Module:Convert/sandbox
-- Convert a value from one unit of measurement to another.
 -- Example: {{convert|123|lb|kg}} --&gt; 123 pounds (56 kg)
 -- See [[:en:Template:Convert/Transwiki guide]] if copying to another wiki.
 
 local MINUS = '−'  -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92)
 local abs = math.abs
 local floor = math.floor
 local format = string.format
 local log10 = math.log10
 local ustring = mw.ustring
 local ulen = ustring.len
 local usub = ustring.sub
 
 -- Configuration options to keep magic values in one location.
 -- Conversion data and message text are defined in separate modules.
 local config, maxsigfig
 local numdot  -- must be '.' or ',' or a character which works in a regex
 local numsep, numsep_remove, numsep_remove2
 local data_code, all_units
 local text_code
 local varname        -- can be a code to use variable names that depend on value
 local from_en_table  -- to translate an output string of en digits to local language
 local to_en_table    -- to translate an input string of digits in local language to en
 -- Use translation_table in convert/text to change the following.
 local en_default           -- true uses lang=en unless convert has lang=local or local digits
 local group_method = 3     -- code for how many digits are in a group
 local per_word = 'per'     -- for units like &quot;liters per kilometer&quot;
 local plural_suffix = 's'  -- only other useful value is probably '' to disable plural unit names
 local omitsep              -- true to omit separator before local symbol/name
 
 -- All units should be defined in the data module. However, to cater for quick changes
 -- and experiments, any unknown unit is looked up in an extra data module, if it exists.
 -- That module would be transcluded in only a small number of pages, so there should be
 -- little server overhead from making changes, and changes should propagate quickly.
 local extra_module  -- name of module with extra units
 local extra_units   -- nil or table of extra units from extra_module
 
 -- Some options in the invoking template can set variables used later in the module.
 local currency_text  -- for a user-defined currency symbol: {{convert|12|$/ha|$=€}} (euro replaces dollar)
 
 local function from_en(text)
 	-- Input is a string representing a number in en digits with '.' decimal mark,
 	-- without digit grouping (which is done just after calling this).
 	-- Return the translation of the string with numdot and digits in local language.
 	if numdot ~= '.' then
 		text = text:gsub('%.', numdot)
 	end
 	if from_en_table then
 		text = text:gsub('%d', from_en_table)
 	end
 	return text
 end
 
 local function to_en(text)
 	-- Input is a string representing a number in the local language with
 	-- an optional numdot decimal mark and numsep digit grouping.
 	-- Return the translation of the string with '.' mark and en digits,
 	-- and no separators (they have to be removed here to handle cases like
 	-- numsep = '.' and numdot = ',' with input &quot;1.234.567,8&quot;).
 	if to_en_table then
 		text = ustring.gsub(text, '%d', to_en_table)
 	end
 	if numsep_remove then
 		text = text:gsub(numsep_remove, '')
 	end
 	if numsep_remove2 then
 		text = text:gsub(numsep_remove2, '')
 	end
 	if numdot ~= '.' then
 		text = text:gsub(numdot, '.')
 	end
 	return text
 end
 
 local function decimal_mark(text)
 	-- Return ',' if text probably is using comma for decimal mark, or has no decimal mark.
 	-- Return '.' if text probably is using dot for decimal mark.
 	-- Otherwise return nothing (decimal mark not known).
 	if not text:find('[.,]') then return ',' end
 	text = text:gsub('^%-', ''):gsub('%+%d+/%d+$', ''):gsub('[Ee]%-?%d+$', '')
 	local decimal =
 		text:match('^0?([.,])%d+$') or
 		text:match('%d([.,])%d?%d?$') or
 		text:match('%d([.,])%d%d%d%d+$')
 	if decimal then return decimal end
 	if text:match('%.%d+%.') then return ',' end
 	if text:match('%,%d+,') then return '.' end
 end
 
 local add_warning, with_separator  -- forward declarations
 local function to_en_with_check(text, parms)
 	-- Version of to_en() for a wiki using numdot = ',' and numsep = '.' to check
 	-- text (an input number as a string) which might have been copied from enwiki.
 	-- For example, in '1.234' the '.' could be a decimal mark or a group separator.
 	-- From viwiki.
 	if to_en_table then
 		text = ustring.gsub(text, '%d', to_en_table)
 	end
 	if decimal_mark(text) == '.' then
 		local original = text
 		text = text:gsub(',', '')  -- for example, interpret &quot;1,234.5&quot; as an enwiki value
 		if parms then
 			add_warning(parms, 0, 'cvt_enwiki_num', original, with_separator({}, text))
 		end
 	else
 		if numsep_remove then
 			text = text:gsub(numsep_remove, '')
 		end
 		if numsep_remove2 then
 			text = text:gsub(numsep_remove2, '')
 		end
 		if numdot ~= '.' then
 			text = text:gsub(numdot, '.')
 		end
 	end
 	return text
 end
 
 local function omit_separator(id)
 	-- Return true if there should be no separator before id (a unit symbol or name).
 	-- For zhwiki, there should be no separator if id uses local characters.
 	-- The following kludge should be a sufficient test.
 	if omitsep then
 		if id:sub(1, 2) == '-{' then  -- for &quot;-{...}-&quot; content language variant
 			return true
 		end
 		if id:byte() &gt; 127 then
 			local first = usub(id, 1, 1)
 			if first ~= 'Å' and first ~= '°' and first ~= 'µ' then
 				return true
 			end
 		end
 	end
 	return id:sub(1, 1) == '/'  -- no separator before units like &quot;/ha&quot;
 end
 
 local spell_module  -- name of module that can spell numbers
 local speller       -- function from that module to handle spelling (set if needed)
 local wikidata_module, wikidata_data_module  -- names of Wikidata modules
 local wikidata_code, wikidata_data  -- exported tables from those modules (set if needed)
 
 local function set_config(args)
 	-- Set configuration options from template #invoke or defaults.
 	config = args
 	maxsigfig = config.maxsigfig or 14  -- maximum number of significant figures
 	local data_module, text_module
 	local sandbox = config.sandbox and ('/' .. config.sandbox) or ''
 	data_module = &quot;Module:Convert/data&quot; .. sandbox
 	text_module = &quot;Module:Convert/text&quot; .. sandbox
 	extra_module = &quot;Module:Convert/extra&quot; .. sandbox
 	wikidata_module = &quot;Module:Convert/wikidata&quot; .. sandbox
 	wikidata_data_module = &quot;Module:Convert/wikidata/data&quot; .. sandbox
 	spell_module = &quot;Module:ConvertNumeric&quot;
 	data_code = mw.loadData(data_module)
 	text_code = mw.loadData(text_module)
 	all_units = data_code.all_units
 	local translation = text_code.translation_table
 	if translation then
 		numdot = translation.numdot
 		numsep = translation.numsep
 		if numdot == ',' and numsep == '.' then
 			if text_code.all_messages.cvt_enwiki_num then
 				to_en = to_en_with_check
 			end
 		end
 		if translation.group then
 			group_method = translation.group
 		end
 		if translation.per_word then
 			per_word = translation.per_word
 		end
 		if translation.plural_suffix then
 			plural_suffix = translation.plural_suffix
 		end
 		varname = translation.varname
 		from_en_table = translation.from_en
 		local use_workaround = true
 		if use_workaround then
 			-- 2013-07-05 workaround bug by making a copy of the required table.
 			-- mw.ustring.gsub fails with a table (to_en_table) as the replacement,
 			-- if the table is accessed via mw.loadData.
 			local source = translation.to_en
 			if source then
 				to_en_table = {}
 				for k, v in pairs(source) do
 					to_en_table[k] = v
 				end
 			end
 		else
 			to_en_table = translation.to_en
 		end
 		if translation.lang == 'en default' then
 			en_default = true  -- for hiwiki
 		end
 		omitsep = translation.omitsep  -- for zhwiki
 	end
 	numdot = config.numdot or numdot or '.'  -- decimal mark before fractional digits
 	numsep = config.numsep or numsep or ','  -- group separator for numbers
 	-- numsep should be ',' or '.' or '' or '&amp;nbsp;' or a Unicode character.
 	-- numsep_remove must work in a regex to identify separators to be removed.
 	if numsep ~= '' then
 		numsep_remove = (numsep == '.') and '%.' or numsep
 	end
 	if numsep ~= ',' and numdot ~= ',' then
 		numsep_remove2 = ','  -- so numbers copied from enwiki will work
 	end
 end
 
 local function collection()
 	-- Return a table to hold items.
 	return {
 		n = 0,
 		add = function (self, item)
 			self.n = self.n + 1
 			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 &lt;= remainder and remainder &lt; 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(&quot;^%s*(.-)%s*$&quot;)
 	end
 end
 
 local function table_len(t)
 	-- Return length (&lt;100) of a numbered table to replace #t which is
 	-- documented to not work if t is accessed via mw.loadData().
 	for i = 1, 100 do
 		if t[i] == nil then
 			return i - 1
 		end
 	end
 end
 
 local function wanted_category(catkey, catsort, want_warning)
 	-- Return message category if it is wanted in current namespace,
 	-- otherwise return ''.
 	local cat
 	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
 				cat = text_code.all_categories[want_warning and 'warning' or catkey]
 				if catsort and catsort ~= '' and cat:sub(-2) == ']]' then
 					cat = cat:sub(1, -3) .. '|' .. mw.text.nowiki(usub(catsort, 1, 20)) .. ']]'
 				end
 				break
 			end
 		end
 	end
 	return cat or ''
 end
 
 local function message(parms, mcode, is_warning)
 	-- 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 '$1' if any in message)
 	--    mcode[3] = 'parm2' (string to replace '$2' if any in message)
 	--    mcode[4] = 'parm3' (string to replace '$3' if any in message)
 	local msg
 	if type(mcode) == 'table' then
 		if mcode[1] == 'cvt_no_output' then
 			-- Some errors should cause convert to output an empty string,
 			-- for example, for an optional field in an infobox.
 			return ''
 		end
 		msg = text_code.all_messages[mcode[1]]
 	end
 	parms.have_problem = true
 	local function subparm(fmt, ...)
 		local rep = {}
 		for i, v in ipairs({...}) do
 			rep['$' .. i] = v
 		end
 		return (fmt:gsub('$%d+', rep))
 	end
 	if msg then
 		local parts = {}
 		local regex, replace = msg.regex, msg.replace
 		for i = 1, 3 do
 			local limit = 40
 			local s = mcode[i + 1]
 			if s then
 				if regex and replace then
 					s = s:gsub(regex, replace)
 					limit = nil  -- allow long &quot;should be&quot; messages
 				end
 				-- Escape user input so it does not break the message.
 				-- To avoid tags (like {{convert|1&lt;math&gt;23&lt;/math&gt;|m}}) breaking
 				-- the mouseover title, any strip marker starting with char(127) is
 				-- replaced with '...' (text not needing i18n).
 				local append
 				local pos = s:find(string.char(127), 1, true)
 				if pos then
 					append = '...'
 					s = s:sub(1, pos - 1)
 				end
 				if limit and ulen(s) &gt; limit then
 					s = usub(s, 1, limit)
 					append = '...'
 				end
 				s = mw.text.nowiki(s) .. (append or '')
 			else
 				s = '?'
 			end
 			parts['$' .. i] = s
 		end
 		local function ispreview()
 			-- Return true if a prominent message should be shown.
 			if parms.test == 'preview' or parms.test == 'nopreview' then
 				-- For testing, can preview a real message or simulate a preview
 				-- when running automated tests.
 				return parms.test == 'preview'
 			end
 			local success, revid = pcall(function ()
 				return (parms.frame):preprocess('{{REVISIONID}}') end)
 			return success and (revid == '')
 		end
 		local want_warning = is_warning and
 			not config.warnings and  -- show unobtrusive warnings if config.warnings not configured
 			not msg.nowarn           -- but use msg settings, not standard warning, if specified
 		local title = string.gsub(msg[1] or 'Missing message', '$%d+', parts)
 		local text = want_warning and '*' or msg[2] or 'Missing message'
 		local cat = wanted_category(msg[3], mcode[2], want_warning)
 		local anchor = msg[4] or ''
 		local fmtkey = ispreview() and 'cvt_format_preview' or
 			(want_warning and 'cvt_format2' or msg.format or 'cvt_format')
 		local fmt = text_code.all_messages[fmtkey] or 'convert: bug'
 		return subparm(fmt, title:gsub('&quot;', '&amp;quot;'), text, cat, anchor)
 	end
 	return 'Convert internal error: unknown message'
 end
 
