Changes behaviour of round to use default rounding mode

[simonbyrne]

This makes the changes discussed in #8750.

[JeffBezanson]

+1

Maybe a NEWS item?

[simonbyrne]

done.

[johnmyleswhite]

+1

[StefanKarpinski]

This is an impressively thorough pull-request. I was under the impression that we had settled on the default rounding mode matching C's round function, no? (I don't really care that much, tbh.)

[JeffBezanson]

Can we synchronize the names with the symbols? I.e. RoundX = RoundingMode{:X}()?

[simonbyrne]

Which do we want to change? The symbols match the terms used in the ieee standard. The names are probably simpler.

[JeffBezanson]

It doesn't really matter to me as long as they match. I would tend to prefer the IEEE names though.

[simonbyrne]

We currently have:

const RoundNearest = RoundingMode{:TiesToEven}()
const RoundToZero = RoundingMode{:TowardZero}()
const RoundUp = RoundingMode{:TowardPositive}()
const RoundDown = RoundingMode{:TowardNegative}()
const RoundFromZero = RoundingMode{:AwayFromZero}() # mpfr only, not in IEEE754
const RoundNearestTiesAway = RoundingMode{:TiesToAway}() # C-style rounding
const RoundNearestTiesUp = RoundingMode{:TiesToPositive}() # Java-style rounding, not IEEE754

Option (a): copy IEEE names

const RoundTiesToEven = RoundingMode{:TiesToEven}()
const RoundTowardZero = RoundingMode{:TowardZero}()
const RoundTowardPositive = RoundingMode{:TowardPositive}()
const RoundTowardDown = RoundingMode{:TowardNegative}()
const RoundAwayFromZero = RoundingMode{:AwayFromZero}() # mpfr only, not in IEEE754
const RoundTiesToAway = RoundingMode{:TiesToAway}() # C-style rounding
const RoundTiesToPositive = RoundingMode{:TiesToPositive}() # Java-style rounding, not IEEE754

Option (b), use simpler names

const RoundNearest = RoundingMode{:Nearest}()
const RoundToZero = RoundingMode{:ToZero}()
const RoundUp = RoundingMode{:Up}()
const RoundDown = RoundingMode{:Down}()
const RoundFromZero = RoundingMode{:FromZero}() # mpfr only, not in IEEE754
const RoundNearestTiesAway = RoundingMode{:NearestTiesAway}() # C-style rounding
const RoundNearestTiesUp = RoundingMode{:NearestTiesUp}() # Java-style rounding, not IEEE754

Option (c): same as (b), except for the last two, we could copy Python which uses "half" instead of "ties":

const RoundHalfAway = RoundingMode{:HalfAway}() # C-style rounding
const RoundHalfUp = RoundingMode{:HalfUp}() # Java-style rounding, not IEEE754

[StefanKarpinski]

I wish the IEEE names were better. Are those really the names in the standard or just what people use? The simpler names are so much clearer, shorter and more memorable. I guess we can go with IEEE names if they're actually commonly used in other systems (C, Python, Matlab, etc). Otherwise I would use the nicer, shorter names.

[simonbyrne]

No, I don't think anyone uses the IEEE names. Having thought about it more, I agree that the simpler names are better.

[simonbyrne]

@StefanKarpinski the proposal was to match C rint, #8750 (comment)

[tkelman]

@simonbyrne sorry to bump a 2-year-old PR, but do you have any thoughts whether the loosening here of what used to be

function round{T<:Integer}(::Type{T}, x::Rational)

to

round{T}(::Type{T}, x::Rational)

was intentional? So it's been possible since this PR to do round(Float32, 2//3) but not round(Float32, 0.7). This came up in #19791 (comment), also at #19791 (comment)

[simonbyrne]

I don't think so, as there are no tests for it.