Module:Convert: Difference between revisions

    From Longevity Wiki
    (Created page with "-- Convert a value from one unit of measurement to another. -- Example: {{convert|123|lb|kg}} --> 123 pounds (56 kg) -- See en:Template:Convert/Transwiki guide if copying...")
    (No difference)

    Revision as of 02:27, 8 December 2023

    See Wikipedia - Module:Convert


    -- Convert a value from one unit of measurement to another.
    -- Example: {{convert|123|lb|kg}} --> 123 pounds (56 kg)
    -- See [[:en:Template:Convert/Transwiki guide]] if copying to another wiki.
    
    local MINUS = '−'  -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92)
    local abs = math.abs
    local floor = math.floor
    local format = string.format
    local log10 = math.log10
    local ustring = mw.ustring
    local ulen = ustring.len
    local usub = ustring.sub
    
    -- Configuration options to keep magic values in one location.
    -- Conversion data and message text are defined in separate modules.
    local config, maxsigfig
    local numdot  -- must be '.' or ',' or a character which works in a regex
    local numsep, numsep_remove, numsep_remove2
    local data_code, all_units
    local text_code
    local varname        -- can be a code to use variable names that depend on value
    local from_en_table  -- to translate an output string of en digits to local language
    local to_en_table    -- to translate an input string of digits in local language to en
    -- Use translation_table in convert/text to change the following.
    local en_default           -- true uses lang=en unless convert has lang=local or local digits
    local group_method = 3     -- code for how many digits are in a group
    local per_word = 'per'     -- for units like "liters per kilometer"
    local plural_suffix = 's'  -- only other useful value is probably '' to disable plural unit names
    local omitsep              -- true to omit separator before local symbol/name
    
    -- All units should be defined in the data module. However, to cater for quick changes
    -- and experiments, any unknown unit is looked up in an extra data module, if it exists.
    -- That module would be transcluded in only a small number of pages, so there should be
    -- little server overhead from making changes, and changes should propagate quickly.
    local extra_module  -- name of module with extra units
    local extra_units   -- nil or table of extra units from extra_module
    
    -- Some options in the invoking template can set variables used later in the module.
    local currency_text  -- for a user-defined currency symbol: {{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 "1.234.567,8").
    	if to_en_table then
    		text = ustring.gsub(text, '%d', to_en_table)
    	end
    	if numsep_remove then
    		text = text:gsub(numsep_remove, '')
    	end
    	if numsep_remove2 then
    		text = text:gsub(numsep_remove2, '')
    	end
    	if numdot ~= '.' then
    		text = text:gsub(numdot, '.')
    	end
    	return text
    end
    
    local function decimal_mark(text)
    	-- Return ',' if text probably is using comma for decimal mark, or has no decimal mark.
    	-- Return '.' if text probably is using dot for decimal mark.
    	-- Otherwise return nothing (decimal mark not known).
    	if not text:find('[.,]') then return ',' end
    	text = text:gsub('^%-', ''):gsub('%+%d+/%d+$', ''):gsub('[Ee]%-?%d+$', '')
    	local decimal =
    		text:match('^0?([.,])%d+$') or
    		text:match('%d([.,])%d?%d?$') or
    		text:match('%d([.,])%d%d%d%d+$')
    	if decimal then return decimal end
    	if text:match('%.%d+%.') then return ',' end
    	if text:match('%,%d+,') then return '.' end
    end
    
    local add_warning, with_separator  -- forward declarations
    local function to_en_with_check(text, parms)
    	-- Version of to_en() for a wiki using numdot = ',' and numsep = '.' to check
    	-- text (an input number as a string) which might have been copied from enwiki.
    	-- For example, in '1.234' the '.' could be a decimal mark or a group separator.
    	-- From viwiki.
    	if to_en_table then
    		text = ustring.gsub(text, '%d', to_en_table)
    	end
    	if decimal_mark(text) == '.' then
    		local original = text
    		text = text:gsub(',', '')  -- for example, interpret "1,234.5" as an enwiki value
    		if parms then
    			add_warning(parms, 0, 'cvt_enwiki_num', original, with_separator({}, text))
    		end
    	else
    		if numsep_remove then
    			text = text:gsub(numsep_remove, '')
    		end
    		if numsep_remove2 then
    			text = text:gsub(numsep_remove2, '')
    		end
    		if numdot ~= '.' then
    			text = text:gsub(numdot, '.')
    		end
    	end
    	return text
    end
    
    local function omit_separator(id)
    	-- Return true if there should be no separator before id (a unit symbol or name).
    	-- For zhwiki, there should be no separator if id uses local characters.
    	-- The following kludge should be a sufficient test.
    	if omitsep then
    		if id:sub(1, 2) == '-{' then  -- for "-{...}-" content language variant
    			return true
    		end
    		if id:byte() > 127 then
    			local first = usub(id, 1, 1)
    			if first ~= 'Å' and first ~= '°' and first ~= 'µ' then
    				return true
    			end
    		end
    	end
    	return id:sub(1, 1) == '/'  -- no separator before units like "/ha"
    end
    
    local spell_module  -- name of module that can spell numbers
    local speller       -- function from that module to handle spelling (set if needed)
    local wikidata_module, wikidata_data_module  -- names of Wikidata modules
    local wikidata_code, wikidata_data  -- exported tables from those modules (set if needed)
    
    local function set_config(args)
    	-- Set configuration options from template #invoke or defaults.
    	config = args
    	maxsigfig = config.maxsigfig or 14  -- maximum number of significant figures
    	local data_module, text_module
    	local sandbox = config.sandbox and ('/' .. config.sandbox) or ''
    	data_module = "Module:Convert/data" .. sandbox
    	text_module = "Module:Convert/text" .. sandbox
    	extra_module = "Module:Convert/extra" .. sandbox
    	wikidata_module = "Module:Convert/wikidata" .. sandbox
    	wikidata_data_module = "Module:Convert/wikidata/data" .. sandbox
    	spell_module = "Module:ConvertNumeric"
    	data_code = mw.loadData(data_module)
    	text_code = mw.loadData(text_module)
    	all_units = data_code.all_units
    	local translation = text_code.translation_table
    	if translation then
    		numdot = translation.numdot
    		numsep = translation.numsep
    		if numdot == ',' and numsep == '.' then
    			if text_code.all_messages.cvt_enwiki_num then
    				to_en = to_en_with_check
    			end
    		end
    		if translation.group then
    			group_method = translation.group
    		end
    		if translation.per_word then
    			per_word = translation.per_word
    		end
    		if translation.plural_suffix then
    			plural_suffix = translation.plural_suffix
    		end
    		varname = translation.varname
    		from_en_table = translation.from_en
    		local use_workaround = true
    		if use_workaround then
    			-- 2013-07-05 workaround bug by making a copy of the required table.
    			-- mw.ustring.gsub fails with a table (to_en_table) as the replacement,
    			-- if the table is accessed via mw.loadData.
    			local source = translation.to_en
    			if source then
    				to_en_table = {}
    				for k, v in pairs(source) do
    					to_en_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 ' ' 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 <= remainder and remainder < denominator) then
    		-- Floating point limits may need this, as in {{convert|160.02|Ym|ydftin}}.
    		remainder = 0
    	end
    	return quotient, remainder
    end
    
    local function split(text, delimiter)
    	-- Return a numbered table with fields from splitting text.
    	-- The delimiter is used in a regex without escaping (for example, '.' would fail).
    	-- Each field has any leading/trailing whitespace removed.
    	local t = {}
    	text = text .. delimiter  -- to get last item
    	for item in text:gmatch('%s*(.-)%s*' .. delimiter) do
    		table.insert(t, item)
    	end
    	return t
    end
    
    local function strip(text)
    	-- If text is a string, return its content with no leading/trailing
    	-- whitespace. Otherwise return nil (a nil argument gives a nil result).
    	if type(text) == 'string' then
    		return text:match("^%s*(.-)%s*$")
    	end
    end
    
