Modul:Convert

-- Convert a value from one unit of measurement to another.-- Example: {{convert|123|lb|kg}} --> 123 pounds (56 kg)-- See [[:en:Template:Convert/Transwiki guide]] if copying to another wiki.local MINUS = '−'  -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92)local abs = math.abslocal floor = math.floorlocal format = string.formatlocal log10 = math.log10local ustring = mw.ustringlocal ulen = ustring.lenlocal usub = ustring.sub-- Configuration options to keep magic values in one location.-- Conversion data and message text are defined in separate modules.local config, maxsigfiglocal numdot  -- must be '.' or ',' or a character which works in a regexlocal numsep, numsep_remove, numsep_remove2local data_code, all_unitslocal text_codelocal varname        -- can be a code to use variable names that depend on valuelocal from_en_table  -- to translate an output string of en digits to local languagelocal 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 digitslocal group_method = 3     -- code for how many digits are in a grouplocal per_word = 'per'     -- for units like "liters per kilometer"local plural_suffix = 's'  -- only other useful value is probably '' to disable plural unit nameslocal 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 unitslocal extra_units   -- nil or table of extra units from extra_module-- Some options in the invoking template can set variables used later in the module.local currency_text  -- for a user-defined currency symbol: {{convert|12|$/ha|$=€}} (euro replaces dollar)local function from_en(text)-- Input is a string representing a number in en digits with '.' decimal mark,-- without digit grouping (which is done just after calling this).-- Return the translation of the string with numdot and digits in local language.if numdot ~= '.' thentext = text:gsub('%.', numdot)endif from_en_table thentext = text:gsub('%d', from_en_table)endreturn textendlocal 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 thentext = ustring.gsub(text, '%d', to_en_table)endif numsep_remove thentext = text:gsub(numsep_remove, '')endif numsep_remove2 thentext = text:gsub(numsep_remove2, '')endif numdot ~= '.' thentext = text:gsub(numdot, '.')endreturn textendlocal 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 ',' endtext = text:gsub('^%-', ''):gsub('%+%d+/%d+$', ''):gsub('[Ee]%-?%d+$', '')local decimal =text:match('^0?([.,])%d+$') ortext:match('%d([.,])%d?%d?$') ortext:match('%d([.,])%d%d%d%d+$')if decimal then return decimal endif text:match('%.%d+%.') then return ',' endif text:match('%,%d+,') then return '.' endendlocal add_warning, with_separator  -- forward declarationslocal 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 thentext = ustring.gsub(text, '%d', to_en_table)endif decimal_mark(text) == '.' thenlocal original = texttext = text:gsub(',', '')  -- for example, interpret "1,234.5" as an enwiki valueif parms thenadd_warning(parms, 0, 'cvt_enwiki_num', original, with_separator({}, text))endelseif numsep_remove thentext = text:gsub(numsep_remove, '')endif numsep_remove2 thentext = text:gsub(numsep_remove2, '')endif numdot ~= '.' thentext = text:gsub(numdot, '.')endendreturn textendlocal 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 thenif id:sub(1, 2) == '-{' then  -- for "-{...}-" content language variantreturn trueendif id:byte() > 127 thenlocal first = usub(id, 1, 1)if first ~= 'Å' and first ~= '°' and first ~= 'µ' thenreturn trueendendendreturn id:sub(1, 1) == '/'  -- no separator before units like "/ha"endlocal spell_module  -- name of module that can spell numberslocal speller       -- function from that module to handle spelling (set if spelling is wanted)local function set_config(args)-- Set configuration options from template #invoke or defaults.config = argsmaxsigfig = config.maxsigfig or 14  -- maximum number of significant figureslocal data_module, text_modulelocal sandbox = config.sandbox and ('/' .. config.sandbox) or ''data_module = "Module:Convert/data" .. sandboxtext_module = "Module:Convert/text" .. sandboxextra_module = "Module:Convert/extra" .. sandboxspell_module = "Module:ConvertNumeric"data_code = mw.loadData(data_module)text_code = mw.loadData(text_module)all_units = data_code.all_unitslocal translation = text_code.translation_tableif translation thennumdot = translation.numdotnumsep = translation.numsepif numdot == ',' and numsep == '.' thenif text_code.all_messages.cvt_enwiki_num thento_en = to_en_with_checkendendif translation.group thengroup_method = translation.groupendif translation.per_word thenper_word = translation.per_wordendif translation.plural_suffix thenplural_suffix = translation.plural_suffixendvarname = translation.varnamefrom_en_table = translation.from_enlocal use_workaround = trueif 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_enif source thento_en_table = {}for k, v in pairs(source) doto_en_table[k] = vendendelseto_en_table = translation.to_enendif translation.lang == 'en default' thenen_default = true  -- for hiwikiendomitsep = translation.omitsep  -- for zhwikiendnumdot = config.numdot or numdot or '.'  -- decimal mark before fractional digitsnumsep = 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 ~= '' thennumsep_remove = (numsep == '.') and '%.' or numsependif numsep ~= ',' and numdot ~= ',' thennumsep_remove2 = ','  -- so numbers copied from enwiki will workendendlocal function collection()-- Return a table to hold items.return {n = 0,add = function (self, item)self.n = self.n + 1self[self.n] = itemend,}endlocal 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 % denominatorif not (0 <= remainder and remainder < denominator) then-- Floating point limits may need this, as in {{convert|160.02|Ym|ydftin}}.remainder = 0endreturn quotient, remainderendlocal 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 itemfor item in text:gmatch('%s*(.-)%s*' .. delimiter) dotable.insert(t, item)endreturn tendlocal 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' thenreturn text:match("^%s*(.-)%s*$")endendlocal 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 doif t[i] == nil thenreturn i - 1endendendlocal function wanted_category(cat)-- Return cat if it is wanted in current namespace, otherwise return nil.-- This is so tracking categories only include pages that need correction.local title = mw.title.getCurrentTitle()if title thenlocal nsdefault = '0'  -- default namespace: '0' = article; '0,10' = article and templatelocal namespace = title.namespacefor _, v in ipairs(split(config.nscat or nsdefault, ',')) doif namespace == tonumber(v) thenreturn catendendendendlocal function message(mcode)-- Return wikitext for an error message, including category if specified-- for the message type.