sum accuracy

[Robin Becker]

On 13/04/2016 18:05, Random832 wrote:
.........
>
> No, it doesn't. Sum works on any type that can be added (except
> strings), it can't make any assumptions about the characteristics of
> floating point types. For non-numeric types, the addition operator may
> not be semantically commutative or associative.
>
I thought as much. My problem was that the sum of an array of small floats was 
being used to compute a grid of points by subtraction like this

height = sum(H)
pos = [height]
for h in H:
	height -= h
	pos.append(height)

the value of height[0] came out negative which was a problem. I could reduce the 
error by using Kahan summation instead of sum, but that required Kahan style 
subtraction as well. In the end it just seemed better to reverse the loop and 
compute pos by addition.


> Look at
> http://code.activestate.com/recipes/393090-binary-floating-point-summation-accurate-to-full-p/
> for an example of a more accurate algorithm, but note that, for example,
> this algorithm wouldn't work on complex numbers (you'd have to sum the
> real and imaginary components separately)
>
yes indeed summation is hard :(

-- 
Robin Becker