    local function table_len(t)
    	-- Return length (<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('$%d+', rep))
    	end
    	if msg then
    		local parts = {}
    		local regex, replace = msg.regex, msg.replace
    		for i = 1, 3 do
    			local limit = 40
    			local s = mcode[i + 1]
    			if s then
    				if regex and replace then
    					s = s:gsub(regex, replace)
    					limit = nil  -- allow long "should be" messages
    				end
    				-- Escape user input so it does not break the message.
    				-- To avoid tags (like {{convert|1<math>23</math>|m}}) breaking
    				-- the mouseover title, any strip marker starting with char(127) is
    				-- replaced with '...' (text not needing i18n).
    				local append
    				local pos = s:find(string.char(127), 1, true)
    				if pos then
    					append = '...'
    					s = s:sub(1, pos - 1)
    				end
    				if limit and ulen(s) > limit then
    					s = usub(s, 1, limit)
    					append = '...'
    				end
    				s = mw.text.nowiki(s) .. (append or '')
    			else
    				s = '?'
    			end
    			parts['$' .. 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;'), 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 <= (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
    	--   ------  ---------  -----------  -------------------
    	--   "1.23"    nil        nil        one point two three
    	--    "1"      "2"        "3"        one and two thirds
    	--    nil      "2"        "3"        two thirds
    	if not speller then
    		local function get_speller(module)
    			return require(module).spell_number
    		end
    		local success
    		success, speller = pcall(get_speller, spell_module)
    		if not success or type(speller) ~= 'function' then
    			add_warning(parms, 1, 'cvt_no_spell', '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 402,499 feet
    	-- mach_table[a + 4] = s where
    	--   a = (altitude / 5000) rounded to nearest integer (-3 to 80)
    	--   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, 701.0,  -- 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
    		614.4, 615.3, 616.7, 619.8, 623.4, 629.7, 635.0, 641.1, 650.6, 660.0,  -- 61 to 70
    		672.5, 674.3, 676.1, 677.9, 679.7, 681.5, 683.3, 685.1, 686.8, 688.6,  -- 71 to 80
    	}
    	altitude = altitude or 0
    	local a = (altitude < 0) and -altitude or altitude
    	a = floor(a / 5000 + 0.5)
    	if altitude < 0 then
    		a = -a
    	end
    	if a < -3 then
    		a = -3
    	elseif a > 80 then
    		a = 80
    	end
    	return mach_table[a + 4] * 0.44704  -- mph converted to m/s
    end
    -- END: Code required only for built-in units.
    ------------------------------------------------------------------------
    
    local function add_style(parms, class)
    	-- Add selected template style to parms if not already present.
    	parms.templatestyles = parms.templatestyles or {}
    	if not parms.templatestyles[class] then
    		parms.templatestyles[class] = parms.frame:extensionTag({
    			name = 'templatestyles', args = { src = text_code.titles[class] }
    		})
    	end
    end
    
    local function get_styles(parms)
    	-- Return string of required template styles, empty if none.
    	if parms.templatestyles then
    		local t = {}
    		for _, v in pairs(parms.templatestyles) do
    			table.insert(t, v)
    		end
    		return table.concat(t)
    	end
    	return ''
    end
    
    local function get_range(word)
    	-- Return a range (string or table) corresponding to word (like "to"),
    	-- or return nil if not a range word.
    	local ranges = text_code.ranges
    	return ranges.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
    			if value == 'l' then value = 'L' end
    		elseif key == 'sym_us' then
    			value = rawget(self, '_sym_us')
    			if value then
    				value = self.si_prefix .. value
    			else
    				value = self.symbol
    			end
    		elseif key == 'name1' then
    			value = prefixed_name(self, self._name1, 1)
    		elseif key == 'name2' then
    			value = rawget(self, '_name2')
    			if value then
    				value = prefixed_name(self, value, 2)
    			else
    				value = self.name1 .. plural_suffix
    			end
    		elseif key == 'name1_us' then
    			value = rawget(self, '_name1_us')
    			if value then
    				value = prefixed_name(self, value, 3)
    			else
    				value = self.name1
    			end
    		elseif key == 'name2_us' then
    			value = rawget(self, '_name2_us')
    			if value then
    				value = prefixed_name(self, value, 4)
    			elseif rawget(self, '_name1_us') then
    				value = self.name1_us .. plural_suffix
    			else
    				value = self.name2
    			end
    		elseif key == 'link' then
    			value = self.name1
    		else
    			value = false
    		end
    		rawset(self, key, value)
    		return value
    	end
    }
    
    local unit_per_mt = {
    	-- Metatable to get values for a per unit of form "x/y".
    	-- This is never called to determine a unit name or link because per units
    	-- are handled as a special case.
    	-- Similarly, the default output is handled elsewhere, and for a symbol
    	-- this is only called from get_default() for default_exceptions.
    	__index = function (self, key)
    		local value
    		if key == 'symbol' then
    			local per = self.per
    			local unit1, unit2 = 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 "&nbsp;" in combinations, so
    	-- replace underscore, "&nbsp;", and multiple spaces with a single space.
    	utable = utable or parms.unittable or all_units
    	fails = fails or {}
    	depth = depth and depth + 1 or 1
    	if depth > 9 then
    		-- There are ways to mistakenly define units which result in infinite
    		-- recursion when lookup() is called. That gives a long delay and very
    		-- confusing error messages, so the depth parameter is used as a guard.
    		return false, { 'cvt_lookup', unitcode }
    	end
    	if unitcode == nil or unitcode == '' then
    		return false, { 'cvt_no_unit' }
    	end
    	unitcode = unitcode:gsub('_', ' '):gsub('&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 "acre+m2+ha" or "acre m2 ha" for output.
    	-- If '+' is used, each unit code can include a space, and any error is fatal.
    	-- If ' ' is used and if each space-separated word is a unit code, it is a combo,
    	-- but errors are not fatal so the unit code can be looked up as an extra unit.
    	local err_is_fatal
    	local combo = collection()
    	if unitcode:find('+', 1, true) then
    		err_is_fatal = true
    		for item in (unitcode .. '+'):gmatch('%s*(.-)%s*%+') do
    			if item ~= '' then
    				combo:add(item)
    			end
    		end
    	elseif unitcode:find('%s') then
    		for item in unitcode:gmatch('%S+') do
    			combo:add(item)
    		end
    	end
    	if combo.n > 1 then
    		local function lookup_combo()
    			if what == 'no_combination' or what == 'only_multiple' then
    				return false, { 'cvt_bad_unit', unitcode }
    			end
    			local result = { combination = {} }
    			local cvt = result.combination
    			for i, v in ipairs(combo) do
    				local success, t = lookup(parms, v, 'only_multiple', utable, fails, depth)
    				if not success then return false, t end
    				if i == 1 then
    					result.utype = t.utype
    				else
    					local mismatch = check_mismatch(result, t)
    					if mismatch then
    						return false, mismatch
    					end
    				end
    				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 "e6cuft"
    	-- (million cubic feet), but not chained prefixes like "e3e6cuft",
    	-- and not if the unit is a combination or multiple,
    	-- and not if the unit has an offset or is a built-in.
    	-- Only en digits are accepted.
    	local exponent, baseunit = unitcode:match('^e(%d+)(.*)')
    	if exponent then
    		local engscale = text_code.eng_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 "x/y" unit code.
    		-- The unitcode must not include extraneous spaces.
    		-- Engineering notation (apart from at start and which has been stripped before here),
    		-- is not supported so do not make a per unit if find text like 'e3' in unitcode.
    		local success, result = call_make_per({ per = {top, bottom} })
    		if success then
    			return true, result
    		end
    	end
    	if not parms.opt_ignore_error and not get_range(unitcode) then
    		-- Want the "what links here" list for the extra_module to show only cases
    		-- where an extra unit is used, so do not require it if invoked from {{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 "km2" becomes "km۲".
    		local en_code = ustring.gsub(unitcode, '%d', to_en_table)
    		if en_code ~= unitcode then
    			return lookup(parms, en_code, what, utable, fails, depth)
    		end
    	end
    	return false, { 'cvt_unknown', unitcode }
    end
    
    local function valid_number(num)
    	-- Return true if num is a valid number.
    	-- In Scribunto (different from some standard Lua), when expressed as a string,
    	-- overflow or other problems are indicated with text like "inf" or "nan"
    	-- which are regarded as invalid here (each contains "n").
    	if type(num) == 'number' and tostring(num):find('n', 1, true) == nil then
    		return true
    	end
    end
    
    local function hyphenated(name, parts)
    	-- Return a hyphenated form of given name (for adjectival usage).
    	-- The name may be linked and the target of the link must not be changed.
    	-- Hypothetical examples:
    	--   [[long ton|ton]]         →  [[long ton|ton]]          (no change)
    	--   [[tonne|long ton]]       →  [[tonne|long-ton]]
    	--   [[metric ton|long ton]]  →  [[metric ton|long-ton]]
    	--   [[long ton]]             →  [[long ton|long-ton]]
    	-- Input can also have multiple links in a single name like:
    	--   [[United States customary units|U.S.]] [[US gallon|gallon]]
    	--   [[mile]]s per [[United States customary units|U.S.]] [[quart]]
    	--   [[long ton]]s per [[short ton]]
    	-- Assume that links cannot be nested (never like "[[abc[[def]]ghi]]").
    	-- This uses a simple and efficient procedure that works for most cases.
    	-- Some units (if used) would require more, and can later think about
    	-- adding a method to handle exceptions.
    	-- The procedure is to replace each space with a hyphen, but
    	-- not a space after ')' [for "(pre-1954&nbsp;US) nautical mile"], and
    	-- not spaces immediately before '(' or in '(...)' [for cases like
    	-- "British thermal unit (ISO)" and "Calorie (International Steam Table)"].
    	if name:find(' ', 1, true) then
    		if parts then
    			local pos
    			if name:sub(1, 1) == '(' then
    				pos = name:find(')', 1, true)
    				if pos then
    					return name:sub(1, pos+1) .. name:sub(pos+2):gsub(' ', '-')
    				end
    			elseif name:sub(-1) == ')' then
    				pos = name:find('(', 1, true)
    				if pos then
    					return name:sub(1, pos-2):gsub(' ', '-') .. name:sub(pos-1)
    				end
    			end
    			return name:gsub(' ', '-')
    		end
    		parts = collection()
    		for before, item, after in name:gmatch('([^[]*)(%[%[[^[]*%]%])([^[]*)') do
    			if item:find(' ', 1, true) then
    				local prefix
    				local plen = item:find('|', 1, true)
    				if plen then
    					prefix = item:sub(1, plen)
    					item = item:sub(plen + 1, -3)
    				else
    					prefix = item:sub(1, -3) .. '|'
    					item = item:sub(3, -3)
    				end
    				item = prefix .. hyphenated(item, parts) .. ']]'
    			end
    			parts:add(before:gsub(' ', '-') .. item .. after:gsub(' ', '-'))
    		end
    		if parts.n == 0 then
    			-- No link like "[[...]]" was found in the original name.
    			parts:add(hyphenated(name, parts))
    		end
    		return table.concat(parts)
    	end
    	return name
    end
    
