# Source code for fontTools.varLib

    """
    Module for dealing with 'gvar'-style font variations, also known as run-time
    interpolation.

    The ideas here are very similar to MutatorMath.  There is even code to read
    MutatorMath .designspace files in the varLib.designspace module.

    For now, if you run this file on a designspace file, it tries to find
    ttf-interpolatable files for the masters and build a variable-font from
    them.  Such ttf-interpolatable and designspace files can be generated from
    a Glyphs source, eg., using noto-source as an example:

    	$ fontmake -o ttf-interpolatable -g NotoSansArabic-MM.glyphs

    Then you can make a variable-font this way:

    	$ fonttools varLib master_ufo/NotoSansArabic.designspace

    API *will* change in near future.
    """
    from typing import List
    from fontTools.misc.vector import Vector
    from fontTools.misc.roundTools import noRound, otRound
    from fontTools.misc.textTools import Tag, tostr
    from fontTools.ttLib import TTFont, newTable
    from fontTools.ttLib.tables._f_v_a_r import Axis, NamedInstance
    from fontTools.ttLib.tables._g_l_y_f import GlyphCoordinates
    from fontTools.ttLib.tables.ttProgram import Program
    from fontTools.ttLib.tables.TupleVariation import TupleVariation
    from fontTools.ttLib.tables import otTables as ot
    from fontTools.ttLib.tables.otBase import OTTableWriter
    from fontTools.varLib import builder, models, varStore
    from fontTools.varLib.merger import VariationMerger, COLRVariationMerger
    from fontTools.varLib.mvar import MVAR_ENTRIES
    from fontTools.varLib.iup import iup_delta_optimize
    from fontTools.varLib.featureVars import addFeatureVariations
    from fontTools.designspaceLib import DesignSpaceDocument, InstanceDescriptor
    from fontTools.designspaceLib.split import splitInterpolable, splitVariableFonts
    from fontTools.varLib.stat import buildVFStatTable
    from fontTools.colorLib.builder import buildColrV1
    from fontTools.colorLib.unbuilder import unbuildColrV1
    from functools import partial
    from collections import OrderedDict, namedtuple
    import os.path
    import logging
    from copy import deepcopy
    from pprint import pformat
    from .errors import VarLibError, VarLibValidationError

    log = logging.getLogger("fontTools.varLib")

    # This is a lib key for the designspace document. The value should be
    # an OpenType feature tag, to be used as the FeatureVariations feature.
    # If present, the DesignSpace <rules processing="..."> flag is ignored.
    FEAVAR_FEATURETAG_LIB_KEY = "com.github.fonttools.varLib.featureVarsFeatureTag"

    #
    # Creation routines
    #

    def _add_fvar(font, axes, instances: List[InstanceDescriptor]):
    	"""
    	Add 'fvar' table to font.

    	axes is an ordered dictionary of DesignspaceAxis objects.

    	instances is list of dictionary objects with 'location', 'stylename',
    	and possibly 'postscriptfontname' entries.
    	"""

    	assert axes
    	assert isinstance(axes, OrderedDict)

    	log.info("Generating fvar")

    	fvar = newTable('fvar')
    	nameTable = font['name']

    	for a in axes.values():
    		axis = Axis()
    		axis.axisTag = Tag(a.tag)
    		# TODO Skip axes that have no variation.
    		axis.minValue, axis.defaultValue, axis.maxValue = a.minimum, a.default, a.maximum
    		axis.axisNameID = nameTable.addMultilingualName(a.labelNames, font, minNameID=256)
    		axis.flags = int(a.hidden)
    		fvar.axes.append(axis)

    	for instance in instances:
    		# Filter out discrete axis locations
    		coordinates = {name: value for name, value in instance.location.items() if name in axes}

    		if "en" not in instance.localisedStyleName:
    			if not instance.styleName:
    				raise VarLibValidationError(
    					f"Instance at location '{coordinates}' must have a default English "
    					"style name ('stylename' attribute on the instance element or a "
    					"stylename element with an 'xml:lang=\"en\"' attribute)."
    				)
    			localisedStyleName = dict(instance.localisedStyleName)
    			localisedStyleName["en"] = tostr(instance.styleName)
    		else:
    			localisedStyleName = instance.localisedStyleName

    		psname = instance.postScriptFontName

    		inst = NamedInstance()
    		inst.subfamilyNameID = nameTable.addMultilingualName(localisedStyleName)
    		if psname is not None:
    			psname = tostr(psname)
    			inst.postscriptNameID = nameTable.addName(psname)
    		inst.coordinates = {axes[k].tag:axes[k].map_backward(v) for k,v in coordinates.items()}
    		#inst.coordinates = {axes[k].tag:v for k,v in coordinates.items()}
    		fvar.instances.append(inst)

    	assert "fvar" not in font
    	font['fvar'] = fvar

    	return fvar

    def _add_avar(font, axes):
    	"""
    	Add 'avar' table to font.

    	axes is an ordered dictionary of AxisDescriptor objects.
    	"""

    	assert axes
    	assert isinstance(axes, OrderedDict)

    	log.info("Generating avar")

    	avar = newTable('avar')

    	interesting = False
    	for axis in axes.values():
    		# Currently, some rasterizers require that the default value maps
    		# (-1 to -1, 0 to 0, and 1 to 1) be present for all the segment
    		# maps, even when the default normalization mapping for the axis
    		# was not modified.
    		# https://github.com/googlei18n/fontmake/issues/295
    		# https://github.com/fonttools/fonttools/issues/1011
    		# TODO(anthrotype) revert this (and 19c4b37) when issue is fixed
    		curve = avar.segments[axis.tag] = {-1.0: -1.0, 0.0: 0.0, 1.0: 1.0}
    		if not axis.map:
    			continue

    		items = sorted(axis.map)
    		keys = [item[0] for item in items]
    		vals = [item[1] for item in items]

