# Module:Convert

-- Convert a value from one unit of measurement to another.  
-- Example: --> 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: (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 '&nbsp;' or a Unicode character.  
-- numsep_remove must work in a regex to identify separators to be removed.  
if numsep ~= '' then  
numsep_remove = (numsep == '.') and '%.' or numsep  
end  
if numsep ~= ',' and numdot ~= ',' then  
numsep_remove2 = ',' -- so numbers copied from enwiki will work  
end  
end  

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

local function divide(numerator, denominator)  
-- Return integers quotient, remainder resulting from dividing the two  
-- given numbers, which should be unsigned integers.  
local quotient, remainder = floor(numerator / denominator), numerator % denominator  
if not (0 <= remainder and remainder < denominator) then  
-- Floating point limits may need this, as in .  
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('$%d+', rep))  
end  
if msg then  
local parts = {}  
local regex, replace = msg.regex, msg.replace  
for i = 1, 3 do  
local limit = 40  
local s = mcode[i + 1]  
if s then  
if regex and replace then  
s = s:gsub(regex, replace)  
limit = nil -- allow long "should be" messages  
end  
-- Escape user input so it does not break the message.  
-- To avoid tags (like ) breaking  
-- the mouseover title, any strip marker starting with char(127) is  
-- replaced with '...' (text not needing i18n).  
local append  
local pos = s:find(string.char(127), 1, true)  
if pos then  
append = '...'  
s = s:sub(1, pos - 1)  
end  
if limit and ulen(s) > limit then  
s = usub(s, 1, limit)  
append = '...'  
end  
s = mw.text.nowiki(s) .. (append or '')  
else  
s = '?'  
end  
parts['$' .. 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.):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('"', '&quot;'), text, cat, anchor)  
end  
return 'Convert internal error: unknown message'  
end  

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

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

---
-- BEGIN: Code required only for built-in units.  
-- LATER: If need much more code, move to another module to simplify this module.  
local function speed_of_sound(altitude)  
-- This is for the Mach built-in unit of speed.  
-- Return speed of sound in metres per second at given altitude in feet.  
-- If no altitude given, use default (zero altitude = sea level).  
-- Table gives speed of sound in miles per hour at various altitudes:  
-- altitude = -17,499 to 402,499 feet  
-- mach_table[a + 4] = s where  
-- a = (altitude / 5000) rounded to nearest integer (-3 to 80)  
-- s = speed of sound (mph) at that altitude  
-- LATER: Should calculate result from an interpolation between the next  
-- lower and higher altitudes in table, rather than rounding to nearest.  
-- From: http://www.aerospaceweb.org/question/atmosphere/q0112.shtml  
local mach_table = { -- a =  
799.5, 787.0, 774.2, 761.207051, -- -3 to 0  
748.0, 734.6, 721.0, 707.0, 692.8, 678.3, 663.5, 660.1, 660.1, 660.1, -- 1 to 10  
660.1, 660.1, 660.1, 662.0, 664.3, 666.5, 668.9, 671.1, 673.4, 675.6, -- 11 to 20  
677.9, 683.7, 689.9, 696.0, 702.1, 708.1, 714.0, 719.9, 725.8, 731.6, -- 21 to 30  
737.3, 737.7, 737.7, 736.2, 730.5, 724.6, 718.8, 712.9, 707.0, 701.0, -- 31 to 40  
695.0, 688.9, 682.8, 676.6, 670.4, 664.1, 657.8, 652.9, 648.3, 643.7, -- 41 to 50  
639.1, 634.4, 629.6, 624.8, 620.0, 615.2, 613.2, 613.2, 613.2, 613.5, -- 51 to 60  
614.4, 615.3, 616.7, 619.8, 623.4, 629.7, 635.0, 641.1, 650.6, 660.0, -- 61 to 70  
672.5, 674.3, 676.1, 677.9, 679.7, 681.5, 683.3, 685.1, 686.8, 688.6, -- 71 to 80  
}  
altitude = altitude or 0  
local a = (altitude < 0) and -altitude or altitude  
a = floor(a / 5000 + 0.5)  
if altitude < 0 then  
a = -a  
end  
if a < -3 then  
a = -3  
elseif a > 80 then  
a = 80  
end  
return mach_table[a + 4] * 0.44704 -- mph converted to m/s  
end  
-- END: Code required only for built-in units.  
---

local function add_style(parms, class)  
-- Add selected template style to parms if not already present.  
parms.templatestyles = parms.templatestyles or {}  
if not parms.templatestyles[class] then  
parms.templatestyles[class] = parms.:extensionTag({  
name = 'templatestyles', args = { src = text_code.titles[class] }  
})  
end  
end  

local function get_styles(parms)  
-- Return string of required template styles, empty if .  
if parms.templatestyles then  
local t = {}  
for _, v in pairs(parms.templatestyles) do  
table.insert(t, v)  
end  
return table.concat(t)  
end  
return ''  
end  

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

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

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

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

local unit_mt = {  
-- Metatable to get missing values for a unit that does not accept SI prefixes.  
-- Warning: The boolean value 'false' is returned for any missing field  
-- so __index is not called twice for the same field in a given unit.  
__index = function (self, key)  
local value  
if key == 'name1' or key == 'sym_us' then  
value = self.symbol  
elseif key == 'name2' then  
value = self.name1 .. plural_suffix  
elseif key == 'name1_us' then  
value = self.name1  
if not rawget(self, 'name2_us') then  
-- If name1_us is 'foot', do not make name2_us by appending plural_suffix.  
self.name2_us = self.name2  
end  
elseif key == 'name2_us' then  
local raw1_us = rawget(self, 'name1_us')  
if raw1_us then  
value = raw1_us .. plural_suffix  
else  
value = self.name2  
end  
elseif key == 'link' then  
value = self.name1  
else  
value = false  
end  
rawset(self, key, value)  
return value  
end  
}  

local function prefixed_name(unit, name, index)  
-- Return unit name with SI prefix inserted at correct position.  
-- index = 1 (name1), 2 (name2), 3 (name1_us), 4 (name2_us).  
-- The position is a byte (not character) index, so use Lua's sub.  
local pos = rawget(unit, 'prefix_position')  
if type(pos) == 'string' then  
pos = tonumber(split(pos, ',')[index])  
end  
if pos then  
return name:sub(1, pos - 1) .. unit.si_name .. name:sub(pos)  
end  
return unit.si_name .. name  
end  