 function add_warning(parms, level, key, text1, text2)  -- for forward declaration above
 	-- If enabled, add a warning that will be displayed after the convert result.
 	-- A higher level is more verbose: more kinds of warnings are displayed.
 	-- To reduce output noise, only the first warning is displayed.
 	if level &lt;= (tonumber(config.warnings) or 1) then
 		if parms.warnings == nil then
 			parms.warnings = message(parms, { key, text1, text2 }, true)
 		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
 	--   ------  ---------  -----------  -------------------
 	--   &quot;1.23&quot;    nil        nil        one point two three
 	--    &quot;1&quot;      &quot;2&quot;        &quot;3&quot;        one and two thirds
 	--    nil      &quot;2&quot;        &quot;3&quot;        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', '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 &lt; 0) and -altitude or altitude
 	a = floor(a / 5000 + 0.5)
 	if altitude &lt; 0 then
 		a = -a
 	end
 	if a &lt; -3 then
 		a = -3
 	elseif a &gt; 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 &quot;to&quot;),
 	-- 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 &quot;x/y&quot;.
 	-- This is never called to determine a unit name or link because per units
 	-- are handled as a special case.
 	-- Similarly, the default output is handled elsewhere, and for a symbol
 	-- this is only called from get_default() for default_exceptions.
 	__index = function (self, key)
 		local value
 		if key == 'symbol' then
 			local per = self.per
 			local unit1, unit2 = 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 make_per(unitcode, unit_table, ulookup)
 	-- Return true, t where t is a per unit with unit codes expanded to unit tables,
 	-- or return false, t where t is an error message table.
 	local result = {
 		unitcode = unitcode,
 		utype = unit_table.utype,
 		per = {}
 	}
 	override_from(result, unit_table, { 'invert', 'iscomplex', 'default', 'link', 'symbol', 'symlink' })
 	result.symbol_raw = (result.symbol or false)  -- to distinguish between a defined exception and a metatable calculation
 	local prefix
 	for i, v in ipairs(unit_table.per) do
 		if i == 1 and v == '' then
 			-- First unit symbol can be empty; that gives a nil first unit table.
 		elseif i == 1 and text_code.currency[v] then
 			prefix = currency_text or v
 		else
 			local success, t = ulookup(v)
 			if not success then return false, t end
 			result.per[i] = t
 		end
 	end
 	local multiplier = unit_table.multiplier
 	if not result.utype then
 		-- Creating an automatic per unit.
 		local unit1 = result.per[1]
 		local utype = (unit1 and unit1.utype or prefix or '') .. '/' .. result.per[2].utype
 		local t = data_code.per_unit_fixups[utype]
 		if t then
 			if type(t) == 'table' then
 				utype = t.utype or utype
 				result.link = result.link or t.link
 				multiplier = multiplier or t.multiplier
 			else
 				utype = t
 			end
 		end
 		result.utype = utype
 	end
 	result.scalemultiplier = multiplier or 1
 	result.vprefix = prefix or false  -- set to non-nil to avoid calling __index
 	return true, setmetatable(result, unit_per_mt)
 end
 
 local function lookup(parms, unitcode, what, utable, fails, depth)
 	-- Return true, t where t is a copy of the unit's converter table,
 	-- or return false, t where t is an error message table.
 	-- Parameter 'what' determines whether combination units are accepted:
 	--   'no_combination'  : single unit only
 	--   'any_combination' : single unit or combination or output multiple
 	--   'only_multiple'   : single unit or output multiple only
 	-- Parameter unitcode is a symbol (like 'g'), with an optional SI prefix (like 'kg').
 	-- If, for example, 'kg' is in this table, that entry is used;
 	-- otherwise the prefix ('k') is applied to the base unit ('g').
 	-- If unitcode is a known combination code (and if allowed by what),
 	-- a table of output multiple unit tables is included in the result.
 	-- For compatibility with the old template, an underscore in a unitcode is
 	-- replaced with a space so usage like {{convert|350|board_feet}} works.
 	-- Wikignomes may also put two spaces or &quot;&amp;nbsp;&quot; in combinations, so
 	-- replace underscore, &quot;&amp;nbsp;&quot;, and multiple spaces with a single space.
 	utable = utable or parms.unittable or all_units
 	fails = fails or {}
 	depth = depth and depth + 1 or 1
 	if depth &gt; 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('&amp;nbsp;', ' '):gsub('  +', ' ')
 	local function call_make_per(t)
 		return make_per(unitcode, t,
 			function (ucode) return lookup(parms, ucode, 'no_combination', utable, fails, depth) end
 		)
 	end
 	local t = utable[unitcode]
 	if t then
 		if t.shouldbe then
 			return false, { 'cvt_should_be', t.shouldbe }
 		end
 		if t.sp_us then
 			parms.opt_sp_us = true
 		end
 		local target = t.target  -- nil, or unitcode is an alias for this target
 		if target then
 			local success, result = lookup(parms, target, what, utable, fails, depth)
 			if not success then return false, result end
 			override_from(result, t, { 'customary', 'default', 'link', 'symbol', 'symlink' })
 			local multiplier = t.multiplier
 			if multiplier then
 				result.multiplier = tostring(multiplier)
 				result.scale = result.scale * multiplier
 			end
 			return true, result
 		end
 		if t.per then
 			return call_make_per(t)
 		end
 		local combo = t.combination  -- nil or a table of unitcodes
 		if combo then
 			local multiple = t.multiple
 			if what == 'no_combination' or (what == 'only_multiple' and not multiple) then
 				return false, { 'cvt_bad_unit', unitcode }
 			end
 			-- Recursively create a combination table containing the
 			-- converter table of each unitcode.
 			local result = { utype = t.utype, multiple = multiple, combination = {} }
 			local cvt = result.combination
 			for i, v in ipairs(combo) do
 				local success, t = lookup(parms, v, multiple and 'no_combination' or 'only_multiple', utable, fails, depth)
 				if not success then return false, t end
 				cvt[i] = t
 			end
 			return true, result
 		end
 		local result = shallow_copy(t)
 		result.unitcode = unitcode
 		if result.prefixes then
 			result.si_name = ''
 			result.si_prefix = ''
 			return true, setmetatable(result, unit_prefixed_mt)
 		end
 		return true, setmetatable(result, unit_mt)
 	end
 	local SIprefixes = text_code.SIprefixes
 	for plen = 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)
 				result.unitcode = unitcode
 				result.si_name = parms.opt_sp_us and si.name_us or si.name
 				result.si_prefix = si.prefix or prefix
 				result.scale = t.scale * 10 ^ (si.exponent * t.prefixes)
 				return true, setmetatable(result, unit_prefixed_mt)
 			end
 		end
 	end
 	-- Accept user-defined combinations like &quot;acre+m2+ha&quot; or &quot;acre m2 ha&quot; for output.
 	-- If '+' is used, each unit code can include a space, and any error is fatal.
 	-- If ' ' is used and if each space-separated word is a unit code, it is a combo,
 	-- but errors are not fatal so the unit code can be looked up as an extra unit.
 	local err_is_fatal
 	local combo = collection()
 	if unitcode:find('+', 1, true) then
 		err_is_fatal = true
 		for item in (unitcode .. '+'):gmatch('%s*(.-)%s*%+') do
 			if item ~= '' then
 				combo:add(item)
 			end
 		end
 	elseif unitcode:find('%s') then
 		for item in unitcode:gmatch('%S+') do
 			combo:add(item)
 		end
 	end
 	if combo.n &gt; 1 then
 		local function lookup_combo()
 			if what == 'no_combination' or what == 'only_multiple' then
 				return false, { 'cvt_bad_unit', unitcode }
 			end
 			local result = { combination = {} }
 			local cvt = result.combination
 			for i, v in ipairs(combo) do
 				local success, t = lookup(parms, v, 'only_multiple', utable, fails, depth)
 				if not success then return false, t end
 				if i == 1 then
 					result.utype = t.utype
 				else
 					local mismatch = check_mismatch(result, t)
 					if mismatch then
 						return false, mismatch
 					end
 				end
 				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
 	-- Accept any unit with an engineering notation prefix like &quot;e6cuft&quot;
 	-- (million cubic feet), but not chained prefixes like &quot;e3e6cuft&quot;,
 	-- and not if the unit is a combination or multiple,
 	-- and not if the unit has an offset or is a built-in.
 	-- Only en digits are accepted.
 	local exponent, baseunit = unitcode:match('^e(%d+)(.*)')
 	if exponent then
 		local engscale = text_code.eng_scales[exponent]
 		if engscale then
 			local success, result = lookup(parms, baseunit, 'no_combination', utable, fails, depth)
 			if success and not (result.offset or result.builtin or result.engscale) then
 				result.unitcode = unitcode  -- 'e6cuft' not 'cuft'
 				result.defkey = unitcode  -- key to lookup default exception
 				result.engscale = engscale
 				result.scale = result.scale * 10 ^ tonumber(exponent)
 				return true, result
 			end
 		end
 	end
 	-- Look for x/y; split on right-most slash to get scale correct (x/y/z is x/y per z).
 	local top, bottom = unitcode:match('^(.-)/([^/]+)$')
 	if top and not unitcode:find('e%d') then
 		-- If valid, create an automatic per unit for an &quot;x/y&quot; unit code.
 		-- The unitcode must not include extraneous spaces.
 		-- Engineering notation (apart from at start and which has been stripped before here),
 		-- is not supported so do not make a per unit if find text like 'e3' in unitcode.
 		local success, result = call_make_per({ per = {top, bottom} })
 		if success then
 			return true, result
 		end
 	end
 	if not parms.opt_ignore_error and not get_range(unitcode) then
 		-- Want the &quot;what links here&quot; list for the extra_module to show only cases
 		-- where an extra unit is used, so do not require it if invoked from {{val}}
 		-- or if looking up a range word which cannot be a unit.
 		if not extra_units then
 			local success, extra = pcall(function () return require(extra_module).extra_units end)
 			if success and type(extra) == 'table' then
 				extra_units = extra
 			end
 		end
 		if extra_units then
 			-- A unit in one data table might refer to a unit in the other table, so
 			-- switch between them, relying on fails or depth to terminate loops.
 			if not fails[unitcode] then
 				fails[unitcode] = true
 				local other = (utable == all_units) and extra_units or all_units
 				local success, result = lookup(parms, unitcode, what, other, fails, depth)
 				if success then
 					return true, result
 				end
 			end
 		end
 	end
 	if to_en_table then
 		-- At fawiki it is common to translate all digits so a unit like &quot;km2&quot; becomes &quot;km۲&quot;.
 		local en_code = ustring.gsub(unitcode, '%d', to_en_table)
 		if en_code ~= unitcode then
 			return lookup(parms, en_code, what, utable, fails, depth)
 		end
 	end
 	return false, { 'cvt_unknown', unitcode }
 end
 
 local function valid_number(num)
 	-- Return true if num is a valid number.
 	-- In Scribunto (different from some standard Lua), when expressed as a string,
 	-- overflow or other problems are indicated with text like &quot;inf&quot; or &quot;nan&quot;
 	-- which are regarded as invalid here (each contains &quot;n&quot;).
 	if type(num) == 'number' and tostring(num):find('n', 1, true) == nil then
 		return true
 	end
 end
 
 local function hyphenated(name, parts)
 	-- Return a hyphenated form of given name (for adjectival usage).
 	-- The name may be linked and the target of the link must not be changed.
 	-- Hypothetical examples:
 	--   [[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 &quot;[[abc[[def]]ghi]]&quot;).
 	-- 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 &quot;(pre-1954&amp;nbsp;US) nautical mile&quot;], and
 	-- not spaces immediately before '(' or in '(...)' [for cases like
 	-- &quot;British thermal unit (ISO)&quot; and &quot;Calorie (International Steam Table)&quot;].
 	if name:find(' ', 1, true) then
 		if parts then
 			local pos
 			if name:sub(1, 1) == '(' then
 				pos = name:find(')', 1, true)
 				if pos then
 					return name:sub(1, pos+1) .. name:sub(pos+2):gsub(' ', '-')
 				end
 			elseif name:sub(-1) == ')' then
 				pos = name:find('(', 1, true)
 				if pos then
 					return name:sub(1, pos-2):gsub(' ', '-') .. name:sub(pos-1)
 				end
 			end
 			return name:gsub(' ', '-')
 		end
 		parts = collection()
 		for before, item, after in name:gmatch('([^[]*)(%[%[[^[]*%]%])([^[]*)') 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 &quot;[[...]]&quot; was found in the original name.
 			parts:add(hyphenated(name, parts))
 		end
 		return table.concat(parts)
 	end
 	return name
 end
 
