+ iRt^RIHtHt^RIt]P !]4t.R OtRt RRlt Rt Rt Rt RtR tR tR tR tR#)a The `OpenType specification `_ 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) )otRoundnearestMultipleShortestReprNc<V^8dQhR\R\R\/#)value precisionBitsreturn)floatint)formats"y/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/fontTools/misc/fixedTools.py __annotate__r *s!(((c(e(c"V^V,, #)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 rrs&&r fixedToFloatr*s$ A& ''rc4\V^V,,4#)aConverts 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 rrs&&r floatToFixedr?s$ 5A./ 00rcD^V,p\W,4V, #)aConverts 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 rrrscales&& r floatToFixedToFloatrTs 2  E 5= !E ))rcH^V,p\W, RV, R7#)aConverts 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. ?factorrrs&& r fixedToStrrqs!0  E &u}S5[ IIrcJ\V4p\V^V,,4#)aConverts 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 r)stringrrs&& r strToFixedr#s" &ME 5A./ 00rcZ\V4p^V,p\W#,4V, #)aConvert 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"rrrs&& r strToFixedToFloatr%s)6 &ME  E 5= !E ))rc<^V,p\VRV, R7#)a9Convert 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. rrrrs&& r floatToFixedToStrr's&  E &uS5[ AArc^VR8d&\V^4p\PRVV4TpV#)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. izDTable version value is a float: %.4f; fix to use hex instead: 0x%08x)rlogwarning)rnewValues& r ensureVersionIsLongr,s8 wr* U    LrcxVPR4'd \V^4M \V4p\V4pV#)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. 0) startswithr r r,)rs&r versionToFixedr0s4#--c22CqMe E  &E Lr) MAX_F2DOT14rrrr'rr#r%r,r0g?)__doc__ roundToolsrrlogging getLogger__name__r)__all__r1rrrrr#r%r'r,r0rrr r8s`&= ! ! (*1**:J81(*@B.4 r