OpenEuphoria

Re: Current implementation of exp() is faulty.

• Posted by CChris <christian.cuvier at agric?lture.gouv.fr> May 09, 2008
• 748 views

Matt Lewis wrote:
> 
> CChris wrote:
> > 
> > }}}
<eucode>
> > include machine.e
> > include math.e
> > ?atom_to_float64(power(E,20.0))
> > ?atom_to_float64
> >
> > (485165195.409790277969106830541540558684638988944847254353610800315977996142709740165979850652747349447833789438961)
> > ?atom_to_float64(power(E,12.0))
> > ?atom_to_float64(
> >
> > 162754.7914190039208080052048984867831702092844787207704435562481385967708355437387292882419094316843)
> > ?atom_to_float64(power(E,10.0))
> > ?atom_to_float64(
> >
> > 22026.46579480671651695790064528424436635351261855678107423542635522520281857079257519912096816452590)
> > ?atom_to_float64(power(E,8.0))
> > ?atom_to_float64(
> >
> > 2980.957987041728274743592099452888673755967939132835702208963530387730725173367530157371871490018139)
> > ?atom_to_float64(power(E,6.0))
> > ?atom_to_float64(
> >
> > 403.4287934927351226083871805433882796058998973571292026139671883251511806339934983051788866512126648)
> > ?atom_to_float64(power(E,5.0))
> > ?atom_to_float64(
> >
> > 148.4131591025766034211155800405522796234876675938789890467528451109120648209585760796884094598990211)
> > ?machine_func(26,0)
> > </eucode>
{{{

> > 
> > Results:
> > {253,231,104,139,8,235,188,65}
> > {3,232,104,139,8,235,188,65}
> > {152,124,211,84,22,222,3,65}
> > {154,124,211,84,22,222,3,65}
> > {93,5,149,207,157,130,213,64}
> > {97,5,149,207,157,130,213,64}
> > {108,12,71,125,234,73,167,64}
> > {110,12,71,125,234,73,167,64}
> > {141,192,144,86,220,54,121,64}
> > {142,192,144,86,220,54,121,64}
> > {142,51,112,153,56,141,98,64}
> > {142,51,112,153,56,141,98,64}
> > 
> > 
> > So, discrepancies start showing up for values of the argument as small as 6,
> > or even smaller.
> 
> Are you certain that it's the implementation of exp and not the parsing 
> of floating point?  You're way beyond the precision that the current
> floating point scanner can handle.  Try changing to scientific notation.
> I just added E+0 to all of your ridiculously precise numbers, and here's
> what I got:
> 
> {251,231,104,139,8,235,188,65}
> {4,232,104,139,8,235,188,65}
> {151,124,211,84,22,222,3,65}
> {154,124,211,84,22,222,3,65}
> {92,5,149,207,157,130,213,64}
> {96,5,149,207,157,130,213,64}
> {107,12,71,125,234,73,167,64}
> {110,12,71,125,234,73,167,64}
> {141,192,144,86,220,54,121,64}
> {143,192,144,86,220,54,121,64}
> {142,51,112,153,56,141,98,64}
> {143,51,112,153,56,141,98,64}
> 
> 
> Frankly, I have idea how close to Mathematica's result these are.  You
> never told us what those answers were.
> 
> Matt

I thought I did....
The pasted value for exp(x) is obtained by ealuating N[Exp[x],100] . When x is
not an integer, it must be entered in fractional form. Otherwise, Mathematica is
aware of the roundoff errors and only returns like 6 or 7 decimal places.
exp(some fraction) can be computed at any precision as a rational approximation.
The process is simply tedious by hand, so I didn't check directly.

CChris