Module:Convert

Documentation for this module may be created at Module:Convert/doc

-- Convert a value from one unit of measurement to another.
-- Example: {{convert|123|lb|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 as used here
local numsep, numsep_remove
local default_exceptions, link_exceptions, 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 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

-- 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

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 numsep_remove ~= '' then
		text = text:gsub(numsep_remove, '')
	end
	if numdot ~= '.' then
		text = text:gsub(numdot, '.')
	end
	if to_en_table then
		text = ustring.gsub(text, '%d', to_en_table)
	end
	return text
end

local spell_module  -- name of module that can spell numbers
local speller       -- function from that module to handle spelling (set if spelling is wanted)

local function set_config(frame)
	-- Set configuration options from template #invoke or defaults.
	config = frame.args
	maxsigfig = config.maxsigfig or 14  -- maximum number of significant figures
	-- Scribunto sets the global variable 'mw'.
	-- A testing program can set the global variable 'is_test_run'.
	local data_module, text_module, data_code
	if is_test_run then
		local langcode = mw.language.getContentLanguage().code
		data_module = "convertdata-" .. langcode
		text_module = "converttext-" .. langcode
		extra_module = "convertextra-" .. langcode
		spell_module = "ConvertNumeric"
	else
		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
		spell_module = "Module:ConvertNumeric"
	end
	data_code = mw.loadData(data_module)
	text_code = mw.loadData(text_module)
	default_exceptions = data_code.default_exceptions
	link_exceptions = data_code.link_exceptions
	all_units = data_code.all_units
	local translation = text_code.translation_table
	if translation then
		numdot = translation.numdot
		numsep = translation.numsep
		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_table[k] = v
				end
			end
		else
			to_en_table = translation.to_en
		end
	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.
	numsep_remove = (numsep == '.') and '%.' or numsep
end

local function collection()
	-- Return a table to hold items.
	return {
		n = 0,
		add = function (self, item)
			self.n = self.n + 1
			self[self.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 <= remainder and remainder < denominator) then
		-- Floating point limits may need this, as in {{convert|160.02|Ym|ydftin}}.
		remainder = 0
	end
	return quotient, remainder
end

local function split(text, delimiter)
	-- Return a numbered table with fields from splitting text.
	-- The delimiter is used in a regex without escaping (for example, '.' would fail).
	-- Each field has any leading/trailing whitespace removed.
	local t = {}
	text = text .. delimiter  -- to get last item
	for item in text:gmatch('%s*(.-)%s*' .. delimiter) do
		table.insert(t, item)
	end
	return t
end

local function strip(text)
	-- If text is a string, return its content with no leading/trailing
	-- whitespace. Otherwise return nil (a nil argument gives a nil result).
	if type(text) == 'string' then
		return text:match("^%s*(.-)%s*$")
	end
end

local function wanted_category(cat)
	-- Return cat if it is wanted in current namespace, otherwise return nil.
	-- This is so tracking categories only include pages that need correction.
	local title = mw.title.getCurrentTitle()
	if title then
		local nsdefault = '0'  -- default namespace: '0' = article; '0,10' = article and template
		local namespace = title.namespace
		for _, v in ipairs(split(config.nscat or nsdefault, ',')) do
			if namespace == tonumber(v) then
				return cat
			end
		end
	end
end

local function message(mcode)
	-- Return wikitext for an error message, including category if specified
	-- for the message type.
	-- mcode = numbered table specifying the message:
	--    mcode[1] = 'cvt_xxx' (string used as a key to get message info)
	--    mcode[2] = 'parm1' (string to replace first %s if any in message)
	--    mcode[3] = 'parm2' (string to replace second %s if any in message)
	--    mcode[4] = 'parm3' (string to replace third %s if any in message)
	local msg = text_code.all_messages[mcode[1]]
	local nowiki = mw.text.nowiki
	if msg then
		local parts = {}
		local regex, replace = msg.regex, msg.replace
		for i = 1, 3 do
			local limit = 40
			local s = mcode[i + 1]
			if s then
				if regex and replace then
					s = s:gsub(regex, replace)
					limit = nil  -- allow long "should be" messages
				end
				-- Escape user input so it does not break the message.
				-- To avoid reference tags (like {{convert|1<ref>xyz</ref>|m}}) or other tags
				-- breaking the mouseover title, any strip marker starting with char(127) is
				-- replaced with escaped '<ref>...</ref>' or '...' (text not needing i18n).
				local append = ''
				local pos = s:find(string.char(127), 1, true)
				if pos then
					if s:find('-ref-', 1, true) then
						append = '&lt;ref&gt;...&lt;/ref&gt;'
					else
						append = '...'
					end
					s = s:sub(1, pos - 1)
				end
				if limit and ulen(s) > limit then
					s = usub(s, 1, limit)
					if append == '' then
						append = '...'
					end
				end
				s = nowiki(s) .. append
			else
				s = '?'
			end
			parts[i] = s
		end
		local title = format(msg[1] or 'Missing message', parts[1], parts[2], parts[3])
		local text = msg[2] or 'Missing message'
		local cat = wanted_category(text_code.all_categories[msg[3]]) or ''
		local anchor = msg[4] or ''
		local fmt = text_code.all_messages['cvt_format'] or 'convert: bug'
		title = title:gsub('"', '&quot;')
		return format(fmt, anchor, title, text, cat)
	end
	return 'Convert internal error: unknown message'
end

local function add_warning(parms, level, mcode, text)
	-- If enabled, add a warning that will be displayed after the convert result.
	-- To reduce output noise, only the first warning is displayed.
	if config.warnings then
		if level <= (tonumber(config.warnings) or 1) then
			if parms.warnings == nil then
				parms.warnings = message({ mcode, text })
			end
		end
	end
end

local function spell_number(parms, inout, number, numerator, denominator)
	-- Return result of spelling (number, numerator, denominator), or
	-- return nil if spelling is not available or not supported for given text.
	-- Examples (each value must be a string or nil):
	--   number  numerator  denominator  output
	--   ------  ---------  -----------  -------------------
	--   "1.23"    nil        nil        one point two three
	--    "1"      "2"        "3"        one and two thirds
	--    nil      "2"        "3"        two thirds
	if not speller then
		local function get_speller(module)
			return require(module).spell_number
		end
		local success
		success, speller = pcall(get_speller, spell_module)
		if not success or type(speller) ~= 'function' then
			add_warning(parms, 1, 'cvt_no_spell')
			return nil
		end
	end
	local case
	if parms.spell_upper == inout then
		case = true
		parms.spell_upper = nil  -- only uppercase first word in a multiple unit
	end
	local sp = not parms.opt_sp_us
	local adj = parms.opt_adjectival
	return speller(number, numerator, denominator, case, sp, adj)
end

------------------------------------------------------------------------
-- BEGIN: Code required only for built-in units.
-- LATER: If need much more code, move to another module to simplify this module.
local function speed_of_sound(altitude)
	-- This is for the Mach built-in unit of speed.
	-- Return speed of sound in metres per second at given altitude in feet.
	-- If no altitude given, use default (zero altitude = sea level).
	-- Table gives speed of sound in miles per hour at various altitudes:
	--   altitude = -17,499 to 302,499 feet
	-- mach_table[a + 4] = s where
	--   a = (altitude / 5000) rounded to nearest integer (-3 to 60)
	--   s = speed of sound (mph) at that altitude
	-- LATER: Should calculate result from an interpolation between the next
	-- lower and higher altitudes in table, rather than rounding to nearest.
	-- From: http://www.aerospaceweb.org/question/atmosphere/q0112.shtml
	local mach_table = {                                                       -- a =
		799.5, 787.0, 774.2, 761.207051,                                       -- -3 to  0
		748.0, 734.6, 721.0, 707.0, 692.8, 678.3, 663.5, 660.1, 660.1, 660.1,  --  1 to 10
		660.1, 660.1, 660.1, 662.0, 664.3, 666.5, 668.9, 671.1, 673.4, 675.6,  -- 11 to 20
		677.9, 683.7, 689.9, 696.0, 702.1, 708.1, 714.0, 719.9, 725.8, 731.6,  -- 21 to 30
		737.3, 737.7, 737.7, 736.2, 730.5, 724.6, 718.8, 712.9, 707.0, 701.1,  -- 31 to 40
		695.0, 688.9, 682.8, 676.6, 670.4, 664.1, 657.8, 652.9, 648.3, 643.7,  -- 41 to 50
		639.1, 634.4, 629.6, 624.8, 620.0, 615.2, 613.2, 613.2, 613.2, 613.5,  -- 51 to 60
	}
	altitude = altitude or 0
	local a = (altitude < 0) and -altitude or altitude
	a = floor(a / 5000 + 0.5)
	if altitude < 0 then
		a = -a
	end
	if a < -3 then
		a = -3
	elseif a > 60 then
		a = 60
	end
	return mach_table[a + 4] * 0.44704  -- mph converted to m/s
end
-- END: Code required only for built-in units.
------------------------------------------------------------------------