-- mcode = numbered table specifying the message:--    mcode[1] = 'cvt_xxx' (string used as a key to get message info)--    mcode[2] = 'parm1' (string to replace first %s if any in message)--    mcode[3] = 'parm2' (string to replace second %s if any in message)--    mcode[4] = 'parm3' (string to replace third %s if any in message)local msg = text_code.all_messages[mcode[1]]local nowiki = mw.text.nowikiif msg thenlocal parts = {}local regex, replace = msg.regex, msg.replacefor i = 1, 3 dolocal limit = 40local s = mcode[i + 1]if s thenif regex and replace thens = s:gsub(regex, replace)limit = nil  -- allow long "should be" messagesend-- Escape user input so it does not break the message.-- To avoid tags (like {{convert|1<math>23</math>|m}}) breaking-- the mouseover title, any strip marker starting with char(127) is-- replaced with '...' (text not needing i18n).local appendlocal pos = s:find(string.char(127), 1, true)if pos thenappend = '...'s = s:sub(1, pos - 1)endif limit and ulen(s) > limit thens = usub(s, 1, limit)append = '...'ends = nowiki(s) .. (append or '')elses = '?'endparts[i] = sendlocal title = format(msg[1] or 'Missing message', parts[1], parts[2], parts[3])local text = msg[2] or 'Missing message'local cat = wanted_category(text_code.all_categories[msg[3]]) or ''local anchor = msg[4] or ''local fmt = text_code.all_messages[msg.format or 'cvt_format'] or 'convert: bug'title = title:gsub('"', '&quot;')return format(fmt, anchor, title, text, cat)endreturn 'Convert internal error: unknown message'endfunction add_warning(parms, level, key, text1, text2)  -- for forward declaration above-- If enabled, add a warning that will be displayed after the convert result.-- To reduce output noise, only the first warning is displayed.if config.warnings or level < 0 thenif level <= (tonumber(config.warnings) or 1) thenif parms.warnings == nil thenparms.warnings = message({ key, text1, text2 })endendendendlocal 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 thirdsif not speller thenlocal function get_speller(module)return require(module).spell_numberendlocal successsuccess, speller = pcall(get_speller, spell_module)if not success or type(speller) ~= 'function' thenadd_warning(parms, 1, 'cvt_no_spell')return nilendendlocal caseif parms.spell_upper == inout thencase = trueparms.spell_upper = nil  -- only uppercase first word in a multiple unitendlocal sp = not parms.opt_sp_uslocal adj = parms.opt_adjectivalreturn speller(number, numerator, denominator, case, sp, adj)end-------------------------------------------------------------------------- BEGIN: Code required only for built-in units.-- LATER: If need much more code, move to another module to simplify this module.local function speed_of_sound(altitude)-- This is for the Mach built-in unit of speed.-- Return speed of sound in metres per second at given altitude in feet.-- If no altitude given, use default (zero altitude = sea level).-- Table gives speed of sound in miles per hour at various altitudes:--   altitude = -17,499 to 302,499 feet-- mach_table[a + 4] = s where--   a = (altitude / 5000) rounded to nearest integer (-3 to 60)--   s = speed of sound (mph) at that altitude-- LATER: Should calculate result from an interpolation between the next-- lower and higher altitudes in table, rather than rounding to nearest.-- From: http://www.aerospaceweb.org/question/atmosphere/q0112.shtmllocal mach_table = {                                                       -- a =799.5, 787.0, 774.2, 761.207051,                                       -- -3 to  0748.0, 734.6, 721.0, 707.0, 692.8, 678.3, 663.5, 660.1, 660.1, 660.1,  --  1 to 10660.1, 660.1, 660.1, 662.0, 664.3, 666.5, 668.9, 671.1, 673.4, 675.6,  -- 11 to 20677.9, 683.7, 689.9, 696.0, 702.1, 708.1, 714.0, 719.9, 725.8, 731.6,  -- 21 to 30737.3, 737.7, 737.7, 736.2, 730.5, 724.6, 718.8, 712.9, 707.0, 701.1,  -- 31 to 40695.0, 688.9, 682.8, 676.6, 670.4, 664.1, 657.8, 652.9, 648.3, 643.7,  -- 41 to 50639.1, 634.4, 629.6, 624.8, 620.0, 615.2, 613.2, 613.2, 613.2, 613.5,  -- 51 to 60}altitude = altitude or 0local a = (altitude < 0) and -altitude or altitudea = floor(a / 5000 + 0.5)if altitude < 0 thena = -aendif a < -3 thena = -3elseif a > 60 thena = 60endreturn mach_table[a + 4] * 0.44704  -- mph converted to m/send-- END: Code required only for built-in units.------------------------------------------------------------------------local function get_range(word)-- Return a range (string or table) corresponding to word (like "to"),-- or return nil if not a range word.local ranges = text_code.rangesreturn ranges.types[word] or ranges.types[ranges.aliases[word]]endlocal 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) thenreturn nilendreturn { 'cvt_mismatch', unit1.utype, unit2.utype }endlocal 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) doif in_table[field] thenout_table[field] = in_table[field]endendendlocal 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) doresult[k] = vendreturn resultendlocal 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 valueif key == 'name1' or key == 'sym_us' thenvalue = self.symbolelseif key == 'name2' thenvalue = self.name1 .. plural_suffixelseif key == 'name1_us' thenvalue = self.name1if not rawget(self, 'name2_us') then-- If name1_us is 'foot', do not make name2_us by appending plural_suffix.self.name2_us = self.name2endelseif key == 'name2_us' thenlocal raw1_us = rawget(self, 'name1_us')if raw1_us thenvalue = raw1_us .. plural_suffixelsevalue = self.name2endelseif key == 'link' thenvalue = self.name1elsevalue = falseendrawset(self, key, value)return valueend}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' thenpos = tonumber(split(pos, ',')[index])endif pos thenreturn name:sub(1, pos - 1) .. unit.si_name .. name:sub(pos)endreturn unit.si_name .. nameendlocal 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 valueif key == 'symbol' thenvalue = self.si_prefix .. self._symbolelseif key == 'sym_us' thenvalue = rawget(self, '_sym_us')if value thenvalue = self.si_prefix .. valueelsevalue = self.symbolendelseif key == 'name1' thenvalue = prefixed_name(self, self._name1, 1)elseif key == 'name2' thenvalue = rawget(self, '_name2')if value thenvalue = prefixed_name(self, value, 2)elsevalue = self.name1 .. plural_suffixendelseif key == 'name1_us' thenvalue = rawget(self, '_name1_us')if value thenvalue = prefixed_name(self, value, 3)elsevalue = self.name1endelseif key == 'name2_us' thenvalue = rawget(self, '_name2_us')if value thenvalue = prefixed_name(self, value, 4)elseif rawget(self, '_name1_us') thenvalue = self.name1_us .. plural_suffixelsevalue = self.name2endelseif key == 'link' thenvalue = self.name1elsevalue = falseendrawset(self, key, value)return valueend}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.