1. x/2

As an approximation to y=sqrt(x), x/2 is exact for x=4, too small for x<4, and too large for x>4:

We can reduce the range of x to be considered using frexp() and ldexp() as follows:

if x != 0

   f = frexp(x,&e), produces f in the range [0.5, 1.0)

   if e is odd, multiply f by 2 and subtract 1 from e

   Now f is in the range [0.5, 2.0) and e is even

   Compute: g = sqrt(f)

   and then construct sqrt(x) using y=ldexp( g, e/2) = (f*2e)½

So we only need to consider approximations to sqrt(f) for 0.5 <= f < 2.0