Mô đun:Convert

-- Convert a value from one unit of measurement to another.
-- Example: kg --> 123 pounds (56 kg)
-- See :en:Template:Convert/Transwiki guide if copying to another wiki.
local MINUS = '−'  -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92)
local abs = math.abs
local floor = math.floor
local format = string.format
local log10 = math.log10
local ustring = mw.ustring
local ulen = ustring.len
local usub = ustring.sub
-- Configuration options to keep magic values in one location.
-- Conversion data and message text are defined in separate modules.
local config, maxsigfig
local numdot  -- must be '.' or ',' or a character which works in a regex
local numsep, numsep_remove, numsep_remove2
local data_code, all_units
local text_code
local varname        -- can be a code to use variable names that depend on value
local from_en_table  -- to translate an output string of en digits to local language
local to_en_table    -- to translate an input string of digits in local language to en
-- Use translation_table in convert/text to change the following.
local en_default           -- true uses lang=en unless convert has lang=local or local digits
local group_method = 3     -- code for how many digits are in a group
local per_word = 'per'     -- for units like "liters per kilometer"
local plural_suffix = 's'  -- only other useful value is probably  to disable plural unit names
local omitsep              -- true to omit separator before local symbol/name
-- All units should be defined in the data module. However, to cater for quick changes
-- and experiments, any unknown unit is looked up in an extra data module, if it exists.
-- That module would be transcluded in only a small number of pages, so there should be
-- little server overhead from making changes, and changes should propagate quickly.
local extra_module  -- name of module with extra units
local extra_units   -- nil or table of extra units from extra_module
-- Some options in the invoking template can set variables used later in the module.
local currency_text  -- for a user-defined currency symbol: $=€ (euro replaces dollar)
local function from_en(text)
	-- Input is a string representing a number in en digits with '.' decimal mark,
	-- without digit grouping (which is done just after calling this).
	-- Return the translation of the string with numdot and digits in local language.
	if numdot ~= '.' then
		text = text:gsub('%.', numdot)
	end
	if from_en_table then
		text = text:gsub('%d', from_en_table)
	end
	return text
end
local function to_en(text)
	-- Input is a string representing a number in the local language with
	-- an optional numdot decimal mark and numsep digit grouping.
	-- Return the translation of the string with '.' mark and en digits,
	-- and no separators (they have to be removed here to handle cases like
	-- numsep = '.' and numdot = ',' with input "1.234.567,8").
	if to_en_table then
		text = ustring.gsub(text, '%d', to_en_table)
	end
	if numsep_remove then
		text = text:gsub(numsep_remove, )
	end
	if numsep_remove2 then
		text = text:gsub(numsep_remove2, )
	end
	if numdot ~= '.' then
		text = text:gsub(numdot, '.')
	end
	return text
end
local function decimal_mark(text)
	-- Return ',' if text probably is using comma for decimal mark, or has no decimal mark.
	-- Return '.' if text probably is using dot for decimal mark.
	-- Otherwise return nothing (decimal mark not known).
	if not text:find('.,') then return ',' end
	text = text:gsub('^%-', ):gsub('%+%d+/%d+$', ):gsub('Ee%-?%d+$', )
	local decimal =
		text:match('^0?(.,)%d+$') or
		text:match('%d(.,)%d?%d?$') or
		text:match('%d(.,)%d%d%d%d+$')
	if decimal then return decimal end
	if text:match('%.%d+%.') then return ',' end
	if text:match('%,%d+,') then return '.' end
end
local add_warning, with_separator  -- forward declarations
local function to_en_with_check(text, parms)
	-- Version of to_en() for a wiki using numdot = ',' and numsep = '.' to check
	-- text (an input number as a string) which might have been copied from enwiki.
	-- For example, in '1.234' the '.' could be a decimal mark or a group separator.
	-- From viwiki.
	if to_en_table then
		text = ustring.gsub(text, '%d', to_en_table)
	end
	if decimal_mark(text) == '.' then
		local original = text
		text = text:gsub(',', )  -- for example, interpret "1,234.5" as an enwiki value
		if parms then
			add_warning(parms, 0, 'cvt_enwiki_num', original, with_separator({}, text))
		end
	else
		if numsep_remove then
			text = text:gsub(numsep_remove, )
		end
		if numsep_remove2 then
			text = text:gsub(numsep_remove2, )
		end
		if numdot ~= '.' then
			text = text:gsub(numdot, '.')
		end
	end
	return text
end
local function omit_separator(id)
	-- Return true if there should be no separator before id (a unit symbol or name).
	-- For zhwiki, there should be no separator if id uses local characters.
	-- The following kludge should be a sufficient test.
	if omitsep then
		if id:sub(1, 2) == '-{' then  -- for "-{...}-" content language variant
			return true
		end
		if id:byte() > 127 then
			local first = usub(id, 1, 1)
			if first ~= 'Å' and first ~= '°' and first ~= 'µ' then
				return true
			end
		end
	end
	return id:sub(1, 1) == '/'  -- no separator before units like "/ha"
end
local spell_module  -- name of module that can spell numbers
local speller       -- function from that module to handle spelling (set if needed)
local wikidata_module, wikidata_data_module  -- names of Wikidata modules
local wikidata_code, wikidata_data  -- exported tables from those modules (set if needed)
local function set_config(args)
	-- Set configuration options from template #invoke or defaults.
	config = args
	maxsigfig = config.maxsigfig or 14  -- maximum number of significant figures
	local data_module, text_module
	local sandbox = config.sandbox and ('/' .. config.sandbox) or 
	data_module = "Module:Convert/data" .. sandbox
	text_module = "Module:Convert/text" .. sandbox
	extra_module = "Module:Convert/extra" .. sandbox
	wikidata_module = "Module:Convert/wikidata" .. sandbox
	wikidata_data_module = "Module:Convert/wikidata/data" .. sandbox
	spell_module = "Module:ConvertNumeric"
	data_code = mw.loadData(data_module)
	text_code = mw.loadData(text_module)
	all_units = data_code.all_units
	local translation = text_code.translation_table
	if translation then
		numdot = translation.numdot
		numsep = translation.numsep
		if numdot == ',' and numsep == '.' then
			if text_code.all_messages.cvt_enwiki_num then
				to_en = to_en_with_check
			end
		end
		if translation.group then
			group_method = translation.group
		end
		if translation.per_word then
			per_word = translation.per_word
		end
		if translation.plural_suffix then
			plural_suffix = translation.plural_suffix
		end
		varname = translation.varname
		from_en_table = translation.from_en
		local use_workaround = true
		if use_workaround then
			-- 2013-07-05 workaround bug by making a copy of the required table.
			-- mw.ustring.gsub fails with a table (to_en_table) as the replacement,
			-- if the table is accessed via mw.loadData.
			local source = translation.to_en
			if source then
				to_en_table = {}
				for k, v in pairs(source) do
					to_en_tablek = v
				end
			end
		else
			to_en_table = translation.to_en
		end
		if translation.lang == 'en default' then
			en_default = true  -- for hiwiki
		end
		omitsep = translation.omitsep  -- for zhwiki
	end
	numdot = config.numdot or numdot or '.'  -- decimal mark before fractional digits
	numsep = config.numsep or numsep or ','  -- group separator for numbers
	-- numsep should be ',' or '.' or  or ' ' or a Unicode character.
	-- numsep_remove must work in a regex to identify separators to be removed.
	if numsep ~=  then
		numsep_remove = (numsep == '.') and '%.' or numsep
	end
	if numsep ~= ',' and numdot ~= ',' then
		numsep_remove2 = ','  -- so numbers copied from enwiki will work
	end
end
local function collection()
	-- Return a table to hold items.
	return {
		n = 0,
		add = function (self, item)
			self.n = self.n + 1
			selfself.n = item
		end,
	}
end
local function divide(numerator, denominator)
	-- Return integers quotient, remainder resulting from dividing the two
	-- given numbers, which should be unsigned integers.
	local quotient, remainder = floor(numerator / denominator), numerator % denominator
	if not (0  limit then
					s = usub(s, 1, limit)
					append = '...'
				end
				s = mw.text.nowiki(s) .. (append or )
			else
				s = '?'
			end
			parts'$' .. i = s
		end
		local function ispreview()
			-- Return true if a prominent message should be shown.
			if parms.test == 'preview' or parms.test == 'nopreview' then
				-- For testing, can preview a real message or simulate a preview
				-- when running automated tests.
				return parms.test == 'preview'
			end
			local success, revid = pcall(function ()
				return (parms.frame):preprocess() end)
			return success and (revid == )
		end
		local want_warning = is_warning and
			not config.warnings and  -- show unobtrusive warnings if config.warnings not configured
			not msg.nowarn           -- but use msg settings, not standard warning, if specified
		local title = string.gsub(msg1 or 'Missing message', '$%d+', parts)
		local text = want_warning and '*' or msg2 or 'Missing message'
		local cat = wanted_category(msg3, mcode2, want_warning)
		local anchor = msg4 or 
		local fmtkey = ispreview() and 'cvt_format_preview' or
			(want_warning and 'cvt_format2' or msg.format or 'cvt_format')
		local fmt = text_code.all_messagesfmtkey or 'convert: bug'
		return subparm(fmt, title:gsub('"', '"'), text, cat, anchor)
	end
	return 'Convert internal error: unknown message'
end
function add_warning(parms, level, key, text1, text2)  -- for forward declaration above
	-- If enabled, add a warning that will be displayed after the convert result.
	-- A higher level is more verbose: more kinds of warnings are displayed.
	-- To reduce output noise, only the first warning is displayed.
	if level  60 then
		a = 60
	end
	return mach_tablea + 4 * 0.44704  -- mph converted to m/s
end
-- END: Code required only for built-in units.
------------------------------------------------------------------------
local function add_style(parms, class)
	-- Add selected template style to parms if not already present.
	parms.templatestyles = parms.templatestyles or {}
	if not parms.templatestylesclass then
		parms.templatestylesclass = parms.frame:extensionTag({
			name = 'templatestyles', args = { src = text_code.titlesclass }
		})
	end
end
local function get_styles(parms)
	-- Return string of required template styles, empty if none.
	if parms.templatestyles then
		local t = {}
		for _, v in pairs(parms.templatestyles) do
			table.insert(t, v)
		end
		return table.concat(t)
	end
	return 
end
local function get_range(word)
	-- Return a range (string or table) corresponding to word (like "to"),
	-- or return nil if not a range word.
	local ranges = text_code.ranges
	return ranges.typesword or ranges.typesranges.aliasesword
end
local function check_mismatch(unit1, unit2)
	-- If unit1 cannot be converted to unit2, return an error message table.
	-- This allows conversion between units of the same type, and between
	-- Nm (normally torque) and ftlb (energy), as in gun-related articles.
	-- This works because Nm is the base unit (scale = 1) for both the
	-- primary type (torque), and the alternate type (energy, where Nm = J).
	-- A match occurs if the primary types are the same, or if unit1 matches
	-- the alternate type of unit2, and vice versa. That provides a whitelist
	-- of which conversions are permitted between normally incompatible types.
	if unit1.utype == unit2.utype or
		(unit1.utype == unit2.alttype and unit1.alttype == unit2.utype) then
		return nil
	end
	return { 'cvt_mismatch', unit1.utype, unit2.utype }
end
local function override_from(out_table, in_table, fields)
	-- Copy the specified fields from in_table to out_table, but do not
	-- copy nil fields (keep any corresponding field in out_table).
	for _, field in ipairs(fields) do
		if in_tablefield then
			out_tablefield = in_tablefield
		end
	end
end
local function shallow_copy(t)
	-- Return a shallow copy of table t.
	-- Do not need the features and overhead of the Scribunto mw.clone().
	local result = {}
	for k, v in pairs(t) do
		resultk = v
	end
	return result
end
local unit_mt = {
	-- Metatable to get missing values for a unit that does not accept SI prefixes.
	-- Warning: The boolean value 'false' is returned for any missing field
	-- so __index is not called twice for the same field in a given unit.