__index = function (self, key)local valueif key == 'symbol' thenlocal per = self.perlocal unit1, unit2 = per[1], per[2]if unit1 thenvalue = unit1[key] .. '/' .. unit2[key]elsevalue = '/' .. unit2[key]endelseif key == 'sym_us' thenvalue = self.symbolelseif key == 'scale' thenlocal per = self.perlocal unit1, unit2 = per[1], per[2]value = (unit1 and unit1.scale or 1) * self.scalemultiplier / unit2.scaleelsevalue = falseendrawset(self, key, value)return valueend}local function make_per(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 = { 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 calculationlocal prefixfor i, v in ipairs(unit_table.per) doif 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] thenprefix = currency_text or velselocal success, t = ulookup(v)if not success then return false, t endresult.per[i] = tendendlocal multiplier = unit_table.multiplierif 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].utypelocal t = data_code.per_unit_fixups[utype]if t thenif type(t) == 'table' thenutype = t.utype or utyperesult.link = result.link or t.linkmultiplier = multiplier or t.multiplierelseutype = tendendresult.utype = utypeendresult.scalemultiplier = multiplier or 1result.vprefix = prefix or false  -- set to non-nil to avoid calling __indexreturn true, setmetatable(result, unit_per_mt)endlocal function lookup(parms, unitcode, what, utable, fails, depth)-- Return true, t where t is a copy of the unit's converter table,-- or return false, t where t is an error message table.-- Parameter 'what' determines whether combination units are accepted:--   'no_combination'  : single unit only--   'any_combination' : single unit or combination or output multiple--   'only_multiple'   : single unit or output multiple only-- Parameter unitcode is a symbol (like 'g'), with an optional SI prefix (like 'kg').-- If, for example, 'kg' is in this table, that entry is used;-- otherwise the prefix ('k') is applied to the base unit ('g').-- If unitcode is a known combination code (and if allowed by what),-- a table of output multiple unit tables is included in the result.-- For compatibility with the old template, an underscore in a unitcode is-- replaced with a space so usage like {{convert|350|board_feet}} works.-- Wikignomes may also put two spaces or "&nbsp;" in combinations, so-- replace underscore, "&nbsp;", and multiple spaces with a single space.utable = utable or all_unitsfails = fails or {}depth = depth and depth + 1 or 1if 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 }endif unitcode == nil or unitcode == '' thenreturn false, { 'cvt_no_unit' }endunitcode = unitcode:gsub('_', ' '):gsub('&nbsp;', ' '):gsub('  +', ' ')local t = utable[unitcode]if t thenif t.shouldbe thenreturn false, { 'cvt_should_be', t.shouldbe }endif t.sp_us thenparms.opt_sp_us = trueendlocal target = t.target  -- nil, or unitcode is an alias for this targetif target thenlocal success, result = lookup(parms, target, what, utable, fails, depth)if not success then return false, result endoverride_from(result, t, { 'customary', 'default', 'link', 'symbol', 'symlink' })local multiplier = t.multiplierif multiplier thenresult.multiplier = tostring(multiplier)result.scale = result.scale * multiplierendreturn true, resultendif t.per thenreturn make_per(t, function (ucode) return lookup(parms, ucode, 'no_combination', utable, fails, depth) end)endlocal combo = t.combination  -- nil or a table of unitcodesif combo thenlocal multiple = t.multipleif what == 'no_combination' or (what == 'only_multiple' and not multiple) thenreturn 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.combinationfor i, v in ipairs(combo) dolocal success, t = lookup(parms, v, multiple and 'no_combination' or 'only_multiple', utable, fails, depth)if not success then return false, t endcvt[i] = tendreturn true, resultendlocal result = shallow_copy(t)if result.prefixes thenresult.si_name = ''result.si_prefix = ''return true, setmetatable(result, unit_prefixed_mt)endreturn true, setmetatable(result, unit_mt)endlocal SIprefixes = text_code.SIprefixesfor 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 thenlocal t = utable[usub(unitcode, plen+1)]if t and t.prefixes thenlocal result = shallow_copy(t)result.si_name = parms.opt_sp_us and si.name_us or si.nameresult.si_prefix = si.prefix or prefixresult.scale = t.scale * 10 ^ (si.exponent * t.prefixes)return true, setmetatable(result, unit_prefixed_mt)endendend-- Accept any unit with an engineering notation prefix like "e6cuft"-- (million cubic feet), but not chained prefixes like "e3e6cuft",-- and not if the unit is a combination or multiple,-- and not if the unit has an offset or is a built-in.-- Only en digits are accepted.local has_plus = unitcode:find('+', 1, true)if not has_plus thenlocal exponent, baseunit = unitcode:match('^e(%d+)(.*)')if exponent thenlocal engscale = text_code.eng_scales[exponent]if engscale thenlocal success, result = lookup(parms, baseunit, 'no_combination', utable, fails, depth)if success and not (result.offset or result.builtin or result.engscale) thenresult.defkey = unitcode  -- key to lookup default exceptionresult.engscale = engscaleresult.scale = result.scale * 10 ^ tonumber(exponent)return true, resultendendendend-- 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_fatallocal combo = collection()if has_plus thenerr_is_fatal = truefor item in (unitcode .. '+'):gmatch('%s*(.-)%s*%+') doif item ~= '' thencombo:add(item)endendelseif unitcode:find('%s') thenfor item in unitcode:gmatch('%S+') docombo:add(item)endendif combo.n > 1 thenlocal function lookup_combo()if what == 'no_combination' or what == 'only_multiple' thenreturn false, { 'cvt_bad_unit', unitcode }endlocal result = { combination = {} }local cvt = result.combinationfor i, v in ipairs(combo) dolocal success, t = lookup(parms, v, 'only_multiple', utable, fails, depth)if not success then return false, t endif i == 1 thenresult.utype = t.utypeelselocal mismatch = check_mismatch(result, t)if mismatch thenreturn false, mismatchendendcvt[i] = tendreturn true, resultendlocal success, result = lookup_combo()if success or err_is_fatal thenreturn success, resultendend-- Look for x/y; split on right-most slash to get scale correct (x/y/z is x/y per z).local top, bottom = unitcode:match('^(.-)/([^/]+)$')if top and not unitcode:find('e%d') then-- If valid, create an automatic per unit for an "x/y" unit code.-- The unitcode must not include extraneous spaces.