Dear Khue,
As mentioned before, you can use Rmpfr to read in strings or compute higher
precision values, like
x = mpfr(1, 192) /10;
# 0.1 with 192 bits precision
# or x = mpfr("0.1", 192);
mpfr(1, 192) /10 - mpfr("0.1", 192)
# 1 'mpfr' number of precision 192 bits
# [1] 0
However, I do not know how easy it is to convert from the mpfr format to the
other format. Maybe the BH-team can add an mpfr constructor to the library.
On a somewhat related topic, I did implement a very basic solver in native R
(and based on Rmpfr). You can have a look on GitHub; it is not a package, but
the script should be self-contained:
https://github.com/discoleo/R/blob/master/Math/Polynomials.Helper.Matrix.mpfr.R
It is very basic - more like a proof of concept. It does not include any
advanced tricks and there is quit some drop of precision in some examples, see:
https://github.com/discoleo/R/blob/master/Math/Polynomials.Helper.mpfr.Tests.R
I was primarily interested in solving systems of polynomial equations
(including complex roots); but did not have time to finish the remaining work.
Extending the algorithm to solve for eigenvalues may be feasible (although I
was less interested in eigenvalues). A native implementation in C++ would be
faster; but I try to avoid any more complicated programming if it is not
absolutely essential!
Sincerely,
Leonard
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