Mô đun:Convert

Tài liệu mô đun[xem] [sửa] [lịch sử] [làm mới]

Mô đun này chuyển đổi một giá trị từ một đơn vị đo lường sang một đơn vị khác, thí dụ:

• {{convert|123|kg|lb}} → 123 kilôgam (270 lb)

Mô đun này được gọi qua một bản mẫu; mô đun sử dụng các tham số của bản mẫu này để điều khiển cách chuyển đổi. Thí dụ có thể viết tắt các đơn vị (như kg) hoặc ghi đầy đủ (như kilôgam), và có thể làm tròn giá trị cho ra theo độ chính xác được xác định. Xem thêm chi tiết về cách sử dụng tại Trợ giúp:Chuyển đổi.

Bản mẫu gọi mô đun này là:

• Bản mẫu:Convert

Các mô đun sau được yêu cầu:

• Mô đun:Convert – (mô đun này) lôgic để chuyển đổi các đơn vị
• Mô đun:Convert/data – các định nghĩa đơn vị
• Mô đun:Convert/text – các thông điệp cùng với các tên và giá trị tham số

Các mô đun sau không nhất thiết phải tồn tại và chỉ được sử dụng khi nào cần nếu tồn tại:

• Mô đun:Convert/extra – các định nghĩa đơn vị (tạm thời) dư; được sử dụng khi nào một đơn vị không có trong Mô đun:Convert/data
• Mô đun:ConvertNumeric – mã nguồn để viết dài giá trị cho vào

Các mô đun sau được yêu cầu để hỗ trợ Wikidata:

• Mô đun:Convert/wikidata
• Mô đun:Convert/wikidata/data

Có sẵn các trang trợ giúp sau:

• en:Help:Convert – giới thiệu
• en:Help:Convert messages – miêu tả các thông điệp lỗi và cảnh báo; các thông điệp liên kết đến trang này
• en:Help:Convert units – tóm lược các đơn vị

Các trang có lỗi chuyển đổi được xếp vào một trong những thể loại sau, miễn là nó nằm trong một không gian tên phù hợp (mặc định là các không gian tên chính):

• Thể loại:Đơn vị chuyển đổi không hợp lệ
• Thể loại:Tùy chọn chuyển đổi không hợp lệ
• Thể loại:Bài có giá trị chuyển đổi không chính xác (vì có số tiếng Anh như "1,234.56")

Các đơn vị được định rõ trong văn bản wiki của danh sách đơn vị đầy đủ.

• Mô đun:Convert/documentation/conversion data/tài liệu – danh sách đầy đủ các định nghĩa đơn vị
• Mô đun:Convert/makeunits – biên soạn văn bản wiki trong danh sách đầy đủ thành mã nguồn Lua
• Thảo luận Mô đun:Convert/makeunits – kết quả makeunits; chép dán văn bản vào Mô đun:Convert/data

Mô đun:Convert/data được gọi bởi mỗi trang sử dụng mô đun Convert, nên thử nghiệm một đơn vị mới trong mô đun đó sẽ tốn nhiều tài nguyên. Để thử nghiệm, hãy sử dụng Mô đun:Convert/extra, mô đun này chỉ được gọi khi nào gặp một đơn vị không được định rõ trong mô đun dũ liệu chính.

Chỗ thử

Khi thực hiện một thay đổi, sao chép các mô đun vào các trang thử và sửa các bản sao thử này:

• Mô đun:Convert/sandbox
• Mô đun:Convert/data/sandbox
• Mô đun:Convert/text/sandbox
• Mô đun:Convert/extra/sandbox
• Mô đun:Convert/wikidata/sandbox
• Mô đun:Convert/wikidata/data/sandbox

Hãy sử dụng bản mẫu sau để xem trước (thí dụ {{convert/sandbox|123|kg|lb}}):

• Bản mẫu:Convert/sandbox

Bản mẫu:Convert/sandbox gọi Mô đun:Convert/sandbox với tham số |sandbox=on, làm cho Convert sử dụng các mô đun thử thay vì các mô đun thường.

Hãy thử các sửa đổi trong các mô đun convert dùng các trang sau.

• Mô đun:Convert/tester – mô đun kiểm thử bằng cách so sánh giá trị cho ra bản mẫu với văn bản định trước
• Mô đun:Convert/sandbox/testcases – các bản mẫu để thử cùng với các giá trị cho ra mong đợi (sử dụng mô đun tester)
• Thảo luận Mô đun:Convert/sandbox/testcases – xem kết quả kiểm thử

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

Thiết lập

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

• {{#gọi: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.

Tài liệu bên trên được truyền tải từ Mô đun:Convert/tài liệu. (sửa | lịch sử)
Biên tập viên sửa đổi có thể thử nghiệm trong các trang chỗ thử (sửa | khác) và trường hợp kiểm thử (tạo) của mô đun này.
Các trang con của mô đun này.

	-- Convert a value from one unit of measurement to another.
-- Example: {{convert|123|lb|kg}} --> 123 pounds (56 kg)

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, numsep  -- each must be a single byte for simple regex search/replace
local default_exceptions, link_exceptions, all_units
local SIprefixes, all_categories, all_messages, customary_units, disp_joins
local en_option_name, en_option_value, eng_scales, range_aliases, range_types
local group_method = 3	 -- code for how many digits are in a group
local per_word = 'một'	 -- for units like "miles per gallon"
local plural_suffix = ''  -- only other useful value is probably '' to disable plural unit names
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

-- All units should be defined in the data module. However, to cater for quick changes
-- and experiments, any unknown unit is looked up in an extra data module, if it exists.
-- That module would be transcluded in only a small number of pages, so there should be
-- little server overhead from making changes, and changes should propagate quickly.
local extra_module  -- name of module with extra units
local extra_units   -- nil or table of extra units from extra_module

local function boolean(text)
	-- Return true if text represents a "true" option value.
	if text then
		text = text:lower()
		if text == 'on' or text == 'yes' or text == 'có' then
			return true
		end
	end
	return false
end

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 decimalPoint(number_str)
	local decimal
	
	number_str = number_str:gsub("%+%d+/%d+$", "")
	number_str = number_str:gsub("[Ee]%-?%d+$", "")
	number_str = number_str:gsub("^%-", "")
	
	if number_str:match("^[^,.]*$") then return "," end
	
	decimal = number_str:match("^0?([.,])%d+$")
	if decimal then return decimal end
	decimal = number_str:match("%d([.,])%d?%d?$") or number_str:match("%d([.,])%d%d%d%d+$")
	if decimal then return decimal end
	if number_str:match("^%d?%d?%d?[,.]%d%d%d$") then return end
	
	if number_str:match("%.%d+%.") then return "," end
	if number_str:match("%,%d+,") then return "." end
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 decimalPoint(text) ~= "." then
		if numsep ~= '' then
			text = text:gsub('[' .. numsep .. ']', '')  -- use '[x]' in case x is '.'
		end
		if numdot ~= '.' then
			text = text:gsub('[' .. numdot .. ']', '.')
		end
	end
	if to_en_table then
		text = ustring.gsub(text, '%d', to_en_table)
	end
	return text
end

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

local function set_config(frame)
	-- Set configuration options from template #invoke or defaults.
	config = frame.args
	numdot = config.numdot or '.'	   -- decimal mark before fractional digits
	numsep = config.numsep or ','	   -- group separator for numbers (',', '.', '')
	maxsigfig = config.maxsigfig or 14  -- maximum number of significant figures
	-- Scribunto sets the global variable 'mw'.
	-- A testing program can set the global variable 'is_test_run'.
	local data_module, text_module, data_code, text_code
	if is_test_run then
		local langcode = mw.language.getContentLanguage().code
		data_module = "convertdata-" .. langcode
		text_module = "converttext-" .. langcode
		extra_module = "convertextra-" .. langcode
		spell_module = "ConvertNumeric"
	else
		local sandbox = boolean(config.sandbox) and '/sandbox' or ''
		data_module = "Mô đun:Convert/data" .. sandbox
		text_module = "Mô đun:Convert/text" .. sandbox
		extra_module = "Mô đun:Convert/extra" .. sandbox
		spell_module = "Mô đun:ConvertNumeric"
	end
	data_code = mw.loadData(data_module)
	text_code = mw.loadData(text_module)
	default_exceptions = data_code.default_exceptions
	link_exceptions = data_code.link_exceptions
	all_units = data_code.all_units
	SIprefixes = text_code.SIprefixes
	all_categories = text_code.all_categories
	all_messages = text_code.all_messages
	customary_units = text_code.customary_units
	disp_joins = text_code.disp_joins
	en_option_name = text_code.en_option_name
	en_option_value = text_code.en_option_value
	eng_scales = text_code.eng_scales
	range_aliases = text_code.range_aliases
	range_types = text_code.range_types
	local translation = text_code.translation_table
	if translation then
		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
		from_en_table = translation.from_en
		local use_workaround = true
		if use_workaround then
			-- 2013-07-05 workaround bug by making a copy of the required table.
			-- mw.ustring.gsub fails with a table (to_en_table) as the replacement,
			-- if the table is accessed via mw.loadData.
			local source = translation.to_en
			if source then
				to_en_table = {}
				for k, v in pairs(source) do
					to_en_table[k] = v
				end
			end
		else
			to_en_table = translation.to_en
		end
	end
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 split(text, delimiter)
	-- Return a numbered table with fields from splitting text.
	-- The delimiter is used in a regex without escaping (for example, '.' would fail).
	-- Each field has any leading/trailing whitespace removed.
	local t = {}
	text = text .. delimiter  -- to get last item
	for item in text:gmatch('%s*(.-)%s*' .. delimiter) do
		table.insert(t, item)
	end
	return t
end

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

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

local function message(mcode)
	-- Return wikitext for an error message, including category if specified
	-- for the message type.
	-- mcode = numbered table specifying the message:
	--	mcode[1] = 'cvt_xxx' (string used as a key to get message info)
	--	mcode[2] = 'parm1' (string to replace first %s if any in message)
	--	mcode[3] = 'parm2' (string to replace second %s if any in message)
	--	mcode[4] = 'parm3' (string to replace third %s if any in message)
	local msg = all_messages[mcode[1]]
	if msg then
		local title = format(msg[1] or 'Thông báo bị thiếu',
			mcode[2] or '?',
			mcode[3] or '?',
			mcode[4] or '?')
		local text = msg[2] or 'Thông báo bị thiếu'
		local cat = wanted_category(all_categories[msg[3]]) or ''
		local anchor = msg[4] or ''
		local fmt = all_messages['cvt_format'] or 'convert: lỗi'
		local regex, replace = msg.regex, msg.replace
		if regex and replace then
			title = title:gsub(regex, replace)
		end
		title = title:gsub('"', '"')
		return format(fmt, anchor, title, text, cat)
	end
	return 'Lỗi nội bộ Convert: thông báo không rõ'
end

