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157 lines
3.7 KiB
Python
157 lines
3.7 KiB
Python
#!/usr/bin/env python
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# -*- coding: utf-8 -*-
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# Stéganô - Stéganô is a basic Python Steganography module.
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# Copyright (C) 2010-2019 Cédric Bonhomme - https://www.cedricbonhomme.org
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#
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# For more information : https://github.com/cedricbonhomme/Stegano
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#
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# This program is free software: you can redistribute it and/or modify
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# it under the terms of the GNU General Public License as published by
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# the Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# This program is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU General Public License for more details.
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#
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# You should have received a copy of the GNU General Public License
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# along with this program. If not, see <http://www.gnu.org/licenses/>
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__author__ = "Cedric Bonhomme"
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__version__ = "$Revision: 0.3 $"
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__date__ = "$Date: 2011/12/28 $"
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__revision__ = "$Date: 2017/03/10 $"
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__license__ = "GPLv3"
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import itertools
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import math
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from typing import Dict, Iterator, List
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def identity() -> Iterator[int]:
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"""f(x) = x
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"""
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n = 0
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while True:
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yield n
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n += 1
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def triangular_numbers() -> Iterator[int]:
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"""Triangular numbers: a(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+...+n.
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http://oeis.org/A000217
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"""
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n = 0
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while True:
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yield (n * (n + 1)) // 2
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n += 1
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def fermat() -> Iterator[int]:
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"""Generate the n-th Fermat Number.
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https://oeis.org/A000215
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"""
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y = 3
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while True:
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yield y
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y = pow(y - 1, 2) + 1
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def mersenne() -> Iterator[int]:
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"""Generate 2^p - 1, where p is prime.
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https://oeis.org/A001348
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"""
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prime_numbers = eratosthenes()
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while True:
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yield 2 ** next(prime_numbers) - 1
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def eratosthenes() -> Iterator[int]:
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"""Generate the prime numbers with the sieve of Eratosthenes.
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https://oeis.org/A000040
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"""
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d = {} # type: Dict[int, List[int]]
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for i in itertools.count(2):
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if i in d:
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for j in d[i]:
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d[i + j] = d.get(i + j, []) + [j]
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del d[i]
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else:
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d[i * i] = [i]
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yield i
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def composite() -> Iterator[int]:
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"""Generate the composite numbers using the sieve of Eratosthenes.
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https://oeis.org/A002808
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"""
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p1 = 3
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for p2 in eratosthenes():
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for n in range(p1 + 1, p2):
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yield n
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p1 = p2
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def carmichael() -> Iterator[int]:
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"""Composite numbers n such that a^(n-1) == 1 (mod n) for every a coprime
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to n.
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https://oeis.org/A002997
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"""
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for m in composite():
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for a in range(2, m):
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if pow(a, m, m) != a:
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break
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else:
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yield m
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def ackermann_naive(m: int, n: int) -> int:
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"""Ackermann number.
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"""
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if m == 0:
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return n + 1
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elif n == 0:
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return ackermann(m - 1, 1)
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else:
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return ackermann(m - 1, ackermann(m, n - 1))
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def ackermann(m: int, n: int) -> int:
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"""Ackermann number.
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"""
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while m >= 4:
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if n == 0:
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n = 1
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else:
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n = ackermann(m, n - 1)
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m -= 1
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if m == 3:
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return (1 << n + 3) - 3
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elif m == 2:
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return (n << 1) + 3
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elif m == 1:
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return n + 2
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else:
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return n + 1
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def fibonacci() -> Iterator[int]:
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"""Generate the sequence of Fibonacci.
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https://oeis.org/A000045
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"""
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a, b = 1, 2
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while True:
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yield a
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a, b = b, a + b
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def log_gen() -> Iterator[int]:
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"""Logarithmic generator.
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"""
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y = 1
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while True:
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adder = max(1, math.pow(10, int(math.log10(y))))
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yield int(y)
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y = y + int(adder)
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