| """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 |