There are some Lisp systems, such as CLISP and SISC (I believe), that
allow arbitrary-precision flonums, the precision of which can be
specified either through the operations used or by some fluid resource
that controls the flonum operations. Fast execution is not really an
issue here; I think that there should be no reason to prohibit this
kind of extension & to provide a way in code to specify IEEE behaviour
explicitly if so desired. Not only is it more flexible to do that,
but it also makes the intent of programs clearer.