local unit_prefixed_mt = {  
-- Metatable to get missing values for a unit that accepts SI prefixes.  
-- Before use, fields si_name, si_prefix must be defined.  
-- The unit must define _symbol, _name1 and  
-- may define _sym_us, _name1_us, _name2_us  
-- (_sym_us, _name2_us may be defined for a language using sp=us  
-- to refer to a variant unrelated to U.S. units).  
__index = function (self, key)  
local value  
if key == 'symbol' then  
value = self.si_prefix .. self._symbol  
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 works.  
-- Wikignomes may also put two spaces or "&nbsp;" in combinations, so  
-- replace underscore, "&nbsp;", and multiple spaces with a single space.  
utable = utable or parms.unittable or all_units  
fails = fails or {}  
depth = depth and depth + 1 or 1  
if depth > 9 then  
-- There are ways to mistakenly define units which result in infinite  
-- recursion when lookup is called. That gives a long delay and very  
-- confusing error messages, so the depth parameter is used as a guard.  
return false, { 'cvt_lookup', unitcode }  
end  
if unitcode == nil or unitcode == '' then  
return false, { 'cvt_no_unit' }  
end  
unitcode = unitcode:gsub('_', ' '):gsub('&nbsp;', ' '):gsub(' +', ' ')  
local function call_make_per(t)  
return make_per(unitcode, t,  
function (ucode) return lookup(parms, ucode, 'no_combination', utable, fails, depth) end  
end  
local t = utable[unitcode]  
if t then  
if t.shouldbe then  
return false, { 'cvt_should_be', t.shouldbe }  
end  
if t.sp_us then  
parms.opt_sp_us = true  
end  
local target = t.target -- nil, or unitcode is an alias for this target  
if target then  
local success, result = lookup(parms, target, what, utable, fails, depth)  
if not success then return false, result end  
override_from(result, t, { 'customary', 'default', 'link', 'symbol', 'symlink' })  
local multiplier = t.multiplier  
if multiplier then  
result.multiplier = tostring(multiplier)  
result.scale = result.scale * multiplier  
end  
return true, result  
end  
if t.per then  
return call_make_per(t)  
end  
local combo = t.combination -- nil or a table of unitcodes  
if combo then  
local multiple = t.multiple  
if what == 'no_combination' or (what == 'only_multiple' and not multiple) then  
return false, { 'cvt_bad_unit', unitcode }  
end  
-- Recursively create a combination table containing the  
-- converter table of each unitcode.  
local result = { utype = t.utype, multiple = multiple, combination = {} }  
local cvt = result.combination  
for i, v in ipairs(combo) do  
local success, t = lookup(parms, v, multiple and 'no_combination' or 'only_multiple', utable, fails, depth)  
if not success then return false, t end  
cvt[i] = t  
end  
return true, result  
end  
local result = shallow_copy(t)  
result.unitcode = unitcode  
if result.prefixes then  
result.si_name = ''  
result.si_prefix = ''  
return true, setmetatable(result, unit_prefixed_mt)  
end  
return true, setmetatable(result, unit_mt)  
end  
local SIprefixes = text_code.SIprefixes  
for plen = SIprefixes[1] or 2, 1, -1 do  
-- Look for an SI prefix; should never occur with an alias.  
-- Check for longer prefix first ('dam' is decametre).  
-- SIprefixes[1] = prefix maximum #characters (as seen by mw.ustring.sub).  
local prefix = usub(unitcode, 1, plen)  
local si = SIprefixes[prefix]  
if si then  
local t = utable[usub(unitcode, plen+1)]  
if t and t.prefixes then  
local result = shallow_copy(t)  
result.unitcode = unitcode  
result.si_name = parms.opt_sp_us and si.name_us or si.name  
result.si_prefix = si.prefix or prefix  
result.scale = t.scale * 10 ^ (si.exponent * t.prefixes)  
return true, setmetatable(result, unit_prefixed_mt)  
end  
end  
end  
-- Accept user-defined combinations like "acre+m2+ha" or "acre m2 ha" for output.  
-- If '+' is used, each unit code can include a space, and any error is fatal.  
-- If ' ' is used and if each space-separated word is a unit code, it is a combo,  
-- but errors are not fatal so the unit code can be looked up as an extra unit.  
local err_is_fatal  
local combo = collection  
if unitcode:find('+', 1, true) then  
err_is_fatal = true  
for item in (unitcode .. '+'):gmatch('%s*(.-)%s*%+') do  
if item ~= '' then  
combo:add(item)  
end  
end  
elseif unitcode:find('%s') then  
for item in unitcode:gmatch('%S+') do  
combo:add(item)  
end  
end  
if combo.n > 1 then  
local function lookup_combo  
if what == 'no_combination' or what == 'only_multiple' then  
return false, { 'cvt_bad_unit', unitcode }  
end  
local result = { combination = {} }  
local cvt = result.combination  
for i, v in ipairs(combo) do  
local success, t = lookup(parms, v, 'only_multiple', utable, fails, depth)  
if not success then return false, t end  
if i == 1 then  
result.utype = t.utype  
else  
local mismatch = check_mismatch(result, t)  
if mismatch then  
return false, mismatch  
end  
end  
cvt[i] = t  
end  
return true, result  
end  
local success, result = lookup_combo  
if success or err_is_fatal then  
return success, result  
end  
end  
-- Accept any unit with an engineering notation prefix like "e6cuft"  
-- (million cubic feet), but not chained prefixes like "e3e6cuft",  
-- and not if the unit is a combination or multiple,  
-- and not if the unit has an offset or is a built-in.  
-- Only en digits are accepted.  
local exponent, baseunit = unitcode:match('^e(%d+)(.*)')  
if exponent then  
local engscale = text_code.eng_scales[exponent]  
if engscale then  
local success, result = lookup(parms, baseunit, 'no_combination', utable, fails, depth)  
if success and not (result.offset or result.builtin or result.engscale) then  
result.unitcode = unitcode -- 'e6cuft' not 'cuft'  
result.defkey = unitcode -- key to lookup default exception  
result.engscale = engscale  
result.scale = result.scale * 10 ^ tonumber(exponent)  
return true, result  
end  
end  
end  
-- Look for x/y; split on -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  
-- 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 "abc[[defghi]]").  
-- This uses a simple and efficient procedure that works for most cases.  
-- Some units (if used) would require more, and can later think about  
-- adding a method to handle exceptions.  
-- The procedure is to replace each space with a hyphen, but  
-- not a space after ')' [for "(pre-1954&nbsp;US) nautical mile"], and  
-- not spaces immediately before '(' or in '(...)' [for cases like  
-- "British thermal unit (ISO)" and "Calorie (International Steam Table)"].  
if name:find(' ', 1, true) then  
if parts then  
local pos  
if name:sub(1, 1) == '(' then  
pos = name:find(')', 1, true)  
if pos then  
return name:sub(1, pos+1) .. name:sub(pos+2):gsub(' ', '-')  
end  
elseif name:sub(-1) == ')' then  
pos = name:find('(', 1, true)  
if pos then  
return name:sub(1, pos-2):gsub(' ', '-') .. name:sub(pos-1)  
end  
end  
return name:gsub(' ', '-')  
end  
parts = collection  
for before, item, after in name:gmatch('([^[]*)(%[%[[^[]*%]%])([^[]*)') do  
if item:find(' ', 1, true) then  
local prefix  
local plen = item:find('|', 1, true)  
if plen then  
prefix = item:sub(1, plen)  
item = item:sub(plen + 1, -3)  
else  
prefix = item:sub(1, -3) .. '|'  
item = item:sub(3, -3)  
end  
item = prefix .. hyphenated(item, parts) .. ']]'  
end  
parts:add(before:gsub(' ', '-') .. item .. after:gsub(' ', '-'))  
end  
if parts.n == 0 then  
-- No link like "..." was found in the original name.  
parts:add(hyphenated(name, parts))  
end  
return table.concat(parts)  
end  
return name  
end  

local function hyphenated_maybe(parms, want_name, sep, id, inout)  
-- Return s, f where  
-- s = id, possibly modified  
-- f = true if hyphenated  
-- Possible modifications: hyphenate; prepend '-'; append mid text.  
if id == nil or id == '' then  
return ''  
end  
local mid = (inout == (parms.opt_flip and 'out' or 'in')) and parms.mid or ''  
if want_name then  
if parms.opt_adjectival then  
return '-' .. hyphenated(id) .. mid, true  
end  
if parms.opt_add_s and id:sub(-1) ~= 's' then  
id = id .. 's' -- for nowiki  
end  
end  
return sep .. id .. mid  
end  

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

local function digit_groups(parms, text, method)  
-- Return a numbered table of groups of digits (-to-, in local language).  
-- Parameter method is a number or nil:  
-- 3 for 3-digit grouping (default), or  
-- 2 for 3-then-2 grouping (only for digits before decimal mark).  
local len_right  
local len_left = text:find('.', 1, true)  
if len_left then  
len_right = #text - len_left  
len_left = len_left - 1  
else  
len_left = #text  
end  
local twos = method == 2 and len_left > 5  
local groups = collection  
local run = len_left  
local n  
if run < 4 or (run == 4 and parms.opt_comma5) then  
if parms.opt_gaps then  
n = run  
else  
n = #text  
end  
elseif twos then  
n = run % 2 == 0 and 1 or 2  
else  
n = run % 3 == 0 and 3 or run % 3  
end  
while run > 0 do  
groups:add(n)  
run = run - n  
n = (twos and run > 3) and 2 or 3  
end  
if len_right then  
if groups.n == 0 then  
groups:add(0)  
end  
if parms.opt_gaps and len_right > 3 then  
local want4 = not parms.opt_gaps3 -- true gives no gap before trailing single digit  
local isfirst = true  
run = len_right  
while run > 0 do  
n = (want4 and run == 4) and 4 or (run > 3 and 3 or run)  
if isfirst then  
isfirst = false  
groups[groups.n] = groups[groups.n] + 1 + n  
else  
groups:add(n)  
end  
run = run - n  
end  
else  
groups[groups.n] = groups[groups.n] + 1 + len_right  
end  
end  
local pos = 1  
for i, length in ipairs(groups) do  
groups[i] = from_en(text:sub(pos, pos + length - 1))  
pos = pos + length  
end  
return groups  
end  

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

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

local function with_exponent(parms, show, exponent)  
-- Return wikitext to display the implied value in scientific notation.  
-- Input uses en digits; output uses digits in local language.  
return format(fmtpower, with_separator(parms, show), from_en('10'), use_minus(from_en(tostring(exponent))))  
end  

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

-- Fraction output format.  
local fracfmt = {  
{ -- Like (fraction slash).  
'<span role="math">{SIGN}<span>{NUM}</span>&frasl;<span>{DEN}</span></span>', -- 1/2  
'<span role="math">{SIGN}{WHOLE}<span>+</span><span>{NUM}</span>&frasl;<span>{DEN}</span></span>', -- 1+2/3,  
},  
{ -- Like (stacked fraction, that is, horizontal bar).  
'<span role="math">{SIGN}<span>{NUM}</span><span>/</span><span>{DEN}</span></span>', -- 1//2  
'<span role="math">{SIGN}{WHOLE}<span>+</span><span><span>{NUM}</span><span>/</span><span>{DEN}</span></span></span>', -- 1+2//3,  
},  
}  

local function format_fraction(parms, inout, negative, wholestr, numstr, denstr, do_spell, style)  
-- Return wikitext for a fraction, possibly spelled.  
-- Inputs use en digits and have no sign; output uses digits in local language.  
local wikitext  
if not style then  
style = parms.opt_fraction_horizontal and 2 or 1  
end  
if wholestr == '' then  
wholestr = nil  
end  
local substitute = {  
SIGN = negative and MINUS or '',  
WHOLE = wholestr and with_separator(parms, wholestr),  
NUM = from_en(numstr),  
DEN = from_en(denstr),  
}  
wikitext = fracfmt[style][wholestr and 2 or 1]:gsub('{(%u+)}', substitute)  
if do_spell then  
if negative then  
if wholestr then  
wholestr = '-' .. wholestr  
else  
numstr = '-' .. numstr  
end  
end  
local s = spell_number(parms, inout, wholestr, numstr, denstr)  
if s then  
return s  
end  
end  
add_style(parms, fracfmt[style].style)  
return wikitext  
end  

