GCD: algorithme d’Euclide dans un « Master Boot Record »

Python

Code Python:

def gcd(a, b):
    while a != b:
        if a > b:
            a = a - b
        else:
            b = b - a
    return a

import sys
print(gcd(int(sys.argv[1]), int(sys.argv[2])))

• https://tenthousandmeters.com/blog/python-behind-the-scenes-5-how-variables-are-implemented-in-cpython/

C

Code C:

#include <stdio.h>
#include <stdlib.h>

int gcd(unsigned short a, unsigned short b)
{
  while (a != b)
    if (a > b)
      a = a - b;
    else
      b = b - a;
  return a;
}

int main(int ac, char *av[])
{
  unsigned short a, b, r;
  a = atoi(av[1]);
  b = atoi(av[2]);
  r = gcd(a, b); 
  printf("%d\n", r);
  return 0;
}

Rust

Code Rust:

pub fn gcd(mut a: u16, mut b: u16) -> u16 {
  while a != b {
    if a > b {
      a = a - b; 
    } else {
      b = b - a;
    }
  }
  a
}

use std::env;

fn main() {
    let args: Vec<String> = env::args().collect();
    let a = args[1].parse::<u16>().expect("not a valid number");
    let b = args[2].parse::<u16>().expect("not a valid number");
    let r = gcd(a, b);
    println!("{r}");
}

Assembleur x86

• http://ref.x86asm.net/index.html

• https://www.felixcloutier.com/x86/

• https://software.intel.com/en-us/download/intel-64-and-ia-32-architectures-sdm-combined-volumes-1-2a-2b-2c-2d-3a-3b-3c-3d-and-4

• https://stackoverflow.com/questions/8287181/how-to-do-source-level-debugging-of-x86-code-with-gdb-inside-qemu

• https://diablohorn.com/2010/01/09/bootloader-development-environment/

• https://binarydebt.wordpress.com/2018/10/06/how-does-an-x86-processor-boot/

code source:

        mov ax, 2345 
        mov bx, 35 
gcd:
        cmp ax, bx
        je end
        jl else
        sub ax, bx 
        jmp gcd
else:
        sub bx, ax 
        jmp gcd 
end:
        mov cx, ax
padding:
times 510-($-$$) db 0
dw 0xaa55

Compilation en format « bin » (ou « raw », ou « com »):

nasm -o gcd_x8086.bin -f bin gcd_x8086.S
ndisasm gcd_x8086.bin

Compilation en format ELF:

nasm -o gcd_x8086.elf -f elf -g gcd_x8086.S
objdump -d gcd_x8086.elf

Exécution du code binaire avec QEMU en mode « déboguable » (-s -S):

qemu-system-i386 -s -S -fda gcd_x8086.bin -boot a

Visualisation de l’exécution du code avec GDB:

$ gdb
target remote localhost:1234
set architecture i8086
display /i ($cs*16)+$pc
stepi  # step into the guest BIOS (seabios)
stepi
stepi
stepi
stepi
stepi
stepi
stepi
stepi
stepi
stepi
br *0x7c00 # set breakpoint in the MBR
cont
stepi
br *0x7c14
layout asm
layout regs
stepi
stepi