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Convert floats to any base and back.
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| """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 |
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