	__index = function (self, key)
		local value
		if key == 'name1' or key == 'sym_us' then
			value = self.symbol
		elseif key == 'name2' then
			value = self.name1 .. plural_suffix
		elseif key == 'name1_us' then
			value = self.name1
			if not rawget(self, 'name2_us') then
				-- If name1_us is 'foot', do not make name2_us by appending plural_suffix.
				self.name2_us = self.name2
			end
		elseif key == 'name2_us' then
			local raw1_us = rawget(self, 'name1_us')
			if raw1_us then
				value = raw1_us .. plural_suffix
			else
				value = self.name2
			end
		elseif key == 'link' then
			value = self.name1
		else
			value = false
		end
		rawset(self, key, value)
		return value
	end
}
local function prefixed_name(unit, name, index)
	-- Return unit name with SI prefix inserted at correct position.
	-- index = 1 (name1), 2 (name2), 3 (name1_us), 4 (name2_us).
	-- The position is a byte (not character) index, so use Lua's sub().
	local pos = rawget(unit, 'prefix_position')
	if type(pos) == 'string' then
		pos = tonumber(split(pos, ',')index)
	end
	if pos then
		return name:sub(1, pos - 1) .. unit.si_name .. name:sub(pos)
	end
	return unit.si_name .. name
end
local unit_prefixed_mt = {
	-- Metatable to get missing values for a unit that accepts SI prefixes.
	-- Before use, fields si_name, si_prefix must be defined.
	-- The unit must define _symbol, _name1 and
	-- may define _sym_us, _name1_us, _name2_us
	-- (_sym_us, _name2_us may be defined for a language using sp=us
	-- to refer to a variant unrelated to U.S. units).
	__index = function (self, key)
		local value
		if key == 'symbol' then
			value = self.si_prefix .. self._symbol
		elseif key == 'sym_us' then
			value = rawget(self, '_sym_us')
			if value then
				value = self.si_prefix .. value
			else
				value = self.symbol
			end
		elseif key == 'name1' then
			value = prefixed_name(self, self._name1, 1)
		elseif key == 'name2' then
			value = rawget(self, '_name2')
			if value then
				value = prefixed_name(self, value, 2)
			else
				value = self.name1 .. plural_suffix
			end
		elseif key == 'name1_us' then
			value = rawget(self, '_name1_us')
			if value then
				value = prefixed_name(self, value, 3)
			else
				value = self.name1
			end
		elseif key == 'name2_us' then
			value = rawget(self, '_name2_us')
			if value then
				value = prefixed_name(self, value, 4)
			elseif rawget(self, '_name1_us') then
				value = self.name1_us .. plural_suffix
			else
				value = self.name2
			end
		elseif key == 'link' then
			value = self.name1
		else
			value = false
		end
		rawset(self, key, value)
		return value
	end
}
local unit_per_mt = {
	-- Metatable to get values for a per unit of form "x/y".
	-- This is never called to determine a unit name or link because per units
	-- are handled as a special case.
	-- Similarly, the default output is handled elsewhere, and for a symbol
	-- this is only called from get_default() for default_exceptions.
	__index = function (self, key)
		local value
		if key == 'symbol' then
			local per = self.per
			local unit1, unit2 = per1, per2
			if unit1 then
				value = unit1key .. '/' .. unit2key
			else
				value = '/' .. unit2key
			end
		elseif key == 'sym_us' then
			value = self.symbol
		elseif key == 'scale' then
			local per = self.per
			local unit1, unit2 = per1, per2
			value = (unit1 and unit1.scale or 1) * self.scalemultiplier / unit2.scale
		else
			value = false
		end
		rawset(self, key, value)
		return value
	end
}
local function make_per(unitcode, unit_table, ulookup)
	-- Return true, t where t is a per unit with unit codes expanded to unit tables,
	-- or return false, t where t is an error message table.
	local result = {
		unitcode = unitcode,
		utype = unit_table.utype,
		per = {}
	}
	override_from(result, unit_table, { 'invert', 'iscomplex', 'default', 'link', 'symbol', 'symlink' })
	result.symbol_raw = (result.symbol or false)  -- to distinguish between a defined exception and a metatable calculation
	local prefix
	for i, v in ipairs(unit_table.per) do
		if i == 1 and v ==  then
			-- First unit symbol can be empty; that gives a nil first unit table.
		elseif i == 1 and text_code.currencyv then
			prefix = currency_text or v
		else
			local success, t = ulookup(v)
			if not success then return false, t end
			result.peri = t
		end
	end
	local multiplier = unit_table.multiplier
	if not result.utype then
		-- Creating an automatic per unit.
		local unit1 = result.per1
		local utype = (unit1 and unit1.utype or prefix or ) .. '/' .. result.per2.utype
		local t = data_code.per_unit_fixupsutype
		if t then
			if type(t) == 'table' then
				utype = t.utype or utype
				result.link = result.link or t.link
				multiplier = multiplier or t.multiplier
			else
				utype = t
			end
		end
		result.utype = utype
	end
	result.scalemultiplier = multiplier or 1
	result.vprefix = prefix or false  -- set to non-nil to avoid calling __index
	return true, setmetatable(result, unit_per_mt)
end
local function lookup(parms, unitcode, what, utable, fails, depth)
	-- Return true, t where t is a copy of the unit's converter table,
	-- or return false, t where t is an error message table.
	-- Parameter 'what' determines whether combination units are accepted:
	--   'no_combination'  : single unit only
	--   'any_combination' : single unit or combination or output multiple
	--   'only_multiple'   : single unit or output multiple only
	-- Parameter unitcode is a symbol (like 'g'), with an optional SI prefix (like 'kg').
	-- If, for example, 'kg' is in this table, that entry is used;
	-- otherwise the prefix ('k') is applied to the base unit ('g').
	-- If unitcode is a known combination code (and if allowed by what),
	-- a table of output multiple unit tables is included in the result.
	-- For compatibility with the old template, an underscore in a unitcode is
	-- replaced with a space so usage like board_feet works.
	-- Wikignomes may also put two spaces or " " in combinations, so
	-- replace underscore, " ", and multiple spaces with a single space.
	utable = utable or parms.unittable or all_units
	fails = fails or {}
	depth = depth and depth + 1 or 1
	if depth > 9 then
		-- There are ways to mistakenly define units which result in infinite
		-- recursion when lookup() is called. That gives a long delay and very
		-- confusing error messages, so the depth parameter is used as a guard.
		return false, { 'cvt_lookup', unitcode }
	end
	if unitcode == nil or unitcode ==  then
		return false, { 'cvt_no_unit' }
	end
	unitcode = unitcode:gsub('_', ' '):gsub(' ', ' '):gsub('  +', ' ')
	local function call_make_per(t)
		return make_per(unitcode, t,
			function (ucode) return lookup(parms, ucode, 'no_combination', utable, fails, depth) end
		)
	end
	local t = utableunitcode
	if t then
		if t.shouldbe then
			return false, { 'cvt_should_be', t.shouldbe }
		end
		if t.sp_us then
			parms.opt_sp_us = true
		end
		local target = t.target  -- nil, or unitcode is an alias for this target
		if target then
			local success, result = lookup(parms, target, what, utable, fails, depth)
			if not success then return false, result end
			override_from(result, t, { 'customary', 'default', 'link', 'symbol', 'symlink' })
			local multiplier = t.multiplier
			if multiplier then
				result.multiplier = tostring(multiplier)
				result.scale = result.scale * multiplier
			end
			return true, result
		end
		if t.per then
			return call_make_per(t)
		end
		local combo = t.combination  -- nil or a table of unitcodes
		if combo then
			local multiple = t.multiple
			if what == 'no_combination' or (what == 'only_multiple' and not multiple) then
				return false, { 'cvt_bad_unit', unitcode }
			end
			-- Recursively create a combination table containing the
			-- converter table of each unitcode.
			local result = { utype = t.utype, multiple = multiple, combination = {} }
			local cvt = result.combination
			for i, v in ipairs(combo) do
				local success, t = lookup(parms, v, multiple and 'no_combination' or 'only_multiple', utable, fails, depth)
				if not success then return false, t end
				cvti = t
			end
			return true, result
		end
		local result = shallow_copy(t)
		result.unitcode = unitcode
		if result.prefixes then
			result.si_name = 
			result.si_prefix = 
			return true, setmetatable(result, unit_prefixed_mt)
		end
		return true, setmetatable(result, unit_mt)
	end
	local SIprefixes = text_code.SIprefixes
	for plen = SIprefixes1 or 2, 1, -1 do
		-- Look for an SI prefix; should never occur with an alias.
		-- Check for longer prefix first ('dam' is decametre).
		-- SIprefixes1 = prefix maximum #characters (as seen by mw.ustring.sub).
		local prefix = usub(unitcode, 1, plen)
		local si = SIprefixesprefix
		if si then
			local t = utableusub(unitcode, plen+1)
			if t and t.prefixes then
				local result = shallow_copy(t)
				result.unitcode = unitcode
				result.si_name = parms.opt_sp_us and si.name_us or si.name
				result.si_prefix = si.prefix or prefix
				result.scale = t.scale * 10 ^ (si.exponent * t.prefixes)
				return true, setmetatable(result, unit_prefixed_mt)
			end
		end
	end
	-- Accept user-defined combinations like "acre+m2+ha" or "acre m2 ha" for output.
	-- If '+' is used, each unit code can include a space, and any error is fatal.
	-- If ' ' is used and if each space-separated word is a unit code, it is a combo,
	-- but errors are not fatal so the unit code can be looked up as an extra unit.
	local err_is_fatal
	local combo = collection()
	if unitcode:find('+', 1, true) then
		err_is_fatal = true
		for item in (unitcode .. '+'):gmatch('%s*(.-)%s*%+') do
			if item ~=  then
				combo:add(item)
			end
		end
	elseif unitcode:find('%s') then
		for item in unitcode:gmatch('%S+') do
			combo:add(item)
		end
	end
	if combo.n > 1 then
		local function lookup_combo()
			if what == 'no_combination' or what == 'only_multiple' then
				return false, { 'cvt_bad_unit', unitcode }
			end
			local result = { combination = {} }
			local cvt = result.combination
			for i, v in ipairs(combo) do
				local success, t = lookup(parms, v, 'only_multiple', utable, fails, depth)
				if not success then return false, t end
				if i == 1 then
					result.utype = t.utype
				else
					local mismatch = check_mismatch(result, t)
					if mismatch then
						return false, mismatch
					end
				end
				cvti = t
			end
			return true, result
		end
		local success, result = lookup_combo()
		if success or err_is_fatal then
			return success, result
		end
	end
	-- Accept any unit with an engineering notation prefix like "e6cuft"
	-- (million cubic feet), but not chained prefixes like "e3e6cuft",
	-- and not if the unit is a combination or multiple,
	-- and not if the unit has an offset or is a built-in.
	-- Only en digits are accepted.
	local exponent, baseunit = unitcode:match('^e(%d+)(.*)')
	if exponent then
		local engscale = text_code.eng_scalesexponent
		if engscale then
			local success, result = lookup(parms, baseunit, 'no_combination', utable, fails, depth)
			if success and not (result.offset or result.builtin or result.engscale) then
				result.unitcode = unitcode  -- 'e6cuft' not 'cuft'
				result.defkey = unitcode  -- key to lookup default exception
				result.engscale = engscale
				result.scale = result.scale * 10 ^ tonumber(exponent)
				return true, result
			end
		end
	end
	-- Look for x/y; split on right-most slash to get scale correct (x/y/z is x/y per z).
	local top, bottom = unitcode:match('^(.-)/(^/+)$')
	if top and not unitcode:find('e%d') then
		-- If valid, create an automatic per unit for an "x/y" unit code.
		-- The unitcode must not include extraneous spaces.
