Any Leftovers?

Problem

Divide a number by 4 and print the remainder.

11. Any leftovers, Comet 64

Solution 1

Assume the input number x is at least 4. Let x := x - 4. If the result is less than 4, we have the remainder. Otherwise, repeat the subtraction process.

int = input;                  // Read in x.
subtract:                     // The "subtract" branch.
    int = int - 4;            // x := x - 4
    check int < 4;            // Is x < 4?
    jump if false: subtract;  // If not, go to "subtract".
output = int;                 // Print the remainder.

Solution 2

Given an input x, we want the remainder when x is divided by 4. The remainder function is

f(x) := x mod 4

This can be implemented as follows. Define the quotient by

q := floor(x / 4)

where the floor(x) function is simply the integer part of a floating point number x. Define the

n := 4 * q

and the remainder can be calculated as

r := x - n

This solution is optimal, according to the game.

reg = input;      // Read number x.
int = reg / 4;    // The quotient q := floor(x / 4).
int = 4 * int;    // The number n := 4 * q.
int = reg - int;  // The remainder r := x - n.
output = int;     // Print the remainder.