Motivated by yet another floating point question on stackoverflow, I decided to print a float value \$x\in[0,1)\$, i.e., the fractional part of a float (I might try printing whole floats later). But not the rounded value like print(x) does but the exact represented value. And only using basic operations:

def print_float(x):

    # Convert float x to integer fraction num/den.
    num, den = 0, 1
    while x:
        x *= 2
        num *= 2
        den *= 2
        if x >= 1:
            x -= 1
            num += 1

    # Print num/den in decimal.
    print('0.', end='')
    while num:
        num *= 10
        print(num // den, end='')
        num %= den

Testing it against a simpler way using string formatting:

from random import random

for _ in range(3):
    x = random()
    print(('%.2000f' % x).rstrip('0'))





Separation of Concerns

Your function is doing too much. It is:

  1. Converting the float to a fraction
  2. Converting the fraction to a string of digits
  3. Printing the string of digits

You should separate these.

Float to Fraction

First, let's move the float-to-fraction code into its own function.

from typing import Tuple

def float_to_fraction(value: float) -> Tuple[int, int]:
    Convert a floating point number in the range [0, 1) into a fraction.

    >>> float_to_fraction(0.625)
    (5, 8)

    >>> float_to_fraction(0.1)
    (3602879701896397, 36028797018963968)

    if not (0 <= value < 1):
        raise ValueError("Value out of range (0 <= value < 1)")
    numerator, denominator = 0, 1
    while value:
        value *= 2
        numerator *= 2
        denominator *= 2
        if value >= 1:
            value -= 1
            numerator += 1
    return numerator, denominator

Here, I've added:

  • type hints, describing the input and output types for the function,
  • a """docstring""" describing how to use the function,
    • including an example formatted for use with the doctest module,
  • input range validation, since your expectation is for the range to be within a narrow range of float values.

I've also changed num to numerator, since it would be easy to misinterpret the abbreviation to mean number. Similarity, den became denominator and x became value.

Fraction to String

Again, converting a numerator/denominator fraction into a series of digits is logical unit of code, which could be reused elsewhere, so I've made it into a function:

def fraction_to_string(numerator: int, denominator: int) -> str:
    Convert a proper fraction into a corresponding series of digits.

    >>> fraction_to_string(5, 8)

    if not (0 <= numerator < denominator):
        raise ValueError("Improper or negative fraction given")

    if denominator & (denominator - 1) != 0:
        raise ValueError("Denominator must be a power of 2")

    digits = '0.'
    while numerator:
        numerator *= 10
        digits += str(numerator // denominator)
        numerator %= denominator

    return digits

Note: str(0.0) returns '0.0' but your code (and my duplication of it here) returns '0.'.

Your code originally guaranteed the denominator was a power of 2. With this new function, a caller could ask for fraction_to_digits(1, 3) which would be an infinitely long string of digits, so I've added a condition restricting the denominator to a power of 2.

Float to String

Now we can compose these two functions, as well as recreate the original function's functionality:

def float_to_string(value: float) -> str:
    numerator, denominator = float_to_fraction(value)
    return fraction_to_string(numerator, denominator)

def print_float(x):

if __name__ == '__main__':
    import doctest

    from random import random

    for _ in range(3):
        x = random()
        print(('%.2000f' % x).rstrip('0'))

Additionally, I've added a "main guard" (always a good idea), and I've added a call to doctest.testmod() so the tests embedded in the """docstrings""" are executed.


The function float_to_fraction(value) may be replaced by the built-in function value.as_integer_ratio().

>>> value = 0.625
>>> value.as_integer_ratio()
(5, 8)
  • 1
    \$\begingroup\$ Thanks. Nice improvements. Didn't know it's that easy to run doctests. fraction_to_string could handle denominators other than powers of 2, like 7/25 or 7/28 would also work. The exact rule might be that after simplifying the fraction, the denominator's only prime factors are 2 and 5. But yeah, for my purpose I don't mind simply requiring powers of 2. \$\endgroup\$ – Manuel Sep 24 '20 at 23:53

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