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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?

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    $\begingroup$ Precision of floating point data types? $\endgroup$ – Yuval Filmus Jun 30 '16 at 23:39
  • $\begingroup$ Sorry, I should have been clearer. Yes, I am referring to floating point data types. $\endgroup$ – user144153 Jun 30 '16 at 23:46
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    $\begingroup$ Yuval may have been suggesting an answer. $\endgroup$ – Spencer Jul 1 '16 at 1:55
  • $\begingroup$ What do you mean by "machine epsilon value"? $\endgroup$ – Raphael Jul 1 '16 at 7:46
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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.

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  • $\begingroup$ 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 '16 at 19:57

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