Calculating average of two values, minimizing errors

Question

I am doing some floating point calculations and the results are not as accurate as I want them to be.

This is the algorithm:

...
center = (max_x + min_x) / 2
distance = old_x - center
new_x = center + (distance * factor)

return new_x

min_x, max_x, and old_x are all floats. I believe that the greatest error is introduced when I'm taking the average of the max and the min, and then the error is multiplied by the factor (which can be a float).

How can I minimize the error due to FP computation so that new_x is as precise as it can be?

Answer 1

If old_x and center are close then you're losing precision.

It's called Loss of significance

You could change the calculation so the subtraction happenS in the end:

center = (max_x + min_x) / 2
new_x = (center + (old_x * factor)) - (center * factor)

Answer 2

Depending on your language, there is probably a fixed/arbitrary precision numeric type you can use such as decimal in python or BigDecimal in Java.

Answer 3

This eliminates at least one source of error from your original algorithm:

# Adding min and max can produce a value of larger magnitude, losing some low-order bits
center = min_x + (max_x - min_x)/2
distance = old_x - center
new_x = center + (distance * factor)

return new_x

If you have more knowledge of the relationship between old_x, min_x andmax_x, you can probably do better than this.