It depends on the types of constraints you have, the precision you want, and the sparsity of the system.
For example, for linear equality constraints, one general approach is iterative refinement [1]. If you are using floats/doubles and have dense systems, Lapack has implementations at some precision levels [2] (although not necessarily those you want).
For arbitrary precision, maybe look at MPFR matrices in flint [3].
If you have sparse systems using doubles there are papers on iterative refinement in suitesparse, but I don't know if the implementations are public.
If you have sparse inequality constraints, you can try SoPlex [4].
Comments
It depends on the types of constraints you have, the precision you want, and the sparsity of the system.
For example, for linear equality constraints, one general approach is iterative refinement [1]. If you are using floats/doubles and have dense systems, Lapack has implementations at some precision levels [2] (although not necessarily those you want).
For arbitrary precision, maybe look at MPFR matrices in flint [3].
If you have sparse systems using doubles there are papers on iterative refinement in suitesparse, but I don't know if the implementations are public.
If you have sparse inequality constraints, you can try SoPlex [4].
[1] https://en.wikipedia.org/wiki/Iterative_refinement
[2] https://netlib.org/lapack/explore-html/d7/d3b/group__double_...
[3] http://flintlib.org/sphinx/mpfr_mat.html
[4] https://soplex.zib.de/doc-1.7.0/html/IR.html