    		# Current avar requirements.  We don't have to enforce
    		# these on the designer and can deduce some ourselves,
    		# but for now just enforce them.
    		if axis.minimum != min(keys):
    			raise VarLibValidationError(
    				f"Axis '{axis.name}': there must be a mapping for the axis minimum "
    				f"value {axis.minimum} and it must be the lowest input mapping value."
    			)
    		if axis.maximum != max(keys):
    			raise VarLibValidationError(
    				f"Axis '{axis.name}': there must be a mapping for the axis maximum "
    				f"value {axis.maximum} and it must be the highest input mapping value."
    			)
    		if axis.default not in keys:
    			raise VarLibValidationError(
    				f"Axis '{axis.name}': there must be a mapping for the axis default "
    				f"value {axis.default}."
    			)
    		# No duplicate input values (output values can be >= their preceeding value).
    		if len(set(keys)) != len(keys):
    			raise VarLibValidationError(
    				f"Axis '{axis.name}': All axis mapping input='...' values must be "
    				"unique, but we found duplicates."
    			)
    		# Ascending values
    		if sorted(vals) != vals:
    			raise VarLibValidationError(
    				f"Axis '{axis.name}': mapping output values must be in ascending order."
    			)

    		keys_triple = (axis.minimum, axis.default, axis.maximum)
    		vals_triple = tuple(axis.map_forward(v) for v in keys_triple)

    		keys = [models.normalizeValue(v, keys_triple) for v in keys]
    		vals = [models.normalizeValue(v, vals_triple) for v in vals]

    		if all(k == v for k, v in zip(keys, vals)):
    			continue
    		interesting = True

    		curve.update(zip(keys, vals))

    		assert 0.0 in curve and curve[0.0] == 0.0
    		assert -1.0 not in curve or curve[-1.0] == -1.0
    		assert +1.0 not in curve or curve[+1.0] == +1.0
    		# curve.update({-1.0: -1.0, 0.0: 0.0, 1.0: 1.0})

    	assert "avar" not in font
    	if not interesting:
    		log.info("No need for avar")
    		avar = None
    	else:
    		font['avar'] = avar

    	return avar

    def _add_stat(font):
    	# Note: this function only gets called by old code that calls `build()`
    	# directly. Newer code that wants to benefit from STAT data from the
    	# designspace should call `build_many()`

    	if "STAT" in font:
    		return

    	from ..otlLib.builder import buildStatTable
    	fvarTable = font['fvar']
    	axes = [dict(tag=a.axisTag, name=a.axisNameID) for a in fvarTable.axes]
    	buildStatTable(font, axes)

    _MasterData = namedtuple('_MasterData', ['glyf', 'hMetrics', 'vMetrics'])

    def _add_gvar(font, masterModel, master_ttfs, tolerance=0.5, optimize=True):
    	if tolerance < 0:
    		raise ValueError("`tolerance` must be a positive number.")

    	log.info("Generating gvar")
    	assert "gvar" not in font
    	gvar = font["gvar"] = newTable('gvar')
    	glyf = font['glyf']
    	defaultMasterIndex = masterModel.reverseMapping[0]

    	master_datas = [_MasterData(m['glyf'],
    				    m['hmtx'].metrics,
    				    getattr(m.get('vmtx'), 'metrics', None))
    			for m in master_ttfs]

    	for glyph in font.getGlyphOrder():
    		log.debug("building gvar for glyph '%s'", glyph)
    		isComposite = glyf[glyph].isComposite()

    		allData = [
    			m.glyf._getCoordinatesAndControls(glyph, m.hMetrics, m.vMetrics)
    			for m in master_datas
    		]

    		if allData[defaultMasterIndex][1].numberOfContours != 0:
    			# If the default master is not empty, interpret empty non-default masters
    			# as missing glyphs from a sparse master
    			allData = [
    				d if d is not None and d[1].numberOfContours != 0 else None
    				for d in allData
    			]

    		model, allData = masterModel.getSubModel(allData)

    		allCoords = [d[0] for d in allData]
    		allControls = [d[1] for d in allData]
    		control = allControls[0]
    		if not models.allEqual(allControls):
    			log.warning("glyph %s has incompatible masters; skipping" % glyph)
    			continue
    		del allControls

    		# Update gvar
    		gvar.variations[glyph] = []
    		deltas = model.getDeltas(allCoords, round=partial(GlyphCoordinates.__round__, round=round))
    		supports = model.supports
    		assert len(deltas) == len(supports)

    		# Prepare for IUP optimization
    		origCoords = deltas[0]
    		endPts = control.endPts

    		for i,(delta,support) in enumerate(zip(deltas[1:], supports[1:])):
    			if all(v == 0 for v in delta.array) and not isComposite:
    				continue
    			var = TupleVariation(support, delta)
    			if optimize:
    				delta_opt = iup_delta_optimize(delta, origCoords, endPts, tolerance=tolerance)

    				if None in delta_opt:
    					"""In composite glyphs, there should be one 0 entry
    					to make sure the gvar entry is written to the font.

