HEAD has now exact fractions

HEAD has now exact fractions

[Marius Vollmer]

Hi,

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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Re: HEAD has now exact fractions

[Neil Jerram]

>>>>> "Marius" == Marius Vollmer <mvo@zagadka.de> writes:

    Marius> Hi, I have committed the exact fraction support from Bill
    Marius> Schottstaedt.  Thanks alot Bill!

Very cool.  Thank you Bill and Marius!

        Neil




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Re: HEAD has now exact fractions

[Kevin Ryde]

Marius Vollmer <mvo@zagadka.de> writes:
>
>     (inexact->exact 1.234)

You might like to show for instance 1.375 there, something that has an
exact binary representation.


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Re: HEAD has now exact fractions

[Marius Vollmer]

Kevin Ryde <user42@zip.com.au> writes:

> Marius Vollmer <mvo@zagadka.de> writes:
>>
>>     (inexact->exact 1.234)
>
> You might like to show for instance 1.375 there, something that has an
> exact binary representation.

Hmm, isn't that part of the point that 1.234 is indeed not exactly
representable and that the result of (inexact->exact 1.234) is not
something simple like 617/500?

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Re: HEAD has now exact fractions

[Kevin Ryde]

Marius Vollmer <mvo@zagadka.de> writes:
>
> Hmm, isn't that part of the point that 1.234 is indeed not exactly
> representable and that the result of (inexact->exact 1.234) is not
> something simple like 617/500?

Yes, though 1.234 is subject to truncation when it's read.  I was just
thinking to avoid any uncertainty that might introduce.


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Re: HEAD has now exact fractions

[Neil Jerram]

>>>>> "Marius" == Marius Vollmer <mvo@zagadka.de> writes:

    Marius> Hi,
    Marius> I have committed the exact fraction support from Bill Schottstaedt.

I'm getting a compile error:

numbers.c: In function `scm_make_ratio':
numbers.c:395: parse error before `int'
numbers.c:397: `divisible_p' undeclared (first use in this function)
numbers.c:397: (Each undeclared identifier is reported only once
numbers.c:397: for each function it appears in.)

I'd guess the fix is just to declare divisible_p at the start of the
block, but I haven't looked closely.

        Neil



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Re: HEAD has now exact fractions

[Marius Vollmer]

Neil Jerram <neil@ossau.uklinux.net> writes:

> I'm getting a compile error:
>
> numbers.c: In function `scm_make_ratio':
> numbers.c:395: parse error before `int'

Right, I've fixed this by avoidin divisible_p completely.  Please
update.  Thanks!

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