		-- Engineering notation (apart from at start and which has been stripped before here),
		-- is not supported so do not make a per unit if find text like 'e3' in unitcode.
		local success, result = call_make_per({ per = {top, bottom} })
		if success then
			return true, result
		end
	end
	if not parms.opt_ignore_error and not get_range(unitcode) then
		-- Want the "what links here" list for the extra_module to show only cases
		-- where an extra unit is used, so do not require it if invoked from 
		-- or if looking up a range word which cannot be a unit.
		if not extra_units then
			local success, extra = pcall(function () return require(extra_module).extra_units end)
			if success and type(extra) == 'table' then
				extra_units = extra
			end
		end
		if extra_units then
			-- A unit in one data table might refer to a unit in the other table, so
			-- switch between them, relying on fails or depth to terminate loops.
			if not failsunitcode then
				failsunitcode = true
				local other = (utable == all_units) and extra_units or all_units
				local success, result = lookup(parms, unitcode, what, other, fails, depth)
				if success then
					return true, result
				end
			end
		end
	end
	if to_en_table then
		-- At fawiki it is common to translate all digits so a unit like "km2" becomes "km۲".
		local en_code = ustring.gsub(unitcode, '%d', to_en_table)
		if en_code ~= unitcode then
			return lookup(parms, en_code, what, utable, fails, depth)
		end
	end
	return false, { 'cvt_unknown', unitcode }
end
local function valid_number(num)
	-- Return true if num is a valid number.
	-- In Scribunto (different from some standard Lua), when expressed as a string,
	-- overflow or other problems are indicated with text like "inf" or "nan"
	-- which are regarded as invalid here (each contains "n").
	if type(num) == 'number' and tostring(num):find('n', 1, true) == nil then
		return true
	end
end
local function hyphenated(name, parts)
	-- Return a hyphenated form of given name (for adjectival usage).
	-- The name may be linked and the target of the link must not be changed.
	-- Hypothetical examples:
	--   ton         →  ton          (no change)
	--   long ton       →  long-ton
	--   long ton  →  long-ton
	--   long ton             →  long-ton
	-- Input can also have multiple links in a single name like:
	--   U.S. gallon
	--   miles per U.S. quart
	--   long tons per short ton
	-- Assume that links cannot be nested (never like "abcdefghi").
	-- This uses a simple and efficient procedure that works for most cases.
	-- Some units (if used) would require more, and can later think about
	-- adding a method to handle exceptions.
	-- The procedure is to replace each space with a hyphen, but
	-- not a space after ')' for "(pre-1954 US) nautical mile", and
	-- not spaces immediately before '(' or in '(...)' for cases like
	-- "British thermal unit (ISO)" and "Calorie (International Steam Table)".
	if name:find(' ', 1, true) then
		if parts then
			local pos
			if name:sub(1, 1) == '(' then
				pos = name:find(')', 1, true)
				if pos then
					return name:sub(1, pos+1) .. name:sub(pos+2):gsub(' ', '-')
				end
			elseif name:sub(-1) == ')' then
				pos = name:find('(', 1, true)
				if pos then
					return name:sub(1, pos-2):gsub(' ', '-') .. name:sub(pos-1)
				end
			end
			return name:gsub(' ', '-')
		end
		parts = collection()
		for before, item, after in name:gmatch('(^*)(%%^*%%)('
					item = item:sub(3, -3)
				end
				item = prefix .. hyphenated(item, parts) .. 
			end
			parts:add(before:gsub(' ', '-') .. item .. after:gsub(' ', '-'))
		end
		if parts.n == 0 then
			-- No link like "..." was found in the original name.
			parts:add(hyphenated(name, parts))
		end
		return table.concat(parts)
	end
	return name
end
local function hyphenated_maybe(parms, want_name, sep, id, inout)
	-- Return s, f where
	--   s = id, possibly modified
	--   f = true if hyphenated
	-- Possible modifications: hyphenate; prepend '-'; append mid text.
	if id == nil or id ==  then
		return 
	end
	local mid = (inout == (parms.opt_flip and 'out' or 'in')) and parms.mid or 
	if want_name then
		if parms.opt_adjectival then
			return '-' .. hyphenated(id) .. mid, true
		end
		if parms.opt_add_s and id:sub(-1) ~= 's' then
			id = id .. 's'  -- for nowiki
		end
	end
	return sep .. id .. mid
end
local function use_minus(text)
	-- Return text with Unicode minus instead of '-', if present.
	if text:sub(1, 1) == '-' then
		return MINUS .. text:sub(2)
	end
	return text
end
local function digit_groups(parms, text, method)
	-- Return a numbered table of groups of digits (left-to-right, in local language).
	-- Parameter method is a number or nil:
	--   3 for 3-digit grouping (default), or
	--   2 for 3-then-2 grouping (only for digits before decimal mark).
	local len_right
	local len_left = text:find('.', 1, true)
	if len_left then
		len_right = #text - len_left
		len_left = len_left - 1
	else
		len_left = #text
	end
	local twos = method == 2 and len_left > 5
	local groups = collection()
	local run = len_left
	local n
	if run  0 do
		groups:add(n)
		run = run - n
		n = (twos and run > 3) and 2 or 3
	end
	if len_right then
		if groups.n == 0 then
			groups:add(0)
		end
		if parms.opt_gaps and len_right > 3 then
			local want4 = not parms.opt_gaps3  -- true gives no gap before trailing single digit
			local isfirst = true
			run = len_right
			while run > 0 do
				n = (want4 and run == 4) and 4 or (run > 3 and 3 or run)
				if isfirst then
					isfirst = false
					groupsgroups.n = groupsgroups.n + 1 + n
				else
					groups:add(n)
				end
				run = run - n
			end
		else
			groupsgroups.n = groupsgroups.n + 1 + len_right
		end
	end
	local pos = 1
	for i, length in ipairs(groups) do
		groupsi = from_en(text:sub(pos, pos + length - 1))
		pos = pos + length
	end
	return groups
end
function with_separator(parms, text)  -- for forward declaration above
	-- Input text is a number in en digits with optional '.' decimal mark.
	-- Return an equivalent, formatted for display:
	--   with a custom decimal mark instead of '.', if wanted
	--   with thousand separators inserted, if wanted
	--   digits in local language
	-- The given text is like '123' or '123.' or '12345.6789'.
	-- The text has no sign (caller inserts that later, if necessary).
	-- When using gaps, they are inserted before and after the decimal mark.
	-- Separators are inserted only before the decimal mark.
	-- A trailing dot (as in '123.') is removed because their use appears to
	-- be accidental, and such a number should be shown as '123' or '123.0'.
	-- It is useful for convert to suppress the dot so, for example, '4000.'
	-- is a simple way of indicating that all the digits are significant.
	if text:sub(-1) == '.' then
		text = text:sub(1, -2)
	end
	if #text '
		local gap = 
		local close = 
		return nowrap .. groups1 .. gap .. table.concat(groups, close .. gap, 2, groups.n) .. close .. close
	end
	return table.concat(groups, numsep)
end
-- An input value like 1.23e12 is displayed using scientific notation (1.23×10¹²).
-- That also makes the output use scientific notation, except for small values.
-- In addition, very small or very large output values use scientific notation.
-- Use format(fmtpower, significand, '10', exponent) where each argument is a string.
local fmtpower = '%s×%s%s'
local function with_exponent(parms, show, exponent)
	-- Return wikitext to display the implied value in scientific notation.
	-- Input uses en digits; output uses digits in local language.
	return format(fmtpower, with_separator(parms, show), from_en('10'), use_minus(from_en(tostring(exponent))))
end
local function make_sigfig(value, sigfig)
	-- Return show, exponent that are equivalent to the result of
	-- converting the number 'value' (where value >= 0) to a string,
	-- rounded to 'sigfig' significant figures.
	-- The returned items are:
	--   show: a string of digits; no sign and no dot;
	--         there is an implied dot before show.
	--   exponent: a number (an integer) to shift the implied dot.
	-- Resulting value = tonumber('.' .. show) * 10^exponent.
	-- Examples:
	--   make_sigfig(23.456, 3) returns '235', 2 (.235 * 10^2).
	--   make_sigfig(0.0023456, 3) returns '235', -2 (.235 * 10^-2).
	--   make_sigfig(0, 3) returns '000', 1 (.000 * 10^1).
	if sigfig  maxsigfig then
		sigfig = maxsigfig
	end
	if value == 0 then
		return string.rep('0', sigfig), 1
	end
	local exp, fracpart = math.modf(log10(value))
	if fracpart >= 0 then
		fracpart = fracpart - 1
		exp = exp + 1
	end
	local digits = format('%.0f', 10^(fracpart + sigfig))
	if #digits > sigfig then
		-- Overflow (for sigfig=3: like 0.9999 rounding to "1000"; need "100").
		digits = digits:sub(1, sigfig)
		exp = exp + 1
	end
	assert(#digits == sigfig, 'Bug: rounded number has wrong length')
	return digits, exp
end
-- Fraction output format.
local fracfmt = {
	{ -- Like  (fraction slash).
		'{SIGN}{NUM}⁄{DEN}',  -- 1/2
		'{SIGN}{WHOLE}+{NUM}⁄{DEN}',  -- 1+2/3
		style = 'frac',
	},
	{ -- Like  (stacked fraction, that is, horizontal bar).
		'{SIGN}{NUM}/{DEN}',  -- 1//2
		'{SIGN}{WHOLE}+{NUM}/{DEN}',  -- 1+2//3
		style = 'sfrac',
	},
}
local function format_fraction(parms, inout, negative, wholestr, numstr, denstr, do_spell, style)
	-- Return wikitext for a fraction, possibly spelled.
	-- Inputs use en digits and have no sign; output uses digits in local language.
	local wikitext
	if not style then
		style = parms.opt_fraction_horizontal and 2 or 1
	end
	if wholestr ==  then
		wholestr = nil
	end
	local substitute = {
		SIGN = negative and MINUS or ,
		WHOLE = wholestr and with_separator(parms, wholestr),
		NUM = from_en(numstr),
		DEN = from_en(denstr),
	}
	wikitext = fracfmtstylewholestr and 2 or 1:gsub('{(%u+)}', substitute)
	if do_spell then
		if negative then
			if wholestr then
				wholestr = '-' .. wholestr
			else
				numstr = '-' .. numstr
			end
		end
		local s = spell_number(parms, inout, wholestr, numstr, denstr)
		if s then
			return s
		end
	end
	add_style(parms, fracfmtstyle.style)
	return wikitext
end
local function format_number(parms, show, exponent, isnegative)
	-- Parameter show is a string or a table containing strings.
	-- Each string is a formatted number in en digits and optional '.' decimal mark.
	-- A table represents a fraction: integer, numerator, denominator;
	-- if a table is given, exponent must be nil.
	-- Return t where t is a table with fields:
	--   show = wikitext formatted to display implied value
	--          (digits in local language)
	--   is_scientific = true if show uses scientific notation
	--   clean = unformatted show (possibly adjusted and with inserted '.')
	--          (en digits)
	--   sign =  or MINUS
	--   exponent = exponent (possibly adjusted)
	-- The clean and exponent fields can be used to calculate the
	-- rounded absolute value, if needed.
	--
	-- The value implied by the arguments is found from:
	--   exponent is nil; and
	--   show is a string of digits (no sign), with an optional dot;
	--   show = '123.4' is value 123.4, '1234' is value 1234.0;
	-- or:
	--   exponent is an integer indicating where dot should be;
	--   show is a string of digits (no sign and no dot);
	--   there is an implied dot before show;
	--   show does not start with '0';
	--   show = '1234', exponent = 3 is value 0.1234*10^3 = 123.4.
	--
	-- The formatted result:
	-- * Is for an output value and is spelled if wanted and possible.
	-- * Includes a Unicode minus if isnegative and not spelled.
	-- * Uses a custom decimal mark, if wanted.
	-- * Has digits grouped where necessary, if wanted.
	-- * Uses scientific notation if requested, or for very small or large values
	--   (which forces result to not be spelled).
