<rant - please excuse>
Programming languages tend to serve the mathematician
poorly for coping with the infinite multiplicity of meanings that
"number" can have. No doubt there are practical advantages in
having the IEEE standards, and processors that have been intensively
developed to use them, but even for modelling real arithmetic the IEEE
formats are a few among an infinity of different possibilities, some
better for particular tasks than others. Did you know that
you can have real arithmetics that are exactly associative
(which the IEEE formats are not)? Google "Abbas Edalat" to find out.
Or you can use modular arithmetic modulo a large prime; or
lazy streams of rational Moebius transformations, .... .
I am afraid that a lot of programmers tend to dismiss arithmetic as a
bothersome technical detail, and are thankful to the cram the
whole business into the IEEE's bed of Procrustes (google if this
particular kind of bed is not familiar!).
</rant>