 local function hyphenated_maybe(parms, want_name, sep, id, inout)
 	-- Return s, f where
 	--   s = id, possibly modified
 	--   f = true if hyphenated
 	-- Possible modifications: hyphenate; prepend '-'; append mid text.
 	if id == nil or id == '' then
 		return ''
 	end
 	local mid = (inout == (parms.opt_flip and 'out' or 'in')) and parms.mid or ''
 	if want_name then
 		if parms.opt_adjectival then
 			return '-' .. hyphenated(id) .. mid, true
 		end
 		if parms.opt_add_s and id:sub(-1) ~= 's' then
 			id = id .. 's'  -- for nowiki
 		end
 	end
 	return sep .. id .. mid
 end
 
 local function use_minus(text)
 	-- Return text with Unicode minus instead of '-', if present.
 	if text:sub(1, 1) == '-' then
 		return MINUS .. text:sub(2)
 	end
 	return text
 end
 
 local function digit_groups(parms, text, method)
 	-- Return a numbered table of groups of digits (left-to-right, in local language).
 	-- Parameter method is a number or nil:
 	--   3 for 3-digit grouping (default), or
 	--   2 for 3-then-2 grouping (only for digits before decimal mark).
 	local len_right
 	local len_left = text:find('.', 1, true)
 	if len_left then
 		len_right = #text - len_left
 		len_left = len_left - 1
 	else
 		len_left = #text
 	end
 	local twos = method == 2 and len_left &gt; 5
 	local groups = collection()
 	local run = len_left
 	local n
 	if run &lt; 4 or (run == 4 and parms.opt_comma5) then
 		if parms.opt_gaps then
 			n = run
 		else
 			n = #text
 		end
 	elseif twos then
 		n = run % 2 == 0 and 1 or 2
 	else
 		n = run % 3 == 0 and 3 or run % 3
 	end
 	while run &gt; 0 do
 		groups:add(n)
 		run = run - n
 		n = (twos and run &gt; 3) and 2 or 3
 	end
 	if len_right then
 		if groups.n == 0 then
 			groups:add(0)
 		end
 		if parms.opt_gaps and len_right &gt; 3 then
 			local want4 = not parms.opt_gaps3  -- true gives no gap before trailing single digit
 			local isfirst = true
 			run = len_right
 			while run &gt; 0 do
 				n = (want4 and run == 4) and 4 or (run &gt; 3 and 3 or run)
 				if isfirst then
 					isfirst = false
 					groups[groups.n] = groups[groups.n] + 1 + n
 				else
 					groups:add(n)
 				end
 				run = run - n
 			end
 		else
 			groups[groups.n] = groups[groups.n] + 1 + len_right
 		end
 	end
 	local pos = 1
 	for i, length in ipairs(groups) do
 		groups[i] = from_en(text:sub(pos, pos + length - 1))
 		pos = pos + length
 	end
 	return groups
 end
 
 function with_separator(parms, text)  -- for forward declaration above
 	-- Input text is a number in en digits with optional '.' decimal mark.
 	-- Return an equivalent, formatted for display:
 	--   with a custom decimal mark instead of '.', if wanted
 	--   with thousand separators inserted, if wanted
 	--   digits in local language
 	-- The given text is like '123' or '123.' or '12345.6789'.
 	-- The text has no sign (caller inserts that later, if necessary).
 	-- When using gaps, they are inserted before and after the decimal mark.
 	-- Separators are inserted only before the decimal mark.
 	-- A trailing dot (as in '123.') is removed because their use appears to
 	-- be accidental, and such a number should be shown as '123' or '123.0'.
 	-- It is useful for convert to suppress the dot so, for example, '4000.'
 	-- is a simple way of indicating that all the digits are significant.
 	if text:sub(-1) == '.' then
 		text = text:sub(1, -2)
 	end
 	if #text &lt; 4 or parms.opt_nocomma or numsep == '' then
 		return from_en(text)
 	end
 	local groups = digit_groups(parms, text, group_method)
 	if parms.opt_gaps then
 		if groups.n &lt;= 1 then
 			return groups[1] or ''
 		end
 		local nowrap = '&lt;span style=&quot;white-space: nowrap&quot;&gt;'
 		local gap = '&lt;span style=&quot;margin-left: 0.25em&quot;&gt;'
 		local close = '&lt;/span&gt;'
 		return nowrap .. groups[1] .. gap .. table.concat(groups, close .. gap, 2, groups.n) .. close .. close
 	end
 	return table.concat(groups, numsep)
 end
 
 -- An input value like 1.23e12 is displayed using scientific notation (1.23×10¹²).
 -- That also makes the output use scientific notation, except for small values.
 -- In addition, very small or very large output values use scientific notation.
 -- Use format(fmtpower, significand, '10', exponent) where each argument is a string.
 local fmtpower = '%s&lt;span style=&quot;margin:0 .15em 0 .25em&quot;&gt;×&lt;/span&gt;%s&lt;sup&gt;%s&lt;/sup&gt;'
 
 local function with_exponent(parms, show, exponent)
 	-- Return wikitext to display the implied value in scientific notation.
 	-- Input uses en digits; output uses digits in local language.
 	return format(fmtpower, with_separator(parms, show), from_en('10'), use_minus(from_en(tostring(exponent))))
 end
 
 local function make_sigfig(value, sigfig)
 	-- Return show, exponent that are equivalent to the result of
 	-- converting the number 'value' (where value &gt;= 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 &lt;= 0 then
 		sigfig = 1
 	elseif sigfig &gt; 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 &gt;= 0 then
 		fracpart = fracpart - 1
 		exp = exp + 1
 	end
 	local digits = format('%.0f', 10^(fracpart + sigfig))
 	if #digits &gt; sigfig then
 		-- Overflow (for sigfig=3: like 0.9999 rounding to &quot;1000&quot;; need &quot;100&quot;).
 		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
 		'&lt;span class=&quot;frac nowrap&quot;&gt;%s&lt;sup&gt;%s&lt;/sup&gt;&amp;frasl;&lt;sub&gt;%s&lt;/sub&gt;&lt;/span&gt;',
 		'&lt;span class=&quot;frac nowrap&quot;&gt;%s&lt;span class=&quot;visualhide&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;sup&gt;%s&lt;/sup&gt;&amp;frasl;&lt;sub&gt;%s&lt;/sub&gt;&lt;/span&gt;',
 	},
 	{ -- 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
 		'&lt;span class=&quot;sfrac nowrap&quot; style=&quot;display:inline-block; vertical-align:-0.5em; font-size:85%%; text-align:center;&quot;&gt;&lt;span style=&quot;display:block; line-height:1em; padding:0 0.1em;&quot;&gt;%s%s&lt;/span&gt;&lt;span class=&quot;visualhide&quot;&gt;/&lt;/span&gt;&lt;span style=&quot;display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;&quot;&gt;%s&lt;/span&gt;&lt;/span&gt;',
 		'&lt;span class=&quot;sfrac nowrap&quot;&gt;%s&lt;span class=&quot;visualhide&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;display:inline-block; vertical-align:-0.5em; font-size:85%%; text-align:center;&quot;&gt;&lt;span style=&quot;display:block; line-height:1em; padding:0 0.1em;&quot;&gt;%s&lt;/span&gt;&lt;span class=&quot;visualhide&quot;&gt;/&lt;/span&gt;&lt;span style=&quot;display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;&quot;&gt;%s&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;',
 	},
 }
 
 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 if requested, or for very small or large values
 	--   (which forces result to not be spelled).
 	-- * Has no more than maxsigfig significant digits
 	--   (same as old template and {{#expr}}).
 	local xhi, xlo  -- these control when scientific notation (exponent) is used
 	if parms.opt_scientific then
 		xhi, xlo = 4, 2  -- default for output if input uses e-notation
 	elseif parms.opt_scientific_always then
 		xhi, xlo = 0, 0  -- always use scientific notation (experimental)
 	else
 		xhi, xlo = 10, 4  -- default
 	end
 	local sign = isnegative and MINUS or ''
 	local maxlen = maxsigfig
 	local tfrac
 	if type(show) == 'table' then
 		tfrac = show
 		show = tfrac.wholestr
 		assert(exponent == nil, 'Bug: exponent given with fraction')
 	end
 	if not tfrac and not exponent then
 		local integer, dot, decimals = show:match('^(%d*)(%.?)(.*)')
 		if integer == '0' or integer == '' then
 			local zeros, figs = decimals:match('^(0*)([^0]?.*)')
 			if #figs == 0 then
 				if #zeros &gt; maxlen then
 					show = '0.' .. zeros:sub(1, maxlen)
 				end
 			elseif #zeros &gt;= xlo then
 				show = figs
 				exponent = -#zeros
 			elseif #figs &gt; maxlen then
 				show = '0.' .. zeros .. figs:sub(1, maxlen)
 			end
 		elseif #integer &gt;= xhi then
 			show = integer .. decimals
 			exponent = #integer
 		else
 			maxlen = maxlen + #dot
 			if #show &gt; maxlen then
 				show = show:sub(1, maxlen)
 			end
 		end
 	end
 	if exponent then
 		local function zeros(n)
 			return string.rep('0', n)
 		end
 		if #show &gt; maxlen then
 			show = show:sub(1, maxlen)
 		end
 		if exponent &gt; xhi or exponent &lt;= -xlo or (exponent == xhi and show ~= '1' .. zeros(xhi - 1)) then
 			-- When xhi, xlo = 10, 4 (the default), scientific notation is used if the
 			-- rounded value satisfies: value &gt;= 1e9 or value &lt; 1e-4 (1e9 = 0.1e10),
 			-- except if show is '1000000000' (1e9), for example:
 			-- {{convert|1000000000|m|m|sigfig=10}} → 1,000,000,000 metres (1,000,000,000 m)
 			local significand
 			if #show &gt; 1 then
 				significand = show:sub(1, 1) .. '.' .. show:sub(2)
 			else
 				significand = show
 			end
 			return {
 				clean = '.' .. show,
 				exponent = exponent,
 				sign = sign,
 				show = sign .. with_exponent(parms, significand, exponent-1),
 				is_scientific = true,
 			}
 		end
 		if exponent &gt;= #show then
 			show = show .. zeros(exponent - #show)  -- result has no dot
 		elseif exponent &lt;= 0 then
 			show = '0.' .. zeros(-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, 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 &quot;12.1+3/4&quot; means 12 hands 1.75 inches
 	--   show is a string (formatted text for display of an input value,
 	--        and is spelled if wanted and possible)
 	--   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 local decimal mark, if any.
 	------------------------------------------------------------------------
 	-- Originally this function accepted x+y/z where x, y, z were any valid
 	-- numbers, possibly with a sign. For example '1.23e+2+1.2/2.4' = 123.5,
 	-- and '2-3/8' = 1.625. However, such usages were found to be errors or
 	-- misunderstandings, so since August 2014 the following restrictions apply:
 	--   x (if present) is an integer or has a single digit after decimal mark
 	--   y and z are unsigned integers
 	--   e-notation is not accepted
 	-- The overall number can start with '+' or '-' (so '12+3/4' and '+12+3/4'
 	-- and '-12-3/4' are valid).
 	-- Any leading negative sign is removed by the caller, so only inputs
 	-- like the following are accepted here (may have whitespace):
 	--   negative = false       false        true (there was a leading '-')
 	--   text     = '2/3'       '+2/3'       '2/3'
 	--   text     = '1+2/3'     '+1+2/3'     '1-2/3'
 	--   text     = '12.3+1/2'  '+12.3+1/2'  '12.3-1/2'
 	-- Values like '12.3+1/2' are accepted, but are intended only for use
 	-- with the hands unit (not worth adding code to enforce that).
 	------------------------------------------------------------------------
 	local leading_plus, prefix, numstr, slashes, denstr =
 		text:match('^%s*(%+?)%s*(.-)%s*(%d+)%s*(/+)%s*(%d+)%s*$')
 	if not leading_plus then
 		-- Accept a single U+2044 fraction slash because that may be pasted.
 		leading_plus, prefix, numstr, denstr =
 			text:match('^%s*(%+?)%s*(.-)%s*(%d+)%s*⁄%s*(%d+)%s*$')
 		slashes = '/'
 	end
 	local numerator = tonumber(numstr)
 	local denominator = tonumber(denstr)
 	if numerator == nil or denominator == nil or (negative and leading_plus ~= '') then
 		return nil
 	end
 	local whole, wholestr
 	if prefix == '' then
 		wholestr = ''
 		whole = 0
 	else
 		-- Any prefix must be like '12+' or '12-' (whole number and fraction sign);
 		-- '12.3+' and '12.3-' are also accepted (single digit after decimal point)
 		-- because '12.3+1/2 hands' is valid (12 hands 3½ inches).
 		local num1, num2, frac_sign = prefix:match('^(%d+)(%.?%d?)%s*([+%-])$')
 		if num1 == nil then return nil end
 		if num2 == '' then  -- num2 must be '' or like '.1' but not '.' or '.12'
 			wholestr = num1
 		else
 			if #num2 ~= 2 then return nil end
 			wholestr = num1 .. num2
 		end
 		if frac_sign ~= (negative and '-' or '+') then return nil end
 		whole = tonumber(wholestr)
 		if whole == nil then return nil end
 	end
 	local value = whole + numerator / denominator
 	if not valid_number(value) then return nil end
 	local altvalue = whole + numerator / (denominator * 10)
 	local style = #slashes  -- kludge: 1 or 2 slashes can be used to select style
 	if style &gt; 2 then style = 2 end
 	local wikitext = format_fraction(parms, 'in', negative, leading_plus .. wholestr, numstr, denstr, parms.opt_spell_in, style)
 	return value, altvalue, wikitext, denominator
 end
 
