Rename eps -> ulp

[Keno]

As discussed on triage, this renames eps to ulp, because the former is a bit of a pun and even the docstring says this computes the unit in last place of the given value. Particularly, because we extend this function to things like Dates, eps is a bit of an awkward name.

[waldyrious]

Shouldn't "machine epsilon" be changed (or adjusted to also mention ULP) here as well?

[stevengj]

eps is nearly universal here: Matlab, Numpy, R, C, C++, Fortran, Ruby, Rust, JavaScript, and many other languages all use it or some other spelling of epsilon. (Rare popular exceptions are Mathematica, which uses MachinePrecision, Swift, which uses ulpOfOne, and C#, which uses both MachineEpsilon and DoublePrecision—leave it to Microsoft to try to please everyone and end up pleasing no one.) It seems crazy to me to abandon it in the 11th hour on the vague grounds that it is "a bit of a pun".

I also don't see any problem in using it for dates or other types — it seems just as easy to define eps as it is to define ulp for those types, since the term "ulp" is also rarely if ever used for anything but floating-point arithmetic.

[stevengj]

I don't like the term "sine" — it's a bad Latin pun arising from an Arabic translation error, and "sin" is literally sinful. I propose that we rename the function to hac (for "half a chord"), which is more logical and agrees with the original Sanskrit. Let's just sneak in the rename right before the 0.7 release; I'm sure no one will mind.

Or we could accept that usage has normalized the term and continue to call this function what everyone else calls it.

[KristofferC]

Or jiba?

[stevengj]

Another problem with ulp is that eps(T) is a relative precision that must be dimensionless, whereas “unit in the last place” sounds dimensionful. Of course, we can define the ulp function to do whatever we want; it’s just a matter of documentation. But the same can be said for eps.

[ViralBShah]

I knew eps/epsilon was generally used, but didn't realize it was this universal.

[JeffBezanson]

Same here; if it's that widely used let's just close this.

[mbauman]

Another problem with ulp is that eps(T) is a relative precision that must be dimensionless, whereas “unit in the last place” sounds dimensionful. Of course, we can define the ulp function to do whatever we want; it’s just a matter of documentation. But the same can be said for eps.

My reason for liking the name ulp is purely in its use for ulp(value) — I don't find the ulp() or ulp(T) forms compelling at all. The distinction between a dimensionless relative precision (for multiplication) and a dimensional measurement of precision (for addition) is extremely pertinent, not unlike one and oneunit. I've definitely seen confusion between "machine epsilon", eps(), and eps(value) (and vaguely remember having such confusion myself) — perhaps splitting this could help? Are there actually two names here, too?

Regardless, @stevengj is correct that — given that this isn't a unanimous slam dunk — it's far too late to try to squeeze it in now.