	-- * Has no more than maxsigfig significant digits
	--   (same as old template and ).
	local xhi, xlo  -- these control when scientific notation (exponent) is used
	if parms.opt_scientific then
		xhi, xlo = 4, 2  -- default for output if input uses e-notation
	elseif parms.opt_scientific_always then
		xhi, xlo = 0, 0  -- always use scientific notation (experimental)
	else
		xhi, xlo = 10, 4  -- default
	end
	local sign = isnegative and MINUS or 
	local maxlen = maxsigfig
	local tfrac
	if type(show) == 'table' then
		tfrac = show
		show = tfrac.wholestr
		assert(exponent == nil, 'Bug: exponent given with fraction')
	end
	if not tfrac and not exponent then
		local integer, dot, decimals = show:match('^(%d*)(%.?)(.*)')
		if integer == '0' or integer ==  then
			local zeros, figs = decimals:match('^(0*)(^0?.*)')
			if #figs == 0 then
				if #zeros > maxlen then
					show = '0.' .. zeros:sub(1, maxlen)
				end
			elseif #zeros >= xlo then
				show = figs
				exponent = -#zeros
			elseif #figs > maxlen then
				show = '0.' .. zeros .. figs:sub(1, maxlen)
			end
		elseif #integer >= xhi then
			show = integer .. decimals
			exponent = #integer
		else
			maxlen = maxlen + #dot
			if #show > maxlen then
				show = show:sub(1, maxlen)
			end
		end
	end
	if exponent then
		local function zeros(n)
			return string.rep('0', n)
		end
		if #show > maxlen then
			show = show:sub(1, maxlen)
		end
		if exponent > xhi or exponent = 1e9 or value  1 then
				significand = show:sub(1, 1) .. '.' .. show:sub(2)
			else
				significand = show
			end
			return {
				clean = '.' .. show,
				exponent = exponent,
				sign = sign,
				show = sign .. with_exponent(parms, significand, exponent-1),
				is_scientific = true,
			}
		end
		if exponent >= #show then
			show = show .. zeros(exponent - #show)  -- result has no dot
		elseif exponent  2 then style = 2 end
	local wikitext = format_fraction(parms, 'in', negative, leading_plus .. wholestr, numstr, denstr, parms.opt_spell_in, style)
	return value, altvalue, wikitext, denominator
end
local function extract_number(parms, text, another, no_fraction)
	-- Return true, info if can extract a number from text,
	-- where info is a table with the result,
	-- or return false, t where t is an error message table.
	-- Input can use en digits or digits in local language and can
	-- have references at the end. Accepting references is intended
	-- for use in infoboxes with a field for a value passed to convert.
	-- Parameter another = true if the expected value is not the first.
	-- Before processing, the input text is cleaned:
	-- * Any thousand separators (valid or not) are removed.
	-- * Any sign is replaced with '-' (if negative) or  (otherwise).
	--   That replaces Unicode minus with '-'.
	-- If successful, the returned info table contains named fields:
	--   value    = a valid number
	--   altvalue = a valid number, usually same as value but different
	--              if fraction used (for hands unit)
	--   singular = true if value is 1 or -1 (to use singular form of units)
	--   clean    = cleaned text with any separators and sign removed
	--              (en digits and '.' decimal mark)
	--   show     = text formatted for output, possibly with ref strip markers
	--              (digits in local language and custom decimal mark)
	-- The resulting show:
	-- * Is for an input value and is spelled if wanted and possible.
	-- * Has a rounded value, if wanted.
	-- * Has digits grouped where necessary, if wanted.
	-- * If negative, a Unicode minus is used; otherwise the sign is
	--   '+' (if the input text used '+'), or is  (if no sign in input).
	text = strip(text or )
	local reference
	local pos = text:find('\127', 1, true)
	if pos then
		local before = text:sub(1, pos - 1)
		local remainder = text:sub(pos)
		local refs = {}
		while #remainder > 0 do
			local ref, spaces
			ref, spaces, remainder = remainder:match('^(\127^\127*UNIQ^\127*%-ref^\127*\127)(%s*)(.*)')
			if ref then
				table.insert(refs, ref)
			else
				refs = {}
				break
			end
		end
		if #refs > 0 then
			text = strip(before)
			reference = table.concat(refs)
		end
	end
	local clean = to_en(text, parms)
	if clean ==  then
		return false, { another and 'cvt_no_num2' or 'cvt_no_num' }
	end
	local isnegative, propersign = false,   -- most common case
	local singular, show, denominator
	local value = tonumber(clean)
	local altvalue
	if value then
		local sign = clean:sub(1, 1)
		if sign == '+' or sign == '-' then
			propersign = (sign == '+') and '+' or MINUS
			clean = clean:sub(2)
		end
		if value = 0.
		-- If the input uses e-notation, show will be displayed using a power of ten, but
		-- we use the number as given so it might not be normalized scientific notation.
		-- The input value is spelled if specified so any e-notation is ignored;
		-- that allows input like 2e6 to be spelled as "two million" which works
		-- because the spell module converts '2e6' to '2000000' before spelling.
		local function rounded(value, default, exponent)
			local precision = parms.opt_ri
			if precision then
				local fmt = '%.' .. format('%d', precision) .. 'f'
				local result = fmt:format(tonumber(value) + 2e-14)  -- fudge for some common cases of bad rounding
				if not exponent then
					singular = (tonumber(result) == 1)
				end
				return result
			end
			return default
		end
		singular = (value == 1)
		local scientific
		local significand, exponent = clean:match('^(%d.+)Ee(+%-?%d+)')
		if significand then
			show = with_exponent(parms, rounded(significand, significand, exponent), exponent)
			scientific = true
		else
			show = with_separator(parms, rounded(value, clean))
		end
		show = propersign .. show
		if parms.opt_spell_in then
			show = spell_number(parms, 'in', propersign .. rounded(value, clean)) or show
			scientific = false
		end
		if scientific then
			parms.opt_scientific = true
		end
	end
	if isnegative and (value ~= 0) then
		value = -value
		altvalue = -(altvalue or value)
	end
	return true, {
		value = value,
		altvalue = altvalue or value,
		singular = singular,
		clean = clean,
		show = show .. (reference or ),
		denominator = denominator,
	}
end
local function get_number(text)
	-- Return v, f where:
	--   v = nil (text is not a number)
	-- or
	--   v = value of text (text is a number)
	--   f = true if value is an integer
	-- Input can use en digits or digits in local language,
	-- but no separators, no Unicode minus, and no fraction.
	if text then
		local number = tonumber(to_en(text))
		if number then
			local _, fracpart = math.modf(number)
			return number, (fracpart == 0)
		end
	end
end
local function gcd(a, b)
	-- Return the greatest common denominator for the given values,
	-- which are known to be positive integers.
	if a > b then
		a, b = b, a
	end
	if a  1e8 then
		return format('%.2f', value)
	end
	local integer, decimals = math.modf(value)
	local numerator = floor((decimals * denominator) +
		0.5 + 2e-14)  -- add fudge for some common cases of bad rounding
	if numerator >= denominator then
		integer = integer + 1
		numerator = 0
	end
	local wholestr = tostring(integer)
	if numerator > 0 then
		local div = gcd(numerator, denominator)
		if div > 1 then
			numerator = numerator / div
			denominator = denominator / div
		end
		return {
			wholestr = (integer > 0) and wholestr or ,
			numstr = tostring(numerator),
			denstr = tostring(denominator),
			value = value,
		}
	end
	return wholestr
end
local function preunits(count, preunit1, preunit2)
	-- If count is 1:
	--     ignore preunit2
	--     return p1
	-- else:
	--     preunit1 is used for preunit2 if the latter is empty
	--     return p1, p2
	-- where:
	--     p1 is text to insert before the input unit
	--     p2 is text to insert before the output unit
	--     p1 or p2 may be nil to mean "no preunit"
	-- Using '+' gives output like "5+ feet" (no space before, but space after).
	local function withspace(text, wantboth)
		-- Return text with space before and, if wantboth, after.
		-- However, no space is added if there is a space or ' ' or '-'
		-- at that position ('-' is for adjectival text).
		-- There is also no space if text starts with '&'
		-- (e.g. '°' would display a degree symbol with no preceding space).
		local char = text:sub(1, 1)
		if char == '&' then
			return text  -- an html entity can be used to specify the exact display
		end
		if not (char == ' ' or char == '-' or char == '+') then
			text = ' ' .. text
		end
		if wantboth then
			char = text:sub(-1, -1)
			if not (char == ' ' or char == '-' or text:sub(-6, -1) == ' ') then
				text = text .. ' '
			end
		end
		return text
	end
	local PLUS = '+ '
	preunit1 = preunit1 or 
	local trim1 = strip(preunit1)
	if count == 1 then
		if trim1 ==  then
			return nil
		end
		if trim1 == '+' then
			return PLUS
		end
		return withspace(preunit1, true)
	end
	preunit1 = withspace(preunit1)
	preunit2 = preunit2 or 
	local trim2 = strip(preunit2)
	if trim1 == '+' then
		if trim2 ==  or trim2 == '+' then
			return PLUS, PLUS
		end
		preunit1 = PLUS
	end
	if trim2 ==  then
		if trim1 ==  then
			return nil, nil
		end
		preunit2 = preunit1
	elseif trim2 == '+' then
		preunit2 = PLUS
	elseif trim2 == ' ' then  -- trick to make preunit2 empty
		preunit2 = nil
	else
		preunit2 = withspace(preunit2)
	end
	return preunit1, preunit2
end
local function range_text(range, want_name, parms, before, after, inout)
	-- Return before .. rtext .. after
	-- where rtext is the text that separates two values in a range.
	local rtext, adj_text, exception
	if type(range) == 'table' then
		-- Table must specify range text for ('off' and 'on') or ('input' and 'output'),
		-- and may specify range text for 'adj=on',
		-- and may specify exception = true.
		rtext = rangewant_name and 'off' or 'on' or
				range((inout == 'in') == (parms.opt_flip == true)) and 'output' or 'input'
		adj_text = range'adj'
		exception = range'exception'
	else
		rtext = range
	end
	if parms.opt_adjectival then
		if want_name or (exception and parms.abbr_org == 'on') then
			rtext = adj_text or rtext:gsub(' ', '-'):gsub(' ', '-')
		end
	end
	if rtext == '–' and after:sub(1, #MINUS) == MINUS then
		rtext = ' – '
	end
	return before .. rtext .. after
end
local function get_composite(parms, iparm, in_unit_table)
	-- Look for a composite input unit. For example, in
	-- would result in a call to this function with
	--   iparm = 3 (parmsiparm = "2", just after the first unit)
	--   in_unit_table = (unit table for "yd"; contains value 1 for number of yards)
	-- Return true, iparm, unit where
	--   iparm = index just after the composite units (7 in above example)
	--   unit = composite unit table holding all input units,
	-- or return true if no composite unit is present in parms,
	-- or return false, t where t is an error message table.
	local default, subinfo
	local composite_units, count = { in_unit_table }, 1
	local fixups = {}
	local total = in_unit_table.valinfo1.value
	local subunit = in_unit_table
	while subunit.subdivs do  -- subdivs is nil or a table of allowed subdivisions
		local subcode = strip(parmsiparm+1)
		local subdiv = subunit.subdivssubcode or subunit.subdivs(all_unitssubcode or {}).target
		if not subdiv then
			break
		end
		local success
		success, subunit = lookup(parms, subcode, 'no_combination')
		if not success then return false, subunit end  -- should never occur
		success, subinfo = extract_number(parms, parmsiparm)
		if not success then return false, subinfo end
		iparm = iparm + 2
		subunit.inout = 'in'
		subunit.valinfo = { subinfo }
		-- Recalculate total as a number of subdivisions.
		-- subdiv1 = number of subdivisions per previous unit (integer > 1).
		total = total * subdiv1 + subinfo.value
		if not default then  -- set by the first subdiv with a default defined
			default = subdiv.default
		end
		count = count + 1
		composite_unitscount = subunit
		if subdiv.unit or subdiv.name then
			fixupscount = { unit = subdiv.unit, name = subdiv.name, valinfo = subunit.valinfo }
		end
	end
	if count == 1 then
		return true  -- no error and no composite unit
	end
	for i, fixup in pairs(fixups) do
		local unit = fixup.unit
		local name = fixup.name
		if not unit or (count > 2 and name) then
			composite_unitsi.fixed_name = name
		else
			local success, alternate = lookup(parms, unit, 'no_combination')
			if not success then return false, alternate end  -- should never occur
			alternate.inout = 'in'
			alternate.valinfo = fixup.valinfo
			composite_unitsi = alternate
		end
	end
	return true, iparm, {
		utype = in_unit_table.utype,
		scale = subunit.scale,  -- scale of last (least significant) unit
		valinfo = { { value = total, clean = subinfo.clean, denominator = subinfo.denominator } },
		composite = composite_units,
		default = default or in_unit_table.default
	}
end
local function translate_parms(parms, kv_pairs)
	-- Update fields in parms by translating each key:value in kv_pairs to terms
	-- used by this module (may involve translating from local language to English).
