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Workaround very slow NAN/Infinities arithmetic?

5 messages · GILLIBERT, Andre, brodie gaslam, iuke-tier@ey m@iii@g oii uiow@@edu +1 more

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GILLIBERT, Andre
# 
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
brodie gaslam
# 
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).

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.

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
GILLIBERT, Andre
#
Brodie Gaslam wrote:
For operators such as '+', randomly placed NAs could slow down AMD processor due to many branch mispredictions. However, the functions using long doubles are mainly "cumulative" functions such as sum, mean, cumsum, etc. They can stop at the first NA found.
When an infinity is found, the rest of the vector must be searched for infinities of the opposite side or NAs.
Mixing NaN and NAs has always been platform-dependent in R, but, on x87, it seems that the first NA/NaN met wins. Being consistent with that behavior is easy.

I wrote a first patch for the sum() function, taking in account all those special +Inf/-Inf/NA/NaN cases. Without any NA, the sum() function was 1.6% slower with my first patch on a Celeron J1900. Not a big deal, in my opinion.

However, I could easily compensate that loss (and much more) by improving the code.
By splitting the na.rm=TRUE and na.rm=FALSE code paths, I could save a useless FP comparison (for NAN), a useless CMOV (for the 'updated' variable) and useless SSE->memory->FP87 moves (high latency).

My new code is x1.75 times faster, for sum(big_vector_without_NAs, na.rm=FALSE).
It is x1.35 times faster for sum(big_vector_without_NAs, na.rm=TRUE)

Of course, it is much faster if there are any NA, because it stops at the first NA found. For infinities on AMD CPUs, it may not necessarily be faster.
iuke-tier@ey m@iii@g oii uiow@@edu
#
On Thu, 30 Sep 2021, brodie gaslam via R-devel wrote:

            

      
      
      
    

        
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.

            

      
      
      
    

        
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

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Gabriel Becker
    

    

      
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Mildly related (?) to this discussion, if you happen to be in a situation
where you know something is a C NAN, but need to check if its a proper R
NA, the R_IsNA function is surprisingly (to me, at least) expensive to do
in a tight loop because it calls the (again, surprisingly expensive to me)
isnan function.  This can happen in known sorted  Altrep REALSXPs where you
can easily determine the C-NAN status of all elements in the vector with a
binary search for the edge of the NANs, so in O(logn) calls to R_isnan. You
could notably also determine finiteness of all elements this way with a
couple more O(logn) passes if you needed to in the sorted case.

This came up when I was developing the patch for the unique/duplicated
fastpass for known-sorted vectors (thanks to Michael for working with me on
that and putting it in); I ended up writing an NAN_IS_R_NA macro to avoid
that isnan call since it's known. This was necessary (well, helpful at
least) because unique/duplicated care about the difference between NA and
NaN, while sorting and REAL_NO_NA (because ALTREP metadata/behavior is
closely linked to sort behavior) do not. In the case where you have a lot
of NAN values of solely one type or the other (by far most often because
they are all NAs and none are NaNs) the difference in speedup was
noticeably significant as I recall. I don't have the numbers handy but I
could run them again if desired.

~G

        
On Thu, Sep 30, 2021 at 10:25 AM <luke-tierney at uiowa.edu> wrote: