on floating-point numbers

[MRAB]

On 2021-09-03 16:13, Chris Angelico wrote:
> On Sat, Sep 4, 2021 at 12:08 AM o1bigtenor <o1bigtenor at gmail.com> wrote:
>> Hmmmmmmm - - - ZI would suggest that you haven't looked into
>> taxation yet!
>> In taxation you get a rational number that MUST be multiplied by
>> the amount in currency.
> 
> (You can, of course, multiply a currency amount by any scalar. Just
> not by another currency amount.)
> 
>> The error rate here is stupendous.
>> Some organizations track each transaction with its taxes rounded.
>> Then some track using  use untaxed and then calculate the taxes
>> on the whole (when you have 2 or 3 or 4 (dunno about more but
>> who knows there are some seriously tax loving jurisdictions out there))
>> the differences between adding amounts and then calculating taxes
>> and calculating taxes on each amount and then adding all items
>> together can have some 'interesting' differences.
>>
>> So financial data MUST be able to handle rational numbers.
>> (I have been bit by the differences enumerated in the previous!)
> 
> The worst problem is knowing WHEN to round. Sometimes you have to do
> intermediate rounding in order to make something agree with something
> else :(
> 
> But if you need finer resolution than the cent, I would still
> recommend trying to use fixed-point arithmetic. The trouble is
> figuring out exactly how much precision you need. Often, 1c precision
> is actually sufficient.
> 
At some point, some finance/legal person has to specify how any 
fractional currency should be handled.