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

iuke-tier@ey m@iii@g oii uiow@@edu iuke-tier@ey m@iii@g oii uiow@@edu
Thu Sep 30 19:24:53 CEST 2021

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

> André,
> 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,
> 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 using 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
>>      [[alternative HTML version deleted]]
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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 using uiowa.edu
Iowa City, IA 52242                 WWW:  http://www.stat.uiowa.edu

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