    local function hyphenated_maybe(parms, want_name, sep, id, inout)
    	-- Return s, f where
    	--   s = id, possibly modified
    	--   f = true if hyphenated
    	-- Possible modifications: hyphenate; prepend '-'; append mid text.
    	if id == nil or id == '' then
    		return ''
    	end
    	local mid = (inout == (parms.opt_flip and 'out' or 'in')) and parms.mid or ''
    	if want_name then
    		if parms.opt_adjectival then
    			return '-' .. hyphenated(id) .. mid, true
    		end
    		if parms.opt_add_s and id:sub(-1) ~= 's' then
    			id = id .. 's'  -- for nowiki
    		end
    	end
    	return sep .. id .. mid
    end
    
    local function use_minus(text)
    	-- Return text with Unicode minus instead of '-', if present.
    	if text:sub(1, 1) == '-' then
    		return MINUS .. text:sub(2)
    	end
    	return text
    end
    
    local function digit_groups(parms, text, method)
    	-- Return a numbered table of groups of digits (left-to-right, in local language).
    	-- Parameter method is a number or nil:
    	--   3 for 3-digit grouping (default), or
    	--   2 for 3-then-2 grouping (only for digits before decimal mark).
    	local len_right
    	local len_left = text:find('.', 1, true)
    	if len_left then
    		len_right = #text - len_left
    		len_left = len_left - 1
    	else
    		len_left = #text
    	end
    	local twos = method == 2 and len_left > 5
    	local groups = collection()
    	local run = len_left
    	local n
    	if run < 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 > 0 do
    		groups:add(n)
    		run = run - n
    		n = (twos and run > 3) and 2 or 3
    	end
    	if len_right then
    		if groups.n == 0 then
    			groups:add(0)
    		end
    		if parms.opt_gaps and len_right > 3 then
    			local want4 = not parms.opt_gaps3  -- true gives no gap before trailing single digit
    			local isfirst = true
    			run = len_right
    			while run > 0 do
    				n = (want4 and run == 4) and 4 or (run > 3 and 3 or run)
    				if isfirst then
    					isfirst = false
    					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 < 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 <= 1 then
    			return groups[1] or ''
    		end
    		local nowrap = '<span style="white-space: nowrap">'
    		local gap = '<span style="margin-left: 0.25em">'
    		local close = '</span>'
    		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<span style="margin:0 .15em 0 .25em">×</span>%s<sup>%s</sup>'
    
    local function with_exponent(parms, show, exponent)
    	-- Return wikitext to display the implied value in scientific notation.
    	-- Input uses en digits; output uses digits in local language.
    	return format(fmtpower, with_separator(parms, show), from_en('10'), use_minus(from_en(tostring(exponent))))
    end
    
    local function make_sigfig(value, sigfig)
    	-- Return show, exponent that are equivalent to the result of
    	-- converting the number 'value' (where value >= 0) to a string,
    	-- rounded to 'sigfig' significant figures.
    	-- The returned items are:
    	--   show: a string of digits; no sign and no dot;
    	--         there is an implied dot before show.
    	--   exponent: a number (an integer) to shift the implied dot.
    	-- Resulting value = tonumber('.' .. show) * 10^exponent.
    	-- Examples:
    	--   make_sigfig(23.456, 3) returns '235', 2 (.235 * 10^2).
    	--   make_sigfig(0.0023456, 3) returns '235', -2 (.235 * 10^-2).
    	--   make_sigfig(0, 3) returns '000', 1 (.000 * 10^1).
    	if sigfig <= 0 then
    		sigfig = 1
    	elseif sigfig > maxsigfig then
    		sigfig = maxsigfig
    	end
    	if value == 0 then
    		return string.rep('0', sigfig), 1
    	end
    	local exp, fracpart = math.modf(log10(value))
    	if fracpart >= 0 then
    		fracpart = fracpart - 1
    		exp = exp + 1
    	end
    	local digits = format('%.0f', 10^(fracpart + sigfig))
    	if #digits > sigfig then
    		-- Overflow (for sigfig=3: like 0.9999 rounding to "1000"; need "100").
    		digits = digits:sub(1, sigfig)
    		exp = exp + 1
    	end
    	assert(#digits == sigfig, 'Bug: rounded number has wrong length')
    	return digits, exp
    end
    
    -- Fraction output format.
    local fracfmt = {
    	{ -- Like {{frac}} (fraction slash).
    		'<span class="frac" role="math">{SIGN}<span class="num">{NUM}</span>&frasl;<span class="den">{DEN}</span></span>',  -- 1/2
    		'<span class="frac" role="math">{SIGN}{WHOLE}<span class="sr-only">+</span><span class="num">{NUM}</span>&frasl;<span class="den">{DEN}</span></span>',  -- 1+2/3
    		style = 'frac',
    	},
    	{ -- Like {{sfrac}} (stacked fraction, that is, horizontal bar).
    		'<span class="sfrac tion" role="math">{SIGN}<span class="num">{NUM}</span><span class="sr-only">/</span><span class="den">{DEN}</span></span>',  -- 1//2
    		'<span class="sfrac" role="math">{SIGN}{WHOLE}<span class="sr-only">+</span><span class="tion"><span class="num">{NUM}</span><span class="sr-only">/</span><span class="den">{DEN}</span></span></span>',  -- 1+2//3
    		style = 'sfrac',
    	},
    }
    
    local function format_fraction(parms, inout, negative, wholestr, numstr, denstr, do_spell, style)
    	-- Return wikitext for a fraction, possibly spelled.
    	-- Inputs use en digits and have no sign; output uses digits in local language.
    	local wikitext
    	if not style then
    		style = parms.opt_fraction_horizontal and 2 or 1
    	end
    	if wholestr == '' then
    		wholestr = nil
    	end
    	local substitute = {
    		SIGN = negative and MINUS or '',
    		WHOLE = wholestr and with_separator(parms, wholestr),
    		NUM = from_en(numstr),
    		DEN = from_en(denstr),
    	}
    	wikitext = fracfmt[style][wholestr and 2 or 1]:gsub('{(%u+)}', substitute)
    	if do_spell then
    		if negative then
    			if wholestr then
    				wholestr = '-' .. wholestr
    			else
    				numstr = '-' .. numstr
    			end
    		end
    		local s = spell_number(parms, inout, wholestr, numstr, denstr)
    		if s then
    			return s
    		end
    	end
    	add_style(parms, fracfmt[style].style)
    	return wikitext
    end
    