-- Engineering notation (apart from at start and which has been stripped before here),-- is not supported so do not make a per unit if find text like 'e3' in unitcode.local success, result = make_per({ per = {top, bottom} }, function (ucode) return lookup(parms, ucode, 'no_combination', utable, fails, depth) end)if success thenreturn true, resultendendif not parms.opt_ignore_error and not get_range(unitcode) then-- Want the "what links here" list for the extra_module to show only cases-- where an extra unit is used, so do not require it if invoked from {{val}}-- or if looking up a range word which cannot be a unit.if not extra_units thenlocal success, extra = pcall(function () return require(extra_module).extra_units end)if success and type(extra) == 'table' thenextra_units = extraendendif 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] thenfails[unitcode] = truelocal other = (utable == all_units) and extra_units or all_unitslocal success, result = lookup(parms, unitcode, what, other, fails, depth)if success thenreturn true, resultendendendendif 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 thenreturn lookup(parms, en_code, what, utable, fails, depth)endendreturn false, { 'cvt_unknown', unitcode }endlocal 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 thenreturn trueendendlocal function hyphenated(name, parts)-- Return a hyphenated form of given name (for adjectival usage).-- The name may be linked and the target of the link must not be changed.-- Hypothetical examples:--   [[long ton|ton]]         →  [[long ton|ton]]          (no change)--   [[tonne|long ton]]       →  [[tonne|long-ton]]--   [[metric ton|long ton]]  →  [[metric ton|long-ton]]--   [[long ton]]             →  [[long ton|long-ton]]-- Input can also have multiple links in a single name like:--   [[United States customary units|U.S.]] [[US gallon|gallon]]--   [[mile]]s per [[United States customary units|U.S.]] [[quart]]--   [[long ton]]s per [[short ton]]-- Assume that links cannot be nested (never like "[[abc[[def]]ghi]]").-- This uses a simple and efficient procedure that works for most cases.-- Some units (if used) would require more, and can later think about-- adding a method to handle exceptions.-- The procedure is to replace each space with a hyphen, but-- not a space after ')' [for "(pre-1954&nbsp;US) nautical mile"], and-- not spaces immediately before '(' or in '(...)' [for cases like-- "British thermal unit (ISO)" and "Calorie (International Steam Table)"].if name:find(' ', 1, true) thenif parts thenlocal posif name:sub(1, 1) == '(' thenpos = name:find(')', 1, true)if pos thenreturn name:sub(1, pos+1) .. name:sub(pos+2):gsub(' ', '-')endelseif name:sub(-1) == ')' thenpos = name:find('(', 1, true)if pos thenreturn name:sub(1, pos-2):gsub(' ', '-') .. name:sub(pos-1)endendreturn name:gsub(' ', '-')endparts = collection()for before, item, after in name:gmatch('([^[]*)(%[%[[^[]*%]%])([^[]*)') doif item:find(' ', 1, true) thenlocal prefixlocal plen = item:find('|', 1, true)if plen thenprefix = item:sub(1, plen)item = item:sub(plen + 1, -3)elseprefix = item:sub(1, -3) .. '|'item = item:sub(3, -3)enditem = prefix .. hyphenated(item, parts) .. ']]'endparts:add(before:gsub(' ', '-') .. item .. after:gsub(' ', '-'))endif parts.n == 0 then-- No link like "[[...]]" was found in the original name.parts:add(hyphenated(name, parts))endreturn table.concat(parts)endreturn nameendlocal 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 == '' thenreturn ''endlocal mid = (inout == (parms.opt_flip and 'out' or 'in')) and parms.mid or ''if want_name thenif parms.opt_adjectival thenreturn '-' .. hyphenated(id) .. mid, trueendif parms.opt_add_s and id:sub(-1) ~= 's' thenid = id .. 's'  -- for nowikiendendreturn sep .. id .. midendlocal function change_sign(text)-- Change sign of text for correct appearance because it is negated.if text:sub(1, 1) == '-' thenreturn text:sub(2)endreturn '-' .. textendlocal function use_minus(text)-- Return text with Unicode minus instead of '-', if present.if text:sub(1, 1) == '-' thenreturn MINUS .. text:sub(2)endreturn textendlocal function digit_groups(parms, text, method)-- Return a numbered table of groups of digits (left-to-right, in local language).-- Parameter method is a number or nil:--   3 for 3-digit grouping (default), or--   2 for 3-then-2 grouping (only for digits before decimal mark).local len_rightlocal len_left = text:find('.', 1, true)if len_left thenlen_right = #text - len_leftlen_left = len_left - 1elselen_left = #textendlocal twos = method == 2 and len_left > 5local groups = collection()local run = len_leftlocal nif run < 4 or (run == 4 and parms.opt_comma5) thenif parms.opt_gaps thenn = runelsen = #textendelseif twos thenn = run % 2 == 0 and 1 or 2elsen = run % 3 == 0 and 3 or run % 3endwhile run > 0 dogroups:add(n)run = run - nn = (twos and run > 3) and 2 or 3endif len_right thenif groups.n == 0 thengroups:add(0)endif parms.opt_gaps and len_right > 3 thenlocal want4 = not parms.opt_gaps3  -- true gives no gap before trailing single digitlocal isfirst = truerun = len_rightwhile run > 0 don = (want4 and run == 4) and 4 or (run > 3 and 3 or run)if isfirst thenisfirst = falsegroups[groups.n] = groups[groups.n] + 1 + nelsegroups:add(n)endrun = run - nendelsegroups[groups.n] = groups[groups.n] + 1 + len_rightendendlocal pos = 1for i, length in ipairs(groups) dogroups[i] = from_en(text:sub(pos, pos + length - 1))pos = pos + lengthendreturn groupsendfunction 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.if #text < 4 or parms.opt_nocomma or numsep == '' thenreturn from_en(text)endlocal groups = digit_groups(parms, text, group_method)if parms.opt_gaps thenif groups.n <= 1 thenreturn groups[1] or ''endlocal nowrap = '<span style="white-space: nowrap">'local gap = '<span style="margin-left: 0.25em">'local close = '</span>'return nowrap .. groups[1] .. gap .. table.concat(groups, close .. gap, 2, groups.n) .. close .. closeendreturn table.concat(groups, numsep)end-- An input value like 1.23e12 is displayed using scientific notation (1.23×10¹²).-- That also makes the output use scientific notation, except for small values.-- In addition, very small or very large output values use scientific notation.-- Use format(fmtpower, significand, '10', exponent) where each argument is a string.local fmtpower = '%s<span style="margin:0 .15em 0 .25em">×</span>%s<sup>%s</sup>'local function with_exponent(parms, show, exponent)-- Return wikitext to display the implied value in scientific notation.-- Input uses en digits; output uses digits in local language.return format(fmtpower, with_separator(parms, show), from_en('10'), use_minus(from_en(tostring(exponent))))endlocal 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 thensigfig = 1elseif sigfig > maxsigfig thensigfig = maxsigfigendif value == 0 thenreturn string.rep('0', sigfig), 1endlocal exp, fracpart = math.modf(log10(value))if fracpart >= 0 thenfracpart = fracpart - 1exp = exp + 1endlocal 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 + 1endassert(#digits == sigfig, 'Bug: rounded number has wrong length')return digits, expend-- Fraction output format.local fracfmt = {{ -- Like {{frac}} (fraction slash).