Some Leftovers

Problem

Divide an integer by 4. Print the integer if the remainder is 3.

12. Some 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. Given the remainder, determine whether it is 3. If so, print the original integer.

reg = input;                  // Read in x.
int = reg;                    // 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".
check int = 3;                // Is remainder = 3?
jump if false: end;           // If not, go to "end".
output = reg;                 // Print the original number.
end:                          // End of program.

Solution 2

Given an input x, we print x if it has a remainder of 3 after division 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 number

n := 4 * q

and the remainder can be calculated as r := x - n. This solution is optimal, according to the game.

reg = input;         // Read in 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.
check int = 3;       // Is the remainder = 3?
jump if false: end;  // If not, go to "end".
output = reg;        // Print x.
end:                 // End of program.