[danbruc]

A floating point representation is not really the issue, the issue is not using base 10, and IEEE 754 specifies base 2 and base 10 floating point formats and operations. But I am of course not sure whether the original comment referred to base 2 or base 10 and given how common the mistake of using base 2 floating point numbers for financial calculations is, you may be correct with the intention of your comment.

[tonysdg]

I'm aware of the fact that you don't use floating point math for finance -- for exactly the reason you described -- but the academic in me wonders if you could formally specify a high-enough degree of precision -- and all the corner cases -- to allow FP math for even just a subset of transactions. This would (in theory) allow to programmers to bypass the Decimal classes in your favorite OO language (or GMP if you're a C fan).

Again, purely an academic inquiry :-)

[danbruc]

My point was more that it is wrong to say that financial calculations should not be done using floating point formats, for example Decimal in .NET and BigDecimal in Java are floating point formats and they are the types you should use for financial calculations. The important difference as compared to formats like IEEE 754 binary32 (formerly single) and binary64 (formerly double) is that the representation is based on base 10 instead of base 2. Fixed point or floating point and base 2 or base 10 are two orthogonal choices.

So when you initially mentioned high precision floating point numbers for financial calculations that was not necessarily a bad idea because you might have thought about base 10 floating point numbers. The comment I replied to however assumed you meant base 2 which of course most people do if they say floating point numbers without specifying the base and which of course is a bad idea for financial calculations more often than not. I just pointed out that assuming base 2 is usually but not technically correct.

And you can of course use base 2 floating point numbers for financial calculations - 32 bit, 64 bit, or 4096 bit - you just have to keep track of the accumulated errors and stop or correct the result before the error grows into the digits you are interested in. But why would one want to do this? The only thing I can really think of is that you need maximum performance and there is no hardware support for base 10 floating point numbers. And just using integers as base 10 fixed point numbers, which would often be a even better solution, must not be an option.