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# -*- coding: utf-8 -*-
"""T2CharString glyph width optimizer.
CFF glyphs whose width equals the CFF Private dictionary's ``defaultWidthX``
value do not need to specify their width in their charstring, saving bytes.
This module determines the optimum ``defaultWidthX`` and ``nominalWidthX``
values for a font, when provided with a list of glyph widths."""
from fontTools.ttLib import TTFont
from collections import defaultdict
from operator import add
from functools import reduce
class missingdict(dict):
def __init__(self, missing_func):
self.missing_func = missing_func
def __missing__(self, v):
return self.missing_func(v)
def cumSum(f, op=add, start=0, decreasing=False):
keys = sorted(f.keys())
minx, maxx = keys[0], keys[-1]
total = reduce(op, f.values(), start)
if decreasing:
missing = lambda x: start if x > maxx else total
domain = range(maxx, minx - 1, -1)
else:
missing = lambda x: start if x < minx else total
domain = range(minx, maxx + 1)
out = missingdict(missing)
v = start
for x in domain:
v = op(v, f[x])
out[x] = v
return out
def byteCost(widths, default, nominal):
if not hasattr(widths, "items"):
d = defaultdict(int)
for w in widths:
d[w] += 1
widths = d
cost = 0
for w, freq in widths.items():
if w == default:
continue
diff = abs(w - nominal)
if diff <= 107:
cost += freq
elif diff <= 1131:
cost += freq * 2
else:
cost += freq * 5
return cost
def optimizeWidthsBruteforce(widths):
"""Bruteforce version. Veeeeeeeeeeeeeeeeery slow. Only works for smallests of fonts."""
d = defaultdict(int)
for w in widths:
d[w] += 1
# Maximum number of bytes using default can possibly save
maxDefaultAdvantage = 5 * max(d.values())
minw, maxw = min(widths), max(widths)
domain = list(range(minw, maxw + 1))
bestCostWithoutDefault = min(byteCost(widths, None, nominal) for nominal in domain)
bestCost = len(widths) * 5 + 1
for nominal in domain:
if byteCost(widths, None, nominal) > bestCost + maxDefaultAdvantage:
continue
for default in domain:
cost = byteCost(widths, default, nominal)
if cost < bestCost:
bestCost = cost
bestDefault = default
bestNominal = nominal
return bestDefault, bestNominal
def optimizeWidths(widths):
"""Given a list of glyph widths, or dictionary mapping glyph width to number of
glyphs having that, returns a tuple of best CFF default and nominal glyph widths.
This algorithm is linear in UPEM+numGlyphs."""
if not hasattr(widths, "items"):
d = defaultdict(int)
for w in widths:
d[w] += 1
widths = d
keys = sorted(widths.keys())
minw, maxw = keys[0], keys[-1]
domain = list(range(minw, maxw + 1))
# Cumulative sum/max forward/backward.
cumFrqU = cumSum(widths, op=add)
cumMaxU = cumSum(widths, op=max)
cumFrqD = cumSum(widths, op=add, decreasing=True)
cumMaxD = cumSum(widths, op=max, decreasing=True)
# Cost per nominal choice, without default consideration.
nomnCostU = missingdict(
lambda x: cumFrqU[x] + cumFrqU[x - 108] + cumFrqU[x - 1132] * 3
)
nomnCostD = missingdict(
lambda x: cumFrqD[x] + cumFrqD[x + 108] + cumFrqD[x + 1132] * 3
)
nomnCost = missingdict(lambda x: nomnCostU[x] + nomnCostD[x] - widths[x])
# Cost-saving per nominal choice, by best default choice.
dfltCostU = missingdict(
lambda x: max(cumMaxU[x], cumMaxU[x - 108] * 2, cumMaxU[x - 1132] * 5)
)
dfltCostD = missingdict(
lambda x: max(cumMaxD[x], cumMaxD[x + 108] * 2, cumMaxD[x + 1132] * 5)
)
dfltCost = missingdict(lambda x: max(dfltCostU[x], dfltCostD[x]))
# Combined cost per nominal choice.
bestCost = missingdict(lambda x: nomnCost[x] - dfltCost[x])
# Best nominal.
nominal = min(domain, key=lambda x: bestCost[x])
# Work back the best default.
bestC = bestCost[nominal]
dfltC = nomnCost[nominal] - bestCost[nominal]
ends = []
if dfltC == dfltCostU[nominal]:
starts = [nominal, nominal - 108, nominal - 1132]
for start in starts:
while cumMaxU[start] and cumMaxU[start] == cumMaxU[start - 1]:
start -= 1
ends.append(start)
else:
starts = [nominal, nominal + 108, nominal + 1132]
for start in starts:
while cumMaxD[start] and cumMaxD[start] == cumMaxD[start + 1]:
start += 1
ends.append(start)
default = min(ends, key=lambda default: byteCost(widths, default, nominal))
return default, nominal
def main(args=None):
"""Calculate optimum defaultWidthX/nominalWidthX values"""
import argparse
parser = argparse.ArgumentParser(
"fonttools cffLib.width",
description=main.__doc__,
)
parser.add_argument(
"inputs", metavar="FILE", type=str, nargs="+", help="Input TTF files"
)
parser.add_argument(
"-b",
"--brute-force",
dest="brute",
action="store_true",
help="Use brute-force approach (VERY slow)",
)
args = parser.parse_args(args)
for fontfile in args.inputs:
font = TTFont(fontfile)
hmtx = font["hmtx"]
widths = [m[0] for m in hmtx.metrics.values()]
if args.brute:
default, nominal = optimizeWidthsBruteforce(widths)
else:
default, nominal = optimizeWidths(widths)
print(
"glyphs=%d default=%d nominal=%d byteCost=%d"
% (len(widths), default, nominal, byteCost(widths, default, nominal))
)
if __name__ == "__main__":
import sys
if len(sys.argv) == 1:
import doctest
sys.exit(doctest.testmod().failed)
main()
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