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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)
"""
from .roundTools import otRound, nearestMultipleShortestRepr
import logging
log = logging.getLogger(__name__)
__all__ = [
"MAX_F2DOT14",
"fixedToFloat",
"floatToFixed",
"floatToFixedToFloat",
"floatToFixedToStr",
"fixedToStr",
"strToFixed",
"strToFixedToFloat",
"ensureVersionIsLong",
"versionToFixed",
]
MAX_F2DOT14 = 0x7FFF / (1 << 14)
def fixedToFloat(value, precisionBits):
"""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
"""
return value / (1 << precisionBits)
def floatToFixed(value, precisionBits):
"""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
"""
return otRound(value * (1 << precisionBits))
def floatToFixedToFloat(value, precisionBits):
"""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
"""
scale = 1 << precisionBits
return otRound(value * scale) / scale
def fixedToStr(value, precisionBits):
"""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.
"""
scale = 1 << precisionBits
return nearestMultipleShortestRepr(value / scale, factor=1.0 / scale)
def strToFixed(string, precisionBits):
"""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
"""
value = float(string)
return otRound(value * (1 << precisionBits))
def strToFixedToFloat(string, precisionBits):
"""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
"""
value = float(string)
scale = 1 << precisionBits
return otRound(value * scale) / scale
def floatToFixedToStr(value, precisionBits):
"""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.
"""
scale = 1 << precisionBits
return nearestMultipleShortestRepr(value, factor=1.0 / scale)
def ensureVersionIsLong(value):
"""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.
"""
if value < 0x10000:
newValue = floatToFixed(value, 16)
log.warning(
"Table version value is a float: %.4f; " "fix to use hex instead: 0x%08x",
value,
newValue,
)
value = newValue
return value
def versionToFixed(value):
"""Ensure 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.
"""
value = int(value, 0) if value.startswith("0") else float(value)
value = ensureVersionIsLong(value)
return value
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