	-- Also, checks are performed which may display warnings, if enabled.
	-- Return true if successful or return false, t where t is an error message table.
	currency_text = nil  -- local testing can hold module in memory; must clear globals
	local accept_any_text = {
		input = true,
		qid = true,
		qual = true,
		stylein = true,
		styleout = true,
		tracking = true,
	}
	if kv_pairs.adj and kv_pairs.sing then
		-- For enwiki (before translation), warn if attempt to use adj and sing
		-- as the latter is a deprecated alias for the former.
		if kv_pairs.adj ~= kv_pairs.sing and kv_pairs.sing ~=  then
			add_warning(parms, 1, 'cvt_unknown_option', 'sing=' .. kv_pairs.sing)
		end
		kv_pairs.sing = nil
	end
	kv_pairs.comma = kv_pairs.comma or config.comma  -- for plwiki who want default comma=5
	for loc_name, loc_value in pairs(kv_pairs) do
		local en_name = text_code.en_option_nameloc_name
		if en_name then
			local en_value
			if en_name == '$' or en_name == 'frac' or en_name == 'sigfig' then
				if loc_value ==  then
					add_warning(parms, 2, 'cvt_empty_option', loc_name)
				elseif en_name == '$' then
					-- Value should be a single character like "€" for the euro currency symbol, but anything is accepted.
					currency_text = (loc_value == 'euro') and '€' or loc_value
				else
					local minimum
					local number, is_integer = get_number(loc_value)
					if en_name == 'frac' then
						minimum = 2
						if number and number = minimum then
						en_value = number
					else
						add_warning(parms, 1, (en_name == 'frac' and 'cvt_bad_frac' or 'cvt_bad_sigfig'), loc_name .. '=' .. loc_value)
					end
				end
			elseif accept_any_texten_name then
				en_value = loc_value ~=  and loc_value or nil  -- accept non-empty user text with no validation
				if en_name == 'input' then
					-- May have something like input= (empty input) if source is an infobox
					-- with optional fields. In that case, want to output nothing rather than an error.
					parms.input_text = loc_value  -- keep input because parms.input is nil if loc_value == 
				end
			else
				en_value = text_code.en_option_valueen_nameloc_value
				if en_value and en_value:sub(-1) == '?' then
					en_value = en_value:sub(1, -2)
					add_warning(parms, -1, 'cvt_deprecated', loc_name .. '=' .. loc_value)
				end
				if en_value == nil then
					if loc_value ==  then
						add_warning(parms, 2, 'cvt_empty_option', loc_name)
					else
						add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)
					end
				elseif en_value ==  then
					en_value = nil  -- an ignored option like adj=off
				elseif type(en_value) == 'string' and en_value:sub(1, 4) == 'opt_' then
					for _, v in ipairs(split(en_value, ',')) do
						local lhs, rhs = v:match('^(.-)=(.+)$')
						if rhs then
							parmslhs = tonumber(rhs) or rhs
						else
							parmsv = true
						end
					end
					en_value = nil
				end
			end
			parmsen_name = en_value
		else
			add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)
		end
	end
	local abbr_entered = parms.abbr
	local cfg_abbr = config.abbr
	if cfg_abbr then
		-- Don't warn if invalid because every convert would show that warning.
		if cfg_abbr == 'on always' then
			parms.abbr = 'on'
		elseif cfg_abbr == 'off always' then
			parms.abbr = 'off'
		elseif parms.abbr == nil then
			if cfg_abbr == 'on default' then
				parms.abbr = 'on'
			elseif cfg_abbr == 'off default' then
				parms.abbr = 'off'
			end
		end
	end
	if parms.abbr then
		if parms.abbr == 'unit' then
			parms.abbr = 'on'
			parms.number_word = true
		end
		parms.abbr_org = parms.abbr  -- original abbr, before any flip
	elseif parms.opt_hand_hh then
		parms.abbr_org = 'on'
		parms.abbr = 'on'
	else
		parms.abbr = 'out'  -- default is to abbreviate output only (use symbol, not name)
	end
	if parms.opt_order_out then
		-- Disable options that do not work in a useful way with order=out.
		parms.opt_flip = nil  -- override adj=flip
		parms.opt_spell_in = nil
		parms.opt_spell_out = nil
		parms.opt_spell_upper = nil
	end
	if parms.opt_spell_out and not abbr_entered then
		parms.abbr = 'off'  -- should show unit name when spelling the output value
	end
	if parms.opt_flip then
		local function swap_in_out(option)
			local value = parmsoption
			if value == 'in' then
				parmsoption = 'out'
			elseif value == 'out' then
				parmsoption = 'in'
			end
		end
		swap_in_out('abbr')
		swap_in_out('lk')
		if parms.opt_spell_in and not parms.opt_spell_out then
			-- For simplicity, and because it does not appear to be needed,
			-- user cannot set an option to spell the output only.
			parms.opt_spell_in = nil
			parms.opt_spell_out = true
		end
	end
	if parms.opt_spell_upper then
		parms.spell_upper = parms.opt_flip and 'out' or 'in'
	end
	if parms.opt_table or parms.opt_tablecen then
		if abbr_entered == nil and parms.lk == nil then
			parms.opt_values = true
		end
		parms.table_align = parms.opt_table and 'right' or 'center'
	end
	if parms.table_align or parms.opt_sortable_on then
		parms.need_table_or_sort = true
	end
	local disp_joins = text_code.disp_joins
	local default_joins = disp_joins'b'
	parms.join_between = default_joins3 or '; '
	local disp = parms.disp
	if disp == nil then  -- special case for the most common setting
		parms.joins = default_joins
	elseif disp == 'x' then
		-- Later, parms.joins is set from the input parameters.
	else
		-- Old template does this.
		local abbr = parms.abbr
		if disp == 'slash' then
			if abbr_entered == nil then
				disp = 'slash-nbsp'
			elseif abbr == 'in' or abbr == 'out' then
				disp = 'slash-sp'
			else
				disp = 'slash-nosp'
			end
		elseif disp == 'sqbr' then
			if abbr == 'on' then
				disp = 'sqbr-nbsp'
			else
				disp = 'sqbr-sp'
			end
		end
		parms.joins = disp_joinsdisp or default_joins
		parms.join_between = parms.joins3 or parms.join_between
		parms.wantname = parms.joins.wantname
	end
	if (en_default and not parms.opt_lang_local and (parms1 or ):find('%d')) or parms.opt_lang_en then
		from_en_table = nil
	end
	if en_default and from_en_table then
		-- For hiwiki: localized symbol/name is defined with the US symbol/name field,
		-- and is used if output uses localized numbers.
		parms.opt_sp_us = true
	end
	return true
end
local function get_values(parms)
	-- If successful, update parms and return true, v, i where
	--   v = table of input values
	--   i = index to next entry in parms after those processed here
	-- or return false, t where t is an error message table.
	local valinfo = collection()  -- numbered table of input values
	local range = collection()  -- numbered table of range items (having, for example, 2 range items requires 3 input values)
	local had_nocomma  -- true if removed "nocomma" kludge from second parameter (like "tonocomma")
	local parm2 = strip(parms2)
	if parm2 and parm2:sub(-7, -1) == 'nocomma' then
		parms2 = strip(parm2:sub(1, -8))
		parms.opt_nocomma = true
		had_nocomma = true
	end
	local function extractor(i)
		-- If the parameter is not a value, try unpacking it as a range ("1-23" for "1 to 23").
		-- However, "-1-2/3" is a negative fraction (-1⅔), so it must be extracted first.
		-- Do not unpack a parameter if it is like "3-1/2" which is sometimes incorrectly
		-- used instead of "3+1/2" (and which should not be interpreted as "3 to ½").
		-- Unpacked items are inserted into the parms table.
		-- The tail recursion allows combinations like "1x2 to 3x4".
		local valstr = strip(parmsi)  -- trim so any '-' as a negative sign will be at start
		local success, result = extract_number(parms, valstr, i > 1)
		if not success and valstr and i  0 then
		if range.n > 30 then  -- limit abuse, although 4 is a more likely upper limit
			return false, { 'cvt_invalid_num' }  -- misleading message but it will do
		end
		parms.range = range
	elseif had_nocomma then
		return false, { 'cvt_unknown', parm2 }
	end
	return true, valinfo, i
end
local function simple_get_values(parms)
	-- If input is like "...",
	-- return true, i, in_unit, in_unit_table
	-- i = index in parms of what follows valid_unit, if anything.
	-- The valid_value is not negative and does not use a fraction, and
	-- no options requiring further processing of the input are used.
	-- Otherwise, return nothing or return false, parm1 for caller to interpret.
	-- Testing shows this function is successful for 96% of converts in articles,
	-- and that on average it speeds up converts by 8%.
	local clean = to_en(strip(parms1 or ), parms)
	if parms.opt_ri or parms.opt_spell_in or #clean > 10 or not clean:match('^0-9.+$') then
		return false, clean
	end
	local value = tonumber(clean)
	if not value then return end
	local info = {
		value = value,
		altvalue = value,
		singular = (value == 1),
		clean = clean,
		show = with_separator(parms, clean),
	}
	local in_unit = strip(parms2)
	local success, in_unit_table = lookup(parms, in_unit, 'no_combination')
	if not success then return end
	in_unit_table.valinfo = { info }
	return true, 3, in_unit, in_unit_table
end
local function wikidata_call(parms, operation, ...)
	-- Return true, s where s is the result of a Wikidata operation,
	-- or return false, t where t is an error message table.
	local function worker(...)
		wikidata_code = wikidata_code or require(wikidata_module)
		wikidata_data = wikidata_data or mw.loadData(wikidata_data_module)
		return wikidata_codeoperation(wikidata_data, ...)
	end
	local success, status, result = pcall(worker, ...)
	if success then
		return status, result
	end
	if parms.opt_sortable_debug then
		-- Use debug=yes to crash if an error while accessing Wikidata.
		error('Error accessing Wikidata: ' .. status, 0)
	end
	return false, { 'cvt_wd_fail' }
end
local function get_parms(parms, args)
	-- If successful, update parms and return true, unit where
	--   parms is a table of all arguments passed to the template
	--        converted to named arguments, and
	--   unit is the input unit table;
	-- or return false, t where t is an error message table.
	-- For special processing (not a convert), can also return
	-- true, wikitext where wikitext is the final result.
	-- The returned input unit table may be for a fake unit using the specified
	-- unit code as the symbol and name, and with bad_mcode = message code table.
	-- MediaWiki removes leading and trailing whitespace from the values of
	-- named arguments. However, the values of numbered arguments include any
	-- whitespace entered in the template, and whitespace is used by some
	-- parameters (example: the numbered parameters associated with "disp=x").
	local kv_pairs = {}  -- table of input key:value pairs where key is a name; needed because cannot iterate parms and add new fields to it
	for k, v in pairs(args) do
		if type(k) == 'number' or k == 'test' then  -- parameter "test" is reserved for testing and is not translated
			parmsk = v
		else
			kv_pairsk = v
		end
	end
	if parms.test == 'wikidata' then
		local ulookup = function (ucode)
			-- Use empty table for parms so it does not accumulate results when used repeatedly.
			return lookup({}, ucode, 'no_combination')
		end
		return wikidata_call(parms, '_listunits', ulookup)
	end
	local success, msg = translate_parms(parms, kv_pairs)
	if not success then return false, msg end
	if parms.input then
		success, msg = wikidata_call(parms, '_adjustparameters', parms, 1)
		if not success then return false, msg end
	end
	local success, i, in_unit, in_unit_table = simple_get_values(parms)
	if not success then
		if type(i) == 'string' and i:match('^NNN+$') then
			-- Some infoboxes have examples like m (3 or more "N").
