વિભાગ:Convert

-- Convert a value from one unit of measurement to another.
-- Example: **Script error: No such module "convert".** --> 123 pounds (56 kg)
-- See en:Template:Convert/Transwiki guide if copying to another wiki.

local MINUS = '−' -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92)
local abs = math.abs
local floor = math.floor
local format = string.format
local log10 = math.log10
local ustring = mw.ustring
local ulen = ustring.len
local usub = ustring.sub

-- Configuration options to keep magic values in one location.
-- Conversion data and message text are defined in separate modules.
local config, maxsigfig
local numdot -- must be '.' or ',' or a character which works in a regex
local numsep, numsep\_remove, numsep\_remove2
local data\_code, all\_units
local text\_code
local varname -- can be a code to use variable names that depend on value
local from\_en\_table -- to translate an output string of en digits to local language
local to\_en\_table -- to translate an input string of digits in local language to en
-- Use translation\_table in convert/text to change the following.
local en\_default -- true uses lang=en unless convert has lang=local or local digits
local group\_method = 3 -- code for how many digits are in a group
local per\_word = 'per' -- for units like "liters per kilometer"
local plural\_suffix = 's' -- only other useful value is probably  *to disable plural unit names*
local omitsep -- true to omit separator before local symbol/name

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

-- Some options in the invoking template can set variables used later in the module.
local currency\_text -- for a user-defined currency symbol: **Script error: No such module "convert".** (euro replaces dollar)

local function from\_en(text)
 -- Input is a string representing a number in en digits with '.' decimal mark,
 -- without digit grouping (which is done just after calling this).
 -- Return the translation of the string with numdot and digits in local language.
 if numdot ~= '.' then
 text = text:gsub('%.', numdot)
 end
 if from\_en\_table then
 text = text:gsub('%d', from\_en\_table)
 end
 return text
end

local function to\_en(text)
 -- Input is a string representing a number in the local language with
 -- an optional numdot decimal mark and numsep digit grouping.
 -- Return the translation of the string with '.' mark and en digits,
 -- and no separators (they have to be removed here to handle cases like
 -- numsep = '.' and numdot = ',' with input "1.234.567,8").
 if to\_en\_table then
 text = ustring.gsub(text, '%d', to\_en\_table)
 end
 if numsep\_remove then
 text = text:gsub(numsep\_remove, *)*
 end
 if numsep\_remove2 then
 text = text:gsub(numsep\_remove2, *)*
 end
 if numdot ~= '.' then
 text = text:gsub(numdot, '.')
 end
 return text
end

local function decimal\_mark(text)
 -- Return ',' if text probably is using comma for decimal mark, or has no decimal mark.
 -- Return '.' if text probably is using dot for decimal mark.
 -- Otherwise return nothing (decimal mark not known).
 if not text:find('[.,]') then return ',' end
 text = text:gsub('^%-', *):gsub('%+%d+/%d+$',* ):gsub('[Ee]%-?%d+$', *)*
 local decimal =
 text:match('^0?([.,])%d+$') or
 text:match('%d([.,])%d?%d?$') or
 text:match('%d([.,])%d%d%d%d+$')
 if decimal then return decimal end
 if text:match('%.%d+%.') then return ',' end
 if text:match('%,%d+,') then return '.' end
end

local add\_warning, with\_separator -- forward declarations
local function to\_en\_with\_check(text, parms)
 -- Version of to\_en() for a wiki using numdot = ',' and numsep = '.' to check
 -- text (an input number as a string) which might have been copied from enwiki.
 -- For example, in '1.234' the '.' could be a decimal mark or a group separator.
 -- From viwiki.
 if to\_en\_table then
 text = ustring.gsub(text, '%d', to\_en\_table)
 end
 if decimal\_mark(text) == '.' then
 local original = text
 text = text:gsub(',', *) -- for example, interpret "1,234.5" as an enwiki value*
 if parms then
 add\_warning(parms, 0, 'cvt\_enwiki\_num', original, with\_separator({}, text))
 end
 else
 if numsep\_remove then
 text = text:gsub(numsep\_remove, *)*
 end
 if numsep\_remove2 then
 text = text:gsub(numsep\_remove2, *)*
 end
 if numdot ~= '.' then
 text = text:gsub(numdot, '.')
 end
 end
 return text
end

local function omit\_separator(id)
 -- Return true if there should be no separator before id (a unit symbol or name).
 -- For zhwiki, there should be no separator if id uses local characters.
 -- The following kludge should be a sufficient test.
 if omitsep then
 if id:sub(1, 2) == '-{' then -- for "-{...}-" content language variant
 return true
 end
 if id:byte() > 127 then
 local first = usub(id, 1, 1)
 if first ~= 'Å' and first ~= '°' and first ~= 'µ' then
 return true
 end
 end
 end
 return id:sub(1, 1) == '/' -- no separator before units like "/ha"
end

local spell\_module -- name of module that can spell numbers
local speller -- function from that module to handle spelling (set if needed)
local wikidata\_module, wikidata\_data\_module -- names of Wikidata modules
local wikidata\_code, wikidata\_data -- exported tables from those modules (set if needed)

local function set\_config(args)
 -- Set configuration options from template #invoke or defaults.
 config = args
 maxsigfig = config.maxsigfig or 14 -- maximum number of significant figures
 local data\_module, text\_module
 local sandbox = config.sandbox and ('/' .. config.sandbox) or
 data\_module = "Module:Convert/data" .. sandbox
 text\_module = "Module:Convert/text" .. sandbox
 extra\_module = "Module:Convert/extra" .. sandbox
 wikidata\_module = "Module:Convert/wikidata" .. sandbox
 wikidata\_data\_module = "Module:Convert/wikidata/data" .. sandbox
 spell\_module = "Module:ConvertNumeric"
 data\_code = mw.loadData(data\_module)
 text\_code = mw.loadData(text\_module)
 all\_units = data\_code.all\_units
 local translation = text\_code.translation\_table
 if translation then
 numdot = translation.numdot
 numsep = translation.numsep
 if numdot == ',' and numsep == '.' then
 if text\_code.all\_messages.cvt\_enwiki\_num then
 to\_en = to\_en\_with\_check
 end
 end
 if translation.group then
 group\_method = translation.group
 end
 if translation.per\_word then
 per\_word = translation.per\_word
 end
 if translation.plural\_suffix then
 plural\_suffix = translation.plural\_suffix
 end
 varname = translation.varname
 from\_en\_table = translation.from\_en
 local use\_workaround = true
 if use\_workaround then
 -- 2013-07-05 workaround bug by making a copy of the required table.
 -- mw.ustring.gsub fails with a table (to\_en\_table) as the replacement,
 -- if the table is accessed via mw.loadData.
 local source = translation.to\_en
 if source then
 to\_en\_table = {}
 for k, v in pairs(source) do
 to\_en\_table[k] = v
 end
 end
 else
 to\_en\_table = translation.to\_en
 end
 if translation.lang == 'en default' then
 en\_default = true -- for hiwiki
 end
 omitsep = translation.omitsep -- for zhwiki
 end
 numdot = config.numdot or numdot or '.' -- decimal mark before fractional digits
 numsep = config.numsep or numsep or ',' -- group separator for numbers
 -- numsep should be ',' or '.' or  *or ' ' or a Unicode character.*
 -- numsep\_remove must work in a regex to identify separators to be removed.
 if numsep ~=  *then*
 numsep\_remove = (numsep == '.') and '%.' or numsep
 end
 if numsep ~= ',' and numdot ~= ',' then
 numsep\_remove2 = ',' -- so numbers copied from enwiki will work
 end
end

local function collection()
 -- Return a table to hold items.
 return {
 n = 0,
 add = function (self, item)
 self.n = self.n + 1
 self[self.n] = item
 end,
 }
end

local function divide(numerator, denominator)
 -- Return integers quotient, remainder resulting from dividing the two
 -- given numbers, which should be unsigned integers.
 local quotient, remainder = floor(numerator / denominator), numerator % denominator
 if not (0 <= remainder and remainder < denominator) then
 -- Floating point limits may need this, as in **Script error: No such module "convert".**.
 remainder = 0
 end
 return quotient, remainder
end

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

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

local function table\_len(t)
 -- Return length (<100) of a numbered table to replace #t which is
 -- documented to not work if t is accessed via mw.loadData().
 for i = 1, 100 do
 if t[i] == nil then
 return i - 1
 end
 end
end

local function wanted\_category(catkey, catsort, want\_warning)
 -- Return message category if it is wanted in current namespace,
 -- otherwise return *.*
 local cat
 local title = mw.title.getCurrentTitle()
 if title then
 local nsdefault = '0' -- default namespace: '0' = article; '0,10' = article and template
 local namespace = title.namespace
 for \_, v in ipairs(split(config.nscat or nsdefault, ',')) do
 if namespace == tonumber(v) then
 cat = text\_code.all\_categories[want\_warning and 'warning' or catkey]
 if catsort and catsort ~=  *and cat:sub(-2) == ']]' then*
 cat = cat:sub(1, -3) .. '|' .. mw.text.nowiki(usub(catsort, 1, 20)) .. ']]'
 end
 break
 end
 end
 end
 return cat or
end

local function message(parms, mcode, is\_warning)
 -- Return wikitext for an error message, including category if specified
 -- for the message type.
 -- mcode = numbered table specifying the message:
 -- mcode[1] = 'cvt\_xxx' (string used as a key to get message info)
 -- mcode[2] = 'parm1' (string to replace '$1' if any in message)
 -- mcode[3] = 'parm2' (string to replace '$2' if any in message)
 -- mcode[4] = 'parm3' (string to replace '$3' if any in message)
 local msg
 if type(mcode) == 'table' then
 if mcode[1] == 'cvt\_no\_output' then
 -- Some errors should cause convert to output an empty string,
 -- for example, for an optional field in an infobox.
 return
 end
 msg = text\_code.all\_messages[mcode[1]]
 end
 parms.have\_problem = true
 local function subparm(fmt, ...)
 local rep = {}
 for i, v in ipairs({...}) do
 rep['$' .. i] = v
 end
 return (fmt:gsub('$%d+', rep))
 end
 if msg then
 local parts = {}
 local regex, replace = msg.regex, msg.replace
 for i = 1, 3 do
 local limit = 40
 local s = mcode[i + 1]
 if s then
 if regex and replace then
 s = s:gsub(regex, replace)
 limit = nil -- allow long "should be" messages
 end
 -- Escape user input so it does not break the message.
 -- To avoid tags (like **Script error: No such module "convert".**) breaking
 -- the mouseover title, any strip marker starting with char(127) is
 -- replaced with '...' (text not needing i18n).
 local append
 local pos = s:find(string.char(127), 1, true)
 if pos then
 append = '...'
 s = s:sub(1, pos - 1)
 end
 if limit and ulen(s) > limit then
 s = usub(s, 1, limit)
 append = '...'
 end
 s = mw.text.nowiki(s) .. (append or *)*
 else
 s = '?'
 end
 parts['$' .. i] = s
 end
 local function ispreview()
 -- Return true if a prominent message should be shown.
 if parms.test == 'preview' or parms.test == 'nopreview' then
 -- For testing, can preview a real message or simulate a preview
 -- when running automated tests.
 return parms.test == 'preview'
 end
 local success, revid = pcall(function ()
 return (parms.frame):preprocess('-') end)
 return success and (revid == *)*
 end
 local want\_warning = is\_warning and
 not config.warnings and -- show unobtrusive warnings if config.warnings not configured
 not msg.nowarn -- but use msg settings, not standard warning, if specified
 local title = string.gsub(msg[1] or 'Missing message', '$%d+', parts)
 local text = want\_warning and '\*' or msg[2] or 'Missing message'
 local cat = wanted\_category(msg[3], mcode[2], want\_warning)
 local anchor = msg[4] or
 local fmtkey = ispreview() and 'cvt\_format\_preview' or
 (want\_warning and 'cvt\_format2' or msg.format or 'cvt\_format')
 local fmt = text\_code.all\_messages[fmtkey] or 'convert: bug'
 return subparm(fmt, title:gsub('"', '"'), text, cat, anchor)
 end
 return 'Convert internal error: unknown message'
end

function add\_warning(parms, level, key, text1, text2) -- for forward declaration above
 -- If enabled, add a warning that will be displayed after the convert result.
 -- A higher level is more verbose: more kinds of warnings are displayed.
 -- To reduce output noise, only the first warning is displayed.
 if level <= (tonumber(config.warnings) or 1) then
 if parms.warnings == nil then
 parms.warnings = message(parms, { key, text1, text2 }, true)
 end
 end
end

local function spell\_number(parms, inout, number, numerator, denominator)
 -- Return result of spelling (number, numerator, denominator), or
 -- return nil if spelling is not available or not supported for given text.
 -- Examples (each value must be a string or nil):
 -- number numerator denominator output
 -- ------ --------- ----------- -------------------
 -- "1.23" nil nil one point two three
 -- "1" "2" "3" one and two thirds
 -- nil "2" "3" two thirds
 if not speller then
 local function get\_speller(module)
 return require(module).spell\_number
 end
 local success
 success, speller = pcall(get\_speller, spell\_module)
 if not success or type(speller) ~= 'function' then
 add\_warning(parms, 1, 'cvt\_no\_spell', 'spell')
 return nil
 end
 end
 local case
 if parms.spell\_upper == inout then
 case = true
 parms.spell\_upper = nil -- only uppercase first word in a multiple unit
 end
 local sp = not parms.opt\_sp\_us
 local adj = parms.opt\_adjectival
 return speller(number, numerator, denominator, case, sp, adj)
end

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

local function get\_range(word)
 -- Return a range (string or table) corresponding to word (like "to"),
 -- or return nil if not a range word.
 local ranges = text\_code.ranges
 return ranges.types[word] or ranges.types[ranges.aliases[word]]
end

local function check\_mismatch(unit1, unit2)
 -- If unit1 cannot be converted to unit2, return an error message table.
 -- This allows conversion between units of the same type, and between
 -- Nm (normally torque) and ftlb (energy), as in gun-related articles.
 -- This works because Nm is the base unit (scale = 1) for both the
 -- primary type (torque), and the alternate type (energy, where Nm = J).
 -- A match occurs if the primary types are the same, or if unit1 matches
 -- the alternate type of unit2, and vice versa. That provides a whitelist
 -- of which conversions are permitted between normally incompatible types.
 if unit1.utype == unit2.utype or
 (unit1.utype == unit2.alttype and unit1.alttype == unit2.utype) then
 return nil
 end
 return { 'cvt\_mismatch', unit1.utype, unit2.utype }
end

local function override\_from(out\_table, in\_table, fields)
 -- Copy the specified fields from in\_table to out\_table, but do not
 -- copy nil fields (keep any corresponding field in out\_table).
 for \_, field in ipairs(fields) do
 if in\_table[field] then
 out\_table[field] = in\_table[field]
 end
 end
end

local function shallow\_copy(t)
 -- Return a shallow copy of table t.
 -- Do not need the features and overhead of the Scribunto mw.clone().
 local result = {}
 for k, v in pairs(t) do
 result[k] = v
 end
 return result
end

local unit\_mt = {
 -- Metatable to get missing values for a unit that does not accept SI prefixes.
 -- Warning: The boolean value 'false' is returned for any missing field
 -- so \_\_index is not called twice for the same field in a given unit.
 \_\_index = function (self, key)
 local value
 if key == 'name1' or key == 'sym\_us' then
 value = self.symbol
 elseif key == 'name2' then
 value = self.name1 .. plural\_suffix
 elseif key == 'name1\_us' then
 value = self.name1
 if not rawget(self, 'name2\_us') then
 -- If name1\_us is 'foot', do not make name2\_us by appending plural\_suffix.
 self.name2\_us = self.name2
 end
 elseif key == 'name2\_us' then
 local raw1\_us = rawget(self, 'name1\_us')
 if raw1\_us then
 value = raw1\_us .. plural\_suffix
 else
 value = self.name2
 end
 elseif key == 'link' then
 value = self.name1
 else
 value = false
 end
 rawset(self, key, value)
 return value
 end
}