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.types[word] or ranges.types[ranges.aliases[word]]
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_table[field] then
			out_table[field] = in_table[field]
		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
		result[k] = 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.
	__index = function (self, key)
		local value
		if key == 'symbol' then
			local per = self.per
			local unit1, unit2 = per[1], per[2]
			if unit1 then
				value = unit1[key] .. '/' .. unit2[key]
			else
				value = '/' .. unit2[key]
			end
		elseif key == 'sym_us' then
			value = self.symbol
		elseif key == 'scale' then
			local per = self.per
			local unit1, unit2 = per[1], per[2]
			value = (unit1 and unit1.scale or 1) * self.scalemultiplier / unit2.scale
		else
			value = false
		end
		rawset(self, key, value)
		return value
	end
}

local function lookup(unitcode, opt_sp_us, 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 opt_sp_us is true for US spelling of SI prefixes and
	-- the symbol and name of the unit. If true, the result includes field
	-- sp_us = true (that field may also have been in the unit definition).
	-- 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 {{convert|350|board_feet}} works.
	-- Wikignomes may also put two spaces or "&nbsp;" in combinations, so
	-- replace underscore, "&nbsp;", and multiple spaces with a single space.
	utable = utable 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('&nbsp;', ' '):gsub('  +', ' ')
	local t = utable[unitcode]
	if t then
		if t.shouldbe then
			return false, { 'cvt_should_be', t.shouldbe }
		end
		local force_sp_us = opt_sp_us
		if t.sp_us then
			force_sp_us = true
			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(target, opt_sp_us, 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
		local per = t.per  -- nil/false, or a numbered table for "x/y" units
		if per then
			local result = { utype = t.utype, per = {} }
			result.scalemultiplier = t.multiplier or 1
			override_from(result, t, { 'invert', 'iscomplex', 'default', 'link', 'symbol', 'symlink' })
			result.symbol_raw = (result.symbol or false)  -- to distinguish between a defined exception and a metatable calculation
			local cvt = result.per
			local prefix
			for i, v in ipairs(per) do
				if i == 1 and text_code.currency[v] then
					prefix = v
				else
					local success, t = lookup(v, opt_sp_us, 'no_combination', utable, fails, depth)
					if not success then return false, t end
					cvt[i] = t
					if t.sp_us then  -- if the top or bottom unit forces sp=us, set the per unit to use the correct name/symbol
						force_sp_us = true
					end
				end
			end
			if prefix then
				result.vprefix = prefix
			else
				result.vprefix = false  -- to avoid calling __index
			end
			result.sp_us = force_sp_us
			return true, setmetatable(result, unit_per_mt)
		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(v, opt_sp_us, multiple and 'no_combination' or 'only_multiple', utable, fails, depth)
				if not success then return false, t end
				cvt[i] = t
			end
			return true, result
		end
		local result = shallow_copy(t)
		result.sp_us = force_sp_us
		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 = SIprefixes[1] or 2, 1, -1 do
		-- Look for an SI prefix; should never occur with an alias.
		-- Check for longer prefix first ('dam' is decametre).
		-- SIprefixes[1] = prefix maximum #characters (as seen by mw.ustring.sub).
		local prefix = usub(unitcode, 1, plen)
		local si = SIprefixes[prefix]
		if si then
			local t = utable[usub(unitcode, plen+1)]
			if t and t.prefixes then
				local result = shallow_copy(t)
				if opt_sp_us then
					result.sp_us = true
				end
				if result.sp_us and si.name_us then
					result.si_name = si.name_us
				else
					result.si_name = si.name
				end
				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 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 has_plus = unitcode:find('+', 1, true)
	if not has_plus then
		local exponent, baseunit = unitcode:match('^e(%d+)(.*)')
		if exponent then
			local engscale = text_code.eng_scales[exponent]
			if engscale then
				local success, result = lookup(baseunit, opt_sp_us, 'no_combination', utable, fails, depth)
				if not success then return false, result end
				if not (result.offset or result.builtin or result.engscale) then
					result.defkey = unitcode  -- key to lookup default exception
					result.engscale = engscale
					result.scale = result.scale * 10 ^ tonumber(exponent)
					return true, result
				end
			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 has_plus 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(v, opt_sp_us, '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
				cvt[i] = t
			end
			return true, result
		end
		local success, result = lookup_combo()
		if success or err_is_fatal then
			return success, result
		end
	end
	if not get_range(unitcode) then  -- do not require extra 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 fails[unitcode] then
				fails[unitcode] = true
				local other = (utable == all_units) and extra_units or all_units
				local success, result = lookup(unitcode, opt_sp_us, 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(en_code, opt_sp_us, 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 ntsh(num, debug)
	-- Return html text to be used for a hidden sort key so that
	-- the given number will be sorted in numeric order.
	-- If debug == true, output is in a box (not hidden).
	-- This implements Template:Ntsh (number table sorting, hidden).
	local result, style
	if not valid_number(num) then
		if num < 0 then
			result = '1000000000000000000'
		else
			result = '9000000000000000000'
		end
	elseif num == 0 then
		result = '5000000000000000000'
	else
		local mag = floor(log10(abs(num)) + 1e-14)
		local prefix
		if num > 0 then
			prefix = 7000 + mag
		else
			prefix = 2999 - mag
			num = num + 10^(mag+1)
		end
		result = format('%d', prefix) .. format('%015.0f', floor(num * 10^(14-mag)))
	end
	if debug then
		style = 'border:1px solid'
	else
		style = 'display:none'
	end
	return '<span style="' .. style .. '">' .. result .. '</span>'
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:
	--   [[long ton|ton]]         →  [[long ton|ton]]          (no change)
	--   [[tonne|long ton]]       →  [[tonne|long-ton]]
	--   [[metric ton|long ton]]  →  [[metric ton|long-ton]]
	--   [[long ton]]             →  [[long ton|long-ton]]
	-- Input can also have multiple links in a single name like:
	--   [[United States customary units|U.S.]] [[US gallon|gallon]]
	--   [[mile]]s per [[United States customary units|U.S.]] [[quart]]
	--   [[long ton]]s per [[short ton]]
	-- Assume that links cannot be nested (never like "[[abc[[def]]ghi]]").
	-- 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&nbsp;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, -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('([^[]*)(%[%[[^[]*%]%])([^[]*)') do
			if item:find(' ', 1, true) then
				local prefix
				local plen = item:find('|', 1, true)
				if plen then
					prefix = item:sub(1, plen)
					item = item:sub(plen + 1, -3)
				else
					prefix = item:sub(1, -3) .. '|'
					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 change_sign(text)
	-- Change sign of text for correct appearance because it is negated.
	if text:sub(1, 1) == '-' then
		return text:sub(2)
	end
	return '-' .. text
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_grouper(method, gaps)
	-- Return a table to hold groups of digits which can be joined with
	-- suitable separators (such as commas).
	-- Each group is separately translated to the local language because
	-- gap separators include digits which should not be translated.
	-- Parameter method is a number or nil:
	--   3 for 3-digit grouping, or
	--   2 for 3-then-2 grouping.
	-- Parameter gaps is true to use <span> gaps (numsep ignored).
	return {
		n = 0,
		add = function (self, digits)
			self.n = self.n + 1
			self[self.n] = from_en(digits)
		end,
		join = function (self, rhs)
			-- Concatenate in reverse order.
			if gaps then
				local result = ''
				for i = 1, self.n - 1 do
					result = '<span style="margin-left: 0.25em">' .. self[i] .. '</span>' .. result
				end
				return '<span style="white-space: nowrap">' .. self[self.n] .. result .. from_en(rhs) .. '</span>'
			else
				local result = self[1]
				for i = 2, self.n do
					result = self[i] .. numsep .. result
				end
				return result .. from_en(rhs)
			end
		end,
		step = 3,
		next_position = function (self, previous)
			-- Return position of digit just before next group.
			-- Digits are grouped from right-to-left (least significant first).
			local result = previous - self.step
			if method == 2 then
				self.step = 2
			end
			return (result < 0) and 0 or result
		end,
	}
end

local function with_separator(parms, text)
	-- Input text is a number in en digits and optional '.' decimal mark.
	-- Return an equivalent of text, 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 '12345.6789' or '1.23e45'
	-- (e notation can only occur when processing an input value).
	-- The text has no sign (caller inserts that later, if necessary).
	-- Separator is inserted only in the integer part of the significand
	-- (not after the decimal mark, and not after 'e' or 'E').
	if parms.opt_nocomma or numsep == '' then
		return from_en(text)
	end
	local last = text:match('()[.eE]')  -- () returns position
	if last == nil then
		last = #text
	else
		last = last - 1  -- index of last character before dot/e/E
	end
	if last < 4 or (last == 4 and parms.opt_comma5) then
		return from_en(text)
	end
	local groups = digit_grouper(group_method, parms.opt_gaps)
	local i = last
	while i > 0 do
		local position = groups:next_position(i)
		groups:add(text:sub(position+1, i))
		i = position
	end
	return groups:join(text:sub(last+1))
end