    					This is to work around an issue with macOS 10.14 and can be
    					removed once the behaviour of macOS is changed.

    					https://github.com/fonttools/fonttools/issues/1381
    					"""
    					if all(d is None for d in delta_opt):
    						delta_opt = [(0, 0)] + [None] * (len(delta_opt) - 1)
    					# Use "optimized" version only if smaller...
    					var_opt = TupleVariation(support, delta_opt)

    					axis_tags = sorted(support.keys()) # Shouldn't matter that this is different from fvar...?
    					tupleData, auxData = var.compile(axis_tags)
    					unoptimized_len = len(tupleData) + len(auxData)
    					tupleData, auxData = var_opt.compile(axis_tags)
    					optimized_len = len(tupleData) + len(auxData)

    					if optimized_len < unoptimized_len:
    						var = var_opt

    			gvar.variations[glyph].append(var)

    def _remove_TTHinting(font):
    	for tag in ("cvar", "cvt ", "fpgm", "prep"):
    		if tag in font:
    			del font[tag]
    	maxp = font['maxp']
    	for attr in ("maxTwilightPoints", "maxStorage", "maxFunctionDefs", "maxInstructionDefs", "maxStackElements", "maxSizeOfInstructions"):
    		setattr(maxp, attr, 0)
    	maxp.maxZones = 1
    	font["glyf"].removeHinting()
    	# TODO: Modify gasp table to deactivate gridfitting for all ranges?

    def _merge_TTHinting(font, masterModel, master_ttfs):

    	log.info("Merging TT hinting")
    	assert "cvar" not in font

    	# Check that the existing hinting is compatible

    	# fpgm and prep table

    	for tag in ("fpgm", "prep"):
    		all_pgms = [m[tag].program for m in master_ttfs if tag in m]
    		if not all_pgms:
    			continue
    		font_pgm = getattr(font.get(tag), 'program', None)
    		if any(pgm != font_pgm for pgm in all_pgms):
    			log.warning("Masters have incompatible %s tables, hinting is discarded." % tag)
    			_remove_TTHinting(font)
    			return

    	# glyf table

    	font_glyf = font['glyf']
    	master_glyfs = [m['glyf'] for m in master_ttfs]
    	for name, glyph in font_glyf.glyphs.items():
    		all_pgms = [
    			getattr(glyf.get(name), 'program', None)
    			for glyf in master_glyfs
    		]
    		if not any(all_pgms):
    			continue
    		glyph.expand(font_glyf)
    		font_pgm = getattr(glyph, 'program', None)
    		if any(pgm != font_pgm for pgm in all_pgms if pgm):
    			log.warning("Masters have incompatible glyph programs in glyph '%s', hinting is discarded." % name)
    			# TODO Only drop hinting from this glyph.
    			_remove_TTHinting(font)
    			return

    	# cvt table

    	all_cvs = [Vector(m["cvt "].values) if 'cvt ' in m else None
    		   for m in master_ttfs]

    	nonNone_cvs = models.nonNone(all_cvs)
    	if not nonNone_cvs:
    		# There is no cvt table to make a cvar table from, we're done here.
    		return

    	if not models.allEqual(len(c) for c in nonNone_cvs):
    		log.warning("Masters have incompatible cvt tables, hinting is discarded.")
    		_remove_TTHinting(font)
    		return

    	variations = []
    	deltas, supports = masterModel.getDeltasAndSupports(all_cvs, round=round) # builtin round calls into Vector.__round__, which uses builtin round as we like
    	for i,(delta,support) in enumerate(zip(deltas[1:], supports[1:])):
    		if all(v == 0 for v in delta):
    			continue
    		var = TupleVariation(support, delta)
    		variations.append(var)

    	# We can build the cvar table now.
    	if variations:
    		cvar = font["cvar"] = newTable('cvar')
    		cvar.version = 1
    		cvar.variations = variations

    _MetricsFields = namedtuple('_MetricsFields',
    	['tableTag', 'metricsTag', 'sb1', 'sb2', 'advMapping', 'vOrigMapping'])

    HVAR_FIELDS = _MetricsFields(tableTag='HVAR', metricsTag='hmtx', sb1='LsbMap',
    	sb2='RsbMap', advMapping='AdvWidthMap', vOrigMapping=None)

    VVAR_FIELDS = _MetricsFields(tableTag='VVAR', metricsTag='vmtx', sb1='TsbMap',
    	sb2='BsbMap', advMapping='AdvHeightMap', vOrigMapping='VOrgMap')

    def _add_HVAR(font, masterModel, master_ttfs, axisTags):
    	_add_VHVAR(font, masterModel, master_ttfs, axisTags, HVAR_FIELDS)

    def _add_VVAR(font, masterModel, master_ttfs, axisTags):
    	_add_VHVAR(font, masterModel, master_ttfs, axisTags, VVAR_FIELDS)

    def _add_VHVAR(font, masterModel, master_ttfs, axisTags, tableFields):

    	tableTag = tableFields.tableTag
    	assert tableTag not in font
    	log.info("Generating " + tableTag)
    	VHVAR = newTable(tableTag)
    	tableClass = getattr(ot, tableTag)
    	vhvar = VHVAR.table = tableClass()
    	vhvar.Version = 0x00010000

    	glyphOrder = font.getGlyphOrder()

    	# Build list of source font advance widths for each glyph
    	metricsTag = tableFields.metricsTag
    	advMetricses = [m[metricsTag].metrics for m in master_ttfs]