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

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

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

local function 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,
	-- or for a unit that accepts prefixes but where no prefix was used.
	-- In the latter case, and before use, fields symbol, name1, name1_us
	-- must be set from _symbol, _name1, _name1_us respectively.
	__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
		elseif key == 'builtin' then
			value = false
		else
			return nil
		end
		rawset(self, key, value)
		return value
	end
}

local unit_prefixed_mt = {
	-- Metatable to get missing values for a unit that accepts SI prefixes,
	-- and where a prefix has been used.
	-- Before use, fields si_name, si_prefix must be defined.
	__index = function (self, key)
		local value
		if key == 'symbol' then
			value = self.si_prefix .. self._symbol
		elseif key == 'sym_us' then
			value = self.symbol  -- always the same as sym_us for prefixed units
		elseif key == 'name1' then
			-- prefix_position is a byte (not character) position, so use Lua's sub().
			local pos = rawget(self, 'prefix_position') or 1
			value = self._name1
			value = value:sub(1, pos - 1) .. self.si_name .. value:sub(pos)
		elseif key == 'name2' then
			value = self.name1 .. plural_suffix
		elseif key == 'name1_us' then
			value = rawget(self, '_name1_us')
			if value then
				local pos = rawget(self, 'prefix_position') or 1
				value = value:sub(1, pos - 1) .. self.si_name .. value:sub(pos)
			else
				value = self.name1
			end
		elseif key == 'name2_us' then
			if rawget(self, '_name1_us') then
				value = self.name1_us .. plural_suffix
			else
				value = self.name2
			end
		elseif key == 'link' then
			value = self.name1
		elseif key == 'builtin' then
			value = false
		else
			return nil
		end
		rawset(self, key, value)
		return value
	end
}

local unit_per_mt = {
	-- Metatable to get values for a "per" unit of form "x/y".
	-- This is never called to determine a unit name or link because "per" units
	-- are handled as a special case.
	__index = function (self, key)
		local value
		if key == 'symbol' then
			local per = self.per
			local unit1, unit2 = per[1], per[2]
			if unit1 then
				value = unit1[key] .. '/' .. unit2[key]
			else
				value = '/' .. unit2[key]
			end
		elseif key == 'sym_us' then
			value = self.symbol
		elseif key == 'scale' then
			local per = self.per
			local unit1, unit2 = per[1], per[2]
			value = (unit1 and unit1.scale or 1) * self.scalemultiplier / unit2.scale
		elseif key == 'builtin' then
			value = false
		else
			return nil
		end
		rawset(self, key, value)
		return value
	end
}

local function lookup(unitcode, opt_sp_us, what, utable, fails, depth)
	-- Return true, t where t is a copy of the unit's converter table,
	-- or return false, t where t is an error message table.
	-- Parameter opt_sp_us is true for US spelling of SI prefixes and
	-- the symbol and name of the unit. If true, the result includes field
	-- sp_us = true (that field may also have been in the unit definition).
	-- Parameter 'what' determines whether combination units are accepted:
	--   'no_combination'  : single unit only
	--   'any_combination' : single unit or combination or output multiple
	--   'only_multiple'   : single unit or output multiple only
	-- Parameter unitcode is a symbol (like 'g'), with an optional SI prefix (like 'kg').
	-- If, for example, 'kg' is in this table, that entry is used;
	-- otherwise the prefix ('k') is applied to the base unit ('g').
	-- If unitcode is a known combination code (and if allowed by what),
	-- a table of output multiple unit tables is included in the result.
	-- For compatibility with the old template, an underscore in a unitcode is
	-- replaced with a space so usage like {{convert|350|board_feet}} works.
	-- Wikignomes may also put two spaces or "&nbsp;" in combinations, so
	-- replace underscore, "&nbsp;", and multiple spaces with a single space.
	utable = utable or all_units
	fails = fails or {}
	depth = depth and depth + 1 or 1
	if depth > 9 then
		-- There are ways to mistakenly define units which result in infinite
		-- recursion when lookup() is called. That gives a long delay and very
		-- confusing error messages, so the depth parameter is used as a guard.
		return false, { 'cvt_lookup', unitcode }
	end
	if unitcode == nil or unitcode == '' then
		return false, { 'cvt_no_unit' }
	end
	unitcode = unitcode:gsub('_', ' '):gsub('&nbsp;', ' '):gsub('  +', ' ')
	local t = utable[unitcode]
	if t then
		if t.shouldbe then
			return false, { 'cvt_should_be', t.shouldbe }
		end
		local force_sp_us = opt_sp_us
		if t.sp_us then
			force_sp_us = true
			opt_sp_us = true
		end
		local target = t.target  -- nil, or unitcode is an alias for this target
		if target then
			local success, result = lookup(target, opt_sp_us, what, utable, fails, depth)
			if not success then return false, result end
			override_from(result, t, { 'customary', 'default', 'link', 'symbol', 'symlink' })
			local multiplier = t.multiplier
			if multiplier then
				result.multiplier = tostring(multiplier)
				result.scale = result.scale * multiplier
			end
			return true, result
		end
		local per = t.per  -- nil/false, or a numbered table for "x/y" units
		if per then
			local result = { utype = t.utype, per = {} }
			result.scalemultiplier = t.multiplier or 1
			override_from(result, t, { 'invert', 'iscomplex', 'default', 'link', 'symbol', 'symlink' })
			result.symbol_raw = (result.symbol or false)  -- to distinguish between a defined exception and a metatable calculation
			local cvt = result.per
			local prefix
			for i, v in ipairs(per) do
				if i == 1 and (v == '$' or v == '£') then
					prefix = v
				else
					local success, t = lookup(v, opt_sp_us, 'no_combination', utable, fails, depth)
					if not success then return false, t end
					cvt[i] = t
					if t.sp_us then  -- if the top or bottom unit forces sp=us, set the per unit to use the correct name/symbol
						force_sp_us = true
					end
				end
			end
			if prefix then
				result.vprefix = prefix
			else
				result.vprefix = false  -- to avoid calling __index
			end
			result.sp_us = force_sp_us
			return true, setmetatable(result, unit_per_mt)
		end
		local combo = t.combination  -- nil or a table of unitcodes
		if combo then
			local multiple = t.multiple
			if what == 'no_combination' or (what == 'only_multiple' and multiple == nil) then
				return false, { 'cvt_bad_unit', unitcode }
			end
			-- Recursively create a combination table containing the
			-- converter table of each unitcode.
			local result = { utype = t.utype, multiple = multiple, combination = {} }
			local cvt = result.combination
			for i, v in ipairs(combo) do
				local success, t = lookup(v, opt_sp_us, multiple and 'no_combination' or 'only_multiple', utable, fails, depth)
				if not success then return false, t end
				cvt[i] = t
			end
			return true, result
		end
		local result = shallow_copy(t)
		result.sp_us = force_sp_us
		if result.prefixes then
			result.symbol = result._symbol
			result.name1 = result._name1
			result.name1_us = result._name1_us
		end
		return true, setmetatable(result, unit_mt)
	end
	for plen = SIprefixes[1] or 2, 1, -1 do
		-- Look for an SI prefix; should never occur with an alias.
		-- Check for longer prefix first ('dam' is decametre).
		-- SIprefixes[1] = prefix maximum #characters (as seen by mw.ustring.sub).
		local prefix = usub(unitcode, 1, plen)
		local si = SIprefixes[prefix]
		if si then
			local t = utable[usub(unitcode, plen+1)]
			if t and t.prefixes then
				local result = shallow_copy(t)
				if opt_sp_us then
					result.sp_us = true
				end
				if result.sp_us and si.name_us then
					result.si_name = si.name_us
				else
					result.si_name = si.name
				end
				result.si_prefix = si.prefix or prefix
				result.scale = t.scale * 10 ^ (si.exponent * t.prefixes)
				return true, setmetatable(result, unit_prefixed_mt)
			end
		end
	end
	-- Accept any unit with an engineering notation prefix like "e6cuft"
	-- (million cubic feet), but not chained prefixes like "e3e6cuft",
	-- and not if the unit is a combination or multiple,
	-- and not if the unit has an offset or is a built-in.
	-- Only en digits are accepted.
	local exponent, baseunit = unitcode:match('^e(%d+)(.*)')
	if exponent then
		local engscale = eng_scales[exponent]
		if engscale then
			local success, result = lookup(baseunit, opt_sp_us, 'no_combination', utable, fails, depth)
			if not success then return false, result end
			if not (result.offset or result.builtin or result.engscale) then
				result.defkey = unitcode  -- key to lookup default exception
				result.engscale = engscale
				result.scale = result.scale * 10 ^ tonumber(exponent)
				return true, result
			end
		end
	end
	-- 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(v, opt_sp_us, 'no_combination', utable, fails, depth)
				if not success then return false, t end
				if i == 1 then
					result.utype = t.utype
				else
					local mismatch = check_mismatch(result, t)
					if mismatch then
						return false, mismatch
					end
				end
				cvt[i] = t
			end
			return true, result
		end
		local success, result = lookup_combo()
		if success or err_is_fatal then
			return success, result
		end
	end
	if not extra_units then
		local success, extra = pcall(function () return require(extra_module).extra_units end)
		if success and type(extra) == 'table' then
			extra_units = extra
		end
	end
	if extra_units then
		-- A unit in one data table might refer to a unit in the other table, so
		-- switch between them, relying on fails or depth to terminate loops.
		if not fails[unitcode] then
			fails[unitcode] = true
			local other = (utable == all_units) and extra_units or all_units
			local success, result = lookup(unitcode, opt_sp_us, what, other, fails, depth)
			if success then
				return true, result
			end
		end
	end
	return false, { 'cvt_unknown', unitcode }
end