-- Input values can use values like 1.23e12, but are never displayed
-- using scientific notation like 1.23×10¹².
-- Very small or very large output values use scientific notation.
-- Use format(fmtpower, significand, '10', exponent) where each arg is a string.
local fmtpower = '%s<span style="margin:0 .15em 0 .25em">×</span>%s<sup>%s</sup>'

local function with_exponent(show, exponent)
	-- Return wikitext to display the implied value in scientific notation.
	-- Input uses en digits; output uses digits in local language.
	if #show > 1 then
		show = show:sub(1, 1) .. '.' .. show:sub(2)
	end
	return format(fmtpower, from_en(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 <= 0 then
		sigfig = 1
	elseif 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 {{frac}} (fraction slash).
		-- 1/2    : sign, numerator, denominator
		-- 1+2/3  : signed_wholenumber, numerator, denominator
		'<span class="frac nowrap">%s<sup>%s</sup>&frasl;<sub>%s</sub></span>',
		'<span class="frac nowrap">%s<span class="visualhide">&nbsp;</span><sup>%s</sup>&frasl;<sub>%s</sub></span>',
	},
	{ -- Like {{sfrac}} (fraction horizontal bar).
		-- 1//2   : sign, numerator, denominator (sign should probably be before the fraction, but then it can wrap, and html is already too long)
		-- 1+2//3 : signed_wholenumber, numerator, denominator
		'<span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%%; text-align:center;"><span style="display:block; line-height:1em; padding:0 0.1em;">%s%s</span><span class="visualhide">/</span><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">%s</span></span>',
		'<span class="sfrac nowrap">%s<span class="visualhide">&nbsp;</span><span style="display:inline-block; vertical-align:-0.5em; font-size:85%%; text-align:center;"><span style="display:block; line-height:1em; padding:0 0.1em;">%s</span><span class="visualhide">/</span><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">%s</span></span></span>',
	},
}

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
	if wholestr then
		local decorated = with_separator(parms, wholestr)
		if negative then
			decorated = MINUS .. decorated
		end
		local fmt = fracfmt[style][2]
		wikitext = format(fmt, decorated, from_en(numstr), from_en(denstr))
	else
		local sign = negative and MINUS or ''
		wikitext = format(fracfmt[style][1], sign, from_en(numstr), from_en(denstr))
	end
	if do_spell then
		if negative then
			if wholestr then
				wholestr = '-' .. wholestr
			else
				numstr = '-' .. numstr
			end
		end
		wikitext = spell_number(parms, inout, wholestr, numstr, denstr) or wikitext
	end
	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 for very small or large values
	--   (which forces output to not be spelled).
	-- * Has no more than maxsigfig significant digits
	--   (same as old template and {{#expr}}).
	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 >= 10 then
			show = integer .. decimals
			exponent = #integer
		elseif 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 >= 4 then
				show = figs
				exponent = -#zeros
			elseif #figs > maxlen then
				show = '0.' .. zeros .. figs:sub(1, maxlen)
			end
		else
			maxlen = maxlen + #dot
			if #show > maxlen then
				show = show:sub(1, maxlen)
			end
		end
	end
	if exponent then
		if #show > maxlen then
			show = show:sub(1, maxlen)
		end
		if exponent > 10 or exponent <= -4 or (exponent == 10 and show ~= '1000000000') then
			-- Rounded value satisfies: value >= 1e9 or value < 1e-4 (1e9 = 0.1e10).
			return {
				clean = '.' .. show,
				exponent = exponent,
				sign = sign,
				show = sign .. with_exponent(show, exponent-1),
				is_scientific = true,
			}
		end
		if exponent >= #show then
			show = show .. string.rep('0', exponent - #show)  -- result has no dot
		elseif exponent <= 0 then
			show = '0.' .. string.rep('0', -exponent) .. show
		else
			show = show:sub(1, exponent) .. '.' .. show:sub(exponent+1)
		end
	end
	local formatted_show
	if tfrac then
		show = tostring(tfrac.value)  -- to set clean in returned table
		formatted_show = format_fraction(parms, 'out', isnegative, tfrac.wholestr, tfrac.numstr, tfrac.denstr, parms.opt_spell_out)
	else
		if isnegative and show:match('^0.?0*$') then
			sign = ''  -- don't show minus if result is negative but rounds to zero
		end
		formatted_show = sign .. with_separator(parms, show)
		if parms.opt_spell_out then
			formatted_show = spell_number(parms, 'out', sign .. show) or formatted_show
		end
	end
	return {
		clean = show,
		sign = sign,
		show = formatted_show,
		is_scientific = false,  -- to avoid calling __index
	}
end

local function extract_fraction(parms, text, negative)
	-- If text represents a fraction, return
	--   value, altvalue, show, spelled, denominator
	-- where
	--   value is a number (value of the fraction in argument text)
	--   altvalue is an alternate interpretation of any fraction for the hands
	--        unit where "14.1+3/4" means 14 hands 1.75 inches!
	--   show is a string (formatted text for display of an input value,
	--        and is spelled if wanted and possible)
	--   spelled is true if show was spelled
	--   denominator is value of the denominator in the fraction
	-- Otherwise, return nil.
	-- Input uses en digits and '.' decimal mark (input has been translated).
	-- Output uses digits in local language and custom decimal mark, if any.
	--
	-- In the following, '(3/8)' represents the wikitext required to
	-- display a fraction with numerator 3 and denominator 8.
	-- In the wikitext, Unicode minus is used for a negative value.
	--   text          value, show            value, show
	--                 if not negative       if negative
	--   3 / 8         0.375, '(3/8)'        -0.375, '−(3/8)'
	--   2 + 3 / 8     2.375, '2(3/8)'       -1.625, '−2(−3/8)'
	--   2 - 3 / 8     1.625, '2(−3/8)'      -2.375, '−2(3/8)'
	--   1 + 20/8      3.5  , '1/(20/8)'     1.5   , '−1/(−20/8)'
	--   1 - 20/8      -1.5., '1(−20/8)'     -3.5  , '−1(20/8)'
	-- Wherever an integer appears above, numbers like 1.25 or 12.5e-3
	-- (which may be negative) are also accepted (like old template).
	-- Old template interprets '1.23e+2+12/24' as '123(12/24)' = 123.5!
	local numstr, whole, value, altvalue
	local lhs, slash, denstr = text:match('^%s*([^/]-)%s*(/+)%s*(.-)%s*$')
	local denominator = tonumber(denstr)
	if denominator == nil then return nil end
	local wholestr, negfrac, rhs = lhs:match('^%s*(.-[^eE])%s*([+-])%s*(.-)%s*$')
	if wholestr == nil or wholestr == '' then
		wholestr = nil
		whole = 0
		numstr = lhs
	else
		whole = tonumber(wholestr)
		if whole == nil then return nil end
		numstr = rhs
	end
	negfrac = (negfrac == '-')
	local numerator = tonumber(numstr)
	if numerator == nil then return nil end
	-- Spelling of silly inputs like "-2+3/8" or "2+3/+8" (mixed or excess signs) is not supported.
	local do_spell
	if negative == negfrac or wholestr == nil then
		value = whole + numerator / denominator
		altvalue = whole + numerator / (denominator * 10)
		do_spell = parms.opt_spell_in
		if do_spell then
			if not (numstr:match('^%d') and denstr:match('^%d')) then  -- if either has a sign
				do_spell = false
			end
		end
	else
		value = whole - numerator / denominator
		altvalue = whole - numerator / (denominator * 10)
		numstr = change_sign(numstr)
		do_spell = false
	end
	if not valid_number(value) then
		return nil  -- overflow or similar
	end
	numstr = use_minus(numstr)
	denstr = use_minus(denstr)
	local style = #slash  -- kludge: 1 or 2 slashes can be used to select style
	if style > 2 then style = 2 end
	local wikitext = format_fraction(parms, 'in', negative, wholestr, numstr, denstr, do_spell, style)
	return value, altvalue, wikitext, do_spell, 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.
	-- 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 (and optional following whitespace) 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 (to use singular form of units)
	--            = false if value is -1 (like old template)
	--   clean    = cleaned text with any separators and sign removed
	--              (en digits and '.' decimal mark)
	--   show     = text formatted for output
	--              (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 clean = to_en(text)
	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 then
			isnegative = true
			value = -value
		end
	else
		local valstr
		for _, prefix in ipairs({ '-', MINUS, '&minus;' }) do
			-- Including '-' means inputs like '- 2' (with space) are accepted as -2.
			-- It also sets isnegative in case input is a fraction like '-2-3/4'.
			local plen = #prefix
			if clean:sub(1, plen) == prefix then
				valstr = clean:sub(plen + 1)
				break
			end
		end
		if valstr then
			isnegative = true
			propersign = MINUS
			clean = valstr
			value = tonumber(clean)
		end
		if value == nil then
			local spelled
			if not no_fraction then
				value, altvalue, show, spelled, denominator = extract_fraction(parms, clean, isnegative)
			end
			if value == nil then
				return false, { 'cvt_bad_num', text }
			end
			if value <= 1 then
				singular = true  -- for example, "½ mile" or "one half mile" (singular unit)
			end
		end
	end
	if not valid_number(value) then  -- for example, "1e310" may overflow
		return false, { 'cvt_invalid_num' }
	end
	if show == nil then
		singular = (value == 1 and not isnegative)
		local precision = parms.input_precision
		if precision and 0 <= precision and precision <= 8 then
			local fmt = '%.' .. format('%d', precision) .. 'f'
			show = fmt:format(value + 2e-14)  -- fudge for some common cases of bad rounding
		else
			show = clean
		end
		show = propersign .. with_separator(parms, show)
		if parms.opt_spell_in then
			show = spell_number(parms, 'in', propersign .. clean) or show
		end
	end
	local altvalue = altvalue or value
	if isnegative and (value ~= 0) then
		value = -value
		altvalue = -altvalue
	end
	return true, {
		value = value,
		altvalue = altvalue,
		singular = singular,
		clean = clean,
		show = show,
		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 integer, 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 <= 0 then
		return b
	end
	local r = b % a
	if r <= 0 then
		return a
	end
	if r == 1 then
		return 1
	end
	return gcd(r, a)
end

