Feature request: round-to-nearest integer division

[eschnett]

Integer division currently offers 3 rounding modes: fld, cld, and div, corresponding to the rounding modes offered by floor, ceil, and trunc (round towards minus infinity, plus infinity, and zero).

I suggest a fourth integer division function, maybe called rdd, that rounds towards the nearest integer, breaking ties towards even, corresponding to the rounding performed by round:

function rdd(x::T, y::T)::T where {T <: Integer}
    round(T, x / y)
end

... except without converting to a floating-point number.

[chethega]

... except without converting to a floating-point number.

What is the problem of the code you wrote?

[simonbyrne]

Rather than add a new function, we can just overload div with rounding mode arguments. See #9283

[eschnett]

@chethega The code I wrote is an experiment with fixed point arithmetic, quite similar to FixedPointNumbers. To implement correct rounding after division, I had to implement an rdd function as described above. The function is non-trivial, and would benefit from low-level optimizations.

@simonbyrne Yes, overloading div seems better than yet another cryptic function name.

(This is the function I wrote:

# Correctly rounded division (breaking ties towards even)
export rdd
function rdd(x::T, y::Signed)::T where {T <: Signed}
    d, m = fldmod(x, y)::Tuple{T, T}
    a2m = abs(m << 1)
    ay = abs(y)
    if a2m > ay
        # Round up
        d += T(1)
    elseif a2m == ay
        # Break tie towards even (round up if the result is odd)
        d += d & T(1)
    end
    d
end

)

[bobcassels]

For the benefit of those who stumble on this issue, Julia div(x, y, RoundNearest) now does this.

It would have saved me some floundering if someone had noted this and closed this issue.