#include

#include

$/*$ compute x$*$y with addition $*/$

uint$64\_$t recmul$($uint$64\_$t a$,$uint$64\_$t b$)\{$

if $($a$==0||$ b$==0)$

return $0$;

else if $($a$==1)$

return b;

else

return b $+$ recmul$($a$-1,$b$)$;

$\}$

$/*$ compute x to the yth power using only addition $*/$

uint$64\_$t recexp$($uint$64\_$t x$,$uint$64\_$t y$)\{$

if $($y $==0)$

return $1$;

else if $($y$==1)$

return x;

else

return recmul$($x$,$recexp$($x$,$y$-1))$;

$\}$

int main$()\{$

printf$("$recexp$(2,2)$ returned $\%$lu$.$

$",$recexp$(2,2))$;

return $0$;

$\}$

Using the disassemble command under gdb$,$ examine the first five instructions of

recmul $($ignoring the endbr$64$ instruction$).$

$1$

a$.$ Compare these instructions to the first five instructions of recexp. What do you notice?

b$.$ What are these instructions doing? $($Hint: recall that the parameters to each function are

passed in registers $\%$rdi and $\%$rsi.$)$

c$.$ Why does the compiler generate this code? $($Hint: look at the instructions before the recursive

call in each function.$)$