local function prefixed\_name(unit, name, index)
 -- Return unit name with SI prefix inserted at correct position.
 -- index = 1 (name1), 2 (name2), 3 (name1\_us), 4 (name2\_us).
 -- The position is a byte (not character) index, so use Lua's sub().
 local pos = rawget(unit, 'prefix\_position')
 if type(pos) == 'string' then
 pos = tonumber(split(pos, ',')[index])
 end
 if pos then
 return name:sub(1, pos - 1) .. unit.si\_name .. name:sub(pos)
 end
 return unit.si\_name .. name
end

local unit\_prefixed\_mt = {
 -- Metatable to get missing values for a unit that accepts SI prefixes.
 -- Before use, fields si\_name, si\_prefix must be defined.
 -- The unit must define \_symbol, \_name1 and
 -- may define \_sym\_us, \_name1\_us, \_name2\_us
 -- (\_sym\_us, \_name2\_us may be defined for a language using sp=us
 -- to refer to a variant unrelated to U.S. units).
 \_\_index = function (self, key)
 local value
 if key == 'symbol' then
 value = self.si\_prefix .. self.\_symbol
 elseif key == 'sym\_us' then
 value = rawget(self, '\_sym\_us')
 if value then
 value = self.si\_prefix .. value
 else
 value = self.symbol
 end
 elseif key == 'name1' then
 value = prefixed\_name(self, self.\_name1, 1)
 elseif key == 'name2' then
 value = rawget(self, '\_name2')
 if value then
 value = prefixed\_name(self, value, 2)
 else
 value = self.name1 .. plural\_suffix
 end
 elseif key == 'name1\_us' then
 value = rawget(self, '\_name1\_us')
 if value then
 value = prefixed\_name(self, value, 3)
 else
 value = self.name1
 end
 elseif key == 'name2\_us' then
 value = rawget(self, '\_name2\_us')
 if value then
 value = prefixed\_name(self, value, 4)
 elseif rawget(self, '\_name1\_us') then
 value = self.name1\_us .. plural\_suffix
 else
 value = self.name2
 end
 elseif key == 'link' then
 value = self.name1
 else
 value = false
 end
 rawset(self, key, value)
 return value
 end
}

local unit\_per\_mt = {
 -- Metatable to get values for a per unit of form "x/y".
 -- This is never called to determine a unit name or link because per units
 -- are handled as a special case.
 -- Similarly, the default output is handled elsewhere, and for a symbol
 -- this is only called from get\_default() for default\_exceptions.
 \_\_index = function (self, key)
 local value
 if key == 'symbol' then
 local per = self.per
 local unit1, unit2 = per[1], per[2]
 if unit1 then
 value = unit1[key] .. '/' .. unit2[key]
 else
 value = '/' .. unit2[key]
 end
 elseif key == 'sym\_us' then
 value = self.symbol
 elseif key == 'scale' then
 local per = self.per
 local unit1, unit2 = per[1], per[2]
 value = (unit1 and unit1.scale or 1) \* self.scalemultiplier / unit2.scale
 else
 value = false
 end
 rawset(self, key, value)
 return value
 end
}

local function make\_per(unitcode, unit\_table, ulookup)
 -- Return true, t where t is a per unit with unit codes expanded to unit tables,
 -- or return false, t where t is an error message table.
 local result = {
 unitcode = unitcode,
 utype = unit\_table.utype,
 per = {}
 }
 override\_from(result, unit\_table, { 'invert', 'iscomplex', 'default', 'link', 'symbol', 'symlink' })
 result.symbol\_raw = (result.symbol or false) -- to distinguish between a defined exception and a metatable calculation
 local prefix
 for i, v in ipairs(unit\_table.per) do
 if i == 1 and v ==  *then*
 -- First unit symbol can be empty; that gives a nil first unit table.
 elseif i == 1 and text\_code.currency[v] then
 prefix = currency\_text or v
 else
 local success, t = ulookup(v)
 if not success then return false, t end
 result.per[i] = t
 end
 end
 local multiplier = unit\_table.multiplier
 if not result.utype then
 -- Creating an automatic per unit.
 local unit1 = result.per[1]
 local utype = (unit1 and unit1.utype or prefix or *) .. '/' .. result.per[2].utype*
 local t = data\_code.per\_unit\_fixups[utype]
 if t then
 if type(t) == 'table' then
 utype = t.utype or utype
 result.link = result.link or t.link
 multiplier = multiplier or t.multiplier
 else
 utype = t
 end
 end
 result.utype = utype
 end
 result.scalemultiplier = multiplier or 1
 result.vprefix = prefix or false -- set to non-nil to avoid calling \_\_index
 return true, setmetatable(result, unit\_per\_mt)
end

local function lookup(parms, unitcode, what, utable, fails, depth)
 -- Return true, t where t is a copy of the unit's converter table,
 -- or return false, t where t is an error message table.
 -- Parameter 'what' determines whether combination units are accepted:
 -- 'no\_combination'  : single unit only
 -- 'any\_combination' : single unit or combination or output multiple
 -- 'only\_multiple'  : single unit or output multiple only
 -- Parameter unitcode is a symbol (like 'g'), with an optional SI prefix (like 'kg').
 -- If, for example, 'kg' is in this table, that entry is used;
 -- otherwise the prefix ('k') is applied to the base unit ('g').
 -- If unitcode is a known combination code (and if allowed by what),
 -- a table of output multiple unit tables is included in the result.
 -- For compatibility with the old template, an underscore in a unitcode is
 -- replaced with a space so usage like **Script error: No such module "convert".** works.
 -- Wikignomes may also put two spaces or " " in combinations, so
 -- replace underscore, " ", and multiple spaces with a single space.
 utable = utable or parms.unittable or all\_units
 fails = fails or {}
 depth = depth and depth + 1 or 1
 if depth > 9 then
 -- There are ways to mistakenly define units which result in infinite
 -- recursion when lookup() is called. That gives a long delay and very
 -- confusing error messages, so the depth parameter is used as a guard.
 return false, { 'cvt\_lookup', unitcode }
 end
 if unitcode == nil or unitcode ==  *then*
 return false, { 'cvt\_no\_unit' }
 end
 unitcode = unitcode:gsub('\_', ' '):gsub(' ', ' '):gsub(' +', ' ')
 local function call\_make\_per(t)
 return make\_per(unitcode, t,
 function (ucode) return lookup(parms, ucode, 'no\_combination', utable, fails, depth) end
 )
 end
 local t = utable[unitcode]
 if t then
 if t.shouldbe then
 return false, { 'cvt\_should\_be', t.shouldbe }
 end
 if t.sp\_us then
 parms.opt\_sp\_us = true
 end
 local target = t.target -- nil, or unitcode is an alias for this target
 if target then
 local success, result = lookup(parms, target, what, utable, fails, depth)
 if not success then return false, result end
 override\_from(result, t, { 'customary', 'default', 'link', 'symbol', 'symlink' })
 local multiplier = t.multiplier
 if multiplier then
 result.multiplier = tostring(multiplier)
 result.scale = result.scale \* multiplier
 end
 return true, result
 end
 if t.per then
 return call\_make\_per(t)
 end
 local combo = t.combination -- nil or a table of unitcodes
 if combo then
 local multiple = t.multiple
 if what == 'no\_combination' or (what == 'only\_multiple' and not multiple) then
 return false, { 'cvt\_bad\_unit', unitcode }
 end
 -- Recursively create a combination table containing the
 -- converter table of each unitcode.
 local result = { utype = t.utype, multiple = multiple, combination = {} }
 local cvt = result.combination
 for i, v in ipairs(combo) do
 local success, t = lookup(parms, v, multiple and 'no\_combination' or 'only\_multiple', utable, fails, depth)
 if not success then return false, t end
 cvt[i] = t
 end
 return true, result
 end
 local result = shallow\_copy(t)
 result.unitcode = unitcode
 if result.prefixes then
 result.si\_name =
 result.si\_prefix =
 return true, setmetatable(result, unit\_prefixed\_mt)
 end
 return true, setmetatable(result, unit\_mt)
 end
 local SIprefixes = text\_code.SIprefixes
 for plen = SIprefixes[1] or 2, 1, -1 do
 -- Look for an SI prefix; should never occur with an alias.
 -- Check for longer prefix first ('dam' is decametre).
 -- SIprefixes[1] = prefix maximum #characters (as seen by mw.ustring.sub).
 local prefix = usub(unitcode, 1, plen)
 local si = SIprefixes[prefix]
 if si then
 local t = utable[usub(unitcode, plen+1)]
 if t and t.prefixes then
 local result = shallow\_copy(t)
 result.unitcode = unitcode
 result.si\_name = parms.opt\_sp\_us and si.name\_us or si.name
 result.si\_prefix = si.prefix or prefix
 result.scale = t.scale \* 10 ^ (si.exponent \* t.prefixes)
 return true, setmetatable(result, unit\_prefixed\_mt)
 end
 end
 end
 -- Accept any unit with an engineering notation prefix like "e6cuft"
 -- (million cubic feet), but not chained prefixes like "e3e6cuft",
 -- and not if the unit is a combination or multiple,
 -- and not if the unit has an offset or is a built-in.
 -- Only en digits are accepted.
 local has\_plus = unitcode:find('+', 1, true)
 if not has\_plus then
 local exponent, baseunit = unitcode:match('^e(%d+)(.\*)')
 if exponent then
 local engscale = text\_code.eng\_scales[exponent]
 if engscale then
 local success, result = lookup(parms, baseunit, 'no\_combination', utable, fails, depth)
 if success and not (result.offset or result.builtin or result.engscale) then
 result.unitcode = unitcode -- 'e6cuft' not 'cuft'
 result.defkey = unitcode -- key to lookup default exception
 result.engscale = engscale
 result.scale = result.scale \* 10 ^ tonumber(exponent)
 return true, result
 end
 end
 end
 end
 -- Accept user-defined combinations like "acre+m2+ha" or "acre m2 ha" for output.
 -- If '+' is used, each unit code can include a space, and any error is fatal.
 -- If ' ' is used and if each space-separated word is a unit code, it is a combo,
 -- but errors are not fatal so the unit code can be looked up as an extra unit.
 local err\_is\_fatal
 local combo = collection()
 if has\_plus then
 err\_is\_fatal = true
 for item in (unitcode .. '+'):gmatch('%s\*(.-)%s\*%+') do
 if item ~=  *then*
 combo:add(item)
 end
 end
 elseif unitcode:find('%s') then
 for item in unitcode:gmatch('%S+') do
 combo:add(item)
 end
 end
 if combo.n > 1 then
 local function lookup\_combo()
 if what == 'no\_combination' or what == 'only\_multiple' then
 return false, { 'cvt\_bad\_unit', unitcode }
 end
 local result = { combination = {} }
 local cvt = result.combination
 for i, v in ipairs(combo) do
 local success, t = lookup(parms, v, 'only\_multiple', utable, fails, depth)
 if not success then return false, t end
 if i == 1 then
 result.utype = t.utype
 else
 local mismatch = check\_mismatch(result, t)
 if mismatch then
 return false, mismatch
 end
 end
 cvt[i] = t
 end
 return true, result
 end
 local success, result = lookup\_combo()
 if success or err\_is\_fatal then
 return success, result
 end
 end
 -- Look for x/y; split on right-most slash to get scale correct (x/y/z is x/y per z).
 local top, bottom = unitcode:match('^(.-)/([^/]+)$')
 if top and not unitcode:find('e%d') then
 -- If valid, create an automatic per unit for an "x/y" unit code.
 -- The unitcode must not include extraneous spaces.
 -- Engineering notation (apart from at start and which has been stripped before here),
 -- is not supported so do not make a per unit if find text like 'e3' in unitcode.
 local success, result = call\_make\_per({ per = {top, bottom} })
 if success then
 return true, result
 end
 end
 if not parms.opt\_ignore\_error and not get\_range(unitcode) then
 -- Want the "what links here" list for the extra\_module to show only cases
 -- where an extra unit is used, so do not require it if invoked from Template:Val
 -- or if looking up a range word which cannot be a unit.
 if not extra\_units then
 local success, extra = pcall(function () return require(extra\_module).extra\_units end)
 if success and type(extra) == 'table' then
 extra\_units = extra
 end
 end
 if extra\_units then
 -- A unit in one data table might refer to a unit in the other table, so
 -- switch between them, relying on fails or depth to terminate loops.
 if not fails[unitcode] then
 fails[unitcode] = true
 local other = (utable == all\_units) and extra\_units or all\_units
 local success, result = lookup(parms, unitcode, what, other, fails, depth)
 if success then
 return true, result
 end
 end
 end
 end
 if to\_en\_table then
 -- At fawiki it is common to translate all digits so a unit like "km2" becomes "km۲".
 local en\_code = ustring.gsub(unitcode, '%d', to\_en\_table)
 if en\_code ~= unitcode then
 return lookup(parms, en\_code, what, utable, fails, depth)
 end
 end
 return false, { 'cvt\_unknown', unitcode }
end

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

local function hyphenated(name, parts)
 -- Return a hyphenated form of given name (for adjectival usage).
 -- The name may be linked and the target of the link must not be changed.
 -- Hypothetical examples:
 -- ton → ton (no change)
 -- long ton → long-ton
 -- long ton → long-ton
 -- long ton → long-ton
 -- Input can also have multiple links in a single name like:
 -- U.S. gallon
 -- miles per U.S. quart
 -- long tons per short ton
 -- Assume that links cannot be nested (never like "[[abcdefghi]]").
 -- This uses a simple and efficient procedure that works for most cases.
 -- Some units (if used) would require more, and can later think about
 -- adding a method to handle exceptions.
 -- The procedure is to replace each space with a hyphen, but
 -- not a space after ')' [for "(pre-1954 US) nautical mile"], and
 -- not spaces immediately before '(' or in '(...)' [for cases like
 -- "British thermal unit (ISO)" and "Calorie (International Steam Table)"].
 if name:find(' ', 1, true) then
 if parts then
 local pos
 if name:sub(1, 1) == '(' then
 pos = name:find(')', 1, true)
 if pos then
 return name:sub(1, pos+1) .. name:sub(pos+2):gsub(' ', '-')
 end
 elseif name:sub(-1) == ')' then
 pos = name:find('(', 1, true)
 if pos then
 return name:sub(1, pos-2):gsub(' ', '-') .. name:sub(pos-1)
 end
 end
 return name:gsub(' ', '-')
 end
 parts = collection()
 for before, item, after in name:gmatch('([^[]\*)(%[%[[^[]\*%]%])([^[]\*)') do
 if item:find(' ', 1, true) then
 local prefix
 local plen = item:find('|', 1, true)
 if plen then
 prefix = item:sub(1, plen)
 item = item:sub(plen + 1, -3)
 else
 prefix = item:sub(1, -3) .. '|'
 item = item:sub(3, -3)
 end
 item = prefix .. hyphenated(item, parts) .. ']]'
 end
 parts:add(before:gsub(' ', '-') .. item .. after:gsub(' ', '-'))
 end
 if parts.n == 0 then
 -- No link like "..." was found in the original name.
 parts:add(hyphenated(name, parts))
 end
 return table.concat(parts)
 end
 return name
end

local function hyphenated\_maybe(parms, want\_name, sep, id, inout)
 -- Return s, f where
 -- s = id, possibly modified
 -- f = true if hyphenated
 -- Possible modifications: hyphenate; prepend '-'; append mid text.
 if id == nil or id ==  *then*
 return
 end
 local mid = (inout == (parms.opt\_flip and 'out' or 'in')) and parms.mid or
 if want\_name then
 if parms.opt\_adjectival then
 return '-' .. hyphenated(id) .. mid, true
 end
 if parms.opt\_add\_s and id:sub(-1) ~= 's' then
 id = id .. 's' -- for nowiki
 end
 end
 return sep .. id .. mid
end

