1
$\begingroup$

I was wondering what factors effect a machine's epsilon value. I was thinking about how modern computers can calculate expressions to higher accuracy then their predecessors, but what hardware and software factors allow for improved accuracy? Is it the implementation of better algorithms for computing various functions (examples welcome), the use of more capable hardware, or another factor I can't think of?

My go to thought is the development of better algorithms, but I can think of any that were developed post 1990.

My second thought was that the increased memory available in modern computers allows arbitrary precision arithmetic to produce more accurate results, however not all applications run with arbitrary precision and you can still run into a software "bottle neck" on the outputted precision.

What factors have the greatest effect on machine precision?

Improve this question
$\endgroup$
4
  • 1
    $\begingroup$ Precision of floating point data types? $\endgroup$
    – Yuval Filmus
    Jun 30, 2016 at 23:39
  • $\begingroup$ Sorry, I should have been clearer. Yes, I am referring to floating point data types. $\endgroup$
    – user144153
    Jun 30, 2016 at 23:46
  • 1
    $\begingroup$ Yuval may have been suggesting an answer. $\endgroup$
    – Spencer
    Jul 1, 2016 at 1:55
  • $\begingroup$ What do you mean by "machine epsilon value"? $\endgroup$
    – Raphael ♦
    Jul 1, 2016 at 7:46

1 Answer 1

Reset to default
4
$\begingroup$

The phrase "machine epsilon" is misleading. In reality, it doesn't depend on the machine at all, but on the floating-point data types that the programmer chooses to use.

Improve this answer
$\endgroup$
1
  • $\begingroup$ I sometimes think of it as the largest relative error of any basic arithmetic operation which can be legitimately blamed on the machine. Anything else is "programmer epsilon". $\endgroup$
    – Pseudonym ♦
    Jul 1, 2016 at 19:57

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.