local function format_number(parms, show, exponent, isnegative)  
-- Parameter show is a string or a table containing strings.  
-- Each string is a formatted number in en digits and optional '.' decimal mark.  
-- A table represents a fraction: integer, numerator, denominator;  
-- if a table is given, exponent must be nil.  
-- Return t where t is a table with fields:  
-- show = wikitext formatted to display implied value  
-- (digits in local language)  
-- is_scientific = true if show uses scientific notation  
-- clean = unformatted show (possibly adjusted and with inserted '.')  
-- (en digits)  
-- sign = '' or MINUS  
-- exponent = exponent (possibly adjusted)  
-- The clean and exponent fields can be used to calculate the  
-- rounded absolute value, if needed.  
---
-- The value implied by the arguments is found from:  
-- exponent is nil; and  
-- show is a string of digits (no sign), with an optional dot;  
-- show = '123.4' is value 123.4, '1234' is value 1234.0;  
-- or:  
-- exponent is an integer indicating where dot should be;  
-- show is a string of digits (no sign and no dot);  
-- there is an implied dot before show;  
-- show does not start with '0';  
-- show = '1234', exponent = 3 is value 0.1234*10^3 = 123.4.  
---
-- The formatted result:  
-- * Is for an output value and is spelled if wanted and possible.  
-- * Includes a Unicode minus if isnegative and not spelled.  
-- * Uses a custom decimal mark, if wanted.  
-- * Has digits grouped where necessary, if wanted.  
-- * Uses scientific notation if requested, or for very small or large values  
-- (which forces result to not be spelled).  
-- * Has no more than maxsigfig significant digits  
-- (same as old template and ).  
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:  
-- → 1,000,000,000 metres (1,000,000,000 m)  
local significand  
if #show > 1 then  
significand = show:sub(1, 1) .. '.' .. show:sub(2)  
else  
significand = show  
end  
return {  
clean = '.' .. show,  
exponent = exponent,  
sign = sign,  
show = sign .. with_exponent(parms, significand, exponent-1),  
is_scientific = true,  
}  
end  
if exponent >= #show then  
show = show .. zeros(exponent - #show) -- result has no dot  
elseif exponent <= 0 then  
show = '0.' .. zeros(-exponent) .. show  
else  
show = show:sub(1, exponent) .. '.' .. show:sub(exponent+1)  
end  
end  
local formatted_show  
if tfrac then  
show = tostring(tfrac.value) -- to set clean in returned table  
formatted_show = format_fraction(parms, 'out', isnegative, tfrac.wholestr, tfrac.numstr, tfrac.denstr, parms.opt_spell_out)  
else  
if isnegative and show:match('^0.?0*$') then  
sign = '' -- don't show minus if result is negative but rounds to zero  
end  
formatted_show = sign .. with_separator(parms, show)  
if parms.opt_spell_out then  
formatted_show = spell_number(parms, 'out', sign .. show) or formatted_show  
end  
end  
return {  
clean = show,  
sign = sign,  
show = formatted_show,  
is_scientific = false, -- to avoid calling __index  
}  
end  

local function extract_fraction(parms, text, negative)  
-- If text represents a fraction, return  
-- value, altvalue, show, denominator  
-- where  
-- value is a number (value of the fraction in argument text)  
-- altvalue is an alternate interpretation of any fraction for the hands  
-- unit where "12.1+3/4" means 12 hands 1.75 inches  
-- show is a string (formatted text for display of an input value,  
-- and is spelled if wanted and possible)  
-- denominator is value of the denominator in the fraction  
-- Otherwise, return nil.  
-- Input uses en digits and '.' decimal mark (input has been translated).  
-- Output uses digits in local language and local decimal mark, if any.  
---
-- Originally this function accepted x+y/z where x, y, z were any valid  
-- numbers, possibly with a sign. For example '1.23e+2+1.2/2.4' = 123.5,  
-- and '2-3/8' = 1.625. However, such usages were found to be errors or  
-- misunderstandings, so since August 2014 the following restrictions apply:  
-- x (if present) is an integer or has a single digit after decimal mark  
-- y and z are unsigned integers  
-- e-notation is not accepted  
-- The overall number can start with '+' or '-' (so '12+3/4' and '+12+3/4'  
-- and '-12-3/4' are valid).  
-- Any leading negative sign is removed by the caller, so only inputs  
-- like the following are accepted here (may have whitespace):  
-- negative = false false true (there was a leading '-')  
-- text = '2/3' '+2/3' '2/3'  
-- text = '1+2/3' '+1+2/3' '1-2/3'  
-- text = '12.3+1/2' '+12.3+1/2' '12.3-1/2'  
-- Values like '12.3+1/2' are accepted, but are intended only for use  
-- with the hands unit (not worth adding code to enforce that).  
---
local leading_plus, prefix, numstr, slashes, denstr =  
text:match('^%s*(%+?)%s*(.-)%s*(%d+)%s*(/+)%s*(%d+)%s*$')  
if not leading_plus then  
-- Accept a single U+2044 fraction slash because that may be pasted.  
leading_plus, prefix, numstr, denstr =  
text:match('^%s*(%+?)%s*(.-)%s*(%d+)%s*⁄%s*(%d+)%s*$')  
slashes = '/'  
end  
local numerator = tonumber(numstr)  
local denominator = tonumber(denstr)  
if numerator == nil or denominator == nil or (negative and leading_plus ~= '') then  
return nil  
end  
local whole, wholestr  
if prefix == '' then  
wholestr = ''  
whole = 0  
else  
-- Any prefix must be like '12+' or '12-' (whole number and fraction sign);  
-- '12.3+' and '12.3-' are also accepted (single digit after decimal point)  
-- because '12.3+1/2 hands' is valid (12 hands 3½ inches).  
local num1, num2, frac_sign = prefix:match('^(%d+)(%.?%d?)%s*([+%-])$')  
if num1 == nil then return nil end  
if num2 == * then -- num2 must be * or like '.1' but not '.' or '.12'  
wholestr = num1  
else  
if #num2 ~= 2 then return nil end  
wholestr = num1 .. num2  
end  
if frac_sign ~= (negative and '-' or '+') then return nil end  
whole = tonumber(wholestr)  
if whole == nil then return nil end  
end  
local value = whole + numerator / denominator  
if not valid_number(value) then return nil end  
local altvalue = whole + numerator / (denominator * 10)  
local style = #slashes -- kludge: 1 or 2 slashes can be used to select style  
if style > 2 then style = 2 end  
local wikitext = format_fraction(parms, 'in', negative, leading_plus .. wholestr, numstr, denstr, parms.opt_spell_in, style)  
return value, altvalue, wikitext, denominator  
end  

local function extract_number(parms, text, another, no_fraction)  
-- Return true, info if can extract a number from text,  
-- where info is a table with the result,  
-- or return false, t where t is an error message table.  
-- Input can use en digits or digits in local language and can  
-- have references at the end. Accepting references is intended  
-- for use in infoboxes with a field for a value passed to convert.  
-- Parameter another = true if the expected value is not the first.  
-- Before processing, the input text is cleaned:  
-- * Any thousand separators (valid or not) are removed.  
-- * Any sign is replaced with '-' (if negative) or '' (otherwise).  
-- That replaces Unicode minus with '-'.  
-- If successful, the returned info table contains named fields:  
-- value = a valid number  
-- altvalue = a valid number, usually same as value but different  
-- if fraction used (for hands unit)  
-- singular = true if value is 1 or -1 (to use singular form of units)  
-- clean = cleaned text with any separators and sign removed  
-- (en digits and '.' decimal mark)  
-- show = text formatted for output, possibly with ref strip markers  
-- (digits in local language and custom decimal mark)  
-- The resulting show:  
-- * Is for an input value and is spelled if wanted and possible.  
-- * Has a rounded value, if wanted.  
-- * Has digits grouped where necessary, if wanted.  
-- * If negative, a Unicode minus is used; otherwise the sign is  
-- '+' (if the input text used '+'), or is '' (if no sign in input).  
text = strip(text or '')  
local reference  
local pos = text:find('\127', 1, true)  
if pos then  
local before = text:sub(1, pos - 1)  
local remainder = text:sub(pos)  
local refs = {}  
while #remainder > 0 do  
local ref, spaces  
ref, spaces, remainder = remainder:match('^(\127[^\127]*UNIQ[^\127]*%-ref[^\127]*\127)(%s*)(.*)')  
if ref then  
table.insert(refs, ref)  
else  
refs = {}  
break  
end  
end  
if #refs > 0 then  
text = strip(before)  
reference = table.concat(refs)  
end  
end  
local clean = to_en(text, parms)  
if clean == '' then  
return false, { another and 'cvt_no_num2' or 'cvt_no_num' }  
end  
local isnegative, propersign = false, '' -- most common case  
local singular, show, denominator  
local value = tonumber(clean)  
local altvalue  
if value then  
local sign = clean:sub(1, 1)  
if sign == '+' or sign == '-' then  
propersign = (sign == '+') and '+' or MINUS  
clean = clean:sub(2)  
end  
if value < 0 then  
isnegative = true  
value = -value  
end  
else  
local valstr  
for _, prefix in ipairs({ '-', MINUS, '&minus;' }) do  
-- Including '-' sets isnegative in case input is a fraction like '-2-3/4'.  
local plen = #prefix  
if clean:sub(1, plen) == prefix then  
valstr = clean:sub(plen + 1)  
if valstr:match('^%s') then -- "- 1" is invalid but "-1 - 1/2" is ok  
return false, { 'cvt_bad_num', text }  
end  
break  
end  
end  
if valstr then  
isnegative = true  
propersign = MINUS  
clean = valstr  
value = tonumber(clean)  
end  
if value == nil then  
if not no_fraction then  
value, altvalue, show, denominator = extract_fraction(parms, clean, isnegative)  
end  
if value == nil then  
return false, { 'cvt_bad_num', text }  
end  
if value <= 1 then  
singular = true -- for example, "½ mile" or "one half mile" (singular unit)  
end  
end  
end  
if not valid_number(value) then -- for example, "1e310" may overflow  
return false, { 'cvt_invalid_num' }  
end  
if show == nil then  
-- clean is a non-empty string with no spaces, and does not represent a fraction,  
-- and value = tonumber(clean) is a number >= 0.  
-- If the input uses e-notation, show will be displayed using a power of ten, but  
-- we use the number as given so it might not be normalized scientific notation.  
-- The input value is spelled if specified so any e-notation is ignored;  
-- that allows input like 2e6 to be spelled as "two million" which works  
-- because the spell module converts '2e6' to '2000000' before spelling.  
local function rounded(value, default, exponent)  
local precision = parms.opt_ri  
if precision then  
local fmt = '%.' .. format('%d', precision) .. 'f'  
local result = fmt:format(tonumber(value) + 2e-14) -- fudge for some common cases of bad rounding  
if not exponent then  
singular = (tonumber(result) == 1)  
end  
return result  
end  
return default  
end  
singular = (value == 1)  
local scientific  
local significand, exponent = clean:match('^([%d.]+)[Ee]([+%-]?%d+)')  
if significand then  
show = with_exponent(parms, rounded(significand, significand, exponent), exponent)  
scientific = true  
else  
show = with_separator(parms, rounded(value, clean))  
end  
show = propersign .. show  
if parms.opt_spell_in then  
show = spell_number(parms, 'in', propersign .. rounded(value, clean)) or show  
scientific = false  
end  
if scientific then  
parms.opt_scientific = true  
end  
end  
if isnegative and (value ~= 0) then  
value = -value  
altvalue = -(altvalue or value)  
end  
return true, {  
value = value,  
altvalue = altvalue or value,  
singular = singular,  
clean = clean,  
show = show .. (reference or ''),  
denominator = denominator,  
}  
end  