    	# Build list of source font vertical origin coords for each glyph
    	if tableTag == 'VVAR' and 'VORG' in master_ttfs[0]:
    		vOrigMetricses = [m['VORG'].VOriginRecords for m in master_ttfs]
    		defaultYOrigs = [m['VORG'].defaultVertOriginY for m in master_ttfs]
    		vOrigMetricses = list(zip(vOrigMetricses, defaultYOrigs))
    	else:
    		vOrigMetricses = None

    	metricsStore, advanceMapping, vOrigMapping = _get_advance_metrics(font,
    		masterModel, master_ttfs, axisTags, glyphOrder, advMetricses,
    		vOrigMetricses)

    	vhvar.VarStore = metricsStore
    	if advanceMapping is None:
    		setattr(vhvar, tableFields.advMapping, None)
    	else:
    		setattr(vhvar, tableFields.advMapping, advanceMapping)
    	if vOrigMapping is not None:
    		setattr(vhvar, tableFields.vOrigMapping, vOrigMapping)
    	setattr(vhvar, tableFields.sb1, None)
    	setattr(vhvar, tableFields.sb2, None)

    	font[tableTag] = VHVAR
    	return

    def _get_advance_metrics(font, masterModel, master_ttfs,
    		axisTags, glyphOrder, advMetricses, vOrigMetricses=None):

    	vhAdvanceDeltasAndSupports = {}
    	vOrigDeltasAndSupports = {}
    	for glyph in glyphOrder:
    		vhAdvances = [metrics[glyph][0] if glyph in metrics else None for metrics in advMetricses]
    		vhAdvanceDeltasAndSupports[glyph] = masterModel.getDeltasAndSupports(vhAdvances, round=round)

    	singleModel = models.allEqual(id(v[1]) for v in vhAdvanceDeltasAndSupports.values())

    	if vOrigMetricses:
    		singleModel = False
    		for glyph in glyphOrder:
    			# We need to supply a vOrigs tuple with non-None default values
    			# for each glyph. vOrigMetricses contains values only for those
    			# glyphs which have a non-default vOrig.
    			vOrigs = [metrics[glyph] if glyph in metrics else defaultVOrig
    				for metrics, defaultVOrig in vOrigMetricses]
    			vOrigDeltasAndSupports[glyph] = masterModel.getDeltasAndSupports(vOrigs, round=round)

    	directStore = None
    	if singleModel:
    		# Build direct mapping
    		supports = next(iter(vhAdvanceDeltasAndSupports.values()))[1][1:]
    		varTupleList = builder.buildVarRegionList(supports, axisTags)
    		varTupleIndexes = list(range(len(supports)))
    		varData = builder.buildVarData(varTupleIndexes, [], optimize=False)
    		for glyphName in glyphOrder:
    			varData.addItem(vhAdvanceDeltasAndSupports[glyphName][0], round=noRound)
    		varData.optimize()
    		directStore = builder.buildVarStore(varTupleList, [varData])

    	# Build optimized indirect mapping
    	storeBuilder = varStore.OnlineVarStoreBuilder(axisTags)
    	advMapping = {}
    	for glyphName in glyphOrder:
    		deltas, supports = vhAdvanceDeltasAndSupports[glyphName]
    		storeBuilder.setSupports(supports)
    		advMapping[glyphName] = storeBuilder.storeDeltas(deltas, round=noRound)

    	if vOrigMetricses:
    		vOrigMap = {}
    		for glyphName in glyphOrder:
    			deltas, supports = vOrigDeltasAndSupports[glyphName]
    			storeBuilder.setSupports(supports)
    			vOrigMap[glyphName] = storeBuilder.storeDeltas(deltas, round=noRound)

    	indirectStore = storeBuilder.finish()
    	mapping2 = indirectStore.optimize(use_NO_VARIATION_INDEX=False)
    	advMapping = [mapping2[advMapping[g]] for g in glyphOrder]
    	advanceMapping = builder.buildVarIdxMap(advMapping, glyphOrder)

    	if vOrigMetricses:
    		vOrigMap = [mapping2[vOrigMap[g]] for g in glyphOrder]

    	useDirect = False
    	vOrigMapping = None
    	if directStore:
    		# Compile both, see which is more compact

    		writer = OTTableWriter()
    		directStore.compile(writer, font)
    		directSize = len(writer.getAllData())

    		writer = OTTableWriter()
    		indirectStore.compile(writer, font)
    		advanceMapping.compile(writer, font)
    		indirectSize = len(writer.getAllData())

    		useDirect = directSize < indirectSize

    	if useDirect:
    		metricsStore = directStore
    		advanceMapping = None
    	else:
    		metricsStore = indirectStore
    		if vOrigMetricses:
    			vOrigMapping = builder.buildVarIdxMap(vOrigMap, glyphOrder)

    	return metricsStore, advanceMapping, vOrigMapping

    def _add_MVAR(font, masterModel, master_ttfs, axisTags):

    	log.info("Generating MVAR")

    	store_builder = varStore.OnlineVarStoreBuilder(axisTags)

    	records = []
    	lastTableTag = None
    	fontTable = None
    	tables = None
    	# HACK: we need to special-case post.underlineThickness and .underlinePosition
    	# and unilaterally/arbitrarily define a sentinel value to distinguish the case
    	# when a post table is present in a given master simply because that's where
    	# the glyph names in TrueType must be stored, but the underline values are not
    	# meant to be used for building MVAR's deltas. The value of -0x8000 (-36768)
    	# the minimum FWord (int16) value, was chosen for its unlikelyhood to appear
    	# in real-world underline position/thickness values.
    	specialTags = {"unds": -0x8000, "undo": -0x8000}

    	for tag, (tableTag, itemName) in sorted(MVAR_ENTRIES.items(), key=lambda kv: kv[1]):
    		# For each tag, fetch the associated table from all fonts (or not when we are
    		# still looking at a tag from the same tables) and set up the variation model
    		# for them.
    		if tableTag != lastTableTag:
    			tables = fontTable = None
    			if tableTag in font:
    				fontTable = font[tableTag]
    				tables = []
    				for master in master_ttfs:
    					if tableTag not in master or (
    						tag in specialTags
    						and getattr(master[tableTag], itemName) == specialTags[tag]
    					):
    						tables.append(None)
    					else:
    						tables.append(master[tableTag])
    				model, tables = masterModel.getSubModel(tables)
    				store_builder.setModel(model)
    			lastTableTag = tableTag

