you can store any number precisely as a fraction of arbitrarily large integers
Okay, how would you store pi precisely as a fraction of arbitrarily large integers? How about the square root of 2? Or e?
My point is, unless you're using unlimited storage, there's always a potential for round-off to occur. It may be very, very miniscule round-off, and it may not affect monetary calculations, but you've always got the potential for introducing such errors, depending on what operations you're performing.
s''(q.S:$/9=(T1';s;(..)(..);$..=substr+crypt($1,$2),2,3;eg;print$..$/
| [reply] |
I don't remember the last time I owed π dollars to someone. Remember, you are starting with finite amounts (fractions of cents), not numbers like π.
There not always a potential for round-off to occur, when the system has bounds. When something is 1/3rd off, the discount will be rounded/ceiled/floored. Infinite precision is not needed.
| [reply] |
"Infinite precision is not needed"
Yes, that's the point I was making.
"I don't remember the last time I owed π dollars to someone"
Well, you did say "you can store any number" :-)
But even if we do limit the calculations to strictly financial ones, it's very easy to demonstrate a case where you'll get round-off.
Assume you have invested $1000, and your average annual interest rate is exactly 4%. According to the The Rule of 72, you can expect your money to double in approximately (72 / 4) = 18 years.
The problem is, this isn't exact. The exact period after which your money will double is given by the formula ln 2 / ln 1.04, which is approximately 17.67298769 years. But my point is, no module is going to give you 100% accuracy for that, because ln 2 and ln 1.04, as well as their quotient, are all transcendental numbers, which means you can't represent them 100% accurately. Which is all I was trying to get across.
s''(q.S:$/9=(T1';s;(..)(..);$..=substr+crypt($1,$2),2,3;eg;print$..$/
| [reply]
[d/l]
[select] |