local function valid_number(num)
	-- Return true if num is a valid number.
	-- In Scribunto (different from some standard Lua), when expressed as a string,
	-- overflow or other problems are indicated with text like "inf" or "nan"
	-- which are regarded as invalid here (each contains "n").
	if type(num) == 'number' and tostring(num):find('n', 1, true) == nil then
		return true
	end
end

local function ntsh(num, debug)
	-- Return html text to be used for a hidden sort key so that
	-- the given number will be sorted in numeric order.
	-- If debug == true, output is in a box (not hidden).
	-- This implements Template:Ntsh (number table sorting, hidden).
	local result, style
	if not valid_number(num) then
		if num < 0 then
			result = '1000000000000000000'
		else
			result = '9000000000000000000'
		end
	elseif num == 0 then
		result = '5000000000000000000'
	else
		local mag = floor(log10(abs(num)) + 1e-14)
		local prefix
		if num > 0 then
			prefix = 7000 + mag
		else
			prefix = 2999 - mag
			num = num + 10^(mag+1)
		end
		result = format('%d', prefix) .. format('%015.0f', floor(num * 10^(14-mag)))
	end
	if debug then
		style = 'border:1px solid'
	else
		style = 'display:none'
	end
	return '<span style="' .. style .. '">' .. result .. '</span>'
end

local function hyphenated(name, parts)
	-- Return an unhyphenated form of given name (for adjectival usage).
	if name:find(' ', 1, true) then
		if parts then
			return name
		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 .. item .. after)
		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
	if parms.opt_adjectival then
		if inout == (parms.opt_flip and 'out' or 'in') then
			mid = parms.mid
		end
		if want_name then
			return ' ' .. hyphenated(id) .. (mid or ''), true
		end
	end
	return sep .. id .. (mid or '')
end

local function change_sign(text)
	-- Change sign of text for correct appearance because it is negated.
	if text:sub(1, 1) == '-' then
		return text:sub(2)
	end
	return '-' .. text
end

local function use_minus(text)
	-- Return text with Unicode minus instead of '-', if present.
	if text:sub(1, 1) == '-' then
		return MINUS .. text:sub(2)
	end
	return text
end

local function digit_grouper(method, gaps)
	-- Return a table to hold groups of digits which can be joined with
	-- suitable separators (such as commas).
	-- Each group is separately translated to the local language because
	-- gap separators include digits which should not be translated.
	-- Parameter method is a number or nil:
	--   3 for 3-digit grouping, or
	--   2 for 3-then-2 grouping.
	-- Parameter gaps is true to use <span> gaps (numsep ignored).
	return {
		n = 0,
		add = function (self, digits)
			self.n = self.n + 1
			self[self.n] = from_en(digits)
		end,
		join = function (self, rhs)
			-- Concatenate in reverse order.
			if gaps then
				local result = ''
				for i = 1, self.n - 1 do
					result = '<span style="margin-left: 0.25em">' .. self[i] .. '</span>' .. result
				end
				return '<span style="white-space: nowrap">' .. self[self.n] .. result .. from_en(rhs) .. '</span>'
			else
				local result = self[1]
				for i = 2, self.n do
					result = self[i] .. numsep .. result
				end
				return result .. from_en(rhs)
			end
		end,
		step = 3,
		next_position = function (self, previous)
			-- Return position of digit just before next group.
			-- Digits are grouped from right-to-left (least significant first).
			local result = previous - self.step
			if method == 2 then
				self.step = 2
			end
			return (result < 0) and 0 or result
		end,
	}
end

local function with_separator(parms, text)
	-- Input text is a number in en digits and with '.' decimal mark.
	-- Return an equivalent of text, formatted for display:
	--   with a custom decimal mark instead of '.', if wanted
	--   with thousand separators inserted, if wanted
	--   digits in local language
	-- The given text is like '123' or '12345.6789' or '1.23e45'
	-- (e notation can only occur when processing an input value).
	-- The text has no sign (caller inserts that later, if necessary).
	-- Separator is inserted only in the integer part of the significand
	-- (not after the decimal mark, and not after 'e' or 'E').
	if parms.opt_nocomma or numsep == '' then
		return from_en(text)
	end
	local last = text:match('()[.eE]')  -- () returns position
	if last == nil then
		last = #text
	else
		last = last - 1  -- index of last character before dot/e/E
	end
	if last < 4 or (last == 4 and parms.opt_comma5) then
		return from_en(text)
	end
	local groups = digit_grouper(group_method, parms.opt_gaps)
	local i = last
	while i > 0 do
		local position = groups:next_position(i)
		groups:add(text:sub(position+1, i))
		i = position
	end
	return groups:join(text:sub(last+1))
end

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

local function with_exponent(show, exponent)
	-- Return wikitext to display the implied value in scientific notation.
	-- Input uses en digits; output uses digits in local language.
	if #show > 1 then
		show = show:sub(1, 1) .. '.' .. show:sub(2)
	end
	return format(fmtpower, from_en(show), from_en('10'), use_minus(from_en(tostring(exponent))))
end

local function make_sigfig(value, sigfig)
	-- Return show, exponent that are equivalent to the result of
	-- converting the number 'value' (where value >= 0) to a string,
	-- rounded to 'sigfig' significant figures.
	-- The returned items are:
	--   show: a string of digits; no sign and no dot;
	--		 there is an implied dot before show.
	--   exponent: a number (an integer) to shift the implied dot.
	-- Resulting value = tonumber('.' .. show) * 10^exponent.
	-- Examples:
	--   make_sigfig(23.456, 3) returns '235', 2 (.235 * 10^2).
	--   make_sigfig(0.0023456, 3) returns '235', -2 (.235 * 10^-2).
	--   make_sigfig(0, 3) returns '000', 1 (.000 * 10^1).
	if sigfig <= 0 then
		sigfig = 1
	elseif sigfig > maxsigfig then
		sigfig = maxsigfig
	end
	if value == 0 then
		return string.rep('0', sigfig), 1
	end
	local exp, frac = math.modf(log10(value))
	if frac >= 0 then
		frac = frac - 1
		exp = exp + 1
	end
	local digits = format('%.0f', 10^(frac + 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, 'Lỗi: Số tròn có số chữ số không chính xác')
	return digits, exp
end

local function format_number(parms, show, exponent, isnegative)
	-- Parameter show is a number in en digits and with '.' decimal mark.
	-- 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.
	-- * Uses a custom decimal mark, if wanted.
	-- * Has digits grouped where necessary, if wanted.
	-- * Uses scientific notation for very small or large values
	--   (which forces output to not be spelled).
	-- * Has no more than maxsigfig significant digits
	--   (same as old template and {{#expr}}).
	local sign = isnegative and MINUS or ''
	local maxlen = maxsigfig
	if exponent == nil then
		local integer, dot, fraction = show:match('^(%d*)(%.?)(.*)')
		if #integer >= 10 then
			show = integer .. fraction
			exponent = #integer
		elseif integer == '0' or integer == '' then
			local zeros, figs = fraction:match('^(0*)([^0]?.*)')
			if #figs == 0 then
				if #zeros > maxlen then
					show = '0.' .. zeros:sub(1, maxlen)
				end
			elseif #zeros >= 4 then
				show = figs
				exponent = -#zeros
			elseif #figs > maxlen then
				show = '0.' .. zeros .. figs:sub(1, maxlen)
			end
		else
			maxlen = maxlen + #dot
			if #show > maxlen then
				show = show:sub(1, maxlen)
			end
		end
	end
	if exponent then
		if #show > maxlen then
			show = show:sub(1, maxlen)
		end
		if exponent > 10 or exponent <= -4 or (exponent == 10 and show ~= '1000000000') then
			-- Rounded value satisfies: value >= 1e9 or value < 1e-4 (1e9 = 0.1e10).
			return {
				clean = '.' .. show,
				exponent = exponent,
				sign = sign,
				show = sign .. with_exponent(show, exponent-1),
				is_scientific = true,
			}
		end
		if exponent >= #show then
			show = show .. string.rep('0', exponent - #show)  -- result has no dot
		elseif exponent <= 0 then
			show = '0.' .. string.rep('0', -exponent) .. show
		else
			show = show:sub(1, exponent) .. '.' .. show:sub(exponent+1)
		end
	end
	if isnegative and show:match('^0.?0*$') then
		sign = ''  -- don't show minus if result is negative but rounds to zero
	end
	local formatted_show = sign .. with_separator(parms, show)
	if parms.opt_spell_out then
		formatted_show = spell_number(parms, sign .. show) or formatted_show
	end
	return {
		clean = show,
		sign = sign,
		show = formatted_show,
	}
end

-- Fraction output format.
-- 2013-07-20 Trying new styles proposed at [[:en:Template talk:Convert]].
local fracfmt = {
 { -- Like {{frac}} (fraction slash).
   -- 1/2	: sign, numerator, denominator
   -- 1+2/3  : signed_wholenumber, numerator, denominator
   '<span class="frac nowrap">%s<sup>%s</sup>⁄<sub>%s</sub></span>',
   '<span class="frac nowrap">%s<sup> %s</sup>⁄<sub>%s</sub></span>',
 },
 { -- Like {{sfrac}} (fraction horizontal bar).
   -- 1//2   : sign, numerator, denominator (sign should probably be before the fraction, but then it can wrap, and html is already too long)
   -- 1+2//3 : signed_wholenumber, numerator, denominator
   '<span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%%; text-align:center;"><span style="display:block; line-height:1em; padding:0 0.1em;">%s%s</span><span style="display:none;">/</span><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">%s</span></span>',
   '<span class="sfrac nowrap">%s<span style="display:none;">&nbsp;</span><span style="display:inline-block; vertical-align:-0.5em; font-size:85%%; text-align:center;"><span style="display:block; line-height:1em; padding:0 0.1em;">%s</span><span style="display:none;">/</span><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">%s</span></span></span>',
 },
 { -- Like old {{convert}} template.
   -- 1///2  : sign, numerator, denominator
   -- 1+2///3: signed_wholenumber, sign, numerator, denominator
   '<span style="white-space:nowrap">%s<sup>%s</sup>⁄<sub>%s</sub></span>',
   '<span class="frac nowrap">%s<s style="display:none">%s</s><sup>%s</sup>⁄<sub>%s</sub></span>',
 },
}

