Lossless Number Conversion

[Chris Spencer]

Is there any library for Python that implements a kind of universal
number object. Something that, if you divide two integers, generates a
ratio instead of a float, or if you take the square root of a negative,
generates a complex number instead of raising an exception? Lisp has
something like this, and it makes number crunching much more convenient.

Chris

[mensanator@aol.com]

Re: Lossless Number Conversion


Chris Spencer wrote:[color=blue]
> Is there any library for Python that implements a kind of universal
> number object. Something that, if you divide two integers, generates a
> ratio instead of a float, or if you take the square root of a negative,
> generates a complex number instead of raising an exception? Lisp has
> something like this, and it makes number crunching much more convenient.
>
> Chris[/color]

The GMPY module has unlimited precision rationals:
[color=blue][color=green][color=darkred]
>>> from gmpy import *[/color][/color][/color]
[color=blue][color=green][color=darkred]
>>> r = mpq(1,1) # create the rational 1/1
>>> for i in range(2,50):[/color][/color][/color]
r = r + mpq(1,i) # add the rational 1/i to the running sum
print r


3/2
11/6
25/12
137/60
49/20
363/140
761/280
7129/2520
7381/2520
83711/27720
86021/27720
1145993/360360
1171733/360360
1195757/360360
2436559/720720
42142223/12252240
14274301/4084080
275295799/77597520
55835135/15519504
18858053/5173168
19093197/5173168
444316699/118982864
1347822955/356948592
34052522467/8923714800
34395742267/8923714800
312536252003/80313433200
315404588903/80313433200
9227046511387/2329089562800
9304682830147/2329089562800
290774257297357/72201776446800
586061125622639/144403552893600

So you can keep absolute precision all the way to the end
of the calculation. And you can always convert it to a float
by dividing the numerator by the denominator:
[color=blue][color=green][color=darkred]
>>> print mpf(r.numer())/mpf(r.denom())[/color][/color][/color]
4.4792053383294 250575604717929 6

[Andreas Kostyrka]

Re: Lossless Number Conversion

Am Sonntag, den 28.08.2005, 21:36 +0000 schrieb Chris Spencer:[color=blue]
> Is there any library for Python that implements a kind of universal
> number object. Something that, if you divide two integers, generates a
> ratio instead of a float, or if you take the square root of a negative,
> generates a complex number instead of raising an exception? Lisp has
> something like this, and it makes number crunching much more convenient.[/color]

Yes and no. There isn't general solution. But for example you want to
allow complex number, just use cmath.

Andreas

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[Raymond L. Buvel]

Re: Lossless Number Conversion

Chris Spencer wrote:[color=blue]
> Is there any library for Python that implements a kind of universal
> number object. Something that, if you divide two integers, generates a
> ratio instead of a float, or if you take the square root of a negative,
> generates a complex number instead of raising an exception? Lisp has
> something like this, and it makes number crunching much more convenient.
>
> Chris[/color]

If you are on any Unix-like platform, you might want to check out clnum.
It works like the gmpy package but has complex versions of rationals
and arbitrary precision floats.

http://calcrpnpy.sourceforge.net/clnum.html