Question

I have a system that is performing lots of calculations using decimals, occasionally it will add up the same numbers, but return different results, +/- 0.000000000000000000000000001

Here is a short example:

decimal a = 2.016879990455473621256359079m;
decimal b = 0.8401819425625631128956517177m;
decimal c = 0.4507062854741283043456903406m;
decimal d = 6.7922317815078349615022988627m;

decimal result1 = a + b + c + d;
decimal result2 = a + d + c + b;

Console.WriteLine((result1 == result2) ? "Same" : "DIFFERENT");
Console.WriteLine(result1);
Console.WriteLine(result2);

That outputs:

DIFFERENT
10.100000000000000000000000000
10.100000000000000000000000001

The differences are so small that there is no practical effect, but has anyone seen something like this before? I expected that when adding up the same numbers you would always get the same results.

Answer 1

The entire field of Numerical analysis is devoted to studying these kind of effects and how to avoid them.

To produce the best result when summing a list of floating point numbers, first sort the list from smallest to largest, and add them up in that order.