algorithm - Kahan summation

Question

Has anyone used Kahan summation in an application? When would the extra precision be useful?

I hear that on some platforms double operations are quicker than float operations. How can I test this on my machine?

Answer 1

Kahan summation works well when you are summing numbers and you need to minimize the worse-case floating point error. Without this technique, you may have significant loss of precision in add operations if you have two numbers that differ in magnitude by the significant digits available (e.g. 1 + 1e-12). Kahan summation compensates for this.

And an excellent resource for floating point issues is here, "What every computer scientist should know about floating-point arithmetic": http://www.validlab.com/goldberg/paper.pdf

On single vs double precision performance: yes, single precision can be significantly faster, but it depends on the particular machine. See: https://www.hpcwire.com/2006/06/16/less_is_more_exploiting_single_precision_math_in_hpc-1/

The best way to test is to write a short example that tests the operations you care about, using both single (float) and double precision, and measure the runtimes.