Why are Intel x87 registers 80 bits wide?

Question

Why is such a “weird” register size used? Is there any documentation on why it is not preferable to use 64 or 128 bits for those registers?

Answer 1

On the Wikipedia page on the IEEE 754-1985 standard there is a pretty good explanation regarding the 80-bit extended format:

"The standard also recommends extended format(s) to be used to perform internal computations at a higher precision than that required for the final result, to minimise round-off errors"

A double precision floating point number is represented in 64 bits. You would want a few more bits to get higher precision for intermediate results, but it would be overkill to use a 128 bit type when you only want 64 bits in the final result.

80 bits is a reasonably even number of bits that is larger than 64 bits.

Consider that the data bus at the time when those standards were established was 8 or 16 bits, not 32 or 64 bits like today. If the standard was written today 96 bits would be a more reasonable number, or perhaps the data would be transmitted as 128 bits even if all those bits wouldn't be used in the calculations.