[Rd] Why is matrix product slower when matrix has very small values?

[Hilmar Berger]

Hi Florian,

just a guess, but couldn't it be that the multiplication of very small 
values leads to FP underflow exceptions which have to be handled by BLAS 
in a less efficient way than "normal" multiplications handled by SIMD 
instructions ?

Best regards,
Hilmar

On 19/11/2019 15:09, Florian Gerber wrote:
> Hi,
>
> I experience surprisingly large timing differences for the
> multiplication of matrices of the same dimension. An example is given
> below. How can this be explained?
> I posted the question on Stackoverflow:
> https://stackoverflow.com/questions/58886111/r-why-is-matrix-product-slower-when-matrix-has-very-small-values
> Somebody could reproduce the behavior but I did not get any useful
> explanations yet.
>
> Many thanks for hints!
> Florian
>
> ## disable openMP
> library(RhpcBLASctl); blas_set_num_threads(1); omp_set_num_threads(1)
>
> A <- exp(-as.matrix(dist(expand.grid(1:60, 1:60))))
> summary(c(A))
> #     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
> # 0.000000 0.000000 0.000000 0.001738 0.000000 1.000000
>
> B <- exp(-as.matrix(dist(expand.grid(1:60, 1:60)))*10)
> summary(c(B))
> #      Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
> # 0.0000000 0.0000000 0.0000000 0.0002778 0.0000000 1.0000000
>
> identical(dim(A), dim(B))
> ## [1] TRUE
>
> system.time(A %*% A)
> #    user  system elapsed
> #   2.387   0.001   2.389
> system.time(B %*% B)
> #    user  system elapsed
> #  21.285   0.020  21.310
>
> sessionInfo()
> # R version 3.6.1 (2019-07-05)
> # Platform: x86_64-pc-linux-gnu (64-bit)
> # Running under: Linux Mint 19.2
>
> # Matrix products: default
> # BLAS:   /usr/lib/x86_64-linux-gnu/openblas/libblas.so.3
> # LAPACK: /usr/lib/x86_64-linux-gnu/libopenblasp-r0.2.20.so
>
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-- 
Dr. Hilmar Berger, MD
Max Planck Institute for Infection Biology
Charitéplatz 1
D-10117 Berlin
GERMANY

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