Precision issue

[Michael Hudson]

Duncan Booth <duncan at NOSPAMrcp.co.uk> writes:

> Alex Martelli <aleax at aleax.it> wrote in
> news:8lvhb.258000$R32.8375967 at news2.tin.it: 
> 
> > Ladvánszky Károly wrote:
> > 
> >> Entering 3.4 in Python yields 3.3999999999999999.
> >> I know it is due to the fact that 3.4 can not be precisely expressed
> >> by the powers of 2. Can the float handling rules of the underlying
> >> layers be set from Python so that 3.4 yield 3.4?
> > 
> > It seems, from the question, that you might not have entirely
> > understood and grasped the explanations you can find at:
> > http://www.python.org/doc/current/tut/node14.html
> > and I quote, in particular:
> 
> I know this is an FAQ, but the one thing I've never seen explained 
> satisfactorily is why repr(3.4) has to be '3.3999999999999999' rather than 
> '3.4'?

I believe "computational and code complexity" is the main answer to
that one.

Start here

    http://citeseer.nj.nec.com/gay90correctly.html

?

> Surely the important thing is that the equality eval(repr(x))==x has to 
> hold for floating point numbers, and that holds just as true for the short 
> 3.4 as it does for the 17 digit version? 
> 
> Microsoft .Net has a numeric format "R" which does a similar job. The R 
> specifier guarantees that a floating point numeric value converted to a 
> string will be parsed back into the same numeric value. It does this by 
> first trying a general format with 15 digits of precision then parsing that 
> back to a number. If the result is not the same as the original it then 
> falls back to the 17 digit value. There's no reason why Python couldn't do 
> the same:
> 
> def float_repr(x):
> 	s = "%.15g" % x
> 	if float(s)==x: return s
> 	return "%.17g" % x
> 
> This would be MUCH friendlier for newcomers to the language.

It would be nice, but I think it's pretty hard to do efficiently.  Tim
Peters would be more certain than me :-)

"Patches welcome" might apply, too.  I don't think your suggested
float repr will fly, I'm afraid...

Cheers,
mwh

-- 
34. The string is a stark data structure and everywhere it is
    passed there is much duplication of process.  It is a perfect
    vehicle for hiding information.
  -- Alan Perlis, http://www.cs.yale.edu/homes/perlis-alan/quotes.html