Talk:Machine epsilon

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[edit] Definition

This page defines the machine epsilon as "the smallest floating point number such that1 \oplus \epsilon > 1". What I have seen more commonly is the definition to be the largest floating point number such that 1 \oplus \epsilon = 1. In fact the equation provided \epsilon = {\beta \over 2} \cdot \beta^{-p} gives the latter definition. Granted the two definitions lead to numbers adjacent on the floating point number line, but I would like to see this article either switch to the other definition or else discuss the presence of two definitions in use. Any thoughts? --Jlenthe 01:01, 9 October 2006 (UTC)

Hi, with a quick Google check I found as expected some confirmations for the "smallest thingy making a difference" definition, not "biggest making no difference". IIRC that's also what I learned two and a half decades ago. 212.82.251.209 20:48, 3 December 2006 (UTC)
Yes; if it didn't make a difference, it wouldn't be an "epsilon". --Quuxplusone 01:05, 19 December 2006 (UTC)

[edit] Code or definition wrong

If you use the code with

float machEps = 1.00001f;

you get smaller numbers with 1+eps>1, Instead the relativ difference between two floating point numers is computed. --Mathemaduenn 10:20, 10 October 2006 (UTC)

I don't see any code in the current article with
float machEps = 1.0001f;
Therefore, I guess this has been resolved, and I'm removing the {{contradict}} tag now. --Quuxplusone 01:05, 19 December 2006 (UTC)

[edit] Calculation wrong

This is wrong: the difference between these numbers is 0.00000000000000000000001, or 2−23. 0.00000000000000000000001 is 10-23, but that is probably not the right number. —Preceding unsigned comment added by 193.78.112.2 (talk) 06:43, 19 October 2007 (UTC)

It's a binary fraction, not a decimal fraction. I agree it's confusing, but I can't think of a better way to explain it. -- BenRG 19:52, 19 October 2007 (UTC)