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

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

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

local function preunits(count, preunit1, preunit2)  
-- If count is 1:  
-- ignore preunit2  
-- return p1  
-- else:  
-- preunit1 is used for preunit2 if the latter is empty  
-- return p1, p2  
-- where:  
-- p1 is text to insert before the input unit  
-- p2 is text to insert before the output unit  
-- p1 or p2 may be nil to mean "no preunit"  
-- Using '+' gives output like "5+ feet" (no space before, but space after).  
local function withspace(text, wantboth)  
-- Return text with space before and, if wantboth, after.  
-- However, no space is added if there is a space or '&nbsp;' or '-'  
-- at that position ('-' is for adjectival text).  
-- There is also no space if text starts with '&'  
-- (e.g. '&deg;' would display a degree symbol with no preceding space).  
local char = text:sub(1, 1)  
if char == '&' then  
return text -- an html entity can be used to specify the exact display  
end  
if not (char == ' ' or char == '-' or char == '+') then  
text = ' ' .. text  
end  
if wantboth then  
char = text:sub(-1, -1)  
if not (char == ' ' or char == '-' or text:sub(-6, -1) == '&nbsp;') then  
text = text .. ' '  
end  
end  
return text  
end  
local PLUS = '+ '  
preunit1 = preunit1 or ''  
local trim1 = strip(preunit1)  
if count == 1 then  
if trim1 == '' then  
return nil  
end  
if trim1 == '+' then  
return PLUS  
end  
return withspace(preunit1, true)  
end  
preunit1 = withspace(preunit1)  
preunit2 = preunit2 or ''  
local trim2 = strip(preunit2)  
if trim1 == '+' then  
if trim2 == '' or trim2 == '+' then  
return PLUS, PLUS  
end  
preunit1 = PLUS  
end  
if trim2 == '' then  
if trim1 == '' then  
return nil, nil  
end  
preunit2 = preunit1  
elseif trim2 == '+' then  
preunit2 = PLUS  
elseif trim2 == '&#32;' then -- trick to make preunit2 empty  
preunit2 = nil  
else  
preunit2 = withspace(preunit2)  
end  
return preunit1, preunit2  
end  

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

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

local function translate_parms(parms, kv_pairs)  
-- Update fields in parms by translating each key:value in kv_pairs to terms  
-- used by this module (may involve translating from local language to English).  
-- Also, checks are performed which may display warnings, if enabled.  
-- Return true if successful or return false, t where t is an error message table.  
currency_text = nil -- local testing can hold module in memory; must clear globals  
if kv_pairs.adj and kv_pairs.sing then  
-- For enwiki (before translation), warn if attempt to use adj and sing  
-- as the latter is a deprecated alias for the former.  
if kv_pairs.adj ~= kv_pairs.sing and kv_pairs.sing ~= '' then  
add_warning(parms, 1, 'cvt_unknown_option', 'sing=' .. kv_pairs.sing)  
end  
kv_pairs.sing = nil  
end  
kv_pairs.comma = kv_pairs.comma or config.comma -- for plwiki who want default comma=5  
for loc_name, loc_value in pairs(kv_pairs) do  
local en_name = text_code.en_option_name[loc_name]  
if en_name then  
local en_value = text_code.en_option_value[en_name]  
if en_value == 'INTEGER' then -- altitude_ft, altitude_m, frac, sigfig  
en_value = nil  
if loc_value == '' then  
add_warning(parms, 2, 'cvt_empty_option', loc_name)  
else  
local minimum  
local number, is_integer = get_number(loc_value)  
if en_name == 'sigfig' then  
minimum = 1  
elseif en_name == 'frac' then  
minimum = 2  
if number and number < 0 then  
parms.opt_fraction_horizontal = true  
number = -number  
end  
else  
minimum = -1e6  
end  
if number and is_integer and number >= minimum then  
en_value = number  
else  
local m  
if en_name == 'frac' then  
m = 'cvt_bad_frac'  
elseif en_name == 'sigfig' then  
m = 'cvt_bad_sigfig'  
else  
m = 'cvt_bad_altitude'  
end  
add_warning(parms, 1, m, loc_name .. '=' .. loc_value)  
end  
end  
elseif en_value == 'TEXT' then -- $, input, qid, qual, stylein, styleout, tracking  
en_value = loc_value ~= '' and loc_value or nil -- accept non-empty user text with no validation  
if not en_value and (en_name == '$' or en_name == 'qid' or en_name == 'qual') then  
add_warning(parms, 2, 'cvt_empty_option', loc_name)  
elseif en_name == '$' then  
-- Value should be a single character like "€" for the euro currency symbol, but anything is accepted.  
currency_text = (loc_value == 'euro') and '€' or loc_value  
elseif en_name == 'input' then  
-- May have something like (empty input) if source is an infobox  
-- with optional fields. In that case, want to output nothing rather than an error.  
parms.input_text = loc_value -- keep input because parms.input is nil if loc_value == ''  
end  
else  
en_value = en_value[loc_value]  
if en_value and en_value:sub(-1) == '?' then  
en_value = en_value:sub(1, -2)  
add_warning(parms, -1, 'cvt_deprecated', loc_name .. '=' .. loc_value)  
end  
if en_value == nil then  
if loc_value == '' then  
add_warning(parms, 2, 'cvt_empty_option', loc_name)  
else  
add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)  
end  
elseif en_value == '' then  
en_value = nil -- an ignored option like adj=off  
elseif type(en_value) == 'string' and en_value:sub(1, 4) == 'opt_' then  
for _, v in ipairs(split(en_value, ',')) do  
local lhs, rhs = v:match('^(.-)=(.+)$')  
if rhs then  
parms[lhs] = tonumber(rhs) or rhs  
else  
parms[v] = true  
end  
end  
en_value = nil  
end  
end  
parms[en_name] = en_value  
else  
add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)  
end  
end  
local abbr_entered = parms.abbr  
local cfg_abbr = config.abbr  
if cfg_abbr then  
-- Don't warn if invalid because every convert would show that warning.  
if cfg_abbr == 'on always' then  
parms.abbr = 'on'  
elseif cfg_abbr == 'off always' then  
parms.abbr = 'off'  
elseif parms.abbr == nil then  
if cfg_abbr == 'on default' then  
parms.abbr = 'on'  
elseif cfg_abbr == 'off default' then  
parms.abbr = 'off'  
end  
end  
end  
if parms.abbr then  
if parms.abbr == 'unit' then  
parms.abbr = 'on'  
parms.number_word = true  
end  
parms.abbr_org = parms.abbr -- original abbr, before any flip  
elseif parms.opt_hand_hh then  
parms.abbr_org = 'on'  
parms.abbr = 'on'  
else  
parms.abbr = 'out' -- default is to abbreviate output only (use symbol, not name)  
end  
if parms.opt_order_out then  
-- Disable options that do not work in a useful way with order=out.  
parms.opt_flip = nil -- override adj=flip  
parms.opt_spell_in = nil  
parms.opt_spell_out = nil  
parms.opt_spell_upper = nil  
end  
if parms.opt_spell_out and not abbr_entered then  
parms.abbr = 'off' -- should show unit name when spelling the output value  
end  
if parms.opt_flip then  
local function swap_in_out(option)  
local value = parms[option]  
if value == 'in' then  
parms[option] = 'out'  
elseif value == 'out' then  
parms[option] = 'in'  
end  
end  
swap_in_out('abbr')  
swap_in_out('lk')  
if parms.opt_spell_in and not parms.opt_spell_out then  
-- For simplicity, and because it does not appear to be needed,  
-- user cannot set an option to spell the output only.  
parms.opt_spell_in = nil  
parms.opt_spell_out = true  
end  
end  
if parms.opt_spell_upper then  
parms.spell_upper = parms.opt_flip and 'out' or 'in'  
end  
if parms.opt_table or parms.opt_tablecen then  
if abbr_entered == nil and parms.lk == nil then  
parms.opt_values = true  
end  
parms.table_align = parms.opt_table and * or *  
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 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 )  
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 "",  
-- return true, i, in_unit, in_unit_table  
-- i = index in parms of what follows valid_unit, if anything.  
-- The valid_value is not negative and does not use a fraction, and  
-- no options requiring further processing of the input are used.  
-- Otherwise, return nothing or return false, parm1 for caller to interpret.  
-- Testing shows this function is successful for 96% of converts in articles,  
-- and that on average it speeds up converts by 8%.  
local clean = to_en(strip(parms[1] or ''), parms)  
if parms.opt_ri or parms.opt_spell_in or #clean > 10 or not clean:match('^[0-9.]+$') then  
return false, clean  
end  
local value = tonumber(clean)  
if not value then return end  
local info = {  
value = value,  
altvalue = value,  
singular = (value == 1),  
clean = clean,  
show = with_separator(parms, clean),  
}  
local in_unit = strip(parms[2])  
local success, in_unit_table = lookup(parms, in_unit, 'no_combination')  
if not success then return end  
in_unit_table.valinfo = { info }  
return true, 3, in_unit, in_unit_table  
end  

local function wikidata_call(parms, operation, ...)  
-- Return true, s where s is the result of a Wikidata operation,  
-- or return false, t where t is an error message table.  
local function worker(...)  
wikidata_code = wikidata_code or require(wikidata_module)  
wikidata_data = wikidata_data or mw.loadData(wikidata_data_module)  
return wikidata_code[operation](wikidata_data, ...)  
end  
local success, status, result = pcall(worker, ...)  
if success then  
return status, result  
end  
if parms.opt_sortable_debug then  
-- Use debug=yes to crash if an error while accessing Wikidata.  
error('Error accessing Wikidata: ' .. status, 0)  
end  
return false, { 'cvt_wd_fail' }  
end  

