On Wed, Sep 8, 2010 at 3:03 PM, Greg Marks <[email protected]> wrote:
> It sounds like a C program using MPFR (http://www.mpfr.org)
> would do what you want.  As MPFR is built into SAGE, you might
> perhaps find it more convenient to invoke MPFR within SAGE.

This is what I would recommend. You can do something like

from sage.rings.real_mpfr cimport *

def square(RealNumber x):
    cdef RealNumber result = x._new()
    mpfr_mul(result.value, x.value, x.value, GMP_RNDN)
    return result

If you really need speed, you can declare, allocate, and free mpfr_t
variables themselves (declared via "cdef mpfr_t var") rather than
using the RealNumber Python objects as wrappers.

Just out of curiosity, what multi-precision root finding tools are you
using? Also, I don't think numpy supports high-precision floating
point arrays (except as arrays of generic objects).

- Robert

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