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HEAD has now exact fractions

From: Marius Vollmer
Subject: HEAD has now exact fractions
Date: Tue, 18 Nov 2003 23:14:21 +0100
User-agent: Gnus/5.1002 (Gnus v5.10.2) Emacs/21.3 (gnu/linux)


I have committed the exact fraction support from Bill Schottstaedt.
Thanks alot Bill!

Please give it a beating and report all things you notice.

I have changed Bill's original code to varying degrees, so don't blame
him for anything that looks wrong.

Here are the relevant NEWS entries:

** Guile now has exact rationals.
Guile can now represent fractions such as 1/3 exactly.  Computing with
them is also done exactly, of course:
    (* 1/3 3/2)
    => 1/2
** 'floor', 'ceiling', 'round' and 'truncate' now return exact numbers
   for exact arguments.
For example: (floor 2) now returns an exact 2 where in the past it
returned an inexact 2.0.  Likewise, (floor 5/4) returns an exact 1.
** inexact->exact no longer returns only integers.
Without exact rationals, the closest exact number was always an
integer, but now inexact->exact returns the fraction that is exactly
equal to a floating point number.  For example:
    (inexact->exact 1.234)
    => 694680242521899/562949953421312
When you want the old behavior, use 'round' explicitely:
    (inexact->exact (round 1.234))
    => 1
** New function 'rationalize'.
This function finds a simple fraction that is close to a given real
number.  For example (and compare with inexact->exact above):
    (rationalize 1.234 0.0005)
    => 58/47
** 'odd?' and 'even?' work also for inexact integers.
Previously, (odd? 1.0) would signal an error since only exact integers
were recognized as integers.  Now (odd? 1.0) returns #t, (odd? 2.0)
returns #f and (odd? 1.5) signals an error.

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