local function get_parms(parms, args)  
-- If successful, update parms and return true, unit where  
-- parms is a table of all arguments passed to the template  
-- converted to named arguments, and  
-- unit is the input unit table;  
-- or return false, t where t is an error message table.  
-- For special processing (not a convert), can also return  
-- true, wikitext where wikitext is the final result.  
-- The returned input unit table may be for a fake unit using the specified  
-- unit code as the symbol and name, and with bad_mcode = message code table.  
-- MediaWiki removes leading and trailing whitespace from the values of  
-- named arguments. However, the values of numbered arguments include any  
-- whitespace entered in the template, and whitespace is used by some  
-- parameters (example: the numbered parameters associated with "disp=x").  
local kv_pairs = {} -- table of input key:value pairs where key is a name; needed because cannot iterate parms and add new fields to it  
for k, v in pairs(args) do  
if type(k) == 'number' or k == 'test' then -- parameter "test" is reserved for testing and is not translated  
parms[k] = v  
else  
kv_pairs[k] = v  
end  
end  
if parms.test == 'wikidata' then  
local ulookup = function (ucode)  
-- Use empty table for parms so it does not accumulate results when used repeatedly.  
return lookup({}, ucode, 'no_combination')  
end  
return wikidata_call(parms, '_listunits', ulookup)  
end  
local success, msg = translate_parms(parms, kv_pairs)  
if not success then return false, msg end  
if parms.input then  
success, msg = wikidata_call(parms, '_adjustparameters', parms, 1)  
if not success then return false, msg end  
end  
local success, i, in_unit, in_unit_table = simple_get_values(parms)  
if not success then  
if type(i) == 'string' and i:match('^NNN+$') then  
-- Some infoboxes have examples like (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 )  
in_unit_table = '' -- suppress error message and prevent processing of output unit  
end  
in_unit_table = setmetatable({  
symbol = in_unit, name2 = in_unit, utype = in_unit,  
scale = 1, default = *, defkey = *, linkey = '',  
bad_mcode = in_unit_table }, unit_mt)  
end  
in_unit_table.valinfo = valinfo  
end  
if parms.test == 'msg' then  
-- Am testing the messages produced when no output unit is specified, and  
-- the input unit has a missing or invalid default.  
-- Set two units for testing that.  
-- LATER: Remove this code.  
if in_unit == 'chain' then  
in_unit_table.default = nil -- no default  
elseif in_unit == 'rd' then  
in_unit_table.default = "ft!X!m" -- an invalid expression  
end  
end  
in_unit_table.inout = 'in' -- this is an input unit  
if not parms.range then  
local success, inext, composite_unit = get_composite(parms, i, in_unit_table)  
if not success then return false, inext end  
if composite_unit then  
in_unit_table = composite_unit  
i = inext  
end  
end  
if in_unit_table.builtin == 'mach' then  
-- As with old template, a number following Mach as the input unit is the altitude.  
-- That is deprecated: should use altitude_ft=NUMBER or altitude_m=NUMBER.  
local success, info  
success = tonumber(parms[i]) -- this will often work and will give correct result for values like 2e4 without forcing output scientific notation  
if success then  
info = { value = success }  
else  
success, info = extract_number(parms, parms[i], false, true)  
end  
if success then  
i = i + 1  
in_unit_table.altitude = info.value  
end  
end  
local word = strip(parms[i])  
i = i + 1  
local precision, is_bad_precision  
local function set_precision(text)  
local number, is_integer = get_number(text)  
if number then  
if is_integer then  
precision = number  
else  
precision = text  
is_bad_precision = true  
end  
return true -- text was used for precision, good or bad  
end  
end  
if word and not set_precision(word) then  
parms.out_unit = parms.out_unit or word  
if set_precision(strip(parms[i])) then  
i = i + 1  
end  
end  
if parms.opt_adj_mid then  
word = parms[i]  
i = i + 1  
if word then -- mid-text words  
if word:sub(1, 1) == '-' then  
parms.mid = word  
else  
parms.mid = ' ' .. word  
end  
end  
end  
if parms.opt_one_preunit then  
parms[parms.opt_flip and 'preunit2' or 'preunit1'] = preunits(1, parms[i])  
i = i + 1  
end  
if parms.disp == 'x' then  
-- Following is reasonably compatible with the old template.  
local first = parms[i] or ''  
local second = parms[i+1] or ''  
i = i + 2  
if strip(first) == '' then -- user can enter '&#32;' rather than ' ' to avoid the default  
first = ' [&nbsp;' .. first  
second = '&nbsp;]' .. second  
end  
parms.joins = { first, second }  
elseif parms.opt_two_preunits then  
local p1, p2 = preunits(2, parms[i], parms[i+1])  
i = i + 2  
if parms.preunit1 then  
-- To simplify documentation, allow unlikely use of adj=pre with disp=preunit  
-- (however, an output unit must be specified with adj=pre and with disp=preunit).  
parms.preunit1 = parms.preunit1 .. p1  
parms.preunit2 = p2  
else  
parms.preunit1, parms.preunit2 = p1, p2  
end  
end  
if precision == nil then  
if set_precision(strip(parms[i])) then  
i = i + 1  
end  
end  
if is_bad_precision then  
add_warning(parms, 1, 'cvt_bad_prec', precision)  
else  
parms.precision = precision  
end  
for j = i, i + 3 do  
local parm = parms[j] -- warn if find a non-empty extraneous parameter  
if parm and parm:match('%S') then  
add_warning(parms, 1, 'cvt_unknown_option', parm)  
break  
end  
end  
return true, in_unit_table  
end  

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

local function default_precision(parms, invalue, inclean, denominator, outvalue, in_current, out_current, extra)  
-- Return a default value for precision (an integer like 2, 0, -2).  
-- If denominator is not nil, it is the value of the denominator in inclean.  
-- Code follows procedures used in old template.  
local fudge = 1e-14 -- adds this, so we do too  
local prec, minprec, adjust  
local subunit_ignore_trailing_zero  
local subunit_more_precision -- kludge for "in" used in input like "|2|ft|6|in"  
local composite = in_current.composite  
if composite then  
subunit_ignore_trailing_zero = true -- input "|2|st|10|lb" has precision 0, not -1  
if composite[#composite].exception == 'subunit_more_precision' then  
subunit_more_precision = true -- do not use standard precision with input like "|2|ft|6|in"  
end  
end  
if denominator and denominator > 0 then  
prec = math.max(log10(denominator), 1)  
else  
-- Count digits after decimal mark, handling cases like '12.345e6'.  
local exponent  
local integer, dot, decimals, expstr = inclean:match('^(%d*)(%.?)(%d*)(.*)')  
local e = expstr:sub(1, 1)  
if e == 'e' or e == 'E' then  
exponent = tonumber(expstr:sub(2))  
end  
if dot == '' then  
prec = subunit_ignore_trailing_zero and 0 or -integer:match('0*$'):len  
else  
prec = #decimals  
end  
if exponent then  
-- So '1230' and '1.23e3' both give prec = -1, and '0.00123' and '1.23e-3' give 5.  
prec = prec - exponent  
end  
end  
if in_current.istemperature and out_current.istemperature then  
-- Converting between common temperatures (°C, °F, °R, K); not keVT.  
-- Kelvin value can be almost zero, or small but negative due to precision problems.  
-- Also, an input value like -300 C (below absolute zero) gives negative kelvins.  
-- Calculate minimum precision from absolute value.  
adjust = 0  
local kelvin = abs((invalue - in_current.offset) * in_current.scale)  
if kelvin < 1e-8 then -- assume nonzero due to input or calculation precision problem  
minprec = 2  
else  
minprec = 2 - floor(log10(kelvin) + fudge) -- 3 sigfigs in kelvin  
end  
else  
if invalue == 0 or outvalue <= 0 then  
-- We are never called with a negative outvalue, but it might be zero.  
-- This is special-cased to avoid calculation exceptions.  
return record_default_precision(parms, out_current, 0)  
end  
if out_current.exception == 'integer_more_precision' and floor(invalue) == invalue then  
-- With certain output units that sometimes give poor results  
-- with default rounding, use more precision when the input  
-- value is equal to an integer. An example of a poor result  
-- is when input 50 gives a smaller output than input 49.5.  
-- Experiment shows this helps, but it does not eliminate all  
-- surprises because it is not clear whether "50" should be  
-- interpreted as "from 45 to 55" or "from 49.5 to 50.5".  
adjust = -log10(in_current.scale)  
elseif subunit_more_precision then  
-- Conversion like "" (where subunit is "in")  
-- has a non-standard adjust value, to give more output precision.  
adjust = log10(out_current.scale) + 2  
else  
adjust = log10(abs(invalue / outvalue))  
end  
adjust = adjust + log10(2)  
-- Ensure that the output has at least two significant figures.  
minprec = 1 - floor(log10(outvalue) + fudge)  
end  
if extra then  
adjust = extra.adjust or adjust  
minprec = extra.minprec or minprec  
end  
return record_default_precision(parms, out_current, math.max(floor(prec + adjust), minprec))  
end  

