f05691246a
extract the code from fixedToStr into its own function (defined in roundTools), to be used for serializing fractional F2Dot14 angles for COLRv1 PaintRotate etc.
252 lines
6.6 KiB
Python
252 lines
6.6 KiB
Python
"""
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The `OpenType specification <https://docs.microsoft.com/en-us/typography/opentype/spec/otff#data-types>`_
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defines two fixed-point data types:
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``Fixed``
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A 32-bit signed fixed-point number with a 16 bit twos-complement
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magnitude component and 16 fractional bits.
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``F2DOT14``
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A 16-bit signed fixed-point number with a 2 bit twos-complement
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magnitude component and 14 fractional bits.
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To support reading and writing data with these data types, this module provides
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functions for converting between fixed-point, float and string representations.
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.. data:: MAX_F2DOT14
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The maximum value that can still fit in an F2Dot14. (1.99993896484375)
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"""
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from .roundTools import otRound, nearestMultipleShortestRepr
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import logging
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log = logging.getLogger(__name__)
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__all__ = [
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"MAX_F2DOT14",
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"fixedToFloat",
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"floatToFixed",
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"floatToFixedToFloat",
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"floatToFixedToStr",
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"fixedToStr",
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"strToFixed",
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"strToFixedToFloat",
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"ensureVersionIsLong",
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"versionToFixed",
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]
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MAX_F2DOT14 = 0x7FFF / (1 << 14)
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def fixedToFloat(value, precisionBits):
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"""Converts a fixed-point number to a float given the number of
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precision bits.
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Args:
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value (int): Number in fixed-point format.
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precisionBits (int): Number of precision bits.
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Returns:
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Floating point value.
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Examples::
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>>> import math
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>>> f = fixedToFloat(-10139, precisionBits=14)
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>>> math.isclose(f, -0.61883544921875)
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True
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"""
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return value / (1 << precisionBits)
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def floatToFixed(value, precisionBits):
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"""Converts a float to a fixed-point number given the number of
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precision bits.
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Args:
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value (float): Floating point value.
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precisionBits (int): Number of precision bits.
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Returns:
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int: Fixed-point representation.
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Examples::
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>>> floatToFixed(-0.61883544921875, precisionBits=14)
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-10139
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>>> floatToFixed(-0.61884, precisionBits=14)
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-10139
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"""
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return otRound(value * (1 << precisionBits))
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def floatToFixedToFloat(value, precisionBits):
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"""Converts a float to a fixed-point number and back again.
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By converting the float to fixed, rounding it, and converting it back
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to float again, this returns a floating point values which is exactly
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representable in fixed-point format.
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Note: this **is** equivalent to ``fixedToFloat(floatToFixed(value))``.
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Args:
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value (float): The input floating point value.
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precisionBits (int): Number of precision bits.
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Returns:
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float: The transformed and rounded value.
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Examples::
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>>> import math
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>>> f1 = -0.61884
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>>> f2 = floatToFixedToFloat(-0.61884, precisionBits=14)
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>>> f1 != f2
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True
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>>> math.isclose(f2, -0.61883544921875)
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True
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"""
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scale = 1 << precisionBits
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return otRound(value * scale) / scale
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def fixedToStr(value, precisionBits):
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"""Converts a fixed-point number to a string representing a decimal float.
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This chooses the float that has the shortest decimal representation (the least
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number of fractional decimal digits).
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For example, to convert a fixed-point number in a 2.14 format, use
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``precisionBits=14``::
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>>> fixedToStr(-10139, precisionBits=14)
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'-0.61884'
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This is pretty slow compared to the simple division used in ``fixedToFloat``.
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Use sporadically when you need to serialize or print the fixed-point number in
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a human-readable form.
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It uses nearestMultipleShortestRepr under the hood.
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Args:
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value (int): The fixed-point value to convert.
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precisionBits (int): Number of precision bits, *up to a maximum of 16*.
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Returns:
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str: A string representation of the value.
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"""
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scale = 1 << precisionBits
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return nearestMultipleShortestRepr(value/scale, factor=1.0/scale)
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def strToFixed(string, precisionBits):
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"""Converts a string representing a decimal float to a fixed-point number.
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Args:
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string (str): A string representing a decimal float.
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precisionBits (int): Number of precision bits, *up to a maximum of 16*.
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Returns:
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int: Fixed-point representation.
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Examples::
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>>> ## to convert a float string to a 2.14 fixed-point number:
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>>> strToFixed('-0.61884', precisionBits=14)
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-10139
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"""
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value = float(string)
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return otRound(value * (1 << precisionBits))
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def strToFixedToFloat(string, precisionBits):
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"""Convert a string to a decimal float with fixed-point rounding.
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This first converts string to a float, then turns it into a fixed-point
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number with ``precisionBits`` fractional binary digits, then back to a
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float again.
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This is simply a shorthand for fixedToFloat(floatToFixed(float(s))).
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Args:
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string (str): A string representing a decimal float.
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precisionBits (int): Number of precision bits.
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Returns:
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float: The transformed and rounded value.
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Examples::
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>>> import math
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>>> s = '-0.61884'
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>>> bits = 14
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>>> f = strToFixedToFloat(s, precisionBits=bits)
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>>> math.isclose(f, -0.61883544921875)
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True
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>>> f == fixedToFloat(floatToFixed(float(s), precisionBits=bits), precisionBits=bits)
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True
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"""
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value = float(string)
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scale = 1 << precisionBits
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return otRound(value * scale) / scale
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def floatToFixedToStr(value, precisionBits):
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"""Convert float to string with fixed-point rounding.
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This uses the shortest decimal representation (ie. the least
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number of fractional decimal digits) to represent the equivalent
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fixed-point number with ``precisionBits`` fractional binary digits.
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It uses nearestMultipleShortestRepr under the hood.
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>>> floatToFixedToStr(-0.61883544921875, precisionBits=14)
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'-0.61884'
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Args:
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value (float): The float value to convert.
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precisionBits (int): Number of precision bits, *up to a maximum of 16*.
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Returns:
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str: A string representation of the value.
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"""
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scale = 1 << precisionBits
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return nearestMultipleShortestRepr(value, factor=1.0/scale)
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def ensureVersionIsLong(value):
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"""Ensure a table version is an unsigned long.
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OpenType table version numbers are expressed as a single unsigned long
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comprising of an unsigned short major version and unsigned short minor
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version. This function detects if the value to be used as a version number
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looks too small (i.e. is less than ``0x10000``), and converts it to
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fixed-point using :func:`floatToFixed` if so.
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Args:
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value (Number): a candidate table version number.
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Returns:
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int: A table version number, possibly corrected to fixed-point.
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"""
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if value < 0x10000:
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newValue = floatToFixed(value, 16)
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log.warning(
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"Table version value is a float: %.4f; "
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"fix to use hex instead: 0x%08x", value, newValue)
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value = newValue
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return value
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def versionToFixed(value):
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"""Ensure a table version number is fixed-point.
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Args:
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value (str): a candidate table version number.
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Returns:
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int: A table version number, possibly corrected to fixed-point.
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"""
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value = int(value, 0) if value.startswith("0") else float(value)
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value = ensureVersionIsLong(value)
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return value
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