Variadic function in C without stdarg header (gcc, linux x86_64)

sum.c

#include <stdio.h>

int sum(int n, ...);

int main(void) {
    printf("sum(5, 5) = %d\n", sum(2, 5, 5));
    printf("sum(10, 20, 30, 40, 50) = %d\n", sum(5, 10, 20, 30, 40, 50));
    printf("sum(9, 8, 7, 6, 5, 4, 3, 2, 1) = %d\n", sum(9, 9, 8, 7, 6, 5, 4, 3, 2, 1));
    return 0;
}

int sum(int n, ...) {
    int result = 0;
    register int esi asm("esi");
    register int edx asm("edx");
    register int ecx asm("ecx");
    register long r8 asm("r8");
    register long r9 asm("r9");
    register long rbp asm("rbp");
    int esiv = esi, edxv = edx, ecxv = ecx, r8v = r8, r9v = r9;
    void *stack = (void *) rbp + 16;
    while(n--) {
        switch(n) {
            case 0:
                result += esiv;
                break;
            case 1:
                result += edxv;
                break;
            case 2:
                result += ecxv;
                break;
            case 3:
                result += r8v;
                break;
            case 4:
                result += r9v;
                break;
            default:
                result += *(int *) stack;
                stack += 8;
                break;
        }
    }
    return result;
}