OpenEuphoria

Re: Implementation of exp()

• Posted by CChris <christian.cuvier at ?gricultur?.gouv.fr> Aug 29, 2007
• 584 views

Al Getz wrote:
> 
> CChris wrote:
> > 
> > Al Getz wrote:
> > > 
> > > Hi there,
> > > 
> > > 
> > > If you dont like the results of power(e,x) then the only alternative
> > > is to implement your own power series.  Taylors is the most popular
> > > and easy to implement, so maybe start there and check the accuracy
> > > of that and compare with power(e,x).
> > > Most of the time when i use exp(x) i implement as power(e,x) unless
> > > i need better accuracy then i go to a big number routine, but
> > > either way i end up using x negative because that comes up so much
> > > more in time domain studies of electrical networks and even networks
> > > that represent other physical processes.
> > > 
> > > Example:
> > >   y=a*exp(-t/b)
> > > where t is time and a,b are constants depending on circuit values
> > > and b is almost always positive.
> > > 
> > > 
> > > Al
> > > 
> > > E boa sorte com sua programacao Euphoria!
> > > 
> > > 
> > > My bumper sticker: "I brake for LED's"
> > > 
> > 
> > No need for such efforts, the standard C library has done it way before us.
> > It has a native exp() function, which I checked against arbitrary precision
> > computation: the native exp() doesn't have issues, only power(E,x) has. And
> > i is not because the value of E is inexact - things are ok as long as x is
> > no
> > greater than 7 or something.
> > 
> > The implementation would duplicate the code for sin(), with a check for
> > overflow
> > (the maximum allowable value for x is 1024*ln(2), which is about 694).
> > 
> > CChris
> > 
> > CChris
> 
> 
> You mean only the Euphoria version of power(e,x) doesnt work
> right?
> 
> 
> Al
> 
> E boa sorte com sua programacao Euphoria!
> 
> 
> My bumper sticker: "I brake for LED's"
> 

Yes.
This has nothing to do with the precision of the E constant - everything is
correct as long as x is below 7 or 8, I'd have to check my test file precisely.
So E is correctly for a 64-bit double number.

I bet the C exp() function is implemented in a way that circumvent this
limitation, probably using powers of 2 rather than powers of an irrational atom,
then converting back. The FPU instruction set (for Inte processors at lest), has
a builtin FYL2X (power(y,ln_2(x)) instruction, which is probably used. I don't
know for sure. What I know is that the results are not exactly what they should
be as computed with arbitrary precision.

CChris