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List:       r-devel
Subject:    Re: [Rd] Why is matrix product slower when matrix has very small values?
From:       Serguei Sokol <sokol () insa-toulouse ! fr>
Date:       2019-11-20 9:14:44
Message-ID: 0de9cebf-7a39-e48a-16f7-396b54b8e658 () insa-toulouse ! fr
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Le 20/11/2019 à 09:56, Hilmar Berger a écrit :
> 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 ?
Another guess is that you are caught by what is called "denormal 
numbers" https://en.wikipedia.org/wiki/Denormal_number.
Arithmetic operations on them are different and slower that those on 
"normal" numbers.

Best,
Serguei.

> 
> 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
> > 
> > ______________________________________________
> > R-devel@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-devel
> 

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