Re: [Rd] bug in sum() on integer vector

From: Hervé Pagès <>
Date: Wed, 14 Dec 2011 17:51:13 -0800

Hi Peter,

On 11-12-14 08:19 AM, peter dalgaard wrote:
> On Dec 14, 2011, at 16:19 , John C Nash wrote:
>> Following this thread, I wondered why nobody tried cumsum to see where the integer
>> overflow occurs. On the shorter xx vector in the little script below I get a message:
>> Warning message:
>> Integer overflow in 'cumsum'; use 'cumsum(as.numeric(.))'
>> But sum() does not give such a warning, which I believe is the point of contention. Since
>> cumsum() does manage to give such a warning, and show where the overflow occurs, should
>> sum() not be able to do so? For the record, I don't class the non-zero answer as an error
>> in itself. I regard the failure to warn as the issue.
> It (sum) does warn if you take the two "halves" separately. The issue is that the overflow is detected at the end of the summation, when the result is to be saved to an integer (which of course happens for all intermediate sums in cumsum)
>> x<- c(rep(1800000003L, 10000000), -rep(1200000002L, 15000000))
>> sum(x[1:10000000])
> [1] NA
> Warning message:
> In sum(x[1:1e+07]) : Integer overflow - use sum(as.numeric(.))
>> sum(x[10000001:25000000])
> [1] NA
> Warning message:
> In sum(x[10000001:1.5e+07]) : Integer overflow - use sum(as.numeric(.))
>> sum(x)
> [1] 4996000
> There's a pretty easy fix, essentially to move
> if(s> INT_MAX || s< R_INT_MIN){
> warningcall(call, _("Integer overflow - use sum(as.numeric(.))"));
> *value = NA_INTEGER;
> }
> inside the summation loop. Obviously, there's a speed penalty from two FP comparisons per element, but I wouldn't know whether it matters in practice for anyone.

Since you want to generate this warning once only, your test (now inside the loop) needs to be something like:

     if (warn && (s > INT_MAX || s < R_INT_MIN)) {
         generate the warning
         warn = 0;

with 'warn' initialized to 1. This makes the isum() function almost twice slower on my machine (64-bit Ubuntu) when compiling with gcc -O2 and when no overflow occurs (the most common use case I guess).

Why not just do the sum in a long double instead of a double? It slows down isum() by only 8% on my machine when compiling with gcc -O2.
But most importantly this solution also has the advantage of making sum(x) consistent with sum(as.double(x)). The latter uses rsum() which does the sum in a long double. So by using a long double in both isum() and rsum(), consistency between sum(x) and sum(as.double(x)) is
Maybe that still doesn't give you the guarantee that sum(x) will always return the correct value (when it does not return NA) because that depends now on the ability of long double to represent exactly the sum of at most INT_MAX arbitrary ints. The nb of bits used for long double seems to vary a lot across platforms/compilers so it's hard to tell. Not an ideal solution, but at least it makes isum() more accurate than the current isum() and it makes sum(x) consistent with sum(as.double(x)) on all platforms, without degrading performance too much.


Hervé Pagès

Program in Computational Biology
Division of Public Health Sciences
Fred Hutchinson Cancer Research Center
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