(Arbitrarily) Long-Division Script

[Geoff Canyon]

I've created similar routines in the past. Are you saying you do or don't
want to allow for arbitrarily-large divisors?

a pseudo-code algo for divisors that LC can handle:

1. remove the decimal points, remembering where they were
2. get the length of the divisor
3. grab that many characters from the dividend as the working dividend
4. if the working dividend is larger than the divisor, divide it by the
divisor to find the quotient and remainder (new working dividend) and put
the quotient after the final quotient
5. put the next character from the dividend after the working dividend and
return to (4) until you run out of dividend
6. figure out where the decimal point goes and insert it

for divisors that LC can't handle, (4) becomes:

4. if the working dividend is larger than the divisor, use your bignum
subtraction to repeatedly subtract the divisor from the working dividend to
find the quotient and remainder (new working dividend) and put the quotient
after the final quotient


On Thu, Oct 30, 2014 at 7:51 PM, Igor de Oliveira Couto <igor at semperuna.com>
wrote:

> Hi all,
>
> I wanted to develop a library to allow me to perform basic maths (add,
> subtract, multiply, divide) with arbitrarily long numbers in LiveCode. My
> requirements are simple:
>
> - integers and floating-point numbers must be supported as all operands in
> all operations, to an arbitrarily large number of decimal cases
>
> - speed is NOT an issue: performances can safely be relatively slow, as it
> is unlikely that it’ll need to perform hundreds of thousands of operations
> per second
>
> - accuracy IS an issue: needless to say, all operations must provide
> *accurate* and *reliable* results, regardless of how many decimal cases are
> used
>
> It proved relatively easy to do the addition, multiplication and
> subtraction operations in LiveCode. I followed the ‘pen-and-paper’
> algorithm, and it all seems to be working really well - I’m happy to
> provide anybody with a copy of the scripts off-list, if you wish (just send
> me an email directly). I’m stuck, however, trying to implement DIVISION.
> There does not seem to be an “easy” pen-and-paper algorithm that would
> support arbitrarily large numbers with unknown number of decimal cases.
>
> Most long-division algorithm seems to expect that the number being divided
> can be of an arbitrarily length, but they expect that the divisor (the
> number we are dividing BY) is going to be low enough, so that the person
> making the division will “know” instinctively how many times it would “fit”
> into the number being divided. These algorithms are not recommended once we
> start dealing with divisor of 3 digits or more. There does not seem to be
> an algorithm that would allow us to procede “digit-by-digit” with the
> division, as can be done with addition/subtraction/multiplication… Or is
> there?
>
> Searching Google and Wikipedia has yielded articles about using bitwise
> operations, or complex mathematical theory, both of which are beyond me. Is
> there a Math Wiz in this list, who could give us a layman’s explantion of
> an algorithm that could be used? Any help would be much appreciated!
>
> Kindest regards to all,
>
> --
> Igor Couto
> Sydney, Australia
>
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