Re: ratio implementation

[Marius Vollmer]

Bill Schottstaedt <address@hidden> writes:

> I made the requested changes (using the Oct-9 CVS Guile):
>
>     ftp://ccrma-ftp.stanford.edu/pub/Lisp/gratio-1.tar.gz

With your new files, I now get

  guile> (inexact->exact 123456789123456789.0)
  0

This might have to do with your clever continued fraction
approximation procedure.

Also:

  guile> (define pi (* 2 (acos 0)))
  guile> (- (inexact->exact pi) pi)
  3.31628058347633e-10

Shouldn't we be able to do better than this?  Double precision is good
to about 2e-16 and I would expect the fraction returned from
inexact->exact to be accurate within that margin.  (I don't know
inexact->really why I expect this, it just seems to make sense.)

What about this approach: find the integer correspondig to the bits of
the mantissa of the double number (a bignum) and then correct for the
scaling and the exponent either by multiplying with a power of two, or
building a fraction with that power of two.

I don't have the details ready yet, but I think I'll try to come up
with code for this... (when it isn't already in GMP).