local function extract_fraction(parms, text, negative)
	-- If text represents a fraction, return
	--   value, altvalue, show, spelled, denominator
	-- where
	--   value is a number (value of the fraction in argument text)
	--   altvalue is an alternate interpretation of any fraction for the hands
	--		unit where "14.1+3/4" means 14 hands 1.75 inches!
	--   show is a string (formatted text for display of an input value,
	--		and is spelled if wanted and possible)
	--   spelled is true if show was spelled
	--   denominator is value of the denominator in the fraction
	-- Otherwise, return nil.
	-- Input uses en digits and '.' decimal mark (input has been translated).
	-- Output uses digits in local language and custom decimal mark, if any.
	--
	-- In the following, '(3/8)' represents the wikitext required to
	-- display a fraction with numerator 3 and denominator 8.
	-- In the wikitext, Unicode minus is used for a negative value.
	--   text		  value, show			value, show
	--				 if not negative	   if negative
	--   3 / 8		 0.375, '(3/8)'		-0.375, '−(3/8)'
	--   2 + 3 / 8	 2.375, '2(3/8)'	   -1.625, '−2(−3/8)'
	--   2 - 3 / 8	 1.625, '2(−3/8)'	  -2.375, '−2(3/8)'
	--   1 + 20/8	  3.5  , '1/(20/8)'	 1.5   , '−1/(−20/8)'
	--   1 - 20/8	  -1.5., '1(−20/8)'	 -3.5  , '−1(20/8)'
	-- Wherever an integer appears above, numbers like 1.25 or 12.5e-3
	-- (which may be negative) are also accepted (like old template).
	-- Template interprets '1.23e+2+12/24' as '123(12/24)' = 123.5!
	local numstr, whole, value, altvalue
	local lhs, slash, denstr = text:match('^%s*([^/]-)%s*(/+)%s*(.-)%s*$')
	local denominator = tonumber(denstr)
	if denominator == nil then return nil end
	local wholestr, negfrac, rhs = lhs:match('^%s*(.-[^eE])%s*([+-])%s*(.-)%s*$')
	if wholestr == nil or wholestr == '' then
		wholestr = nil
		whole = 0
		numstr = lhs
	else
		whole = tonumber(wholestr)
		if whole == nil then return nil end
		numstr = rhs
	end
	negfrac = (negfrac == '-')
	local numerator = tonumber(numstr)
	if numerator == nil then return nil end
	-- Spelling of silly inputs like "-2+3/8" or "2+3/+8" (mixed or excess signs) is not supported.
	local do_spell
	if negative == negfrac or wholestr == nil then
		value = whole + numerator / denominator
		altvalue = whole + numerator / (denominator * 10)
		do_spell = parms.opt_spell_in
		if do_spell then
			if not (numstr:match('^%d') and denstr:match('^%d')) then  -- if either has a sign
				do_spell = false
			end
		end
	else
		value = whole - numerator / denominator
		altvalue = whole - numerator / (denominator * 10)
		numstr = change_sign(numstr)
		do_spell = false
	end
	if not valid_number(value) then
		return nil  -- overflow or similar
	end
	numstr = use_minus(numstr)
	denstr = use_minus(denstr)
	local style = #slash  -- kludge: 1, 2, or 3 slashes can be used to select style
	if style > 3 then style = 3 end
	local wikitext
	if wholestr then
		if negative then
			wholestr = change_sign(wholestr)
		end
		local fmt = fracfmt[style][2]
		if style < 3 then
			wikitext = format(fmt, use_minus(from_en(wholestr)), from_en(numstr), from_en(denstr))
		else
			local sign = negative and MINUS or '+'
			wikitext = format(fmt, use_minus(from_en(wholestr)), sign, from_en(numstr), from_en(denstr))
		end
	else
		local sign = negative and MINUS or ''
		wikitext = format(fracfmt[style][1], sign, from_en(numstr), from_en(denstr))
	end
	if do_spell then
		local numsign = (wholestr or not negative) and '' or '-'
		wikitext = spell_number(parms, wholestr, numsign .. numstr, denstr) or wikitext
	end
	return value, altvalue, wikitext, do_spell, denominator
end

local function extract_number(parms, text, another, no_fraction)
	-- Return true, info if can extract a number from text,
	-- where info is a table with the result,
	-- or return false, t where t is an error message table.
	-- Input can use en digits or digits in local language.
	-- Parameter another = true if the expected value is not the first.
	-- Before processing, the input text is cleaned:
	-- * Any thousand separators (valid or not) are removed.
	-- * Any sign (and optional following whitespace) is replaced with
	--   '-' (if negative) or '' (otherwise).
	--   That replaces Unicode minus with '-'.
	-- If successful, the returned info table contains named fields:
	--   value	= a valid number
	--   altvalue = a valid number, usually same as value but different
	--			  if fraction used (for hands unit)
	--   singular = true if value is 1 (to use singular form of units)
	--			= false if value is -1 (like old template)
	--   clean	= cleaned text with any separators and sign removed
	--			  (en digits and '.' decimal mark)
	--   show	 = text formatted for output
	--			  (digits in local language and custom decimal mark)
	-- The resulting show:
	-- * Is for an input value and is spelled if wanted and possible.
	-- * Has a rounded value, if wanted.
	-- * Has digits grouped where necessary, if wanted.
	-- * If negative, a Unicode minus is used; otherwise the sign is
	--   '+' (if the input text used '+'), or is '' (if no sign in input).
	text = strip(text or '')
	local clean = to_en(text)
	if clean == '' then
		return false, { another and 'cvt_no_num2' or 'cvt_no_num' }
	end
	local isnegative, propersign = false, ''  -- most common case
	local singular, show, denominator
	local value = tonumber(clean)
	local altvalue
	if value then
		local sign = clean:sub(1, 1)
		if sign == '+' or sign == '-' then
			propersign = (sign == '+') and '+' or MINUS
			clean = clean:sub(2)
		end
		if value < 0 then
			isnegative = true
			value = -value
		end
	else
		local valstr
		for _, prefix in ipairs({ '-', MINUS, '&minus;' }) do
			-- Including '-' means inputs like '- 2' (with space) are accepted as -2.
			-- It also sets isnegative in case input is a fraction like '-2-3/4'.
			local plen = #prefix
			if clean:sub(1, plen) == prefix then
				valstr = clean:sub(plen + 1)
				break
			end
		end
		if valstr then
			isnegative = true
			propersign = MINUS
			clean = valstr
			value = tonumber(clean)
		end
		if value == nil then
			local spelled
			if not no_fraction then
				value, altvalue, show, spelled, denominator = extract_fraction(parms, clean, isnegative)
			end
			if value == nil then
				return false, { 'cvt_bad_num', text }
			end
			if spelled and value <= 1 then
				singular = true  -- for example, "one half mile" (singular unit)
			else
				singular = false -- any numeric fraction (even with value 1) is regarded as plural
			end
		end
	end
	if not valid_number(value) then  -- for example, "1e310" may overflow
		return false, { 'cvt_invalid_num' }
	end
	if show == nil then
		singular = (value == 1 and not isnegative)
		local precision = parms.input_precision
		if precision and 0 <= precision and precision <= 8 then
			value = value + 2e-14  -- fudge for some common cases of bad rounding
			local fmt = '%.' .. format('%d', precision) .. 'f'
			show = fmt:format(value)
		else
			show = clean
		end
		show = propersign .. with_separator(parms, show)
		if parms.opt_spell_in then
			show = spell_number(parms, propersign .. clean) or show
		end
	end
	if isnegative and (value ~= 0) then
		value = -value
	end
	return true, {
		value = value,
		altvalue = altvalue or value,
		singular = singular,
		clean = clean,
		show = show,
		denominator = denominator,
	}
end

local function get_number(text)
	-- Return v, f where:
	--   v = nil (text is not a number)
	-- or
	--   v = value of text (text is a number)
	--   f = true if value is an integer
	-- Input can use en digits or digits in local language,
	-- but no separators, no Unicode minus, and no fraction.
	if text then
		local number = tonumber(to_en(text))
		if number then
			local integer, fraction = math.modf(number)
			return number, (fraction == 0)
		end
	end
end

local function preunits(count, preunit1, preunit2)
	-- If count is 1:
	--	 ignore preunit2
	--	 return p1
	-- else:
	--	 preunit1 is used for preunit2 if the latter is empty
	--	 return p1, p2
	-- where:
	--	 p1 is text to insert before the input unit
	--	 p2 is text to insert before the output unit
	--	 p1 or p2 may be nil to mean "no preunit"
	-- Using '+ ' gives output like "5+ feet" (no preceding space).
	local function withspace(text, i)
		-- Insert space at beginning if i == 1, or at end if i == -1.
		-- However, no space is inserted if there is a space or '&nbsp;'
		-- or '-' at that position ('-' is for adjectival text).
		local current = text:sub(i, i)
		if current == ' ' or current == '-' then
			return text
		end
		if i == 1 then
			current = text:sub(1, 6)
		else
			current = text:sub(-6, -1)
		end
		if current == '&nbsp;' then
			return text
		end
		if i == 1 then
			return ' ' .. text
		end
		return text .. ' '
	end
	preunit1 = preunit1 or ''
	local trim1 = strip(preunit1)
	if count == 1 then
		if trim1 == '' then
			return nil
		end
		return withspace(withspace(preunit1, 1), -1)
	end
	preunit2 = preunit2 or ''
	local trim2 = strip(preunit2)
	if trim1 == '' and trim2 == '' then
		return nil, nil
	end
	if trim1 ~= '+' then
		preunit1 = withspace(preunit1, 1)
	end
	if trim2 == '&#32;' then  -- trick to make preunit2 empty
		preunit2 = nil
	elseif trim2 == '' then
		preunit2 = preunit1
	elseif trim2 ~= '+' then
		preunit2 = withspace(preunit2, 1)
	end
	return preunit1, preunit2
end

local function range_text(range, want_name, parms, before, after)
	-- Return before .. rtext .. after
	-- where rtext is the text that separates two values in a range.
	local rtext, adj_text, exception
	if type(range) == 'table' then
		-- Table must specify range text for abbr=off and for abbr=on,
		-- and may specify range text for 'adj=on',
		-- and may specify exception = true.
		rtext = range[want_name and 'off' or 'on']
		adj_text = range['adj']
		exception = range['exception']
	else
		rtext = range
	end
	if parms.opt_adjectival then
		if want_name or (exception and parms.abbr_org == 'on') then
			rtext = adj_text or rtext
		end
	end
	if rtext == '–' and after:sub(1, #MINUS) == MINUS then
		rtext = '&nbsp;– '
	end
	return before .. rtext .. after
end

