JOMP

JOMP is an OISC, which is a type of Esoteric programming language with one instruction. It uses prime factorisation to simulate a Minsky machine using Godel numbering, a form of mAME.

Memory model

JOMP's memory model is as simple as it gets, one register, which is named R.

The instruction

This is the instruction in C pseudocode.

x = R * a % b; R = (x ? R : R*a/b); goto(x ? j : ip+1)

The instruction itself bring written as

a / b : j

But to understand it, you need to know what JOMP stands for, it stands for Jump Or Multiply Proper Fraction. The instruction has 3 operands, a, b, and j. What it does, is that it sets a CPU flag named x to the result of R * a (mod b) and checks if the flag is zero, if it is, R is set to R * a / b, else nothing happens. Then, the CPU flag named x is checked again, if it is zero, execution goes to the next instruction, else, execution jumps to program address j.

Computational class

JOMP is Turing-complete. And its turing-completeness can be proven using 2 methods.

Method 1

JOMP can simulate FRACTRAN, as the fractran instruction

a / b

is equivalent to the JOMP instruction

a / b : 0

where 0 is the start of the program

Method 2

JOMP can simulate a Minsky Machine as said above in the introduction. let us say that the 2 counters of the minsky machine are numbered 2 and 3. The state of the minsky machine can be encoded as 2^x*3^y, with x and y being the actual values of the minsky machine's registers: Incrementing counter "2" is equal to the JOMP instruction

2 / 1 : ip+1

where ip+1 is whatever the instruction pointer is, plus one.

Incrementing counter "3" is equal to the JOMP instruction

3 / 1 : ip+1

with ip+1 being whatever the instruction pointer is, plus one.

Decrementing counter "2" and jumping if zero is equal to the JOMP instruction

1 / 2 : j

with j being the jump address.

Decrementing counter "3" and jumping if zero is equal to the JOMP instruction

1 / 3 : j

with j being the jump address.

See also

• Fractran
• Fractran++
• OISC
• Miny