 local function extract_number(parms, text, another, no_fraction)
 	-- Return true, info if can extract a number from text,
 	-- where info is a table with the result,
 	-- or return false, t where t is an error message table.
 	-- Input can use en digits or digits in local language and can
 	-- have references at the end. Accepting references is intended
 	-- for use in infoboxes with a field for a value passed to convert.
 	-- Parameter another = true if the expected value is not the first.
 	-- Before processing, the input text is cleaned:
 	-- * Any thousand separators (valid or not) are removed.
 	-- * Any sign is replaced with '-' (if negative) or '' (otherwise).
 	--   That replaces Unicode minus with '-'.
 	-- If successful, the returned info table contains named fields:
 	--   value    = a valid number
 	--   altvalue = a valid number, usually same as value but different
 	--              if fraction used (for hands unit)
 	--   singular = true if value is 1 or -1 (to use singular form of units)
 	--   clean    = cleaned text with any separators and sign removed
 	--              (en digits and '.' decimal mark)
 	--   show     = text formatted for output, possibly with ref strip markers
 	--              (digits in local language and custom decimal mark)
 	-- The resulting show:
 	-- * Is for an input value and is spelled if wanted and possible.
 	-- * Has a rounded value, if wanted.
 	-- * Has digits grouped where necessary, if wanted.
 	-- * If negative, a Unicode minus is used; otherwise the sign is
 	--   '+' (if the input text used '+'), or is '' (if no sign in input).
 	text = strip(text or '')
 	local reference
 	local pos = text:find('\127', 1, true)
 	if pos then
 		local before = text:sub(1, pos - 1)
 		local remainder = text:sub(pos)
 		local refs = {}
 		while #remainder &gt; 0 do
 			local ref, spaces
 			ref, spaces, remainder = remainder:match('^(\127[^\127]*UNIQ[^\127]*%-ref[^\127]*\127)(%s*)(.*)')
 			if ref then
 				table.insert(refs, ref)
 			else
 				refs = {}
 				break
 			end
 		end
 		if #refs &gt; 0 then
 			text = strip(before)
 			reference = table.concat(refs)
 		end
 	end
 	local clean = to_en(text, parms)
 	if clean == '' then
 		return false, { another and 'cvt_no_num2' or 'cvt_no_num' }
 	end
 	local isnegative, propersign = false, ''  -- most common case
 	local singular, show, denominator
 	local value = tonumber(clean)
 	local altvalue
 	if value then
 		local sign = clean:sub(1, 1)
 		if sign == '+' or sign == '-' then
 			propersign = (sign == '+') and '+' or MINUS
 			clean = clean:sub(2)
 		end
 		if value &lt; 0 then
 			isnegative = true
 			value = -value
 		end
 	else
 		local valstr
 		for _, prefix in ipairs({ '-', MINUS, '&amp;minus;' }) do
 			-- Including '-' 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)
 				if valstr:match('^%s') then  -- &quot;- 1&quot; is invalid but &quot;-1 - 1/2&quot; is ok
 					return false, { 'cvt_bad_num', text }
 				end
 				break
 			end
 		end
 		if valstr then
 			isnegative = true
 			propersign = MINUS
 			clean = valstr
 			value = tonumber(clean)
 		end
 		if value == nil then
 			if not no_fraction then
 				value, altvalue, show, denominator = extract_fraction(parms, clean, isnegative)
 			end
 			if value == nil then
 				return false, { 'cvt_bad_num', text }
 			end
 			if value &lt;= 1 then
 				singular = true  -- for example, &quot;½ mile&quot; or &quot;one half mile&quot; (singular unit)
 			end
 		end
 	end
 	if not valid_number(value) then  -- for example, &quot;1e310&quot; may overflow
 		return false, { 'cvt_invalid_num' }
 	end
 	if show == nil then
 		-- clean is a non-empty string with no spaces, and does not represent a fraction,
 		-- and value = tonumber(clean) is a number &gt;= 0.
 		-- If the input uses e-notation, show will be displayed using a power of ten, but
 		-- we use the number as given so it might not be normalized scientific notation.
 		-- The input value is spelled if specified so any e-notation is ignored;
 		-- that allows input like 2e6 to be spelled as &quot;two million&quot; which works
 		-- because the spell module converts '2e6' to '2000000' before spelling.
 		local function rounded(value, default, exponent)
 			local precision = parms.opt_ri
 			if precision then
 				local fmt = '%.' .. format('%d', precision) .. 'f'
 				local result = fmt:format(tonumber(value) + 2e-14)  -- fudge for some common cases of bad rounding
 				if not exponent then
 					singular = (tonumber(result) == 1)
 				end
 				return result
 			end
 			return default
 		end
 		singular = (value == 1)
 		local scientific
 		local significand, exponent = clean:match('^([%d.]+)[Ee]([+%-]?%d+)')
 		if significand then
 			show = with_exponent(parms, rounded(significand, significand, exponent), exponent)
 			scientific = true
 		else
 			show = with_separator(parms, rounded(value, clean))
 		end
 		show = propersign .. show
 		if parms.opt_spell_in then
 			show = spell_number(parms, 'in', propersign .. rounded(value, clean)) or show
 			scientific = false
 		end
 		if scientific then
 			parms.opt_scientific = true
 		end
 	end
 	if isnegative and (value ~= 0) then
 		value = -value
 		altvalue = -(altvalue or value)
 	end
 	return true, {
 		value = value,
 		altvalue = altvalue or value,
 		singular = singular,
 		clean = clean,
 		show = show .. (reference or ''),
 		denominator = denominator,
 	}
 end
 
 local function get_number(text)
 	-- Return v, f where:
 	--   v = nil (text is not a number)
 	-- or
 	--   v = value of text (text is a number)
 	--   f = true if value is an integer
 	-- Input can use en digits or digits in local language,
 	-- but no separators, no Unicode minus, and no fraction.
 	if text then
 		local number = tonumber(to_en(text))
 		if number then
 			local _, fracpart = math.modf(number)
 			return number, (fracpart == 0)
 		end
 	end
 end
 
 local function gcd(a, b)
 	-- Return the greatest common denominator for the given values,
 	-- which are known to be positive integers.
 	if a &gt; b then
 		a, b = b, a
 	end
 	if a &lt;= 0 then
 		return b
 	end
 	local r = b % a
 	if r &lt;= 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 &lt;= 0 then
 		return '0'
 	end
 	if denominator &lt;= 0 or value &gt; 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 &gt;= denominator then
 		integer = integer + 1
 		numerator = 0
 	end
 	local wholestr = tostring(integer)
 	if numerator &gt; 0 then
 		local div = gcd(numerator, denominator)
 		if div &gt; 1 then
 			numerator = numerator / div
 			denominator = denominator / div
 		end
 		return {
 			wholestr = (integer &gt; 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 &quot;no preunit&quot;
 	-- Using '+' gives output like &quot;5+ feet&quot; (no space before, but space after).
 	local function withspace(text, wantboth)
 		-- Return text with space before and, if wantboth, after.
 		-- However, no space is added if there is a space or '&amp;nbsp;' or '-'
 		-- at that position ('-' is for adjectival text).
 		-- There is also no space if text starts with '&amp;'
 		-- (e.g. '&amp;deg;' would display a degree symbol with no preceding space).
 		local char = text:sub(1, 1)
 		if char == '&amp;' then
 			return text  -- an html entity can be used to specify the exact display
 		end
 		if not (char == ' ' or char == '-' or char == '+') then
 			text = ' ' .. text
 		end
 		if wantboth then
 			char = text:sub(-1, -1)
 			if not (char == ' ' or char == '-' or text:sub(-6, -1) == '&amp;nbsp;') then
 				text = text .. ' '
 			end
 		end
 		return text
 	end
 	local PLUS = '+ '
 	preunit1 = preunit1 or ''
 	local trim1 = strip(preunit1)
 	if count == 1 then
 		if trim1 == '' then
 			return nil
 		end
 		if trim1 == '+' then
 			return PLUS
 		end
 		return withspace(preunit1, true)
 	end
 	preunit1 = withspace(preunit1)
 	preunit2 = preunit2 or ''
 	local trim2 = strip(preunit2)
 	if trim1 == '+' then
 		if trim2 == '' or trim2 == '+' then
 			return PLUS, PLUS
 		end
 		preunit1 = PLUS
 	end
 	if trim2 == '' then
 		if trim1 == '' then
 			return nil, nil
 		end
 		preunit2 = preunit1
 	elseif trim2 == '+' then
 		preunit2 = PLUS
 	elseif trim2 == '&amp;#32;' then  -- trick to make preunit2 empty
 		preunit2 = nil
 	else
 		preunit2 = withspace(preunit2)
 	end
 	return preunit1, preunit2
 end
 
 local function range_text(range, want_name, parms, before, after, inout)
 	-- Return before .. rtext .. after
 	-- where rtext is the text that separates two values in a range.
 	local rtext, adj_text, exception
 	if type(range) == 'table' then
 		-- Table must specify range text for ('off' and 'on') or ('input' and 'output'),
 		-- and may specify range text for 'adj=on',
 		-- and may specify exception = true.
 		rtext = range[want_name and 'off' or 'on'] or
 				range[((inout == 'in') == (parms.opt_flip == true)) and 'output' or 'input']
 		adj_text = range['adj']
 		exception = range['exception']
 	else
 		rtext = range
 	end
 	if parms.opt_adjectival then
 		if want_name or (exception and parms.abbr_org == 'on') then
 			rtext = adj_text or rtext:gsub(' ', '-'):gsub('&amp;nbsp;', '-')
 		end
 	end
 	if rtext == '–' and after:sub(1, #MINUS) == MINUS then
 		rtext = '&amp;nbsp;– '
 	end
 	return before .. rtext .. after
 end
 