    		if tables is None:  # Tag not applicable to the master font.
    			continue

    		# TODO support gasp entries

    		master_values = [getattr(table, itemName) for table in tables]
    		if models.allEqual(master_values):
    			base, varIdx = master_values[0], None
    		else:
    			base, varIdx = store_builder.storeMasters(master_values)
    		setattr(fontTable, itemName, base)

    		if varIdx is None:
    			continue
    		log.info('	%s: %s.%s	%s', tag, tableTag, itemName, master_values)
    		rec = ot.MetricsValueRecord()
    		rec.ValueTag = tag
    		rec.VarIdx = varIdx
    		records.append(rec)

    	assert "MVAR" not in font
    	if records:
    		store = store_builder.finish()
    		# Optimize
    		mapping = store.optimize()
    		for rec in records:
    			rec.VarIdx = mapping[rec.VarIdx]

    		MVAR = font["MVAR"] = newTable('MVAR')
    		mvar = MVAR.table = ot.MVAR()
    		mvar.Version = 0x00010000
    		mvar.Reserved = 0
    		mvar.VarStore = store
    		# XXX these should not be hard-coded but computed automatically
    		mvar.ValueRecordSize = 8
    		mvar.ValueRecordCount = len(records)
    		mvar.ValueRecord = sorted(records, key=lambda r: r.ValueTag)

    def _add_BASE(font, masterModel, master_ttfs, axisTags):

    	log.info("Generating BASE")

    	merger = VariationMerger(masterModel, axisTags, font)
    	merger.mergeTables(font, master_ttfs, ['BASE'])
    	store = merger.store_builder.finish()

    	if not store:
    		return
    	base = font['BASE'].table
    	assert base.Version == 0x00010000
    	base.Version = 0x00010001
    	base.VarStore = store

    def _merge_OTL(font, model, master_fonts, axisTags):

    	log.info("Merging OpenType Layout tables")
    	merger = VariationMerger(model, axisTags, font)

    	merger.mergeTables(font, master_fonts, ['GSUB', 'GDEF', 'GPOS'])
    	store = merger.store_builder.finish()
    	if not store:
    		return
    	try:
    		GDEF = font['GDEF'].table
    		assert GDEF.Version <= 0x00010002
    	except KeyError:
    		font['GDEF'] = newTable('GDEF')
    		GDEFTable = font["GDEF"] = newTable('GDEF')
    		GDEF = GDEFTable.table = ot.GDEF()
    		GDEF.GlyphClassDef = None
    		GDEF.AttachList = None
    		GDEF.LigCaretList = None
    		GDEF.MarkAttachClassDef = None
    		GDEF.MarkGlyphSetsDef = None

    	GDEF.Version = 0x00010003
    	GDEF.VarStore = store

    	# Optimize
    	varidx_map = store.optimize()
    	GDEF.remap_device_varidxes(varidx_map)
    	if 'GPOS' in font:
    		font['GPOS'].table.remap_device_varidxes(varidx_map)

    def _add_GSUB_feature_variations(font, axes, internal_axis_supports, rules, featureTag):

    	def normalize(name, value):
    		return models.normalizeLocation(
    			{name: value}, internal_axis_supports
    		)[name]

    	log.info("Generating GSUB FeatureVariations")

    	axis_tags = {name: axis.tag for name, axis in axes.items()}

    	conditional_subs = []
    	for rule in rules:

    		region = []
    		for conditions in rule.conditionSets:
    			space = {}
    			for condition in conditions:
    				axis_name = condition["name"]
    				if condition["minimum"] is not None:
    					minimum = normalize(axis_name, condition["minimum"])
    				else:
    					minimum = -1.0
    				if condition["maximum"] is not None:
    					maximum = normalize(axis_name, condition["maximum"])
    				else:
    					maximum = 1.0
    				tag = axis_tags[axis_name]
    				space[tag] = (minimum, maximum)
    			region.append(space)

    		subs = {k: v for k, v in rule.subs}

    		conditional_subs.append((region, subs))

    	addFeatureVariations(font, conditional_subs, featureTag)

    _DesignSpaceData = namedtuple(
    	"_DesignSpaceData",
    	[
    		"axes",
    		"internal_axis_supports",
    		"base_idx",
    		"normalized_master_locs",
    		"masters",
    		"instances",
    		"rules",
    		"rulesProcessingLast",
    		"lib",
    	],
    )

    def _add_CFF2(varFont, model, master_fonts):
    	from .cff import merge_region_fonts
    	glyphOrder = varFont.getGlyphOrder()
    	if "CFF2" not in varFont:
    		from .cff import convertCFFtoCFF2
    		convertCFFtoCFF2(varFont)
    	ordered_fonts_list = model.reorderMasters(master_fonts, model.reverseMapping)
    	# re-ordering the master list simplifies building the CFF2 data item lists.
    	merge_region_fonts(varFont, model, ordered_fonts_list, glyphOrder)

    def _add_COLR(font, model, master_fonts, axisTags, colr_layer_reuse=True):
    	merger = COLRVariationMerger(model, axisTags, font, allowLayerReuse=colr_layer_reuse)
    	merger.mergeTables(font, master_fonts)
    	store = merger.store_builder.finish()

    	colr = font["COLR"].table
    	if store:
    		mapping = store.optimize()
    		colr.VarStore = store
    		# don't add DeltaSetIndexMap for identity mapping
    		colr.VarIndexMap = None
    		varIdxes = [mapping[v] for v in merger.varIdxes]
    		if any(i != varIdxes[i] for i in range(len(varIdxes))):
    			colr.VarIndexMap = builder.buildDeltaSetIndexMap(varIdxes)

    def load_designspace(designspace):
    	# TODO: remove this and always assume 'designspace' is a DesignSpaceDocument,
    	# never a file path, as that's already handled by caller
    	if hasattr(designspace, "sources"):  # Assume a DesignspaceDocument
    		ds = designspace
    	else:  # Assume a file path
    		ds = DesignSpaceDocument.fromfile(designspace)

    	masters = ds.sources
    	if not masters:
    		raise VarLibValidationError("Designspace must have at least one source.")
    	instances = ds.instances