local function get_composite(parms, iparm, total, in_unit_table)
	-- Look for a composite input unit. For example, "{{convert|1|yd|2|ft|3|in}}"
	-- would result in a call to this function with
	--   iparm = 3 (parms[iparm] = "2", just after the first unit)
	--   total = 1 (number of yards)
	--   in_unit_table = (unit table for "yd")
	-- Return true, iparm, unit where
	--   iparm = index just after the composite units (7 in above example)
	--   unit = composite unit table holding all input units,
	-- or return true if no composite unit is present in parms,
	-- or return false, t where t is an error message table.
	local default, subinfo
	local composite_units, count = { in_unit_table }, 1
	local fixups = {}
	local subunit = in_unit_table
	while subunit.subdivs do  -- subdivs is nil or a table of allowed subdivisions
		local subcode = strip(parms[iparm+1])
		local subdiv = subunit.subdivs[subcode]
		if not subdiv then
			break
		end
		local success
		success, subunit = lookup(subcode, parms.opt_sp_us, 'no_combination')
		if not success then return false, subunit end  -- should never occur
		success, subinfo = extract_number(parms, parms[iparm])
		if not success then return false, subinfo end
		iparm = iparm + 2
		subunit.inout = 'in'
		subunit.valinfo = { subinfo }
		-- Recalculate total as a number of subdivisions.
		-- subdiv[1] = number of subdivisions per previous unit (integer > 1).
		total = total * subdiv[1] + subinfo.value
		if not default then  -- set by the first subdiv with a default defined
			default = subdiv.default
		end
		count = count + 1
		composite_units[count] = subunit
		if subdiv.unit or subdiv.name then
			fixups[count] = { unit = subdiv.unit, name = subdiv.name, valinfo = subunit.valinfo }
		end
	end
	if count == 1 then
		return true  -- no error and no composite unit
	end
	for i, fixup in pairs(fixups) do
		local unit = fixup.unit
		local name = fixup.name
		if not unit or (count > 2 and name) then
			composite_units[i].fixed_name = name
		else
			local success, alternate = lookup(unit, parms.opt_sp_us, 'no_combination')
			if not success then return false, alternate end  -- should never occur
			alternate.inout = 'in'
			alternate.valinfo = fixup.valinfo
			composite_units[i] = alternate
		end
	end
	return true, iparm, {
		utype = in_unit_table.utype,
		scale = subunit.scale,  -- scale of last (least significant) unit
		valinfo = { { value = total, clean = subinfo.clean, denominator = subinfo.denominator } },
		composite = composite_units,
		default = default or in_unit_table.default
	}
end

local function translate_parms(parms, kv_pairs)
	-- Update fields in parms by translating each key:value in kv_pairs to terms
	-- used by this module (may involve translating from local language to English).
	-- Also, checks are performed which may display warnings, if enabled.
	-- Return true if successful or return false, t where t is an error message table.
	if kv_pairs.adj and kv_pairs.sing then
		-- For en.wiki (before translation), warn if attempt to use adj and sing
		-- as the latter is a deprecated alias for the former.
		if kv_pairs.adj ~= kv_pairs.sing and kv_pairs.sing ~= '' then
			add_warning(parms, 1, 'cvt_unknown_option', 'sing=' .. kv_pairs.sing)
		end
		kv_pairs.sing = nil
	end
	for loc_name, loc_value in pairs(kv_pairs) do
		local en_name = en_option_name[loc_name]
		if en_name then
			local en_value
			if en_name == 'sigfig' then
				if loc_value == '' then
					add_warning(parms, 2, 'cvt_empty_option', loc_name)
				else
					local number, is_integer = get_number(loc_value)
					if number and is_integer and number > 0 then
						en_value = number
					else
						add_warning(parms, 1, 'cvt_bad_sigfig', loc_value)
					end
				end
			else
				en_value = en_option_value[en_name][loc_value]
				if en_value == nil then
					if loc_value == '' then
						add_warning(parms, 2, 'cvt_empty_option', loc_name)
					else
						-- loc_value can no longer be nil here (at one time, that could occur
						-- with aliases like |sing=off|adj=on), but am retaining safety check.
						local text = loc_value and (loc_name .. '=' .. loc_value) or loc_name
						add_warning(parms, 1, 'cvt_unknown_option', text)
					end
				elseif en_value == '' then
					en_value = nil  -- an ignored option like adj=off
				elseif type(en_value) == 'string' and en_value:sub(1, 4) == 'opt_' then
					for _, v in ipairs(split(en_value, ',')) do
						parms[v] = true
					end
					en_value = nil
				end
			end
			parms[en_name] = en_value
		else
			add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)
		end
	end
	if parms.adj then
		if parms.adj:sub(1, 2) == 'ri' then
			-- It is known that adj is 'ri1' or 'ri2' or 'ri3', so precision is valid.
			-- Only en digits are accepted.
			parms.input_precision = tonumber(parms.adj:sub(-1))
			parms.adj = nil
		end
	end
	if parms.abbr then
		parms.abbr_org = parms.abbr  -- original abbr that was set, before any flip
	else
		parms.abbr = 'out'  -- default is to abbreviate output only (use symbol, not name)
	end
	if parms.opt_flip then
		local function swap_in_out(option)
			local value = parms[option]
			if value == 'in' then
				parms[option] = 'out'
			elseif value == 'out' then
				parms[option] = 'in'
			end
		end
		swap_in_out('abbr')
		swap_in_out('lk')
		if parms.opt_spell_in then
			-- For simplicity, and because it does not appear to be needed,
			-- user cannot set an option to spell the output.
			parms.opt_spell_in = nil
			parms.opt_spell_out = true
		end
	end
	if parms.opt_table or parms.opt_tablecen then
		if parms.abbr_org == nil and parms.lk == nil then
			parms.opt_values = true
		end
		local align = format('align="%s"', parms.opt_table and 'right' or 'center')
		parms.table_joins = { align .. '|', '\n|' .. align .. '|' }
	end
	if parms.opt_lang_en then
		from_en_table = nil
	end
	return true
end

local function get_values(parms)
	-- If successful, update parms and return true, v, i where
	--   v = table of input values
	--   i = index to next entry in parms after those processed here
	-- or return false, t where t is an error message table.
	local valinfo = collection()  -- numbered table of input values
	local range = collection()  -- numbered table of range items (having, for example, 2 range items requires 3 input values)
	local had_nocomma  -- true if removed "nocomma" kludge from second parameter (like "tonocomma")
	local parm2 = strip(parms[2])
	if parm2 and parm2:sub(-7, -1) == 'nocomma' then
		parms[2] = strip(parm2:sub(1, -8))
		parms.opt_nocomma = true
		had_nocomma = true
	end
	local i = 1
	while true do
		local success, info = extract_number(parms, parms[i], i > 1)  -- need to set parms.opt_nocomma before calling this
		if not success then return false, info end
		i = i + 1
		valinfo:add(info)
		local next = strip(parms[i])
		local range_item = range_types[next] or range_types[range_aliases[next]]
		if not range_item then
			break
		end
		i = i + 1
		range:add(range_item)
		parms.is_range_x = (type(range_item) == 'table') and range_item.is_range_x or nil
	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 get_parms(pframe)
	-- If successful, return true, parms, unit where
	--   parms is a table of all arguments passed to the template
	--		converted to named arguments, and
	--   unit is the input unit table;
	-- or return false, t where t is an error message table.
	-- The returned input unit table may be for a fake unit using the specified
	-- unit code as the symbol and name, and with bad_mcode = message code table.
	-- MediaWiki removes leading and trailing whitespace from the values of
	-- named arguments. However, the values of numbered arguments include any
	-- whitespace entered in the template, and whitespace is used by some
	-- parameters (example: the numbered parameters associated with "disp=x").
	local parms = {}  -- arguments passed to template, after translation
	local kv_pairs = {}  -- table of input key:value pairs where key is a name; needed because cannot iterate parms and add new fields to it
	for k, v in pairs(pframe.args) do
		if type(k) == 'number' or k == 'test' then  -- parameter "test" is reserved for testing and is not translated
			parms[k] = v
		else
			kv_pairs[k] = v
		end
	end
	local success, msg = translate_parms(parms, kv_pairs)
	if not success then return false, msg end
	local success, valinfo, i = get_values(parms)
	if not success then return false, valinfo end
	local in_unit = strip(parms[i])
	i = i + 1
	local success, in_unit_table = lookup(in_unit, parms.opt_sp_us, 'no_combination')
	if not success then
		if in_unit == nil then
			in_unit = ''
		end
		in_unit_table = setmetatable({ symbol = in_unit, name2 = in_unit, utype = "length", scale = 1, bad_mcode = in_unit_table }, unit_mt)
	end
	if parms.test == 'msg' then
		-- Am testing the messages produced when no output unit is specified, and
		-- the input unit has a missing or invalid default.
		-- Set two units for testing that.
		-- LATER: Remove this code.
		if in_unit == 'chain' then
			in_unit_table.default = nil  -- no default
		elseif in_unit == 'rd' then
			in_unit_table.default  = "ft!X!m"  -- an invalid expression
		end
	end
	in_unit_table.valinfo = valinfo
	in_unit_table.inout = 'in'  -- this is an input unit
	if not parms.range then
		local success, inext, composite_unit = get_composite(parms, i, valinfo[1].value, in_unit_table)
		if not success then return false, inext end
		if composite_unit then
			in_unit_table = composite_unit
			i = inext
		end
	end
	if in_unit_table.builtin == 'mach' then
		-- As with old template, a number following Mach as the input unit is the altitude,
		-- and there is no way to specify an altitude for the output unit.
		-- Could put more code in this function to get any output unit and check for
		-- an altitude following that unit.
		local success, info = extract_number(parms, parms[i], false, true)
		if success then
			i = i + 1
			in_unit_table.altitude = info.value
		end
	end
	local next = strip(parms[i])
	i = i + 1
	local precision, is_bad_precision
	local function set_precision(text)
		local number, is_integer = get_number(text)
		if number then
			if is_integer then
				precision = number
			else
				precision = text
				is_bad_precision = true
			end
			return true  -- text was used for precision, good or bad
		end
	end
	if not set_precision(next) then
		parms.out_unit = next
		if set_precision(strip(parms[i])) then
			i = i + 1
		end
	end
	if parms.opt_adj_mid then
		parms.opt_adjectival = true
		next = parms[i]
		i = i + 1
		if next then  -- mid-text words
			if next:sub(1, 1) == '-' then
				parms.mid = next
			else
				parms.mid = ' ' .. next
			end
		end
	end
	if parms.opt_one_preunit then
		parms[parms.opt_flip and 'preunit2' or 'preunit1'] = preunits(1, parms[i])
		i = i + 1
	end
	if parms.disp == 'x' then
		-- Following is reasonably compatible with the old template.
		local first = parms[i] or ''
		local second = parms[i+1] or ''
		i = i + 2
		if strip(first) == '' then  -- user can enter '&#32;' rather than ' ' to avoid the default
			first = ' [&nbsp;' .. first
			second = '&nbsp;]' .. second
		end
		parms.joins = { first, second }
	elseif parms.opt_two_preunits then
		local p1, p2 = preunits(2, parms[i], parms[i+1])
		i = i + 2
		if parms.preunit1 then
			-- To simplify documentation, allow unlikely use of adj=pre with disp=preunit
			-- (however, an output unit must be specified with adj=pre and with disp=preunit).
			parms.preunit1 = parms.preunit1 .. p1
			parms.preunit2 = p2
		else
			parms.preunit1, parms.preunit2 = p1, p2
		end
	end
	if precision == nil then
		if set_precision(strip(parms[i])) then
			i = i + 1
		end
	end
	if is_bad_precision then
		add_warning(parms, 1, 'cvt_bad_prec', precision)
	else
		parms.precision = precision
	end
	return true, parms, in_unit_table
end

