mpf_root?

[Paul Zimmermann]

> Hi, I'm trying to convert some code from PARI/GP to C, using gmp-4.2.2.
> The code requires only (big) integer arithmetic, except for one calculation:
>   c = floor(1 / (sqrtn(p / q, n) - 1))
> .. in which q < p < 2^128 and 3 <= n <= 8.
> 
> Now I have a fair amount of experience in integer calculations, but much
> less in fp maths: in the above form I would need the equivalent of an
> mpf_root() function, which of course isn't in the library.
> 
> I think I can see how to converge on the result using the inequality:
>   p . c^n <= q . (c+1)^n
> using integer arithmetic only, effectively doing a binary chop (though
> I need to think whether I can find a way to calculate the upper bound
> without another set of trial calculations). Can anyone suggest a better
> way?

a possible alternative is to use mpfr (mpfr.org), which extends mpf:

 -- Function: int mpfr_cbrt (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
 -- Function: int mpfr_root (mpfr_t ROP, mpfr_t OP, unsigned long int
          K, mp_rnd_t RND)
     Set ROP to the cubic root (resp. the Kth root) of OP rounded in
     the direction RND.  An odd (resp. even) root of a negative number
     (including -Inf) returns a negative number (resp. NaN).  The Kth
     root of -0 is defined to be -0, whatever the parity of K.

Paul Zimmermann