Convert floats to any base and back.

based.py

"""Converts floats to/from any base.
2021-03-25 v1.1 by Cees Timmerman"""

import math

NUMERALS = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"


def numeral(i):
    try:
        i = int(i)
    except ValueError:
        return i
    if i >= len(NUMERALS):
        return f"({i})"
    return NUMERALS[i]


def list2str(a, sep=""):
    return sep.join(map(numeral, a))


def int2list(num, base=2):
    """Convert a decimal integer >= 1 to base > 0.
    >>> int2list(255, 16)
    [15, 15]
    >>> int2list(3, 1)
    [1, 1, 1]
    >>> int2list(3, 0.5)
    [1, '.', 1]
    >>> int2list(10, 0.5)
    [0, '.', 1, 0, 1]
    >>> int2list(5.0625, 1.5)
    [1, 0, 0, 0]
    >>> int2list(1, 1.5)
    [1]
    """
    if base == 1:
        return [1] * num
    invert = False
    if 0 < base < 1:
        base = 1 / base
        invert = True
    a = []
    if num == 0:
        return [0]
    while num != 0:
        num, rem = divmod(num, base)
        a.insert(0, int(rem))
    if invert:
        a.reverse()
        a.insert(1, ".")
    return a


def fraction2list(num, base=2, depth=1):
    """Convert a 0 <= decimal < 1 to 0 < base != 1.
    >>> fraction2list(0, 1.5)
    [0]
    >>> fraction2list(0.6666666666666666, 1.5)
    [1]
    >>> fraction2list(0.4444444444444444, 1.5)
    [0, 1]
    >>> fraction2list(0.5, 2)
    [1]
    >>> fraction2list(0.25, 0.5)
    [1, 0, 0]
    """
    invert = False
    if 0 < base < 1:
        base = 1 / base
        invert = True
    a = []
    if num == 0:
        return [0]
    try:
        depth = 0
        while True:
            depth += 1
            if depth > 100:
                break
            num, rem = divmod(num, 1 / base ** depth)
            a.append(int(num))
            if rem:
                num = rem
            else:
                break
    except ZeroDivisionError:
        pass
    if invert:
        a.reverse()
        a.append(0)
    return a


def float2list(num, base=2):
    """Convert a decimal float to base > 1.
    >>> float2list(10.1, 16)
    [10, '.', 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8]
    >>> float2list(41.5, 42)
    [41, '.', 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 38, 10, 39, 41, 34, 24, 40, 40, 6, 4, 24, 13, 37, 15, 16, 41, 22, 13, 30, 26, 39, 11, 29, 12, 25, 29, 21, 9, 33, 2, 37, 1, 23, 13, 6, 25, 37, 41, 0, 6, 39, 24, 5, 12, 7, 26, 36, 25, 41, 25, 22, 10, 10, 35, 30, 37, 32, 23, 39, 38, 5, 13, 40, 15, 32, 35, 3, 21, 26, 21, 5, 26, 41, 16, 18, 31, 25, 13, 0, 34, 18, 40, 38, 5, 25, 9, 38, 14, 1]
    >>> float2list(0)
    [0, '.', 0]
    >>> float2list(-1.25)
    ['-', 1, '.', 0, 1]
    >>> float2list(-0.75)
    ['-', 0, '.', 1, 1]
    """
    sign = []
    if num < 0:
        sign = ['-']
        num = abs(num)
    fractional, whole = math.modf(num)
    return sign + int2list(whole, base) + ["."] + fraction2list(fractional, base)


def list2float(num, base=2):
    """
    >>> list2float([1, 1])
    3.0
    >>> list2float([1, 41, '.', 21], 42)
    83.5
    >>> list2float(['-', 1, 0, '.', 0, 8], 16)
    -16.03125
    """
    sign = 1
    if '-' in num:
        num = num[1:]
        sign = -1
    total = 0.0
    try:
        dot = num.index(".")
    except ValueError:
        dot = len(num)
    whole = num[:dot]
    fraction = num[dot + 1 :]
    for i, numeral in enumerate(whole + fraction):
        if type(numeral) == str:
            numeral = NUMERALS.index(numeral)
        total += numeral * base ** (dot - i - 1)
    return sign * total


def str2float(s, base=2):
    """Convert any base string to decimal float.
    >>> str2float("1010.1")
    10.5
    >>> str2float("1010.0001100110011001100110011001100110011001100110011")
    10.1
    >>> str2float("A.1999999999998", 16)
    10.1
    >>> str2float("2B.7C9", 15)
    41.52266666666667
    >>> str2float('111', 1)
    3.0
    >>> str2float('10', 1.5)
    1.5
    >>> str2float('100', 1.5)
    2.25
    >>> str2float('0.1', 1.5)
    0.6666666666666666
    >>> str2float('ABCDEFG', 0)
    16.0
    >>> str2float('FF.FF', -1)
    0.0
    >>> str2float('FF.FF', -1.5)
    -10.833333333333334
    """
    return list2float(list(s), base)


def float2str(num, base=2):
    """Convert a decimal float to base >= 1.
    >>> float2str(10.5)
    '1010.1'
    >>> float2str(10.5, 16)
    'A.8'
    >>> float2str(10.1)
    '1010.0001100110011001100110011001100110011001100110011'
    >>> float2str(10.1, 16)
    'A.1999999999998'
    >>> float2str(41.5, 42)
    '(41).L000000000J(38)A(39)(41)YO(40)(40)64OD(37)FG(41)MDUQ(39)BTCPTL9X2(37)1ND6P(37)(41)06(39)O5C7Q(36)P(41)PMAAZU(37)WN(39)(38)5D(40)FWZ3LQL5Q(41)GIVPD0YI(40)(38)5P9(38)E1'
    >>> float2str(0)
    '0.0'
    """
    return list2str(float2list(num, base))


if __name__ == "__main__":
    import doctest

    print(doctest.testmod())

    if 0:
        import timeit

        print(timeit.timeit("int2str(255)", globals=globals()))  # 2.5032687
        print(timeit.timeit("int2list(255)", globals=globals()))  # 1.4733017