formatnumber.py

#!/usr/bin/env python
# -*- coding: utf-8 -*-

import math


_DIGIT_CHAR_OFFSET = ord('0')
_SIGN_TABLE = ('-', '')


def _round_frac(frac, digits):
    if len(frac) <= digits or frac[digits] < '5':
        return (frac[:digits], 0)

    result = []
    carry = 1
    for x in reversed(frac[:digits]):
        x = chr(
            (ord(x) - _DIGIT_CHAR_OFFSET + carry) % 10 + _DIGIT_CHAR_OFFSET)
        carry = int(x == '0' and carry > 0)
        result.append(x)

    return (''.join(reversed(result)), carry)


def _extract_decimal_digits(value, digits):
    # The number 52 represents the amount of significant decimal digits
    # printed out when using the module `decimal`. It's somehow matching
    # the 52 bits used to store the mantissa of a double precision
    # floating-point but these shouldn't be related.
    # What really matters is that we do provide a high enough number so that
    # the `format` function doesn't round the value.
    return '{:.52f}'.format(value).split('.')[-1][:digits]


def format_number(value, digits):
    sign = int(value >= 0) * 2 - 1
    frac, trunc = math.modf(value)
    trunc = abs(int(trunc))
    frac = _extract_decimal_digits(frac, digits + 1)
    frac, carry = _round_frac(frac, digits)
    trunc += carry
    return ('{}{}.{}'.format(_SIGN_TABLE[int(sign * 0.5 + 1)], trunc, frac)
            .rstrip('0')
            .rstrip('.'))

# ------------------------------------------------------------------------------

def test(value, digits, expected=None):
    rounded_default = ('{{:.{}f}}'.format(digits).format(value)
                       .rstrip('0')
                       .rstrip('.'))
    rounded_custom = format_number(value, digits)

    if expected is None:
        assert rounded_default == rounded_custom
    else:
        print("{:+.16f} -> {}".format(value, rounded_custom))
        assert rounded_default == rounded_custom == expected


def run_custom_tests():
    print("# testing rounding to 3 digits")

    print('-' * 80)

    test(0, 3, '0')
    test(1, 3, '1')
    test(1.5, 3, '1.5')
    test(-0, 3, '0')
    test(-1, 3, '-1')
    test(-1.5, 3, '-1.5')

    print('-' * 80)

    test(1.001, 3, '1.001')
    test(1.099, 3, '1.099')
    test(1.999, 3, '1.999')

    print('-' * 80)

    test(1.0001, 3, '1')
    test(1.0099, 3, '1.01')
    test(1.9999, 3, '2')

    print('-' * 80)

    test(-1.001, 3, '-1.001')
    test(-1.099, 3, '-1.099')
    test(-1.999, 3, '-1.999')

    print('-' * 80)

    test(-1.0001, 3, '-1')
    test(-1.0099, 3, '-1.01')
    test(-1.9999, 3, '-2')

    print('-' * 80)

    test(1.2345e-1, 3, '0.123')
    test(-1.2345e-1, 3, '-0.123')


def run_random_tests():
    import random

    random.seed(0)
    for _ in range(1000):
        test(random.uniform(-1e-9, 1e9), 3)


def main():
    run_custom_tests()
    run_random_tests()


if __name__ == '__main__':
    main()