local function fraction_table(value, denominator)
	-- Return value as a string or a table:
	-- * If result is a string, there is no fraction, and the result
	--   is value formatted as a string of en digits.
	-- * If result is a table, it represents a fraction with named fields:
	--   wholestr, numstr, denstr (strings of en digits for integer, numerator, denominator).
	-- The result is rounded to the nearest multiple of (1/denominator).
	-- If the multiple is zero, no fraction is included.
	-- No fraction is included if value is very large as the fraction would
	-- be unhelpful, particularly if scientific notation is required.
	-- Input value is a non-negative number.
	-- Input denominator is a positive integer for the desired fraction.
	if value <= 0 then
		return '0'
	end
	if denominator <= 0 or value > 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 preceding space).
	local function withspace(text, i)
		-- Insert space at beginning if i == 1, or at end if i == -1.
		-- However, no space is inserted if there is a space or '&nbsp;'
		-- or '-' at that position ('-' is for adjectival text).
		local current = text:sub(i, i)
		if current == ' ' or current == '-' then
			return text
		end
		if i == 1 then
			current = text:sub(1, 6)
		else
			current = text:sub(-6, -1)
		end
		if current == '&nbsp;' then
			return text
		end
		if i == 1 then
			return ' ' .. text
		end
		return text .. ' '
	end
	preunit1 = preunit1 or ''
	local trim1 = strip(preunit1)
	if count == 1 then
		if trim1 == '' then
			return nil
		end
		return withspace(withspace(preunit1, 1), -1)
	end
	preunit2 = preunit2 or ''
	local trim2 = strip(preunit2)
	if trim1 == '' and trim2 == '' then
		return nil, nil
	end
	if trim1 ~= '+' then
		preunit1 = withspace(preunit1, 1)
	end
	if trim2 == '&#32;' then  -- trick to make preunit2 empty
		preunit2 = nil
	elseif trim2 == '' then
		preunit2 = preunit1
	elseif trim2 ~= '+' then
		preunit2 = withspace(preunit2, 1)
	end
	return preunit1, preunit2
end

local function range_text(range, want_name, parms, before, after)
	-- 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 abbr=off and for abbr=on,
		-- and may specify range text for 'adj=on',
		-- and may specify exception = true.
		rtext = range[want_name and 'off' or 'on']
		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('&nbsp;', '-')
		end
	end
	if rtext == '–' and after:sub(1, #MINUS) == MINUS then
		rtext = '&nbsp;– '
	end
	return before .. rtext .. after
end

local function get_composite(parms, iparm, total, in_unit_table)
	-- Look for a composite input unit. For example, "{{convert|1|yd|2|ft|3|in}}"
	-- would result in a call to this function with
	--   iparm = 3 (parms[iparm] = "2", just after the first unit)
	--   total = 1 (number of yards)
	--   in_unit_table = (unit table for "yd")
	-- 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 subunit = in_unit_table
	while subunit.subdivs do  -- subdivs is nil or a table of allowed subdivisions
		local subcode = strip(parms[iparm+1])
		local subdiv = subunit.subdivs[subcode]
		if not subdiv then
			break
		end
		local success
		success, subunit = lookup(subcode, parms.opt_sp_us, 'no_combination')
		if not success then return false, subunit end  -- should never occur
		success, subinfo = extract_number(parms, parms[iparm])
		if not success then return false, subinfo end
		iparm = iparm + 2
		subunit.inout = 'in'
		subunit.valinfo = { subinfo }
		-- Recalculate total as a number of subdivisions.
		-- subdiv[1] = number of subdivisions per previous unit (integer > 1).
		total = total * subdiv[1] + subinfo.value
		if not default then  -- set by the first subdiv with a default defined
			default = subdiv.default
		end
		count = count + 1
		composite_units[count] = subunit
		if subdiv.unit or subdiv.name then
			fixups[count] = { 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_units[i].fixed_name = name
		else
			local success, alternate = lookup(unit, parms.opt_sp_us, 'no_combination')
			if not success then return false, alternate end  -- should never occur
			alternate.inout = 'in'
			alternate.valinfo = fixup.valinfo
			composite_units[i] = 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.
	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
	for loc_name, loc_value in pairs(kv_pairs) do
		local en_name = text_code.en_option_name[loc_name]
		if en_name then
			local en_value
			if en_name == 'frac' or en_name == 'sigfig' then
				if loc_value == '' then
					add_warning(parms, 2, 'cvt_empty_option', loc_name)
				else
					local minimum
					local number, is_integer = get_number(loc_value)
					if en_name == 'frac' then
						minimum = 2
						if number and number < 0 then
							parms.opt_fraction_horizontal = true
							number = -number
						end
					else
						minimum = 1
					end
					if number and is_integer and number >= minimum then
						en_value = number
					else
						add_warning(parms, 1, (en_name == 'frac' and 'cvt_bad_frac' or 'cvt_bad_sigfig'), loc_value)
					end
				end
			else
				en_value = text_code.en_option_value[en_name][loc_value]
				if en_value == nil then
					if loc_value == '' then
						add_warning(parms, 2, 'cvt_empty_option', loc_name)
					else
						-- loc_value can no longer be nil here (at one time, that could occur
						-- with aliases like |sing=off|adj=on), but am retaining safety check.
						local text = loc_value and (loc_name .. '=' .. loc_value) or loc_name
						add_warning(parms, 1, 'cvt_unknown_option', text)
					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
						parms[v] = true
					end
					en_value = nil
				end
			end
			parms[en_name] = en_value
		else
			add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)
		end
	end
	if parms.adj then
		if parms.adj:sub(1, 2) == 'ri' then
			-- It is known that adj is 'riN' where N is a single digit, so precision is valid.
			-- Only a single en digit is accepted.
			parms.input_precision = tonumber(parms.adj:sub(-1))
			parms.adj = nil
		end
	end
	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
		parms.abbr_org = parms.abbr  -- original abbr that was set, 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_flip then
		local function swap_in_out(option)
			local value = parms[option]
			if value == 'in' then
				parms[option] = 'out'
			elseif value == 'out' then
				parms[option] = '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 parms.abbr_org == nil and parms.lk == nil then
			parms.opt_values = true
		end
		local align = format('align="%s"', parms.opt_table and 'right' or 'center')
		parms.table_joins = { align .. '|', '\n|' .. align .. '|' }
	end
	if parms.opt_lang_en then
		from_en_table = nil
	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(parms[2])
	if parm2 and parm2:sub(-7, -1) == 'nocomma' then
		parms[2] = 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.
		-- Unpacked items are inserted into the parms table.
		local valstr = strip(parms[i])  -- 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 < 20 then  -- check i to limit abuse
			for _, sep in ipairs(text_code.ranges.words) do
				local start, stop = valstr:find(sep, 2, true)  -- start at 2 to skip any negative sign for range '-'
				if start then
					parms[i] = valstr:sub(stop + 1)
					table.insert(parms, i, sep)
					table.insert(parms, i, valstr:sub(1, start - 1))
					return extractor(i)  -- this allows combinations like "1 x 2 to 3 x 4"
				end
			end
		end
		return success, result
	end
	local i = 1
	local is_change
	while true do
		local success, info = extractor(i)  -- need to set parms.opt_nocomma before calling this
		if not success then return false, info end
		i = i + 1
		if is_change then
			info.is_change = true  -- value is after "±" and so is a change (significant for range like {{convert|5|±|5|°C}})
			is_change = nil
		end
		valinfo:add(info)
		local next = strip(parms[i])
		local range_item = get_range(next)
		if not range_item then
			break
		end
		i = i + 1
		range:add(range_item)
		if type(range_item) == 'table' then
			parms.is_range_x = range_item.is_range_x
			is_change = range_item.is_range_change
		end
	end
	if range.n > 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 "{{convert|valid_value|valid_unit|...}}",
	-- return true, v, 3, in_unit, in_unit_table
	-- (as for get_values(), but with a unit name and table for a valid unit;
	-- 3 = index in parms of whatever 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 and caller will reparse the input.
	-- Testing shows this function is successful for 96% of converts in articles,
	-- and that on average it speeds up converts by 8%.
	if parms.input_precision or parms.opt_spell_in then return end
	local clean = to_en(strip(parms[1] or ''))
	if #clean > 10 or not clean:match('^[0-9.]+$') then return 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(parms[2])
	local success, in_unit_table = lookup(in_unit, parms.opt_sp_us, 'no_combination')
	if not success then return end
	return true, { info }, 3, in_unit, in_unit_table
end