 local function get_composite(parms, iparm, 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] = &quot;2&quot;, just after the first unit)
 	--   in_unit_table = (unit table for &quot;yd&quot;; contains value 1 for number of yards)
 	-- Return true, iparm, unit where
 	--   iparm = index just after the composite units (7 in above example)
 	--   unit = composite unit table holding all input units,
 	-- or return true if no composite unit is present in parms,
 	-- or return false, t where t is an error message table.
 	local default, subinfo
 	local composite_units, count = { in_unit_table }, 1
 	local fixups = {}
 	local total = in_unit_table.valinfo[1].value
 	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] or subunit.subdivs[(all_units[subcode] or {}).target]
 		if not subdiv then
 			break
 		end
 		local success
 		success, subunit = lookup(parms, subcode, 'no_combination')
 		if not success then return false, subunit end  -- should never occur
 		success, subinfo = extract_number(parms, 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 &gt; 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 &gt; 2 and name) then
 			composite_units[i].fixed_name = name
 		else
 			local success, alternate = lookup(parms, unit, 'no_combination')
 			if not success then return false, alternate end  -- should never occur
 			alternate.inout = 'in'
 			alternate.valinfo = fixup.valinfo
 			composite_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.
 	currency_text = nil  -- local testing can hold module in memory; must clear globals
 	local accept_any_text = {
 		input = true,
 		qid = true,
 		qual = true,
 		stylein = true,
 		styleout = true,
 		tracking = true,
 	}
 	if kv_pairs.adj and kv_pairs.sing then
 		-- For enwiki (before translation), warn if attempt to use adj and sing
 		-- as the latter is a deprecated alias for the former.
 		if kv_pairs.adj ~= kv_pairs.sing and kv_pairs.sing ~= '' then
 			add_warning(parms, 1, 'cvt_unknown_option', 'sing=' .. kv_pairs.sing)
 		end
 		kv_pairs.sing = nil
 	end
 	kv_pairs.comma = kv_pairs.comma or config.comma  -- for plwiki who want default comma=5
 	for loc_name, loc_value in pairs(kv_pairs) do
 		local en_name = text_code.en_option_name[loc_name]
 		if en_name then
 			local en_value
 			if en_name == '$' or en_name == 'frac' or en_name == 'sigfig' then
 				if loc_value == '' then
 					add_warning(parms, 2, 'cvt_empty_option', loc_name)
 				elseif en_name == '$' then
 					-- Value should be a single character like &quot;€&quot; for the euro currency symbol, but anything is accepted.
 					currency_text = (loc_value == 'euro') and '€' or loc_value
 				else
 					local minimum
 					local number, is_integer = get_number(loc_value)
 					if en_name == 'frac' then
 						minimum = 2
 						if number and number &lt; 0 then
 							parms.opt_fraction_horizontal = true
 							number = -number
 						end
 					else
 						minimum = 1
 					end
 					if number and is_integer and number &gt;= minimum then
 						en_value = number
 					else
 						add_warning(parms, 1, (en_name == 'frac' and 'cvt_bad_frac' or 'cvt_bad_sigfig'), loc_name .. '=' .. loc_value)
 					end
 				end
 			elseif accept_any_text[en_name] then
 				en_value = loc_value ~= '' and loc_value or nil  -- accept non-empty user text with no validation
 				if en_name == 'input' then
 					-- May have something like {{convert|input=}} (empty input) if source is an infobox
 					-- with optional fields. In that case, want to output nothing rather than an error.
 					parms.input_text = loc_value  -- keep input because parms.input is nil if loc_value == ''
 				end
 			else
 				en_value = text_code.en_option_value[en_name][loc_value]
 				if en_value and en_value:sub(-1) == '?' then
 					en_value = en_value:sub(1, -2)
 					add_warning(parms, -1, 'cvt_deprecated', loc_name .. '=' .. loc_value)
 				end
 				if en_value == nil then
 					if loc_value == '' then
 						add_warning(parms, 2, 'cvt_empty_option', loc_name)
 					else
 						add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)
 					end
 				elseif en_value == '' then
 					en_value = nil  -- an ignored option like adj=off
 				elseif type(en_value) == 'string' and en_value:sub(1, 4) == 'opt_' then
 					for _, v in ipairs(split(en_value, ',')) do
 						local lhs, rhs = v:match('^(.-)=(.+)$')
 						if rhs then
 							parms[lhs] = tonumber(rhs) or rhs
 						else
 							parms[v] = true
 						end
 					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
 	local abbr_entered = parms.abbr
 	local cfg_abbr = config.abbr
 	if cfg_abbr then
 		-- Don't warn if invalid because every convert would show that warning.
 		if cfg_abbr == 'on always' then
 			parms.abbr = 'on'
 		elseif cfg_abbr == 'off always' then
 			parms.abbr = 'off'
 		elseif parms.abbr == nil then
 			if cfg_abbr == 'on default' then
 				parms.abbr = 'on'
 			elseif cfg_abbr == 'off default' then
 				parms.abbr = 'off'
 			end
 		end
 	end
 	if parms.abbr then
 		if parms.abbr == 'unit' then
 			parms.abbr = 'on'
 			parms.number_word = true
 		end
 		parms.abbr_org = parms.abbr  -- original abbr, before any flip
 	elseif parms.opt_hand_hh then
 		parms.abbr_org = 'on'
 		parms.abbr = 'on'
 	else
 		parms.abbr = 'out'  -- default is to abbreviate output only (use symbol, not name)
 	end
 	if parms.opt_order_out then
 		-- Disable options that do not work in a useful way with order=out.
 		parms.opt_flip = nil  -- override adj=flip
 		parms.opt_spell_in = nil
 		parms.opt_spell_out = nil
 		parms.opt_spell_upper = nil
 	end
 	if parms.opt_spell_out and not abbr_entered then
 		parms.abbr = 'off'  -- should show unit name when spelling the output value
 	end
 	if parms.opt_flip then
 		local function swap_in_out(option)
 			local value = 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 abbr_entered == nil and parms.lk == nil then
 			parms.opt_values = true
 		end
 		parms.table_align = parms.opt_table and 'right' or 'center'
 	end
 	if parms.table_align or parms.opt_sortable_on then
 		parms.need_table_or_sort = true
 	end
 	local disp_joins = text_code.disp_joins
 	local default_joins = disp_joins['b']
 	parms.join_between = default_joins[3] or '; '
 	local disp = parms.disp
 	if disp == nil then  -- special case for the most common setting
 		parms.joins = default_joins
 	elseif disp == 'x' then
 		-- Later, parms.joins is set from the input parameters.
 	else
 		-- Old template does this.
 		local abbr = parms.abbr
 		if disp == 'slash' then
 			if abbr_entered == nil then
 				disp = 'slash-nbsp'
 			elseif abbr == 'in' or abbr == 'out' then
 				disp = 'slash-sp'
 			else
 				disp = 'slash-nosp'
 			end
 		elseif disp == 'sqbr' then
 			if abbr == 'on' then
 				disp = 'sqbr-nbsp'
 			else
 				disp = 'sqbr-sp'
 			end
 		end
 		parms.joins = disp_joins[disp] or default_joins
 		parms.join_between = parms.joins[3] or parms.join_between
 		parms.wantname = parms.joins.wantname
 	end
 	if (en_default and not parms.opt_lang_local and (parms[1] or ''):find('%d')) or parms.opt_lang_en then
 		from_en_table = nil
 	end
 	if en_default and from_en_table then
 		-- For hiwiki: localized symbol/name is defined with the US symbol/name field,
 		-- and is used if output uses localized numbers.
 		parms.opt_sp_us = true
 	end
 	return true
 end
 
 local function get_values(parms)
 	-- If successful, update parms and return true, v, i where
 	--   v = table of input values
 	--   i = index to next entry in parms after those processed here
 	-- or return false, t where t is an error message table.
 	local valinfo = collection()  -- numbered table of input values
 	local range = collection()  -- numbered table of range items (having, for example, 2 range items requires 3 input values)
 	local had_nocomma  -- true if removed &quot;nocomma&quot; kludge from second parameter (like &quot;tonocomma&quot;)
 	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 (&quot;1-23&quot; for &quot;1 to 23&quot;).
 		-- However, &quot;-1-2/3&quot; is a negative fraction (-1⅔), so it must be extracted first.
 		-- Do not unpack a parameter if it is like &quot;3-1/2&quot; which is sometimes incorrectly
 		-- used instead of &quot;3+1/2&quot; (and which should not be interpreted as &quot;3 to ½&quot;).
 		-- Unpacked items are inserted into the parms table.
 		-- The tail recursion allows combinations like &quot;1x2 to 3x4&quot;.
 		local valstr = strip(parms[i])  -- trim so any '-' as a negative sign will be at start
 		local success, result = extract_number(parms, valstr, i &gt; 1)
 		if not success and valstr and i &lt; 20 then  -- check i to limit abuse
 			local lhs, sep, rhs = valstr:match('^(%S+)%s+(%S+)%s+(%S.*)')
 			if lhs and not (sep == '-' and rhs:match('/')) then
 				if sep:find('%d') then
 					return success, result  -- to reject {{convert|1 234 567|m}} with a decent message (en only)
 				end
 				parms[i] = rhs
 				table.insert(parms, i, sep)
 				table.insert(parms, i, lhs)
 				return extractor(i)
 			end
 			if not valstr:match('%-.*/') then
 				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)
 					end
 				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 &quot;±&quot; and so is a change (significant for range like {{convert|5|±|5|°C}})
 			is_change = nil
 		end
 		valinfo:add(info)
 		local range_item = get_range(strip(parms[i]))
 		if not range_item then
 			break
 		end
 		i = i + 1
 		range:add(range_item)
 		if type(range_item) == 'table' then
 			-- For range &quot;x&quot;, if append unit to some values, append it to all.
 			parms.in_range_x = parms.in_range_x or range_item.in_range_x
 			parms.out_range_x = parms.out_range_x or range_item.out_range_x
 			parms.abbr_range_x = parms.abbr_range_x or range_item.abbr_range_x
 			is_change = range_item.is_range_change
 		end
 	end
 	if range.n &gt; 0 then
 		if range.n &gt; 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 &quot;{{convert|valid_value|valid_unit|...}}&quot;,
 	-- return true, i, in_unit, in_unit_table
 	-- i = index in parms of what follows valid_unit, if anything.
 	-- The valid_value is not negative and does not use a fraction, and
 	-- no options requiring further processing of the input are used.
 	-- Otherwise, return nothing or return false, parm1 for caller to interpret.
 	-- Testing shows this function is successful for 96% of converts in articles,
 	-- and that on average it speeds up converts by 8%.
 	local clean = to_en(strip(parms[1] or ''), parms)
 	if parms.opt_ri or parms.opt_spell_in or #clean &gt; 10 or not clean:match('^[0-9.]+$') then
 		return false, clean
 	end
 	local value = tonumber(clean)
 	if not value then return end
 	local info = {
 		value = value,
 		altvalue = value,
 		singular = (value == 1),
 		clean = clean,
 		show = with_separator(parms, clean),
 	}
 	local in_unit = strip(parms[2])
 	local success, in_unit_table = lookup(parms, in_unit, 'no_combination')
 	if not success then return end
 	in_unit_table.valinfo = { info }
 	return true, 3, in_unit, in_unit_table
 end
 
 local function wikidata_call(parms, operation, ...)
 	-- Return true, s where s is the result of a Wikidata operation,
 	-- or return false, t where t is an error message table.
 	local function worker(...)
 		wikidata_code = wikidata_code or require(wikidata_module)
 		wikidata_data = wikidata_data or mw.loadData(wikidata_data_module)
 		return wikidata_code[operation](wikidata_data, ...)
 	end
 	local success, status, result = pcall(worker, ...)
 	if success then
 		return status, result
 	end
 	if parms.opt_sortable_debug then
 		-- Use debug=yes to crash if an error while accessing Wikidata.
 		error('Error accessing Wikidata: ' .. status, 0)
 	end
 	return false, { 'cvt_wd_fail' }
 end
 
 local function get_parms(parms, args)
 	-- If successful, update parms and return true, unit where
 	--   parms is a table of all arguments passed to the template
 	--        converted to named arguments, and
 	--   unit is the input unit table;
 	-- or return false, t where t is an error message table.
 	-- For special processing (not a convert), can also return
 	-- true, wikitext where wikitext is the final result.
 	-- The returned input unit table may be for a fake unit using the specified
 	-- unit code as the symbol and name, and with bad_mcode = message code table.
 	-- MediaWiki removes leading and trailing whitespace from the values of
 	-- named arguments. However, the values of numbered arguments include any
 	-- whitespace entered in the template, and whitespace is used by some
 	-- parameters (example: the numbered parameters associated with &quot;disp=x&quot;).
 	local kv_pairs = {}  -- table of input key:value pairs where key is a name; needed because cannot iterate parms and add new fields to it
 	for k, v in pairs(args) do
 		if type(k) == 'number' or k == 'test' then  -- parameter &quot;test&quot; is reserved for testing and is not translated
 			parms[k] = v
 		else
 			kv_pairs[k] = v
 		end
 	end
 	if parms.test == 'wikidata' then
 		local ulookup = function (ucode)
 			-- Use empty table for parms so it does not accumulate results when used repeatedly.
 			return lookup({}, ucode, 'no_combination')
 		end
 		return wikidata_call(parms, '_listunits', ulookup)
 	end
 	local success, msg = translate_parms(parms, kv_pairs)
 	if not success then return false, msg end
 	if parms.input then
 		success, msg = wikidata_call(parms, '_adjustparameters', parms, 1)
 		if not success then return false, msg end
 	end
 	local success, i, in_unit, in_unit_table = simple_get_values(parms)
 	if not success then
 		if type(i) == 'string' and i:match('^NNN+$') then
 			-- Some infoboxes have examples like {{convert|NNN|m}} (3 or more &quot;N&quot;).
 			-- Output an empty string for these.
 			return false, { 'cvt_no_output' }
 		end
 		local valinfo
 		success, valinfo, i = get_values(parms)
 		if not success then return false, valinfo end
 		in_unit = strip(parms[i])
 		i = i + 1
 		success, in_unit_table = lookup(parms, in_unit, 'no_combination')
 		if not success then
 			in_unit = in_unit or ''
 			if parms.opt_ignore_error then  -- display given unit code with no error (for use with {{val}})
 				in_unit_table = ''  -- suppress error message and prevent processing of output unit
 			end
 			in_unit_table = setmetatable({
 				symbol = in_unit, name2 = in_unit, utype = in_unit,
 				scale = 1, default = '', defkey = '', linkey = '',
 				bad_mcode = in_unit_table }, unit_mt)
 		end
 		in_unit_table.valinfo = valinfo
 	end
 	if parms.test == 'msg' then
 		-- Am testing the messages produced when no output unit is specified, and
 		-- the input unit has a missing or invalid default.
 		-- Set two units for testing that.
 		-- LATER: Remove this code.
 		if in_unit == 'chain' then
 			in_unit_table.default = nil  -- no default
 		elseif in_unit == 'rd' then
 			in_unit_table.default  = &quot;ft!X!m&quot;  -- an invalid expression
 		end
 	end
 	in_unit_table.inout = 'in'  -- this is an input unit
 	if not parms.range then
 		local success, inext, composite_unit = get_composite(parms, i, in_unit_table)
 		if not success then return false, inext end
 		if composite_unit then
 			in_unit_table = composite_unit
 			i = inext
 		end
 	end
 	if in_unit_table.builtin == 'mach' then
 		-- As with old template, a number following Mach as the input unit is the altitude,
 		-- and there is no way to specify an altitude for the output unit.
 		-- Could put more code in this function to get any output unit and check for
 		-- an altitude following that unit.
 		local success, info = extract_number(parms, parms[i], false, true)
 		if success then
 			i = i + 1
 			in_unit_table.altitude = info.value
 		end
 	end
 	local word = 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 word and not set_precision(word) then
 		parms.out_unit = parms.out_unit or word
 		if set_precision(strip(parms[i])) then
 			i = i + 1
 		end
 	end
 	if parms.opt_adj_mid then
 		word = parms[i]
 		i = i + 1
 		if word then  -- mid-text words
 			if word:sub(1, 1) == '-' then
 				parms.mid = word
 			else
 				parms.mid = ' ' .. word
 			end
 		end
 	end
 	if parms.opt_one_preunit then
 		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 '&amp;#32;' rather than ' ' to avoid the default
 			first = ' [&amp;nbsp;' .. first
 			second = '&amp;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
 	for j = i, i + 3 do
 		local parm = parms[j]  -- warn if find a non-empty extraneous parameter
 		if parm and parm:match('%S') then
 			add_warning(parms, 1, 'cvt_unknown_option', parm)
 			break
 		end
 	end
 	return true, in_unit_table
 end
 
