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

[Florian Gerber]

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