    local function format_number(parms, show, exponent, isnegative)
    	-- Parameter show is a string or a table containing strings.
    	-- Each string is a formatted number in en digits and optional '.' decimal mark.
    	-- A table represents a fraction: integer, numerator, denominator;
    	-- if a table is given, exponent must be nil.
    	-- Return t where t is a table with fields:
    	--   show = wikitext formatted to display implied value
    	--          (digits in local language)
    	--   is_scientific = true if show uses scientific notation
    	--   clean = unformatted show (possibly adjusted and with inserted '.')
    	--          (en digits)
    	--   sign = '' or MINUS
    	--   exponent = exponent (possibly adjusted)
    	-- The clean and exponent fields can be used to calculate the
    	-- rounded absolute value, if needed.
    	--
    	-- The value implied by the arguments is found from:
    	--   exponent is nil; and
    	--   show is a string of digits (no sign), with an optional dot;
    	--   show = '123.4' is value 123.4, '1234' is value 1234.0;
    	-- or:
    	--   exponent is an integer indicating where dot should be;
    	--   show is a string of digits (no sign and no dot);
    	--   there is an implied dot before show;
    	--   show does not start with '0';
    	--   show = '1234', exponent = 3 is value 0.1234*10^3 = 123.4.
    	--
    	-- The formatted result:
    	-- * Is for an output value and is spelled if wanted and possible.
    	-- * Includes a Unicode minus if isnegative and not spelled.
    	-- * Uses a custom decimal mark, if wanted.
    	-- * Has digits grouped where necessary, if wanted.
    	-- * Uses scientific notation if requested, or for very small or large values
    	--   (which forces result to not be spelled).
    	-- * Has no more than maxsigfig significant digits
    	--   (same as old template and {{#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 > maxlen then
    					show = '0.' .. zeros:sub(1, maxlen)
    				end
    			elseif #zeros >= xlo then
    				show = figs
    				exponent = -#zeros
    			elseif #figs > maxlen then
    				show = '0.' .. zeros .. figs:sub(1, maxlen)
    			end
    		elseif #integer >= xhi then
    			show = integer .. decimals
    			exponent = #integer
    		else
    			maxlen = maxlen + #dot
    			if #show > maxlen then
    				show = show:sub(1, maxlen)
    			end
    		end
    	end
    	if exponent then
    		local function zeros(n)
    			return string.rep('0', n)
    		end
    		if #show > maxlen then
    			show = show:sub(1, maxlen)
    		end
    		if exponent > xhi or exponent <= -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 >= 1e9 or value < 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 > 1 then
    				significand = show:sub(1, 1) .. '.' .. show:sub(2)
    			else
    				significand = show
    			end
    			return {
    				clean = '.' .. show,
    				exponent = exponent,
    				sign = sign,
    				show = sign .. with_exponent(parms, significand, exponent-1),
    				is_scientific = true,
    			}
    		end
    		if exponent >= #show then
    			show = show .. zeros(exponent - #show)  -- result has no dot
    		elseif exponent <= 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 "12.1+3/4" 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 > 2 then style = 2 end
    	local wikitext = format_fraction(parms, 'in', negative, leading_plus .. wholestr, numstr, denstr, parms.opt_spell_in, style)
    	return value, altvalue, wikitext, denominator
    end
    
    local function extract_number(parms, text, another, no_fraction)
    	-- Return true, info if can extract a number from text,
    	-- where info is a table with the result,
    	-- or return false, t where t is an error message table.
    	-- Input can use en digits or digits in local language and can
    	-- have references at the end. Accepting references is intended
    	-- for use in infoboxes with a field for a value passed to convert.
    	-- Parameter another = true if the expected value is not the first.
    	-- Before processing, the input text is cleaned:
    	-- * Any thousand separators (valid or not) are removed.
    	-- * Any sign is replaced with '-' (if negative) or '' (otherwise).
    	--   That replaces Unicode minus with '-'.
    	-- If successful, the returned info table contains named fields:
    	--   value    = a valid number
    	--   altvalue = a valid number, usually same as value but different
    	--              if fraction used (for hands unit)
    	--   singular = true if value is 1 or -1 (to use singular form of units)
    	--   clean    = cleaned text with any separators and sign removed
    	--              (en digits and '.' decimal mark)
    	--   show     = text formatted for output, possibly with ref strip markers
    	--              (digits in local language and custom decimal mark)
    	-- The resulting show:
    	-- * Is for an input value and is spelled if wanted and possible.
    	-- * Has a rounded value, if wanted.
    	-- * Has digits grouped where necessary, if wanted.
    	-- * If negative, a Unicode minus is used; otherwise the sign is
    	--   '+' (if the input text used '+'), or is '' (if no sign in input).
    	text = strip(text or '')
    	local reference
    	local pos = text:find('\127', 1, true)
    	if pos then
    		local before = text:sub(1, pos - 1)
    		local remainder = text:sub(pos)
    		local refs = {}
    		while #remainder > 0 do
    			local ref, spaces
    			ref, spaces, remainder = remainder:match('^(\127[^\127]*UNIQ[^\127]*%-ref[^\127]*\127)(%s*)(.*)')
    			if ref then
    				table.insert(refs, ref)
    			else
    				refs = {}
    				break
    			end
    		end
    		if #refs > 0 then
    			text = strip(before)
    			reference = table.concat(refs)
    		end
    	end
    	local clean = to_en(text, parms)
    	if clean == '' then
    		return false, { another and 'cvt_no_num2' or 'cvt_no_num' }
    	end
    	local isnegative, propersign = false, ''  -- most common case
    	local singular, show, denominator
    	local value = tonumber(clean)
    	local altvalue
    	if value then
    		local sign = clean:sub(1, 1)
    		if sign == '+' or sign == '-' then
    			propersign = (sign == '+') and '+' or MINUS
    			clean = clean:sub(2)
    		end
    		if value < 0 then
    			isnegative = true
    			value = -value
    		end
    	else
    		local valstr
    		for _, prefix in ipairs({ '-', MINUS, '&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  -- "- 1" is invalid but "-1 - 1/2" 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 <= 1 then
    				singular = true  -- for example, "½ mile" or "one half mile" (singular unit)
    			end
    		end
    	end
    	if not valid_number(value) then  -- for example, "1e310" may overflow
    		return false, { 'cvt_invalid_num' }
    	end
    	if show == nil then
    		-- clean is a non-empty string with no spaces, and does not represent a fraction,
    		-- and value = tonumber(clean) is a number >= 0.
    		-- If the input uses e-notation, show will be displayed using a power of ten, but
    		-- we use the number as given so it might not be normalized scientific notation.
    		-- The input value is spelled if specified so any e-notation is ignored;
    		-- that allows input like 2e6 to be spelled as "two million" which works
    		-- because the spell module converts '2e6' to '2000000' before spelling.
    		local function rounded(value, default, exponent)
    			local precision = parms.opt_ri
    			if precision then
    				local fmt = '%.' .. format('%d', precision) .. 'f'
    				local result = fmt:format(tonumber(value) + 2e-14)  -- fudge for some common cases of bad rounding
    				if not exponent then
    					singular = (tonumber(result) == 1)
    				end
    				return result
    			end
    			return default
    		end
    		singular = (value == 1)
    		local scientific
    		local significand, exponent = clean:match('^([%d.]+)[Ee]([+%-]?%d+)')
    		if significand then
    			show = with_exponent(parms, rounded(significand, significand, exponent), exponent)
    			scientific = true
    		else
    			show = with_separator(parms, rounded(value, clean))
    		end
    		show = propersign .. show
    		if parms.opt_spell_in then
    			show = spell_number(parms, 'in', propersign .. rounded(value, clean)) or show
    			scientific = false
    		end
    		if scientific then
    			parms.opt_scientific = true
    		end
    	end
    	if isnegative and (value ~= 0) then
    		value = -value
    		altvalue = -(altvalue or value)
    	end
    	return true, {
    		value = value,
    		altvalue = altvalue or value,
    		singular = singular,
    		clean = clean,
    		show = show .. (reference or ''),
    		denominator = denominator,
    	}
    end
    
    local function get_number(text)
    	-- Return v, f where:
    	--   v = nil (text is not a number)
    	-- or
    	--   v = value of text (text is a number)
    	--   f = true if value is an integer
    	-- Input can use en digits or digits in local language or separators,
    	-- but no Unicode minus, and no fraction.
    	if text then
    		local number = tonumber(to_en(text))
    		if number then
    			local _, fracpart = math.modf(number)
    			return number, (fracpart == 0)
    		end
    	end
    end
    
    local function gcd(a, b)
    	-- Return the greatest common denominator for the given values,
    	-- which are known to be positive integers.
    	if a > b then
    		a, b = b, a
    	end
    	if a <= 0 then
    		return b
    	end
    	local r = b % a
    	if r <= 0 then
    		return a
    	end
    	if r == 1 then
    		return 1
    	end
    	return gcd(r, a)
    end
    
    local function fraction_table(value, denominator)
    	-- Return value as a string or a table:
    	-- * If result is a string, there is no fraction, and the result
    	--   is value formatted as a string of en digits.
    	-- * If result is a table, it represents a fraction with named fields:
    	--   wholestr, numstr, denstr (strings of en digits for integer, numerator, denominator).
    	-- The result is rounded to the nearest multiple of (1/denominator).
    	-- If the multiple is zero, no fraction is included.
    	-- No fraction is included if value is very large as the fraction would
    	-- be unhelpful, particularly if scientific notation is required.
    	-- Input value is a non-negative number.
    	-- Input denominator is a positive integer for the desired fraction.
    	if value <= 0 then
    		return '0'
    	end
    	if denominator <= 0 or value > 1e8 then
    		return format('%.2f', value)
    	end
    	local integer, decimals = math.modf(value)
    	local numerator = floor((decimals * denominator) +
    		0.5 + 2e-14)  -- add fudge for some common cases of bad rounding
    	if numerator >= denominator then
    		integer = integer + 1
    		numerator = 0
    	end
    	local wholestr = tostring(integer)
    	if numerator > 0 then
    		local div = gcd(numerator, denominator)
    		if div > 1 then
    			numerator = numerator / div
    			denominator = denominator / div
    		end
    		return {
    			wholestr = (integer > 0) and wholestr or '',
    			numstr = tostring(numerator),
    			denstr = tostring(denominator),
    			value = value,
    		}
    	end
    	return wholestr
    end
    
