(42, all flavours) Integer Division - how?

[Werner]

(12-15-2020 02:51 PM)Albert Chan Wrote:  I also added a fast-path, to speed things up.

PHP Code:

function idiv3c(a,b)        -- assumed b > 0
    local q, c = ceil(a/b), b+1
    if q*b > a then return q-1 end
    a, b = a%b - a%c, q%c   -- a-b = (-2c, c-1)
    if a==b or a==b-c then return q end
    return q-1
end 


That fast path wouldn't be useful in my case: I wanted to use integer division to correctly split
Cc00 = Qq*Xx + Rr, where each letter is a half-length integer and Cc<Xx

For instance, in a 2-digit calculator:
2300 = 57*40 + 20, but 2300/40=58
2700 = 37*72 + 36

What I did up till now is determine Q and q separately with
Cc0 = Q*Xx + Aa
Aa0 = q*Xx + Rr

and each split Yy0=Q*Xx+Rr is carried out as
Q := Yy0/Xx;
Rr := MOD(Yy0,Xx);
if FRC(Q) >0
then Q := INT(Q);
else
if Rr>0 then
Q := ROUND(Q - Rr/Xx,0);
end;
end;

sadly, that still is faster than the integer division - mainly because the rounding part is almost never reached, certainly not in the 34-digit Free42..

Werner