Lib/fontTools/misc/fixedTools.py

"""fontTools.misc.fixedTools.py -- tools for working with fixed numbers.
"""

from __future__ import print_function, division, absolute_import
from fontTools.misc.py23 import *
import math
import logging

log = logging.getLogger(__name__)

__all__ = [
	"otRound",
	"fixedToFloat",
	"floatToFixed",
    "floatToFixedToFloat",
	"ensureVersionIsLong",
	"versionToFixed",
]


def otRound(value):
	"""Round float value to nearest integer towards +Infinity.
	For fractional values of 0.5 and higher, take the next higher integer;
	for other fractional values, truncate.

	https://docs.microsoft.com/en-us/typography/opentype/spec/otvaroverview
	https://github.com/fonttools/fonttools/issues/1248#issuecomment-383198166
	"""
	return int(math.floor(value + 0.5))


def fixedToFloat(value, precisionBits):
	"""Converts a fixed-point number to a float, choosing the float
	that has the shortest decimal reprentation.  Eg. to convert a
	fixed number in a 2.14 format, use precisionBits=14.  This is
	pretty slow compared to a simple division.  Use sporadically.

	precisionBits is only supported up to 16.
	"""
	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 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)
	value = fmt % value
	return float(value)

def floatToFixed(value, precisionBits):
	"""Converts a float to a fixed-point number given the number of
	precisionBits.  Ie. round(value * (1<<precisionBits)).
	"""
	return otRound(value * (1<<precisionBits))

def floatToFixedToFloat(value, precisionBits):
	"""Converts a float to a fixed-point number given the number of
	precisionBits, round it, then convert it back to float again.
	Ie. round(value * (1<<precisionBits)) / (1<<precisionBits)
	Note: this is *not* equivalent to fixedToFloat(floatToFixed(value)),
	which would return the shortest representation of the rounded value.
	"""
	scale = 1<<precisionBits
	return otRound(value * scale) / scale

def ensureVersionIsLong(value):
	"""Ensure a table version is an unsigned long (unsigned short major,
	unsigned short minor) instead of a float."""
	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):
	"""Converts a table version to a fixed"""
	value = int(value, 0) if value.startswith("0") else float(value)
	value = ensureVersionIsLong(value)
	return value