 local function record_default_precision(parms, out_current, precision)
 	-- If necessary, adjust parameters and return a possibly adjusted precision.
 	-- When converting a range of values where a default precision is required,
 	-- that default is calculated for each value because the result sometimes
 	-- depends on the precise input and output values. This function may cause
 	-- the entire convert process to be repeated in order to ensure that the
 	-- same default precision is used for each individual convert.
 	-- If that were not done, a range like 1000 to 1000.4 may give poor results
 	-- because the first output could be heavily rounded, while the second is not.
 	-- For range 1000.4 to 1000, this function can give the second convert the
 	-- same default precision that was used for the first.
 	if not parms.opt_round_each then
 		local maxdef = out_current.max_default_precision
 		if maxdef then
 			if maxdef &lt; 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 subunit_ignore_trailing_zero
 	local subunit_more_precision  -- kludge for &quot;in&quot; used in input like &quot;|2|ft|6|in&quot;
 	local composite = in_current.composite
 	if composite then
 		subunit_ignore_trailing_zero = true  -- input &quot;|2|st|10|lb&quot; 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 &quot;|2|ft|6|in&quot;
 		end
 	end
 	if denominator and denominator &gt; 0 then
 		prec = math.max(log10(denominator), 1)
 	else
 		-- Count digits after decimal mark, handling cases like '12.345e6'.
 		local exponent
 		local integer, dot, decimals, expstr = inclean:match('^(%d*)(%.?)(%d*)(.*)')
 		local e = expstr:sub(1, 1)
 		if e == 'e' or e == 'E' then
 			exponent = tonumber(expstr:sub(2))
 		end
 		if dot == '' then
 			prec = subunit_ignore_trailing_zero and 0 or -integer:match('0*$'):len()
 		else
 			prec = #decimals
 		end
 		if exponent then
 			-- So '1230' and '1.23e3' both give prec = -1, and '0.00123' and '1.23e-3' give 5.
 			prec = prec - exponent
 		end
 	end
 	if in_current.istemperature and out_current.istemperature then
 		-- Converting between common temperatures (°C, °F, °R, K); not keVT.
 		-- Kelvin value can be almost zero, or small but negative due to precision problems.
 		-- Also, an input value like -300 C (below absolute zero) gives negative kelvins.
 		-- Calculate minimum precision from absolute value.
 		adjust = 0
 		local kelvin = abs((invalue - in_current.offset) * in_current.scale)
 		if kelvin &lt; 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 &lt;= 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 &quot;50&quot; should be
 			-- interpreted as &quot;from 45 to 55&quot; or &quot;from 49.5 to 50.5&quot;.
 			adjust = -log10(in_current.scale)
 		elseif subunit_more_precision then
 			-- Conversion like &quot;{{convert|6|ft|1|in|cm}}&quot; (where subunit is &quot;in&quot;)
 			-- 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) &lt; 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 &quot;inches&quot; not &quot;in&quot; 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 function user_style(parms, i)
 	-- Return text for a user-specified style for a table cell, or '' if none,
 	-- given i = 1 (input style) or 2 (output style).
 	local style = parms[(i == 1) and 'stylein' or 'styleout']
 	if style then
 		style = style:gsub('&quot;', '')
 		if style ~= '' then
 			if style:sub(-1) ~= ';' then
 				style = style .. ';'
 			end
 			return style
 		end
 	end
 	return ''
 end
 
 local function make_table_or_sort(parms, invalue, info, in_current, scaled_top)
 	-- Set options to handle output for a table or a sort key, or both.
 	-- The text sort key is based on the value resulting from converting
 	-- the input to a fake base unit with scale = 1, and other properties
 	-- required for a conversion derived from the input unit.
 	-- For other modules, return the sort key in a hidden span element, and
 	-- the scaled value used to generate the sort key.
 	-- If scaled_top is set, it is the scaled value of the numerator of a per unit
 	-- to be combined with this unit (the denominator) to make the sort key.
 	-- Scaling only works with units that convert with a factor (not temperature).
 	local sortkey, scaled_value
 	if parms.opt_sortable_on then
 		local base = {  -- a fake unit with enough fields for a valid convert
 			scale = 1,
 			invert = in_current.invert and 1,
 			iscomplex = in_current.iscomplex,
 			offset = in_current.offset and 0,
 		}
 		local outvalue, extra = convert(parms, invalue, info, in_current, base)
 		if extra then
 			outvalue = extra.outvalue
 		end
 		if in_current.istemperature then
 			-- Have converted to kelvin; assume numbers close to zero have a
 			-- rounding error and should be zero.
 			if abs(outvalue) &lt; 1e-12 then
 				outvalue = 0
 			end
 		end
 		if scaled_top and outvalue ~= 0 then
 			outvalue = scaled_top / outvalue
 		end
 		scaled_value = outvalue
 		if not valid_number(outvalue) then
 			if outvalue &lt; 0 then
 				sortkey = '1000000000000000000'
 			else
 				sortkey = '9000000000000000000'
 			end
 		elseif outvalue == 0 then
 			sortkey = '5000000000000000000'
 		else
 			local mag = floor(log10(abs(outvalue)) + 1e-14)
 			local prefix
 			if outvalue &gt; 0 then
 				prefix = 7000 + mag
 			else
 				prefix = 2999 - mag
 				outvalue = outvalue + 10^(mag+1)
 			end
 			sortkey = format('%d', prefix) .. format('%015.0f', floor(outvalue * 10^(14-mag)))
 		end
 	end
 	local sortspan
 	if sortkey and not parms.table_align then
 		sortspan = parms.opt_sortable_debug and
 			'&lt;span data-sort-value=&quot;' .. sortkey .. '♠&quot;&gt;&lt;span style=&quot;border:1px solid&quot;&gt;' .. sortkey .. '♠&lt;/span&gt;&lt;/span&gt;' or
 			'&lt;span data-sort-value=&quot;' .. sortkey .. '♠&quot;&gt;&lt;/span&gt;'
 		parms.join_before = sortspan
 	end
 	if parms.table_align then
 		local sort
 		if sortkey then
 			sort = ' data-sort-value=&quot;' .. sortkey .. '&quot;'
 			if parms.opt_sortable_debug then
 				parms.join_before = '&lt;span style=&quot;border:1px solid&quot;&gt;' .. sortkey .. '&lt;/span&gt;'
 			end
 		else
 			sort = ''
 		end
 		local style = 'style=&quot;text-align:' .. parms.table_align .. ';'
 		local joins = {}
 		for i = 1, 2 do
 			joins[i] = (i == 1 and '' or '\n|') .. style .. user_style(parms, i) .. '&quot;' .. sort .. '|'
 		end
 		parms.table_joins = joins
 	end
 	return sortspan, scaled_value
 end
 
 local cvt_to_hand
 
 local function cvtround(parms, info, in_current, out_current)
 	-- Return true, t where t is a table with the conversion results; fields:
 	--   show = rounded, formatted string with the result of converting value in info,
 	--      using the rounding specified in parms.
 	--   singular = true if result (after rounding and ignoring any negative sign)
 	--      is &quot;1&quot;, or like &quot;1.00&quot;, or is a fraction with value &lt; 1;
 	--   (and more fields shown below, and a calculated 'absvalue' field).
 	-- 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.
 	if out_current.builtin == 'hand' then
 		return cvt_to_hand(parms, info, in_current, out_current)
 	end
 	local invalue = in_current.builtin == 'hand' and info.altvalue or info.value
 	local outvalue, extra = convert(parms, invalue, info, in_current, out_current)
 	if parms.need_table_or_sort then
 		parms.need_table_or_sort = nil  -- process using first input value only
 		make_table_or_sort(parms, invalue, info, in_current)
 	end
 	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 &lt; 0 then
 		isnegative = true
 		outvalue = -outvalue
 	end
 	local precision, show, exponent
 	local denominator = out_current.frac
 	if denominator then
 		show = fraction_table(outvalue, denominator)
 	else
 		precision = parms.precision
 		if not precision then
 			if parms.sigfig then
 				show, exponent = make_sigfig(outvalue, parms.sigfig)
 			elseif parms.opt_round then
 				local n = parms.opt_round
 				if n == 0.5 then
 					local integer, fracpart = math.modf(floor(2 * outvalue + 0.5) / 2)
 					if fracpart == 0 then
 						show = format('%.0f', integer)
 					else
 						show = format('%.1f', integer + fracpart)
 					end
 				else
 					show = format('%.0f', floor((outvalue / n) + 0.5) * n)
 				end
 			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 &gt;= 0 then
 			local fudge
 			if precision &lt;= 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)
 	if type(show) == 'string' then
 		-- Set singular using match because on some systems 0.99999999999999999 is 1.0.
 		if exponent then
 			t.singular = (exponent == 1 and show:match('^10*$'))
 		else
 			t.singular = (show == '1' or show:match('^1%.0*$'))
 		end
 	else
 		t.fraction_table = show
 		t.singular = (outvalue &lt;= 1)  -- cannot have 'fraction == 1', but if it were possible it would be singular
 	end
 	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 &gt; 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 &quot;hand in&quot; is used, the inches
 		-- value is rounded to match the hands value. Also, displaying say &quot;61½&quot; 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 &lt;= 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 &quot;15.0½&quot;) because &quot;15½&quot; 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 &lt; 9
 	--    v * 9 &lt; 9
 	-- where
 	--    'v' is replaced with value
 	--    9 is any number (as defined by Lua tonumber)
 	--      only en digits are accepted
 	--    '&lt;' can also be '&lt;=' or '&gt;' or '&gt;='
 	-- 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*([*]?)(.-)([&lt;&gt;]=?)(.*)$')
 		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 == '&lt;' then
 			return value &lt; limit
 		elseif compop == '&lt;=' then
 			return value &lt;= limit
 		elseif compop == '&gt;' then
 			return value &gt; limit
 		elseif compop == '&gt;=' then
 			return value &gt;= 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 &lt; 120 ! small ! big ! suffix' (suffix is optional)
 	-- evaluates 'v &lt; 120' as a boolean with result
 	-- 'smallsuffix' if (value &lt; 120), or 'bigsuffix' otherwise.
 	-- Input must use en digits and '.' decimal mark.
 	local default = data_code.default_exceptions[unit_table.defkey or unit_table.symbol] or unit_table.default
 	if not default then
 		local per = unit_table.per
 		if per then
 			local function a_default(v, u)
 				local success, ucode = get_default(v, u)
 				if not success then
 					return '?'  -- an unlikely error has occurred; will cause lookup of default to fail
 				end
 				-- Attempt to use only the first unit if a combination or output multiple.
 				-- This is not bulletproof but should work for most cases.
 				-- Where it does not work, the convert will need to specify the wanted output unit.
 				local t = all_units[ucode]
 				if t then
 					local combo = t.combination
 					if combo then
 						-- For a multiple like ftin, the &quot;first&quot; unit (ft) is last in the combination.
 						local i = t.multiple and table_len(combo) or 1
 						ucode = combo[i]
 					end
 				else
 					-- Try for an automatically generated combination.
 					local item = ucode:match('^(.-)%+') or ucode:match('^(%S+)%s')
 					if all_units[item] then
 						return item
 					end
 				end
 				return ucode
 			end
 			local unit1, unit2 = per[1], per[2]
 			local def1 = (unit1 and a_default(value, unit1) or unit_table.vprefix or '')
 			local def2 = a_default(1, unit2)  -- 1 because per unit of denominator
 			return true, def1 .. '/' .. def2
 		end
 		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 unlink(unit_table)
 	-- Forget that the given unit has previously been linked (if it has).
 	-- That is needed when processing a range of inputs or outputs when an id
 	-- for the first range value may have been evaluated, but only an id for
 	-- the last value is displayed, and that id may need to be linked.
 	linked_pages[unit_table.unitcode or unit_table] = nil
 end
 