			-- Output an empty string for these.
			return false, { 'cvt_no_output' }
		end
		local valinfo
		success, valinfo, i = get_values(parms)
		if not success then return false, valinfo end
		in_unit = strip(parmsi)
		i = i + 1
		success, in_unit_table = lookup(parms, in_unit, 'no_combination')
		if not success then
			in_unit = in_unit or 
			if parms.opt_ignore_error then  -- display given unit code with no error (for use with )
				in_unit_table =   -- suppress error message and prevent processing of output unit
			end
			in_unit_table = setmetatable({
				symbol = in_unit, name2 = in_unit, utype = in_unit,
				scale = 1, default = , defkey = , linkey = ,
				bad_mcode = in_unit_table }, unit_mt)
		end
		in_unit_table.valinfo = valinfo
	end
	if parms.test == 'msg' then
		-- Am testing the messages produced when no output unit is specified, and
		-- the input unit has a missing or invalid default.
		-- Set two units for testing that.
		-- LATER: Remove this code.
		if in_unit == 'chain' then
			in_unit_table.default = nil  -- no default
		elseif in_unit == 'rd' then
			in_unit_table.default  = "ft!X!m"  -- an invalid expression
		end
	end
	in_unit_table.inout = 'in'  -- this is an input unit
	if not parms.range then
		local success, inext, composite_unit = get_composite(parms, i, in_unit_table)
		if not success then return false, inext end
		if composite_unit then
			in_unit_table = composite_unit
			i = inext
		end
	end
	if in_unit_table.builtin == 'mach' then
		-- As with old template, a number following Mach as the input unit is the altitude,
		-- and there is no way to specify an altitude for the output unit.
		-- Could put more code in this function to get any output unit and check for
		-- an altitude following that unit.
		local success, info = extract_number(parms, parmsi, false, true)
		if success then
			i = i + 1
			in_unit_table.altitude = info.value
		end
	end
	local word = strip(parmsi)
	i = i + 1
	local precision, is_bad_precision
	local function set_precision(text)
		local number, is_integer = get_number(text)
		if number then
			if is_integer then
				precision = number
			else
				precision = text
				is_bad_precision = true
			end
			return true  -- text was used for precision, good or bad
		end
	end
	if word and not set_precision(word) then
		parms.out_unit = parms.out_unit or word
		if set_precision(strip(parmsi)) then
			i = i + 1
		end
	end
	if parms.opt_adj_mid then
		word = parmsi
		i = i + 1
		if word then  -- mid-text words
			if word:sub(1, 1) == '-' then
				parms.mid = word
			else
				parms.mid = ' ' .. word
			end
		end
	end
	if parms.opt_one_preunit then
		parmsparms.opt_flip and 'preunit2' or 'preunit1' = preunits(1, parmsi)
		i = i + 1
	end
	if parms.disp == 'x' then
		-- Following is reasonably compatible with the old template.
		local first = parmsi or 
		local second = parmsi+1 or 
		i = i + 2
		if strip(first) ==  then  -- user can enter ' ' rather than ' ' to avoid the default
			first = '  ' .. first
			second = ' ' .. second
		end
		parms.joins = { first, second }
	elseif parms.opt_two_preunits then
		local p1, p2 = preunits(2, parmsi, parmsi+1)
		i = i + 2
		if parms.preunit1 then
			-- To simplify documentation, allow unlikely use of adj=pre with disp=preunit
			-- (however, an output unit must be specified with adj=pre and with disp=preunit).
			parms.preunit1 = parms.preunit1 .. p1
			parms.preunit2 = p2
		else
			parms.preunit1, parms.preunit2 = p1, p2
		end
	end
	if precision == nil then
		if set_precision(strip(parmsi)) then
			i = i + 1
		end
	end
	if is_bad_precision then
		add_warning(parms, 1, 'cvt_bad_prec', precision)
	else
		parms.precision = precision
	end
	for j = i, i + 3 do
		local parm = parmsj  -- warn if find a non-empty extraneous parameter
		if parm and parm:match('%S') then
			add_warning(parms, 1, 'cvt_unknown_option', parm)
			break
		end
	end
	return true, in_unit_table
end
local function record_default_precision(parms, out_current, precision)
	-- If necessary, adjust parameters and return a possibly adjusted precision.
	-- When converting a range of values where a default precision is required,
	-- that default is calculated for each value because the result sometimes
	-- depends on the precise input and output values. This function may cause
	-- the entire convert process to be repeated in order to ensure that the
	-- same default precision is used for each individual convert.
	-- If that were not done, a range like 1000 to 1000.4 may give poor results
	-- because the first output could be heavily rounded, while the second is not.
	-- For range 1000.4 to 1000, this function can give the second convert the
	-- same default precision that was used for the first.
	if not parms.opt_round_each then
		local maxdef = out_current.max_default_precision
		if maxdef then
			if maxdef  0 then
		prec = math.max(log10(denominator), 1)
	else
		-- Count digits after decimal mark, handling cases like '12.345e6'.
		local exponent
		local integer, dot, decimals, expstr = inclean:match('^(%d*)(%.?)(%d*)(.*)')
		local e = expstr:sub(1, 1)
		if e == 'e' or e == 'E' then
			exponent = tonumber(expstr:sub(2))
		end
		if dot ==  then
			prec = subunit_ignore_trailing_zero and 0 or -integer:match('0*$'):len()
		else
			prec = #decimals
		end
		if exponent then
			-- So '1230' and '1.23e3' both give prec = -1, and '0.00123' and '1.23e-3' give 5.
			prec = prec - exponent
		end
	end
	if in_current.istemperature and out_current.istemperature then
		-- Converting between common temperatures (°C, °F, °R, K); not keVT.
		-- Kelvin value can be almost zero, or small but negative due to precision problems.
		-- Also, an input value like -300 C (below absolute zero) gives negative kelvins.
		-- Calculate minimum precision from absolute value.
		adjust = 0
		local kelvin = abs((invalue - in_current.offset) * in_current.scale)
		if kelvin  0 then
				prefix = 7000 + mag
			else
				prefix = 2999 - mag
				outvalue = outvalue + 10^(mag+1)
			end
			sortkey = format('%d', prefix) .. format('%015.0f', floor(outvalue * 10^(14-mag)))
		end
	end
	local sortspan
	if sortkey and not parms.table_align then
		sortspan = parms.opt_sortable_debug and
			 .. sortkey .. '♠' or
			
		parms.join_before = sortspan
	end
	if parms.table_align then
		local sort
		if sortkey then
			sort = ' data-sort-value="' .. sortkey .. '"'
			if parms.opt_sortable_debug then
				parms.join_before =  .. sortkey .. 
			end
		else
			sort = 
		end
		local style = 'style="text-align:' .. parms.table_align .. ';'
		local joins = {}
		for i = 1, 2 do
			joinsi = (i == 1 and  or '\n|') .. style .. user_style(parms, i) .. '"' .. sort .. '|'
		end
		parms.table_joins = joins
	end
	return sortspan, scaled_value
end
local cvt_to_hand
local function cvtround(parms, info, in_current, out_current)
	-- Return true, t where t is a table with the conversion results; fields:
	--   show = rounded, formatted string with the result of converting value in info,
	--      using the rounding specified in parms.
	--   singular = true if result (after rounding and ignoring any negative sign)
	--      is "1", or like "1.00", or is a fraction with value = 0 then
			local fudge
			if precision  1 then
		frac = (precision == 2) and 2 or 4
	end
	local out_next = out_current.out_next
	if out_next then
		-- Use magic knowledge to determine whether the next unit is inches without requiring i18n.
		-- The following ensures that when the output combination "hand in" is used, the inches
		-- value is rounded to match the hands value. Also, displaying say "61½" instead of 61.5
		-- is better as 61.5 implies the value is not 61.4.
		if out_next.exception == 'subunit_more_precision' then
			out_next.frac = frac
		end
	end
	-- Convert to inches; calculate hands from that.
	local dummy_unit_table = { scale = out_current.scale / 4, frac = frac }
	local success, outinfo = cvtround(parms, info, in_current, dummy_unit_table)
	if not success then return false, outinfo end
	local tfrac = outinfo.fraction_table
	local inches = outinfo.raw_absvalue
	if tfrac then
		inches = floor(inches)  -- integer part only; fraction added later
	else
		inches = floor(inches + 0.5)  -- a hands measurement never shows decimals of an inch
	end
	local hands, inches = divide(inches, 4)
	outinfo.absvalue = hands + inches/4  -- supposed to be the absolute rounded value, but this is close enough
	local inchstr = tostring(inches)  -- '0', '1', '2' or '3'
	if precision and precision ' or '>='
	-- In addition, the following form is supported:
	--    LHS and RHS
	-- where
	--    LHS, RHS = any of above expressions.
	local function compare(value, text)
		local arithop, factor, compop, limit = text:match('^%s*v%s*(*?)(.-)(=?)(.*)$')
		if arithop == nil then
			error('Invalid default expression', 0)
		elseif arithop == '*' then
			factor = tonumber(factor)
			if factor == nil then
				error('Invalid default expression', 0)
			end
			value = value * factor
		end
		limit = tonumber(limit)
		if limit == nil then
			error('Invalid default expression', 0)
		end
		if compop ==  then
			return value > limit
		elseif compop == '>=' then
			return value >= limit
		end
		error('Invalid default expression', 0)  -- should not occur
	end
	local lhs, rhs = condition:match('^(.-%W)and(%W.*)')
	if lhs == nil then
		return compare(value, condition)
	end
	return compare(value, lhs) and compare(value, rhs)
end
local function get_default(value, unit_table)
	-- Return true, s where s = name of unit's default output unit,
	-- or return false, t where t is an error message table.
	-- Some units have a default that depends on the input value
	-- (the first value if a range of values is used).
	-- If '!' is in the default, the first bang-delimited field is an
	-- expression that uses 'v' to represent the input value.
	-- Example: 'v  mile
	--   miles --> miles
	-- However, just id is returned if:
	-- * no link given (so caller does not need to check if a link was defined); or
	-- * link has previously been used during the current convert (to avoid overlinking).
	local link_key
	if unit_table then
		link_key = unit_table.unitcode or unit_table
	else
		link_key = link
	end
	if not link or link ==  or linked_pageslink_key then
		return id
	end
	linked_pageslink_key = true
	-- Following only works for language en, but it should be safe on other wikis,
	-- and overhead of doing it generally does not seem worthwhile.
	local l = link:sub(1, 1):lower() .. link:sub(2)
	if link == id or l == id then
		return  .. id .. 
	elseif link .. 's' == id or l .. 's' == id then
		return  .. id:sub(1, -2) .. 's'
	else
		return  .. id .. 
	end
end
local function variable_name(clean, unit_table)
	-- For slwiki, a unit name depends on the value.
	-- Parameter clean is the unsigned rounded value in en digits, as a string.
	-- Value             Source    Example for "m"
	-- integer 1:        name1     meter  (also is the name of the unit)
	-- integer 2:        var{1}    metra
	-- integer 3 and 4:  var{2}    metri
	-- integer else:     var{3}    metrov (0 and 5 or more)
	-- real/fraction:    var{4}    metra
	-- var{i} means the i'th field in unit_table.varname if it exists and has
	-- an i'th field, otherwise name2.
	-- Fields are separated with "!" and are not empty.
	-- A field for a unit using an SI prefix has the prefix name inserted,
	-- replacing '#' if found, or before the field otherwise.
	local vname
	if clean == '1' then
		vname = unit_table.name1
	elseif unit_table.varname then
		local i
		if clean == '2' then
			i = 1
		elseif clean == '3' or clean == '4' then
			i = 2
		elseif clean:find('.', 1, true) then
			i = 4
		else
			i = 3
		end
		if i > 1 and varname == 'pl' then
			i = i - 1
		end
		vname = split(unit_table.varname, '!')i
	end
	if vname then
		local si_name = rawget(unit_table, 'si_name') or 
		local pos = vname:find('#', 1, true)
		if pos then
			vname = vname:sub(1, pos - 1) .. si_name .. vname:sub(pos + 1)
		else
			vname = si_name .. vname
		end
		return vname
	end
	return unit_table.name2
end
local function linked_id(parms, unit_table, key_id, want_link, clean)
	-- Return final unit id (symbol or name), optionally with a wikilink,
	-- and update unit_table.sep if required.