    	# TODO: Use fontTools.designspaceLib.tagForAxisName instead.
    	standard_axis_map = OrderedDict([
    		('weight',  ('wght', {'en': u'Weight'})),
    		('width',   ('wdth', {'en': u'Width'})),
    		('slant',   ('slnt', {'en': u'Slant'})),
    		('optical', ('opsz', {'en': u'Optical Size'})),
    		('italic',  ('ital', {'en': u'Italic'})),
    		])

    	# Setup axes
    	if not ds.axes:
    		raise VarLibValidationError(f"Designspace must have at least one axis.")

    	axes = OrderedDict()
    	for axis_index, axis in enumerate(ds.axes):
    		axis_name = axis.name
    		if not axis_name:
    			if not axis.tag:
    				raise VarLibValidationError(f"Axis at index {axis_index} needs a tag.")
    			axis_name = axis.name = axis.tag

    		if axis_name in standard_axis_map:
    			if axis.tag is None:
    				axis.tag = standard_axis_map[axis_name][0]
    			if not axis.labelNames:
    				axis.labelNames.update(standard_axis_map[axis_name][1])
    		else:
    			if not axis.tag:
    				raise VarLibValidationError(f"Axis at index {axis_index} needs a tag.")
    			if not axis.labelNames:
    				axis.labelNames["en"] = tostr(axis_name)

    		axes[axis_name] = axis
    	log.info("Axes:\n%s", pformat([axis.asdict() for axis in axes.values()]))

    	# Check all master and instance locations are valid and fill in defaults
    	for obj in masters+instances:
    		obj_name = obj.name or obj.styleName or ''
    		loc = obj.getFullDesignLocation(ds)
    		obj.designLocation = loc
    		if loc is None:
    			raise VarLibValidationError(
    				f"Source or instance '{obj_name}' has no location."
    			)
    		for axis_name in loc.keys():
    			if axis_name not in axes:
    				raise VarLibValidationError(
    					f"Location axis '{axis_name}' unknown for '{obj_name}'."
    				)
    		for axis_name,axis in axes.items():
    			v = axis.map_backward(loc[axis_name])
    			if not (axis.minimum <= v <= axis.maximum):
    				raise VarLibValidationError(
    					f"Source or instance '{obj_name}' has out-of-range location "
    					f"for axis '{axis_name}': is mapped to {v} but must be in "
    					f"mapped range [{axis.minimum}..{axis.maximum}] (NOTE: all "
    					"values are in user-space)."
    				)

    	# Normalize master locations

    	internal_master_locs = [o.getFullDesignLocation(ds) for o in masters]
    	log.info("Internal master locations:\n%s", pformat(internal_master_locs))

    	# TODO This mapping should ideally be moved closer to logic in _add_fvar/avar
    	internal_axis_supports = {}
    	for axis in axes.values():
    		triple = (axis.minimum, axis.default, axis.maximum)
    		internal_axis_supports[axis.name] = [axis.map_forward(v) for v in triple]
    	log.info("Internal axis supports:\n%s", pformat(internal_axis_supports))

    	normalized_master_locs = [models.normalizeLocation(m, internal_axis_supports) for m in internal_master_locs]
    	log.info("Normalized master locations:\n%s", pformat(normalized_master_locs))

    	# Find base master
    	base_idx = None
    	for i,m in enumerate(normalized_master_locs):
    		if all(v == 0 for v in m.values()):
    			if base_idx is not None:
    				raise VarLibValidationError(
    					"More than one base master found in Designspace."
    				)
    			base_idx = i
    	if base_idx is None:
    		raise VarLibValidationError(
    			"Base master not found; no master at default location?"
    		)
    	log.info("Index of base master: %s", base_idx)

    	return _DesignSpaceData(
    		axes,
    		internal_axis_supports,
    		base_idx,
    		normalized_master_locs,
    		masters,
    		instances,
    		ds.rules,
    		ds.rulesProcessingLast,
    		ds.lib,
    	)

    # https://docs.microsoft.com/en-us/typography/opentype/spec/os2#uswidthclass
    WDTH_VALUE_TO_OS2_WIDTH_CLASS = {
    	50: 1,
    	62.5: 2,
    	75: 3,
    	87.5: 4,
    	100: 5,
    	112.5: 6,
    	125: 7,
    	150: 8,
    	200: 9,
    }

    def set_default_weight_width_slant(font, location):
    	if "OS/2" in font:
    		if "wght" in location:
    			weight_class = otRound(max(1, min(location["wght"], 1000)))
    			if font["OS/2"].usWeightClass != weight_class:
    				log.info("Setting OS/2.usWeightClass = %s", weight_class)
    				font["OS/2"].usWeightClass = weight_class