 local function make_link(link, id, unit_table)
 	-- Return wikilink &quot;[[link|id]]&quot;, possibly abbreviated as in examples:
 	--   [[Mile|mile]]  --&gt; [[mile]]
 	--   [[Mile|miles]] --&gt; [[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).
 	local link_key
 	if unit_table then
 		link_key = unit_table.unitcode or unit_table
 	else
 		link_key = link
 	end
 	if not link or link == '' or linked_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, a unit name depends on the value.
 	-- Parameter clean is the unsigned rounded value in en digits, as a string.
 	-- Value             Source    Example for &quot;m&quot;
 	-- 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 &quot;!&quot; and are not empty.
 	-- A field for a unit using an SI prefix has the prefix name inserted,
 	-- replacing '#' if found, or before the field otherwise.
 	local vname
 	if clean == '1' then
 		vname = unit_table.name1
 	elseif unit_table.varname then
 		local i
 		if clean == '2' then
 			i = 1
 		elseif clean == '3' or clean == '4' then
 			i = 2
 		elseif clean:find('.', 1, true) then
 			i = 4
 		else
 			i = 3
 		end
 		if i &gt; 1 and varname == 'pl' then
 			i = i - 1
 		end
 		vname = split(unit_table.varname, '!')[i]
 	end
 	if vname then
 		local si_name = rawget(unit_table, 'si_name') or ''
 		local pos = vname:find('#', 1, true)
 		if pos then
 			vname = vname:sub(1, pos - 1) .. si_name .. vname:sub(pos + 1)
 		else
 			vname = si_name .. vname
 		end
 		return vname
 	end
 	return unit_table.name2
 end
 
 local function linked_id(parms, unit_table, key_id, want_link, clean)
 	-- Return final unit id (symbol or name), optionally with a wikilink,
 	-- and update unit_table.sep if required.
 	-- key_id is one of: 'symbol', 'sym_us', 'name1', 'name1_us', 'name2', 'name2_us'.
 	local abbr_on = (key_id == 'symbol' or key_id == 'sym_us')
 	if abbr_on and want_link then
 		local symlink = rawget(unit_table, 'symlink')
 		if symlink then
 			return symlink  -- for exceptions that have the linked symbol built-in
 		end
 	end
 	local multiplier = rawget(unit_table, 'multiplier')
 	local per = unit_table.per
 	if per then
 		local paren1, paren2 = '', ''  -- possible parentheses around bottom unit
 		local unit1 = 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 &quot;$2/acre&quot;
 			end
 			if not want_link then
 				local symbol = unit_table.symbol_raw
 				if symbol then
 					return symbol  -- for exceptions that have the symbol built-in
 				end
 			end
 			if (unit2.symbol):find('⋅', 1, true) then
 				paren1, paren2 = '(', ')'
 			end
 		end
 		local key_id2  -- unit2 is always singular
 		if key_id == 'name2' then
 			key_id2 = 'name1'
 		elseif key_id == 'name2_us' then
 			key_id2 = 'name1_us'
 		else
 			key_id2 = key_id
 		end
 		local result
 		if abbr_on then
 			result = '/'
 		elseif omitsep then
 			result = per_word
 		elseif unit1 then
 			result = ' ' .. per_word .. ' '
 		else
 			result = per_word .. ' '
 		end
 		if want_link and unit_table.link then
 			if abbr_on or not varname then
 				result = (unit1 and linked_id(parms, unit1, key_id, false, clean) or '') .. result .. linked_id(parms, unit2, key_id2, false, '1')
 			else
 				result = (unit1 and variable_name(clean, unit1) or '') .. result .. variable_name('1', unit2)
 			end
 			if omit_separator(result) then
 				unit_table.sep = ''
 			end
 			return make_link(unit_table.link, result, unit_table)
 		end
 		if unit1 then
 			result = linked_id(parms, unit1, key_id, want_link, clean) .. result
 			if unit1.sep then
 				unit_table.sep = unit1.sep
 			end
 		elseif omitsep then
 			unit_table.sep = ''
 		end
 		return result .. paren1 .. linked_id(parms, unit2, key_id2, want_link, '1') .. paren2
 	end
 	if multiplier then
 		-- A multiplier (like &quot;100&quot; in &quot;100km&quot;) forces the unit to be plural.
 		multiplier = from_en(multiplier)
 		if not omitsep then
 			multiplier = multiplier .. (abbr_on and '&amp;nbsp;' or ' ')
 		end
 		if not abbr_on then
 			if key_id == 'name1' then
 				key_id = 'name2'
 			elseif key_id == 'name1_us' then
 				key_id = 'name2_us'
 			end
 		end
 	else
 		multiplier = ''
 	end
 	local id = unit_table.fixed_name or ((varname and not abbr_on) and variable_name(clean, unit_table) or unit_table[key_id])
 	if omit_separator(id) then
 		unit_table.sep = ''
 	end
 	if want_link then
 		local link = data_code.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 parms.opt_sp_us then
 				i = 2  -- show &quot;U.S.&quot; not &quot;US&quot;
 			end
 			if i == 3 and abbr_on then
 				i = 4  -- abbreviate &quot;imperial&quot; to &quot;imp&quot;
 			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 &quot;/USgal&quot; to display as &quot;/U.S. gal&quot;, not &quot;U.S. /gal&quot;.
 					pertext = '/'
 					id = id:sub(2)
 				elseif id:sub(1, 4) == 'per ' then
 					-- Similarly want &quot;per U.S. gallon&quot;, not &quot;U.S. per gallon&quot; (but in practice this is unlikely to be used).
 					pertext = 'per '
 					id = id:sub(5)
 				else
 					pertext = ''
 				end
 				-- Omit any &quot;US&quot;/&quot;U.S.&quot;/&quot;imp&quot;/&quot;imperial&quot; from start of id since that will be inserted.
 				local removes = (i &lt; 3) and { 'US&amp;nbsp;', 'US ', 'U.S.&amp;nbsp;', 'U.S. ' } or { 'imp&amp;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 the value for index '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 '&amp;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 lk = parms.lk
 	local want_link = (lk == 'on' or lk == inout)
 	local usename = unit_table.usename
 	local singular = info.singular
 	local want_name
 	if usename then
 		want_name = true
 	else
 		if abbr_org == nil then
 			if parms.wantname 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 = '&amp;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 &lt; value and value &lt; 1.0001)
 			end
 		end
 		if unit_table.engscale then
 			-- engscale: so &quot;|1|e3kg&quot; gives &quot;1 thousand kilograms&quot; (plural)
 			singular = false
 		end
 		key = (adjectival or singular) and 'name1' or 'name2'
 		if parms.opt_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 = '&amp;nbsp;'
 		key = parms.opt_sp_us and 'sym_us' or 'symbol'
 	end
 	return linked_id(parms, unit_table, key, want_link, info.clean), want_name
 end
 
 local function decorate_value(parms, unit_table, which, number_word)
 	-- 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 &quot;display:none&quot; to allow some
 	-- browsers to copy, for example, &quot;10³&quot; as &quot;10^3&quot;, rather than as &quot;103&quot;.
 	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
 		if engscale then
 			local inout = unit_table.inout
 			local abbr = parms.abbr
 			if (abbr == 'on' or abbr == inout) and not parms.number_word then
 				info.show = info.show ..
 					'&lt;span style=&quot;margin-left:0.2em&quot;&gt;×&lt;span style=&quot;margin-left:0.1em&quot;&gt;' ..
 					from_en('10') ..
 					'&lt;/span&gt;&lt;/span&gt;&lt;s style=&quot;display:none&quot;&gt;^&lt;/s&gt;&lt;sup&gt;' ..
 					from_en(tostring(engscale.exponent)) .. '&lt;/sup&gt;'
 			elseif number_word then
 				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 &quot;&amp;nbsp;&quot; in values like &quot;12 million&quot;.
 				info.show = info.show .. (parms.opt_adjectival and '-' or '&amp;nbsp;') .. number_id
 			end
 		end
 		if prefix then
 			info.show = prefix .. info.show
 		end
 	end
 end
 
 local function process_input(parms, in_current)
 	-- Processing required once per conversion.
 	-- Return block of text to represent input (value/unit).
 	if parms.opt_output_only or parms.opt_output_number_only or parms.opt_output_unit_only then
 		parms.joins = { '', '' }
 		return ''
 	end
 	local first_unit
 	local composite = in_current.composite  -- nil or table of units
 	if composite then
 		first_unit = 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 &gt; 1 then
 					table.insert(parts, (make_id(parms, 1, unit)))
 				end
 			end
 			id1 = table.concat(parts, ' ')
 		end
 		if want_name and parms.opt_adjectival then
 			return preunit .. hyphenated(id1)
 		end
 		return  preunit .. id1
 	end
 	if parms.opt_also_symbol and not composite and not parms.opt_flip then
 		local join1 = parms.joins[1]
 		if join1 == ' (' or join1 == ' [' then
 			parms.joins = { ' [' .. first_unit[parms.opt_sp_us and 'sym_us' or 'symbol'] .. ']' .. join1 , parms.joins[2] }
 		end
 	end
 	if in_current.builtin == 'mach' and first_unit.sep ~= '' then  -- '' means omitsep with non-enwiki name
 		local prefix = id1 .. '&amp;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) .. '&amp;nbsp;'
 			result = range_text(range[1], want_name, parms, result, prefix2 .. valinfo[2].show, 'in')
 		end
 		return preunit .. result
 	end
 	if composite then
 		-- Simplify: assume there is no range, and no decoration.
 		local mid = (not parms.opt_flip) and parms.mid or ''
 		local sep1 = '&amp;nbsp;'
 		local sep2 = ' '
 		if parms.opt_adjectival and want_name then
 			sep1 = '-'
 			sep2 = '-'
 		end
 		if omitsep and sep == '' then
 			-- Testing the id of the most significant unit should be sufficient.
 			sep1 = ''
 			sep2 = ''
 		end
 		local parts = { first_unit.valinfo[1].show .. sep1 .. id1 }
 		for i, unit in ipairs(composite) do
 			if i &gt; 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 add_unit = (parms.abbr == 'mos') or
 		parms[parms.opt_flip and 'out_range_x' or 'in_range_x'] or
 		(not want_name and parms.abbr_range_x)
 	local range = parms.range
 	if range and not add_unit then
 		unlink(first_unit)
 	end
 	local id = range and make_id(parms, range.n + 1, first_unit) or id1
 	local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, 'in')
 	if was_hyphenated then
 		add_unit = false
 	end
 	local result
 	local valinfo = first_unit.valinfo
 	if range then
 		for i = 0, range.n do
 			local number_word
 			if i == range.n then
 				add_unit = false
 				number_word = true
 			end
 			decorate_value(parms, first_unit, i+1, number_word)
 			local show = valinfo[i+1].show
 			if add_unit then
 				show = show .. first_unit.sep .. (i == 0 and id1 or make_id(parms, i+1, first_unit))
 			end
 			if i == 0 then
 				result = show
 			else
 				result = range_text(range[i], want_name, parms, result, show, 'in')
 			end
 		end
 	else
 		decorate_value(parms, first_unit, 1, true)
 		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 inout = out_current.inout  -- normally 'out' but can be 'in' for order=out
 	local id1, want_name = make_id(parms, 1, out_current)
 	local sep = out_current.sep  -- set by make_id
 	local preunit = parms.preunit2
 	if preunit then
 		sep = ''  -- any separator is included in preunit
 	else
 		preunit = ''
 	end
 	if parms.opt_output_unit_only then
 		if want_name and parms.opt_adjectival then
 			return preunit .. hyphenated(id1)
 		end
 		return preunit .. id1
 	end
 	if out_current.builtin == 'mach' and out_current.sep ~= '' then  -- '' means omitsep with non-enwiki name
 		local prefix = id1 .. '&amp;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, inout)
 		end
 		return preunit .. result
 	end
 	local add_unit = (parms[parms.opt_flip and 'in_range_x' or 'out_range_x'] or
 		(not want_name and parms.abbr_range_x)) and
 		not parms.opt_output_number_only
 	local range = parms.range
 	if range and not add_unit then
 		unlink(out_current)
 	end
 	local id = range and make_id(parms, range.n + 1, out_current) or id1
 	local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, inout)
 	if was_hyphenated then
 		add_unit = false
 	end
 	local result
 	local valinfo = out_current.valinfo
 	if range then
 		for i = 0, range.n do
 			local number_word
 			if i == range.n then
 				add_unit = false
 				number_word = true
 			end
 			decorate_value(parms, out_current, i+1, number_word)
 			local show = valinfo[i+1].show
 			if add_unit then
 				show = show .. out_current.sep .. (i == 0 and id1 or make_id(parms, i+1, out_current))
 			end
 			if i == 0 then
 				result = show
 			else
 				result = range_text(range[i], want_name, parms, result, show, inout)
 			end
 		end
 	else
 		decorate_value(parms, out_current, 1, true)
 		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.
 	if parms.opt_order_out and in_unit_table.unitcode == out_unit_table.unitcode then
 		out_unit_table.valinfo = in_unit_table.valinfo
 	else
 		out_unit_table.valinfo = collection()
 		for _, v in ipairs(in_unit_table.valinfo) do
 			local success, info = cvtround(parms, v, in_unit_table, out_unit_table)
 			if not success then return false, info end
 			out_unit_table.valinfo:add(info)
 		end
 	end
 	return true, process_one_output(parms, out_unit_table)
 end
 
