Lib/fontTools/misc/fixedTools.py

"""
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