-- 1/2    : sign, numerator, denominator-- 1+2/3  : signed_wholenumber, numerator, denominator'<span class="frac nowrap">%s<sup>%s</sup>&frasl;<sub>%s</sub></span>','<span class="frac nowrap">%s<span class="visualhide">&nbsp;</span><sup>%s</sup>&frasl;<sub>%s</sub></span>',},{ -- Like {{sfrac}} (fraction horizontal bar).-- 1//2   : sign, numerator, denominator (sign should probably be before the fraction, but then it can wrap, and html is already too long)-- 1+2//3 : signed_wholenumber, numerator, denominator'<span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%%; text-align:center;"><span style="display:block; line-height:1em; padding:0 0.1em;">%s%s</span><span class="visualhide">/</span><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">%s</span></span>','<span class="sfrac nowrap">%s<span class="visualhide">&nbsp;</span><span style="display:inline-block; vertical-align:-0.5em; font-size:85%%; text-align:center;"><span style="display:block; line-height:1em; padding:0 0.1em;">%s</span><span class="visualhide">/</span><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">%s</span></span></span>',},}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 wikitextif not style thenstyle = parms.opt_fraction_horizontal and 2 or 1endif wholestr == '' thenwholestr = nilendif wholestr thenlocal decorated = with_separator(parms, wholestr)if negative thendecorated = MINUS .. decoratedendlocal fmt = fracfmt[style][2]wikitext = format(fmt, decorated, from_en(numstr), from_en(denstr))elselocal sign = negative and MINUS or ''wikitext = format(fracfmt[style][1], sign, from_en(numstr), from_en(denstr))endif do_spell thenif negative thenif wholestr thenwholestr = '-' .. wholestrelsenumstr = '-' .. numstrendendwikitext = spell_number(parms, inout, wholestr, numstr, denstr) or wikitextendreturn wikitextendlocal function format_number(parms, show, exponent, isnegative)-- Parameter show is a string or a table containing strings.-- Each string is a formatted number in en digits and optional '.' decimal mark.-- A table represents a fraction: integer, numerator, denominator;-- if a table is given, exponent must be nil.-- Return t where t is a table with fields:--   show = wikitext formatted to display implied value--          (digits in local language)--   is_scientific = true if show uses scientific notation--   clean = unformatted show (possibly adjusted and with inserted '.')--          (en digits)--   sign = '' or MINUS--   exponent = exponent (possibly adjusted)-- The clean and exponent fields can be used to calculate the-- rounded absolute value, if needed.---- The value implied by the arguments is found from:--   exponent is nil; and--   show is a string of digits (no sign), with an optional dot;--   show = '123.4' is value 123.4, '1234' is value 1234.0;-- or:--   exponent is an integer indicating where dot should be;--   show is a string of digits (no sign and no dot);--   there is an implied dot before show;--   show does not start with '0';--   show = '1234', exponent = 3 is value 0.1234*10^3 = 123.4.---- The formatted result:-- * Is for an output value and is spelled if wanted and possible.-- * Includes a Unicode minus if isnegative and not spelled.-- * Uses a custom decimal mark, if wanted.-- * Has digits grouped where necessary, if wanted.-- * Uses scientific notation if requested, or for very small or large values--   (which forces result to not be spelled).-- * Has no more than maxsigfig significant digits--   (same as old template and {{#expr}}).local xhi, xlo  -- these control when scientific notation (exponent) is usedif parms.opt_scientific thenxhi, xlo = 4, 2  -- default for output if input uses e-notationelseif parms.opt_scientific_always thenxhi, xlo = 0, 0  -- always use scientific notation (experimental)elsexhi, xlo = 10, 4  -- defaultendlocal sign = isnegative and MINUS or ''local maxlen = maxsigfiglocal tfracif type(show) == 'table' thentfrac = showshow = tfrac.wholestrassert(exponent == nil, 'Bug: exponent given with fraction')endif not tfrac and not exponent thenlocal integer, dot, decimals = show:match('^(%d*)(%.?)(.*)')if integer == '0' or integer == '' thenlocal zeros, figs = decimals:match('^(0*)([^0]?.*)')if #figs == 0 thenif #zeros > maxlen thenshow = '0.' .. zeros:sub(1, maxlen)endelseif #zeros >= xlo thenshow = figsexponent = -#zeroselseif #figs > maxlen thenshow = '0.' .. zeros .. figs:sub(1, maxlen)endelseif #integer >= xhi thenshow = integer .. decimalsexponent = #integerelsemaxlen = maxlen + #dotif #show > maxlen thenshow = show:sub(1, maxlen)endendendif exponent thenlocal function zeros(n)return string.rep('0', n)endif #show > maxlen thenshow = show:sub(1, maxlen)endif exponent > xhi or exponent <= -xlo or (exponent == xhi and show ~= '1' .. zeros(xhi - 1)) then-- When xhi, xlo = 10, 4 (the default), scientific notation is used if the-- rounded value satisfies: value >= 1e9 or value < 1e-4 (1e9 = 0.1e10),-- except if show is '1000000000' (1e9), for example:-- {{convert|1000000000|m|m|sigfig=10}} → 1,000,000,000 metres (1,000,000,000 m)local significandif #show > 1 thensignificand = show:sub(1, 1) .. '.' .. show:sub(2)elsesignificand = showendreturn {clean = '.' .. show,exponent = exponent,sign = sign,show = sign .. with_exponent(parms, significand, exponent-1),is_scientific = true,}endif exponent >= #show thenshow = show .. zeros(exponent - #show)  -- result has no dotelseif exponent <= 0 thenshow = '0.' .. zeros(-exponent) .. showelseshow = show:sub(1, exponent) .. '.' .. show:sub(exponent+1)endendlocal formatted_showif tfrac thenshow = tostring(tfrac.value)  -- to set clean in returned tableformatted_show = format_fraction(parms, 'out', isnegative, tfrac.wholestr, tfrac.numstr, tfrac.denstr, parms.opt_spell_out)elseif isnegative and show:match('^0.?0*$') thensign = ''  -- don't show minus if result is negative but rounds to zeroendformatted_show = sign .. with_separator(parms, show)if parms.opt_spell_out thenformatted_show = spell_number(parms, 'out', sign .. show) or formatted_showendendreturn {clean = show,sign = sign,show = formatted_show,is_scientific = false,  -- to avoid calling __index}endlocal 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 numstr, wholelocal 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 = '/'endlocal numerator = tonumber(numstr)local denominator = tonumber(denstr)if numerator == nil or denominator == nil or (negative and leading_plus ~= '') thenreturn nilendlocal wholestrif prefix == '' thenwholestr = ''whole = 0else-- 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 endif num2 == '' then  -- num2 must be '' or like '.1' but not '.' or '.12'wholestr = num1elseif #num2 ~= 2 then return nil endwholestr = num1 .. num2endif frac_sign ~= (negative and '-' or '+') then return nil endwhole = tonumber(wholestr)if whole == nil then return nil endendlocal value = whole + numerator / denominatorif not valid_number(value) then return nil endlocal altvalue = whole + numerator / (denominator * 10)local style = #slashes  -- kludge: 1 or 2 slashes can be used to select styleif style > 2 then style = 2 endlocal wikitext = format_fraction(parms, 'in', negative, leading_plus .. wholestr, numstr, denstr, parms.opt_spell_in, style)return value, altvalue, wikitext, denominatorendlocal function extract_number(parms, text, another, no_fraction)-- Return true, info if can extract a number from text,-- where info is a table with the result,-- or return false, t where t is an error message table.-- Input can use en digits or digits in local language and can-- have references at the end. Accepting references is intended-- for use in infoboxes with a field for a value passed to convert.-- Parameter another = true if the expected value is not the first.-- Before processing, the input text is cleaned:-- * Any thousand separators (valid or not) are removed.-- * Any sign (and optional following whitespace) is replaced with--   '-' (if negative) or '' (otherwise).--   That replaces Unicode minus with '-'.-- If successful, the returned info table contains named fields:--   value    = a valid number--   altvalue = a valid number, usually same as value but different--              if fraction used (for hands unit)--   singular = true if value is 1 or -1 (to use singular form of units)--   clean    = cleaned text with any separators and sign removed--              (en digits and '.' decimal mark)--   show     = text formatted for output, possibly with ref strip markers--              (digits in local language and custom decimal mark)-- The resulting show:-- * Is for an input value and is spelled if wanted and possible.-- * Has a rounded value, if wanted.-- * Has digits grouped where necessary, if wanted.-- * If negative, a Unicode minus is used; otherwise the sign is--   '+' (if the input text used '+'), or is '' (if no sign in input).text = strip(text or '')local referencelocal pos = text:find('\127', 1, true)if pos thenlocal before = text:sub(1, pos - 1)local remainder = text:sub(pos)local refs = {}while #remainder > 0 dolocal ref, spacesref, spaces, remainder = remainder:match('^(\127UNIQ[^\127]*%-ref%-%x+%-QINU\127)(%s*)(.*)')if ref thentable.insert(refs, ref)elserefs = {}breakendendif #refs > 0 thentext = strip(before)reference = table.concat(refs)endendlocal clean = to_en(text, parms)if clean == '' thenreturn false, { another and 'cvt_no_num2' or 'cvt_no_num' }endlocal isnegative, propersign = false, ''  -- most common caselocal singular, show, denominatorlocal value = tonumber(clean)local altvalueif value thenlocal sign = clean:sub(1, 1)if sign == '+' or sign == '-' thenpropersign = (sign == '+') and '+' or MINUSclean = clean:sub(2)endif value < 0 thenisnegative = truevalue = -valueendelselocal valstrfor _, prefix in ipairs({ '-', MINUS, '&minus;' }) do-- Including '-' means inputs like '- 2' (with space) are accepted as -2.-- It also sets isnegative in case input is a fraction like '-2-3/4'.local plen = #prefixif clean:sub(1, plen) == prefix thenvalstr = clean:sub(plen + 1)breakendendif valstr thenisnegative = truepropersign = MINUSclean = valstrvalue = tonumber(clean)endif value == nil thenif not no_fraction thenvalue, altvalue, show, denominator = extract_fraction(parms, clean, isnegative)endif value == nil thenreturn false, { 'cvt_bad_num', text }endif value <= 1 thensingular = true  -- for example, "½ mile" or "one half mile" (singular unit)endendendif not valid_number(value) then  -- for example, "1e310" may overflowreturn false, { 'cvt_invalid_num' }endif 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_riif precision thenlocal fmt = '%.' .. format('%d', precision) .. 'f'local result = fmt:format(tonumber(value) + 2e-14)  -- fudge for some common cases of bad roundingif not exponent thensingular = (tonumber(result) == 1)endreturn resultendreturn defaultendsingular = (value == 1)local scientificlocal significand, exponent = clean:match('^([%d.]+)[Ee]([+%-]?%d+)')if significand thenshow = with_exponent(parms, rounded(significand, significand, exponent), exponent)scientific = trueelseshow = with_separator(parms, rounded(value, clean))endshow = propersign .. showif parms.opt_spell_in thenshow = spell_number(parms, 'in', propersign .. rounded(value, clean)) or showscientific = falseendif scientific thenparms.opt_scientific = trueendendlocal altvalue = altvalue or valueif isnegative and (value ~= 0) thenvalue = -valuealtvalue = -altvalueendreturn true, {value = value,altvalue = altvalue,singular = singular,clean = clean,show = show .. (reference or ''),denominator = denominator,}endlocal function get_number(text)-- Return v, f where:--   v = nil (text is not a number)-- or--   v = value of text (text is a number)--   f = true if value is an integer-- Input can use en digits or digits in local language,-- but no separators, no Unicode minus, and no fraction.if text thenlocal number = tonumber(to_en(text))if number thenlocal integer, fracpart = math.modf(number)return number, (fracpart == 0)endendendlocal function gcd(a, b)-- Return the greatest common denominator for the given values,-- which are known to be positive integers.if a > b thena, b = b, aendif a <= 0 thenreturn bendlocal r = b % aif r <= 0 thenreturn aendif r == 1 thenreturn 1endreturn gcd(r, a)endlocal 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 thenreturn '0'endif denominator <= 0 or value > 1e8 thenreturn format('%.2f', value)endlocal integer, decimals = math.modf(value)local numerator = floor((decimals * denominator) +0.5 + 2e-14)  -- add fudge for some common cases of bad roundingif numerator >= denominator theninteger = integer + 1numerator = 0endlocal wholestr = tostring(integer)if numerator > 0 thenlocal div = gcd(numerator, denominator)if div > 1 thennumerator = numerator / divdenominator = denominator / divendreturn {wholestr = (integer > 0) and wholestr or '',numstr = tostring(numerator),denstr = tostring(denominator),value = value,}endreturn wholestrendlocal function preunits(count, preunit1, preunit2)-- If count is 1:--     ignore preunit2--     return p1-- else:--     preunit1 is used for preunit2 if the latter is empty--     return p1, p2-- where:--     p1 is text to insert before the input unit--     p2 is text to insert before the output unit--     p1 or p2 may be nil to mean "no preunit"-- Using '+ ' gives output like "5+ feet" (no preceding space).local function withspace(text, i)-- Insert space at beginning if i == 1, or at end if i == -1.