
    h                         S r SSKJrJr  SSKr\R
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The `OpenType specification <https://docs.microsoft.com/en-us/typography/opentype/spec/otff#data-types>`_
defines two fixed-point data types:

``Fixed``
        A 32-bit signed fixed-point number with a 16 bit twos-complement
        magnitude component and 16 fractional bits.
``F2DOT14``
        A 16-bit signed fixed-point number with a 2 bit twos-complement
        magnitude component and 14 fractional bits.

To support reading and writing data with these data types, this module provides
functions for converting between fixed-point, float and string representations.

.. data:: MAX_F2DOT14

        The maximum value that can still fit in an F2Dot14. (1.99993896484375)
   )otRoundnearestMultipleShortestRepr    N)
MAX_F2DOT14fixedToFloatfloatToFixedfloatToFixedToFloatfloatToFixedToStr
fixedToStr
strToFixedstrToFixedToFloatensureVersionIsLongversionToFixedg    ?c                     U SU-  -  $ )a~  Converts a fixed-point number to a float given the number of
precision bits.

Args:
        value (int): Number in fixed-point format.
        precisionBits (int): Number of precision bits.

Returns:
        Floating point value.

Examples::

        >>> import math
        >>> f = fixedToFloat(-10139, precisionBits=14)
        >>> math.isclose(f, -0.61883544921875)
        True
r    valueprecisionBitss     K/var/www/html/env/lib/python3.13/site-packages/fontTools/misc/fixedTools.pyr   r   *   s    $ A&''    c                 $    [        U SU-  -  5      $ )a  Converts a float to a fixed-point number given the number of
precision bits.

Args:
        value (float): Floating point value.
        precisionBits (int): Number of precision bits.

Returns:
        int: Fixed-point representation.

Examples::

        >>> floatToFixed(-0.61883544921875, precisionBits=14)
        -10139
        >>> floatToFixed(-0.61884, precisionBits=14)
        -10139
r   r   r   s     r   r   r   ?   s    $ 5A./00r   c                 ,    SU-  n[        X-  5      U-  $ )a  Converts a float to a fixed-point number and back again.

By converting the float to fixed, rounding it, and converting it back
to float again, this returns a floating point values which is exactly
representable in fixed-point format.

Note: this **is** equivalent to ``fixedToFloat(floatToFixed(value))``.

Args:
        value (float): The input floating point value.
        precisionBits (int): Number of precision bits.

Returns:
        float: The transformed and rounded value.

Examples::
        >>> import math
        >>> f1 = -0.61884
        >>> f2 = floatToFixedToFloat(-0.61884, precisionBits=14)
        >>> f1 != f2
        True
        >>> math.isclose(f2, -0.61883544921875)
        True
r   r   r   r   scales      r   r	   r	   T   s     2 E5=!E))r   c                 *    SU-  n[        X-  SU-  S9$ )a  Converts a fixed-point number to a string representing a decimal float.

This chooses the float that has the shortest decimal representation (the least
number of fractional decimal digits).

For example, to convert a fixed-point number in a 2.14 format, use
``precisionBits=14``::

        >>> fixedToStr(-10139, precisionBits=14)
        '-0.61884'

This is pretty slow compared to the simple division used in ``fixedToFloat``.
Use sporadically when you need to serialize or print the fixed-point number in
a human-readable form.
It uses nearestMultipleShortestRepr under the hood.

Args:
        value (int): The fixed-point value to convert.
        precisionBits (int): Number of precision bits, *up to a maximum of 16*.

Returns:
        str: A string representation of the value.
r         ?factorr   r   s      r   r   r   q   s!    0 E&u}S5[IIr   c                 :    [        U 5      n[        USU-  -  5      $ )a  Converts a string representing a decimal float to a fixed-point number.

Args:
        string (str): A string representing a decimal float.
        precisionBits (int): Number of precision bits, *up to a maximum of 16*.

Returns:
        int: Fixed-point representation.

Examples::

        >>> ## to convert a float string to a 2.14 fixed-point number:
        >>> strToFixed('-0.61884', precisionBits=14)
        -10139
r   floatr   )stringr   r   s      r   r   r      s"      &ME5A./00r   c                 B    [        U 5      nSU-  n[        X#-  5      U-  $ )a  Convert a string to a decimal float with fixed-point rounding.

This first converts string to a float, then turns it into a fixed-point
number with ``precisionBits`` fractional binary digits, then back to a
float again.

This is simply a shorthand for fixedToFloat(floatToFixed(float(s))).

Args:
        string (str): A string representing a decimal float.
        precisionBits (int): Number of precision bits.

Returns:
        float: The transformed and rounded value.

Examples::

        >>> import math
        >>> s = '-0.61884'
        >>> bits = 14
        >>> f = strToFixedToFloat(s, precisionBits=bits)
        >>> math.isclose(f, -0.61883544921875)
        True
        >>> f == fixedToFloat(floatToFixed(float(s), precisionBits=bits), precisionBits=bits)
        True
r   r"   )r$   r   r   r   s       r   r   r      s)    6 &MEE5=!E))r   c                 &    SU-  n[        U SU-  S9$ )a9  Convert float to string with fixed-point rounding.

This uses the shortest decimal representation (ie. the least
number of fractional decimal digits) to represent the equivalent
fixed-point number with ``precisionBits`` fractional binary digits.
It uses nearestMultipleShortestRepr under the hood.

>>> floatToFixedToStr(-0.61883544921875, precisionBits=14)
'-0.61884'

Args:
        value (float): The float value to convert.
        precisionBits (int): Number of precision bits, *up to a maximum of 16*.

Returns:
        str: A string representation of the value.

r   r   r   r    r   s      r   r
   r
      s    & E&uS5[AAr   c                 \    U S:  a%  [        U S5      n[        R                  SU U5        Un U $ )a  Ensure a table version is an unsigned long.

OpenType table version numbers are expressed as a single unsigned long
comprising of an unsigned short major version and unsigned short minor
version. This function detects if the value to be used as a version number
looks too small (i.e. is less than ``0x10000``), and converts it to
fixed-point using :func:`floatToFixed` if so.

Args:
        value (Number): a candidate table version number.

Returns:
        int: A table version number, possibly corrected to fixed-point.
i      zDTable version value is a float: %.4f; fix to use hex instead: 0x%08x)r   logwarning)r   newValues     r   r   r      s8     wr*U	

 Lr   c                 v    U R                  S5      (       a  [        U S5      O
[        U 5      n [        U 5      n U $ )zEnsure a table version number is fixed-point.

Args:
        value (str): a candidate table version number.

Returns:
        int: A table version number, possibly corrected to fixed-point.
0r   )
startswithintr#   r   )r   s    r   r   r      s4     #--c22CqMeE&ELr   )__doc__
roundToolsr   r   logging	getLogger__name__r)   __all__r   r   r   r	   r   r   r   r
   r   r   r   r   r   <module>r6      s`   & = ! !(*1**:J81(*@B.4r   