Numerical representation

[Robert Kern]

On 3/4/11 4:32 PM, Jon Herman wrote:
> Hello all,
>
> I am new to the Python language and writing a Runge-Kutta-Fellberg 7(8)
> integrator in Python, which requires an extreme numerical precision for my
> particular application. Unfortunately, I can not seem to attain it.
> The interesting part is if I take my exact code and translate it to Matlab code
> (so I use the exact same process and numbers), I get a far superior precision
> (the one I am expecting, in fact). This leads me to think I need to call a
> certain command in my Python script in order to make sure no truncation errors
> are building up over my integration.
>
> Has anyone had similar problems? Is there a difference between how Matlab and
> Python store numbers, and if so how do I make Python more accurate?

No, there is no difference in how they store numbers. Both use double-precision 
floating point numbers, almost certainly IEEE-754 doubles on your platform. Can 
you show us the output you get and the output you expect?

They do *display* floating point numbers differently. MATLAB will often truncate 
floats while Python will display as many digits as necessary (often more, 
actually) to faithfully reconstruct the binary floating point number. This can 
create the perception that MATLAB is doing things more accurately.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
  that is made terrible by our own mad attempt to interpret it as though it had
  an underlying truth."
   -- Umberto Eco