blob: c5119abd6255bc283a68d9b9d74d2e33e532ef92 [file] [log] [blame]
""" -- 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__ = [
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.
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]:
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)
"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