/* Recursive popcount */ long pcount_r(unsigned long x) { if (x == 0) return 0; else return (x & 1) + pcount_r(x >> 1); } pcount_r: movl $0, $eax testa frdi, $rdi je .L6 pusha frbx mova frdi, &rbx andi $1, %ebx shra %rdi call pcountur adda rbx, frax popa %rbx .L6: rep; ret # if x==0 # done # save $rbx # x -> 8 rbx # x & 1 # x >> 1 # recurse # retval # restore rbx Problem 3. This problem considers the growth of the stack in the execution of a recursive function. Consider the recursive version of the "popcount" function (pcount.r()), as described in Lecture L10 (beginning on slide 6). Suppose that function is called with actual parameter 0x00000012, from a point where register %rbx contains 0x0000ffff, and where the address of the next instruction is Oxfff60548. Assume the address of the (recursive) call instruction is 0xffff703000, and it is a three-byte instruction. a. Including that original invocation, what is the maximum number of frames for pcounts that will be on the stack as a result? b. Draw a diagram showing the contents of the stack at the point of maximum depth of recursion. Include the value of all the items pushed onto the stack for each invocation. /* Recursive popcount */ long pcount_r(unsigned long x) { if (x == 0) return 0; else return (x & 1) + pcount_r(x >> 1); } pcount_r: movl $0, $eax testa frdi, $rdi je .L6 pusha frbx mova frdi, &rbx andi $1, %ebx shra %rdi call pcountur adda rbx, frax popa %rbx .L6: rep; ret # if x==0 # done # save $rbx # x -> 8 rbx # x & 1 # x >> 1 # recurse # retval # restore rbx Problem 3. This problem considers the growth of the stack in the execution of a recursive function. Consider the recursive version of the "popcount" function (pcount.r()), as described in Lecture L10 (beginning on slide 6). Suppose that function is called with actual parameter 0x00000012, from a point where register %rbx contains 0x0000ffff, and where the address of the next instruction is Oxfff60548. Assume the address of the (recursive) call instruction is 0xffff703000, and it is a three-byte instruction. a. Including that original invocation, what is the maximum number of frames for pcounts that will be on the stack as a result? b. Draw a diagram showing the contents of the stack at the point of maximum depth of recursion. Include the value of all the items pushed onto the stack for each invocation