Question

a) Write the following C function in Assembly. You must follow the System V 64-bit calling convention and use AT&T Syntax notation. Note: You cannot change the algorithm in any way so your assembly function must still be recursive. (20 points) long Catalan(long n) { long sum = 0; if (n == 0) return 1; for (int i = 0; i < n; i++) { sum += Catalan(i) * Catalan(n - i - 1); } return sum; } b) The Windows x86-64 calling convention passes function parameters in the registers RCX, RDX, R8 and R9 and returns values on register RAX. Caller saved registers are: RAX, RCX, RDX, R8, R9, R10 and R11, while callee-saved registers are RBX, RBP, RDI, RSI, RSP, R12, R13, R14, and R15. Rewrite the assembly function from Part A using the Windows x86-64 calling convention instead of the System V 64- bit calling convention. (16 points)

1) Assembly Programming a) Write the following C function in Assembly. You must follow the System V 64-bit calling convention and use AT&T Syntax notation. Note: You cannot change the algorithm in any way so your assembly function must still be recursive. (20 points) long Catalan(long n) { long sum if (n 0) return 1; 0; i < n; i++ for (int i { Catalan(i) Catalan(n - i - 1); sum += } return sum } b) The Windows x86-64 calling convention passes function parameters in the registers RCX, RDX, R8 and R9 and returns values on register RAX. Caller saved registers are: RAX, RCX RDX, R8, R9, R10 and R11, while callee-saved registers are RBX, RBP, RDI, RSI, RSP, R12, R13, R14, and R15. Rewrite the assembly function from Part A using the Windows x86- 64 calling convention instead of the System V 64- bit calling convention. (16 points)

Answer 1

//Answer for Second Question(conversoion of c program to x86-64 calling convention)

Catalan(long):

push rbp

mov rbp, rsp

push rbx

sub rsp, 40

mov QWORD PTR [rbp-40], rdi

mov QWORD PTR [rbp-24], 0

cmp QWORD PTR [rbp-40], 0

jne .L2

mov eax, 1

jmp .L3

.L2:

mov DWORD PTR [rbp-28], 0

.L5:

mov eax, DWORD PTR [rbp-28]

cdqe

cmp QWORD PTR [rbp-40], rax

jle .L4

mov eax, DWORD PTR [rbp-28]

cdqe

mov rdi, rax

call Catalan(long)

mov rbx, rax

mov eax, DWORD PTR [rbp-28]

cdqe

mov rdx, QWORD PTR [rbp-40]

sub rdx, rax

mov rax, rdx

sub rax, 1

mov rdi, rax

call Catalan(long)

imul rax, rbx

add QWORD PTR [rbp-24], rax

add DWORD PTR [rbp-28], 1

jmp .L5

.L4:

mov rax, QWORD PTR [rbp-24]

.L3:

add rsp, 40

pop rbx

pop rbp

ret