local function get_parms(pframe)
	-- If successful, return true, parms, 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.
	-- 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 parms = {}  -- arguments passed to template, after translation
	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(pframe.args) do
		if type(k) == 'number' or k == 'test' then  -- parameter "test" is reserved for testing and is not translated
			parms[k] = v
		else
			kv_pairs[k] = v
		end
	end
	local success, msg = translate_parms(parms, kv_pairs)
	if not success then return false, msg end
	local success, valinfo, i, in_unit, in_unit_table = simple_get_values(parms)
	if not success then
		success, valinfo, i = get_values(parms)
		if not success then return false, valinfo end
		in_unit = strip(parms[i])
		i = i + 1
		success, in_unit_table = lookup(in_unit, parms.opt_sp_us, 'no_combination')
		if not success then
			if in_unit == nil then
				in_unit = ''
			end
			if parms.opt_ignore_error then  -- display given unit code with no error (for use with {{val}})
				in_unit_table = ''  -- suppress error message and prevent processing of output unit
			end
			in_unit_table = setmetatable({ symbol = in_unit, name2 = in_unit,
				default = "m", defkey = "m", linkey = "m",
				utype = "length", scale = 1, bad_mcode = in_unit_table }, unit_mt)
		end
	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.valinfo = valinfo
	in_unit_table.inout = 'in'  -- this is an input unit
	if not parms.range then
		local success, inext, composite_unit = get_composite(parms, i, valinfo[1].value, 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, parms[i], false, true)
		if success then
			i = i + 1
			in_unit_table.altitude = info.value
		end
	end
	local next = strip(parms[i])
	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 not set_precision(next) then
		parms.out_unit = next
		if set_precision(strip(parms[i])) then
			i = i + 1
		end
	end
	if parms.opt_adj_mid then
		next = parms[i]
		i = i + 1
		if next then  -- mid-text words
			if next:sub(1, 1) == '-' then
				parms.mid = next
			else
				parms.mid = ' ' .. next
			end
		end
	end
	if parms.opt_one_preunit then
		parms[parms.opt_flip and 'preunit2' or 'preunit1'] = preunits(1, parms[i])
		i = i + 1
	end
	if parms.disp == 'x' then
		-- Following is reasonably compatible with the old template.
		local first = parms[i] or ''
		local second = parms[i+1] or ''
		i = i + 2
		if strip(first) == '' then  -- user can enter '&#32;' rather than ' ' to avoid the default
			first = ' [&nbsp;' .. first
			second = '&nbsp;]' .. second
		end
		parms.joins = { first, second }
	elseif parms.opt_two_preunits then
		local p1, p2 = preunits(2, parms[i], parms[i+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(parms[i])) then
			i = i + 1
		end
	end
	if is_bad_precision then
		add_warning(parms, 1, 'cvt_bad_prec', precision)
	else
		parms.precision = precision
	end
	return true, parms, 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 < precision then
				parms.do_convert_again = true
				out_current.max_default_precision = precision
			else
				precision = out_current.max_default_precision
			end
		else
			out_current.max_default_precision = precision
		end
	end
	return precision
end

local function default_precision(parms, invalue, inclean, denominator, outvalue, in_current, out_current, extra)
	-- Return a default value for precision (an integer like 2, 0, -2).
	-- If denominator is not nil, it is the value of the denominator in inclean.
	-- Code follows procedures used in old template.
	local fudge = 1e-14  -- {{Order of magnitude}} adds this, so we do too
	local prec, minprec, adjust
	local utype = out_current.utype
	local subunit_ignore_trailing_zero
	local subunit_more_precision  -- kludge for "in" used in input like "|2|ft|6|in"
	local composite = in_current.composite
	if composite then
		subunit_ignore_trailing_zero = true  -- input "|2|st|10|lb" has precision 0, not -1
		if composite[#composite].exception == 'subunit_more_precision' then
			subunit_more_precision = true  -- do not use standard precision with input like "|2|ft|6|in"
		end
	end
	if denominator and denominator > 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, MK.
		-- 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 < 1e-8 then  -- assume nonzero due to input or calculation precision problem
			minprec = 2
		else
			minprec = 2 - floor(log10(kelvin) + fudge)  -- 3 sigfigs in kelvin
		end
	else
		if invalue == 0 or outvalue <= 0 then
			-- We are never called with a negative outvalue, but it might be zero.
			-- This is special-cased to avoid calculation exceptions.
			return record_default_precision(parms, out_current, 0)
		end
		if out_current.exception == 'integer_more_precision' and floor(invalue) == invalue then
			-- With certain output units that sometimes give poor results
			-- with default rounding, use more precision when the input
			-- value is equal to an integer. An example of a poor result
			-- is when input 50 gives a smaller output than input 49.5.
			-- Experiment shows this helps, but it does not eliminate all
			-- surprises because it is not clear whether "50" should be
			-- interpreted as "from 45 to 55" or "from 49.5 to 50.5".
			adjust = -log10(in_current.scale)
		elseif subunit_more_precision then
			-- Conversion like "{{convert|6|ft|1|in|cm}}" (where subunit is "in")
			-- has a non-standard adjust value, to give more output precision.
			adjust = log10(out_current.scale) + 2
		else
			adjust = log10(abs(invalue / outvalue))
		end
		adjust = adjust + log10(2)
		-- Ensure that the output has at least two significant figures.
		minprec = 1 - floor(log10(outvalue) + fudge)
	end
	if extra then
		adjust = extra.adjust or adjust
		minprec = extra.minprec or minprec
	end
	return record_default_precision(parms, out_current, math.max(floor(prec + adjust), minprec))
end