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

local function digit\_groups(parms, text, method)
 -- Return a numbered table of groups of digits (left-to-right, in local language).
 -- Parameter method is a number or nil:
 -- 3 for 3-digit grouping (default), or
 -- 2 for 3-then-2 grouping (only for digits before decimal mark).
 local len\_right
 local len\_left = text:find('.', 1, true)
 if len\_left then
 len\_right = #text - len\_left
 len\_left = len\_left - 1
 else
 len\_left = #text
 end
 local twos = method == 2 and len\_left > 5
 local groups = collection()
 local run = len\_left
 local n
 if run < 4 or (run == 4 and parms.opt\_comma5) then
 if parms.opt\_gaps then
 n = run
 else
 n = #text
 end
 elseif twos then
 n = run % 2 == 0 and 1 or 2
 else
 n = run % 3 == 0 and 3 or run % 3
 end
 while run > 0 do
 groups:add(n)
 run = run - n
 n = (twos and run > 3) and 2 or 3
 end
 if len\_right then
 if groups.n == 0 then
 groups:add(0)
 end
 if parms.opt\_gaps and len\_right > 3 then
 local want4 = not parms.opt\_gaps3 -- true gives no gap before trailing single digit
 local isfirst = true
 run = len\_right
 while run > 0 do
 n = (want4 and run == 4) and 4 or (run > 3 and 3 or run)
 if isfirst then
 isfirst = false
 groups[groups.n] = groups[groups.n] + 1 + n
 else
 groups:add(n)
 end
 run = run - n
 end
 else
 groups[groups.n] = groups[groups.n] + 1 + len\_right
 end
 end
 local pos = 1
 for i, length in ipairs(groups) do
 groups[i] = from\_en(text:sub(pos, pos + length - 1))
 pos = pos + length
 end
 return groups
end

function with\_separator(parms, text) -- for forward declaration above
 -- Input text is a number in en digits with optional '.' decimal mark.
 -- Return an equivalent, formatted for display:
 -- with a custom decimal mark instead of '.', if wanted
 -- with thousand separators inserted, if wanted
 -- digits in local language
 -- The given text is like '123' or '123.' or '12345.6789'.
 -- The text has no sign (caller inserts that later, if necessary).
 -- When using gaps, they are inserted before and after the decimal mark.
 -- Separators are inserted only before the decimal mark.
 -- A trailing dot (as in '123.') is removed because their use appears to
 -- be accidental, and such a number should be shown as '123' or '123.0'.
 -- It is useful for convert to suppress the dot so, for example, '4000.'
 -- is a simple way of indicating that all the digits are significant.
 if text:sub(-1) == '.' then
 text = text:sub(1, -2)
 end
 if #text < 4 or parms.opt\_nocomma or numsep ==  *then*
 return from\_en(text)
 end
 local groups = digit\_groups(parms, text, group\_method)
 if parms.opt\_gaps then
 if groups.n <= 1 then
 return groups[1] or
 end
 local nowrap = ''
 local gap = ''
 local close = ''
 return nowrap .. groups[1] .. gap .. table.concat(groups, close .. gap, 2, groups.n) .. close .. close
 end
 return table.concat(groups, numsep)
end

-- An input value like 1.23e12 is displayed using scientific notation (1.23×10¹²).
-- That also makes the output use scientific notation, except for small values.
-- In addition, very small or very large output values use scientific notation.
-- Use format(fmtpower, significand, '10', exponent) where each argument is a string.
local fmtpower = '%s×%s%s'

local function with\_exponent(parms, show, exponent)
 -- Return wikitext to display the implied value in scientific notation.
 -- Input uses en digits; output uses digits in local language.
 return format(fmtpower, with\_separator(parms, show), from\_en('10'), use\_minus(from\_en(tostring(exponent))))
end

local function make\_sigfig(value, sigfig)
 -- Return show, exponent that are equivalent to the result of
 -- converting the number 'value' (where value >= 0) to a string,
 -- rounded to 'sigfig' significant figures.
 -- The returned items are:
 -- show: a string of digits; no sign and no dot;
 -- there is an implied dot before show.
 -- exponent: a number (an integer) to shift the implied dot.
 -- Resulting value = tonumber('.' .. show) \* 10^exponent.
 -- Examples:
 -- make\_sigfig(23.456, 3) returns '235', 2 (.235 \* 10^2).
 -- make\_sigfig(0.0023456, 3) returns '235', -2 (.235 \* 10^-2).
 -- make\_sigfig(0, 3) returns '000', 1 (.000 \* 10^1).
 if sigfig <= 0 then
 sigfig = 1
 elseif sigfig > maxsigfig then
 sigfig = maxsigfig
 end
 if value == 0 then
 return string.rep('0', sigfig), 1
 end
 local exp, fracpart = math.modf(log10(value))
 if fracpart >= 0 then
 fracpart = fracpart - 1
 exp = exp + 1
 end
 local digits = format('%.0f', 10^(fracpart + sigfig))
 if #digits > sigfig then
 -- Overflow (for sigfig=3: like 0.9999 rounding to "1000"; need "100").
 digits = digits:sub(1, sigfig)
 exp = exp + 1
 end
 assert(#digits == sigfig, 'Bug: rounded number has wrong length')
 return digits, exp
end

-- Fraction output format.
local fracfmt = {
 { -- Like Template:Frac (fraction slash).
 -- 1/2  : sign, numerator, denominator
 -- 1+2/3  : signed\_wholenumber, numerator, denominator
 '%s%s⁄%s',
 '%s %s⁄%s',
 },
 { -- Like Template: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
 '%s%s/%s',
 '%s %s/%s',
 },
}

local function format\_fraction(parms, inout, negative, wholestr, numstr, denstr, do\_spell, style)
 -- Return wikitext for a fraction, possibly spelled.
 -- Inputs use en digits and have no sign; output uses digits in local language.
 local wikitext
 if not style then
 style = parms.opt\_fraction\_horizontal and 2 or 1
 end
 if wholestr ==  *then*
 wholestr = nil
 end
 if wholestr then
 local decorated = with\_separator(parms, wholestr)
 if negative then
 decorated = MINUS .. decorated
 end
 local fmt = fracfmt[style][2]
 wikitext = format(fmt, decorated, from\_en(numstr), from\_en(denstr))
 else
 local sign = negative and MINUS or
 wikitext = format(fracfmt[style][1], sign, from\_en(numstr), from\_en(denstr))
 end
 if do\_spell then
 if negative then
 if wholestr then
 wholestr = '-' .. wholestr
 else
 numstr = '-' .. numstr
 end
 end
 wikitext = spell\_number(parms, inout, wholestr, numstr, denstr) or wikitext
 end
 return wikitext
end

local function format\_number(parms, show, exponent, isnegative)
 -- Parameter show is a string or a table containing strings.
 -- Each string is a formatted number in en digits and optional '.' decimal mark.
 -- A table represents a fraction: integer, numerator, denominator;
 -- if a table is given, exponent must be nil.
 -- Return t where t is a table with fields:
 -- show = wikitext formatted to display implied value
 -- (digits in local language)
 -- is\_scientific = true if show uses scientific notation
 -- clean = unformatted show (possibly adjusted and with inserted '.')
 -- (en digits)
 -- sign =  *or MINUS*
 -- exponent = exponent (possibly adjusted)
 -- The clean and exponent fields can be used to calculate the
 -- rounded absolute value, if needed.
 --
 -- The value implied by the arguments is found from:
 -- exponent is nil; and
 -- show is a string of digits (no sign), with an optional dot;
 -- show = '123.4' is value 123.4, '1234' is value 1234.0;
 -- or:
 -- exponent is an integer indicating where dot should be;
 -- show is a string of digits (no sign and no dot);
 -- there is an implied dot before show;
 -- show does not start with '0';
 -- show = '1234', exponent = 3 is value 0.1234\*10^3 = 123.4.
 --
 -- The formatted result:
 -- \* Is for an output value and is spelled if wanted and possible.
 -- \* Includes a Unicode minus if isnegative and not spelled.
 -- \* Uses a custom decimal mark, if wanted.
 -- \* Has digits grouped where necessary, if wanted.
 -- \* Uses scientific notation if requested, or for very small or large values
 -- (which forces result to not be spelled).
 -- \* Has no more than maxsigfig significant digits
 -- (same as old template and {{#expr}}).
 local xhi, xlo -- these control when scientific notation (exponent) is used
 if parms.opt\_scientific then
 xhi, xlo = 4, 2 -- default for output if input uses e-notation
 elseif parms.opt\_scientific\_always then
 xhi, xlo = 0, 0 -- always use scientific notation (experimental)
 else
 xhi, xlo = 10, 4 -- default
 end
 local sign = isnegative and MINUS or
 local maxlen = maxsigfig
 local tfrac
 if type(show) == 'table' then
 tfrac = show
 show = tfrac.wholestr
 assert(exponent == nil, 'Bug: exponent given with fraction')
 end
 if not tfrac and not exponent then
 local integer, dot, decimals = show:match('^(%d\*)(%.?)(.\*)')
 if integer == '0' or integer ==  *then*
 local zeros, figs = decimals:match('^(0\*)([^0]?.\*)')
 if #figs == 0 then
 if #zeros > maxlen then
 show = '0.' .. zeros:sub(1, maxlen)
 end
 elseif #zeros >= xlo then
 show = figs
 exponent = -#zeros
 elseif #figs > maxlen then
 show = '0.' .. zeros .. figs:sub(1, maxlen)
 end
 elseif #integer >= xhi then
 show = integer .. decimals
 exponent = #integer
 else
 maxlen = maxlen + #dot
 if #show > maxlen then
 show = show:sub(1, maxlen)
 end
 end
 end
 if exponent then
 local function zeros(n)
 return string.rep('0', n)
 end
 if #show > maxlen then
 show = show:sub(1, maxlen)
 end
 if exponent > xhi or exponent <= -xlo or (exponent == xhi and show ~= '1' .. zeros(xhi - 1)) then
 -- When xhi, xlo = 10, 4 (the default), scientific notation is used if the
 -- rounded value satisfies: value >= 1e9 or value < 1e-4 (1e9 = 0.1e10),
 -- except if show is '1000000000' (1e9), for example:
 -- **Script error: No such module "convert".** → 1,000,000,000 metres (1,000,000,000 m)
 local significand
 if #show > 1 then
 significand = show:sub(1, 1) .. '.' .. show:sub(2)
 else
 significand = show
 end
 return {
 clean = '.' .. show,
 exponent = exponent,
 sign = sign,
 show = sign .. with\_exponent(parms, significand, exponent-1),
 is\_scientific = true,
 }
 end
 if exponent >= #show then
 show = show .. zeros(exponent - #show) -- result has no dot
 elseif exponent <= 0 then
 show = '0.' .. zeros(-exponent) .. show
 else
 show = show:sub(1, exponent) .. '.' .. show:sub(exponent+1)
 end
 end
 local formatted\_show
 if tfrac then
 show = tostring(tfrac.value) -- to set clean in returned table
 formatted\_show = format\_fraction(parms, 'out', isnegative, tfrac.wholestr, tfrac.numstr, tfrac.denstr, parms.opt\_spell\_out)
 else
 if isnegative and show:match('^0.?0\*$') then
 sign =  *-- don't show minus if result is negative but rounds to zero*
 end
 formatted\_show = sign .. with\_separator(parms, show)
 if parms.opt\_spell\_out then
 formatted\_show = spell\_number(parms, 'out', sign .. show) or formatted\_show
 end
 end
 return {
 clean = show,
 sign = sign,
 show = formatted\_show,
 is\_scientific = false, -- to avoid calling \_\_index
 }
end

local function extract\_fraction(parms, text, negative)
 -- If text represents a fraction, return
 -- value, altvalue, show, denominator
 -- where
 -- value is a number (value of the fraction in argument text)
 -- altvalue is an alternate interpretation of any fraction for the hands
 -- unit where "12.1+3/4" means 12 hands 1.75 inches
 -- show is a string (formatted text for display of an input value,
 -- and is spelled if wanted and possible)
 -- denominator is value of the denominator in the fraction
 -- Otherwise, return nil.
 -- Input uses en digits and '.' decimal mark (input has been translated).
 -- Output uses digits in local language and local decimal mark, if any.

 -- Originally this function accepted x+y/z where x, y, z were any valid
 -- numbers, possibly with a sign. For example '1.23e+2+1.2/2.4' = 123.5,
 -- and '2-3/8' = 1.625. However, such usages were found to be errors or
 -- misunderstandings, so since August 2014 the following restrictions apply:
 -- x (if present) is an integer or has a single digit after decimal mark
 -- y and z are unsigned integers
 -- e-notation is not accepted
 -- The overall number can start with '+' or '-' (so '12+3/4' and '+12+3/4'
 -- and '-12-3/4' are valid).
 -- Any leading negative sign is removed by the caller, so only inputs
 -- like the following are accepted here (may have whitespace):
 -- negative = false false true (there was a leading '-')
 -- text = '2/3' '+2/3' '2/3'
 -- text = '1+2/3' '+1+2/3' '1-2/3'
 -- text = '12.3+1/2' '+12.3+1/2' '12.3-1/2'
 -- Values like '12.3+1/2' are accepted, but are intended only for use
 -- with the hands unit (not worth adding code to enforce that).

 local leading\_plus, prefix, numstr, slashes, denstr =
 text:match('^%s\*(%+?)%s\*(.-)%s\*(%d+)%s\*(/+)%s\*(%d+)%s\*$')
 if not leading\_plus then
 -- Accept a single U+2044 fraction slash because that may be pasted.
 leading\_plus, prefix, numstr, denstr =
 text:match('^%s\*(%+?)%s\*(.-)%s\*(%d+)%s\*⁄%s\*(%d+)%s\*$')
 slashes = '/'
 end
 local numerator = tonumber(numstr)
 local denominator = tonumber(denstr)
 if numerator == nil or denominator == nil or (negative and leading\_plus ~= *) then*
 return nil
 end
 local whole, wholestr
 if prefix ==  *then*
 wholestr =
 whole = 0
 else
 -- Any prefix must be like '12+' or '12-' (whole number and fraction sign);
 -- '12.3+' and '12.3-' are also accepted (single digit after decimal point)
 -- because '12.3+1/2 hands' is valid (12 hands 3½ inches).
 local num1, num2, frac\_sign = prefix:match('^(%d+)(%.?%d?)%s\*([+%-])$')
 if num1 == nil then return nil end
 if num2 ==  *then -- num2 must be*  or like '.1' but not '.' or '.12'
 wholestr = num1
 else
 if #num2 ~= 2 then return nil end
 wholestr = num1 .. num2
 end
 if frac\_sign ~= (negative and '-' or '+') then return nil end
 whole = tonumber(wholestr)
 if whole == nil then return nil end
 end
 local value = whole + numerator / denominator
 if not valid\_number(value) then return nil end
 local altvalue = whole + numerator / (denominator \* 10)
 local style = #slashes -- kludge: 1 or 2 slashes can be used to select style
 if style > 2 then style = 2 end
 local wikitext = format\_fraction(parms, 'in', negative, leading\_plus .. wholestr, numstr, denstr, parms.opt\_spell\_in, style)
 return value, altvalue, wikitext, denominator
end

