[fpc-devel] Arbitrary-precision arithmetic unit

[Mehmet Erol Sanliturk]

Dear Alexander S. Klenin ,

> 3) Finally, and relevantly for this list,
>   should something like this be included into FPC?

I think , in the long run such a facility may be very useful ,
because some times it is becoming necessary to resort such 
techniques . 

In those days I am working on my Fortran programs to improve them .

There is a test matrix : Finite segments H ( n ) of Infinite 
Hilbert matrix : h ( i , j )  = 1 / ( i + j -1 ) , i = 1 ,, n , j = 1 ,, n .

This is a very ill-conditioned matrix . In double precision it is not possible 
to invert around H ( 20 ) because determinant becomes very  small .

In Free Pascal  , by using Extended arithmetic ,  epsilon as 1.0E-777 , it is 
not possible to reach H ( 25 ) .

This means that in such situations it is necessary to resort multiple
precision arithmetic .

Personally , I will use an existing multiple precision Fortran package
( I will study contents of www.netlib.org )  , or
If I can not find a suitable one , I will write such a Fortran set of 
subroutines .

For the Free Pascal community , having such a facility at hand during
solving numerical analysis problems would be very useful .

Another important problem is decimal floating point arithmetic ,
especially for financial or legally required computations .
For example , around 1970 , in IBM System/360 , there was BCD : Binary
Coded Decimal . ( I do not know previous state prior that date ) .


Thank you very much .

Mehmet Erol Sanliturk