local function default_precision(invalue, inclean, denominator, outvalue, in_current, out_current, extra)
	-- Return a default value for precision (an integer like 2, 0, -2).
	-- If denominator is not nil, it is the value of the denominator in inclean.
	-- Code follows procedures used in old template.
	local fudge = 1e-14  -- {{Order of magnitude}} adds this, so we do too
	local prec, minprec, adjust
	local utype = out_current.utype
	local subunit_ignore_trailing_zero
	local subunit_more_precision  -- kludge for "in" used in input like "|2|ft|6|in"
	local composite = in_current.composite
	if composite then
		subunit_ignore_trailing_zero = true  -- input "|2|st|10|lb" has precision 0, not -1
		if composite[#composite].exception == 'subunit_more_precision' then
			subunit_more_precision = true  -- do not use standard precision with input like "|2|ft|6|in"
		end
	end
	if denominator and denominator > 0 then
		prec = math.max(log10(denominator), 1)
	else
		-- Count digits after decimal mark, handling cases like '12.345e6'.
		local exponent
		local integer, dot, fraction, 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 = #fraction
		end
		if exponent then
			-- So '1230' and '1.23e3' both give prec = -1, and '0.00123' and '1.23e-3' give 5.
			prec = prec - exponent
		end
	end
	if in_current.istemperature and out_current.istemperature then
		-- Converting between common temperatures (°C, °F, °R, K); not keVT, MK.
		-- Kelvin value can be almost zero, or small but negative due to precision problems.
		-- Also, an input value like -300 C (below absolute zero) gives negative kelvins.
		-- Calculate minimum precision from absolute value.
		adjust = 0
		local kelvin = abs((invalue - in_current.offset) * in_current.scale)
		if kelvin < 1e-8 then  -- assume nonzero due to input or calculation precision problem
			minprec = 2
		else
			minprec = 2 - floor(log10(kelvin) + fudge)  -- 3 sigfigs in kelvin
		end
	else
		if invalue == 0 or outvalue <= 0 then
			-- We are never called with a negative outvalue, but it might be zero.
			-- This is special-cased to avoid calculation exceptions.
			return 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 math.max(floor(prec + adjust), minprec)
end

local function convert(invalue, inclean, 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 then
		-- Fuel efficiency (there are no built-ins for this type of unit).
		if in_current.invert * out_current.invert < 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).
		return (invalue - in_current.offset) * (inscale / outscale) + out_current.offset
	else
		-- Built-in unit.
		local in_builtin = in_current.builtin
		local out_builtin = out_current.builtin
		if in_builtin and out_builtin then
			if in_builtin == out_builtin then
				return invalue
			end
			-- There are no cases (yet) where need to convert from one
			-- built-in unit to another, so this should never occur.
			return false, { 'cvt_bug_convert' }
		end
		if in_builtin == 'mach' or out_builtin == 'mach' then
			local adjust
			if in_builtin == 'mach' then
				inscale = speed_of_sound(in_current.altitude)
				adjust = outscale / 0.1
			else
				outscale = speed_of_sound(out_current.altitude)
				adjust = 0.1 / inscale
			end
			return true, {
				outvalue = invalue * (inscale / outscale),
				adjust = log10(adjust) + log10(2),
			}
		elseif in_builtin == 'hand' then
			-- 1 hand = 4 inches; 1.2 hands = 6 inches.
			-- Fractions 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 fraction 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, fraction = math.modf(invalue)
			local outvalue = (integer + 2.5 * fraction) * (inscale / outscale)
			local inch_value = 4 * integer + 10 * fraction  -- equivalent number of inches
			local fracstr = inclean:match('%.(.*)') or ''
			local fmt
			if fracstr == '' then
				fmt = '%.0f'
			else
				fmt = '%.' .. format('%d', #fracstr - 1) .. 'f'
			end
			return true, {
				invalue = inch_value,
				inclean = format(fmt, inch_value),
				outvalue = outvalue,
				minprec = 0,
			}
		end
	end
	return false, { 'cvt_bug_convert' }  -- should never occur
end

local function cvtround(parms, info, in_current, out_current)
	-- Return true, t where t is a table with the conversion results; fields:
	--   show = rounded, formatted string with the result of converting value in info,
	--	  using the rounding specified in parms.
	--   singular = true if result is positive, and (after rounding)
	--	  is "1", or like "1.00";
	--   (and more fields shown below, and a calculated 'absvalue' field).
	-- or return true, nil if no value specified;
	-- or return false, t where t is an error message table.
	-- Input info.clean uses en digits (it has been translated, if necessary).
	-- Output show uses en or non-en digits as appropriate, or can be spelled.
	local invalue, inclean
	if info then
		invalue, inclean = info.value, info.clean
		if in_current.builtin == 'hand' then
			invalue = info.altvalue
		end
	end
	if invalue == nil or invalue == '' then
		return true, nil
	end
	if out_current.builtin == 'hand' then
		-- Convert to hands, then convert the fractional part to inches.
		-- Code is not correct when output is spelled, and it ignores any requested
		-- precision if the output uses scientific notation (very large, or very
		-- small). Not worth more complexity as these cases should be very rare.
		if parms.abbr_org == nil then
			out_current.usename = true  -- default is to show name not symbol
		end
		local dummy_unit_table = { scale = out_current.scale }
		local success, outinfo = cvtround(parms, info, in_current, dummy_unit_table)
		if not success then return false, outinfo end
		local fmt
		if outinfo.is_scientific then
			fmt = '%.1f'
		else
			local fraction = (outinfo.show):match('[' .. numdot .. '](.*)') or ''  -- outinfo.show is in local language
			if fraction == '' then
				if not outinfo.use_default_precision then
					return true, outinfo
				end
				fmt = '%.0f'
			else
				fmt = '%.' .. format('%d', ulen(fraction) - 1) .. 'f'
			end
		end
		local hands, inches = math.modf(outinfo.raw_absvalue)
		inches = format(fmt, inches * 4)
		if inches:sub(1, 1) == '4' then
			hands = hands + 1
			inches = '0' .. inches:sub(2)
			if tonumber(inches) == 0 then
				inches = '0'
			end
		end
		if inches:sub(2, 2) == '.' then
			inches = inches:sub(1, 1) .. inches:sub(3)
		end
		outinfo.show = outinfo.sign .. with_separator(parms, format('%d', hands)) .. numdot .. from_en(inches)
		return true, outinfo
	end
	local outvalue, extra = convert(invalue, inclean, in_current, out_current)
	if extra then
		if not outvalue then return false, extra end
		invalue = extra.invalue or invalue
		inclean = extra.inclean or inclean
		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 success, use_default_precision, show, exponent
	local precision = parms.precision
	if not precision then
		local sigfig = parms.sigfig
		if sigfig then
			show, exponent = make_sigfig(outvalue, sigfig)
		elseif parms.opt_round5 then
			show = format('%.0f', floor((outvalue / 5) + 0.5) * 5)
		else
			use_default_precision = true
			precision = default_precision(invalue, inclean, info.denominator, outvalue, in_current, out_current, extra)
		end
	end
	if precision then
		if precision >= 0 then
			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.
				outvalue = outvalue + 2e-14
			end
			local fmt = '%.' .. format('%d', precision) .. 'f'
			local success
			success, show = pcall(format, fmt, outvalue)
			if not success then
				return false, { 'cvt_big_prec', tostring(precision) }
			end
		else
			precision = -precision  -- #digits to zero (in addition to any digits after dot)
			local shift = 10 ^ precision
			show = format('%.0f', outvalue/shift)
			if show ~= '0' then
				exponent = #show + precision
			end
		end
	end
	local t = format_number(parms, show, exponent, isnegative)
	-- Set singular using match because on some systems 0.99999999999999999 is 1.0.
	t.singular = ((show == '1' or show:match('^1%.0*$') ~= nil) and not isnegative)
	t.raw_absvalue = outvalue  -- absolute value before rounding
	t.use_default_precision = use_default_precision
	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