local function extract\_number(parms, text, another, no\_fraction)
 -- Return true, info if can extract a number from text,
 -- where info is a table with the result,
 -- or return false, t where t is an error message table.
 -- Input can use en digits or digits in local language and can
 -- have references at the end. Accepting references is intended
 -- for use in infoboxes with a field for a value passed to convert.
 -- Parameter another = true if the expected value is not the first.
 -- Before processing, the input text is cleaned:
 -- \* Any thousand separators (valid or not) are removed.
 -- \* Any sign (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 or -1 (to use singular form of units)
 -- clean = cleaned text with any separators and sign removed
 -- (en digits and '.' decimal mark)
 -- show = text formatted for output, possibly with ref strip markers
 -- (digits in local language and custom decimal mark)
 -- The resulting show:
 -- \* Is for an input value and is spelled if wanted and possible.
 -- \* Has a rounded value, if wanted.
 -- \* Has digits grouped where necessary, if wanted.
 -- \* If negative, a Unicode minus is used; otherwise the sign is
 -- '+' (if the input text used '+'), or is  *(if no sign in input).*
 text = strip(text or *)*
 local reference
 local pos = text:find('\127', 1, true)
 if pos then
 local before = text:sub(1, pos - 1)
 local remainder = text:sub(pos)
 local refs = {}
 while #remainder > 0 do
 local ref, spaces
 ref, spaces, remainder = remainder:match('^(\127[^\127]\*UNIQ[^\127]\*%-ref[^\127]\*\127)(%s\*)(.\*)')
 if ref then
 table.insert(refs, ref)
 else
 refs = {}
 break
 end
 end
 if #refs > 0 then
 text = strip(before)
 reference = table.concat(refs)
 end
 end
 local clean = to\_en(text, parms)
 if clean ==  *then*
 return false, { another and 'cvt\_no\_num2' or 'cvt\_no\_num' }
 end
 local isnegative, propersign = false,  *-- most common case*
 local singular, show, denominator
 local value = tonumber(clean)
 local altvalue
 if value then
 local sign = clean:sub(1, 1)
 if sign == '+' or sign == '-' then
 propersign = (sign == '+') and '+' or MINUS
 clean = clean:sub(2)
 end
 if value < 0 then
 isnegative = true
 value = -value
 end
 else
 local valstr
 for \_, prefix in ipairs({ '-', MINUS, '−' }) 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
 if not no\_fraction then
 value, altvalue, show, denominator = extract\_fraction(parms, clean, isnegative)
 end
 if value == nil then
 return false, { 'cvt\_bad\_num', text }
 end
 if value <= 1 then
 singular = true -- for example, "½ mile" or "one half mile" (singular unit)
 end
 end
 end
 if not valid\_number(value) then -- for example, "1e310" may overflow
 return false, { 'cvt\_invalid\_num' }
 end
 if show == nil then
 -- clean is a non-empty string with no spaces, and does not represent a fraction,
 -- and value = tonumber(clean) is a number >= 0.
 -- If the input uses e-notation, show will be displayed using a power of ten, but
 -- we use the number as given so it might not be normalized scientific notation.
 -- The input value is spelled if specified so any e-notation is ignored;
 -- that allows input like 2e6 to be spelled as "two million" which works
 -- because the spell module converts '2e6' to '2000000' before spelling.
 local function rounded(value, default, exponent)
 local precision = parms.opt\_ri
 if precision then
 local fmt = '%.' .. format('%d', precision) .. 'f'
 local result = fmt:format(tonumber(value) + 2e-14) -- fudge for some common cases of bad rounding
 if not exponent then
 singular = (tonumber(result) == 1)
 end
 return result
 end
 return default
 end
 singular = (value == 1)
 local scientific
 local significand, exponent = clean:match('^([%d.]+)[Ee]([+%-]?%d+)')
 if significand then
 show = with\_exponent(parms, rounded(significand, significand, exponent), exponent)
 scientific = true
 else
 show = with\_separator(parms, rounded(value, clean))
 end
 show = propersign .. show
 if parms.opt\_spell\_in then
 show = spell\_number(parms, 'in', propersign .. rounded(value, clean)) or show
 scientific = false
 end
 if scientific then
 parms.opt\_scientific = true
 end
 end
 if isnegative and (value ~= 0) then
 value = -value
 altvalue = -(altvalue or value)
 end
 return true, {
 value = value,
 altvalue = altvalue or value,
 singular = singular,
 clean = clean,
 show = show .. (reference or *),*
 denominator = denominator,
 }
end

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

local function gcd(a, b)
 -- Return the greatest common denominator for the given values,
 -- which are known to be positive integers.
 if a > b then
 a, b = b, a
 end
 if a <= 0 then
 return b
 end
 local r = b % a
 if r <= 0 then
 return a
 end
 if r == 1 then
 return 1
 end
 return gcd(r, a)
end

local function fraction\_table(value, denominator)
 -- Return value as a string or a table:
 -- \* If result is a string, there is no fraction, and the result
 -- is value formatted as a string of en digits.
 -- \* If result is a table, it represents a fraction with named fields:
 -- wholestr, numstr, denstr (strings of en digits for integer, numerator, denominator).
 -- The result is rounded to the nearest multiple of (1/denominator).
 -- If the multiple is zero, no fraction is included.
 -- No fraction is included if value is very large as the fraction would
 -- be unhelpful, particularly if scientific notation is required.
 -- Input value is a non-negative number.
 -- Input denominator is a positive integer for the desired fraction.
 if value <= 0 then
 return '0'
 end
 if denominator <= 0 or value > 1e8 then
 return format('%.2f', value)
 end
 local integer, decimals = math.modf(value)
 local numerator = floor((decimals \* denominator) +
 0.5 + 2e-14) -- add fudge for some common cases of bad rounding
 if numerator >= denominator then
 integer = integer + 1
 numerator = 0
 end
 local wholestr = tostring(integer)
 if numerator > 0 then
 local div = gcd(numerator, denominator)
 if div > 1 then
 numerator = numerator / div
 denominator = denominator / div
 end
 return {
 wholestr = (integer > 0) and wholestr or *,*
 numstr = tostring(numerator),
 denstr = tostring(denominator),
 value = value,
 }
 end
 return wholestr
end

local function preunits(count, preunit1, preunit2)
 -- If count is 1:
 -- ignore preunit2
 -- return p1
 -- else:
 -- preunit1 is used for preunit2 if the latter is empty
 -- return p1, p2
 -- where:
 -- p1 is text to insert before the input unit
 -- p2 is text to insert before the output unit
 -- p1 or p2 may be nil to mean "no preunit"
 -- Using '+' gives output like "5+ feet" (no space before, but space after).
 local function withspace(text, wantboth)
 -- Return text with space before and, if wantboth, after.
 -- However, no space is added if there is a space or ' ' or '-'
 -- at that position ('-' is for adjectival text).
 -- There is also no space if text starts with '&'
 -- (e.g. '°' would display a degree symbol with no preceding space).
 local char = text:sub(1, 1)
 if char == '&' then
 return text -- an html entity can be used to specify the exact display
 end
 if not (char == ' ' or char == '-' or char == '+') then
 text = ' ' .. text
 end
 if wantboth then
 char = text:sub(-1, -1)
 if not (char == ' ' or char == '-' or text:sub(-6, -1) == ' ') then
 text = text .. ' '
 end
 end
 return text
 end
 local PLUS = '+ '
 preunit1 = preunit1 or
 local trim1 = strip(preunit1)
 if count == 1 then
 if trim1 ==  *then*
 return nil
 end
 if trim1 == '+' then
 return PLUS
 end
 return withspace(preunit1, true)
 end
 preunit1 = withspace(preunit1)
 preunit2 = preunit2 or
 local trim2 = strip(preunit2)
 if trim1 == '+' then
 if trim2 ==  *or trim2 == '+' then*
 return PLUS, PLUS
 end
 preunit1 = PLUS
 end
 if trim2 ==  *then*
 if trim1 ==  *then*
 return nil, nil
 end
 preunit2 = preunit1
 elseif trim2 == '+' then
 preunit2 = PLUS
 elseif trim2 == ' ' then -- trick to make preunit2 empty
 preunit2 = nil
 else
 preunit2 = withspace(preunit2)
 end
 return preunit1, preunit2
end

local function range\_text(range, want\_name, parms, before, after, inout)
 -- Return before .. rtext .. after
 -- where rtext is the text that separates two values in a range.
 local rtext, adj\_text, exception
 if type(range) == 'table' then
 -- Table must specify range text for ('off' and 'on') or ('input' and 'output'),
 -- and may specify range text for 'adj=on',
 -- and may specify exception = true.
 rtext = range[want\_name and 'off' or 'on'] or
 range[((inout == 'in') == (parms.opt\_flip == true)) and 'output' or 'input']
 adj\_text = range['adj']
 exception = range['exception']
 else
 rtext = range
 end
 if parms.opt\_adjectival then
 if want\_name or (exception and parms.abbr\_org == 'on') then
 rtext = adj\_text or rtext:gsub(' ', '-'):gsub(' ', '-')
 end
 end
 if rtext == '–' and after:sub(1, #MINUS) == MINUS then
 rtext = ' – '
 end
 return before .. rtext .. after
end

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

local function translate\_parms(parms, kv\_pairs)
 -- Update fields in parms by translating each key:value in kv\_pairs to terms
 -- used by this module (may involve translating from local language to English).
 -- Also, checks are performed which may display warnings, if enabled.
 -- Return true if successful or return false, t where t is an error message table.
 currency\_text = nil -- local testing can hold module in memory; must clear globals
 local accept\_any\_text = {
 input = true,
 qid = true,
 qual = true,
 stylein = true,
 styleout = true,
 tracking = true,
 }
 if kv\_pairs.adj and kv\_pairs.sing then
 -- For enwiki (before translation), warn if attempt to use adj and sing
 -- as the latter is a deprecated alias for the former.
 if kv\_pairs.adj ~= kv\_pairs.sing and kv\_pairs.sing ~=  *then*
 add\_warning(parms, 1, 'cvt\_unknown\_option', 'sing=' .. kv\_pairs.sing)
 end
 kv\_pairs.sing = nil
 end
 for loc\_name, loc\_value in pairs(kv\_pairs) do
 local en\_name = text\_code.en\_option\_name[loc\_name]
 if en\_name then
 local en\_value
 if en\_name == '$' or en\_name == 'frac' or en\_name == 'sigfig' then
 if loc\_value ==  *then*
 add\_warning(parms, 2, 'cvt\_empty\_option', loc\_name)
 elseif en\_name == '$' then
 -- Value should be a single character like "€" for the euro currency symbol, but anything is accepted.
 currency\_text = (loc\_value == 'euro') and '€' or loc\_value
 else
 local minimum
 local number, is\_integer = get\_number(loc\_value)
 if en\_name == 'frac' then
 minimum = 2
 if number and number < 0 then
 parms.opt\_fraction\_horizontal = true
 number = -number
 end
 else
 minimum = 1
 end
 if number and is\_integer and number >= minimum then
 en\_value = number
 else
 add\_warning(parms, 1, (en\_name == 'frac' and 'cvt\_bad\_frac' or 'cvt\_bad\_sigfig'), loc\_name .. '=' .. loc\_value)
 end
 end
 elseif accept\_any\_text[en\_name] then
 en\_value = loc\_value ~=  *and loc\_value or nil -- accept non-empty user text with no validation*
 if en\_name == 'input' then
 -- May have something like **Script error: No such module "convert".** (empty input) if source is an infobox
 -- with optional fields. In that case, want to output nothing rather than an error.
 parms.input\_text = loc\_value -- keep input because parms.input is nil if loc\_value ==
 end
 else
 en\_value = text\_code.en\_option\_value[en\_name][loc\_value]
 if en\_value and en\_value:sub(-1) == '?' then
 en\_value = en\_value:sub(1, -2)
 add\_warning(parms, -1, 'cvt\_deprecated', loc\_name .. '=' .. loc\_value)
 end
 if en\_value == nil then
 if loc\_value ==  *then*
 add\_warning(parms, 2, 'cvt\_empty\_option', loc\_name)
 else
 add\_warning(parms, 1, 'cvt\_unknown\_option', loc\_name .. '=' .. loc\_value)
 end
 elseif en\_value ==  *then*
 en\_value = nil -- an ignored option like adj=off
 elseif type(en\_value) == 'string' and en\_value:sub(1, 4) == 'opt\_' then
 for \_, v in ipairs(split(en\_value, ',')) do
 local lhs, rhs = v:match('^(.-)=(.+)$')
 if rhs then
 parms[lhs] = tonumber(rhs) or rhs
 else
 parms[v] = true
 end
 end
 en\_value = nil
 end
 end
 parms[en\_name] = en\_value
 else
 add\_warning(parms, 1, 'cvt\_unknown\_option', loc\_name .. '=' .. loc\_value)
 end
 end
 local abbr\_entered = parms.abbr
 local cfg\_abbr = config.abbr
 if cfg\_abbr then
 -- Don't warn if invalid because every convert would show that warning.
 if cfg\_abbr == 'on always' then
 parms.abbr = 'on'
 elseif cfg\_abbr == 'off always' then
 parms.abbr = 'off'
 elseif parms.abbr == nil then
 if cfg\_abbr == 'on default' then
 parms.abbr = 'on'
 elseif cfg\_abbr == 'off default' then
 parms.abbr = 'off'
 end
 end
 end
 if parms.abbr then
 if parms.abbr == 'unit' then
 parms.abbr = 'on'
 parms.number\_word = true
 end
 parms.abbr\_org = parms.abbr -- original abbr, before any flip
 elseif parms.opt\_hand\_hh then
 parms.abbr\_org = 'on'
 parms.abbr = 'on'
 else
 parms.abbr = 'out' -- default is to abbreviate output only (use symbol, not name)
 end
 if parms.opt\_order\_out then
 -- Disable options that do not work in a useful way with order=out.
 parms.opt\_flip = nil -- override adj=flip
 parms.opt\_spell\_in = nil
 parms.opt\_spell\_out = nil
 parms.opt\_spell\_upper = nil
 end
 if parms.opt\_spell\_out and not abbr\_entered then
 parms.abbr = 'off' -- should show unit name when spelling the output value
 end
 if parms.opt\_flip then
 local function swap\_in\_out(option)
 local value = parms[option]
 if value == 'in' then
 parms[option] = 'out'
 elseif value == 'out' then
 parms[option] = 'in'
 end
 end
 swap\_in\_out('abbr')
 swap\_in\_out('lk')
 if parms.opt\_spell\_in and not parms.opt\_spell\_out then
 -- For simplicity, and because it does not appear to be needed,
 -- user cannot set an option to spell the output only.
 parms.opt\_spell\_in = nil
 parms.opt\_spell\_out = true
 end
 end
 if parms.opt\_spell\_upper then
 parms.spell\_upper = parms.opt\_flip and 'out' or 'in'
 end
 if parms.opt\_table or parms.opt\_tablecen then
 if abbr\_entered == nil and parms.lk == nil then
 parms.opt\_values = true
 end
 parms.table\_align = parms.opt\_table and 'right' or 'center'
 end
 if parms.table\_align or parms.opt\_sortable\_on then
 parms.need\_table\_or\_sort = true
 end
 local disp\_joins = text\_code.disp\_joins
 local default\_joins = disp\_joins['b']
 parms.join\_between = default\_joins[3] or '; '
 local disp = parms.disp
 if disp == nil then -- special case for the most common setting
 parms.joins = default\_joins
 elseif disp == 'x' then
 -- Later, parms.joins is set from the input parameters.
 else
 -- Old template does this.
 local abbr = parms.abbr
 if disp == 'slash' then
 if abbr\_entered == nil then
 disp = 'slash-nbsp'
 elseif abbr == 'in' or abbr == 'out' then
 disp = 'slash-sp'
 else
 disp = 'slash-nosp'
 end
 elseif disp == 'sqbr' then
 if abbr == 'on' then
 disp = 'sqbr-nbsp'
 else
 disp = 'sqbr-sp'
 end
 end
 parms.joins = disp\_joins[disp] or default\_joins
 parms.join\_between = parms.joins[3] or parms.join\_between
 parms.wantname = parms.joins.wantname
 end
 if (en\_default and not parms.opt\_lang\_local and (parms[1] or *):find('%d')) or parms.opt\_lang\_en then*
 from\_en\_table = nil
 end
 if en\_default and from\_en\_table then
 -- For hiwiki: localized symbol/name is defined with the US symbol/name field,
 -- and is used if output uses localized numbers.
 parms.opt\_sp\_us = true
 end
 return true
end