    local function preunits(count, preunit1, preunit2)
    	-- If count is 1:
    	--     ignore preunit2
    	--     return p1
    	-- else:
    	--     preunit1 is used for preunit2 if the latter is empty
    	--     return p1, p2
    	-- where:
    	--     p1 is text to insert before the input unit
    	--     p2 is text to insert before the output unit
    	--     p1 or p2 may be nil to mean "no preunit"
    	-- Using '+' gives output like "5+ feet" (no 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 '&nbsp;' or '-'
    		-- at that position ('-' is for adjectival text).
    		-- There is also no space if text starts with '&'
    		-- (e.g. '&deg;' would display a degree symbol with no preceding space).
    		local char = text:sub(1, 1)
    		if char == '&' then
    			return text  -- an html entity can be used to specify the exact display
    		end
    		if not (char == ' ' or char == '-' or char == '+') then
    			text = ' ' .. text
    		end
    		if wantboth then
    			char = text:sub(-1, -1)
    			if not (char == ' ' or char == '-' or text:sub(-6, -1) == '&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 == '&#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, options)
    	-- Return before .. rtext .. after
    	-- where rtext is the text that separates two values in a range.
    	local rtext, adj_text, exception
    	options = options or {}
    	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('&nbsp;', '-')
    		end
    	end
    	if rtext == '–' and (options.spaced or after:sub(1, #MINUS) == MINUS) then
    		rtext = '&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] = "2", just after the first unit)
    	--   in_unit_table = (unit table for "yd"; contains value 1 for number of yards)
    	-- Return true, iparm, unit where
    	--   iparm = index just after the composite units (7 in above example)
    	--   unit = composite unit table holding all input units,
    	-- or return true if no composite unit is present in parms,
    	-- or return false, t where t is an error message table.
    	local default, subinfo
    	local composite_units, count = { in_unit_table }, 1
    	local fixups = {}
    	local total = in_unit_table.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 > 1).
    		total = total * subdiv[1] + subinfo.value
    		if not default then  -- set by the first subdiv with a default defined
    			default = subdiv.default
    		end
    		count = count + 1
    		composite_units[count] = subunit
    		if subdiv.unit or subdiv.name then
    			fixups[count] = { unit = subdiv.unit, name = subdiv.name, valinfo = subunit.valinfo }
    		end
    	end
    	if count == 1 then
    		return true  -- no error and no composite unit
    	end
    	for i, fixup in pairs(fixups) do
    		local unit = fixup.unit
    		local name = fixup.name
    		if not unit or (count > 2 and name) then
    			composite_units[i].fixed_name = name
    		else
    			local success, alternate = lookup(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
    	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 = text_code.en_option_value[en_name]
    			if en_value == 'INTEGER' then  -- altitude_ft, altitude_m, frac, sigfig
    				en_value = nil
    				if loc_value == '' then
    					add_warning(parms, 2, 'cvt_empty_option', loc_name)
    				else
    					local minimum
    					local number, is_integer = get_number(loc_value)
    					if en_name == 'sigfig' then
    						minimum = 1
    					elseif en_name == 'frac' then
    						minimum = 2
    						if number and number < 0 then
    							parms.opt_fraction_horizontal = true
    							number = -number
    						end
    					else
    						minimum = -1e6
    					end
    					if number and is_integer and number >= minimum then
    						en_value = number
    					else
    						local m
    						if en_name == 'frac' then
    							m = 'cvt_bad_frac'
    						elseif en_name == 'sigfig' then
    							m = 'cvt_bad_sigfig'
    						else
    							m = 'cvt_bad_altitude'
    						end
    						add_warning(parms, 1, m, loc_name .. '=' .. loc_value)
    					end
    				end
    			elseif en_value == 'TEXT' then  -- $, input, qid, qual, stylein, styleout, tracking
    				en_value = loc_value ~= '' and loc_value or nil  -- accept non-empty user text with no validation
    				if not en_value and (en_name == '$' or en_name == 'qid' or en_name == 'qual') then
    					add_warning(parms, 2, 'cvt_empty_option', loc_name)
    				elseif en_name == '$' then
    					-- Value should be a single character like "€" for the euro currency symbol, but anything is accepted.
    					currency_text = (loc_value == 'euro') and '€' or loc_value
    				elseif en_name == 'input' then
    					-- May have something like {{convert|input=}} (empty input) if source is an infobox
    					-- with optional fields. In that case, want to output nothing rather than an error.
    					parms.input_text = loc_value  -- keep input because parms.input is nil if loc_value == ''
    				end
    			else
    				en_value = en_value[loc_value]
    				if en_value and en_value:sub(-1) == '?' then
    					en_value = en_value:sub(1, -2)
    					add_warning(parms, -1, 'cvt_deprecated', loc_name .. '=' .. loc_value)
    				end
    				if en_value == nil then
    					if loc_value == '' then
    						add_warning(parms, 2, 'cvt_empty_option', loc_name)
    					else
    						add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)
    					end
    				elseif en_value == '' then
    					en_value = nil  -- an ignored option like adj=off
    				elseif type(en_value) == 'string' and en_value:sub(1, 4) == 'opt_' then
    					for _, v in ipairs(split(en_value, ',')) do
    						local lhs, rhs = v:match('^(.-)=(.+)$')
    						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 "nocomma" kludge from second parameter (like "tonocomma")
    	local parm2 = strip(parms[2])
    	if parm2 and parm2:sub(-7, -1) == 'nocomma' then
    		parms[2] = strip(parm2:sub(1, -8))
    		parms.opt_nocomma = true
    		had_nocomma = true
    	end
    	local function extractor(i)
    		-- If the parameter is not a value, try unpacking it as a range ("1-23" for "1 to 23").
    		-- However, "-1-2/3" is a negative fraction (-1⅔), so it must be extracted first.
    		-- Do not unpack a parameter if it is like "3-1/2" which is sometimes incorrectly
    		-- used instead of "3+1/2" (and which should not be interpreted as "3 to ½").
    		-- Unpacked items are inserted into the parms table.
    		-- The tail recursion allows combinations like "1x2 to 3x4".
    		local valstr = strip(parms[i])  -- trim so any '-' as a negative sign will be at start
    		local success, result = extract_number(parms, valstr, i > 1)
    		if not success and valstr and i < 20 then  -- check i to limit abuse
    			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 "±" 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 "x", 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 > 0 then
    		if range.n > 30 then  -- limit abuse, although 4 is a more likely upper limit
    			return false, { 'cvt_invalid_num' }  -- misleading message but it will do
    		end
    		parms.range = range
    	elseif had_nocomma then
    		return false, { 'cvt_unknown', parm2 }
    	end
    	return true, valinfo, i
    end
    