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('Biểu thức mặc định không hợp lệ', 0)
		elseif arithop == '*' then
			factor = tonumber(factor)
			if factor == nil then
				error('Biểu thức mặc định không hợp lệ', 0)
			end
			value = value * factor
		end
		limit = tonumber(limit)
		if limit == nil then
			error('Biểu thức mặc định không hợp lệ', 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('Biểu thức mặc định không hợp lệ', 0)  -- should not occur
	end
	local lhs, rhs = condition:match('^(.-%W)and(%W.*)')
	if lhs == nil then
		return compare(value, condition)
	end
	return compare(value, lhs) and compare(value, rhs)
end

local function get_default(value, unit_table)
	-- Return true, s where s = name of unit's default output unit,
	-- or return false, t where t is an error message table.
	-- Some units have a default that depends on the input value
	-- (the first value if a range of values is used).
	-- If '!' is in the default, the first bang-delimited field is an
	-- expression that uses 'v' to represent the input value.
	-- Example: 'v < 120 ! small ! big ! suffix' (suffix is optional)
	-- evaluates 'v < 120' as a boolean with result
	-- 'smallsuffix' if (value < 120), or 'bigsuffix' otherwise.
	-- Input must use en digits and '.' decimal mark.
	local default = default_exceptions[unit_table.defkey or unit_table.symbol] or unit_table.default
	if default == nil then
		return false, { 'cvt_no_default', unit_table.symbol }
	end
	if default:find('!', 1, true) == nil then
		return true, default
	end
	local t = split(default, '!')
	if #t == 3 or #t == 4 then
		local success, result = pcall(evaluate_condition, value, t[1])
		if success then
			default = result and t[2] or t[3]
			if #t == 4 then
				default = default .. t[4]
			end
			return true, default
		end
	end
	return false, { 'cvt_bad_default', unit_table.symbol }
end

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

local function make_link(link, id, link_key)
	-- Return wikilink "[[link|id]]", possibly abbreviated as in examples:
	--   [[Mile|mile]]  --> [[mile]]
	--   [[Mile|miles]] --> [[mile]]s
	-- However, just id is returned if:
	-- * no link given (so caller does not need to check if a link was defined); or
	-- * link has previously been used during the current convert (to avoid overlinking).
	-- Linking with a unit uses the unit table as the link key, which fails to detect
	-- overlinking for conversions like (each links "mile" twice):
	--   {{convert|1|impgal/mi|USgal/mi|lk=on}}
	--   {{convert|1|l/km|impgal/mi USgal/mi|lk=on}}
	link_key = link_key or link  -- use key if given (the key, but not the link, may be known when need to cancel a link record)
	if link == nil 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 linked_id(unit_table, key_id, want_link)
	-- Return final unit id (symbol or name), optionally with a wikilink,
	-- and update unit_table.sep if required.
	-- key_id is one of: 'symbol', 'sym_us', 'name1', 'name1_us', 'name2', 'name2_us'.
	local abbr_on = (key_id == 'symbol' or key_id == 'sym_us')
	if abbr_on and want_link then
		local symlink = rawget(unit_table, 'symlink')
		if symlink then
			return symlink  -- for exceptions that have the linked symbol built-in
		end
	end
	local multiplier = rawget(unit_table, 'multiplier')
	local per = unit_table.per
	if per then
		local unit1 = per[1]  -- top unit_table, or nil
		local unit2 = per[2]  -- bottom unit_table
		if abbr_on then
			if not unit1 then
				unit_table.sep = ''  -- no separator in "$2/acre"
			end
			if not want_link then
				local symbol = unit_table.symbol_raw
				if symbol then
					return symbol  -- for exceptions that have the symbol built-in
				end
			end
		end
		local key_id2  -- unit2 is always singular
		if key_id == 'name2' then
			key_id2 = 'name1'
		elseif key_id == 'name2_us' then
			key_id2 = 'name1_us'
		else
			key_id2 = key_id
		end
		local result
		if abbr_on then
			result = '/'
		elseif unit1 then
			result = ' ' .. per_word .. ' '
		else
			result = per_word .. ' '
		end
		if want_link and unit_table.link then
			result = (unit1 and unit1[key_id] or '') .. result .. unit2[key_id2]
			return make_link(unit_table.link, result, unit_table)
		end
		if unit1 then
			result = linked_id(unit1, key_id, want_link) .. result
		end
		return result .. linked_id(unit2, key_id2, want_link)
	end
	if multiplier then
		-- A multiplier (like "100" in "100km") forces the unit to be plural.
		multiplier = from_en(multiplier)
		if abbr_on then
			multiplier = multiplier .. '&nbsp;'
		else
			multiplier = multiplier .. ' '
			if key_id == 'name1' then
				key_id = 'name2'
			elseif key_id == 'name1_us' then
				key_id = 'name2_us'
			end
		end
	else
		multiplier = ''
	end
	local id = unit_table.fixed_name or unit_table[key_id]
	if want_link then
		local link = link_exceptions[unit_table.symbol] or unit_table.link
		if link then
			local before = ''
			local i = unit_table.customary
			if i == 1 and unit_table.sp_us then
				i = 2  -- show "U.S." not "US"
			end
			if i == 3 and abbr_on then
				i = 4  -- abbreviate "imperial" to "imp"
			end
			local customary = 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 { '&nbsp;Mỹ', ' Mỹ' } or { '&nbsp;Anh', ' Anh' }
				for _, suffix in ipairs(removes) do
					id = mw.ustring.gsub(suffix + "$", "")
				end
				before = pertext .. make_link(customary.link, customary[1]) .. ' '
			end
			id = before .. make_link(link, id, unit_table)
		end
	end
	return multiplier .. id
end

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

local function decorate_value(parms, unit_table, which)
	-- If needed, update unit_table so values will be shown with extra information.
	-- For consistency with the old template (but different from fmtpower),
	-- the style to display powers of 10 includes "display:none" to allow some
	-- browsers to copy, for example, "10³" as "10^3", rather than as "103".
	local engscale = unit_table.engscale
	if engscale then
		local inout = unit_table.inout
		local info = unit_table.valinfo[which]
		local abbr = parms.abbr
		if abbr == 'on' or abbr == inout then
			info.show = info.show ..
				'<span style="margin-left:0.2em">×<span style="margin-left:0.1em">' ..
				from_en('10') ..
				'</span></span><s style="display:none">^</s><sup>' ..
				from_en(tostring(engscale.exponent)) .. '</sup>'
		else
			local number_id
			local lk = parms.lk
			if lk == 'on' or lk == inout then
				number_id = make_link(engscale.link, engscale[1])
			else
				number_id = engscale[1]
			end
			-- WP:NUMERAL recommends "&nbsp;" in values like "12 million".
			info.show = info.show .. '&nbsp;' .. number_id
		end
	end
	local prefix = unit_table.vprefix
	if prefix then
		local info = unit_table.valinfo[which]
		info.show = prefix .. info.show
	end
end

local function process_input(parms, in_current)
	-- Processing required once per conversion.
	-- Return block of text to represent input (value/unit).
	if parms.opt_output_only or parms.opt_output_number_only or parms.opt_output_unit_only then
		parms.joins = { '', '' }
		return ''
	end
	local first_unit
	local composite = in_current.composite  -- nil or table of units
	if composite then
		first_unit = composite[1]
	else
		first_unit = in_current
	end
	local id1, want_name = make_id(parms, 1, first_unit)
	local sep = first_unit.sep  -- separator between value and unit, set by make_id
	local preunit = parms.preunit1
	if preunit then
		sep = ''  -- any separator is included in preunit
	else
		preunit = ''
	end
	if parms.opt_input_unit_only then
		parms.joins = { '', '' }
		if composite then
			local parts = { id1 }
			for i, unit in ipairs(composite) do
				if i > 1 then
					table.insert(parts, (make_id(parms, 1, unit)))
				end
			end
			id1 = table.concat(parts, ' ')
		end
		if want_name and parms.opt_adjectival then
			return preunit .. hyphenated(id1)
		end
		return  preunit .. id1
	end
	local abbr = parms.abbr
	local disp = parms.disp
	if disp == nil then  -- special case for the most common setting
		parms.joins = disp_joins['b']
	elseif disp ~= 'x' then
		-- Old template does this.
		if disp == 'slash' then
			if parms.abbr_org == nil then
				disp = 'slash-nbsp'
			elseif abbr == 'in' or abbr == 'out' then
				disp = 'slash-sp'
			else
				disp = 'slash-nosp'
			end
		elseif disp == 'sqbr' then
			if abbr == 'on' then
				disp = 'sqbr-nbsp'
			else
				disp = 'sqbr-sp'
			end
		end
		parms.joins = disp_joins[disp] or disp_joins['b']
	end
	if parms.opt_also_symbol and not composite then
		local join1 = parms.joins[1]
		if join1 == ' (' or join1 == ' [' then
			parms.joins = { join1 .. first_unit[first_unit.sp_us and 'sym_us' or 'symbol'] .. ', ', parms.joins[2] }
		end
	end
	if in_current.builtin == 'mach' then
		local prefix = id1 .. '&nbsp;'
		local range = parms.range
		local valinfo = first_unit.valinfo
		local result = prefix .. valinfo[1].show
		if range then
			-- For simplicity and because more not needed, handle one range item only.
			local prefix2 = make_id(parms, 2, first_unit) .. '&nbsp;'
			result = range_text(range[1], want_name, parms, result, prefix2 .. valinfo[2].show)
		end
		return preunit .. result
	end
	if composite then
		-- Simplify: assume there is no range, and no decoration.
		local mid = ''
		local sep1 = '&nbsp;'
		local sep2 = ' '
		if parms.opt_adjectival then
			if not parms.opt_flip then
				mid = parms.mid or ''
			end
			if want_name then
--				sep1 = '-'
--				sep2 = '-'
			end
		end
		local parts = { first_unit.valinfo[1].show .. sep1 .. id1 }
		for i, unit in ipairs(composite) do
			if i > 1 then
				table.insert(parts, unit.valinfo[1].show .. sep1 .. (make_id(parms, 1, unit)))
			end
		end
		return table.concat(parts, sep2) .. mid
	end
	local result, mos
	local range = parms.range
	if range then
		mos = (abbr == 'mos')
		if not (mos or (parms.is_range_x and not want_name)) then
			linked_pages[first_unit] = nil  -- so the second and only id will be linked, if wanted
		end
	end
	local id = (range == nil) and id1 or make_id(parms, 2, first_unit)
	local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, 'in')
	if mos and was_hyphenated then
		mos = false  -- suppress repeat of unit in a range
		if linked_pages[first_unit] then
			linked_pages[first_unit] = nil
			id = make_id(parms, 2, first_unit)
			extra = hyphenated_maybe(parms, want_name, sep, id, 'in')
		end
	end
	local valinfo = first_unit.valinfo
	if range then
		if range.n == 1 then
			-- Like {{convert|1|x|2|ft}} (one range item; two values).
			-- Do what old template did.
			local sep1 = first_unit.sep
			if mos then
				decorate_value(parms, in_current, 1)
				decorate_value(parms, in_current, 2)
				result = valinfo[1].show .. sep1 .. id1
			elseif parms.is_range_x and not want_name then
				if abbr == 'in' or abbr == 'on' then
					decorate_value(parms, in_current, 1)
				end
				decorate_value(parms, in_current, 2)
				result = valinfo[1].show .. sep1 .. id1
			else
				if abbr == 'in' or abbr == 'on' then
					decorate_value(parms, in_current, 1)
				end
				decorate_value(parms, in_current, 2)
				result = valinfo[1].show
			end
			result = range_text(range[1], want_name, parms, result, valinfo[2].show)
		else
			-- Like {{convert|1|x|2|x|3|ft}} (two or more range items): simplify.
			decorate_value(parms, in_current, 1)
			result = valinfo[1].show
			for i = 1, range.n do
				decorate_value(parms, in_current, i+1)
				result = range_text(range[i], want_name, parms, result, valinfo[i+1].show)
			end
		end
	else
		decorate_value(parms, first_unit, 1)
		result = valinfo[1].show
	end
	return result .. preunit .. extra
end