-- However, no space is inserted if there is a space or '&nbsp;'-- or '-' at that position ('-' is for adjectival text).local current = text:sub(i, i)if current == ' ' or current == '-' thenreturn textendif i == 1 thencurrent = text:sub(1, 6)elsecurrent = text:sub(-6, -1)endif current == '&nbsp;' thenreturn textendif i == 1 thenreturn ' ' .. textendreturn text .. ' 'endpreunit1 = preunit1 or ''local trim1 = strip(preunit1)if count == 1 thenif trim1 == '' thenreturn nilendreturn withspace(withspace(preunit1, 1), -1)endpreunit2 = preunit2 or ''local trim2 = strip(preunit2)if trim1 == '' and trim2 == '' thenreturn nil, nilendif trim1 ~= '+' thenpreunit1 = withspace(preunit1, 1)endif trim2 == '&#32;' then  -- trick to make preunit2 emptypreunit2 = nilelseif trim2 == '' thenpreunit2 = preunit1elseif trim2 ~= '+' thenpreunit2 = withspace(preunit2, 1)endreturn preunit1, preunit2endlocal function range_text(range, want_name, parms, before, after, inout)-- Return before .. rtext .. after-- where rtext is the text that separates two values in a range.local rtext, adj_text, exceptionif 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'] orrange[((inout == 'in') == (parms.opt_flip == true)) and 'output' or 'input']adj_text = range['adj']exception = range['exception']elsertext = rangeendif parms.opt_adjectival thenif want_name or (exception and parms.abbr_org == 'on') thenrtext = adj_text or rtext:gsub(' ', '-'):gsub('&nbsp;', '-')endendif rtext == '–' and after:sub(1, #MINUS) == MINUS thenrtext = '&nbsp;– 'endreturn before .. rtext .. afterendlocal function get_composite(parms, iparm, in_unit_table)-- Look for a composite input unit. For example, "{{convert|1|yd|2|ft|3|in}}"-- would result in a call to this function with--   iparm = 3 (parms[iparm] = "2", just after the first unit)--   in_unit_table = (unit table for "yd"; contains value 1 for number of yards)-- Return true, iparm, unit where--   iparm = index just after the composite units (7 in above example)--   unit = composite unit table holding all input units,-- or return true if no composite unit is present in parms,-- or return false, t where t is an error message table.local default, subinfolocal composite_units, count = { in_unit_table }, 1local fixups = {}local total = in_unit_table.valinfo[1].valuelocal subunit = in_unit_tablewhile subunit.subdivs do  -- subdivs is nil or a table of allowed subdivisionslocal subcode = strip(parms[iparm+1])local subdiv = subunit.subdivs[subcode] or subunit.subdivs[(all_units[subcode] or {}).target]if not subdiv thenbreakendlocal successsuccess, subunit = lookup(parms, subcode, 'no_combination')if not success then return false, subunit end  -- should never occursuccess, subinfo = extract_number(parms, parms[iparm])if not success then return false, subinfo endiparm = iparm + 2subunit.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.valueif not default then  -- set by the first subdiv with a default defineddefault = subdiv.defaultendcount = count + 1composite_units[count] = subunitif subdiv.unit or subdiv.name thenfixups[count] = { unit = subdiv.unit, name = subdiv.name, valinfo = subunit.valinfo }endendif count == 1 thenreturn true  -- no error and no composite unitendfor i, fixup in pairs(fixups) dolocal unit = fixup.unitlocal name = fixup.nameif not unit or (count > 2 and name) thencomposite_units[i].fixed_name = nameelselocal success, alternate = lookup(parms, unit, 'no_combination')if not success then return false, alternate end  -- should never occuralternate.inout = 'in'alternate.valinfo = fixup.valinfocomposite_units[i] = alternateendendreturn true, iparm, {utype = in_unit_table.utype,scale = subunit.scale,  -- scale of last (least significant) unitvalinfo = { { value = total, clean = subinfo.clean, denominator = subinfo.denominator } },composite = composite_units,default = default or in_unit_table.default}endlocal 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 globalsif 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 ~= '' thenadd_warning(parms, 1, 'cvt_unknown_option', 'sing=' .. kv_pairs.sing)endkv_pairs.sing = nilendfor loc_name, loc_value in pairs(kv_pairs) dolocal en_name = text_code.en_option_name[loc_name]if en_name thenlocal en_valueif en_name == '$' or en_name == 'frac' or en_name == 'sigfig' thenif loc_value == '' thenadd_warning(parms, 2, 'cvt_empty_option', loc_name)elseif en_name == '$' then-- Value should be a single character like "€" for the euro currency symbol, but anything is accepted.currency_text = (loc_value == 'euro') and '€' or loc_valueelselocal minimumlocal number, is_integer = get_number(loc_value)if en_name == 'frac' thenminimum = 2if number and number < 0 thenparms.opt_fraction_horizontal = truenumber = -numberendelseminimum = 1endif number and is_integer and number >= minimum thenen_value = numberelseadd_warning(parms, 1, (en_name == 'frac' and 'cvt_bad_frac' or 'cvt_bad_sigfig'), loc_value)endendelseif en_name == 'stylein' or en_name == 'styleout' thenen_value = loc_value  -- accept user text with no validationelseen_value = text_code.en_option_value[en_name][loc_value]if en_value and en_value:sub(-1) == '?' thenen_value = en_value:sub(1, -2)add_warning(parms, -1, 'cvt_deprecated', loc_name .. '=' .. loc_value)endif en_value == nil thenif loc_value == '' thenadd_warning(parms, 2, 'cvt_empty_option', loc_name)elseadd_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)endelseif en_value == '' thenen_value = nil  -- an ignored option like adj=offelseif type(en_value) == 'string' and en_value:sub(1, 4) == 'opt_' thenfor _, v in ipairs(split(en_value, ',')) dolocal lhs, rhs = v:match('^(.-)=(.