    local function simple_get_values(parms)
    	-- If input is like "{{convert|valid_value|valid_unit|...}}",
    	-- return true, 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 > 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 "disp=x").
    	local kv_pairs = {}  -- table of input key:value pairs where key is a name; needed because cannot iterate parms and add new fields to it
    	for k, v in pairs(args) do
    		if type(k) == 'number' or k == 'test' then  -- parameter "test" is reserved for testing and is not translated
    			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 "N").
    			-- Output an empty string for these.
    			return false, { 'cvt_no_output' }
    		end
    		local valinfo
    		success, valinfo, i = get_values(parms)
    		if not success then return false, valinfo end
    		in_unit = strip(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  = "ft!X!m"  -- an invalid expression
    		end
    	end
    	in_unit_table.inout = 'in'  -- this is an input unit
    	if not parms.range then
    		local success, inext, composite_unit = get_composite(parms, i, in_unit_table)
    		if not success then return false, inext end
    		if composite_unit then
    			in_unit_table = composite_unit
    			i = inext
    		end
    	end
    	if in_unit_table.builtin == 'mach' then
    		-- As with old template, a number following Mach as the input unit is the altitude.
    		-- That is deprecated: should use altitude_ft=NUMBER or altitude_m=NUMBER.
    		local success, info
    		success = tonumber(parms[i])  -- this will often work and will give correct result for values like 2e4 without forcing output scientific notation
    		if success then
    			info = { value = success }
    		else
    			success, info = extract_number(parms, parms[i], false, true)
    		end
    		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 '&#32;' rather than ' ' to avoid the default
    			first = ' [&nbsp;' .. first
    			second = '&nbsp;]' .. second
    		end
    		parms.joins = { first, second }
    	elseif parms.opt_two_preunits then
    		local p1, p2 = preunits(2, parms[i], parms[i+1])
    		i = i + 2
    		if parms.preunit1 then
    			-- To simplify documentation, allow unlikely use of adj=pre with disp=preunit
    			-- (however, an output unit must be specified with adj=pre and with disp=preunit).
    			parms.preunit1 = parms.preunit1 .. p1
    			parms.preunit2 = p2
    		else
    			parms.preunit1, parms.preunit2 = p1, p2
    		end
    	end
    	if precision == nil then
    		if set_precision(strip(parms[i])) then
    			i = i + 1
    		end
    	end
    	if is_bad_precision then
    		add_warning(parms, 1, 'cvt_bad_prec', precision)
    	else
    		parms.precision = precision
    	end
    	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 < 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 "in" used in input like "|2|ft|6|in"
    	local composite = in_current.composite
    	if composite then
    		subunit_ignore_trailing_zero = true  -- input "|2|st|10|lb" has precision 0, not -1
    		if composite[#composite].exception == 'subunit_more_precision' then
    			subunit_more_precision = true  -- do not use standard precision with input like "|2|ft|6|in"
    		end
    	end
    	if denominator and denominator > 0 then
    		prec = math.max(log10(denominator), 1)
    	else
    		-- Count digits after decimal mark, handling cases like '12.345e6'.
    		local exponent
    		local integer, dot, decimals, expstr = inclean:match('^(%d*)(%.?)(%d*)(.*)')
    		local e = expstr:sub(1, 1)
    		if e == 'e' or e == 'E' then
    			exponent = tonumber(expstr:sub(2))
    		end
    		if dot == '' then
    			prec = subunit_ignore_trailing_zero and 0 or -integer:match('0*$'):len()
    		else
    			prec = #decimals
    		end
    		if exponent then
    			-- So '1230' and '1.23e3' both give prec = -1, and '0.00123' and '1.23e-3' give 5.
    			prec = prec - exponent
    		end
    	end
    	if in_current.istemperature and out_current.istemperature then
    		-- Converting between common temperatures (°C, °F, °R, K); not keVT.
    		-- Kelvin value can be almost zero, or small but negative due to precision problems.
    		-- Also, an input value like -300 C (below absolute zero) gives negative kelvins.
    		-- Calculate minimum precision from absolute value.
    		adjust = 0
    		local kelvin = abs((invalue - in_current.offset) * in_current.scale)
    		if kelvin < 1e-8 then  -- assume nonzero due to input or calculation precision problem
    			minprec = 2
    		else
    			minprec = 2 - floor(log10(kelvin) + fudge)  -- 3 sigfigs in kelvin
    		end
    	else
    		if invalue == 0 or outvalue <= 0 then
    			-- We are never called with a negative outvalue, but it might be zero.
    			-- This is special-cased to avoid calculation exceptions.
    			return record_default_precision(parms, out_current, 0)
    		end
    		if out_current.exception == 'integer_more_precision' and floor(invalue) == invalue then
    			-- With certain output units that sometimes give poor results
    			-- with default rounding, use more precision when the input
    			-- value is equal to an integer. An example of a poor result
    			-- is when input 50 gives a smaller output than input 49.5.
    			-- Experiment shows this helps, but it does not eliminate all
    			-- surprises because it is not clear whether "50" should be
    			-- interpreted as "from 45 to 55" or "from 49.5 to 50.5".
    			adjust = -log10(in_current.scale)
    		elseif subunit_more_precision then
    			-- Conversion like "{{convert|6|ft|1|in|cm}}" (where subunit is "in")
    			-- has a non-standard adjust value, to give more output precision.
    			adjust = log10(out_current.scale) + 2
    		else
    			adjust = log10(abs(invalue / outvalue))
    		end
    		adjust = adjust + log10(2)
    		-- Ensure that the output has at least two significant figures.
    		minprec = 1 - floor(log10(outvalue) + fudge)
    	end
    	if extra then
    		adjust = extra.adjust or adjust
    		minprec = extra.minprec or minprec
    	end
    	return record_default_precision(parms, out_current, math.max(floor(prec + adjust), minprec))
    end
    
    local function convert(parms, invalue, info, in_current, out_current)
    	-- Convert given input value from one unit to another.
    	-- Return output_value (a number) if a simple convert, or
    	-- return f, t where
    	--   f = true, t = table of information with results, or
    	--   f = false, t = error message table.
    	local inscale = in_current.scale
    	local outscale = out_current.scale
    	if not in_current.iscomplex and not out_current.iscomplex then
    		return invalue * (inscale / outscale)  -- minimize overhead for most common case
    	end
    	if in_current.invert or out_current.invert then
    		-- Inverted units, such as inverse length, inverse time, or
    		-- fuel efficiency. Built-in units do not have invert set.
    		if (in_current.invert or 1) * (out_current.invert or 1) < 0 then
    			return 1 / (invalue * inscale * outscale)
    		end
    		return invalue * (inscale / outscale)
    	elseif in_current.offset then
    		-- Temperature (there are no built-ins for this type of unit).
    		if info.is_change then
    			return invalue * (inscale / outscale)
    		end
    		return (invalue - in_current.offset) * (inscale / outscale) + out_current.offset
    	else
    		-- Built-in unit.
    		local in_builtin = in_current.builtin
    		local out_builtin = out_current.builtin
    		if in_builtin and out_builtin then
    			if in_builtin == out_builtin then
    				return invalue
    			end
    			-- There are no cases (yet) where need to convert from one
    			-- built-in unit to another, so this should never occur.
    			return false, { 'cvt_bug_convert' }
    		end
    		if in_builtin == 'mach' or out_builtin == 'mach' then
    			-- Should check that only one altitude is given but am planning to remove
    			-- in_current.altitude (which can only occur when Mach is the input unit),
    			-- and out_current.altitude cannot occur.
    			local alt = parms.altitude_ft or in_current.altitude
    			if not alt and parms.altitude_m then
    				alt = parms.altitude_m / 0.3048  -- 1 ft = 0.3048 m
    			end
    			local spd = speed_of_sound(alt)
    			if in_builtin == 'mach' then
    				inscale = spd
    				return invalue * (inscale / outscale)
    			end
    			outscale = spd
    			local adjust = 0.1 / inscale
    			return true, {
    				outvalue = invalue * (inscale / outscale),
    				adjust = log10(adjust) + log10(2),
    			}
    		elseif in_builtin == 'hand' then
    			-- 1 hand = 4 inches; 1.2 hands = 6 inches.
    			-- Decimals of a hand are only defined for the first digit, and
    			-- the first fractional digit should be a number of inches (1, 2 or 3).
    			-- However, this code interprets the entire fractional part as the number
    			-- of inches / 10 (so 1.75 inches would be 0.175 hands).
    			-- A value like 12.3 hands is exactly 12*4 + 3 inches; base default precision on that.
    			local integer, fracpart = math.modf(invalue)
    			local inch_value = 4 * integer + 10 * fracpart  -- equivalent number of inches
    			local factor = inscale / outscale
    			if factor == 4 then
    				-- Am converting to inches: show exact result, and use "inches" not "in" by default.
    				if parms.abbr_org == nil then
    					out_current.usename = true
    				end
    				local show = format('%g', abs(inch_value))  -- show and clean are unsigned
    				if not show:find('e', 1, true) then
    					return true, {
    						invalue = inch_value,
    						outvalue = inch_value,
    						clean = show,
    						show = show,
    					}
    				end
    			end
    			local outvalue = (integer + 2.5 * fracpart) * factor
    			local fracstr = info.clean:match('%.(.*)') or ''
    			local fmt
    			if fracstr == '' then
    				fmt = '%.0f'
    			else
    				fmt = '%.' .. format('%d', #fracstr - 1) .. 'f'
    			end
    			return true, {
    				invalue = inch_value,
    				clean = format(fmt, inch_value),
    				outvalue = outvalue,
    				minprec = 0,
    			}
    		end
    	end
    	return false, { 'cvt_bug_convert' }  -- should never occur
    end
    
    local 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('"', '')
    		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) < 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 < 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 > 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
    			'<span data-sort-value="' .. sortkey .. '♠"><span style="border:1px solid">' .. sortkey .. '♠</span></span>' or
    			'<span data-sort-value="' .. sortkey .. '♠"></span>'
    		parms.join_before = sortspan
    	end
    	if parms.table_align then
    		local sort
    		if sortkey then
    			sort = ' data-sort-value="' .. sortkey .. '"'
    			if parms.opt_sortable_debug then
    				parms.join_before = '<span style="border:1px solid">' .. sortkey .. '</span>'
    			end
    		else
    			sort = ''
    		end
    		local style = 'style="text-align:' .. parms.table_align .. ';'
    		local joins = {}
    		for i = 1, 2 do
    			joins[i] = (i == 1 and '' or '\n|') .. style .. user_style(parms, i) .. '"' .. sort .. '|'
    		end
    		parms.table_joins = joins
    	end
    	return sortspan, scaled_value
    end
    