    		if "wdth" in location:
    			# map 'wdth' axis (50..200) to OS/2.usWidthClass (1..9), rounding to closest
    			widthValue = min(max(location["wdth"], 50), 200)
    			widthClass = otRound(
    				models.piecewiseLinearMap(widthValue, WDTH_VALUE_TO_OS2_WIDTH_CLASS)
    			)
    			if font["OS/2"].usWidthClass != widthClass:
    				log.info("Setting OS/2.usWidthClass = %s", widthClass)
    				font["OS/2"].usWidthClass = widthClass

    	if "slnt" in location and "post" in font:
    		italicAngle = max(-90, min(location["slnt"], 90))
    		if font["post"].italicAngle != italicAngle:
    			log.info("Setting post.italicAngle = %s", italicAngle)
    			font["post"].italicAngle = italicAngle

    def build_many(
    	designspace: DesignSpaceDocument,
    	master_finder=lambda s:s,
    	exclude=[],
    	optimize=True,
    	skip_vf=lambda vf_name: False,
    	colr_layer_reuse=True,
    ):
    	"""
    	Build variable fonts from a designspace file, version 5 which can define
    	several VFs, or version 4 which has implicitly one VF covering the whole doc.

    	If master_finder is set, it should be a callable that takes master
    	filename as found in designspace file and map it to master font
    	binary as to be opened (eg. .ttf or .otf).

    	skip_vf can be used to skip building some of the variable fonts defined in
    	the input designspace. It's a predicate that takes as argument the name
    	of the variable font and returns `bool`.

    	Always returns a Dict[str, TTFont] keyed by VariableFontDescriptor.name
    	"""
    	res = {}
    	for _location, subDoc in splitInterpolable(designspace):
    		for name, vfDoc in splitVariableFonts(subDoc):
    			if skip_vf(name):
    				log.debug(f"Skipping variable TTF font: {name}")
    				continue
    			vf = build(
    				vfDoc,
    				master_finder,
    				exclude=list(exclude) + ["STAT"],
    				optimize=optimize,
    				colr_layer_reuse=colr_layer_reuse,
    			)[0]
    			if "STAT" not in exclude:
    				buildVFStatTable(vf, designspace, name)
    			res[name] = vf
    	return res

    def build(
    	designspace,
    	master_finder=lambda s:s,
    	exclude=[],
    	optimize=True,
    	colr_layer_reuse=True,
    ):
    	"""
    	Build variation font from a designspace file.

    	If master_finder is set, it should be a callable that takes master
    	filename as found in designspace file and map it to master font
    	binary as to be opened (eg. .ttf or .otf).
    	"""
    	if hasattr(designspace, "sources"):  # Assume a DesignspaceDocument
    		pass
    	else:  # Assume a file path
    		designspace = DesignSpaceDocument.fromfile(designspace)

    	ds = load_designspace(designspace)
    	log.info("Building variable font")

    	log.info("Loading master fonts")
    	master_fonts = load_masters(designspace, master_finder)

    	# TODO: 'master_ttfs' is unused except for return value, remove later
    	master_ttfs = []
    	for master in master_fonts:
    		try:
    			master_ttfs.append(master.reader.file.name)
    		except AttributeError:
    			master_ttfs.append(None)  # in-memory fonts have no path

    	# Copy the base master to work from it
    	vf = deepcopy(master_fonts[ds.base_idx])

    	# TODO append masters as named-instances as well; needs .designspace change.
    	fvar = _add_fvar(vf, ds.axes, ds.instances)
    	if 'STAT' not in exclude:
    		_add_stat(vf)
    	if 'avar' not in exclude:
    		_add_avar(vf, ds.axes)

    	# Map from axis names to axis tags...
    	normalized_master_locs = [
    		{ds.axes[k].tag: v for k,v in loc.items()} for loc in ds.normalized_master_locs
    	]
    	# From here on, we use fvar axes only
    	axisTags = [axis.axisTag for axis in fvar.axes]

    	# Assume single-model for now.
    	model = models.VariationModel(normalized_master_locs, axisOrder=axisTags)
    	assert 0 == model.mapping[ds.base_idx]

    	log.info("Building variations tables")
    	if 'BASE' not in exclude and 'BASE' in vf:
    		_add_BASE(vf, model, master_fonts, axisTags)
    	if 'MVAR' not in exclude:
    		_add_MVAR(vf, model, master_fonts, axisTags)
    	if 'HVAR' not in exclude:
    		_add_HVAR(vf, model, master_fonts, axisTags)
    	if 'VVAR' not in exclude and 'vmtx' in vf:
    		_add_VVAR(vf, model, master_fonts, axisTags)
    	if 'GDEF' not in exclude or 'GPOS' not in exclude:
    		_merge_OTL(vf, model, master_fonts, axisTags)
    	if 'gvar' not in exclude and 'glyf' in vf:
    		_add_gvar(vf, model, master_fonts, optimize=optimize)
    	if 'cvar' not in exclude and 'glyf' in vf:
    		_merge_TTHinting(vf, model, master_fonts)
    	if 'GSUB' not in exclude and ds.rules:
    		featureTag = ds.lib.get(
    			FEAVAR_FEATURETAG_LIB_KEY,
    			"rclt" if ds.rulesProcessingLast else "rvrn"
    		)
    		_add_GSUB_feature_variations(vf, ds.axes, ds.internal_axis_supports, ds.rules, featureTag)
    	if 'CFF2' not in exclude and ('CFF ' in vf or 'CFF2' in vf):
    		_add_CFF2(vf, model, master_fonts)
    		if "post" in vf:
    			# set 'post' to format 2 to keep the glyph names dropped from CFF2
    			post = vf["post"]
    			if post.formatType != 2.0:
    				post.formatType = 2.0
    				post.extraNames = []
    				post.mapping = {}
    	if 'COLR' not in exclude and 'COLR' in vf and vf['COLR'].version > 0:
    		_add_COLR(vf, model, master_fonts, axisTags, colr_layer_reuse)

    	set_default_weight_width_slant(
    		vf, location={axis.axisTag: axis.defaultValue for axis in vf["fvar"].axes}
    	)

    	for tag in exclude:
    		if tag in vf:
    			del vf[tag]

