R 2.12.1 Windows 32bit and 64bit - are numerical differences expected?

Should one expect minor numerical differences between 64bit and 32bit R on
Windows? Hunting around the lists I've not been able to find a definitive
answer yet. Seems plausible using different precision arithmetic, but waned
to confirm from those who might know for sure.

BACKGROUND

A colleague was trying to replicate some modelling results (from a soon to
be published book) using rpart, ada, and randomForest, for example. My 64bit
Linux and 64bit Windows 7 always agree (so far), but not their 32bit
Windows. I've distilled it to a few simple lines of code to replicate the
differences (but had to stay with the weather dataset from rattle since
could not replicate on standard datasets yet).

library(rpart)
library(rattle)
set.seed(41)
model<- rpart(RainTomorrow ~ ., data=weather[-c(1, 2,
23)], control=rpart.control(minbucket=0))
print(model$cptable)

Final row on 32bit: 9 0.01000000     23 0.1515152 1.1060606 0.1158273
Final row on 64bit: 9 0.01000000     23 0.1515152 1.0909091 0.1152273

Pretty minor, but different. I've not found any seed other than 41 (only
tried a few) that results in a difference.

library(ada) # using rpart underneath
set.seed(41)
model<- ada(RainTomorrow ~ ., data=weather[-c(1, 2, 23)])
print(model)

On 32bit: Train Error: 0.057
On 64bit: Train Error: 0.055

Changing the seed to 42, for example, brings them into sync.

library(randomForest)
set.seed(41)
model<- randomForest(RainTomorrow ~ ., data=weather[-c(1, 2, 23)],
                       importance=TRUE, na.action=na.roughfix)
print(model)

On 32bit:  OOB estimate of  error rate: 12.84%
On 64bit:  OOB estimate of  error rate: 11.75%

sessionInfo()

R version 2.12.1 (2010-12-16)
Platform: i386-pc-mingw32/i386 (32-bit)

locale:
[1] LC_COLLATE=English_Australia.1252  LC_CTYPE=English_Australia.1252
[3] LC_MONETARY=English_Australia.1252 LC_NUMERIC=C
[5] LC_TIME=English_Australia.1252

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] randomForest_4.5-36 pmml_1.2.27         XML_3.2-0.2
[4] colorspace_1.0-1    RGtk2_2.20.3        ada_2.0-2
[7] rattle_2.6.2        rpart_3.1-47

loaded via a namespace (and not attached):
[1] tools_2.12.1

sessionInfo()

R version 2.12.1 (2010-12-16)
Platform: x86_64-pc-mingw32/x64 (64-bit)
...


Thanks,
Graham

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Should one expect minor numerical differences between 64bit and 32bit R on
Windows? Hunting around the lists I've not been able to find a definitive
answer yet. Seems plausible using different precision arithmetic, but waned
to confirm from those who might know for sure.

On Thu, Feb 10, 2011 at 10:37:09PM +1100, Graham Williams wrote:

Should one expect minor numerical differences between 64bit and 32bit R on
Windows? Hunting around the lists I've not been able to find a definitive
answer yet. Seems plausible using different precision arithmetic, but waned
to confirm from those who might know for sure.

One of the sources for the difference between platforms are different
settings of the compiler. On Intel processors, the options may influence,
whether the registers use 80 bit or 64 bit representation of floating
point numbers. In memory, it is always 64 bit. Testing, whether there is
a difference between registers and memory may be done for example using
the code

 #include <stdio.h>
 #define n 3
 int main(int agc, char *argv[])
 {
     double x[n];
     int i;
     for (i=0; i<n; i++) {
         x[i] = 1.0/(i + 5);
     }
     for (i=0; i<n; i++) {
         if (x[i] != 1.0/(i + 5)) {
             printf("difference for %d\n", i);
         }
     }
     return 0;
 }

If the compiler uses SSE arithmetic (-mfpmath=sse), then the output is empty.
If Intel's extended arithmetic is used, then we get

 difference for 0
 difference for 1
 difference for 2

On 32 bit Linuxes, the default was Intel's extended arithmetic, while on
64 bit Linuxes, the default is sometimes SSE. I do not know the situation
on Windows.

Another source of difference is different optimization of expressions.

It is sometimes possible to obtain identical results on different platforms,
however, it cannot be generally guaranteed. For tree construction, even
minor differences in rounding may influence comparisons and this may
result in a different form of the tree.

Petr Savicky.