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This limitation is due to the endless loop detection threshold [see
comments below] in your preferences. In my amibroker it was 100,000,
so if the steps of the loop are >100,000 it is "endless".
Dimitris Tsokakis
--- In amibroker@xxxxxxxxxxxxxxx, "Mr Valley" <valleymj@xxxx> wrote:
> Why does one get an error message if you change precision to 8?
> Is this a limitation within AB? Shouldn't one be able to set it to
any
> number?
> Mr. Valley
> -----Original Message-----
> From: DIMITRIS TSOKAKIS [mailto:TSOKAKIS@x...]
> Sent: Thursday, January 29, 2004 4:57 AM
> To: amibroker@xxxxxxxxxxxxxxx
> Subject: [amibroker] Re: Successive Approximation in afl
>
>
> Herman,
> We may have another approach through while() statement.
> [For the simplicity, the //next decimals are in a loop form ]
>
> //Sqrt(X) approximation
> X=2;Precision=7;
> a=1;b=2;
> st0=0.1;//the initial step
> z=0;
> //1st decimal
> i=a;
> while(i^2<X)
> {
> z=i;
> i=i+st0;
> }
> //next decimals
> for(n=1;n<Precision;n++)
> {
> st0=0.1*st0;
> i=z;
> while(i^2<x)
> {
> z=i;
> i=i+st0;
> }
> }
> Title="Sqrt("+WriteVal(X,1.0)+")="+WriteVal(z,1+0.1*n);
>
> When we have the Sqrt(2)=1.41, the next loop will search 1.411,
> 1.412, 1.413, 1.414, 1.415 and will stop there, since 1.415 gives
> false output.
> In this way, the 3rd loop needs 5 steps instead of 10. Since
decimals
> will be equally disributed below and above 5 [I hope you dont
always
> search an 1.99999 !!] we gain many steps.
> Without this, one should begin from 1 and search every 0.00001 up
to
> 1.41421.
> This is done by the full code
>
> //Sqrt(X) full approximation
> X=2;Precision=5;
> a=1;b=2;
> st0=10^(-Precision);//the initial step
> z=0;
> //decimals
> i=a;
> while(i^2<X)
> {
> z=i;
> i=i+st0;
> }
> Title="Sqrt("+WriteVal(X,1.0)+")="+WriteVal(z,1+0.1*Precision);
>
> and it is not the best choice !!
>
> A simple criterion to see the difference, is your endless loop
> detection threshold.
> If it is set, for example, to 100000 iterations, the first method
> will permit Precision=7 whereas the 2nd[full] method will not go
more
> than Precision=5.
>
> The steps of the 1st method depend on the result : You will not be
> that lucky with Sqrt(3.56). It is 1.886796, all the decimal digits
> are >5 and the steps per digit will be 9+9+7+8+10+7
respectively !!
> It is much better to search Sqrt(2.2811), it is 1.510331 and will
> take 6+2+1+4+4+2 steps per digit.
> You may also put a small counter to count the total steps of the
> approximation, it is interesting.
> Dimitris Tsokakis
>
>
>
>
> --- In amibroker@xxxxxxxxxxxxxxx, "Herman vandenBergen"
<psytek@xxxx>
> wrote:
> > Thank you DT, as usual your reply is not only informative but
> entertaining
> > :-) an 8x improvement in speed would be just fine. If my own
> solution is
> > general I will post it.
> >
> > I think I received enough ideas to try a few things, solving a
small
> > challenge with your owninput is half the fun and a better way to
> learn.
> >
> > Thanks everybody and have a great day!
> > herman
> > -----Original Message-----
> > From: DIMITRIS TSOKAKIS [mailto:TSOKAKIS@x...]
> > Sent: January 29, 2004 2:16 AM
> > To: amibroker@xxxxxxxxxxxxxxx
> > Subject: [amibroker] Re: Successive Approximation in afl
> >
> >
> > Herman,
> > my method is a bit different.
> > I begin with the 1st digit accuracy [10 steps maximum, 1.0 to
1.9]
> > and localize
> > 1.4<sqrt(2)<1.5
> > Then, for the 2nd digit, 10 steps [maximum] again to obtain
> > 1.41<sqrt(2)<1.42
> > and so on.
> > In the average, I need 5 steps per digit and, for a 3-decimal
> > accuracy it will take about
> > 5*5*5=125 steps instead of the normal 1000.
> > Archimedes, the copyright of the method, was not working with
> > decimals.
> > For some reason [not explained anywhere], his first choice
was
> the
> > sevenths of the unity 1/7, 2/7, 3/7 etc .
> > So, in his famous "Measurement of a Circle", he proves that
> > 3+1/7>pi>3+10/71
> > As you see, he slightly increases the denominator [he does not
> > increase the numerator].
> > There are some obscure statements, he never explained, for
> example,
> > how did he came to the [useful approximation]
> > 265/153<sqrt(3)<1351/780 [!!!].
> > but, we can not always have what we want...
> > Dimitris Tsokakis
> > --- In amibroker@xxxxxxxxxxxxxxx, "Herman vandenBergen"
> <psytek@xxxx>
> > wrote:
> > > thanks DT, I have to study your code but I think you have
the
> > general idea.
> > > I have an impossible formula to transform (it contains HHV
and
> LLVs,
> > > stochastic mutation) and want to find the x that would give
me
> the
> > given y.
> > > Right now I linearly increment x untill I hit my y-target,
> this is
> > awfully
> > > slow.
> > >
> > > like y = function(x); // y ranges 0-100 and I want 2 decimal
> places
> > for x
> > > that gives me a given y
> > >
> > > I thought cutting the range in half, see whether it is
greater
> or
> > less, cut
> > > the result in half again, etc. I am not a math guy but I
have
> used
> > > AD-converters that worked like that and what we can do in
> hardware
> > we can do
> > > in software :-)
> > >
> > > thanks for the starter DT,
> > > herman
> > >
> > >
> > >
> > >
> > > -----Original Message-----
> > > From: DIMITRIS TSOKAKIS [mailto:TSOKAKIS@x...]
> > > Sent: January 28, 2004 9:18 PM
> > > To: amibroker@xxxxxxxxxxxxxxx
> > > Subject: [amibroker] Re: Successive Approximation in afl
> > >
> > >
> > > Herman,
> > > You mean a procedure like this
> > >
> > > a=1;b=2;z=0;
> > > st0=0.1;st1=0.01;st2=0.01;
> > > //1st decimal
> > > for(i=a;i<b;i=i+st0)
> > > {
> > > if(i^2<2 AND (i+st0)^2>2)
> > > z=i;
> > > }
> > > //2nd decimal
> > > for(i=z;i<z+st0;i=i+st1)
> > > {
> > > if(i^2<2 AND (i+st1)^2>2)
> > > z=i;
> > > }
> > > //...etc
> > > Plot(z,"sqrt(2)",1,1);
> > >
> > > to find sqrt(2) without using all the values from 1 to 2 ?
> > > Dimitris Tsokakis
> > > --- In amibroker@xxxxxxxxxxxxxxx, "Herman vandenBergen"
> > <psytek@xxxx>
> > > wrote:
> > > > Hello,
> > > >
> > > > has anybody come accross a successive approximation
routine
> in
> > afl?
> > > Or
> > > > perhaps js?
> > > >
> > > > thanks,
> > > > herman
> > >
> > >
> > >
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