Understanding and predict round-off errors sign on simple functions

Hi,



May be it is a basic thing but I would like to know if we can anticipate
round-off errors sign.



Here is an example :



# numerical matrix

m <- matrix(data=cbind(rnorm(10, 0), rnorm(10, 2), rnorm(10, 5)), nrow=10,
ncol=3)

m

            [,1]      [,2]     [,3]

[1,]  0.4816247 1.1973502 3.855641

[2,] -1.2174937 0.7356427 4.393279

[3,]  0.8504074 2.5286509 2.689196

[4,]  1.8048642 1.8580804 6.665237

[5,] -0.6749397 1.0944277 4.838608

[6,]  0.8252034 1.5595268 3.681695

[7,]  1.3002208 0.9582693 4.561577

[8,]  1.6950923 3.5677921 6.005078

[9,]  0.6509285 0.9025964 5.082288

[10,] -0.5676040 1.3281102 4.446451



#weird moving average of period 1 !

mma <- apply(m, 2, SMA, n=1)

mma

            [,1]      [,2]     [,3]

[1,]         NA        NA       NA

[2,] -1.2174937 0.7356427 4.393279

[3,]  0.8504074 2.5286509 2.689196

[4,]  1.8048642 1.8580804 6.665237

[5,] -0.6749397 1.0944277 4.838608

[6,]  0.8252034 1.5595268 3.681695

[7,]  1.3002208 0.9582693 4.561577

[8,]  1.6950923 3.5677921 6.005078

[9,]  0.6509285 0.9025964 5.082288

[10,] -0.5676040 1.3281102 4.446451





#difference should be 0 but here is the result

m - mma

               [,1]         [,2]          [,3]

[1,]            NA           NA            NA

[2,]  0.000000e+00 0.000000e+00 -8.881784e-16

[3,]  0.000000e+00 0.000000e+00 -8.881784e-16

[4,]  0.000000e+00 4.440892e-16 -8.881784e-16

[5,] -1.110223e-16 4.440892e-16 -8.881784e-16

[6,] -1.110223e-16 2.220446e-16 -4.440892e-16

[7,] -2.220446e-16 2.220446e-16  0.000000e+00

[8,] -2.220446e-16 0.000000e+00  0.000000e+00

[9,] -3.330669e-16 2.220446e-16 -8.881784e-16

[10,] -3.330669e-16 4.440892e-16 -8.881784e-16



SMA function use runMean

# TTR / R / MovingAverages.R

"SMA" <- function(x, n=10, ...) { # Simple Moving Average

   ma <- runMean( x, n )

   if(!is.null(dim(ma))) {

     colnames(ma) <- "SMA"

   }

  return(ma)

}





Can anyone explain me that round error type?

Is it possible to reproduce this same error generation in another language
like C++ or C# ?



Thanks in advance for your answers



Regards



Chris




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