[Rd] Discrepancy: R sum() VS C or Fortran sum

Pierre Chausse pchausse at uwaterloo.ca
Fri Mar 16 15:58:35 CET 2018

```Hi all,

I found a discrepancy between the sum() in R and either a sum done in C
or Fortran for vector of just 5 elements. The difference is very small,
but this is a very small part of a much larger numerical problem in
which first and second derivatives are computed numerically. This is
part of a numerical method course I am teaching in which I want to
compare speeds of R versus Fortran (We solve a general equilibrium
problem all numerically, if you want to know). Because of this
discrepancy, the Jacobian and Hessian in R versus in Fortran are quite
different, which results in the Newton method producing a different
solution (for a given stopping rule). Since the solution computed in
Fortran is almost identical to the analytical solution, I suspect that
the sum in Fortran may be more accurate (That's just a guess).  Most of
the time the sum produces identical results, but for some numbers, it is
different. The following example, shows what happens:

set.seed(12233)
n <- 5
a <- runif(n,1,5)
e <- runif(n, 5*(1:n),10*(1:n))
s <- runif(1, 1.2, 4)
p <- runif(5, 3, 10)
x <- c(e[-5], (sum(e*p)-sum(e[-5]*p[-5]))/p[5])
u <- a^(1/s)*x^((s-1)/s)

u[1] <- u[1]+.0001 ### If we do not add .0001, all differences are 0
s1 <- sum(u)
s2 <- .Fortran("sumf", as.double(u), as.integer(n), sf1=double(1),
sf2=double(1))[3:4]
s3 <- .C("sumc", as.double(u), as.integer(n), sC=double(1))[[3]]

s1-s2[[1]] ## R versus compiler sum() (Fortran)

[1] -7.105427e-15

s1-s2[[2]] ## R versus manual sum (Fortran

[1] -7.105427e-15

s1-s3 ## R Versus manual sum in C

[1] -7.105427e-15

s2[[2]]-s2[[1]] ## manual sum versus compiler sum() (Fortran)

[1] 0

s3-s2[[2]] ## Fortran versus C

[1] 0

My sumf and sumc are

subroutine sumf(x, n, sx1, sx2)
integer i, n
double precision x(n), sx1, sx2
sx1 = sum(x)
sx2 = 0.0d0
do i=1,n
sx2 = sx2+x(i)
end do
end

void sumc(double *x, int *n, double *sum)
{
int i;
double sum1 = 0.0;
for (i=0; i< *n; i++) {
sum1 += x[i];
}
*sum = sum1;
}

Can that be a bug?  Thanks.

--
Pierre Chaussé
Assistant Professor
Department of Economics
University of Waterloo

```