Why does MATLAB 7.4 (R2007a) give an erroneous answer using SUM(single(:))?

MATLAB gives erronous answers using the SUM function when the dataset is very large. for example:

n=25e6 ;

a=ones(n,1,'single');

b=sum(a(:))

The value of variable 'b' would be 16777216 which is 32% different from the correct answer of 25e6.

If SUM(SUM(a)) was used the discrepancy would not exist.

Answer 1

[MathWorks Support Team]

The problem starts when too many numbers have been added together. The accumulator in the SUM function gets too big compared to the numbers added. As a result, either some precision is lost in the addition, or the small numbers are completely ignored.