local function process_one_output(parms, out_current)
	-- Processing required for each output unit.
	-- Return block of text to represent output (value/unit).
	local id1, want_name = make_id(parms, 1, out_current)
	local sep = out_current.sep  -- set by make_id
	local preunit = parms.preunit2
	if preunit then
		sep = ''  -- any separator is included in preunit
	else
		preunit = ''
	end
	if parms.opt_output_unit_only then
		if want_name and parms.opt_adjectival then
			return preunit .. hyphenated(id1)
		end
		return preunit .. id1
	end
	if out_current.builtin == 'mach' then
		local prefix = id1 .. '&nbsp;'
		local range = parms.range
		local valinfo = out_current.valinfo
		local result = prefix .. valinfo[1].show
		if range then
			-- For simplicity and because more not needed, handle one range item only.
			result = range_text(range[1], want_name, parms, result, prefix .. valinfo[2].show)
		end
		return preunit .. result
	end
	local result
	local range = parms.range
	if range then
		if not (parms.is_range_x and not want_name) then
			linked_pages[out_current] = nil  -- so the second and only id will be linked, if wanted
		end
	end
	local id = (range == nil) and id1 or make_id(parms, 2, out_current)
	local extra = hyphenated_maybe(parms, want_name, sep, id, 'out')
	local valinfo = out_current.valinfo
	if range then
		if range.n == 1 then
			local sep1 = out_current.sep
			local abbr = parms.abbr
			if parms.is_range_x and not want_name then
				if abbr == 'out' or abbr == 'on' then
					decorate_value(parms, out_current, 1)
				end
				decorate_value(parms, out_current, 2)
				result = valinfo[1].show .. sep1 .. id1
			else
				if abbr == 'out' or abbr == 'on' then
					decorate_value(parms, out_current, 1)
				end
				decorate_value(parms, out_current, 2)
				result = valinfo[1].show
			end
			result = range_text(range[1], want_name, parms, result, valinfo[2].show)
		else
			-- Like {{convert|1|x|2|x|3|ft}} (two or more range items): simplify.
			decorate_value(parms, out_current, 1)
			result = valinfo[1].show
			for i = 1, range.n do
				decorate_value(parms, out_current, i+1)
				result = range_text(range[i], want_name, parms, result, valinfo[i+1].show)
			end
		end
	else
		decorate_value(parms, out_current, 1)
		result = valinfo[1].show
	end
	if parms.opt_output_number_only then
		return result
	end
	return result .. preunit .. extra
end

local function make_output_single(parms, in_unit_table, out_unit_table)
	-- Return true, item where item = wikitext of the conversion result
	-- for a single output (which is not a combination or a multiple);
	-- or return false, t where t is an error message table.
	out_unit_table.valinfo = collection()
	local range = parms.range
	for i = 1, (range and (range.n + 1) or 1) do
		local success, info = cvtround(parms, in_unit_table.valinfo[i], in_unit_table, out_unit_table)
		if not success then return false, info end
		out_unit_table.valinfo:add(info)
	end
	return true, process_one_output(parms, out_unit_table)
end

local function make_output_multiple(parms, in_unit_table, out_unit_table)
	-- Return true, item where item = wikitext of the conversion result
	-- for an output which is a multiple (like 'ftin');
	-- or return false, t where t is an error message table.
	local multiple = out_unit_table.multiple  -- table of scaling factors (will not be nil)
	local combos = out_unit_table.combination  -- table of unit tables (will not be nil)
	local abbr = parms.abbr
	local abbr_org = parms.abbr_org
	local disp = parms.disp
	local want_name = (abbr_org == nil and (disp == 'or' or disp == 'slash')) or
					  not (abbr == 'on' or abbr == 'out' or abbr == 'mos')
	local want_link = (parms.lk == 'on' or parms.lk == 'out')
	local mid = ''
	local sep1 = '&nbsp;'
	local sep2 = ' '
	if parms.opt_adjectival then
		if parms.opt_flip then
			mid = parms.mid or ''
		end
		if want_name then
--			sep1 = '-'
--			sep2 = '-'
		end
	end
	local function make_result(info)
		local fmt, outvalue, sign
		local results = {}
		for i = 1, #combos do
			local thisvalue, strforce
			local out_current = combos[i]
			out_current.inout = 'out'
			local scale = multiple[i]
			if i == 1 then  -- least significant unit ('in' from 'ftin')
				local fraction
				local success, outinfo = cvtround(parms, info, in_unit_table, out_current)
				if not success then return false, outinfo end
				sign = outinfo.sign
				if outinfo.is_scientific then
					strforce = outinfo.show
					fraction = ''
				else
					fraction = (outinfo.show):match('[' .. numdot .. '](.*)') or ''  -- outinfo.show is in local language
				end
				fmt = '%.' .. ulen(fraction) .. 'f'  -- to reproduce precision
				if fraction == '' then
					outvalue = floor(outinfo.raw_absvalue + 0.5)  -- keep all integer digits of least significant unit
				else
					outvalue = outinfo.absvalue
				end
			end
			if scale then
				outvalue, thisvalue = floor(outvalue / scale), outvalue % scale
			else
				thisvalue = outvalue
			end
			local id
			if want_name then
				id = out_current[(thisvalue == 1) and 'name1' or 'name2']
			else
				id = out_current['symbol']
			end
			if want_link then
				local link = out_current.link
				if link then
					id = make_link(link, id, out_current)
				end
			end
			local strval
			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
			else
				strval = (thisvalue == 0) and from_en('0') or with_separator(parms, format(fmt, thisvalue))
			end
			table.insert(results, strval .. sep1 .. id)
			if outvalue == 0 then
				break
			end
			fmt = '%.0f'  -- only least significant unit can have a fraction
		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])
	if not success then return false, result end
	local range = parms.range
	if range then
		for i = 1, range.n do
			local success, result2 = make_result(valinfo[i+1])
			if not success then return false, result2 end
			result = range_text(range[i], want_name, parms, result, result2)
		end
	end
	return true, result .. mid
end

local function process(parms, in_unit_table)
	-- Return true, s where s = final wikitext result,
	-- or return false, t where t is an error message table.
	linked_pages = {}
	local success, bad_output, out_unit_table
	local bad_input_mcode = in_unit_table.bad_mcode  -- nil if input unit is valid
	local invalue1 = in_unit_table.valinfo[1].value
	local out_unit = parms.out_unit
	if out_unit == nil or out_unit == '' then
		if bad_input_mcode then
			bad_output = ''
		else
			success, out_unit = get_default(invalue1, in_unit_table)
			if not success then
				bad_output = out_unit
			end
		end
	end
	if not bad_output then
		success, out_unit_table = lookup(out_unit, parms.opt_sp_us, 'any_combination')
		if success then
			local mismatch = check_mismatch(in_unit_table, out_unit_table)
			if mismatch then
				bad_output = mismatch
			end
		else
			bad_output = out_unit_table
		end
	end
	local flipped = parms.opt_flip and not bad_input_mcode
	local parts = {}
	for part = 1, 2 do
		-- The LHS (parts[1]) is normally the input, but is the output if flipped.
		-- Process LHS first so it will be linked, if wanted.
		-- Linking to the same item is suppressed in the RHS to avoid overlinking.
		if (part == 1 and not flipped) or (part == 2 and flipped) then
			parts[part] = process_input(parms, in_unit_table)
		elseif bad_output then
			if bad_output ~= '' then
				parts[part] = message(bad_output)
			end
		else
			local outputs = {}
			local combos  -- nil (for 'ft' or 'ftin'), or table of unit tables (for 'm ft')
			if out_unit_table.multiple == nil then  -- nil ('ft' or 'm ft'), or table of factors ('ftin')
				combos = out_unit_table.combination
			end
			local imax = combos and #combos or 1  -- 1 (single unit) or number of unit tables
			for i = 1, imax do
				local success, item
				local out_current = combos and combos[i] or out_unit_table
				out_current.inout = 'out'
				if out_current.multiple == nil then
					success, item = make_output_single(parms, in_unit_table, out_current)
				else
					success, item = make_output_multiple(parms, in_unit_table, out_current)
				end
				if not success then return false, item end
				table.insert(outputs, item)
			end
			parts[part] = parms.opt_input_unit_only and '' or table.concat(outputs, '; ')
		end
	end
	if parms.opt_sortable then
		parts[1] = ntsh(invalue1, parms.opt_sortable_debug) .. parts[1]
	end
	local wikitext
	if bad_input_mcode then
		wikitext = parts[1] .. message(bad_input_mcode)
	elseif parms.table_joins then
		wikitext = parms.table_joins[1] .. parts[1] .. parms.table_joins[2] .. parts[2]
	else
		wikitext = parts[1] .. parms.joins[1] .. parts[2] .. parms.joins[2]
	end
	if parms.warnings and not bad_input_mcode then
		wikitext = wikitext .. parms.warnings
	end
	if decimalPoint(parms[1]) == "." then
		wikitext = wikitext .. message({"cvt_english_num", parms[1], from_en(parms[1])})
	end
	return true, wikitext
end

local function main_convert(frame)
	set_config(frame)
	local result
	local success, parms, in_unit_table = get_parms(frame:getParent())
	if success then
		success, result = process(parms, in_unit_table)
	else
		result = parms
	end
	if success then
		return result
	end
	return message(result)
end

return { convert = main_convert }