Divmeq

Divmeq (derived from 'DIVide and branch, if Modulo EQuals 0') is a one-instruction Turing-complete esoteric programming language created by User:TheCanon2.

Commands

Divmeq has a single accumulator, x. Lines in Divmeq have two parameters, A and B.

If x is divisible by A, divide X by A and jump to line B. Else, move 1 line forward.

There is 1 exception to this rule, the special case that A == 0.

If the line number is even, find 2 ** x and jump to line B. If the line number is odd, if x is positive but not 1, find the binary log of x and move 1 line forward, else jump to line B.

Line numbers start at 0 and increment by 1 for each line in the program. If the line number is greater than the length of the program, halt. The line number is generally omitted.

Divmeq accepts a numeric input at the beginning of a program, which is written to the accumulator. The accumulator is set to 1 if no input is given.

Examples

Truth machine

0: 2 2
1: 1 1

This halts if 0 and doesn't halt if 1.

XKCD Random Number

0: 0.25 1

Sets the accumulator to 4.

Computational class

Divmeq is Turing-complete for it can simulate a one-register Minsky machine.

0: 1/n 1 Multiply by n

0: n A Check if x is divisible by n, and if so, divide by n and jump to A

Implementations

The following Python script is an interpreter.

import math
prgm = [[]]
prgm.pop(0)
while True:
    line = input('%s: ' % len(prgm)) # Does not accept line numbering
    if line != "eof":
        line = list(line.split(" "))
        prgm.append([float(line[0]), int(line[1])])
    else:
        break
init = input('>i ') # Grabs user input
if init == "":
    x = 1
else: x = float(init)
# Executes the program
def divmeq(A, B):
    global x
    global inst
    if A != 0:
        if x % A < 1e-16 or x % A > (A - 1e-16): # Hinders TC, but fixes issues with floats
            x /= A
            inst = B
        else: inst += 1
    else:
        if inst % 2 == 0:
            x = 2 ** x
            inst = B
        else:
            if x > 0 and x != 1:
                x = math.log2(x)
                inst += 1
            else: inst = B
inst = 0
while inst < len(prgm):
    divmeq(prgm[inst][0], prgm[inst][1])
    print(x, end=" ")

This interpreter uses the symbol eof to mark the end of a program.

Any subsequent parameters after A and B are ignored, allowing for comments. This interpreter also prints the value of the accumulator after every instruction for ease of programming.