[GNC] Rounding & formulas

[Fred Bone]

On 23 December 2020 at 0:25, Thomas Lenherr said:

> Thank you all for your responses.
> 
> For the record, this is for private bookkeeping purposes (mainly splitting
> costs for different things with roommates), and so regulations generally
> don't apply as accuracy to a cent is more than enough and I mostly just
> want to prevent having to fix imbalances often. Having done this for the
> past ~12 years, for anything between 5-10 monthly transactions, I was
> hoping to automate this ever so slightly more, as is the trend with
> software.
> 
> Given the late rounding, somebody mentioned the idea earlier that adding
> or subtracting 0.005 could be used to turn the "normal rounding" into
> either "rounding up" or "rounding down", I haven't tested that yet, but I
> suspect that could work, at least as long as the amount only has be split
> between two parties:
> 
> my_expense_amount = (total_amount / 2)  # Normal rounding
> roommates_expense_amount = (total_amount / 2) - 0.005  # Rounding down

No, you have it backwards (at least when the quotient is truncated, i.e. 
rounded down, as seems to be the case):

winner = (total+0.01)/2
(or, equivalently, winner = total/2 + 0.005)
loser = total/2

> This is a little messier than I hoped and only works well when splitting
> two-ways (when you do 3+-ways it gets a little trickier). I was wondering
> if any devs here could comment on the options to rather supporting a
> function to explicitly trigger the rounding early, that way the above
> could e.g. be written as:
> 
> roommates_expense_amount = (total_amount / 2)  # Or really any fraction
> could work with this my_expense_account = total_amount -
> roommates_expense_amount = total_amount - gnc_round(total_amount / 2)
> 
> I'm aware that custom functions can be added to fin.scm, but I didn't dig
> deep enough yet to understand how I could explicitly trigger the
> rounding-step from there, if at all. Plus it seemed like there's a slim
> chance this could be a useful function to include by default since gnucash
> doing rounding is an omnipresent operation.

The only difficult bit about sharing among three is deciding how to 
distribute the odd amounts. Exactly as with dividing by two.

winner2 = (total+0.02)/3
winner1 = (total+0.01)/3
loser = total/3