local function get\_values(parms)
 -- If successful, update parms and return true, v, i where
 -- v = table of input values
 -- i = index to next entry in parms after those processed here
 -- or return false, t where t is an error message table.
 local valinfo = collection() -- numbered table of input values
 local range = collection() -- numbered table of range items (having, for example, 2 range items requires 3 input values)
 local had\_nocomma -- true if removed "nocomma" kludge from second parameter (like "tonocomma")
 local parm2 = strip(parms[2])
 if parm2 and parm2:sub(-7, -1) == 'nocomma' then
 parms[2] = strip(parm2:sub(1, -8))
 parms.opt\_nocomma = true
 had\_nocomma = true
 end
 local function extractor(i)
 -- If the parameter is not a value, try unpacking it as a range ("1-23" for "1 to 23").
 -- However, "-1-2/3" is a negative fraction (-1⅔), so it must be extracted first.
 -- Do not unpack a parameter if it is like "3-1/2" which is sometimes incorrectly
 -- used instead of "3+1/2" (and which should not be interpreted as "3 to ½").
 -- Unpacked items are inserted into the parms table.
 -- The tail recursion allows combinations like "1x2 to 3x4".
 local valstr = strip(parms[i]) -- trim so any '-' as a negative sign will be at start
 local success, result = extract\_number(parms, valstr, i > 1)
 if not success and valstr and i < 20 then -- check i to limit abuse
 local lhs, sep, rhs = valstr:match('^(%S+)%s+(%S+)%s+(%S.\*)')
 if lhs and not (sep == '-' and rhs:match('/')) then
 if sep:find('%d') then
 return success, result -- to reject **Script error: No such module "convert".** with a decent message (en only)
 end
 parms[i] = rhs
 table.insert(parms, i, sep)
 table.insert(parms, i, lhs)
 return extractor(i)
 end
 if not valstr:match('%-.\*/') then
 for \_, sep in ipairs(text\_code.ranges.words) do
 local start, stop = valstr:find(sep, 2, true) -- start at 2 to skip any negative sign for range '-'
 if start then
 parms[i] = valstr:sub(stop + 1)
 table.insert(parms, i, sep)
 table.insert(parms, i, valstr:sub(1, start - 1))
 return extractor(i)
 end
 end
 end
 end
 return success, result
 end
 local i = 1
 local is\_change
 while true do
 local success, info = extractor(i) -- need to set parms.opt\_nocomma before calling this
 if not success then return false, info end
 i = i + 1
 if is\_change then
 info.is\_change = true -- value is after "±" and so is a change (significant for range like **Script error: No such module "convert".**)
 is\_change = nil
 end
 valinfo:add(info)
 local range\_item = get\_range(strip(parms[i]))
 if not range\_item then
 break
 end
 i = i + 1
 range:add(range\_item)
 if type(range\_item) == 'table' then
 -- For range "x", if append unit to some values, append it to all.
 parms.in\_range\_x = parms.in\_range\_x or range\_item.in\_range\_x
 parms.out\_range\_x = parms.out\_range\_x or range\_item.out\_range\_x
 parms.abbr\_range\_x = parms.abbr\_range\_x or range\_item.abbr\_range\_x
 is\_change = range\_item.is\_range\_change
 end
 end
 if range.n > 0 then
 if range.n > 30 then -- limit abuse, although 4 is a more likely upper limit
 return false, { 'cvt\_invalid\_num' } -- misleading message but it will do
 end
 parms.range = range
 elseif had\_nocomma then
 return false, { 'cvt\_unknown', parm2 }
 end
 return true, valinfo, i
end

local function simple\_get\_values(parms)
 -- If input is like "**Script error: No such module "convert".**",
 -- return true, i, in\_unit, in\_unit\_table
 -- i = index in parms of what follows valid\_unit, if anything.
 -- The valid\_value is not negative and does not use a fraction, and
 -- no options requiring further processing of the input are used.
 -- Otherwise, return nothing or return false, parm1 for caller to interpret.
 -- Testing shows this function is successful for 96% of converts in articles,
 -- and that on average it speeds up converts by 8%.
 if parms.opt\_ri or parms.opt\_spell\_in then return end
 local clean = to\_en(strip(parms[1] or *), parms)*
 if #clean > 10 or not clean:match('^[0-9.]+$') then
 return false, clean
 end
 local value = tonumber(clean)
 if not value then return end
 local info = {
 value = value,
 altvalue = value,
 singular = (value == 1),
 clean = clean,
 show = with\_separator(parms, clean),
 }
 local in\_unit = strip(parms[2])
 local success, in\_unit\_table = lookup(parms, in\_unit, 'no\_combination')
 if not success then return end
 in\_unit\_table.valinfo = { info }
 return true, 3, in\_unit, in\_unit\_table
end

local function wikidata\_call(parms, operation, ...)
 -- Return true, s where s is the result of a Wikidata operation,
 -- or return false, t where t is an error message table.
 local function worker(...)
 wikidata\_code = wikidata\_code or require(wikidata\_module)
 wikidata\_data = wikidata\_data or mw.loadData(wikidata\_data\_module)
 return wikidata\_code[operation](wikidata\_data, ...)
 end
 local success, status, result = pcall(worker, ...)
 if success then
 return status, result
 end
 if parms.opt\_sortable\_debug then
 -- Use debug=yes to crash if an error while accessing Wikidata.
 error('Error accessing Wikidata: ' .. status, 0)
 end
 return false, { 'cvt\_wd\_fail' }
end

local function get\_parms(parms, args)
 -- If successful, update parms and return true, unit where
 -- parms is a table of all arguments passed to the template
 -- converted to named arguments, and
 -- unit is the input unit table;
 -- or return false, t where t is an error message table.
 -- For special processing (not a convert), can also return
 -- true, wikitext where wikitext is the final result.
 -- The returned input unit table may be for a fake unit using the specified
 -- unit code as the symbol and name, and with bad\_mcode = message code table.
 -- MediaWiki removes leading and trailing whitespace from the values of
 -- named arguments. However, the values of numbered arguments include any
 -- whitespace entered in the template, and whitespace is used by some
 -- parameters (example: the numbered parameters associated with "disp=x").
 local kv\_pairs = {} -- table of input key:value pairs where key is a name; needed because cannot iterate parms and add new fields to it
 for k, v in pairs(args) do
 if type(k) == 'number' or k == 'test' then -- parameter "test" is reserved for testing and is not translated
 parms[k] = v
 else
 kv\_pairs[k] = v
 end
 end
 if parms.test == 'wikidata' then
 local ulookup = function (ucode)
 -- Use empty table for parms so it does not accumulate results when used repeatedly.
 return lookup({}, ucode, 'no\_combination')
 end
 return wikidata\_call(parms, '\_listunits', ulookup)
 end
 local success, msg = translate\_parms(parms, kv\_pairs)
 if not success then return false, msg end
 if parms.input then
 success, msg = wikidata\_call(parms, '\_adjustparameters', parms, 1)
 if not success then return false, msg end
 end
 local success, i, in\_unit, in\_unit\_table = simple\_get\_values(parms)
 if not success then
 if type(i) == 'string' and i:match('^NNN+$') then
 -- Some infoboxes have examples like **Script error: No such module "convert".** (3 or more "N").
 -- Output an empty string for these.
 return false, { 'cvt\_no\_output' }
 end
 local valinfo
 success, valinfo, i = get\_values(parms)
 if not success then return false, valinfo end
 in\_unit = strip(parms[i])
 i = i + 1
 success, in\_unit\_table = lookup(parms, in\_unit, 'no\_combination')
 if not success then
 in\_unit = in\_unit or
 if parms.opt\_ignore\_error then -- display given unit code with no error (for use with Template:Val)
 in\_unit\_table =  *-- suppress error message and prevent processing of output unit*
 end
 in\_unit\_table = setmetatable({
 symbol = in\_unit, name2 = in\_unit, utype = in\_unit,
 scale = 1, default = *, defkey =* , linkey = *,*
 bad\_mcode = in\_unit\_table }, unit\_mt)
 end
 in\_unit\_table.valinfo = valinfo
 end
 if parms.test == 'msg' then
 -- Am testing the messages produced when no output unit is specified, and
 -- the input unit has a missing or invalid default.
 -- Set two units for testing that.
 -- LATER: Remove this code.
 if in\_unit == 'chain' then
 in\_unit\_table.default = nil -- no default
 elseif in\_unit == 'rd' then
 in\_unit\_table.default = "ft!X!m" -- an invalid expression
 end
 end
 in\_unit\_table.inout = 'in' -- this is an input unit
 if not parms.range then
 local success, inext, composite\_unit = get\_composite(parms, i, in\_unit\_table)
 if not success then return false, inext end
 if composite\_unit then
 in\_unit\_table = composite\_unit
 i = inext
 end
 end
 if in\_unit\_table.builtin == 'mach' then
 -- As with old template, a number following Mach as the input unit is the altitude,
 -- and there is no way to specify an altitude for the output unit.
 -- Could put more code in this function to get any output unit and check for
 -- an altitude following that unit.
 local success, info = extract\_number(parms, parms[i], false, true)
 if success then
 i = i + 1
 in\_unit\_table.altitude = info.value
 end
 end
 local word = strip(parms[i])
 i = i + 1
 local precision, is\_bad\_precision
 local function set\_precision(text)
 local number, is\_integer = get\_number(text)
 if number then
 if is\_integer then
 precision = number
 else
 precision = text
 is\_bad\_precision = true
 end
 return true -- text was used for precision, good or bad
 end
 end
 if word and not set\_precision(word) then
 parms.out\_unit = parms.out\_unit or word
 if set\_precision(strip(parms[i])) then
 i = i + 1
 end
 end
 if parms.opt\_adj\_mid then
 word = parms[i]
 i = i + 1
 if word then -- mid-text words
 if word:sub(1, 1) == '-' then
 parms.mid = word
 else
 parms.mid = ' ' .. word
 end
 end
 end
 if parms.opt\_one\_preunit then
 parms[parms.opt\_flip and 'preunit2' or 'preunit1'] = preunits(1, parms[i])
 i = i + 1
 end
 if parms.disp == 'x' then
 -- Following is reasonably compatible with the old template.
 local first = parms[i] or
 local second = parms[i+1] or
 i = i + 2
 if strip(first) ==  *then -- user can enter ' ' rather than ' ' to avoid the default*
 first = ' [ ' .. first
 second = ' ]' .. second
 end
 parms.joins = { first, second }
 elseif parms.opt\_two\_preunits then
 local p1, p2 = preunits(2, parms[i], parms[i+1])
 i = i + 2
 if parms.preunit1 then
 -- To simplify documentation, allow unlikely use of adj=pre with disp=preunit
 -- (however, an output unit must be specified with adj=pre and with disp=preunit).
 parms.preunit1 = parms.preunit1 .. p1
 parms.preunit2 = p2
 else
 parms.preunit1, parms.preunit2 = p1, p2
 end
 end
 if precision == nil then
 if set\_precision(strip(parms[i])) then
 i = i + 1
 end
 end
 if is\_bad\_precision then
 add\_warning(parms, 1, 'cvt\_bad\_prec', precision)
 else
 parms.precision = precision
 end
 for j = i, i + 3 do
 local parm = parms[j] -- warn if find a non-empty extraneous parameter
 if parm and parm:match('%S') then
 add\_warning(parms, 1, 'cvt\_unknown\_option', parm)
 break
 end
 end
 return true, in\_unit\_table
end

local function record\_default\_precision(parms, out\_current, precision)
 -- If necessary, adjust parameters and return a possibly adjusted precision.
 -- When converting a range of values where a default precision is required,
 -- that default is calculated for each value because the result sometimes
 -- depends on the precise input and output values. This function may cause
 -- the entire convert process to be repeated in order to ensure that the
 -- same default precision is used for each individual convert.
 -- If that were not done, a range like 1000 to 1000.4 may give poor results
 -- because the first output could be heavily rounded, while the second is not.
 -- For range 1000.4 to 1000, this function can give the second convert the
 -- same default precision that was used for the first.
 if not parms.opt\_round\_each then
 local maxdef = out\_current.max\_default\_precision
 if maxdef then
 if maxdef < precision then
 parms.do\_convert\_again = true
 out\_current.max\_default\_precision = precision
 else
 precision = out\_current.max\_default\_precision
 end
 else
 out\_current.max\_default\_precision = precision
 end
 end
 return precision
end

local function default\_precision(parms, invalue, inclean, denominator, outvalue, in\_current, out\_current, extra)
 -- Return a default value for precision (an integer like 2, 0, -2).
 -- If denominator is not nil, it is the value of the denominator in inclean.
 -- Code follows procedures used in old template.
 local fudge = 1e-14 -- Template:Order of magnitude adds this, so we do too
 local prec, minprec, adjust
 local subunit\_ignore\_trailing\_zero
 local composite = in\_current.composite
 if composite then
 if composite[#composite].exception == 'subunit\_more\_precision' then
 end
 end
 if denominator and denominator > 0 then
 prec = math.max(log10(denominator), 1)
 else
 -- Count digits after decimal mark, handling cases like '12.345e6'.
 local exponent
 local integer, dot, decimals, expstr = inclean:match('^(%d\*)(%.?)(%d\*)(.\*)')
 local e = expstr:sub(1, 1)
 if e == 'e' or e == 'E' then
 exponent = tonumber(expstr:sub(2))
 end
 if dot ==  *then*
 prec = subunit\_ignore\_trailing\_zero and 0 or -integer:match('0\*$'):len()
 else
 prec = #decimals
 end
 if exponent then
 -- So '1230' and '1.23e3' both give prec = -1, and '0.00123' and '1.23e-3' give 5.
 prec = prec - exponent
 end
 end
 if in\_current.istemperature and out\_current.istemperature then
 -- Converting between common temperatures (°C, °F, °R, K); not keVT.
 -- Kelvin value can be almost zero, or small but negative due to precision problems.
 -- Also, an input value like -300 C (below absolute zero) gives negative kelvins.
 -- Calculate minimum precision from absolute value.
 adjust = 0
 local kelvin = abs((invalue - in\_current.offset) \* in\_current.scale)
 if kelvin < 1e-8 then -- assume nonzero due to input or calculation precision problem
 minprec = 2
 else
 minprec = 2 - floor(log10(kelvin) + fudge) -- 3 sigfigs in kelvin
 end
 else
 if invalue == 0 or outvalue <= 0 then
 -- We are never called with a negative outvalue, but it might be zero.
 -- This is special-cased to avoid calculation exceptions.
 return record\_default\_precision(parms, out\_current, 0)
 end
 if out\_current.exception == 'integer\_more\_precision' and floor(invalue) == invalue then
 -- With certain output units that sometimes give poor results
 -- with default rounding, use more precision when the input
 -- value is equal to an integer. An example of a poor result
 -- is when input 50 gives a smaller output than input 49.5.
 -- Experiment shows this helps, but it does not eliminate all
 -- surprises because it is not clear whether "50" should be
 -- interpreted as "from 45 to 55" or "from 49.5 to 50.5".
 adjust = -log10(in\_current.scale)
 elseif subunit\_more\_precision then
 -- Conversion like "**Script error: No such module "convert".**" (where subunit is "in")
 -- has a non-standard adjust value, to give more output precision.
 adjust = log10(out\_current.scale) + 2
 else
 adjust = log10(abs(invalue / outvalue))
 end
 adjust = adjust + log10(2)
 -- Ensure that the output has at least two significant figures.
 minprec = 1 - floor(log10(outvalue) + fudge)
 end
 if extra then
 adjust = extra.adjust or adjust
 minprec = extra.minprec or minprec
 end
 return record\_default\_precision(parms, out\_current, math.max(floor(prec + adjust), minprec))
end

