Floating Point Programming, Today?

An anonymous reader asks: "I'm rather new with programming and stumbled across these twe articles: The Perils of Floating Point from 1996 and What Every Computer Scientist Should Know About Floating-Point Arithmetic from 1991. I tried some of the examples in these articles with Intel's Fortran Compiler and g77 and noted that some of those issue reported no longer seem valid whereas quite a few still very much are around. Could someone, please, give me a pointer to some newer thoughts and/or new facts surrounding floating point programming. What has been improved since those articles were written? What is still the same? How is the future, especially with the new platforms IA64 and AMD64? I am most interested in the x86 and x86-64 architectures. Thank you for your kind help."

Comments

Floating point operations are not that bad.

[stj]

Well, I have a lot of experience with that since I've been doing numerical computations for last 7 years. First of all, it's not all that bad. With 64 bit 'double' in C, you get around 15 decimal digits of accuracy (theoretically 18, but in practice don't count on the end). You have to understand that numbers are stored in logarithmic format: mantissa and a factor to multiply it (in computers exponent of 2). If there is no overlap between two numbers in addition (that is for example one number is 1.234*2^64, and the other is 1.234*2^-15), the smaller one is always lost. The are two ways to get around it:

extend mantissa so there is enough overlap - usually involves some kind of multiple precision libraries like mentioned in other post GNU MP and many others. I've implemented one for my own use, too. Generally means lots of overhead since there will be less than 5% of operations actually benefitting from greater precision.

postpone such operations until there is overlap - store such numbers together and do operations on them together, too. Sometimes additions in loops will add up small parts so actually there will be overlap with big part and additions can be done with enough precision.
On a side, interesting thing is that in computers multiplications and divisions are better (that is more accurate) than additions and subtractions because of logarithmic format.
I know that Sun was working on a variable precision floating-point CPU. I'm not sure how that project is going and what the end effect is, but I remember it being an interesting idea.

Multiple precision libraries are usually decent with only one problem, they are always slower by a couple orders of magnitude than regular CPU operations, so using them is just such a pain.