	-- key_id is one of: 'symbol', 'sym_us', 'name1', 'name1_us', 'name2', 'name2_us'.
	local abbr_on = (key_id == 'symbol' or key_id == 'sym_us')
	if abbr_on and want_link then
		local symlink = rawget(unit_table, 'symlink')
		if symlink then
			return symlink  -- for exceptions that have the linked symbol built-in
		end
	end
	local multiplier = rawget(unit_table, 'multiplier')
	local per = unit_table.per
	if per then
		local paren1, paren2 = ,   -- possible parentheses around bottom unit
		local unit1 = per1  -- top unit_table, or nil
		local unit2 = per2  -- bottom unit_table
		if abbr_on then
			if not unit1 then
				unit_table.sep =   -- no separator in "$2/acre"
			end
			if not want_link then
				local symbol = unit_table.symbol_raw
				if symbol then
					return symbol  -- for exceptions that have the symbol built-in
				end
			end
			if (unit2.symbol):find('⋅', 1, true) then
				paren1, paren2 = '(', ')'
			end
		end
		local key_id2  -- unit2 is always singular
		if key_id == 'name2' then
			key_id2 = 'name1'
		elseif key_id == 'name2_us' then
			key_id2 = 'name1_us'
		else
			key_id2 = key_id
		end
		local result
		if abbr_on then
			result = '/'
		elseif omitsep then
			result = per_word
		elseif unit1 then
			result = ' ' .. per_word .. ' '
		else
			result = per_word .. ' '
		end
		if want_link and unit_table.link then
			if abbr_on or not varname then
				result = (unit1 and linked_id(parms, unit1, key_id, false, clean) or ) .. result .. linked_id(parms, unit2, key_id2, false, '1')
			else
				result = (unit1 and variable_name(clean, unit1) or ) .. result .. variable_name('1', unit2)
			end
			if omit_separator(result) then
				unit_table.sep = 
			end
			return make_link(unit_table.link, result, unit_table)
		end
		if unit1 then
			result = linked_id(parms, unit1, key_id, want_link, clean) .. result
			if unit1.sep then
				unit_table.sep = unit1.sep
			end
		elseif omitsep then
			unit_table.sep = 
		end
		return result .. paren1 .. linked_id(parms, unit2, key_id2, want_link, '1') .. paren2
	end
	if multiplier then
		-- A multiplier (like "100" in "100km") forces the unit to be plural.
		multiplier = from_en(multiplier)
		if not omitsep then
			multiplier = multiplier .. (abbr_on and ' ' or ' ')
		end
		if not abbr_on then
			if key_id == 'name1' then
				key_id = 'name2'
			elseif key_id == 'name1_us' then
				key_id = 'name2_us'
			end
		end
	else
		multiplier = 
	end
	local id = unit_table.fixed_name or ((varname and not abbr_on) and variable_name(clean, unit_table) or unit_tablekey_id)
	if omit_separator(id) then
		unit_table.sep = 
	end
	if want_link then
		local link = data_code.link_exceptionsunit_table.linkey or unit_table.symbol or unit_table.link
		if link then
			local before = 
			local i = unit_table.customary
			if i == 1 and parms.opt_sp_us then
				i = 2  -- show "U.S." not "US"
			end
			if i == 3 and abbr_on then
				i = 4  -- abbreviate "imperial" to "imp"
			end
			local customary = text_code.customary_unitsi
			if customary then
				-- LATER: This works for language en only, but it's esoteric so ignore for now.
				local pertext
				if id:sub(1, 1) == '/' then
					-- Want unit "/USgal" to display as "/U.S. gal", not "U.S. /gal".
					pertext = '/'
					id = id:sub(2)
				elseif id:sub(1, 4) == 'per ' then
					-- Similarly want "per U.S. gallon", not "U.S. per gallon" (but in practice this is unlikely to be used).
					pertext = 'per '
					id = id:sub(5)
				else
					pertext = 
				end
				-- Omit any "US"/"U.S."/"imp"/"imperial" from start of id since that will be inserted.
				local removes = (i ×' ..
					from_en('10') ..
					'^' ..
					from_en(tostring(engscale.exponent)) .. 
			elseif number_word then
				local number_id
				local lk = parms.lk
				if lk == 'on' or lk == inout then
					number_id = make_link(engscale.link, engscale1)
				else
					number_id = engscale1
				end
				-- :en:WP:NUMERAL recommends " " in values like "12 million".
				info.show = info.show .. (parms.opt_adjectival and '-' or ' ') .. number_id
			end
		end
		if prefix then
			info.show = prefix .. info.show
		end
	end
end
local function process_input(parms, in_current)
	-- Processing required once per conversion.
	-- Return block of text to represent input (value/unit).
	if parms.opt_output_only or parms.opt_output_number_only or parms.opt_output_unit_only then
		parms.joins = { ,  }
		return 
	end
	local first_unit
	local composite = in_current.composite  -- nil or table of units
	if composite then
		first_unit = composite1
	else
		first_unit = in_current
	end
	local id1, want_name = make_id(parms, 1, first_unit)
	local sep = first_unit.sep  -- separator between value and unit, set by make_id
	local preunit = parms.preunit1
	if preunit then
		sep =   -- any separator is included in preunit
	else
		preunit = 
	end
	if parms.opt_input_unit_only then
		parms.joins = { ,  }
		if composite then
			local parts = { id1 }
			for i, unit in ipairs(composite) do
				if i > 1 then
					table.insert(parts, (make_id(parms, 1, unit)))
				end
			end
			id1 = table.concat(parts, ' ')
		end
		if want_name and parms.opt_adjectival then
			return preunit .. hyphenated(id1)
		end
		return  preunit .. id1
	end
	if parms.opt_also_symbol and not composite and not parms.opt_flip then
		local join1 = parms.joins1
		if join1 == ' (' or join1 == ' ' then
			parms.joins = { ' ' .. first_unitparms.opt_sp_us and 'sym_us' or 'symbol' ..  .. join1 , parms.joins2 }
		end
	end
	if in_current.builtin == 'mach' and first_unit.sep ~=  then  --  means omitsep with non-enwiki name
		local prefix = id1 .. ' '
		local range = parms.range
		local valinfo = first_unit.valinfo
		local result = prefix .. valinfo1.show
		if range then
			-- For simplicity and because more not needed, handle one range item only.
			local prefix2 = make_id(parms, 2, first_unit) .. ' '
			result = range_text(range1, want_name, parms, result, prefix2 .. valinfo2.show, 'in')
		end
		return preunit .. result
	end
	if composite then
		-- Simplify: assume there is no range, and no decoration.
		local mid = (not parms.opt_flip) and parms.mid or 
		local sep1 = ' '
		local sep2 = ' '
		if parms.opt_adjectival and want_name then
			sep1 = '-'
			sep2 = '-'
		end
		if omitsep and sep ==  then
			-- Testing the id of the most significant unit should be sufficient.
			sep1 = 
			sep2 = 
		end
		local parts = { first_unit.valinfo1.show .. sep1 .. id1 }
		for i, unit in ipairs(composite) do
			if i > 1 then
				table.insert(parts, unit.valinfo1.show .. sep1 .. (make_id(parms, 1, unit)))
			end
		end
		return table.concat(parts, sep2) .. mid
	end
	local add_unit = (parms.abbr == 'mos') or
		parmsparms.opt_flip and 'out_range_x' or 'in_range_x' or
		(not want_name and parms.abbr_range_x)
	local range = parms.range
	if range and not add_unit then
		unlink(first_unit)
	end
	local id = range and make_id(parms, range.n + 1, first_unit) or id1
	local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, 'in')
	if was_hyphenated then
		add_unit = false
	end
	local result
	local valinfo = first_unit.valinfo
	if range then
		for i = 0, range.n do
			local number_word
			if i == range.n then
				add_unit = false
				number_word = true
			end
			decorate_value(parms, first_unit, i+1, number_word)
			local show = valinfoi+1.show
			if add_unit then
				show = show .. first_unit.sep .. (i == 0 and id1 or make_id(parms, i+1, first_unit))
			end
			if i == 0 then
				result = show
			else
				result = range_text(rangei, want_name, parms, result, show, 'in')
			end
		end
	else
		decorate_value(parms, first_unit, 1, true)
		result = valinfo1.show
	end
	return result .. preunit .. extra
end
local function process_one_output(parms, out_current)
	-- Processing required for each output unit.
	-- Return block of text to represent output (value/unit).
	local inout = out_current.inout  -- normally 'out' but can be 'in' for order=out
	local id1, want_name = make_id(parms, 1, out_current)
	local sep = out_current.sep  -- set by make_id
	local preunit = parms.preunit2
	if preunit then
		sep =   -- any separator is included in preunit
	else
		preunit = 
	end
	if parms.opt_output_unit_only then
		if want_name and parms.opt_adjectival then
			return preunit .. hyphenated(id1)
		end
		return preunit .. id1
	end
	if out_current.builtin == 'mach' and out_current.sep ~=  then  --  means omitsep with non-enwiki name
		local prefix = id1 .. ' '
		local range = parms.range
		local valinfo = out_current.valinfo
		local result = prefix .. valinfo1.show
		if range then
			-- For simplicity and because more not needed, handle one range item only.
			result = range_text(range1, want_name, parms, result, prefix .. valinfo2.show, inout)
		end
		return preunit .. result
	end
	local add_unit = (parmsparms.opt_flip and 'in_range_x' or 'out_range_x' or
		(not want_name and parms.abbr_range_x)) and
		not parms.opt_output_number_only
	local range = parms.range
	if range and not add_unit then
		unlink(out_current)
	end
	local id = range and make_id(parms, range.n + 1, out_current) or id1
	local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, inout)
	if was_hyphenated then
		add_unit = false
	end
	local result
	local valinfo = out_current.valinfo
	if range then
		for i = 0, range.n do
			local number_word
			if i == range.n then
				add_unit = false
				number_word = true
			end
			decorate_value(parms, out_current, i+1, number_word)
			local show = valinfoi+1.show
			if add_unit then
				show = show .. out_current.sep .. (i == 0 and id1 or make_id(parms, i+1, out_current))
			end
			if i == 0 then
				result = show
			else
				result = range_text(rangei, want_name, parms, result, show, inout)
			end
		end
	else
		decorate_value(parms, out_current, 1, true)
		result = valinfo1.show
	end
	if parms.opt_output_number_only then
		return result
	end
	return result .. preunit .. extra
end
local function make_output_single(parms, in_unit_table, out_unit_table)
	-- Return true, item where item = wikitext of the conversion result
	-- for a single output (which is not a combination or a multiple);
	-- or return false, t where t is an error message table.
	if parms.opt_order_out and in_unit_table.unitcode == out_unit_table.unitcode then
		out_unit_table.valinfo = in_unit_table.valinfo
	else
		out_unit_table.valinfo = collection()
		for _, v in ipairs(in_unit_table.valinfo) do
			local success, info = cvtround(parms, v, in_unit_table, out_unit_table)
			if not success then return false, info end
			out_unit_table.valinfo:add(info)
		end
	end
	return true, process_one_output(parms, out_unit_table)
end
local function make_output_multiple(parms, in_unit_table, out_unit_table)
	-- Return true, item where item = wikitext of the conversion result
	-- for an output which is a multiple (like 'ftin');
	-- or return false, t where t is an error message table.
