mpmath puzzle

[kyosohma at gmail.com]

On Nov 14, 3:20 am, "Fredrik Johansson" <fredrik.johans... at gmail.com>
wrote:
> Dick Moores wrote:
> > For 1234 ** 10.9, why the wrong result from mpmath.power()?
>
> > ========================================
> > #!/usr/bin/env python
> > #coding=utf-8
> > from mpmath import *
>
> > mpf.dps = 32
>
> > x = mpf(1234)
> > y = mpf(10.9)
>
> > print power(x,y)
> > print "4.9583278648155041477415234438717e+33" # from Windows calculator
>
> > """
> > output:
> > 4.9583278648155166864966558721921e+33
> > 4.9583278648155041477415234438717e+33
> > """
> > ========================================
> >  (Code is also at <http://python.pastebin.com/m72a277b8>)
>
> >  Thanks,
>
> >  Dick Moores
>
> Hi,
>
> When you create y, you first create an inexact Python float whose
> value is actually 10.900000000000000355... and then pass it to mpf,
> which just copies that value along with the error. To create an
> accurate representation of a fractional number (integers are safe),
> pass a string instead:
>
> >>> from mpmath import *
>
> >>> mpf.dps = 32
> >>> x = mpf(1234)
> >>> y = mpf('10.9')
> >>> print power(x,y)
>
> 4.9583278648155041477415234438719e+33
>
> The last printed digit is wrong, which is to be expected in binary
> arithmetic since 10.9 still cannot be represented exactly (with
> mpf.dps = 32, the error is about 5e-033); computing a power amplifies
> that error. You can temporarily increase the precision by a couple of
> digits during calculations and then reduce it before printing the
> final value if you want all digits to be right.
>
> I should update the mpmath documentation to be much clearer about all this.
>
> Fredrik

You could also use the Decimal module to keep things accurate. Some
people like numpy or scipy for the more complex math problems they do.

Mike