Re: GMP precision problem - only getting 15 places of PI

[nmenuj]

David Kastrup wrote:
> nmenuj@gmail.com writes:
>
> > I installed the GNU MP package only today, and wanted to experiment
> > with the C++ interface. Can someone tell me why I am unable to get more
> > than 15 correct digits of PI with the following simple program? I
> > experimented with the PREC variable and the loop upper bounds, but no
> > luck - the bad digits start at the exact same spot.
> >
> > If someone has another multi-precision library installed, I request
> > that you check the code against your library, to rule out a bug in the
> > program. I suspect the problem is with a temporary assuming a smaller
> > precision, but the mpf_set_default_prec should have addressed that...
> >
> > #include <iostream>
> > #include <gmpxx.h>
> >
> > using namespace std;
> > const int PREC=20000;
> >
> > mpf_class pival(0.0, PREC);
> > mpf_class d2(1.0, PREC), d3(1.0,PREC);
> > int main()
> > {
> >         int i = 0;
> >         mpf_set_default_prec(PREC);
> >         d2 = mpf_class(1.0/2.0,PREC);
> >         pival = d2 - (d2/4.0)/3.0;
> >         for (i=5;i<10000;i+=4)
> >         {
> >                 d2 /= 16.0;
> >                 pival = pival + d2/i;
> >                 pival = pival - (d2/4.0)/(i + 2);
> >         }
> >         cout << "def prec " << mpf_get_default_prec() << '\n';
> >         d3 = mpf_class(1.0/3.0, PREC);
>                          ^^^^^^^ Uh, oh!

Thanks David! I won't be able to test it just yet, but I'm sure that's
it.
Also, my compliments to the developers of GMP, the speed is most
impressive!

>
> >         pival = pival +  d3 - (d3/9.0)/3.0;
> >         for (i=5;i<10000;i+=4)
> >         {
> >                 d3 /= 81.0;
> >                 pival = pival + d3/i;
> >                 pival = pival - (d3/9.0)/(i + 2);
> >         }
> >         cout.precision(100);
> >         cout << pival * 4.0 << '\n';
> >         return 0;
> > }
> 
> -- 
> David Kastrup, Kriemhildstr. 15, 44793 Bochum