# What's a floating-point operation and how to count them (in MATLAB)?

I have an assignment where I basically need to count the number of floating point operations in a simple program, which involves a loop, a matrix, and operations such as *, + and ^.

From my understanding, a floating-point operation is an operation that involves floating-point numbers, and we may be interested in counting these operations because I think they may be more expensive for the computer. If you want to add more details to this part, it would be nice.

My problem is that I've no idea of knowing exactly which operations involve floating-point numbers, unless I use functions, such as `isfloat`. In that case, would just one of the numbers in the operation be necessary to be floating-point to the operation be considered a floating-point operation, right? If not, why? Can you add more details on this?

For example, suppose I've the following simple function:

``````function [r, n] = naive(c, x)
% c is the vector of coefficients of the polynomial
% The coeffiecients should be given as follows
% c(1) = coefficient of x^0 (or 1).
% c(length(c)) = coefficient of the largest power of x
% x is the point to evaluate the polynomial at
% r is the result of the evaluation
% (Assumes that the entries are integers)

r = c(1);
n = 0;

for i=2:length(c)
r = r + c(i) * x^(i - 1);
n = n + 2 + (i - 1);
end

end
``````

which basically calculates a normal polynomial evaluated at `x` given the coefficients in a vector `c`.

As you can see from the code, `n` is actually keeping track of floating-point operations. But actually, I'm counting every mathematical operation (except the assignment) as a floating-point operation, but this of course might not be right, or is it? If yes or no, why?

Both the coefficients and `c` might be floating-point numbers. So, instead of counting every operation as a floating point operation, should we first check with for example `isfloat` if the numbers are floating point, and only then increment `n`?

Note, I'm aware of the function `flops`, which, from what I understood, it should count the floating-point operations, but it's deprecated, and mostly I would like to learn better these concepts, and therefore try to count them manually.

Thanks for any help!

• I think you are over-counting by one in each iteration. There are `i-1` multiplications and one addition. Mar 4, 2016 at 12:28
• @PatriciaShanahan That might be correct, since x^y = xx...*x, that is we have `y` `x`s, but the multiplications are just `y - 1`.
– nbro
Mar 4, 2016 at 14:12
• Another way to think of it: Write a list of the terms that need to be multiplied, y followed by i-1 instances of x, a total of i terms. Now put a multiplication sign between each pair of terms. You will have i-1 multiplication signs. Mar 4, 2016 at 15:53
• @PatriciaShanahan By the way, do you have any ideas regarding my other doubts/problems?
– nbro
Mar 4, 2016 at 16:09
• FYI, the `flops` function was deprecated way back in 2000 for reasons detailed in this article (see near end) by MathWorks founder Cleve Moler. This is a fine exercise, but you (and your instructor) should be aware it may not be a useful to characterize Matlab performance (even more so with modern JIT compilation). Mar 4, 2016 at 16:09