Subtraction.fractran.txt

# Subtraction in FRACTRAN

## The Program

INPUT (n): 2^a * 3^b
OUTPUT:    2^a - b (or) 3^b - a

r2: a // first number
r3: b // second number


### Pseudocode

while true {
    // Fraction A
    if (r2 >= 1 && r3 >= 1) {
        decrement r2 and r3;
    } else {
        break;
    }
}


### FRACTRAN

(
    1 / 6
)


## Examples

### Example 1

We will test is that 5 - 2 == 3. Our initial value (n) should be 2^5 * 3^2. Our
result should be r2 == 3.

r2: 5
r3: 2
n: 2^5 * 3^2

Begin Program:

Decrement both values.
A: (2^5 * 3^2) * (1^1 / 2^1 * 3^1)
n: 2^4 * 3^1

Decrement both values.
A: (2^4 * 3^1) * (1^1 / 2^1 * 3^1)
n: 2^3

HALT


### Example 2

We will test that 3 - 3 == 0. Our initial value (n) should be 2^3 * 3^3. Our
result should be r2 == 0.

r2: 3
r3: 3
n: 2^3 * 3^3 = 216

Begin Program:

Decrement both values.
A: 2^3 * 3^3 * (1) / 2^1 * 3^1
n: 2^2 * 3^2

Decrement both values.
A: 2^2 * 3^2 * (1) / 2^1 * 3^1
n: 2^1 * 3^1

Decrement both values.
A: 2^1 * 3^1 * (1) / 2^1 * 3^1
n: 1 or 2^0 * 3^0

HALT