    	# TODO: Only return vf for 4.0+, the rest is unused.
    	return vf, model, master_ttfs

    def _open_font(path, master_finder=lambda s: s):
    	# load TTFont masters from given 'path': this can be either a .TTX or an
    	# OpenType binary font; or if neither of these, try use the 'master_finder'
    	# callable to resolve the path to a valid .TTX or OpenType font binary.
    	from fontTools.ttx import guessFileType

    	master_path = os.path.normpath(path)
    	tp = guessFileType(master_path)
    	if tp is None:
    		# not an OpenType binary/ttx, fall back to the master finder.
    		master_path = master_finder(master_path)
    		tp = guessFileType(master_path)
    	if tp in ("TTX", "OTX"):
    		font = TTFont()
    		font.importXML(master_path)
    	elif tp in ("TTF", "OTF", "WOFF", "WOFF2"):
    		font = TTFont(master_path)
    	else:
    		raise VarLibValidationError("Invalid master path: %r" % master_path)
    	return font

    def load_masters(designspace, master_finder=lambda s: s):
    	"""Ensure that all SourceDescriptor.font attributes have an appropriate TTFont
    	object loaded, or else open TTFont objects from the SourceDescriptor.path
    	attributes.

    	The paths can point to either an OpenType font, a TTX file, or a UFO. In the
    	latter case, use the provided master_finder callable to map from UFO paths to
    	the respective master font binaries (e.g. .ttf, .otf or .ttx).

    	Return list of master TTFont objects in the same order they are listed in the
    	DesignSpaceDocument.
    	"""
    	for master in designspace.sources:
    		# If a SourceDescriptor has a layer name, demand that the compiled TTFont
    		# be supplied by the caller. This spares us from modifying MasterFinder.
    		if master.layerName and master.font is None:
    			raise VarLibValidationError(
    				f"Designspace source '{master.name or '<Unknown>'}' specified a "
    				"layer name but lacks the required TTFont object in the 'font' "
    				"attribute."
    			)

    	return designspace.loadSourceFonts(_open_font, master_finder=master_finder)

    class MasterFinder(object):

    	def __init__(self, template):
    		self.template = template

    	def __call__(self, src_path):
    		fullname = os.path.abspath(src_path)
    		dirname, basename = os.path.split(fullname)
    		stem, ext = os.path.splitext(basename)
    		path = self.template.format(
    			fullname=fullname,
    			dirname=dirname,
    			basename=basename,
    			stem=stem,
    			ext=ext,
    		)
    		return os.path.normpath(path)

    def main(args=None):
    	"""Build a variable font from a designspace file and masters"""
    	from argparse import ArgumentParser
    	from fontTools import configLogger

    	parser = ArgumentParser(prog='varLib', description = main.__doc__)
    	parser.add_argument('designspace')
    	parser.add_argument(
    		'-o',
    		metavar='OUTPUTFILE',
    		dest='outfile',
    		default=None,
    		help='output file'
    	)
    	parser.add_argument(
    		'-x',
    		metavar='TAG',
    		dest='exclude',
    		action='append',
    		default=[],
    		help='exclude table'
    	)
    	parser.add_argument(
    		'--disable-iup',
    		dest='optimize',
    		action='store_false',
    		help='do not perform IUP optimization'
    	)
    	parser.add_argument(
    		'--no-colr-layer-reuse',
    		dest='colr_layer_reuse',
    		action='store_false',
    		help='do not rebuild variable COLR table to optimize COLR layer reuse',
    	)
    	parser.add_argument(
    		'--master-finder',
    		default='master_ttf_interpolatable/{stem}.ttf',
    		help=(
    			'templated string used for finding binary font '
    			'files given the source file names defined in the '
    			'designspace document. The following special strings '
    			'are defined: {fullname} is the absolute source file '
    			'name; {basename} is the file name without its '
    			'directory; {stem} is the basename without the file '
    			'extension; {ext} is the source file extension; '
    			'{dirname} is the directory of the absolute file '
    			'name. The default value is "%(default)s".'
    		)
    	)
    	logging_group = parser.add_mutually_exclusive_group(required=False)
    	logging_group.add_argument(
    		"-v", "--verbose",
                    action="store_true",
                    help="Run more verbosely.")
    	logging_group.add_argument(
    		"-q", "--quiet",
                    action="store_true",
                    help="Turn verbosity off.")
    	options = parser.parse_args(args)

    	configLogger(level=(
    		"DEBUG" if options.verbose else
    		"ERROR" if options.quiet else
    		"INFO"))

    	designspace_filename = options.designspace
    	finder = MasterFinder(options.master_finder)

    	vf, _, _ = build(
    		designspace_filename,
    		finder,
    		exclude=options.exclude,
    		optimize=options.optimize,
    		colr_layer_reuse=options.colr_layer_reuse,
    	)

    	outfile = options.outfile
    	if outfile is None:
    		ext = "otf" if vf.sfntVersion == "OTTO" else "ttf"
    		outfile = os.path.splitext(designspace_filename)[0] + '-VF.' + ext

    	log.info("Saving variation font %s", outfile)
    	vf.save(outfile)

    if __name__ == "__main__":
    	import sys
    	if len(sys.argv) > 1:
    		sys.exit(main())
    	import doctest
    	sys.exit(doctest.testmod().failed)