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Gilles commented on MATH843:

bq. On some machines, the expression 1 + Precision.EPSILON in the test 1 + Precision.EPSILON
== 1 might be hold in a register with extended precision and thus may be greater than 1. The
expression then returns false.
Did you actually see that?
I would (maybe naively) think that "1 + ESPILON" would be cast to a 64bit double before the
comparison. If so, wouldn't the equality still hold?
bq. Regarding the other definition: [...]
No problem to add this comment if you provide it here in a "noformat" block with all the references
as HTML links ("<a href="...">...</a>") which I can copy/paste into the code.
Thanks.
> Precision.EPSILON: wrong documentation
> 
>
> Key: MATH843
> URL: https://issues.apache.org/jira/browse/MATH843
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.0
> Reporter: Dominik Gruntz
> Priority: Minor
> Labels: documentation
> Original Estimate: 0.5h
> Remaining Estimate: 0.5h
>
> The documentation of the Field {{EPSILON}} in class {{org.apache.commons.math3.util.Precision}}
states, that {{EPSILON}} is the smallest positive number such that {{1  EPSILON}} is not
numerically equal to 1, and its value is defined as 1.1102230246251565E16.
> However, this is NOT the smallest positive number with this property.
> Consider the following program:
> {code}
> public class Eps {
> public static void main(String[] args) {
> double e = Double.longBitsToDouble(0x3c90000000000001L);
> double e1 = 1e;
> System.out.println(e);
> System.out.println(1e);
> System.out.println(1e != 1);
> }
> }
> {code}
> The output is:
> {code}
> % java Eps
> 5.551115123125784E17
> 0.9999999999999999
> true
> {code}
> This proves, that there are smaller positive numbers with the property that 1eps !=
1.
> I propose not to change the constant value, but to update the documentation. The value
{{Precision.EPSILON}} is
> an upper bound on the relative error which occurs when a real number is
> rounded to its nearest Double floatingpoint number. I propose to update
> the api docs in this sense.

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