[External] Re: Workaround very slow NAN/Infinities arithmetic?

On Thu, 30 Sep 2021, brodie gaslam via R-devel wrote:

Andr?,

I'm not an R core member, but happen to have looked a little bit at this
issue myself.  I've seen similar things on Skylake and Coffee Lake 2
(9700, one generation past your latest) too.  I think it would make sense
to have some handling of this, although I would want to show the

trade-off

with performance impacts on CPUs that are not affected by this, and on
vectors that don't actually have NAs and similar.  I think the

performance

impact is likely to be small so long as branch prediction is active, but
since branch prediction is involved you might need to check with

different

ratios of NAs (not for your NA bailout branch, but for e.g. interaction
of what you add and the existing `na.rm=TRUE` logic).

I would want to see realistic examples where this matters, not
microbenchmarks, before thinking about complicating the code. Not all
but most cases where sum(x) returns NaN/NA would eventually result in
an error; getting to the error faster is not likely to be useful.

My understanding is that arm64 does not support proper long doubles
(they are the same as regular doubles). So code using long doubles
isn't getting the hoped-for improved precision. Since that
architecture is becoming more common we should probably be looking at
replacing uses of long doubles with better algorithms that can work
with regular doubles, e.g Kahan summation or variants for sum.

You'll also need to think of cases such as c(Inf, NA), c(NaN, NA), etc.,
which might complicate the logic a fair bit.

Presumably the x87 FPU will remain common for a long time, but if there
was reason to think otherwise, then the value of this becomes
questionable.

Either way, I would probably wait to see what R Core says.

For reference this 2012 blog post[1] discusses some aspects of the issue,
including that at least "historically" AMD was not affected.

Since we're on the topic I want to point out that the default NA in R
starts off as a signaling NA:

    example(numToBits)   # for `bitC`
    bitC(NA_real_)
    ## [1] 0 11111111111 |

0000000000000000000000000000000000000000011110100010

    bitC(NA_real_ + 0)
    ## [1] 0 11111111111 |

1000000000000000000000000000000000000000011110100010

Notice the leading bit of the significant starts off as zero, which marks
it as a signaling NA, but becomes 1, i.e. non-signaling, after any
operation[2].

This is meaningful because the mere act of loading a signaling NA into

the

x87 FPU is sufficient to trigger the slowdowns, even if the NA is not
actually used in arithmetic operations.  This happens sometimes under

some

optimization levels.  I don't now of any benefit of starting off with a
signaling NA, especially since the encoding is lost pretty much as soon

as

it is used.  If folks are interested I can provide patch to turn the NA
quiet by default.

In principle this might be a good idea, but the current bit pattern is
unfortunately baked into a number of packages and documents on
internals, as well as serialized objects. The work needed to sort that
out is probably not worth the effort.

It also doesn't seem to affect the performance issue here since
setting b[1] <- NA_real_ + 0 produces the same slowdown (at least on
my current Intel machine).

Best,

luke

Best,

B.

[1]:

https://randomascii.wordpress.com/2012/05/20/thats-not-normalthe-performance-of-odd-floats/

[2]: https://en.wikipedia.org/wiki/NaN#Encoding

On Thursday, September 30, 2021, 06:52:59 AM EDT, GILLIBERT, Andre <

andre.gillibert at chu-rouen.fr> wrote:

Dear R developers,

By default, R uses the "long double" data type to get extra precision

for intermediate computations, with a small performance tradeoff.

Unfortunately, on all Intel x86 computers I have ever seen, long

doubles (implemented in the x87 FPU) are extremely slow whenever a special
representation (NA, NaN or infinities) is used; probably because it
triggers poorly optimized microcode in the CPU firmware. A function such as
sum() becomes more than hundred times slower!

Test code:
a=runif(1e7);system.time(for(i in 1:100)sum(a))
b=a;b[1]=NA;system.time(sum(b))

The slowdown factors are as follows on a few intel CPU:

1)      Pentium Gold G5400 (Coffee Lake, 8th generation) with R 64 bits

: 140 times slower with NA

2)      Pentium G4400 (Skylake, 6th generation) with R 64 bits : 150

times slower with NA

3)      Pentium G3220 (Haswell, 4th generation) with R 64 bits : 130

times slower with NA

4)      Celeron J1900 (Atom Silvermont) with R 64 bits : 45 times

slower with NA

I do not have access to more recent Intel CPUs, but I doubt that it has

improved much.

Recent AMD CPUs have no significant slowdown.
There is no significant slowdown on Intel CPUs (more recent than Sandy

Bridge) for 64 bits floating point calculations based on SSE2. Therefore,
operators using doubles, such as '+' are unaffected.

I do not know whether recent ARM CPUs have slowdowns on FP64... Maybe

somebody can test.

Since NAs are not rare in real-life, I think that it would worth an

extra check in functions based on long doubles, such as sum(). The check
for special representations do not necessarily have to be done at each
iteration for cumulative functions.

If you are interested, I can write a bunch of patches to fix the main

functions using long doubles: cumsum, cumprod, sum, prod, rowSums, colSums,
matrix multiplication (matprod="internal").

What do you think of that?

--
Sincerely
Andr? GILLIBERT

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--
Luke Tierney
Ralph E. Wareham Professor of Mathematical Sciences
University of Iowa                  Phone:             319-335-3386
Department of Statistics and        Fax:               319-335-3017
    Actuarial Science
241 Schaeffer Hall                  email:   luke-tierney at uiowa.edu
Iowa City, IA 52242                 WWW:  http://www.stat.uiowa.edu