(42, all flavours) Integer Division - how?

[Albert Chan]

remainder() based idiv is very elegant.

PHP Code:

function idiv6(a, b)    -- assumed b > 0
    local r = a/b
    local q = floor(r)
    if q == r and remainder(a, b) < 0 then q=q-1 end
    return q
end 


Above is similar to this (6a version possibly faster, only tried to get remainder sign)

PHP Code:

function idiv6a(a, b)   -- assumed b > 0
    local r = a/b
    local q = floor(r)
    if q ~= r then return q end
    r = a % (b+b)
    local R = r < b and r or r-b
    local h = 0.5*b    -- halfway
    if R < h or r == h then return q end
    return q - 1
end 


All the code for mod/half-way test is the last if line.

R < h:

if residual is less than half of b, q had rounded-down. For floor divide, no need for correction.

r == h:

if residual is half of b, q (because of round-to-even) is even.
But, r also guaranteed even q -> no need for correction.

Update: slightly faster version 6b, removed R, and r shifted, with range = [-2h, 2h)

PHP Code:

function idiv6b(a, b)   -- assumed b > 0
    local r = a/b
    local q = floor(r)
    if q ~= r then return q end
    r = a % (b+b) - b
    local h = 0.5*b     -- halfway
    if r <= -h or (r < h and r >= 0) then return q end
    return q - 1
end