    local cvt_to_hand
    
    local function cvtround(parms, info, in_current, out_current)
    	-- Return true, t where t is a table with the conversion results; fields:
    	--   show = rounded, formatted string with the result of converting value in info,
    	--      using the rounding specified in parms.
    	--   singular = true if result (after rounding and ignoring any negative sign)
    	--      is "1", or like "1.00", or is a fraction with value < 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 < 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
    			elseif in_current.builtin == 'mach' then
    				local sigfig = info.clean:gsub('^[0.]+', ''):gsub('%.', ''):len() + 1
    				show, exponent = make_sigfig(outvalue, sigfig)
    			else
    				local inclean = info.clean
    				if extra then
    					inclean = extra.clean or inclean
    					show = extra.show
    				end
    				if not show then
    					precision = default_precision(parms, invalue, inclean, info.denominator, outvalue, in_current, out_current, extra)
    				end
    			end
    		end
    	end
    	if precision then
    		if precision >= 0 then
    			local fudge
    			if precision <= 8 then
    				-- Add a fudge to handle common cases of bad rounding due to inability
    				-- to precisely represent some values. This makes the following work:
    				-- {{convert|-100.1|C|K}} and {{convert|5555000|um|m|2}}.
    				-- Old template uses #expr round, which invokes PHP round().
    				-- LATER: Investigate how PHP round() works.
    				fudge = 2e-14
    			else
    				fudge = 0
    			end
    			local fmt = '%.' .. format('%d', precision) .. 'f'
    			local success
    			success, show = pcall(format, fmt, outvalue + fudge)
    			if not success then
    				return false, { 'cvt_big_prec', tostring(precision) }
    			end
    		else
    			precision = -precision  -- #digits to zero (in addition to any digits after dot)
    			local shift = 10 ^ precision
    			show = format('%.0f', outvalue/shift)
    			if show ~= '0' then
    				exponent = #show + precision
    			end
    		end
    	end
    	local t = format_number(parms, show, exponent, isnegative)
    	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 <= 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 > 1 then
    		frac = (precision == 2) and 2 or 4
    	end
    	local out_next = out_current.out_next
    	if out_next then
    		-- Use magic knowledge to determine whether the next unit is inches without requiring i18n.
    		-- The following ensures that when the output combination "hand in" is used, the inches
    		-- value is rounded to match the hands value. Also, displaying say "61½" instead of 61.5
    		-- is better as 61.5 implies the value is not 61.4.
    		if out_next.exception == 'subunit_more_precision' then
    			out_next.frac = frac
    		end
    	end
    	-- Convert to inches; calculate hands from that.
    	local dummy_unit_table = { scale = out_current.scale / 4, frac = frac }
    	local success, outinfo = cvtround(parms, info, in_current, dummy_unit_table)
    	if not success then return false, outinfo end
    	local tfrac = outinfo.fraction_table
    	local inches = outinfo.raw_absvalue
    	if tfrac then
    		inches = floor(inches)  -- integer part only; fraction added later
    	else
    		inches = floor(inches + 0.5)  -- a hands measurement never shows decimals of an inch
    	end
    	local hands, inches = divide(inches, 4)
    	outinfo.absvalue = hands + inches/4  -- supposed to be the absolute rounded value, but this is close enough
    	local inchstr = tostring(inches)  -- '0', '1', '2' or '3'
    	if precision and precision <= 0 then  -- using negative or 0 for precision rounds to nearest hand
    		hands = floor(outinfo.raw_absvalue/4 + 0.5)
    		inchstr = ''
    	elseif tfrac then
    		-- Always show an integer before fraction (like "15.0½") because "15½" means 15-and-a-half hands.
    		inchstr = numdot .. format_fraction(parms, 'out', false, inchstr, tfrac.numstr, tfrac.denstr)
    	else
    		inchstr = numdot .. from_en(inchstr)
    	end
    	outinfo.show = outinfo.sign .. with_separator(parms, format('%.0f', hands)) .. inchstr
    	return true, outinfo
    end
    
    local function evaluate_condition(value, condition)
    	-- Return true or false from applying a conditional expression to value,
    	-- or throw an error if invalid.
    	-- A very limited set of expressions is supported:
    	--    v < 9
    	--    v * 9 < 9
    	-- where
    	--    'v' is replaced with value
    	--    9 is any number (as defined by Lua tonumber)
    	--      only en digits are accepted
    	--    '<' can also be '<=' or '>' or '>='
    	-- In addition, the following form is supported:
    	--    LHS and RHS
    	-- where
    	--    LHS, RHS = any of above expressions.
    	local function compare(value, text)
    		local arithop, factor, compop, limit = text:match('^%s*v%s*([*]?)(.-)([<>]=?)(.*)$')
    		if arithop == nil then
    			error('Invalid default expression', 0)
    		elseif arithop == '*' then
    			factor = tonumber(factor)
    			if factor == nil then
    				error('Invalid default expression', 0)
    			end
    			value = value * factor
    		end
    		limit = tonumber(limit)
    		if limit == nil then
    			error('Invalid default expression', 0)
    		end
    		if compop == '<' then
    			return value < limit
    		elseif compop == '<=' then
    			return value <= limit
    		elseif compop == '>' then
    			return value > limit
    		elseif compop == '>=' then
    			return value >= limit
    		end
    		error('Invalid default expression', 0)  -- should not occur
    	end
    	local lhs, rhs = condition:match('^(.-%W)and(%W.*)')
    	if lhs == nil then
    		return compare(value, condition)
    	end
    	return compare(value, lhs) and compare(value, rhs)
    end
    
    local function get_default(value, unit_table)
    	-- Return true, s where s = name of unit's default output unit,
    	-- or return false, t where t is an error message table.
    	-- Some units have a default that depends on the input value
    	-- (the first value if a range of values is used).
    	-- If '!' is in the default, the first bang-delimited field is an
    	-- expression that uses 'v' to represent the input value.
    	-- Example: 'v < 120 ! small ! big ! suffix' (suffix is optional)
    	-- evaluates 'v < 120' as a boolean with result
    	-- 'smallsuffix' if (value < 120), or 'bigsuffix' otherwise.
    	-- Input must use en digits and '.' decimal mark.
    	local default = 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 "first" 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 "[[link|id]]", possibly abbreviated as in examples:
    	--   [[Mile|mile]]  --> [[mile]]
    	--   [[Mile|miles]] --> [[mile]]s
    	-- However, just id is returned if:
    	-- * no link given (so caller does not need to check if a link was defined); or
    	-- * link has previously been used during the current convert (to avoid overlinking).
    	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 "m"
    	-- integer 1:        name1     meter  (also is the name of the unit)
    	-- integer 2:        var{1}    metra
    	-- integer 3 and 4:  var{2}    metri
    	-- integer else:     var{3}    metrov (0 and 5 or more)
    	-- real/fraction:    var{4}    metra
    	-- var{i} means the i'th field in unit_table.varname if it exists and has
    	-- an i'th field, otherwise name2.
    	-- Fields are separated with "!" and are not empty.
    	-- A field for a unit using an SI prefix has the prefix name inserted,
    	-- replacing '#' if found, or before the field otherwise.
    	local vname
    	if clean == '1' then
    		vname = unit_table.name1
    	elseif unit_table.varname then
    		local i
    		if clean == '2' then
    			i = 1
    		elseif clean == '3' or clean == '4' then
    			i = 2
    		elseif clean:find('.', 1, true) then
    			i = 4
    		else
    			i = 3
    		end
    		if i > 1 and varname == 'pl' then
    			i = i - 1
    		end
    		vname = split(unit_table.varname, '!')[i]
    	end
    	if vname then
    		local si_name = rawget(unit_table, 'si_name') or ''
    		local pos = vname:find('#', 1, true)
    		if pos then
    			vname = vname:sub(1, pos - 1) .. si_name .. vname:sub(pos + 1)
    		else
    			vname = si_name .. vname
    		end
    		return vname
    	end
    	return unit_table.name2
    end
    
