| """ |
| 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 |
| 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. |
| |
| 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. |
| """ |
| if not value: return "0.0" |
| |
| scale = 1 << precisionBits |
| value /= scale |
| eps = .5 / scale |
| lo = value - eps |
| hi = value + eps |
| # If the range of valid choices spans an integer, return the integer. |
| if int(lo) != int(hi): |
| return str(float(round(value))) |
| fmt = "%.8f" |
| lo = fmt % lo |
| hi = fmt % hi |
| assert len(lo) == len(hi) and lo != hi |
| for i in range(len(lo)): |
| if lo[i] != hi[i]: |
| break |
| period = lo.find('.') |
| assert period < i |
| fmt = "%%.%df" % (i - period) |
| return fmt % value |
| |
| |
| 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 fixedToStr 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. |
| |
| """ |
| fixed = otRound(value * (1 << precisionBits)) |
| return fixedToStr(fixed, precisionBits) |
| |
| |
| 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 |