# Source code for ly.duration

    # This file is part of python-ly, https://pypi.python.org/pypi/python-ly
    #
    # Copyright (c) 2008 - 2015 by Wilbert Berendsen
    #
    # This program is free software; you can redistribute it and/or
    # modify it under the terms of the GNU General Public License
    # as published by the Free Software Foundation; either version 2
    # of the License, or (at your option) any later version.
    #
    # This program is distributed in the hope that it will be useful,
    # but WITHOUT ANY WARRANTY; without even the implied warranty of
    # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    # GNU General Public License for more details.
    #
    # You should have received a copy of the GNU General Public License
    # along with this program; if not, write to the Free Software
    # Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
    # See http://www.gnu.org/licenses/ for more information.

    """
    LilyPond information and logic concerning durations
    """

    from __future__ import unicode_literals

    from fractions import Fraction

    durations = [
        '\\maxima', '\\longa', '\\breve',
        '1', '2', '4', '8', '16', '32', '64', '128', '256', '512', '1024', '2048'
    ]

    def tostring(dur, dots=0, factor=1):
        r"""Returns the LilyPond string representation of a given logarithmic duration.

        Supports values from -3 up to and including 11.
        -2 = '\longa', 0  = '1' (whole note), etc.

        Adds the number of dots (defaults to 0) and the fraction factor if given.

        """
        s = durations[dur + 3] + '.' * dots
        if factor != 1:
            s += '*{0}'.format(factor)
        return s

    def base_scaling(tokens):
        """Return (base, scaling) as two Fractions for the list of tokens."""
        base = Fraction(8, 1 << durations.index(tokens[0]))
        scaling = Fraction(1)
        half = base
        for t in tokens[1:]:
            if t == '.':
                half /= 2
                base += half
            elif t.startswith('*'):
                scaling *= Fraction(t[1:])
        return base, scaling

    def base_scaling_string(duration):
        """Return (base, scaling) as two Fractions for the specified string."""
        items = duration.split('*')
        dots = items[0].split('.')
        base = Fraction(8, 1 << durations.index(dots[0].strip()))
        scaling = Fraction(1)
        half = base
        for dot in dots[1:]:
            half /= 2
            base += half
        for f in items[1:]:
            scaling *= Fraction(f.strip())
        return base, scaling

    def fraction(tokens):
        """Return the duration of the Duration tokens as a Fraction."""
        base, scaling = base_scaling(tokens)
        return base * scaling

    def fraction_string(duration):
        """Return the duration of the specified string as a Fraction."""
        base, scaling = base_scaling_string(duration)
        return base * scaling

    def format_fraction(value):
        """Format the value as "5/1" etc."""
        if value == 0:
            return "0"
        elif isinstance(value, Fraction):
            return "{0}/{1}".format(value.numerator, value.denominator)
        else:
            return "{0}/1".format(value)