Float compression [Re: floating point math results question]
Jonathan Hogg
jonathan at onegoodidea.com
Sun Jan 27 14:27:02 CET 2002
On 26/1/2002 21:07, in article
mailman.1012079405.13099.python-list at python.org, "François Pinard"
<pinard at iro.umontreal.ca> wrote:
> I guess that it is an interesting exercise, trying to represent an arbitrary
> float number within a given tolerance, with a small number of bits.
>
> Let's take math.pi, say. It can be represented by 355:113 if the tolerance
> is over 0.00000027. Maybe we could find efficient binary representations
> for 355 followed by 113, and this probably turns out into finding efficient
> ways for coding the bit length of each.
Interesting perhaps, but who needs a space-efficient representation anymore?
Given that memory is cheap and non-aligned/bitwise operations are expensive.
What we need is a 'rational' type, in a similar vein to the existing
'complex' type:
n = rational( 8, 10 )
A more interesting problem is an efficient algorithm for refactoring an
arbitrary rational number into a sequence of the form:
... + 100.k[2] + 10.k[1] + k[0] + k[-1]/10 + k[-2]/100 + ...
where 0 <= k[i] < 10, which you would want for printing out the
representation as a normal floating point number. [Of course noting that
many rationals are non-terminating as floats.]
Does NumPy or something similar already have rational types? I don't do
numerical stuff in Python so I have no idea if this is a solved problem with
a simple download.
Jonathan
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