Module:Convert

From OODA WIKI

This category is an index of templates which use TemplateStyles. It is automatically populated by {{Uses TemplateStyles}}.

This module converts a value from one unit of measurement to another. For example:

  • {{convert|123|lb|kg}} → 123 pounds (56 kg)

The module is called using a template—parameters passed to the template are used by this module to control how a conversion is performed. For example, units can be abbreviated (like kg), or displayed as names (like kilogram), and the output value can be rounded to a specified precision. For usage information, see Help:Convert.

Templates and modules

Templates that invoke this module are:

The following modules are required:

The following modules are optional and are used only if required and if the module exists:

For Wikidata support the following modules are required:

The following help pages are available:

A page containing a convert error is added to the following hidden category, providing the page is in a specified namespace (articles, by default):

Units are defined in the wikitext of the master list of units.

Module:Convert/data is transcluded into every page using the convert module, so experimenting with a new unit in that module would involve a significant overhead. The Module:Convert/extra module is an alternative which is only transcluded on pages with a unit that is not defined in the main data module.

Module talk:Convert/show lists all unit links so they can be checked.

Sandbox

When making a change, copy the current modules to the sandbox pages, then edit the sandbox copies: Script error: No such module "convert/tester".

Use the following template to test the results (example {{convert/sandbox|123|lb|kg}}):

Template:Convert/sandbox invokes Module:Convert/sandbox with parameter |sandbox=sandbox which causes convert to use the sandbox modules rather than the normal modules.

The following should be used to test the results of editing the convert modules.

It is not necessary to save a testcases page before viewing test results. For example, Template:Convert/testcases/sandbox4 could be edited to change the tests. While still editing that page, paste "Template talk:Convert/testcases/sandbox4" (without quotes) into the page title box under "Preview page with this template", then click "Show preview".

Configuration

The template that invokes this module can define options to configure the module. For example:

  • {{#invoke:convert|convert|numdot=,|numsep=.}}
Sets the decimal mark to be a comma, and the thousands separator to be a dot.

Other options, with default values, are:

  • |maxsigfig=14 – maximum number of significant figures
  • |nscat=0 – namespaces (comma separated) in which an error or warning adds a category to the page
  • |warnings=0 – 0 (zero) disables warnings; 1 shows important warnings; 2 shows all warnings

An option in the template can specify that the sandbox versions of the modules be used. If specified, the text on the right-hand side of the equals sign must be the name of the subpage for each sandbox module.

  • |sandbox=sandbox – omit for normal operation

All text used for input parameters and for output messages and categories can be customized. For example, at enwiki the option |lk=on can be used to link each displayed unit to its article. The "lk" and "on" can be replaced with any desired text. In addition, input and output numbers can be formatted and can use digits in the local language. See the translation guide for more information.

To do

Document the modules to access Wikidata!

Module version history

-- 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 }
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