    local function linked_id(parms, unit_table, key_id, want_link, clean)
    	-- Return final unit id (symbol or name), optionally with a wikilink,
    	-- and update unit_table.sep if required.
    	-- key_id is one of: 'symbol', 'sym_us', 'name1', 'name1_us', 'name2', 'name2_us'.
    	local abbr_on = (key_id == 'symbol' or key_id == 'sym_us')
    	if abbr_on and want_link then
    		local symlink = rawget(unit_table, 'symlink')
    		if symlink then
    			return symlink  -- for exceptions that have the linked symbol built-in
    		end
    	end
    	local multiplier = rawget(unit_table, 'multiplier')
    	local per = unit_table.per
    	if per then
    		local paren1, paren2 = '', ''  -- possible parentheses around bottom unit
    		local unit1 = per[1]  -- top unit_table, or nil
    		local unit2 = per[2]  -- bottom unit_table
    		if abbr_on then
    			if not unit1 then
    				unit_table.sep = ''  -- no separator in "$2/acre"
    			end
    			if not want_link then
    				local symbol = unit_table.symbol_raw
    				if symbol then
    					return symbol  -- for exceptions that have the symbol built-in
    				end
    			end
    			if (unit2.symbol):find('⋅', 1, true) then
    				paren1, paren2 = '(', ')'
    			end
    		end
    		local key_id2  -- unit2 is always singular
    		if key_id == 'name2' then
    			key_id2 = 'name1'
    		elseif key_id == 'name2_us' then
    			key_id2 = 'name1_us'
    		else
    			key_id2 = key_id
    		end
    		local result
    		if abbr_on then
    			result = '/'
    		elseif omitsep then
    			result = per_word
    		elseif unit1 then
    			result = ' ' .. per_word .. ' '
    		else
    			result = per_word .. ' '
    		end
    		if want_link and unit_table.link then
    			if abbr_on or not varname then
    				result = (unit1 and linked_id(parms, unit1, key_id, false, clean) or '') .. result .. linked_id(parms, unit2, key_id2, false, '1')
    			else
    				result = (unit1 and variable_name(clean, unit1) or '') .. result .. variable_name('1', unit2)
    			end
    			if omit_separator(result) then
    				unit_table.sep = ''
    			end
    			return make_link(unit_table.link, result, unit_table)
    		end
    		if unit1 then
    			result = linked_id(parms, unit1, key_id, want_link, clean) .. result
    			if unit1.sep then
    				unit_table.sep = unit1.sep
    			end
    		elseif omitsep then
    			unit_table.sep = ''
    		end
    		return result .. paren1 .. linked_id(parms, unit2, key_id2, want_link, '1') .. paren2
    	end
    	if multiplier then
    		-- A multiplier (like "100" in "100km") forces the unit to be plural.
    		multiplier = from_en(multiplier)
    		if not omitsep then
    			multiplier = multiplier .. (abbr_on and '&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 "U.S." not "US"
    			end
    			if i == 3 and abbr_on then
    				i = 4  -- abbreviate "imperial" to "imp"
    			end
    			local customary = text_code.customary_units[i]
    			if customary then
    				-- LATER: This works for language en only, but it's esoteric so ignore for now.
    				local pertext
    				if id:sub(1, 1) == '/' then
    					-- Want unit "/USgal" to display as "/U.S. gal", not "U.S. /gal".
    					pertext = '/'
    					id = id:sub(2)
    				elseif id:sub(1, 4) == 'per ' then
    					-- Similarly want "per U.S. gallon", not "U.S. per gallon" (but in practice this is unlikely to be used).
    					pertext = 'per '
    					id = id:sub(5)
    				else
    					pertext = ''
    				end
    				-- Omit any "US"/"U.S."/"imp"/"imperial" from start of id since that will be inserted.
    				local removes = (i < 3) and { 'US&nbsp;', 'US ', 'U.S.&nbsp;', 'U.S. ' } or { 'imp&nbsp;', 'imp ', 'imperial ' }
    				for _, prefix in ipairs(removes) do
    					local plen = #prefix
    					if id:sub(1, plen) == prefix then
    						id = id:sub(plen + 1)
    						break
    					end
    				end
    				before = pertext .. make_link(customary.link, customary[1]) .. ' '
    			end
    			id = before .. make_link(link, id, unit_table)
    		end
    	end
    	return multiplier .. id
    end
    
    local function make_id(parms, which, unit_table)
    	-- Return id, f where
    	--   id = unit name or symbol, possibly modified
    	--   f = true if id is a name, or false if id is a symbol
    	-- using 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 '&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 = '&nbsp;'
    		else
    			unit_table.sep = ' '
    		end
    		if parms.opt_singular then
    			local value
    			if inout == 'in' then
    				value = info.value
    			else
    				value = info.absvalue
    			end
    			if value then  -- some unusual units do not always set value field
    				value = abs(value)
    				singular = (0 < value and value < 1.0001)
    			end
    		end
    		if unit_table.engscale then
    			-- engscale: so "|1|e3kg" gives "1 thousand kilograms" (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 = '&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 "display:none" to allow some
    	-- browsers to copy, for example, "10³" as "10^3", rather than as "103".
    	local info
    	local engscale = unit_table.engscale
    	local prefix = unit_table.vprefix
    	if engscale or prefix then
    		info = unit_table.valinfo[which]
    		if info.decorated then
    			return  -- do not redecorate if repeating convert
    		end
    		info.decorated = true
    		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 ..
    					'<span style="margin-left:0.2em">×<span style="margin-left:0.1em">' ..
    					from_en('10') ..
    					'</span></span><s style="display:none">^</s><sup>' ..
    					from_en(tostring(engscale.exponent)) .. '</sup>'
    			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 "&nbsp;" in values like "12 million".
    				info.show = info.show .. (parms.opt_adjectival and '-' or '&nbsp;') .. number_id
    			end
    		end
    		if prefix then
    			info.show = prefix .. info.show
    		end
    	end
    end
    
    local function process_input(parms, in_current)
    	-- Processing required once per conversion.
    	-- Return block of text to represent input (value/unit).
    	if parms.opt_output_only or parms.opt_output_number_only or parms.opt_output_unit_only then
    		parms.joins = { '', '' }
    		return ''
    	end
    	local first_unit
    	local composite = in_current.composite  -- nil or table of units
    	if composite then
    		first_unit = composite[1]
    	else
    		first_unit = in_current
    	end
    	local id1, want_name = make_id(parms, 1, first_unit)
    	local sep = first_unit.sep  -- separator between value and unit, set by make_id
    	local preunit = parms.preunit1
    	if preunit then
    		sep = ''  -- any separator is included in preunit
    	else
    		preunit = ''
    	end
    	if parms.opt_input_unit_only then
    		parms.joins = { '', '' }
    		if composite then
    			local parts = { id1 }
    			for i, unit in ipairs(composite) do
    				if i > 1 then
    					table.insert(parts, (make_id(parms, 1, unit)))
    				end
    			end
    			id1 = table.concat(parts, ' ')
    		end
    		if want_name and parms.opt_adjectival then
    			return preunit .. hyphenated(id1)
    		end
    		return  preunit .. id1
    	end
    	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 .. '&nbsp;'
    		local range = parms.range
    		local valinfo = first_unit.valinfo
    		local result = prefix .. valinfo[1].show
    		if range then
    			-- For simplicity and because more not needed, handle one range item only.
    			local prefix2 = make_id(parms, 2, first_unit) .. '&nbsp;'
    			result = range_text(range[1], want_name, parms, result, prefix2 .. valinfo[2].show, 'in', {spaced=true})
    		end
    		return preunit .. result
    	end
    	if composite then
    		-- Simplify: assume there is no range, and no decoration.
    		local mid = (not parms.opt_flip) and parms.mid or ''
    		local sep1 = '&nbsp;'
    		local sep2 = ' '
    		if parms.opt_adjectival and want_name then
    			sep1 = '-'
    			sep2 = '-'
    		end
    		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 > 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 .. '&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, {spaced=true})
    		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 = '&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 < thisvalue and thisvalue < 1.0001 then
    							key = 'name1'
    						end
    					else
    						if thisvalue == 1 then
    							key = 'name1'
    						end
    					end
    					id = out_current[key]
    				end
    			else
    				id = out_current['symbol']
    			end
    			if 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 > 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, {spaced=true})
    		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 > 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, get_styles(parms) .. wikitext, out_unit_table
    end
    
    local function main_convert(frame)
    	-- Do convert, and if needed, do it again with higher default precision.
    	local parms = { frame = frame }  -- will hold template arguments, after translation
    	set_config(frame.args)
    	local success, result = get_parms(parms, frame:getParent().args)
    	if success then
    		if type(result) ~= 'table' then
    			return tostring(result)
    		end
    		local in_unit_table = result
    		local out_unit_table
    		for _ = 1, 2 do  -- use counter so cannot get stuck repeating convert
    			success, result, out_unit_table = process(parms, in_unit_table, out_unit_table)
    			if success and parms.do_convert_again then
    				parms.do_convert_again = false
    			else
    				break
    			end
    		end
    	end
    	-- If input=x gives a problem, the result should be just the user input
    	-- (if x is a property like P123 it has been replaced with '').
    	-- An unknown input unit would display the input and an error message
    	-- with success == true at this point.
    	-- Also, can have success == false with a message that outputs an empty string.
    	if parms.input_text then
    		if success and not parms.have_problem then
    			return result
    		end
    		local cat
    		if parms.tracking then
    			-- Add a tracking category using the given text as the category sort key.
    			-- There is currently only one type of tracking, but in principle multiple
    			-- items could be tracked, using different sort keys for convenience.
    			cat = wanted_category('tracking', parms.tracking)
    		end
    		return parms.input_text .. (cat or '')
    	end
    	return success and result or message(parms, result)
    end
    
    local function _unit(unitcode, options)
    	-- Helper function for Module:Val to look up a unit.
    	-- Parameter unitcode must be a string to identify the wanted unit.
    	-- Parameter options must be nil or a table with optional fields:
    	--   value = number (for sort key; default value is 1)
    	--   scaled_top = nil for a normal unit, or a number for a unit which is
    	--                the denominator of a per unit (for sort key)
    	--   si = { 'symbol', 'link' }
    	--                (a table with two strings) to make an SI unit
    	--                that will be used for the look up
    	--   link = true if result should be [[linked]]
    	--   sort = 'on' or 'debug' if result should include a sort key in a
    	--                span element ('debug' makes the key visible)
    	--   name = true for the name of the unit instead of the symbol
    	--   us = true for the US spelling of the unit, if any
    	-- Return nil if unitcode is not a non-empty string.
    	-- Otherwise return a table with fields:
    	--   text = requested symbol or name of unit, optionally linked
    	--   scaled_value = input value adjusted by unit scale; used for sort key
    	--   sortspan = span element with sort key like that provided by {{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
    
    return { convert = main_convert, _unit = _unit }