local function convert(parms, invalue, info, in_current, out_current)  
-- Convert given input value from one unit to another.  
-- Return output_value (a number) if a simple convert, or  
-- return f, t where  
-- f = true, t = table of information with results, or  
-- f = false, t = error message table.  
local inscale = in_current.scale  
local outscale = out_current.scale  
if not in_current.iscomplex and not out_current.iscomplex then  
return invalue * (inscale / outscale) -- minimize overhead for most common case  
end  
if in_current.invert or out_current.invert then  
-- Inverted units, such as inverse length, inverse time, or  
-- fuel efficiency. Built-in units do not have invert set.  
if (in_current.invert or 1) * (out_current.invert or 1) < 0 then  
return 1 / (invalue * inscale * outscale)  
end  
return invalue * (inscale / outscale)  
elseif in_current.offset then  
-- Temperature (there are no built-ins for this type of unit).  
if info.is_change then  
return invalue * (inscale / outscale)  
end  
return (invalue - in_current.offset) * (inscale / outscale) + out_current.offset  
else  
-- Built-in unit.  
local in_builtin = in_current.builtin  
local out_builtin = out_current.builtin  
if in_builtin and out_builtin then  
if in_builtin == out_builtin then  
return invalue  
end  
-- There are no cases (yet) where need to convert from one  
-- built-in unit to another, so this should never occur.  
return false, { 'cvt_bug_convert' }  
end  
if in_builtin == 'mach' or out_builtin == 'mach' then  
-- Should check that only one altitude is given but am planning to remove  
-- in_current.altitude (which can only occur when Mach is the input unit),  
-- and out_current.altitude cannot occur.  
local alt = parms.altitude_ft or in_current.altitude  
if not alt and parms.altitude_m then  
alt = parms.altitude_m / 0.3048 -- 1 ft = 0.3048 m  
end  
local spd = speed_of_sound(alt)  
if in_builtin == 'mach' then  
inscale = spd  
return invalue * (inscale / outscale)  
end  
outscale = spd  
local adjust = 0.1 / inscale  
return true, {  
outvalue = invalue * (inscale / outscale),  
adjust = log10(adjust) + log10(2),  
}  
elseif in_builtin == 'hand' then  
-- 1 hand = 4 inches; 1.2 hands = 6 inches.  
-- Decimals of a hand are only defined for the first digit, and  
-- the first fractional digit should be a number of inches (1, 2 or 3).  
-- However, this code interprets the entire fractional part as the number  
-- of inches / 10 (so 1.75 inches would be 0.175 hands).  
-- A value like 12.3 hands is exactly 12*4 + 3 inches; base default precision on that.  
local integer, fracpart = math.modf(invalue)  
local inch_value = 4 * integer + 10 * fracpart -- equivalent number of inches  
local factor = inscale / outscale  
if factor == 4 then  
-- Am converting to inches: show exact result, and use "inches" not "in" by default.  
if parms.abbr_org == nil then  
out_current.usename = true  
end  
local show = format('%g', abs(inch_value)) -- show and clean are unsigned  
if not show:find('e', 1, true) then  
return true, {  
invalue = inch_value,  
outvalue = inch_value,  
clean = show,  
show = show,  
}  
end  
end  
local outvalue = (integer + 2.5 * fracpart) * factor  
local fracstr = info.clean:match('%.(.*)') or ''  
local fmt  
if fracstr == '' then  
fmt = '%.0f'  
else  
fmt = '%.' .. format('%d', #fracstr - 1) .. 'f'  
end  
return true, {  
invalue = inch_value,  
clean = format(fmt, inch_value),  
outvalue = outvalue,  
minprec = 0,  
}  
end  
end  
return false, { 'cvt_bug_convert' } -- should never occur  
end  

local function user_style(parms, i)  
-- Return text for a user-specified style for a table cell, or '' if ,  
-- given i = 1 (input style) or 2 (output style).  
local style = parms[(i == 1) and 'stylein' or 'styleout']  
if style then  
style = style:gsub('"', '')  
if style ~= '' then  
if style:sub(-1) ~= ';' then  
style = style .. ';'  
end  
return style  
end  
end  
return ''  
end  

local function make_table_or_sort(parms, invalue, info, in_current, scaled_top)  
-- Set options to handle output for a table or a sort key, or both.  
-- The text sort key is based on the value resulting from converting  
-- the input to a fake base unit with scale = 1, and other properties  
-- required for a conversion derived from the input unit.  
-- For other modules, return the sort key in a hidden span element, and  
-- the scaled value used to generate the sort key.  
-- If scaled_top is set, it is the scaled value of the numerator of a per unit  
-- to be combined with this unit (the denominator) to make the sort key.  
-- Scaling only works with units that convert with a factor (not temperature).  
local sortkey, scaled_value  
if parms.opt_sortable_on then  
local base = { -- a fake unit with enough fields for a valid convert  
scale = 1,  
invert = in_current.invert and 1,  
iscomplex = in_current.iscomplex,  
offset = in_current.offset and 0,  
}  
local outvalue, extra = convert(parms, invalue, info, in_current, base)  
if extra then  
outvalue = extra.outvalue  
end  
if in_current.istemperature then  
-- Have converted to kelvin; assume numbers close to zero have a  
-- rounding error and should be zero.  
if abs(outvalue) < 1e-12 then  
outvalue = 0  
end  
end  
if scaled_top and outvalue ~= 0 then  
outvalue = scaled_top / outvalue  
end  
scaled_value = outvalue  
if not valid_number(outvalue) then  
if outvalue < 0 then  
sortkey = '1000000000000000000'  
else  
sortkey = '9000000000000000000'  
end  
elseif outvalue == 0 then  
sortkey = '5000000000000000000'  
else  
local mag = floor(log10(abs(outvalue)) + 1e-14)  
local prefix  
if outvalue > 0 then  
prefix = 7000 + mag  
else  
prefix = 2999 - mag  
outvalue = outvalue + 10^(mag+1)  
end  
sortkey = format('%d', prefix) .. format('%015.0f', floor(outvalue * 10^(14-mag)))  
end  
end  
local sortspan  
if sortkey and not parms.table_align then  
sortspan = parms.opt_sortable_debug and  
'<span data-sort-value="' .. sortkey .. '♠"><span>' .. sortkey .. '♠</span></span>' or  
'<span data-sort-value="' .. sortkey .. '♠"></span>'  
parms.join_before = sortspan  
end  
if parms.table_align then  
local sort  
if sortkey then  
sort = ' data-sort-value="' .. sortkey .. '"'  
if parms.opt_sortable_debug then  
parms.join_before = '<span>' .. sortkey .. '</span>'  
end  
else  
sort = ''  
end  
local .. sort .. '|'  
end  
parms.table_joins = joins  
end  
return sortspan, scaled_value  
end  

local cvt_to_hand  

local function cvtround(parms, info, in_current, out_current)  
-- Return true, t where t is a table with the conversion results; fields:  
-- show = rounded, formatted string with the result of converting value in info,  
-- using the rounding specified in parms.  
-- singular = true if result (after rounding and ignoring any negative sign)  
-- is "1", or like "1.00", or is a fraction with value < 1;  
-- (and more fields shown below, and a calculated 'absvalue' field).  
-- or return false, t where t is an error message table.  
-- Input info.clean uses en digits (it has been translated, if necessary).  
-- Output show uses en or non-en digits as appropriate, or can be spelled.  
if out_current.builtin == 'hand' then  
return cvt_to_hand(parms, info, in_current, out_current)  
end  
local invalue = in_current.builtin == 'hand' and info.altvalue or info.value  
local outvalue, extra = convert(parms, invalue, info, in_current, out_current)  
if parms.need_table_or_sort then  
parms.need_table_or_sort = nil -- process using first input value only  
make_table_or_sort(parms, invalue, info, in_current)  
end  
if extra then  
if not outvalue then return false, extra end  
invalue = extra.invalue or invalue  
outvalue = extra.outvalue  
end  
if not valid_number(outvalue) then  
return false, { 'cvt_invalid_num' }  
end  
local isnegative  
if outvalue < 0 then  
isnegative = true  
outvalue = -outvalue  
end  
local precision, show, exponent  
local denominator = out_current.frac  
if denominator then  
show = fraction_table(outvalue, denominator)  
else  
precision = parms.precision  
if not precision then  
if parms.sigfig then  
show, exponent = make_sigfig(outvalue, parms.sigfig)  
elseif parms.opt_round then  
local n = parms.opt_round  
if n == 0.5 then  
local integer, fracpart = math.modf(floor(2 * outvalue + 0.5) / 2)  
if fracpart == 0 then  
show = format('%.0f', integer)  
else  
show = format('%.1f', integer + fracpart)  
end  
else  
show = format('%.0f', floor((outvalue / n) + 0.5) * n)  
end  
elseif in_current.builtin == 'mach' then  
local sigfig = info.clean:gsub('^[0.]+', *):gsub('%.', *):len + 1  
show, exponent = make_sigfig(outvalue, sigfig)  
else  
local inclean = info.clean  
if extra then  
inclean = extra.clean or inclean  
show = extra.show  
end  
if not show then  
precision = default_precision(parms, invalue, inclean, info.denominator, outvalue, in_current, out_current, extra)  
end  
end  
end  
end  
if precision then  
if precision >= 0 then  
local fudge  
if precision <= 8 then  
-- Add a fudge to handle common cases of bad rounding due to inability  
-- to precisely represent some values. This makes the following work:  
-- and .  
-- 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 '&nbsp;' or ' ')  
end  
if not abbr_on then  
if key_id == 'name1' then  
key_id = 'name2'  
elseif key_id == 'name1_us' then  
key_id = 'name2_us'  
end  
end  
else  
multiplier = ''  
end  
local id = unit_table.fixed_name or ((varname and not abbr_on) and variable_name(clean, unit_table) or unit_table[key_id])  
if omit_separator(id) then  
unit_table.sep = ''  
end  
if want_link then  
local link = data_code.link_exceptions[unit_table.linkey or unit_table.symbol] or unit_table.link  
if link then  
local before = ''  
local i = unit_table.customary  
if i == 1 and parms.opt_sp_us then  
i = 2 -- show "U.S." not "US"  
end  
if i == 3 and abbr_on then  
i = 4 -- abbreviate "imperial" to "imp"  
end  
local customary = text_code.customary_units[i]  
if customary then  
-- LATER: This works for language en only, but it's esoteric so ignore for now.  
local pertext  
if id:sub(1, 1) == '/' then  
-- Want unit "/USgal" to display as "/U.S. gal", not "U.S. /gal".  
pertext = '/'  
id = id:sub(2)  
elseif id:sub(1, 4) == 'per ' then  
-- Similarly want "per U.S. gallon", not "U.S. per gallon" (but in practice this is unlikely to be used).  
pertext = 'per '  
id = id:sub(5)  
else  
pertext = ''  
end  
-- Omit any "US"/"U.S."/"imp"/"imperial" from start of id since that will be inserted.  
local removes = (i < 3) and { 'US&nbsp;', 'US ', 'U.S.&nbsp;', 'U.S. ' } or { 'imp&nbsp;', 'imp ', 'imperial ' }  
for _, prefix in ipairs(removes) do  
local plen = #prefix  
if id:sub(1, plen) == prefix then  
id = id:sub(plen + 1)  
break  
end  
end  
before = pertext .. make_link(customary.link, customary[1]) .. ' '  
end  
id = before .. make_link(link, id, unit_table)  
end  
end  
return multiplier .. id  
end  