local function convert(parms, invalue, info, in\_current, out\_current)
 -- Convert given input value from one unit to another.
 -- Return output\_value (a number) if a simple convert, or
 -- return f, t where
 -- f = true, t = table of information with results, or
 -- f = false, t = error message table.
 local inscale = in\_current.scale
 local outscale = out\_current.scale
 if not in\_current.iscomplex and not out\_current.iscomplex then
 return invalue \* (inscale / outscale) -- minimize overhead for most common case
 end
 if in\_current.invert or out\_current.invert then
 -- Inverted units, such as inverse length, inverse time, or
 -- fuel efficiency. Built-in units do not have invert set.
 if (in\_current.invert or 1) \* (out\_current.invert or 1) < 0 then
 return 1 / (invalue \* inscale \* outscale)
 end
 return invalue \* (inscale / outscale)
 elseif in\_current.offset then
 -- Temperature (there are no built-ins for this type of unit).
 if info.is\_change then
 return invalue \* (inscale / outscale)
 end
 return (invalue - in\_current.offset) \* (inscale / outscale) + out\_current.offset
 else
 -- Built-in unit.
 local in\_builtin = in\_current.builtin
 local out\_builtin = out\_current.builtin
 if in\_builtin and out\_builtin then
 if in\_builtin == out\_builtin then
 return invalue
 end
 -- There are no cases (yet) where need to convert from one
 -- built-in unit to another, so this should never occur.
 return false, { 'cvt\_bug\_convert' }
 end
 if in\_builtin == 'mach' or out\_builtin == 'mach' then
 local adjust
 if in\_builtin == 'mach' then
 inscale = speed\_of\_sound(in\_current.altitude)
 adjust = outscale / 0.1
 else
 outscale = speed\_of\_sound(out\_current.altitude)
 adjust = 0.1 / inscale
 end
 return true, {
 outvalue = invalue \* (inscale / outscale),
 adjust = log10(adjust) + log10(2),
 }
 elseif in\_builtin == 'hand' then
 -- 1 hand = 4 inches; 1.2 hands = 6 inches.
 -- Decimals of a hand are only defined for the first digit, and
 -- the first fractional digit should be a number of inches (1, 2 or 3).
 -- However, this code interprets the entire fractional part as the number
 -- of inches / 10 (so 1.75 inches would be 0.175 hands).
 -- A value like 12.3 hands is exactly 12\*4 + 3 inches; base default precision on that.
 local integer, fracpart = math.modf(invalue)
 local inch\_value = 4 \* integer + 10 \* fracpart -- equivalent number of inches
 local factor = inscale / outscale
 if factor == 4 then
 -- Am converting to inches: show exact result, and use "inches" not "in" by default.
 if parms.abbr\_org == nil then
 out\_current.usename = true
 end
 local show = format('%g', abs(inch\_value)) -- show and clean are unsigned
 if not show:find('e', 1, true) then
 return true, {
 invalue = inch\_value,
 outvalue = inch\_value,
 clean = show,
 show = show,
 }
 end
 end
 local outvalue = (integer + 2.5 \* fracpart) \* factor
 local fracstr = info.clean:match('%.(.\*)') or
 local fmt
 if fracstr ==  *then*
 fmt = '%.0f'
 else
 fmt = '%.' .. format('%d', #fracstr - 1) .. 'f'
 end
 return true, {
 invalue = inch\_value,
 clean = format(fmt, inch\_value),
 outvalue = outvalue,
 minprec = 0,
 }
 end
 end
 return false, { 'cvt\_bug\_convert' } -- should never occur
end

local function user\_style(parms, i)
 -- Return text for a user-specified style for a table cell, or  *if none,*
 -- given i = 1 (input style) or 2 (output style).
 local style = parms[(i == 1) and 'stylein' or 'styleout']
 if style then
 style = style:gsub('"', *)*
 if style ~=  *then*
 if style:sub(-1) ~= ';' then
 style = style .. ';'
 end
 return style
 end
 end
 return
end

local function make\_table\_or\_sort(parms, invalue, info, in\_current, scaled\_top)
 -- Set options to handle output for a table or a sort key, or both.
 -- The text sort key is based on the value resulting from converting
 -- the input to a fake base unit with scale = 1, and other properties
 -- required for a conversion derived from the input unit.
 -- For other modules, return the sort key in a hidden span element, and
 -- the scaled value used to generate the sort key.
 -- If scaled\_top is set, it is the scaled value of the numerator of a per unit
 -- to be combined with this unit (the denominator) to make the sort key.
 -- Scaling only works with units that convert with a factor (not temperature).
 local sortkey, scaled\_value
 if parms.opt\_sortable\_on then
 local base = { -- a fake unit with enough fields for a valid convert
 scale = 1,
 invert = in\_current.invert and 1,
 iscomplex = in\_current.iscomplex,
 offset = in\_current.offset and 0,
 }
 local outvalue, extra = convert(parms, invalue, info, in\_current, base)
 if extra then
 outvalue = extra.outvalue
 end
 if in\_current.istemperature then
 -- Have converted to kelvin; assume numbers close to zero have a
 -- rounding error and should be zero.
 if abs(outvalue) < 1e-12 then
 outvalue = 0
 end
 end
 if scaled\_top and outvalue ~= 0 then
 outvalue = scaled\_top / outvalue
 end
 scaled\_value = outvalue
 if not valid\_number(outvalue) then
 if outvalue < 0 then
 sortkey = '1000000000000000000'
 else
 sortkey = '9000000000000000000'
 end
 elseif outvalue == 0 then
 sortkey = '5000000000000000000'
 else
 local mag = floor(log10(abs(outvalue)) + 1e-14)
 local prefix
 if outvalue > 0 then
 prefix = 7000 + mag
 else
 prefix = 2999 - mag
 outvalue = outvalue + 10^(mag+1)
 end
 sortkey = format('%d', prefix) .. format('%015.0f', floor(outvalue \* 10^(14-mag)))
 end
 end
 local sortspan
 if sortkey and (parms.opt\_sortable\_debug or not parms.table\_align) then
 sortspan = parms.opt\_sortable\_debug and
 '' .. sortkey .. '♠' or
 '' .. sortkey .. '♠'
 parms.join\_before = sortspan
 end
 if parms.table\_align then
 local style = 'style="text-align:' .. parms.table\_align .. ';'
 local sort = sortkey and ' data-sort-value="' .. sortkey .. '"' or
 local joins = {}
 for i = 1, 2 do
 joins[i] = (i == 1 and  *or '\n|') .. style .. user\_style(parms, i) .. '"' .. sort .. '|'*
 end
 parms.table\_joins = joins
 end
 return sortspan, scaled\_value
end

local cvt\_to\_hand

local function cvtround(parms, info, in\_current, out\_current)
 -- Return true, t where t is a table with the conversion results; fields:
 -- show = rounded, formatted string with the result of converting value in info,
 -- using the rounding specified in parms.
 -- singular = true if result (after rounding and ignoring any negative sign)
 -- is "1", or like "1.00", or is a fraction with value < 1;
 -- (and more fields shown below, and a calculated 'absvalue' field).
 -- or return false, t where t is an error message table.
 -- Input info.clean uses en digits (it has been translated, if necessary).
 -- Output show uses en or non-en digits as appropriate, or can be spelled.
 if out\_current.builtin == 'hand' then
 return cvt\_to\_hand(parms, info, in\_current, out\_current)
 end
 local invalue = in\_current.builtin == 'hand' and info.altvalue or info.value
 local outvalue, extra = convert(parms, invalue, info, in\_current, out\_current)
 if parms.need\_table\_or\_sort then
 parms.need\_table\_or\_sort = nil -- process using first input value only
 make\_table\_or\_sort(parms, invalue, info, in\_current)
 end
 if extra then
 if not outvalue then return false, extra end
 invalue = extra.invalue or invalue
 outvalue = extra.outvalue
 end
 if not valid\_number(outvalue) then
 return false, { 'cvt\_invalid\_num' }
 end
 local isnegative
 if outvalue < 0 then
 isnegative = true
 outvalue = -outvalue
 end
 local precision, show, exponent
 local denominator = out\_current.frac
 if denominator then
 show = fraction\_table(outvalue, denominator)
 else
 precision = parms.precision
 if not precision then
 if parms.sigfig then
 show, exponent = make\_sigfig(outvalue, parms.sigfig)
 elseif parms.opt\_round then
 local n = parms.opt\_round
 if n == 0.5 then
 local integer, fracpart = math.modf(floor(2 \* outvalue + 0.5) / 2)
 if fracpart == 0 then
 show = format('%.0f', integer)
 else
 show = format('%.1f', integer + fracpart)
 end
 else
 show = format('%.0f', floor((outvalue / n) + 0.5) \* n)
 end
 else
 local inclean = info.clean
 if extra then
 inclean = extra.clean or inclean
 show = extra.show
 end
 if not show then
 precision = default\_precision(parms, invalue, inclean, info.denominator, outvalue, in\_current, out\_current, extra)
 end
 end
 end
 end
 if precision then
 if precision >= 0 then
 local fudge
 if precision <= 8 then
 -- Add a fudge to handle common cases of bad rounding due to inability
 -- to precisely represent some values. This makes the following work:
 -- **Script error: No such module "convert".** and **Script error: No such module "convert".**.
 -- Old template uses #expr round, which invokes PHP round().
 -- LATER: Investigate how PHP round() works.
 fudge = 2e-14
 else
 fudge = 0
 end
 local fmt = '%.' .. format('%d', precision) .. 'f'
 local success
 success, show = pcall(format, fmt, outvalue + fudge)
 if not success then
 return false, { 'cvt\_big\_prec', tostring(precision) }
 end
 else
 precision = -precision -- #digits to zero (in addition to any digits after dot)
 local shift = 10 ^ precision
 show = format('%.0f', outvalue/shift)
 if show ~= '0' then
 exponent = #show + precision
 end
 end
 end
 local t = format\_number(parms, show, exponent, isnegative)
 if type(show) == 'string' then
 -- Set singular using match because on some systems 0.99999999999999999 is 1.0.
 if exponent then
 t.singular = (exponent == 1 and show:match('^10\*$'))
 else
 t.singular = (show == '1' or show:match('^1%.0\*$'))
 end
 else
 t.fraction\_table = show
 t.singular = (outvalue <= 1) -- cannot have 'fraction == 1', but if it were possible it would be singular
 end
 t.raw\_absvalue = outvalue -- absolute value before rounding
 return true, setmetatable(t, {
 \_\_index = function (self, key)
 if key == 'absvalue' then
 -- Calculate absolute value after rounding, if needed.
 local clean, exponent = rawget(self, 'clean'), rawget(self, 'exponent')
 local value = tonumber(clean) -- absolute value (any negative sign has been ignored)
 if exponent then
 value = value \* 10^exponent
 end
 rawset(self, key, value)
 return value
 end
 end })
end

function cvt\_to\_hand(parms, info, in\_current, out\_current)
 -- Convert input to hands, inches.
 -- Return true, t where t is a table with the conversion results;
 -- or return false, t where t is an error message table.
 if parms.abbr\_org == nil then
 out\_current.usename = true -- default is to show name not symbol
 end
 local precision = parms.precision
 local frac = out\_current.frac
 if not frac and precision and precision > 1 then
 frac = (precision == 2) and 2 or 4
 end
 local out\_next = out\_current.out\_next
 if out\_next then
 -- Use magic knowledge to determine whether the next unit is inches without requiring i18n.
 -- The following ensures that when the output combination "hand in" is used, the inches
 -- value is rounded to match the hands value. Also, displaying say "61½" instead of 61.5
 -- is better as 61.5 implies the value is not 61.4.
 if out\_next.exception == 'subunit\_more\_precision' then
 out\_next.frac = frac
 end
 end
 -- Convert to inches; calculate hands from that.
 local dummy\_unit\_table = { scale = out\_current.scale / 4, frac = frac }
 local success, outinfo = cvtround(parms, info, in\_current, dummy\_unit\_table)
 if not success then return false, outinfo end
 local tfrac = outinfo.fraction\_table
 local inches = outinfo.raw\_absvalue
 if tfrac then
 inches = floor(inches) -- integer part only; fraction added later
 else
 inches = floor(inches + 0.5) -- a hands measurement never shows decimals of an inch
 end
 local hands, inches = divide(inches, 4)
 outinfo.absvalue = hands + inches/4 -- supposed to be the absolute rounded value, but this is close enough
 local inchstr = tostring(inches) -- '0', '1', '2' or '3'
 if precision and precision <= 0 then -- using negative or 0 for precision rounds to nearest hand
 hands = floor(outinfo.raw\_absvalue/4 + 0.5)
 inchstr =
 elseif tfrac then
 -- Always show an integer before fraction (like "15.0½") because "15½" means 15-and-a-half hands.
 inchstr = numdot .. format\_fraction(parms, 'out', false, inchstr, tfrac.numstr, tfrac.denstr)
 else
 inchstr = numdot .. from\_en(inchstr)
 end
 outinfo.show = outinfo.sign .. with\_separator(parms, format('%.0f', hands)) .. inchstr
 return true, outinfo
end

local function evaluate\_condition(value, condition)
 -- Return true or false from applying a conditional expression to value,
 -- or throw an error if invalid.
 -- A very limited set of expressions is supported:
 -- v < 9
 -- v \* 9 < 9
 -- where
 -- 'v' is replaced with value
 -- 9 is any number (as defined by Lua tonumber)
 -- only en digits are accepted
 -- '<' can also be '<=' or '>' or '>='
 -- In addition, the following form is supported:
 -- LHS and RHS
 -- where
 -- LHS, RHS = any of above expressions.
 local function compare(value, text)
 local arithop, factor, compop, limit = text:match('^%s\*v%s\*([\*]?)(.-)([<>]=?)(.\*)$')
 if arithop == nil then
 error('Invalid default expression', 0)
 elseif arithop == '\*' then
 factor = tonumber(factor)
 if factor == nil then
 error('Invalid default expression', 0)
 end
 value = value \* factor
 end
 limit = tonumber(limit)
 if limit == nil then
 error('Invalid default expression', 0)
 end
 if compop == '<' then
 return value < limit
 elseif compop == '<=' then
 return value <= limit
 elseif compop == '>' then
 return value > limit
 elseif compop == '>=' then
 return value >= limit
 end
 error('Invalid default expression', 0) -- should not occur
 end
 local lhs, rhs = condition:match('^(.-%W)and(%W.\*)')
 if lhs == nil then
 return compare(value, condition)
 end
 return compare(value, lhs) and compare(value, rhs)
end

local function get\_default(value, unit\_table)
 -- Return true, s where s = name of unit's default output unit,
 -- or return false, t where t is an error message table.
 -- Some units have a default that depends on the input value
 -- (the first value if a range of values is used).
 -- If '!' is in the default, the first bang-delimited field is an
 -- expression that uses 'v' to represent the input value.
 -- Example: 'v < 120 ! small ! big ! suffix' (suffix is optional)
 -- evaluates 'v < 120' as a boolean with result
 -- 'smallsuffix' if (value < 120), or 'bigsuffix' otherwise.
 -- Input must use en digits and '.' decimal mark.
 local default = data\_code.default\_exceptions[unit\_table.defkey or unit\_table.symbol] or unit\_table.default
 if not default then
 local per = unit\_table.per
 if per then
 local function a\_default(v, u)
 local success, ucode = get\_default(v, u)
 if not success then
 return '?' -- an unlikely error has occurred; will cause lookup of default to fail
 end
 -- Attempt to use only the first unit if a combination or output multiple.
 -- This is not bulletproof but should work for most cases.
 -- Where it does not work, the convert will need to specify the wanted output unit.
 local t = all\_units[ucode]
 if t then
 local combo = t.combination
 if combo then
 -- For a multiple like ftin, the "first" unit (ft) is last in the combination.
 local i = t.multiple and table\_len(combo) or 1
 ucode = combo[i]
 end
 else
 -- Try for an automatically generated combination.
 local item = ucode:match('^(.-)%+') or ucode:match('^(%S+)%s')
 if all\_units[item] then
 return item
 end
 end
 return ucode
 end
 local unit1, unit2 = per[1], per[2]
 local def1 = (unit1 and a\_default(value, unit1) or unit\_table.vprefix or *)*
 local def2 = a\_default(1, unit2) -- 1 because per unit of denominator
 return true, def1 .. '/' .. def2
 end
 return false, { 'cvt\_no\_default', unit\_table.symbol }
 end
 if default:find('!', 1, true) == nil then
 return true, default
 end
 local t = split(default, '!')
 if #t == 3 or #t == 4 then
 local success, result = pcall(evaluate\_condition, value, t[1])
 if success then
 default = result and t[2] or t[3]
 if #t == 4 then
 default = default .. t[4]
 end
 return true, default
 end
 end
 return false, { 'cvt\_bad\_default', unit\_table.symbol }
end

