Fibinaries and Pribinaries

readme.md

#Fibinaries and Pribinaries

Silly script to create numbers in a positional notation using the fibonacci sequence and prime numbers as bases.

xbinary.py

import math
from functools import partial

BITS = 16

def is_prime(n):
	if n % 2 == 0 and n > 2:
		return False
	return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))

def make_primes(n):
	count = 0
	num = 1
	while count < n:
		if is_prime(num):
			count += 1
			yield num
		num += 1

def fibonacci(n):
	if n <= 1:
		return 1
	return fibonacci(n-1) + fibonacci(n-2)

def make_fibonacci(n):
	fibs = 0
	num = 0
	while fibs < n:
		fibs += 1
		yield fibonacci(num)
		num += 1

primes = list(make_primes(BITS))
fibonaccis = list(make_fibonacci(BITS + 1))[1:]

def decimal_to_base_x(num, base_list, length=BITS):
	result = ""
	for pos in range(length - 1, -1, -1):
		if num >= base_list[pos]:
			num -= base_list[pos]
			result += "1"
		else:
			result += "0"
	return result

def base_x_to_decimal(num, base_list):
	return sum(base_list[index] for index, bit in enumerate(reversed(num)) if bit == "1")

def add(num1, num2, length=BITS):
	"""Not all additions work, maybe convert back to decimal"""
	carry = 0
	result = ""
	for i in range(len(num1) - 1, -1, -1):
		n = carry
		n += 1 if num1[i] == '1' else 0
		n += 1 if num2[i] == '1' else 0

		result = ('1' if n % 2 == 1 else '0') + result
		carry = 0 if n < 2 else 1

	if carry != 0:
		result = '1' + result

	return result

decimal_to_fibinary = partial(decimal_to_base_x, base_list=fibonaccis)
decimal_to_pribinary = partial(decimal_to_base_x, base_list=primes)

fibinary_to_decimal = partial(base_x_to_decimal, base_list=fibonaccis)
pribinary_to_decimal = partial(base_x_to_decimal, base_list=primes)

if __name__ == '__main__':
	print("With {} bits it is possible to have the following ranges:".format(BITS))
	print("Prime base: [1 .. {}]".format(sum(primes)))
	print("Fibonacci base: [1 .. {}]".format(sum(fibonaccis)))
	print("(For reference, normal base-2: [1 .. {}])".format(2**BITS))

	print("-- Examples --")
	print("Converting 22")
	print(decimal_to_fibinary(22))
	print(fibinary_to_decimal("0000000001000001"))
	assert fibinary_to_decimal("0000000001000001") == 22

	print(decimal_to_pribinary(22))
	print(pribinary_to_decimal("0000000100000100"))
	assert pribinary_to_decimal("0000000100000100") == 22

	a = 7
	b = 43
	c = a + b

	a_ = decimal_to_fibinary(a)
	b_ = decimal_to_fibinary(b)
	c_ = add(a_, b_)

	assert fibinary_to_decimal(c_) == c