local function convert(parms, invalue, info, in_current, out_current)
	-- Convert given input value from one unit to another.
	-- Return output_value (a number) if a simple convert, or
	-- return f, t where
	--   f = true, t = table of information with results, or
	--   f = false, t = error message table.
	local inscale = in_current.scale
	local outscale = out_current.scale
	if not in_current.iscomplex and not out_current.iscomplex then
		return invalue * (inscale / outscale)  -- minimize overhead for most common case
	end
	if in_current.invert or out_current.invert then
		-- Inverted units, such as inverse length, inverse time, or
		-- fuel efficiency. Built-in units do not have invert set.
		if (in_current.invert or 1) * (out_current.invert or 1) < 0 then
			return 1 / (invalue * inscale * outscale)
		end
		return invalue * (inscale / outscale)
	elseif in_current.offset then
		-- Temperature (there are no built-ins for this type of unit).
		if info.is_change then
			return invalue * (inscale / outscale)
		end
		return (invalue - in_current.offset) * (inscale / outscale) + out_current.offset
	else
		-- Built-in unit.
		local in_builtin = in_current.builtin
		local out_builtin = out_current.builtin
		if in_builtin and out_builtin then
			if in_builtin == out_builtin then
				return invalue
			end
			-- There are no cases (yet) where need to convert from one
			-- built-in unit to another, so this should never occur.
			return false, { 'cvt_bug_convert' }
		end
		if in_builtin == 'mach' or out_builtin == 'mach' then
			local adjust
			if in_builtin == 'mach' then
				inscale = speed_of_sound(in_current.altitude)
				adjust = outscale / 0.1
			else
				outscale = speed_of_sound(out_current.altitude)
				adjust = 0.1 / inscale
			end
			return true, {
				outvalue = invalue * (inscale / outscale),
				adjust = log10(adjust) + log10(2),
			}
		elseif in_builtin == 'hand' then
			-- 1 hand = 4 inches; 1.2 hands = 6 inches.
			-- Decimals of a hand are only defined for the first digit, and
			-- the first fractional digit should be a number of inches (1, 2 or 3).
			-- However, this code interprets the entire fractional part as the number
			-- of inches / 10 (so 1.75 inches would be 0.175 hands).
			-- A value like 12.3 hands is exactly 12*4 + 3 inches; base default precision on that.
			local integer, fracpart = math.modf(invalue)
			local inch_value = 4 * integer + 10 * fracpart  -- equivalent number of inches
			local factor = inscale / outscale
			if factor == 4 then
				-- Am converting to inches: show exact result, and use "inches" not "in" by default.
				if parms.abbr_org == nil then
					out_current.usename = true
				end
				local show = format('%g', abs(inch_value))  -- show and clean are unsigned
				if not show:find('e', 1, true) then
					return true, {
						invalue = inch_value,
						outvalue = inch_value,
						clean = show,
						show = show,
					}
				end
			end
			local outvalue = (integer + 2.5 * fracpart) * factor
			local fracstr = info.clean:match('%.(.*)') or ''
			local fmt
			if fracstr == '' then
				fmt = '%.0f'
			else
				fmt = '%.' .. format('%d', #fracstr - 1) .. 'f'
			end
			return true, {
				invalue = inch_value,
				clean = format(fmt, inch_value),
				outvalue = outvalue,
				minprec = 0,
			}
		end
	end
	return false, { 'cvt_bug_convert' }  -- should never occur
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 is positive, and (after rounding)
	--      is "1", or like "1.00";
	--   (and more fields shown below, and a calculated 'absvalue' field).
	-- or return true, nil if no value specified;
	-- or return false, t where t is an error message table.
	-- Input info.clean uses en digits (it has been translated, if necessary).
	-- Output show uses en or non-en digits as appropriate, or can be spelled.
	local invalue
	if info then
		invalue = info.value
		if in_current.builtin == 'hand' then
			invalue = info.altvalue
		end
	end
	if invalue == nil or invalue == '' then
		return true, nil
	end
	if out_current.builtin == 'hand' then
		return cvt_to_hand(parms, info, in_current, out_current)
	end
	local outvalue, extra = convert(parms, invalue, info, in_current, out_current)
	if extra then
		if not outvalue then return false, extra end
		invalue = extra.invalue or invalue
		outvalue = extra.outvalue
	end
	if not valid_number(outvalue) then
		return false, { 'cvt_invalid_num' }
	end
	local isnegative
	if outvalue < 0 then
		isnegative = true
		outvalue = -outvalue
	end
	local numerator, precision, success, show, exponent
	local denominator = out_current.frac
	if denominator then
		show = fraction_table(outvalue, denominator)
	else
		precision = parms.precision
		if not precision then
			local sigfig = parms.sigfig
			if sigfig then
				show, exponent = make_sigfig(outvalue, sigfig)
			elseif parms.opt_round5 or parms.opt_round25  then
				local n = parms.opt_round5 and 5 or 25
				show = format('%.0f', floor((outvalue / n) + 0.5) * n)
			else
				local inclean = info.clean
				if extra then
					inclean = extra.clean or inclean
					show = extra.show
				end
				if not show then
					precision = default_precision(parms, invalue, inclean, info.denominator, outvalue, in_current, out_current, extra)
				end
			end
		end
	end
	if precision then
		if precision >= 0 then
			local fudge
			if precision <= 8 then
				-- Add a fudge to handle common cases of bad rounding due to inability
				-- to precisely represent some values. This makes the following work:
				-- {{convert|-100.1|C|K}} and {{convert|5555000|um|m|2}}.
				-- Old template uses #expr round, which invokes PHP round().
				-- LATER: Investigate how PHP round() works.
				fudge = 2e-14
			else
				fudge = 0
			end
			local fmt = '%.' .. format('%d', precision) .. 'f'
			local success
			success, show = pcall(format, fmt, outvalue + fudge)
			if not success then
				return false, { 'cvt_big_prec', tostring(precision) }
			end
		else
			precision = -precision  -- #digits to zero (in addition to any digits after dot)
			local shift = 10 ^ precision
			show = format('%.0f', outvalue/shift)
			if show ~= '0' then
				exponent = #show + precision
			end
		end
	end
	local t = format_number(parms, show, exponent, isnegative)
	-- Set singular using match because on some systems 0.99999999999999999 is 1.0.
	t.singular = (type(show) == 'string' and (show == '1' or show:match('^1%.0*$') ~= nil) and not isnegative)
	t.fraction_table = (type(show) == 'table') and show or nil
	t.raw_absvalue = outvalue  -- absolute value before rounding
	return true, setmetatable(t, {
		__index = function (self, key)
			if key == 'absvalue' then
				-- Calculate absolute value after rounding, if needed.
				local clean, exponent = rawget(self, 'clean'), rawget(self, 'exponent')
				local value = tonumber(clean)  -- absolute value (any negative sign has been ignored)
				if exponent then
					value = value * 10^exponent
				end
				rawset(self, key, value)
				return value
			end
		end })
end

function cvt_to_hand(parms, info, in_current, out_current)
	-- Convert input to hands, inches.
	-- Return true, t where t is a table with the conversion results;
	-- or return false, t where t is an error message table.
	if parms.abbr_org == nil then
		out_current.usename = true  -- default is to show name not symbol
	end
	local precision = parms.precision
	local frac = out_current.frac
	if not frac and precision and 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 <= 0 then  -- using negative or 0 for precision rounds to nearest hand
		hands = floor(outinfo.raw_absvalue/4 + 0.5)
		inchstr = ''
	elseif tfrac then
		-- Always show an integer before fraction (like "15.0½") because "15½" means 15-and-a-half hands.
		inchstr = numdot .. format_fraction(parms, 'out', false, inchstr, tfrac.numstr, tfrac.denstr)
	else
		inchstr = numdot .. from_en(inchstr)
	end
	outinfo.show = outinfo.sign .. with_separator(parms, format('%.0f', hands)) .. inchstr
	return true, outinfo
end

local function evaluate_condition(value, condition)
	-- Return true or false from applying a conditional expression to value,
	-- or throw an error if invalid.
	-- A very limited set of expressions is supported:
	--    v < 9
	--    v * 9 < 9
	-- where
	--    'v' is replaced with value
	--    9 is any number (as defined by Lua tonumber)
	--      only en digits are accepted
	--    '<' can also be '<=' or '>' 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
		elseif 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 < 120 ! small ! big ! suffix' (suffix is optional)
	-- evaluates 'v < 120' as a boolean with result
	-- 'smallsuffix' if (value < 120), or 'bigsuffix' otherwise.
	-- Input must use en digits and '.' decimal mark.
	local default = default_exceptions[unit_table.defkey or unit_table.symbol] or unit_table.default
	if not default then
		return false, { 'cvt_no_default', unit_table.symbol }
	end
	if default:find('!', 1, true) == nil then
		return true, default
	end
	local t = split(default, '!')
	if #t == 3 or #t == 4 then
		local success, result = pcall(evaluate_condition, value, t[1])
		if success then
			default = result and t[2] or t[3]
			if #t == 4 then
				default = default .. t[4]
			end
			return true, default
		end
	end
	return false, { 'cvt_bad_default', unit_table.symbol }
end

local linked_pages  -- to record linked pages so will not link to the same page more than once