	local inout = out_unit_table.inout  -- normally 'out' but can be 'in' for order=out
	local multiple = out_unit_table.multiple  -- table of scaling factors (will not be nil)
	local combos = out_unit_table.combination  -- table of unit tables (will not be nil)
	local abbr = parms.abbr
	local abbr_org = parms.abbr_org
	local disp = parms.disp
	local want_name = (abbr_org == nil and (disp == 'or' or disp == 'slash')) or
						not (abbr == 'on' or abbr == inout or abbr == 'mos')
	local want_link = (parms.lk == 'on' or parms.lk == inout)
	local mid = parms.opt_flip and parms.mid or 
	local sep1 = ' '
	local sep2 = ' '
	if parms.opt_adjectival and want_name then
		sep1 = '-'
		sep2 = '-'
	end
	local do_spell = parms.opt_spell_out
	parms.opt_spell_out = nil  -- so the call to cvtround does not spell the value
	local function make_result(info, isfirst)
		local fmt, outvalue, sign
		local results = {}
		for i = 1, #combos do
			local tfrac, thisvalue, strforce
			local out_current = combosi
			out_current.inout = inout
			local scale = multiplei
			if i == 1 then  -- least significant unit ('in' from 'ftin')
				local decimals
				out_current.frac = out_unit_table.frac
				local success, outinfo = cvtround(parms, info, in_unit_table, out_current)
				if not success then return false, outinfo end
				if isfirst then
					out_unit_table.valinfo = { outinfo }  -- in case output value of first least significant unit is needed
				end
				sign = outinfo.sign
				tfrac = outinfo.fraction_table
				if outinfo.is_scientific then
					strforce = outinfo.show
					decimals = 
				elseif tfrac then
					decimals = 
				else
					local show = outinfo.show  -- number as a string in local language
					local p1, p2 = show:find(numdot, 1, true)
					decimals = p1 and show:sub(p2 + 1) or   -- text after numdot, if any
				end
				fmt = '%.' .. ulen(decimals) .. 'f'  -- to reproduce precision
				if decimals ==  then
					if tfrac then
						outvalue = floor(outinfo.raw_absvalue)  -- integer part only; fraction added later
					else
						outvalue = floor(outinfo.raw_absvalue + 0.5)  -- keep all integer digits of least significant unit
					end
				else
					outvalue = outinfo.absvalue
				end
			end
			if scale then
				outvalue, thisvalue = divide(outvalue, scale)
			else
				thisvalue = outvalue
			end
			local id
			if want_name then
				if varname then
					local clean
					if strforce or tfrac then
						clean = '.1'  -- dummy value to force name for floating point
					else
						clean = format(fmt, thisvalue)
					end
					id = variable_name(clean, out_current)
				else
					local key = 'name2'
					if parms.opt_adjectival then
						key = 'name1'
					elseif tfrac then
						if thisvalue == 0 then
							key = 'name1'
						end
					elseif parms.opt_singular then
						if 0  0) and tostring(thisvalue) or nil
				strval = format_fraction(parms, spell_inout, false, wholestr, tfrac.numstr, tfrac.denstr, do_spell)
			else
				strval = (thisvalue == 0) and from_en('0') or with_separator(parms, format(fmt, thisvalue))
				if do_spell then
					strval = spell_number(parms, spell_inout, strval) or strval
				end
			end
			table.insert(results, strval .. sep1 .. id)
			if outvalue == 0 then
				break
			end
			fmt = '%.0f'  -- only least significant unit can have a non-integral value
		end
		local reversed, count = {}, #results
		for i = 1, count do
			reversedi = resultscount + 1 - i
		end
		return true, sign .. table.concat(reversed, sep2)
	end
	local valinfo = in_unit_table.valinfo
	local success, result = make_result(valinfo1, true)
	if not success then return false, result end
	local range = parms.range
	if range then
		for i = 1, range.n do
			local success, result2 = make_result(valinfoi+1)
			if not success then return false, result2 end
			result = range_text(rangei, want_name, parms, result, result2, inout)
		end
	end
	return true, result .. mid
end
local function process(parms, in_unit_table, out_unit_table)
	-- Return true, s, outunit where s = final wikitext result,
	-- or return false, t where t is an error message table.
	linked_pages = {}
	local success, bad_output
	local bad_input_mcode = in_unit_table.bad_mcode  -- nil if input unit is a valid convert unit
	local out_unit = parms.out_unit
	if out_unit == nil or out_unit ==  or type(out_unit) == 'function' then
		if bad_input_mcode or parms.opt_input_unit_only then
			bad_output = 
		else
			local getdef = type(out_unit) == 'function' and out_unit or get_default
			success, out_unit = getdef(in_unit_table.valinfo1.value, in_unit_table)
			parms.out_unit = out_unit
			if not success then
				bad_output = out_unit
			end
		end
	end
	if not bad_output and not out_unit_table then
		success, out_unit_table = lookup(parms, out_unit, 'any_combination')
		if success then
			local mismatch = check_mismatch(in_unit_table, out_unit_table)
			if mismatch then
				bad_output = mismatch
			end
		else
			bad_output = out_unit_table
		end
	end
	local lhs, rhs
	local flipped = parms.opt_flip and not bad_input_mcode
	if bad_output then
		rhs = (bad_output == ) and  or message(parms, bad_output)
	elseif parms.opt_input_unit_only then
		rhs = 
	else
		local combos  -- nil (for 'ft' or 'ftin'), or table of unit tables (for 'm ft')
		if not out_unit_table.multiple then  -- nil/false ('ft' or 'm ft'), or table of factors ('ftin')
			combos = out_unit_table.combination
		end
		local frac = parms.frac  -- nil or denominator of fraction for output values
		if frac then
			-- Apply fraction to the unit (if only one), or to non-SI units (if a combination),
			-- except that if a precision is also specified, the fraction only applies to
			-- the hand unit; that allows the following result:
			-- frac=2 → 156 centimetres (61.4 in; 15.1½ hands)
			-- However, the following is handled elsewhere as a special case:
			-- frac=2 → 156 centimetres (15.1½ hands; 61½ in)
			if combos then
				local precision = parms.precision
				for _, unit in ipairs(combos) do
					if unit.builtin == 'hand' or (not precision and not unit.prefixes) then
						unit.frac = frac
					end
				end
			else
				out_unit_table.frac = frac
			end
		end
		local outputs = {}
		local imax = combos and #combos or 1  -- 1 (single unit) or number of unit tables
		if imax == 1 then
			parms.opt_order_out = nil  -- only useful with an output combination
		end
		if not flipped and not parms.opt_order_out then
			-- Process left side first so any duplicate links (from lk=on) are suppressed
			-- on right. Example: lk=on
			lhs = process_input(parms, in_unit_table)
		end
		for i = 1, imax do
			local success, item
			local out_current = combos and combosi or out_unit_table
			out_current.inout = 'out'
			if i == 1 then
				if imax > 1 and out_current.builtin == 'hand' then
					out_current.out_next = combos2  -- built-in hand can influence next unit in a combination
				end
				if parms.opt_order_out then
					out_current.inout = 'in'
				end
			end
			if out_current.multiple then
				success, item = make_output_multiple(parms, in_unit_table, out_current)
			else
				success, item = make_output_single(parms, in_unit_table, out_current)
			end
			if not success then return false, item end
			outputsi = item
		end
		if parms.opt_order_out then
			lhs = outputs1
			table.remove(outputs, 1)
		end
		local sep = parms.table_joins and parms.table_joins2 or parms.join_between
		rhs = table.concat(outputs, sep)
	end
	if flipped or not lhs then
		local input = process_input(parms, in_unit_table)
		if flipped then
			lhs = rhs
			rhs = input
		else
			lhs = input
		end
	end
	if parms.join_before then
		lhs = parms.join_before .. lhs
	end
	local wikitext
	if bad_input_mcode then
		if bad_input_mcode ==  then
			wikitext = lhs
		else
			wikitext = lhs .. message(parms, bad_input_mcode)
		end
	elseif parms.table_joins then
		wikitext = parms.table_joins1 .. lhs .. parms.table_joins2 .. rhs
	else
		wikitext = lhs .. parms.joins1 .. rhs .. parms.joins2
	end
	if parms.warnings and not bad_input_mcode then
		wikitext = wikitext .. parms.warnings
	end
	return true, get_styles(parms) .. wikitext, out_unit_table
end
local function main_convert(frame)
	-- Do convert, and if needed, do it again with higher default precision.
	local parms = { frame = frame }  -- will hold template arguments, after translation
	set_config(frame.args)
	local success, result = get_parms(parms, frame:getParent().args)
	if success then
		if type(result) ~= 'table' then
			return tostring(result)
		end
		local in_unit_table = result
		local out_unit_table
		for _ = 1, 2 do  -- use counter so cannot get stuck repeating convert
			success, result, out_unit_table = process(parms, in_unit_table, out_unit_table)
			if success and parms.do_convert_again then
				parms.do_convert_again = false
			else
				break
			end
		end
	end
	-- If input=x gives a problem, the result should be just the user input
	-- (if x is a property like P123 it has been replaced with ).
	-- An unknown input unit would display the input and an error message
	-- with success == true at this point.
	-- Also, can have success == false with a message that outputs an empty string.
	if parms.input_text then
		if success and not parms.have_problem then
			return result
		end
		local cat
		if parms.tracking then
			-- Add a tracking category using the given text as the category sort key.
			-- There is currently only one type of tracking, but in principle multiple
			-- items could be tracked, using different sort keys for convenience.
			cat = wanted_category('tracking', parms.tracking)
		end
		return parms.input_text .. (cat or )
	end
	return success and result or message(parms, result)
end
local function _unit(unitcode, options)
	-- Helper function for Module:Val to look up a unit.
	-- Parameter unitcode must be a string to identify the wanted unit.
	-- Parameter options must be nil or a table with optional fields:
	--   value = number (for sort key; default value is 1)
	--   scaled_top = nil for a normal unit, or a number for a unit which is
	--                the denominator of a per unit (for sort key)
	--   si = { 'symbol', 'link' }
	--                (a table with two strings) to make an SI unit
	--                that will be used for the look up
	--   link = true if result should be linked
	--   sort = 'on' or 'debug' if result should include a sort key in a
	--                span element ('debug' makes the key visible)
	--   name = true for the name of the unit instead of the symbol
	--   us = true for the US spelling of the unit, if any
	-- Return nil if unitcode is not a non-empty string.
	-- Otherwise return a table with fields:
	--   text = requested symbol or name of unit, optionally linked
	--   scaled_value = input value adjusted by unit scale; used for sort key
	--   sortspan = span element with sort key like that provided by ,
	--     calculated from the result of converting value
	--     to a base unit with scale 1.
	--   unknown = true if the unitcode was not known
	unitcode = strip(unitcode)
	if unitcode == nil or unitcode ==  then
		return nil
	end
	set_config({})
	linked_pages = {}
	options = options or {}
	local parms = {
		abbr = options.name and 'off' or 'on',
		lk = options.link and 'on' or nil,
		opt_sp_us = options.us and true or nil,
		opt_ignore_error = true,  -- do not add pages using this function to 'what links here' for Module:Convert/extra
		opt_sortable_on = options.sort == 'on' or options.sort == 'debug',
		opt_sortable_debug = options.sort == 'debug',
	}
	if options.si then
		-- Make a dummy table of units (just one unit) for lookup to use.
		-- This makes lookup recognize any SI prefix in the unitcode.
		local symbol = options.si1 or '?'
		parms.unittable = { symbol = {
			_name1 = symbol,
			_name2 = symbol,
			_symbol = symbol,
			utype = symbol,
			scale = symbol == 'g' and 0.001 or 1,
			prefixes = 1,
			default = symbol,
			link = options.si2,
		}}
	end
	local success, unit_table = lookup(parms, unitcode, 'no_combination')
	if not success then
		unit_table = setmetatable({
			symbol = unitcode, name2 = unitcode, utype = unitcode,
			scale = 1, default = , defkey = , linkey =  }, unit_mt)
	end
	local value = tonumber(options.value) or 1
	local clean = tostring(abs(value))
	local info = {
		value = value,
		altvalue = value,
		singular = (clean == '1'),
		clean = clean,
		show = clean,
	}
	unit_table.inout = 'in'
	unit_table.valinfo = { info }
	local sortspan, scaled_value
	if options.sort then
		sortspan, scaled_value = make_table_or_sort(parms, value, info, unit_table, options.scaled_top)
	end
	return {
		text = make_id(parms, 1, unit_table),
		sortspan = sortspan,
		scaled_value = scaled_value,
		unknown = not success and true or nil,
	}
end
return { convert = main_convert, _unit = _unit }