ZERO) THEN
TEMP = ALPHA*B(L,J)
DO 70 I = 1,M
C(I,J) = C(I,J) + TEMP*A(I,L)
70 CONTINUE
END IF
80 CONTINUE
90 CONTINUE
You suggest to remove the IF statement so that NaNs are correctly
propagated.
So as I said, we (LAPACK folks) are discussing this.
A related question. How do you feel about the other of IF statements
if DGEMM?
For example: (always on DGEMM)
(1) if BETA = 0, we set C to ZERO, then we follow with computation,
etc. So if BETA = 0 and NaN in C, the NaN in C are removed. Are you
OK with this?
(2) if ALPHA = 0 and BETA = 1, we return directly. So if ALPHA = 0
and BETA = 1, and NaNs in A or in B, these NaNs are not propagated to
output C. Are you OK with this?
What I am trying to say is that there are plenty of other places
where NaN are not necessarily propagated within DGEMM.
(Pretty much each time there is an IF statement in the DGEMM
subroutine is a case of this.)
So my question is how do you feel about the other places where NaN in
input (A, B, C, or alpha, or beta) do not propagate?
Cheers,
Julien.
On Jul 7, 2014, at 9:58 AM, Tom Callaway <tcallawa@Domain.Removed
<mailto:tcallawa@Domain.Removed>> wrote:
Hello LAPACK people,
Martyn & Lejeczek (on CC) reported an issue to Fedora relating to R
using our system copy of BLAS (from LAPACK).
As noted in the R administration and Installation Manual, "R relies on
ISO/IEC 60559 compliance of an external BLAS. This can be broken if for
example the code assumes that terms with a zero factor are always zero
and do not need to be computed  whereas x*0 can be NaN. This is checked
in the test suite."
In the stock BLAS, DGBMV, DGEMM, and DGEMV fail this. R has been
patching their bundled BLAS to resolve this issue since 2010, but Fedora
now uses the system BLAS.
Attached is a patch (from upstream R) to fix this issue in the LAPACK
BLAS. Please consider applying it.
Thanks,
~tom
==
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