 local function make_output_multiple(parms, in_unit_table, out_unit_table)
 	-- Return true, item where item = wikitext of the conversion result
 	-- for an output which is a multiple (like 'ftin');
 	-- or return false, t where t is an error message table.
 	local inout = out_unit_table.inout  -- normally 'out' but can be 'in' for order=out
 	local multiple = out_unit_table.multiple  -- table of scaling factors (will not be nil)
 	local combos = out_unit_table.combination  -- table of unit tables (will not be nil)
 	local abbr = parms.abbr
 	local abbr_org = parms.abbr_org
 	local disp = parms.disp
 	local want_name = (abbr_org == nil and (disp == 'or' or disp == 'slash')) or
 						not (abbr == 'on' or abbr == inout or abbr == 'mos')
 	local want_link = (parms.lk == 'on' or parms.lk == inout)
 	local mid = parms.opt_flip and parms.mid or ''
 	local sep1 = '&amp;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 = inout
 			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 &lt; thisvalue and thisvalue &lt; 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 i == 1 and omit_separator(id) then
 				-- Testing the id of the least significant unit should be sufficient.
 				sep1 = ''
 				sep2 = ''
 			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 spell_inout = (i == #combos or outvalue == 0) and inout 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 &gt; 0) and tostring(thisvalue) or nil
 				strval = format_fraction(parms, spell_inout, false, wholestr, tfrac.numstr, tfrac.denstr, do_spell)
 			else
 				strval = (thisvalue == 0) and from_en('0') or with_separator(parms, format(fmt, thisvalue))
 				if do_spell then
 					strval = spell_number(parms, spell_inout, strval) or strval
 				end
 			end
 			table.insert(results, strval .. sep1 .. id)
 			if outvalue == 0 then
 				break
 			end
 			fmt = '%.0f'  -- only least significant unit can have a non-integral value
 		end
 		local reversed, count = {}, #results
 		for i = 1, count do
 			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, inout)
 		end
 	end
 	return true, result .. mid
 end
 
 local function process(parms, in_unit_table, out_unit_table)
 	-- Return true, s, outunit where s = final wikitext result,
 	-- or return false, t where t is an error message table.
 	linked_pages = {}
 	local success, bad_output
 	local bad_input_mcode = in_unit_table.bad_mcode  -- nil if input unit is a valid convert unit
 	local out_unit = parms.out_unit
 	if out_unit == nil or out_unit == '' or type(out_unit) == 'function' then
 		if bad_input_mcode or parms.opt_input_unit_only then
 			bad_output = ''
 		else
 			local getdef = type(out_unit) == 'function' and out_unit or get_default
 			success, out_unit = getdef(in_unit_table.valinfo[1].value, in_unit_table)
 			parms.out_unit = out_unit
 			if not success then
 				bad_output = out_unit
 			end
 		end
 	end
 	if not bad_output and not out_unit_table then
 		success, out_unit_table = lookup(parms, out_unit, 'any_combination')
 		if success then
 			local mismatch = check_mismatch(in_unit_table, out_unit_table)
 			if mismatch then
 				bad_output = mismatch
 			end
 		else
 			bad_output = out_unit_table
 		end
 	end
 	local lhs, rhs
 	local flipped = parms.opt_flip and not bad_input_mcode
 	if bad_output then
 		rhs = (bad_output == '') and '' or message(parms, bad_output)
 	elseif parms.opt_input_unit_only then
 		rhs = ''
 	else
 		local combos  -- nil (for 'ft' or 'ftin'), or table of unit tables (for 'm ft')
 		if not out_unit_table.multiple then  -- nil/false ('ft' or 'm ft'), or table of factors ('ftin')
 			combos = out_unit_table.combination
 		end
 		local frac = parms.frac  -- nil or denominator of fraction for output values
 		if frac then
 			-- Apply fraction to the unit (if only one), or to non-SI units (if a combination),
 			-- except that if a precision is also specified, the fraction only applies to
 			-- the hand unit; that allows the following result:
 			-- {{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 outputs = {}
 		local imax = combos and #combos or 1  -- 1 (single unit) or number of unit tables
 		if imax == 1 then
 			parms.opt_order_out = nil  -- only useful with an output combination
 		end
 		if not flipped and not parms.opt_order_out then
 			-- Process left side first so any duplicate links (from lk=on) are suppressed
 			-- on right. Example: {{convert|28|e9pc|e9ly|abbr=off|lk=on}}
 			lhs = process_input(parms, in_unit_table)
 		end
 		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
 				if imax &gt; 1 and out_current.builtin == 'hand' then
 					out_current.out_next = combos[2]  -- built-in hand can influence next unit in a combination
 				end
 				if parms.opt_order_out then
 					out_current.inout = 'in'
 				end
 			end
 			if out_current.multiple then
 				success, item = make_output_multiple(parms, in_unit_table, out_current)
 			else
 				success, item = make_output_single(parms, in_unit_table, out_current)
 			end
 			if not success then return false, item end
 			outputs[i] = item
 		end
 		if parms.opt_order_out then
 			lhs = outputs[1]
 			table.remove(outputs, 1)
 		end
 		local sep = parms.table_joins and parms.table_joins[2] or parms.join_between
 		rhs = table.concat(outputs, sep)
 	end
 	if flipped or not lhs then
 		local input = process_input(parms, in_unit_table)
 		if flipped then
 			lhs = rhs
 			rhs = input
 		else
 			lhs = input
 		end
 	end
 	if parms.join_before then
 		lhs = parms.join_before .. lhs
 	end
 	local wikitext
 	if bad_input_mcode then
 		if bad_input_mcode == '' then
 			wikitext = lhs
 		else
 			wikitext = lhs .. message(parms, bad_input_mcode)
 		end
 	elseif parms.table_joins then
 		wikitext = parms.table_joins[1] .. lhs .. parms.table_joins[2] .. rhs
 	else
 		wikitext = lhs .. parms.joins[1] .. rhs .. 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.
 	local parms = { frame = frame }  -- will hold template arguments, after translation
 	set_config(frame.args)
 	local success, result = get_parms(parms, frame:getParent().args)
 	if success then
 		if type(result) ~= 'table' then
 			return tostring(result)
 		end
 		local in_unit_table = result
 		local out_unit_table
 		for _ = 1, 2 do  -- use counter so cannot get stuck repeating convert
 			success, result, out_unit_table = process(parms, in_unit_table, out_unit_table)
 			if success and parms.do_convert_again then
 				parms.do_convert_again = false
 			else
 				break
 			end
 		end
 	end
 	-- If input=x gives a problem, the result should be just the user input
 	-- (if x is a property like P123 it has been replaced with '').
 	-- An unknown input unit would display the input and an error message
 	-- with success == true at this point.
 	-- Also, can have success == false with a message that outputs an empty string.
 	if parms.input_text then
 		if success and not parms.have_problem then
 			return result
 		end
 		local cat
 		if parms.tracking then
 			-- Add a tracking category using the given text as the category sort key.
 			-- There is currently only one type of tracking, but in principle multiple
 			-- items could be tracked, using different sort keys for convenience.
 			cat = wanted_category('tracking', parms.tracking)
 		end
 		return parms.input_text .. (cat or '')
 	end
 	return success and result or message(parms, result)
 end
 
 local function _unit(unitcode, options)
 	-- Helper function for Module:Val to look up a unit.
 	-- Parameter unitcode must be a string to identify the wanted unit.
 	-- Parameter options must be nil or a table with optional fields:
 	--   value = number (for sort key; default value is 1)
 	--   scaled_top = nil for a normal unit, or a number for a unit which is
 	--                the denominator of a per unit (for sort key)
 	--   si = { 'symbol', 'link' }
 	--                (a table with two strings) to make an SI unit
 	--                that will be used for the look up
 	--   link = true if result should be [[linked]]
 	--   sort = 'on' or 'debug' if result should include a sort key in a
 	--                span element ('debug' makes the key visible)
 	--   name = true for the name of the unit instead of the symbol
 	--   us = true for the US spelling of the unit, if any
 	-- Return nil if unitcode is not a non-empty string.
 	-- Otherwise return a table with fields:
 	--   text = requested symbol or name of unit, optionally linked
 	--   scaled_value = input value adjusted by unit scale; used for sort key
 	--   sortspan = span element with sort key like that provided by {{ntsh}},
 	--     calculated from the result of converting value
 	--     to a base unit with scale 1.
 	--   unknown = true if the unitcode was not known
 	unitcode = strip(unitcode)
 	if unitcode == nil or unitcode == '' then
 		return nil
 	end
 	set_config({})
 	linked_pages = {}
 	options = options or {}
 	local parms = {
 		abbr = options.name and 'off' or 'on',
 		lk = options.link and 'on' or nil,
 		opt_sp_us = options.us and true or nil,
 		opt_ignore_error = true,  -- do not add pages using this function to 'what links here' for Module:Convert/extra
 		opt_sortable_on = options.sort == 'on' or options.sort == 'debug',
 		opt_sortable_debug = options.sort == 'debug',
 	}
 	if options.si then
 		-- Make a dummy table of units (just one unit) for lookup to use.
 		-- This makes lookup recognize any SI prefix in the unitcode.
 		local symbol = options.si[1] or '?'
 		parms.unittable = { [symbol] = {
 			_name1 = symbol,
 			_name2 = symbol,
 			_symbol = symbol,
 			utype = symbol,
 			scale = symbol == 'g' and 0.001 or 1,
 			prefixes = 1,
 			default = symbol,
 			link = options.si[2],
 		}}
 	end
 	local success, unit_table = lookup(parms, unitcode, 'no_combination')
 	if not success then
 		unit_table = setmetatable({
 			symbol = unitcode, name2 = unitcode, utype = unitcode,
 			scale = 1, default = '', defkey = '', linkey = '' }, unit_mt)
 	end
 	local value = tonumber(options.value) or 1
 	local clean = tostring(abs(value))
 	local info = {
 		value = value,
 		altvalue = value,
 		singular = (clean == '1'),
 		clean = clean,
 		show = clean,
 	}
 	unit_table.inout = 'in'
 	unit_table.valinfo = { info }
 	local sortspan, scaled_value
 	if options.sort then
 		sortspan, scaled_value = make_table_or_sort(parms, value, info, unit_table, options.scaled_top)
 	end
 	return {
 		text = make_id(parms, 1, unit_table),
 		sortspan = sortspan,
 		scaled_value = scaled_value,
 		unknown = not success and true or nil,
 	}
 end