[GiNaC-list] Unwanted digits when performing arithmetic computations

[Dr. Mithun Bairagi]

Thank you for your nice explanation 👍

On Sun, 27 Oct 2024, 3:41 am Richard B. Kreckel, <kreckel at in.terlu.de>
wrote:

> Hello,
>
> On 10/26/24 5:38 PM, Dr. Mithun Bairagi wrote:
> > Dear all ginac lovers, I have got some wrong results when performing
> > some simple computations using ginac.
>
> These results are not "wrong", see below.
>
> > I have compiled and run the following c++ program using ginac-1.8.7,
> > cln-1.3.7  (mingw64 compiler,  gcc version 14.2.0, windows 10 os),
> >
> > #include <ginac/ginac.h>
> >
> > using namespace std;
> > using namespace GiNaC;
> >
> > int main()
> > {
> >      cout<<(numeric(0.1)+numeric(7))<<endl;
> >      cout<<(numeric("0.01")*numeric("9"))<<endl;
> >      cout<<(numeric("0.01")*numeric("99"))<<endl;
> > }
> >
> > the above program shows the following result:
> > 7.1000000000000000056
> > 0.089999999999999999996
> > 0.98999999999999999995
> >
> > I have got some unwanted digits which look very ugly. I think the result
> > should be
> > 7.1
> > 0.09
> > 0.99
>
> This result is to be expected. Remember that CLN and GiNaC (and many
> other systems) represent floating-point numbers in base 2, not in base 10.
>
> In such systems, each floating-point number is an exact rational number
> where the denominator happens to be a power of two.
>
> An exact decimal fraction (such as 7.1 = 71/10 in decimal notation) can
> be converted to an exact binary fraction if and only if the numerator is
> a power of 2.
>
> This is not the case for 71/10. On the other hand, it is the case for
> e.g 75/10 = 15/2, so 7.5 can be converted from string "7.5" to an
> internal representation exactly.
>
> As an alternative, maybe you can use rational numbers such as 71/10
> throughout your computations? Apart from that, there is no solution to
> what you perceive as a "problem".
>
> Mankind made a big mistake settling for base 10 millennia ago.
>
>     -richy.
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