local function make_link(link, id, link_key)
	-- Return wikilink "[[link|id]]", possibly abbreviated as in examples:
	--   [[Mile|mile]]  --> [[mile]]
	--   [[Mile|miles]] --> [[mile]]s
	-- 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).
	-- Linking with a unit uses the unit table as the link key, which fails to detect
	-- overlinking for conversions like the following (each links "mile" twice):
	--   {{convert|1|impgal/mi|USgal/mi|lk=on}}
	--   {{convert|1|l/km|impgal/mi USgal/mi|lk=on}}
	link_key = link_key or link  -- use key if given (the key, but not the link, may be known when need to cancel a link record)
	if not link or link == '' or linked_pages[link_key] then
		return id
	end
	linked_pages[link_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 '[[' .. link .. '|' .. id .. ']]'
	end
end

local function variable_name(clean, unit_table)
	-- For slwiki (Slovenian Wikipedia), 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
		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(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 unit1 = per[1]  -- top unit_table, or nil
		local unit2 = per[2]  -- 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
		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 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 unit1[key_id] or '') .. result .. unit2[key_id2]
			else
				result = (unit1 and variable_name(clean, unit1) or '') .. result .. variable_name('1', unit2)
			end
			return make_link(unit_table.link, result, unit_table)
		end
		if unit1 then
			result = linked_id(unit1, key_id, want_link, clean) .. result
		end
		return result .. linked_id(unit2, key_id2, want_link, '1')
	end
	if multiplier then
		-- A multiplier (like "100" in "100km") forces the unit to be plural.
		multiplier = from_en(multiplier)
		if abbr_on then
			multiplier = multiplier .. '&nbsp;'
		else
			multiplier = multiplier .. ' '
			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_table[key_id])
	if want_link then
		local link = link_exceptions[unit_table.linkey or unit_table.symbol] or unit_table.link
		if link then
			local before = ''
			local i = unit_table.customary
			if i == 1 and unit_table.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_units[i]
			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 < 3) and { 'US&nbsp;', 'US ', 'U.S.&nbsp;', 'U.S. ' } or { 'imp&nbsp;', 'imp ', 'imperial ' }
				for _, prefix in ipairs(removes) do
					local plen = #prefix
					if id:sub(1, plen) == prefix then
						id = id:sub(plen + 1)
						break
					end
				end
				before = pertext .. make_link(customary.link, customary[1]) .. ' '
			end
			id = before .. make_link(link, id, unit_table)
		end
	end
	return multiplier .. id
end

local function make_id(parms, which, unit_table)
	-- Return id, f where
	--   id = unit name or symbol, possibly modified
	--   f = true if id is a name, or false if id is a symbol
	-- using 1st or 2nd values (which), and for 'in' or 'out' (unit_table.inout).
	-- Result is '' if no symbol/name is to be used.
	-- In addition, set unit_table.sep = ' ' or '&nbsp;' or ''
	-- (the separator that caller will normally insert before the id).
	if parms.opt_values then
		unit_table.sep = ''
		return ''
	end
	local inout = unit_table.inout
	local info = unit_table.valinfo[which]
	local abbr_org = parms.abbr_org
	local adjectival = parms.opt_adjectival
	local disp = parms.disp
	local lk = parms.lk
	local want_link = (lk == 'on' or lk == inout)
	local usename = unit_table.usename
	local singular = info.singular
	if usename then
		-- Old template does something like this.
		if want_link then
			-- A linked unit uses the standard singular.
		else
			-- Set non-standard singular.
			local flipped = parms.opt_flip
			if inout == 'in' then
				if not adjectival and (abbr_org == 'out' or flipped) then
					local value = info.value
					singular = (0 < value and value < 1.0001)
				end
			else
				if (abbr_org == 'on') or
				(not flipped and (abbr_org == nil or abbr_org == 'out')) or
				(flipped and abbr_org == 'in') then
					singular = (info.absvalue < 1.0001 and
								not info.is_scientific)
				end
			end
		end
	end
	local want_name
	if usename then
		want_name = true
	else
		if abbr_org == nil then
			if disp == 'br' or disp == 'or' or disp == 'slash' then
				want_name = true
			end
			if unit_table.usesymbol then
				want_name = false
			end
		end
		if want_name == nil then
			local abbr = parms.abbr
			if abbr == 'on' or abbr == inout or (abbr == 'mos' and inout == 'out') then
				want_name = false
			else
				want_name = true
			end
		end
	end
	local key
	if want_name then
		if lk == nil and unit_table.builtin == 'hand' then
			want_link = true
		end
		if parms.opt_use_nbsp then
			unit_table.sep = '&nbsp;'
		else
			unit_table.sep = ' '
		end
		if parms.opt_singular then
			local value
			if inout == 'in' then
				value = info.value
			else
				value = info.absvalue
			end
			if value then  -- some unusual units do not always set value field
				value = abs(value)
				singular = (0 < value and value < 1.0001)
			end
		end
		if unit_table.engscale or parms.is_range_x then
			-- engscale: so "|1|e3kg" gives "1 thousand kilograms" (plural)
			-- is_range_x: so "|0.5|x|0.9|mi" gives "0.5 by 0.9 miles" (plural)
			singular = false
		end
		key = (adjectival or singular) and 'name1' or 'name2'
		if unit_table.sp_us then
			key = key .. '_us'
		end
	else
		if unit_table.builtin == 'hand' then
			if parms.opt_hand_hh then
				unit_table.symbol = 'hh'  -- LATER: might want i18n applied to this
			end
		end
		unit_table.sep = '&nbsp;'
		key = unit_table.sp_us and 'sym_us' or 'symbol'
	end
	return linked_id(unit_table, key, want_link, info.clean), want_name
end

