Show that Algorithm $4$ uses $O(qloga)$ bit operations, assuming that $a>d.$

ALGORITHM $4$ Computing div and mod.

procedure division algorithm$(a$ : integer, $d$ : positive integer$)$

$q$:$=0$

$r$:$=|a|$

while $rd$

$,r$:$=r-d$

$,q$:$=q+1$

while $rd$

if $a<mn\; id="EditorElement\_9106273">0</mn>$ and $r>0$ then

$r$:$=d-r$

$q$:$=-(q+1)$

return is the quotient, $r=$amodd is the remainder