local function make_id(parms, which, unit_table)  
-- Return id, f where  
-- id = unit name or symbol, possibly modified  
-- f = true if id is a name, or false if id is a symbol  
-- using the value for index 'which', and for 'in' or 'out' (unit_table.inout).  
-- Result is '' if no symbol/name is to be used.  
-- In addition, set unit_table.sep = ' ' or '&nbsp;' or ''  
-- (the separator that caller will normally insert before the id).  
if parms.opt_values then  
unit_table.sep = ''  
return ''  
end  
local inout = unit_table.inout  
local info = unit_table.valinfo[which]  
local abbr_org = parms.abbr_org  
local adjectival = parms.opt_adjectival  
local lk = parms.lk  
local want_link = (lk == 'on' or lk == inout)  
local usename = unit_table.usename  
local singular = info.singular  
local want_name  
if usename then  
want_name = true  
else  
if abbr_org == nil then  
if parms.wantname then  
want_name = true  
end  
if unit_table.usesymbol then  
want_name = false  
end  
end  
if want_name == nil then  
local abbr = parms.abbr  
if abbr == 'on' or abbr == inout or (abbr == 'mos' and inout == 'out') then  
want_name = false  
else  
want_name = true  
end  
end  
end  
local key  
if want_name then  
if lk == nil and unit_table.builtin == 'hand' then  
want_link = true  
end  
if parms.opt_use_nbsp then  
unit_table.sep = '&nbsp;'  
else  
unit_table.sep = ' '  
end  
if parms.opt_singular then  
local value  
if inout == 'in' then  
value = info.value  
else  
value = info.absvalue  
end  
if value then -- some unusual units do not always set value field  
value = abs(value)  
singular = (0 < value and value < 1.0001)  
end  
end  
if unit_table.engscale then  
-- engscale: so "|1|e3kg" gives "1 thousand kilograms" (plural)  
singular = false  
end  
key = (adjectival or singular) and 'name1' or 'name2'  
if parms.opt_sp_us then  
key = key .. '_us'  
end  
else  
if unit_table.builtin == 'hand' then  
if parms.opt_hand_hh then  
unit_table.symbol = 'hh' -- LATER: might want i18n applied to this  
end  
end  
unit_table.sep = '&nbsp;'  
key = parms.opt_sp_us and 'sym_us' or 'symbol'  
end  
return linked_id(parms, unit_table, key, want_link, info.clean), want_name  
end  

local function decorate_value(parms, unit_table, which, number_word)  
-- If needed, update unit_table so values will be shown with extra information.  
-- For consistency with the old template (but different from fmtpower),  
-- the style to display powers of 10 includes "display:" to allow some  
-- browsers to copy, for example, "10³" as "10^3", rather than as "103".  
local info  
local engscale = unit_table.engscale  
local prefix = unit_table.vprefix  
if engscale or prefix then  
info = unit_table.valinfo[which]  
if info.decorated then  
return -- do not redecorate if repeating convert  
end  
info.decorated = true  
if engscale then  
local inout = unit_table.inout  
local abbr = parms.abbr  
if (abbr == 'on' or abbr == inout) and not parms.number_word then  
info.show = info.show ..  
'<span>×<span>' ..  
from_en('10') ..  
'</span></span>
^
<sup>' ..  
from_en(tostring(engscale.exponent)) .. '</sup>'  
elseif number_word then  
local number_id  
local lk = parms.lk  
if lk == 'on' or lk == inout then  
number_id = make_link(engscale.link, engscale[1])  
else  
number_id = engscale[1]  
end  
-- WP:NUMERAL recommends "&nbsp;" in values like "12 million".  
info.show = info.show .. (parms.opt_adjectival and '-' or '&nbsp;') .. number_id  
end  
end  
if prefix then  
info.show = prefix .. info.show  
end  
end  
end  

local function process_input(parms, in_current)  
-- Processing required once per conversion.  
-- Return block of text to represent input (value/unit).  
if parms.opt_output_only or parms.opt_output_number_only or parms.opt_output_unit_only then  
parms.joins = { *, * }  
return ''  
end  
local first_unit  
local composite = in_current.composite -- nil or table of units  
if composite then  
first_unit = composite[1]  
else  
first_unit = in_current  
end  
local id1, want_name = make_id(parms, 1, first_unit)  
local sep = first_unit.sep -- separator between value and unit, set by make_id  
local preunit = parms.preunit1  
if preunit then  
sep = '' -- any separator is included in preunit  
else  
preunit = ''  
end  
if parms.opt_input_unit_only then  
parms.joins = { *, * }  
if composite then  
local parts = { id1 }  
for i, unit in ipairs(composite) do  
if i > 1 then  
table.insert(parts, (make_id(parms, 1, unit)))  
end  
end  
id1 = table.concat(parts, ' ')  
end  
if want_name and parms.opt_adjectival then  
return preunit .. hyphenated(id1)  
end  
return preunit .. id1  
end  
if parms.opt_also_symbol and not composite and not parms.opt_flip then  
local join1 = parms.joins[1]  
if join1 == ' (' or join1 == ' [' then  
parms.joins = { ' [' .. first_unit[parms.opt_sp_us and 'sym_us' or 'symbol'] .. ']' .. join1 , parms.joins[2] }  
end  
end  
if in_current.builtin == 'mach' and first_unit.sep ~= * then -- * means omitsep with non-enwiki name  
local prefix = id1 .. '&nbsp;'  
local range = parms.range  
local valinfo = first_unit.valinfo  
local result = prefix .. valinfo[1].show  
if range then  
-- For simplicity and because more not needed, handle one range item only.  
local prefix2 = make_id(parms, 2, first_unit) .. '&nbsp;'  
result = range_text(range[1], want_name, parms, result, prefix2 .. valinfo[2].show, 'in', {spaced=true})  
end  
return preunit .. result  
end  
if composite then  
-- Simplify: assume there is no range, and no decoration.  
local mid = (not parms.opt_flip) and parms.mid or ''  
local sep1 = '&nbsp;'  
local sep2 = ' '  
if parms.opt_adjectival and want_name then  
sep1 = '-'  
sep2 = '-'  
end  
if omitsep and sep == '' then  
-- Testing the id of the most significant unit should be sufficient.  
sep1 = ''  
sep2 = ''  
end  
local parts = { first_unit.valinfo[1].show .. sep1 .. id1 }  
for i, unit in ipairs(composite) do  
if i > 1 then  
table.insert(parts, unit.valinfo[1].show .. sep1 .. (make_id(parms, 1, unit)))  
end  
end  
return table.concat(parts, sep2) .. mid  
end  
local add_unit = (parms.abbr == 'mos') or  
parms[parms.opt_flip and 'out_range_x' or 'in_range_x'] or  
(not want_name and parms.abbr_range_x)  
local range = parms.range  
if range and not add_unit then  
unlink(first_unit)  
end  
local id = range and make_id(parms, range.n + 1, first_unit) or id1  
local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, 'in')  
if was_hyphenated then  
add_unit = false  
end  
local result  
local valinfo = first_unit.valinfo  
if range then  
for i = 0, range.n do  
local number_word  
if i == range.n then  
add_unit = false  
number_word = true  
end  
decorate_value(parms, first_unit, i+1, number_word)  
local show = valinfo[i+1].show  
if add_unit then  
show = show .. first_unit.sep .. (i == 0 and id1 or make_id(parms, i+1, first_unit))  
end  
if i == 0 then  
result = show  
else  
result = range_text(range[i], want_name, parms, result, show, 'in')  
end  
end  
else  
decorate_value(parms, first_unit, 1, true)  
result = valinfo[1].show  
end  
return result .. preunit .. extra  
end  

local function process_one_output(parms, out_current)  
-- Processing required for each output unit.  
-- Return block of text to represent output (value/unit).  
local inout = out_current.inout -- normally 'out' but can be 'in' for order=out  
local id1, want_name = make_id(parms, 1, out_current)  
local sep = out_current.sep -- set by make_id  
local preunit = parms.preunit2  
if preunit then  
sep = '' -- any separator is included in preunit  
else  
preunit = ''  
end  
if parms.opt_output_unit_only then  
if want_name and parms.opt_adjectival then  
return preunit .. hyphenated(id1)  
end  
return preunit .. id1  
end  
if out_current.builtin == 'mach' and out_current.sep ~= * then -- * means omitsep with non-enwiki name  
local prefix = id1 .. '&nbsp;'  
local range = parms.range  
local valinfo = out_current.valinfo  
local result = prefix .. valinfo[1].show  
if range then  
-- For simplicity and because more not needed, handle one range item only.  
result = range_text(range[1], want_name, parms, result, prefix .. valinfo[2].show, inout, {spaced=true})  
end  
return preunit .. result  
end  
local add_unit = (parms[parms.opt_flip and 'in_range_x' or 'out_range_x'] or  
(not want_name and parms.abbr_range_x)) and  
not parms.opt_output_number_only  
local range = parms.range  
if range and not add_unit then  
unlink(out_current)  
end  
local id = range and make_id(parms, range.n + 1, out_current) or id1  
local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, inout)  
if was_hyphenated then  
add_unit = false  
end  
local result  
local valinfo = out_current.valinfo  
if range then  
for i = 0, range.n do  
local number_word  
if i == range.n then  
add_unit = false  
number_word = true  
end  
decorate_value(parms, out_current, i+1, number_word)  
local show = valinfo[i+1].show  
if add_unit then  
show = show .. out_current.sep .. (i == 0 and id1 or make_id(parms, i+1, out_current))  
end  
if i == 0 then  
result = show  
else  
result = range_text(range[i], want_name, parms, result, show, inout)  
end  
end  
else  
decorate_value(parms, out_current, 1, true)  
result = valinfo[1].show  
end  
if parms.opt_output_number_only then  
return result  
end  
return result .. preunit .. extra  
end  

