Newton's square root

Find the square root of the number in the stdin box without the fsqrtFd = sqrt(Fn) (S or D form). instruction, using the rule Isaac Newton's method gives for square roots: if guess is a guess at the root of n, then

next = (guess + n / guess) / 2

is a better one. Start at or above the root (n itself, or 1.0 when n is below 1) and every step lands closer, always from above. In exact arithmetic that goes on forever; in floating point the guesses soon stop getting smaller, because a double holds only so many digits. So repeat the rule, compare each next with guess using fcmpSet NZCV from Fn vs Fm (S or D form)., and stop as soon as next is not smaller. guess is then the answer. Do not count steps: a big n needs far more of them than a small one.

Print the root with the %.6f format in .data, which reads a double from d0. Two inputs need care before the loop:

• a negative number has no real square root: print no real square root and return 1
• the root of 0 is 0; left to the loop, the guess shrinks to zero and 0 / 0 is not a number, so the loop never ends

What is checked

• the root printed for the number in the stdin box, and for more numbers you cannot see
• the exit status (0, or 1 for a negative number)
• the loop is yours: fdivFd = Fn / Fm (S or D form). and fcmpSet NZCV from Fn vs Fm (S or D form). present, no fsqrtFd = sqrt(Fn) (S or D form).