111 lines
3.1 KiB
Python
111 lines
3.1 KiB
Python
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"""
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Various round-to-integer helpers.
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"""
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import math
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import functools
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import logging
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log = logging.getLogger(__name__)
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__all__ = [
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"noRound",
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"otRound",
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"maybeRound",
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"roundFunc",
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"nearestMultipleShortestRepr",
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]
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def noRound(value):
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return value
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def otRound(value):
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"""Round float value to nearest integer towards ``+Infinity``.
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The OpenType spec (in the section on `"normalization" of OpenType Font Variations <https://docs.microsoft.com/en-us/typography/opentype/spec/otvaroverview#coordinate-scales-and-normalization>`_)
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defines the required method for converting floating point values to
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fixed-point. In particular it specifies the following rounding strategy:
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for fractional values of 0.5 and higher, take the next higher integer;
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for other fractional values, truncate.
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This function rounds the floating-point value according to this strategy
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in preparation for conversion to fixed-point.
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Args:
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value (float): The input floating-point value.
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Returns
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float: The rounded value.
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"""
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# See this thread for how we ended up with this implementation:
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# https://github.com/fonttools/fonttools/issues/1248#issuecomment-383198166
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return int(math.floor(value + 0.5))
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def maybeRound(v, tolerance, round=otRound):
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rounded = round(v)
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return rounded if abs(rounded - v) <= tolerance else v
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def roundFunc(tolerance, round=otRound):
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if tolerance < 0:
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raise ValueError("Rounding tolerance must be positive")
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if tolerance == 0:
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return noRound
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if tolerance >= 0.5:
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return round
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return functools.partial(maybeRound, tolerance=tolerance, round=round)
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def nearestMultipleShortestRepr(value: float, factor: float) -> str:
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"""Round to nearest multiple of factor and return shortest decimal representation.
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This chooses the float that is closer to a multiple of the given factor while
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having the shortest decimal representation (the least number of fractional decimal
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digits).
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For example, given the following:
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>>> nearestMultipleShortestRepr(-0.61883544921875, 1.0/(1<<14))
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'-0.61884'
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Useful when you need to serialize or print a fixed-point number (or multiples
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thereof, such as F2Dot14 fractions of 180 degrees in COLRv1 PaintRotate) in
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a human-readable form.
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Args:
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value (value): The value to be rounded and serialized.
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factor (float): The value which the result is a close multiple of.
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Returns:
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str: A compact string representation of the value.
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"""
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if not value:
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return "0.0"
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value = otRound(value / factor) * factor
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eps = 0.5 * factor
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lo = value - eps
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hi = value + eps
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# If the range of valid choices spans an integer, return the integer.
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if int(lo) != int(hi):
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return str(float(round(value)))
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fmt = "%.8f"
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lo = fmt % lo
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hi = fmt % hi
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assert len(lo) == len(hi) and lo != hi
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for i in range(len(lo)):
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if lo[i] != hi[i]:
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break
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period = lo.find(".")
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assert period < i
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fmt = "%%.%df" % (i - period)
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return fmt % value
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