local function make_output_single(parms, in_unit_table, out_unit_table)  
-- Return true, item where item = wikitext of the conversion result  
-- for a single output (which is not a combination or a multiple);  
-- or return false, t where t is an error message table.  
if parms.opt_order_out and in_unit_table.unitcode == out_unit_table.unitcode then  
out_unit_table.valinfo = in_unit_table.valinfo  
else  
out_unit_table.valinfo = collection  
for _, v in ipairs(in_unit_table.valinfo) do  
local success, info = cvtround(parms, v, in_unit_table, out_unit_table)  
if not success then return false, info end  
out_unit_table.valinfo:add(info)  
end  
end  
return true, process_one_output(parms, out_unit_table)  
end  

local function make_output_multiple(parms, in_unit_table, out_unit_table)  
-- Return true, item where item = wikitext of the conversion result  
-- for an output which is a multiple (like 'ftin');  
-- or return false, t where t is an error message table.  
local inout = out_unit_table.inout -- normally 'out' but can be 'in' for order=out  
local multiple = out_unit_table.multiple -- table of scaling factors (will not be nil)  
local combos = out_unit_table.combination -- table of unit tables (will not be nil)  
local abbr = parms.abbr  
local abbr_org = parms.abbr_org  
local disp = parms.disp  
local want_name = (abbr_org == nil and (disp == 'or' or disp == 'slash')) or  
not (abbr == 'on' or abbr == inout or abbr == 'mos')  
local want_link = (parms.lk == 'on' or parms.lk == inout)  
local mid = parms.opt_flip and parms.mid or ''  
local sep1 = '&nbsp;'  
local sep2 = ' '  
if parms.opt_adjectival and want_name then  
sep1 = '-'  
sep2 = '-'  
end  
local do_spell = parms.opt_spell_out  
parms.opt_spell_out = nil -- so the call to cvtround does not spell the value  
local function make_result(info, isfirst)  
local fmt, outvalue, sign  
local results = {}  
for i = 1, #combos do  
local tfrac, thisvalue, strforce  
local out_current = combos[i]  
out_current.inout = inout  
local scale = multiple[i]  
if i == 1 then -- least significant unit ('in' from 'ftin')  
local decimals  
out_current.frac = out_unit_table.frac  
local success, outinfo = cvtround(parms, info, in_unit_table, out_current)  
if not success then return false, outinfo end  
if isfirst then  
out_unit_table.valinfo = { outinfo } -- in case output value of first least significant unit is needed  
end  
sign = outinfo.sign  
tfrac = outinfo.fraction_table  
if outinfo.is_scientific then  
strforce = outinfo.show  
decimals = ''  
elseif tfrac then  
decimals = ''  
else  
local show = outinfo.show -- number as a string in local language  
local p1, p2 = show:find(numdot, 1, true)  
decimals = p1 and show:sub(p2 + 1) or '' -- text after numdot, if any  
end  
fmt = '%.' .. ulen(decimals) .. 'f' -- to reproduce precision  
if decimals == '' then  
if tfrac then  
outvalue = floor(outinfo.raw_absvalue) -- integer part only; fraction added later  
else  
outvalue = floor(outinfo.raw_absvalue + 0.5) -- keep all integer digits of least significant unit  
end  
else  
outvalue = outinfo.absvalue  
end  
end  
if scale then  
outvalue, thisvalue = divide(outvalue, scale)  
else  
thisvalue = outvalue  
end  
local id  
if want_name then  
if varname then  
local clean  
if strforce or tfrac then  
clean = '.1' -- dummy value to force name for floating point  
else  
clean = format(fmt, thisvalue)  
end  
id = variable_name(clean, out_current)  
else  
local key = 'name2'  
if parms.opt_adjectival then  
key = 'name1'  
elseif tfrac then  
if thisvalue == 0 then  
key = 'name1'  
end  
elseif parms.opt_singular then  
if 0 < thisvalue and thisvalue < 1.0001 then  
key = 'name1'  
end  
else  
if thisvalue == 1 then  
key = 'name1'  
end  
end  
id = out_current[key]  
end  
else  
id = out_current['symbol']  
end  
if i == 1 and omit_separator(id) then  
-- Testing the id of the least significant unit should be sufficient.  
sep1 = ''  
sep2 = ''  
end  
if want_link then  
local link = out_current.link  
if link then  
id = make_link(link, id, out_current)  
end  
end  
local strval  
local spell_inout = (i == #combos or outvalue == 0) and inout or '' -- trick so the last value processed (first displayed) has uppercase, if requested  
if strforce and outvalue == 0 then  
sign = '' -- any sign is in strforce  
strval = strforce -- show small values in scientific notation; will only use least significant unit  
elseif tfrac then  
local wholestr = (thisvalue > 0) and tostring(thisvalue) or nil  
strval = format_fraction(parms, spell_inout, false, wholestr, tfrac.numstr, tfrac.denstr, do_spell)  
else  
strval = (thisvalue == 0) and from_en('0') or with_separator(parms, format(fmt, thisvalue))  
if do_spell then  
strval = spell_number(parms, spell_inout, strval) or strval  
end  
end  
table.insert(results, strval .. sep1 .. id)  
if outvalue == 0 then  
break  
end  
fmt = '%.0f' -- only least significant unit can have a non-integral value  
end  
local reversed, count = {}, #results  
for i = 1, count do  
reversed[i] = results[count + 1 - i]  
end  
return true, sign .. table.concat(reversed, sep2)  
end  
local valinfo = in_unit_table.valinfo  
local success, result = make_result(valinfo[1], true)  
if not success then return false, result end  
local range = parms.range  
if range then  
for i = 1, range.n do  
local success, result2 = make_result(valinfo[i+1])  
if not success then return false, result2 end  
result = range_text(range[i], want_name, parms, result, result2, inout, {spaced=true})  
end  
end  
return true, result .. mid  
end  

local function process(parms, in_unit_table, out_unit_table)  
-- Return true, s, outunit where s = final wikitext result,  
-- or return false, t where t is an error message table.  
linked_pages = {}  
local success, bad_output  
local bad_input_mcode = in_unit_table.bad_mcode -- nil if input unit is a valid convert unit  
local out_unit = parms.out_unit  
if out_unit == nil or out_unit == '' or type(out_unit) == 'function' then  
if bad_input_mcode or parms.opt_input_unit_only then  
bad_output = ''  
else  
local getdef = type(out_unit) == 'function' and out_unit or get_default  
success, out_unit = getdef(in_unit_table.valinfo[1].value, in_unit_table)  
parms.out_unit = out_unit  
if not success then  
bad_output = out_unit  
end  
end  
end  
if not bad_output and not out_unit_table then  
success, out_unit_table = lookup(parms, out_unit, 'any_combination')  
if success then  
local mismatch = check_mismatch(in_unit_table, out_unit_table)  
if mismatch then  
bad_output = mismatch  
end  
else  
bad_output = out_unit_table  
end  
end  
local lhs, rhs  
local flipped = parms.opt_flip and not bad_input_mcode  
if bad_output then  
rhs = (bad_output == *) and * or message(parms, bad_output)  
elseif parms.opt_input_unit_only then  
rhs = ''  
else  
local combos -- nil (for 'ft' or 'ftin'), or table of unit tables (for 'm ft')  
if not out_unit_table.multiple then -- nil/false ('ft' or 'm ft'), or table of factors ('ftin')  
combos = out_unit_table.combination  
end  
local frac = parms.frac -- nil or denominator of fraction for output values  
if frac then  
-- Apply fraction to the unit (if only one), or to non-SI units (if a combination),  
-- except that if a precision is also specified, the fraction only applies to  
-- the hand unit; that allows the following result:  
-- → 156 centimetres (61.4 in; 15.1½ hands)  
-- However, the following is handled elsewhere as a special case:  
-- → 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 side first so any duplicate links (from lk=on) are suppressed  
-- on . Example:  
lhs = process_input(parms, in_unit_table)  
end  
for i = 1, imax do  
local success, item  
local out_current = combos and combos[i] or out_unit_table  
out_current.inout = 'out'  
if i == 1 then  
if imax > 1 and out_current.builtin == 'hand' then  
out_current.out_next = combos[2] -- built-in hand can influence next unit in a combination  
end  
if parms.opt_order_out then  
out_current.inout = 'in'  
end  
end  
if out_current.multiple then  
success, item = make_output_multiple(parms, in_unit_table, out_current)  
else  
success, item = make_output_single(parms, in_unit_table, out_current)  
end  
if not success then return false, item end  
outputs[i] = item  
end  
if parms.opt_order_out then  
lhs = outputs[1]  
table.remove(outputs, 1)  
end  
local sep = parms.table_joins and parms.table_joins[2] or parms.join_between  
rhs = table.concat(outputs, sep)  
end  
if flipped or not lhs then  
local input = process_input(parms, in_unit_table)  
if flipped then  
lhs = rhs  
rhs = input  
else  
lhs = input  
end  
end  
if parms.join_before then  
lhs = parms.join_before .. lhs  
end  
local wikitext  
if bad_input_mcode then  
if bad_input_mcode == '' then  
wikitext = lhs  
else  
wikitext = lhs .. message(parms, bad_input_mcode)  
end  
elseif parms.table_joins then  
wikitext = parms.table_joins[1] .. lhs .. parms.table_joins[2] .. rhs  
else  
wikitext = lhs .. parms.joins[1] .. rhs .. parms.joins[2]  
end  
if parms.warnings and not bad_input_mcode then  
wikitext = wikitext .. parms.warnings  
end  
return true, get_styles(parms) .. wikitext, out_unit_table  
end  

local function main_convert  
-- Do convert, and if needed, do it again with higher default precision.  
local parms = { = } -- will hold template arguments, after translation  
set_config(.args)  
local success, result = get_parms(parms, :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 ,  
-- 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 }