🚀 go-pugleaf

I'm looking for info that would be useful in implementing short
floating point numbers for Lisp/Smalltalk/etc.

The basic idea is that I want short (1-word) floating point numbers to
fit in one 32-bit words, *with* a runtime tag included.  My plan is
to store the number shifted left a few bits, at a tag in the lower bits.
Having the number fit in a word is a big advantage, especially if you've
got a generational garbage collector.  (They have to be careful about
pointer creation, in ways that can needlessly slow down programs that
allocate a lot of floats.)

Of course, this means I have to sacrifice a few bits of a standard 32-bit
float to make it fit.

I figure that I can just lop a couple of bits of of the exponent part, and
leave the fraction part alone.  That way, I sacrifice range of floats
but not precision.  If a float result goes out of that range, I'll make
a full-sized floating point object on the heap, and use a tagged
pointer to it.  This is analogous to the "fixnum" (immediate short int) /
"bignum" (long, heap-allocated) strategy used for integers.

Now the question:

How far can I carry this?  Can I take five bits out of the exponent
and still express most numbers most people would use?  (How many bits
do IEEE 32-bit floats use for the expt in the first place?)  If not
5, can I do 4, 3, or 2?

Has anybody done any studies of the distribution of floating point values
for real programs?  My guess is that most programs don't generate *any*
floating point values outside of a fairly narrow range, so that most 
programs would not require *any* big floats.   (I'm not looking for Lisp
program data here -- I wouldn't want to assume that people only want
to run the kinds of programs traditionally written in Lisp.  C and Fortran
data would be fine.)

And if I've made any stupid assumptions, such that this is a bad idea
anyway, please gently clue me in.  (I know close to nothing about
computer arithmetic.)


Thanks,

   Paul


Paul R. Wilson                         
Software Systems Laboratory               lab ph.: (312) 996-9216
U. of Illin. at C. EECS Dept. (M/C 154)   wilson@bert.eecs.uic.edu
Box 4348   Chicago,IL 60680 
Paul R. Wilson                         
Software Systems Laboratory               lab ph.: (312) 996-9216
U. of Illin. at C. EECS Dept. (M/C 154)   wilson@bert.eecs.uic.edu
Box 4348   Chicago,IL 60680