The 8087 came out when the premier numerics processors worldwide were the various Cray/CRI products, and if you know this much about the 8087's extended register format then it's likely you already know about Seymour's opinion expressed in silicon about the handling of the LSBs. As a freshly minted computational mathematician I was worried about the Cray systems accuracy on long running computations but after 5 years right on the front lines of the 1-4 highest throughput systems worldwide, with, ISTR, zero practical effect on any computation that ever mattered. Huh turns out Seymour was smarter than me. Should've picked up a shovel.

As far as delivered accuracy of the 8087, performing the operations at 80 bits, rather than 64 it was better than non-extended formats. Anyway you can read all about it here:

https://en.wikipedia.org/wiki/Extended_precision#x86_extende...

Kahan endorsed is all I needed to know.

I can't remember the details from back then but the initial Sun java implementation did something weird with this.

Sun wanted the jvm to "replicate exactly" between machines so they chopped off the precision of all intermediate operations to 64 or 32 (double/single) which infuriated kahan