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

local function unlink(unit\_table)
 -- Forget that the given unit has previously been linked (if it has).
 -- That is needed when processing a range of inputs or outputs when an id
 -- for the first range value may have been evaluated, but only an id for
 -- the last value is displayed, and that id may need to be linked.
 linked\_pages[unit\_table.unitcode or unit\_table] = nil
end

local function make\_link(link, id, unit\_table)
 -- Return wikilink "id", possibly abbreviated as in examples:
 -- mile --> mile
 -- miles --> miles
 -- However, just id is returned if:
 -- \* no link given (so caller does not need to check if a link was defined); or
 -- \* link has previously been used during the current convert (to avoid overlinking).
 local link\_key
 if unit\_table then
 link\_key = unit\_table.unitcode or unit\_table
 else
 link\_key = link
 end
 if not link or link ==  *or linked\_pages[link\_key] then*
 return id
 end
 linked\_pages[link\_key] = true
 -- Following only works for language en, but it should be safe on other wikis,
 -- and overhead of doing it generally does not seem worthwhile.
 local l = link:sub(1, 1):lower() .. link:sub(2)
 if link == id or l == id then
 return '' .. id .. ''
 elseif link .. 's' == id or l .. 's' == id then
 return '' .. id:sub(1, -2) .. 's'
 else
 return '' .. id .. ''
 end
end

local function variable\_name(clean, unit\_table)
 -- For slwiki, a unit name depends on the value.
 -- Parameter clean is the unsigned rounded value in en digits, as a string.
 -- Value Source Example for "m"
 -- integer 1: name1 meter (also is the name of the unit)
 -- integer 2: var{1} metra
 -- integer 3 and 4: var{2} metri
 -- integer else: var{3} metrov (0 and 5 or more)
 -- real/fraction: var{4} metra
 -- var{i} means the i'th field in unit\_table.varname if it exists and has
 -- an i'th field, otherwise name2.
 -- Fields are separated with "!" and are not empty.
 -- A field for a unit using an SI prefix has the prefix name inserted,
 -- replacing '#' if found, or before the field otherwise.
 local vname
 if clean == '1' then
 vname = unit\_table.name1
 elseif unit\_table.varname then
 local i
 if clean == '2' then
 i = 1
 elseif clean == '3' or clean == '4' then
 i = 2
 elseif clean:find('.', 1, true) then
 i = 4
 else
 i = 3
 end
 if i > 1 and varname == 'pl' then
 i = i - 1
 end
 vname = split(unit\_table.varname, '!')[i]
 end
 if vname then
 local si\_name = rawget(unit\_table, 'si\_name') or
 local pos = vname:find('#', 1, true)
 if pos then
 vname = vname:sub(1, pos - 1) .. si\_name .. vname:sub(pos + 1)
 else
 vname = si\_name .. vname
 end
 return vname
 end
 return unit\_table.name2
end

local function linked\_id(parms, unit\_table, key\_id, want\_link, clean)
 -- Return final unit id (symbol or name), optionally with a wikilink,
 -- and update unit\_table.sep if required.
 -- key\_id is one of: 'symbol', 'sym\_us', 'name1', 'name1\_us', 'name2', 'name2\_us'.
 local abbr\_on = (key\_id == 'symbol' or key\_id == 'sym\_us')
 if abbr\_on and want\_link then
 local symlink = rawget(unit\_table, 'symlink')
 if symlink then
 return symlink -- for exceptions that have the linked symbol built-in
 end
 end
 local multiplier = rawget(unit\_table, 'multiplier')
 local per = unit\_table.per
 if per then
 local paren1, paren2 = *,*  -- possible parentheses around bottom unit
 local unit1 = per[1] -- top unit\_table, or nil
 local unit2 = per[2] -- bottom unit\_table
 if abbr\_on then
 if not unit1 then
 unit\_table.sep =  *-- no separator in "$2/acre"*
 end
 if not want\_link then
 local symbol = unit\_table.symbol\_raw
 if symbol then
 return symbol -- for exceptions that have the symbol built-in
 end
 end
 if (unit2.symbol):find('⋅', 1, true) then
 paren1, paren2 = '(', ')'
 end
 end
 local key\_id2 -- unit2 is always singular
 if key\_id == 'name2' then
 key\_id2 = 'name1'
 elseif key\_id == 'name2\_us' then
 key\_id2 = 'name1\_us'
 else
 key\_id2 = key\_id
 end
 local result
 if abbr\_on then
 result = '/'
 elseif omitsep then
 result = per\_word
 elseif unit1 then
 result = ' ' .. per\_word .. ' '
 else
 result = per\_word .. ' '
 end
 if want\_link and unit\_table.link then
 if abbr\_on or not varname then
 result = (unit1 and linked\_id(parms, unit1, key\_id, false, clean) or *) .. result .. linked\_id(parms, unit2, key\_id2, false, '1')*
 else
 result = (unit1 and variable\_name(clean, unit1) or *) .. result .. variable\_name('1', unit2)*
 end
 if omit\_separator(result) then
 unit\_table.sep =
 end
 return make\_link(unit\_table.link, result, unit\_table)
 end
 if unit1 then
 result = linked\_id(parms, unit1, key\_id, want\_link, clean) .. result
 if unit1.sep then
 unit\_table.sep = unit1.sep
 end
 elseif omitsep then
 unit\_table.sep =
 end
 return result .. paren1 .. linked\_id(parms, unit2, key\_id2, want\_link, '1') .. paren2
 end
 if multiplier then
 -- A multiplier (like "100" in "100km") forces the unit to be plural.
 multiplier = from\_en(multiplier)
 if not omitsep then
 multiplier = multiplier .. (abbr\_on and ' ' or ' ')
 end
 if not abbr\_on then
 if key\_id == 'name1' then
 key\_id = 'name2'
 elseif key\_id == 'name1\_us' then
 key\_id = 'name2\_us'
 end
 end
 else
 multiplier =
 end
 local id = unit\_table.fixed\_name or ((varname and not abbr\_on) and variable\_name(clean, unit\_table) or unit\_table[key\_id])
 if omit\_separator(id) then
 unit\_table.sep =
 end
 if want\_link then
 local link = data\_code.link\_exceptions[unit\_table.linkey or unit\_table.symbol] or unit\_table.link
 if link then
 local before =
 local i = unit\_table.customary
 if i == 1 and parms.opt\_sp\_us then
 i = 2 -- show "U.S." not "US"
 end
 if i == 3 and abbr\_on then
 i = 4 -- abbreviate "imperial" to "imp"
 end
 local customary = text\_code.customary\_units[i]
 if customary then
 -- LATER: This works for language en only, but it's esoteric so ignore for now.
 local pertext
 if id:sub(1, 1) == '/' then
 -- Want unit "/USgal" to display as "/U.S. gal", not "U.S. /gal".
 pertext = '/'
 id = id:sub(2)
 elseif id:sub(1, 4) == 'per ' then
 -- Similarly want "per U.S. gallon", not "U.S. per gallon" (but in practice this is unlikely to be used).
 pertext = 'per '
 id = id:sub(5)
 else
 pertext =
 end
 -- Omit any "US"/"U.S."/"imp"/"imperial" from start of id since that will be inserted.
 local removes = (i < 3) and { 'US ', 'US ', 'U.S. ', 'U.S. ' } or { 'imp ', 'imp ', 'imperial ' }
 for \_, prefix in ipairs(removes) do
 local plen = #prefix
 if id:sub(1, plen) == prefix then
 id = id:sub(plen + 1)
 break
 end
 end
 before = pertext .. make\_link(customary.link, customary[1]) .. ' '
 end
 id = before .. make\_link(link, id, unit\_table)
 end
 end
 return multiplier .. id
end

local function make\_id(parms, which, unit\_table)
 -- Return id, f where
 -- id = unit name or symbol, possibly modified
 -- f = true if id is a name, or false if id is a symbol
 -- using the value for index 'which', and for 'in' or 'out' (unit\_table.inout).
 -- Result is  *if no symbol/name is to be used.*
 -- In addition, set unit\_table.sep = ' ' or ' ' or
 -- (the separator that caller will normally insert before the id).
 if parms.opt\_values then
 unit\_table.sep =
 return
 end
 local inout = unit\_table.inout
 local info = unit\_table.valinfo[which]
 local abbr\_org = parms.abbr\_org
 local adjectival = parms.opt\_adjectival
 local lk = parms.lk
 local want\_link = (lk == 'on' or lk == inout)
 local usename = unit\_table.usename
 local singular = info.singular
 local want\_name
 if usename then
 want\_name = true
 else
 if abbr\_org == nil then
 if parms.wantname then
 want\_name = true
 end
 if unit\_table.usesymbol then
 want\_name = false
 end
 end
 if want\_name == nil then
 local abbr = parms.abbr
 if abbr == 'on' or abbr == inout or (abbr == 'mos' and inout == 'out') then
 want\_name = false
 else
 want\_name = true
 end
 end
 end
 local key
 if want\_name then
 if lk == nil and unit\_table.builtin == 'hand' then
 want\_link = true
 end
 if parms.opt\_use\_nbsp then
 unit\_table.sep = ' '
 else
 unit\_table.sep = ' '
 end
 if parms.opt\_singular then
 local value
 if inout == 'in' then
 value = info.value
 else
 value = info.absvalue
 end
 if value then -- some unusual units do not always set value field
 value = abs(value)
 singular = (0 < value and value < 1.0001)
 end
 end
 if unit\_table.engscale then
 -- engscale: so "|1|e3kg" gives "1 thousand kilograms" (plural)
 singular = false
 end
 key = (adjectival or singular) and 'name1' or 'name2'
 if parms.opt\_sp\_us then
 key = key .. '\_us'
 end
 else
 if unit\_table.builtin == 'hand' then
 if parms.opt\_hand\_hh then
 unit\_table.symbol = 'hh' -- LATER: might want i18n applied to this
 end
 end
 unit\_table.sep = ' '
 key = parms.opt\_sp\_us and 'sym\_us' or 'symbol'
 end
 return linked\_id(parms, unit\_table, key, want\_link, info.clean), want\_name
end

local function decorate\_value(parms, unit\_table, which, number\_word)
 -- If needed, update unit\_table so values will be shown with extra information.
 -- For consistency with the old template (but different from fmtpower),
 -- the style to display powers of 10 includes "display:none" to allow some
 -- browsers to copy, for example, "10³" as "10^3", rather than as "103".
 local info
 local engscale = unit\_table.engscale
 local prefix = unit\_table.vprefix
 if engscale or prefix then
 info = unit\_table.valinfo[which]
 if info.decorated then
 return -- do not redecorate if repeating convert
 end
 info.decorated = true
 if engscale then
 local inout = unit\_table.inout
 local abbr = parms.abbr
 if (abbr == 'on' or abbr == inout) and not parms.number\_word then
 info.show = info.show ..
 '×' ..
 from\_en('10') ..
 '~~^~~' ..
 from\_en(tostring(engscale.exponent)) .. ''
 elseif number\_word then
 local number\_id
 local lk = parms.lk
 if lk == 'on' or lk == inout then
 number\_id = make\_link(engscale.link, engscale[1])
 else
 number\_id = engscale[1]
 end
 -- WP:NUMERAL recommends " " in values like "12 million".
 info.show = info.show .. (parms.opt\_adjectival and '-' or ' ') .. number\_id
 end
 end
 if prefix then
 info.show = prefix .. info.show
 end
 end
end

local function process\_input(parms, in\_current)
 -- Processing required once per conversion.
 -- Return block of text to represent input (value/unit).
 if parms.opt\_output\_only or parms.opt\_output\_number\_only or parms.opt\_output\_unit\_only then
 parms.joins = { *,*  }
 return
 end
 local first\_unit
 local composite = in\_current.composite -- nil or table of units
 if composite then
 first\_unit = composite[1]
 else
 first\_unit = in\_current
 end
 local id1, want\_name = make\_id(parms, 1, first\_unit)
 local sep = first\_unit.sep -- separator between value and unit, set by make\_id
 local preunit = parms.preunit1
 if preunit then
 sep =  *-- any separator is included in preunit*
 else
 preunit =
 end
 if parms.opt\_input\_unit\_only then
 parms.joins = { *,*  }
 if composite then
 local parts = { id1 }
 for i, unit in ipairs(composite) do
 if i > 1 then
 table.insert(parts, (make\_id(parms, 1, unit)))
 end
 end
 id1 = table.concat(parts, ' ')
 end
 if want\_name and parms.opt\_adjectival then
 return preunit .. hyphenated(id1)
 end
 return preunit .. id1
 end
 if parms.opt\_also\_symbol and not composite and not parms.opt\_flip then
 local join1 = parms.joins[1]
 if join1 == ' (' or join1 == ' [' then
 parms.joins = { ' [' .. first\_unit[parms.opt\_sp\_us and 'sym\_us' or 'symbol'] .. ']' .. join1 , parms.joins[2] }
 end
 end
 if in\_current.builtin == 'mach' and first\_unit.sep ~=  *then --*  means omitsep with non-enwiki name
 local prefix = id1 .. ' '
 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) .. ' '
 result = range\_text(range[1], want\_name, parms, result, prefix2 .. valinfo[2].show, 'in')
 end
 return preunit .. result
 end
 if composite then
 -- Simplify: assume there is no range, and no decoration.
 local mid = (not parms.opt\_flip) and parms.mid or
 local sep1 = ' '
 local sep2 = ' '
 if parms.opt\_adjectival and want\_name then
 sep1 = '-'
 sep2 = '-'
 end
 if omitsep and sep ==  *then*
 -- Testing the id of the most significant unit should be sufficient.
 sep1 =
 sep2 =
 end
 local parts = { first\_unit.valinfo[1].show .. sep1 .. id1 }
 for i, unit in ipairs(composite) do
 if i > 1 then
 table.insert(parts, unit.valinfo[1].show .. sep1 .. (make\_id(parms, 1, unit)))
 end
 end
 return table.concat(parts, sep2) .. mid
 end
 local add\_unit = (parms.abbr == 'mos') or
 parms[parms.opt\_flip and 'out\_range\_x' or 'in\_range\_x'] or
 (not want\_name and parms.abbr\_range\_x)
 local range = parms.range
 if range and not add\_unit then
 unlink(first\_unit)
 end
 local id = range and make\_id(parms, range.n + 1, first\_unit) or id1
 local extra, was\_hyphenated = hyphenated\_maybe(parms, want\_name, sep, id, 'in')
 if was\_hyphenated then
 add\_unit = false
 end
 local result
 local valinfo = first\_unit.valinfo
 if range then
 for i = 0, range.n do
 local number\_word
 if i == range.n then
 add\_unit = false
 number\_word = true
 end
 decorate\_value(parms, first\_unit, i+1, number\_word)
 local show = valinfo[i+1].show
 if add\_unit then
 show = show .. first\_unit.sep .. (i == 0 and id1 or make\_id(parms, i+1, first\_unit))
 end
 if i == 0 then
 result = show
 else
 result = range\_text(range[i], want\_name, parms, result, show, 'in')
 end
 end
 else
 decorate\_value(parms, first\_unit, 1, true)
 result = valinfo[1].show
 end
 return result .. preunit .. extra
end

local function process\_one\_output(parms, out\_current)
 -- Processing required for each output unit.
 -- Return block of text to represent output (value/unit).
 local inout = out\_current.inout -- normally 'out' but can be 'in' for order=out
 local id1, want\_name = make\_id(parms, 1, out\_current)
 local sep = out\_current.sep -- set by make\_id
 local preunit = parms.preunit2
 if preunit then
 sep =  *-- any separator is included in preunit*
 else
 preunit =
 end
 if parms.opt\_output\_unit\_only then
 if want\_name and parms.opt\_adjectival then
 return preunit .. hyphenated(id1)
 end
 return preunit .. id1
 end
 if out\_current.builtin == 'mach' and out\_current.sep ~=  *then --*  means omitsep with non-enwiki name
 local prefix = id1 .. ' '
 local range = parms.range
 local valinfo = out\_current.valinfo
 local result = prefix .. valinfo[1].show
 if range then
 -- For simplicity and because more not needed, handle one range item only.
 result = range\_text(range[1], want\_name, parms, result, prefix .. valinfo[2].show, inout)
 end
 return preunit .. result
 end
 local add\_unit = (parms[parms.opt\_flip and 'in\_range\_x' or 'out\_range\_x'] or
 (not want\_name and parms.abbr\_range\_x)) and
 not parms.opt\_output\_number\_only
 local range = parms.range
 if range and not add\_unit then
 unlink(out\_current)
 end
 local id = range and make\_id(parms, range.n + 1, out\_current) or id1
 local extra, was\_hyphenated = hyphenated\_maybe(parms, want\_name, sep, id, inout)
 if was\_hyphenated then
 add\_unit = false
 end
 local result
 local valinfo = out\_current.valinfo
 if range then
 for i = 0, range.n do
 local number\_word
 if i == range.n then
 add\_unit = false
 number\_word = true
 end
 decorate\_value(parms, out\_current, i+1, number\_word)
 local show = valinfo[i+1].show
 if add\_unit then
 show = show .. out\_current.sep .. (i == 0 and id1 or make\_id(parms, i+1, out\_current))
 end
 if i == 0 then
 result = show
 else
 result = range\_text(range[i], want\_name, parms, result, show, inout)
 end
 end
 else
 decorate\_value(parms, out\_current, 1, true)
 result = valinfo[1].show
 end
 if parms.opt\_output\_number\_only then
 return result
 end
 return result .. preunit .. extra
end

