What are the applications/benefits of an 80-bit extended precision data type?

Question

Yeah, I meant to say 80-bit. That's not a typo...

My experience with floating point variables has always involved 4-byte multiples, like singles (32 bit), doubles (64 bit), and long doubles (which I've seen referred to as either 96-bit or 128-bit). That's why I was a bit confused when I came across an 80-bit extended precision data type while I was working on some code to read and write to AIFF (Audio Interchange File Format) files: an extended precision variable was chosen to store the sampling rate of the audio track.

When I skimmed through Wikipedia, I found the link above along with a brief mention of 80-bit formats in the IEEE 754-1985 standard summary (but not in the IEEE 754-2008 standard summary). It appears that on certain architectures "extended" and "long double" are synonymous.

One thing I haven't come across are specific applications that make use of extended precision data types (except for, of course, AIFF file sampling rates). This led me to wonder:

• Has anyone come across a situation where extended precision was necessary/beneficial for some programming application?
• What are the benefits of an 80-bit floating point number, other than the obvious "it's a little more precision than a double but fewer bytes than most implementations of a long double"?
• Is its applicability waning?

Answer 1

Intel's FPUs use the 80-bit format internally to get more precision for intermediate results.

That is, you may have 32-bit or 64-bit variables, but when they are loaded into the FPU registers, they are converted to 80 bit; the FPU then (by default) performs all calculations in 80 but; after the calculation, the result is stored back into a 32-bit or 64-bit variables.

BTW - A somewhat unfortunate consequence of this is that debug and release builds may produce slightly different results: in the release build, the optimizer may keep an intermediate variable in an 80-bit FPU register, while in the debug build, it will be stored in a 64-bit variable, causing loss of precision. You can avoid this by using 80-bit variables, or use an FPU switch (or compiler option) to perform all calculations in 64 bit.