serie of sqrt

[Kevin Ryde]

"laurent couraud" <l.couraud at free.fr> writes:
>
> Because the entire part of the square root of a + n*h and the entire part
>  of the square root of a + (n + 1)*h can be equal or very near, if we inject
> the initial value in the Newton algorithm we probably gain the square root
> with a very small number of iteration.

I'm not sure I understand.

If you calculate the square root (s) and remainder (r) using
mpz_sqrtrem of some value x, then I think from that you can know where
nearby perfect squares are located using some additions.  x-r is the
next lower one (ie. s^2 of course), and the next higher one would be
x-r+2*s+1, then x-r+4*s+4, etc.