local function decorate_value(parms, unit_table, which)
	-- If needed, update unit_table so values will be shown with extra information.
	-- For consistency with the old template (but different from fmtpower),
	-- the style to display powers of 10 includes "display:none" to allow some
	-- browsers to copy, for example, "10³" as "10^3", rather than as "103".
	local info
	local engscale = unit_table.engscale
	local prefix = unit_table.vprefix
	if engscale or prefix then
		info = unit_table.valinfo[which]
		if info.decorated then
			return  -- do not redecorate if repeating convert
		end
		info.decorated = true
	end
	if engscale then
		local inout = unit_table.inout
		local abbr = parms.abbr
		if abbr == 'on' or abbr == inout then
			info.show = info.show ..
				'<span style="margin-left:0.2em">×<span style="margin-left:0.1em">' ..
				from_en('10') ..
				'</span></span><s style="display:none">^</s><sup>' ..
				from_en(tostring(engscale.exponent)) .. '</sup>'
		else
			local number_id
			local lk = parms.lk
			if lk == 'on' or lk == inout then
				number_id = make_link(engscale.link, engscale[1])
			else
				number_id = engscale[1]
			end
			-- WP:NUMERAL recommends "&nbsp;" in values like "12 million".
			info.show = info.show .. (parms.opt_adjectival and '-' or '&nbsp;') .. number_id
		end
	end
	if prefix then
		info.show = prefix .. info.show
	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 = composite[1]
	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
	local disp_joins = text_code.disp_joins
	local abbr = parms.abbr
	local disp = parms.disp
	if disp == nil then  -- special case for the most common setting
		parms.joins = disp_joins['b']
	elseif disp ~= 'x' then
		-- Old template does this.
		if disp == 'slash' then
			if parms.abbr_org == 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_joins[disp] or disp_joins['b']
	end
	if parms.opt_also_symbol and not composite then
		local join1 = parms.joins[1]
		if join1 == ' (' or join1 == ' [' then
			parms.joins = { join1 .. first_unit[first_unit.sp_us and 'sym_us' or 'symbol'] .. ', ', parms.joins[2] }
		end
	end
	if in_current.builtin == 'mach' then
		local prefix = id1 .. '&nbsp;'
		local range = parms.range
		local valinfo = first_unit.valinfo
		local result = prefix .. valinfo[1].show
		if range then
			-- For simplicity and because more not needed, handle one range item only.
			local prefix2 = make_id(parms, 2, first_unit) .. '&nbsp;'
			result = range_text(range[1], want_name, parms, result, prefix2 .. valinfo[2].show)
		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 = '&nbsp;'
		local sep2 = ' '
		if parms.opt_adjectival and want_name then
			sep1 = '-'
			sep2 = '-'
		end
		local parts = { first_unit.valinfo[1].show .. sep1 .. id1 }
		for i, unit in ipairs(composite) do
			if i > 1 then
				table.insert(parts, unit.valinfo[1].show .. sep1 .. (make_id(parms, 1, unit)))
			end
		end
		return table.concat(parts, sep2) .. mid
	end
	local result, mos
	local range = parms.range
	if range then
		mos = (abbr == 'mos')
		if not (mos or (parms.is_range_x and not want_name)) then
			linked_pages[first_unit] = nil  -- so the second and only id will be linked, if wanted
		end
	end
	local id = (range == nil) and id1 or make_id(parms, 2, first_unit)
	local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, 'in')
	if mos and was_hyphenated then
		mos = false  -- suppress repeat of unit in a range
		if linked_pages[first_unit] then
			linked_pages[first_unit] = nil
			id = make_id(parms, 2, first_unit)
			extra = hyphenated_maybe(parms, want_name, sep, id, 'in')
		end
	end
	local valinfo = first_unit.valinfo
	if range then
		if range.n == 1 then
			-- Like {{convert|1|x|2|ft}} (one range item; two values).
			-- Do what old template did.
			local sep1 = first_unit.sep
			if mos then
				decorate_value(parms, in_current, 1)
				decorate_value(parms, in_current, 2)
				result = valinfo[1].show .. sep1 .. id1
			elseif parms.is_range_x and not want_name then
				if abbr == 'in' or abbr == 'on' then
					decorate_value(parms, in_current, 1)
				end
				decorate_value(parms, in_current, 2)
				result = valinfo[1].show .. sep1 .. id1
			else
				if abbr == 'in' or abbr == 'on' then
					decorate_value(parms, in_current, 1)
				end
				decorate_value(parms, in_current, 2)
				result = valinfo[1].show
			end
			result = range_text(range[1], want_name, parms, result, valinfo[2].show)
		else
			-- Like {{convert|1|x|2|x|3|ft}} (two or more range items): simplify.
			decorate_value(parms, in_current, 1)
			result = valinfo[1].show
			for i = 1, range.n do
				decorate_value(parms, in_current, i+1)
				result = range_text(range[i], want_name, parms, result, valinfo[i+1].show)
			end
		end
	else
		decorate_value(parms, first_unit, 1)
		result = valinfo[1].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 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' then
		local prefix = id1 .. '&nbsp;'
		local range = parms.range
		local valinfo = out_current.valinfo
		local result = prefix .. valinfo[1].show
		if range then
			-- For simplicity and because more not needed, handle one range item only.
			result = range_text(range[1], want_name, parms, result, prefix .. valinfo[2].show)
		end
		return preunit .. result
	end
	local result
	local range = parms.range
	if range then
		if not (parms.is_range_x and not want_name) then
			linked_pages[out_current] = nil  -- so the second and only id will be linked, if wanted
		end
	end
	local id = (range == nil) and id1 or make_id(parms, 2, out_current)
	local extra = hyphenated_maybe(parms, want_name, sep, id, 'out')
	local valinfo = out_current.valinfo
	if range then
		if range.n == 1 then
			local sep1 = out_current.sep
			local abbr = parms.abbr
			if parms.is_range_x and not want_name then
				if abbr == 'out' or abbr == 'on' then
					decorate_value(parms, out_current, 1)
				end
				decorate_value(parms, out_current, 2)
				result = valinfo[1].show .. sep1 .. id1
			else
				if abbr == 'out' or abbr == 'on' then
					decorate_value(parms, out_current, 1)
				end
				decorate_value(parms, out_current, 2)
				result = valinfo[1].show
			end
			result = range_text(range[1], want_name, parms, result, valinfo[2].show)
		else
			-- Like {{convert|1|x|2|x|3|ft}} (two or more range items): simplify.
			decorate_value(parms, out_current, 1)
			result = valinfo[1].show
			for i = 1, range.n do
				decorate_value(parms, out_current, i+1)
				result = range_text(range[i], want_name, parms, result, valinfo[i+1].show)
			end
		end
	else
		decorate_value(parms, out_current, 1)
		result = valinfo[1].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.
	out_unit_table.valinfo = collection()
	local range = parms.range
	for i = 1, (range and (range.n + 1) or 1) do
		local success, info = cvtround(parms, in_unit_table.valinfo[i], in_unit_table, out_unit_table)
		if not success then return false, info end
		out_unit_table.valinfo:add(info)
	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 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 == 'out' or abbr == 'mos')
	local want_link = (parms.lk == 'on' or parms.lk == 'out')
	local mid = parms.opt_flip and parms.mid or ''
	local sep1 = '&nbsp;'
	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 = combos[i]
			out_current.inout = 'out'
			local scale = multiple[i]
			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 < thisvalue and thisvalue < 1.0001 then
							key = 'name1'
						end
					else
						if thisvalue == 1 then
							key = 'name1'
						end
					end
					id = out_current[key]
				end
			else
				id = out_current['symbol']
			end
			if want_link then
				local link = out_current.link
				if link then
					id = make_link(link, id, out_current)
				end
			end
			local strval
			local inout = (i == #combos or outvalue == 0) and 'out' or ''  -- trick so the last value processed (first displayed) has uppercase, if requested
			if strforce and outvalue == 0 then
				sign = ''  -- any sign is in strforce
				strval = strforce  -- show small values in scientific notation; will only use least significant unit
			elseif tfrac then
				local wholestr = (thisvalue > 0) and tostring(thisvalue) or nil
				strval = format_fraction(parms, 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, 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
			reversed[i] = results[count + 1 - i]
		end
		return true, sign .. table.concat(reversed, sep2)
	end
	local valinfo = in_unit_table.valinfo
	local success, result = make_result(valinfo[1], 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(valinfo[i+1])
			if not success then return false, result2 end
			result = range_text(range[i], want_name, parms, result, result2)
		end
	end
	return true, result .. mid
end

local function process(parms, in_unit_table, out_unit_table)
	-- Return true, s where s = final wikitext result,
	-- or return false, t where t is an error message table.
	linked_pages = {}
	local success, bad_output, out_first
	local bad_input_mcode = in_unit_table.bad_mcode  -- false if input unit is valid
	local invalue1 = in_unit_table.valinfo[1].value
	local out_unit = parms.out_unit
	if out_unit == nil or out_unit == '' then
		if bad_input_mcode then
			bad_output = ''
		else
			success, out_unit = get_default(invalue1, 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(out_unit, parms.opt_sp_us, '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 flipped = parms.opt_flip and not bad_input_mcode
	local parts = {}
	for part = 1, 2 do
		-- The LHS (parts[1]) is normally the input, but is the output if flipped.
		-- Process LHS first so it will be linked, if wanted.
		-- Linking to the same item is suppressed in the RHS to avoid overlinking.
		if (part == 1 and not flipped) or (part == 2 and flipped) then
			parts[part] = process_input(parms, in_unit_table)
		elseif bad_output then
			if bad_output ~= '' then
				parts[part] = message(bad_output)
			end
		else
			local outputs = {}
			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:
				-- {{convert|156|cm|in hand|1|frac=2}} → 156 centimetres (61.4 in; 15.1½ hands)
				-- However, the following is handled elsewhere as a special case:
				-- {{convert|156|cm|hand in|1|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 imax = combos and #combos or 1  -- 1 (single unit) or number of unit tables
			for i = 1, imax do
				local success, item
				local out_current = combos and combos[i] or out_unit_table
				out_current.inout = 'out'
				if i == 1 then
					out_first = out_current
					if imax > 1 and out_current.builtin == 'hand' then
						out_current.out_next = combos[2]  -- built-in hand can influence next unit in a combination
					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
				table.insert(outputs, item)
			end
			local sep = parms.table_joins and parms.table_joins[2] or '; '
			parts[part] = parms.opt_input_unit_only and '' or table.concat(outputs, sep)
		end
	end
	if parms.opt_sortable_in or parms.opt_sortable_out then
		local value
		if parms.opt_sortable_in then
			value = invalue1
		else
			local info = out_first and out_first.valinfo
			if info then
				info = info[1]
				value = info.raw_absvalue
				if value and info.sign == MINUS then
					value = -value
				end
			end
		end
		parts[1] = ntsh((value or 0), parms.opt_sortable_debug) .. parts[1]
	end
	local wikitext
	if bad_input_mcode then
		if bad_input_mcode == '' then
			wikitext = parts[1]
		else
			wikitext = parts[1] .. message(bad_input_mcode)
		end
	elseif parms.table_joins then
		wikitext = parms.table_joins[1] .. parts[1] .. parms.table_joins[2] .. parts[2]
	else
		wikitext = parts[1] .. parms.joins[1] .. parts[2] .. parms.joins[2]
	end
	if parms.warnings and not bad_input_mcode then
		wikitext = wikitext .. parms.warnings
	end
	return true, wikitext, out_unit_table
end

local function main_convert(frame)
	-- Do convert, and if needed, do it again with higher default precision.
	set_config(frame)
	local result, out_unit_table
	local success, parms, in_unit_table = get_parms(frame:getParent())
	if success then
		for i = 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
	else
		result = parms
	end
	if success then
		return result
	end
	return message(result)
end

return { convert = main_convert }