Re^3: Decimal Arithmetic

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,$2),2,3;eg;print$..$/

Comment on Re^3: Decimal Arithmetic

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Re^4: Decimal Arithmetic by ikegami (Patriarch) on Feb 06, 2007 at 03:47 UTC
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]
Re^5: Decimal Arithmetic by liverpole (Monsignor) on Feb 06, 2007 at 16:06 UTC
"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]
Re^6: Decimal Arithmetic by ikegami (Patriarch) on Feb 06, 2007 at 20:08 UTC
Well, you did say "you can store any number" :-) Point made. I wasn't precise enough. and your average annual interest rate is exactly 4% That's the thing, it isn't. The interest will be rounded/ceiled/floored. If you want to calculate it accurately, you need a loop. Furthermore, logarithms is not one of the operations I allowed.	[reply]