local function make\_output\_single(parms, in\_unit\_table, out\_unit\_table)
 -- Return true, item where item = wikitext of the conversion result
 -- for a single output (which is not a combination or a multiple);
 -- or return false, t where t is an error message table.
 if parms.opt\_order\_out and in\_unit\_table.unitcode == out\_unit\_table.unitcode then
 out\_unit\_table.valinfo = in\_unit\_table.valinfo
 else
 out\_unit\_table.valinfo = collection()
 for \_, v in ipairs(in\_unit\_table.valinfo) do
 local success, info = cvtround(parms, v, in\_unit\_table, out\_unit\_table)
 if not success then return false, info end
 out\_unit\_table.valinfo:add(info)
 end
 end
 return true, process\_one\_output(parms, out\_unit\_table)
end

local function make\_output\_multiple(parms, in\_unit\_table, out\_unit\_table)
 -- Return true, item where item = wikitext of the conversion result
 -- for an output which is a multiple (like 'ftin');
 -- or return false, t where t is an error message table.
 local inout = out\_unit\_table.inout -- normally 'out' but can be 'in' for order=out
 local multiple = out\_unit\_table.multiple -- table of scaling factors (will not be nil)
 local combos = out\_unit\_table.combination -- table of unit tables (will not be nil)
 local abbr = parms.abbr
 local abbr\_org = parms.abbr\_org
 local disp = parms.disp
 local want\_name = (abbr\_org == nil and (disp == 'or' or disp == 'slash')) or
 not (abbr == 'on' or abbr == inout or abbr == 'mos')
 local want\_link = (parms.lk == 'on' or parms.lk == inout)
 local mid = parms.opt\_flip and parms.mid or
 local sep1 = ' '
 local sep2 = ' '
 if parms.opt\_adjectival and want\_name then
 sep1 = '-'
 sep2 = '-'
 end
 local do\_spell = parms.opt\_spell\_out
 parms.opt\_spell\_out = nil -- so the call to cvtround does not spell the value
 local function make\_result(info, isfirst)
 local fmt, outvalue, sign
 local results = {}
 for i = 1, #combos do
 local tfrac, thisvalue, strforce
 local out\_current = combos[i]
 out\_current.inout = inout
 local scale = multiple[i]
 if i == 1 then -- least significant unit ('in' from 'ftin')
 local decimals
 out\_current.frac = out\_unit\_table.frac
 local success, outinfo = cvtround(parms, info, in\_unit\_table, out\_current)
 if not success then return false, outinfo end
 if isfirst then
 out\_unit\_table.valinfo = { outinfo } -- in case output value of first least significant unit is needed
 end
 sign = outinfo.sign
 tfrac = outinfo.fraction\_table
 if outinfo.is\_scientific then
 strforce = outinfo.show
 decimals =
 elseif tfrac then
 decimals =
 else
 local show = outinfo.show -- number as a string in local language
 local p1, p2 = show:find(numdot, 1, true)
 decimals = p1 and show:sub(p2 + 1) or  *-- text after numdot, if any*
 end
 fmt = '%.' .. ulen(decimals) .. 'f' -- to reproduce precision
 if decimals ==  *then*
 if tfrac then
 outvalue = floor(outinfo.raw\_absvalue) -- integer part only; fraction added later
 else
 outvalue = floor(outinfo.raw\_absvalue + 0.5) -- keep all integer digits of least significant unit
 end
 else
 outvalue = outinfo.absvalue
 end
 end
 if scale then
 outvalue, thisvalue = divide(outvalue, scale)
 else
 thisvalue = outvalue
 end
 local id
 if want\_name then
 if varname then
 local clean
 if strforce or tfrac then
 clean = '.1' -- dummy value to force name for floating point
 else
 clean = format(fmt, thisvalue)
 end
 id = variable\_name(clean, out\_current)
 else
 local key = 'name2'
 if parms.opt\_adjectival then
 key = 'name1'
 elseif tfrac then
 if thisvalue == 0 then
 key = 'name1'
 end
 elseif parms.opt\_singular then
 if 0 < thisvalue and thisvalue < 1.0001 then
 key = 'name1'
 end
 else
 if thisvalue == 1 then
 key = 'name1'
 end
 end
 id = out\_current[key]
 end
 else
 id = out\_current['symbol']
 end
 if i == 1 and omit\_separator(id) then
 -- Testing the id of the least significant unit should be sufficient.
 sep1 =
 sep2 =
 end
 if want\_link then
 local link = out\_current.link
 if link then
 id = make\_link(link, id, out\_current)
 end
 end
 local strval
 local spell\_inout = (i == #combos or outvalue == 0) and inout or  *-- trick so the last value processed (first displayed) has uppercase, if requested*
 if strforce and outvalue == 0 then
 sign =  *-- any sign is in strforce*
 strval = strforce -- show small values in scientific notation; will only use least significant unit
 elseif tfrac then
 local wholestr = (thisvalue > 0) and tostring(thisvalue) or nil
 strval = format\_fraction(parms, spell\_inout, false, wholestr, tfrac.numstr, tfrac.denstr, do\_spell)
 else
 strval = (thisvalue == 0) and from\_en('0') or with\_separator(parms, format(fmt, thisvalue))
 if do\_spell then
 strval = spell\_number(parms, spell\_inout, strval) or strval
 end
 end
 table.insert(results, strval .. sep1 .. id)
 if outvalue == 0 then
 break
 end
 fmt = '%.0f' -- only least significant unit can have a non-integral value
 end
 local reversed, count = {}, #results
 for i = 1, count do
 reversed[i] = results[count + 1 - i]
 end
 return true, sign .. table.concat(reversed, sep2)
 end
 local valinfo = in\_unit\_table.valinfo
 local success, result = make\_result(valinfo[1], true)
 if not success then return false, result end
 local range = parms.range
 if range then
 for i = 1, range.n do
 local success, result2 = make\_result(valinfo[i+1])
 if not success then return false, result2 end
 result = range\_text(range[i], want\_name, parms, result, result2, inout)
 end
 end
 return true, result .. mid
end

local function process(parms, in\_unit\_table, out\_unit\_table)
 -- Return true, s, outunit where s = final wikitext result,
 -- or return false, t where t is an error message table.
 linked\_pages = {}
 local success, bad\_output
 local bad\_input\_mcode = in\_unit\_table.bad\_mcode -- nil if input unit is a valid convert unit
 local out\_unit = parms.out\_unit
 if out\_unit == nil or out\_unit ==  *or type(out\_unit) == 'function' then*
 if bad\_input\_mcode or parms.opt\_input\_unit\_only then
 bad\_output =
 else
 local getdef = type(out\_unit) == 'function' and out\_unit or get\_default
 success, out\_unit = getdef(in\_unit\_table.valinfo[1].value, in\_unit\_table)
 parms.out\_unit = out\_unit
 if not success then
 bad\_output = out\_unit
 end
 end
 end
 if not bad\_output and not out\_unit\_table then
 success, out\_unit\_table = lookup(parms, out\_unit, 'any\_combination')
 if success then
 local mismatch = check\_mismatch(in\_unit\_table, out\_unit\_table)
 if mismatch then
 bad\_output = mismatch
 end
 else
 bad\_output = out\_unit\_table
 end
 end
 local lhs, rhs
 local flipped = parms.opt\_flip and not bad\_input\_mcode
 if bad\_output then
 rhs = (bad\_output == *) and*  or message(parms, bad\_output)
 elseif parms.opt\_input\_unit\_only then
 rhs =
 else
 local combos -- nil (for 'ft' or 'ftin'), or table of unit tables (for 'm ft')
 if not out\_unit\_table.multiple then -- nil/false ('ft' or 'm ft'), or table of factors ('ftin')
 combos = out\_unit\_table.combination
 end
 local frac = parms.frac -- nil or denominator of fraction for output values
 if frac then
 -- Apply fraction to the unit (if only one), or to non-SI units (if a combination),
 -- except that if a precision is also specified, the fraction only applies to
 -- the hand unit; that allows the following result:
 -- **Script error: No such module "convert".** → 156 centimetres (61.4 in; 15.1½ hands)
 -- However, the following is handled elsewhere as a special case:
 -- **Script error: No such module "convert".** → 156 centimetres (15.1½ hands; 61½ in)
 if combos then
 local precision = parms.precision
 for \_, unit in ipairs(combos) do
 if unit.builtin == 'hand' or (not precision and not unit.prefixes) then
 unit.frac = frac
 end
 end
 else
 out\_unit\_table.frac = frac
 end
 end
 local outputs = {}
 local imax = combos and #combos or 1 -- 1 (single unit) or number of unit tables
 if imax == 1 then
 parms.opt\_order\_out = nil -- only useful with an output combination
 end
 if not flipped and not parms.opt\_order\_out then
 -- Process left side first so any duplicate links (from lk=on) are suppressed
 -- on right. Example: **Script error: No such module "convert".**
 lhs = process\_input(parms, in\_unit\_table)
 end
 for i = 1, imax do
 local success, item
 local out\_current = combos and combos[i] or out\_unit\_table
 out\_current.inout = 'out'
 if i == 1 then
 if imax > 1 and out\_current.builtin == 'hand' then
 out\_current.out\_next = combos[2] -- built-in hand can influence next unit in a combination
 end
 if parms.opt\_order\_out then
 out\_current.inout = 'in'
 end
 end
 if out\_current.multiple then
 success, item = make\_output\_multiple(parms, in\_unit\_table, out\_current)
 else
 success, item = make\_output\_single(parms, in\_unit\_table, out\_current)
 end
 if not success then return false, item end
 outputs[i] = item
 end
 if parms.opt\_order\_out then
 lhs = outputs[1]
 table.remove(outputs, 1)
 end
 local sep = parms.table\_joins and parms.table\_joins[2] or parms.join\_between
 rhs = table.concat(outputs, sep)
 end
 if flipped or not lhs then
 local input = process\_input(parms, in\_unit\_table)
 if flipped then
 lhs = rhs
 rhs = input
 else
 lhs = input
 end
 end
 if parms.join\_before then
 lhs = parms.join\_before .. lhs
 end
 local wikitext
 if bad\_input\_mcode then
 if bad\_input\_mcode ==  *then*
 wikitext = lhs
 else
 wikitext = lhs .. message(parms, bad\_input\_mcode)
 end
 elseif parms.table\_joins then
 wikitext = parms.table\_joins[1] .. lhs .. parms.table\_joins[2] .. rhs
 else
 wikitext = lhs .. parms.joins[1] .. rhs .. parms.joins[2]
 end
 if parms.warnings and not bad\_input\_mcode then
 wikitext = wikitext .. parms.warnings
 end
 return true, wikitext, out\_unit\_table
end

local function main\_convert(frame)
 -- Do convert, and if needed, do it again with higher default precision.
 local parms = { frame = frame } -- will hold template arguments, after translation
 set\_config(frame.args)
 local success, result = get\_parms(parms, frame:getParent().args)
 if success then
 if type(result) ~= 'table' then
 return tostring(result)
 end
 local in\_unit\_table = result
 local out\_unit\_table
 for \_ = 1, 2 do -- use counter so cannot get stuck repeating convert
 success, result, out\_unit\_table = process(parms, in\_unit\_table, out\_unit\_table)
 if success and parms.do\_convert\_again then
 parms.do\_convert\_again = false
 else
 break
 end
 end
 end
 -- If input=x gives a problem, the result should be just the user input
 -- (if x is a property like P123 it has been replaced with *).*
 -- An unknown input unit would display the input and an error message
 -- with success == true at this point.
 -- Also, can have success == false with a message that outputs an empty string.
 if parms.input\_text then
 if success and not parms.have\_problem then
 return result
 end
 local cat
 if parms.tracking then
 -- Add a tracking category using the given text as the category sort key.
 -- There is currently only one type of tracking, but in principle multiple
 -- items could be tracked, using different sort keys for convenience.
 cat = wanted\_category('tracking', parms.tracking)
 end
 return parms.input\_text .. (cat or *)*
 end
 return success and result or message(parms, result)
end

local function \_unit(unitcode, options)
 -- Helper function for Module:Val to look up a unit.
 -- Parameter unitcode must be a string to identify the wanted unit.
 -- Parameter options must be nil or a table with optional fields:
 -- value = number (for sort key; default value is 1)
 -- scaled\_top = nil for a normal unit, or a number for a unit which is
 -- the denominator of a per unit (for sort key)
 -- si = { 'symbol', 'link' }
 -- (a table with two strings) to make an SI unit
 -- that will be used for the look up
 -- link = true if result should be linked
 -- sort = 'on' or 'debug' if result should include a sort key in a
 -- span element ('debug' makes the key visible)
 -- name = true for the name of the unit instead of the symbol
 -- us = true for the US spelling of the unit, if any
 -- Return nil if unitcode is not a non-empty string.
 -- Otherwise return a table with fields:
 -- text = requested symbol or name of unit, optionally linked
 -- scaled\_value = input value adjusted by unit scale; used for sort key
 -- sortspan = span element with sort key like that provided by Template:Ntsh,
 -- calculated from the result of converting value
 -- to a base unit with scale 1.
 -- unknown = true if the unitcode was not known
 unitcode = strip(unitcode)
 if unitcode == nil or unitcode ==  *then*
 return nil
 end
 set\_config({})
 linked\_pages = {}
 options = options or {}
 local parms = {
 abbr = options.name and 'off' or 'on',
 lk = options.link and 'on' or nil,
 opt\_sp\_us = options.us and true or nil,
 opt\_ignore\_error = true, -- do not add pages using this function to 'what links here' for Module:Convert/extra
 opt\_sortable\_on = options.sort == 'on' or options.sort == 'debug',
 opt\_sortable\_debug = options.sort == 'debug',
 }
 if options.si then
 -- Make a dummy table of units (just one unit) for lookup to use.
 -- This makes lookup recognize any SI prefix in the unitcode.
 local symbol = options.si[1] or '?'
 parms.unittable = { [symbol] = {
 \_name1 = symbol,
 \_name2 = symbol,
 \_symbol = symbol,
 utype = symbol,
 scale = symbol == 'g' and 0.001 or 1,
 prefixes = 1,
 default = symbol,
 link = options.si[2],
 }}
 end
 local success, unit\_table = lookup(parms, unitcode, 'no\_combination')
 if not success then
 unit\_table = setmetatable({
 symbol = unitcode, name2 = unitcode, utype = unitcode,
 scale = 1, default = *, defkey =* , linkey =  *}, unit\_mt)*
 end
 local value = tonumber(options.value) or 1
 local clean = tostring(abs(value))
 local info = {
 value = value,
 altvalue = value,
 singular = (clean == '1'),
 clean = clean,
 show = clean,
 }
 unit\_table.inout = 'in'
 unit\_table.valinfo = { info }
 local sortspan, scaled\_value
 if options.sort then
 sortspan, scaled\_value = make\_table\_or\_sort(parms, value, info, unit\_table, options.scaled\_top)
 end
 return {
 text = make\_id(parms, 1, unit\_table),
 sortspan = sortspan,
 scaled\_value = scaled\_value,
 unknown = not success and true or nil,
 }
end

return { convert = main\_convert, \_unit = \_unit }