+)$')if rhs thenparms[lhs] = tonumber(rhs) or rhselseparms[v] = trueendenden_value = nilendendparms[en_name] = en_valueelseadd_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)endendlocal abbr_entered = parms.abbrlocal cfg_abbr = config.abbrif cfg_abbr then-- Don't warn if invalid because every convert would show that warning.if cfg_abbr == 'on always' thenparms.abbr = 'on'elseif cfg_abbr == 'off always' thenparms.abbr = 'off'elseif parms.abbr == nil thenif cfg_abbr == 'on default' thenparms.abbr = 'on'elseif cfg_abbr == 'off default' thenparms.abbr = 'off'endendendif parms.abbr thenparms.abbr_org = parms.abbr  -- original abbr, before any flipelseif parms.opt_hand_hh thenparms.abbr_org = 'on'parms.abbr = 'on'elseparms.abbr = 'out'  -- default is to abbreviate output only (use symbol, not name)endif parms.opt_spell_out and not abbr_entered thenparms.abbr = 'off'  -- should show unit name when spelling the output valueendif parms.opt_flip thenlocal function swap_in_out(option)local value = parms[option]if value == 'in' thenparms[option] = 'out'elseif value == 'out' thenparms[option] = 'in'endendswap_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 = nilparms.opt_spell_out = trueendendif parms.opt_spell_upper thenparms.spell_upper = parms.opt_flip and 'out' or 'in'endif parms.opt_table or parms.opt_tablecen thenif abbr_entered == nil and parms.lk == nil thenparms.opt_values = trueendparms.table_align = parms.opt_table and 'right' or 'center'endif parms.table_align or parms.opt_sortable_on thenparms.need_table_or_sort = trueendlocal disp_joins = text_code.disp_joinslocal default_joins = disp_joins['b']parms.join_between = default_joins[3] or '; 'local disp = parms.dispif disp == nil then  -- special case for the most common settingparms.joins = default_joinselseif disp == 'x' then-- Later, parms.joins is set from the input parameters.else-- Old template does this.local abbr = parms.abbrif disp == 'slash' thenif abbr_entered == nil thendisp = 'slash-nbsp'elseif abbr == 'in' or abbr == 'out' thendisp = 'slash-sp'elsedisp = 'slash-nosp'endelseif disp == 'sqbr' thenif abbr == 'on' thendisp = 'sqbr-nbsp'elsedisp = 'sqbr-sp'endendparms.joins = disp_joins[disp] or default_joinsparms.join_between = parms.joins[3] or parms.join_betweenparms.wantname = parms.joins.wantnameendif (en_default and not parms.opt_lang_local and (parms[1] or ''):find('%d')) or parms.opt_lang_en thenfrom_en_table = nilendif 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 = trueendreturn trueendlocal 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 valueslocal 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' thenparms[2] = strip(parm2:sub(1, -8))parms.opt_nocomma = truehad_nocomma = trueendlocal 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 startlocal success, result = extract_number(parms, valstr, i > 1)if not success and valstr and i < 20 then  -- check i to limit abuselocal lhs, sep, rhs = valstr:match('^(%S+)%s+(%S+)%s+(%S.*)')if lhs and not (sep == '-' and rhs:match('/')) thenif sep:find('%d') thenreturn success, result  -- to reject {{convert|1 234 567|m}} with a decent message (en only)endparms[i] = rhstable.insert(parms, i, sep)table.insert(parms, i, lhs)return extractor(i)endif not valstr:match('%-.*/') thenfor _, sep in ipairs(text_code.ranges.words) dolocal start, stop = valstr:find(sep, 2, true)  -- start at 2 to skip any negative sign for range '-'if start thenparms[i] = valstr:sub(stop + 1)table.insert(parms, i, sep)table.insert(parms, i, valstr:sub(1, start - 1))return extractor(i)endendendendreturn success, resultendlocal i = 1local is_changewhile true dolocal success, info = extractor(i)  -- need to set parms.opt_nocomma before calling thisif not success then return false, info endi = i + 1if is_change theninfo.is_change = true  -- value is after "±" and so is a change (significant for range like {{convert|5|±|5|°C}})is_change = nilendvalinfo:add(info)local range_item = get_range(strip(parms[i]))if not range_item thenbreakendi = i + 1range: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_xparms.out_range_x = parms.out_range_x or range_item.out_range_xparms.abbr_range_x = parms.abbr_range_x or range_item.abbr_range_xis_change = range_item.is_range_changeendendif range.n > 0 thenif range.n > 30 then  -- limit abuse, although 4 is a more likely upper limitreturn false, { 'cvt_invalid_num' }  -- misleading message but it will doendparms.range = rangeelseif had_nocomma thenreturn false, { 'cvt_unknown', parm2 }endreturn true, valinfo, iendlocal function simple_get_values(parms)-- If input is like "{{convert|valid_value|valid_unit|...}}",-- return true, 3, in_unit, in_unit_table-- 3 = index in parms of whatever 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 and caller will reparse the input.-- Testing shows this function is successful for 96% of converts in articles,-- and that on average it speeds up converts by 8%.if parms.opt_ri or parms.opt_spell_in then return endlocal clean = to_en(strip(parms[1] or ''), parms)if #clean > 10 or not clean:match('^[0-9.]+$') then return endlocal value = tonumber(clean)if not value then return endlocal 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 endin_unit_table.valinfo = { info }return true, 3, in_unit, in_unit_tableendlocal function get_parms(args)-- If successful, return true, parms, unit where--   parms is a table of all arguments passed to the template--        converted to named arguments, and--   unit is the input unit table;-- or return false, t where t is an error message table.-- The returned input unit table may be for a fake unit using the specified-- unit code as the symbol and name, and with bad_mcode = message code table.-- MediaWiki removes leading and trailing whitespace from the values of-- named arguments. However, the values of numbered arguments include any-- whitespace entered in the template, and whitespace is used by some-- parameters (example: the numbered parameters associated with "disp=x").local parms = {}  -- arguments passed to template, after translationlocal kv_pairs = {}  -- table of input key:value pairs where key is a name; needed because cannot iterate parms and add new fields to itfor k, v in pairs(args) doif type(k) == 'number' or k == 'test' then  -- parameter "test" is reserved for testing and is not translatedparms[k] = velsekv_pairs[k] = vendendlocal success, msg = translate_parms(parms, kv_pairs)if not success then return false, msg endlocal success, i, in_unit, in_unit_table = simple_get_values(parms)if not success thenlocal valinfosuccess, valinfo, i = get_values(parms)if not success then return false, valinfo endin_unit = strip(parms[i])i = i + 1success, in_unit_table = lookup(parms, in_unit, 'no_combination')if not success thenif in_unit == nil thenin_unit = ''endif parms.opt_ignore_error then  -- display given unit code with no error (for use with {{val}})in_unit_table = ''  -- suppress error message and prevent processing of output unitendin_unit_table = setmetatable({ symbol = in_unit, name2 = in_unit,default = "m", defkey = "m", linkey = "m",utype = "length", scale = 1, bad_mcode = in_unit_table }, unit_mt)endin_unit_table.valinfo = valinfoendif 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' thenin_unit_table.default = nil  -- no defaultelseif in_unit == 'rd' thenin_unit_table.default  = "ft!X!m"  -- an invalid expressionendendin_unit_table.inout = 'in'  -- this is an input unitif not parms.range thenlocal success, inext, composite_unit = get_composite(parms, i, in_unit_table)if not success then return false, inext endif composite_unit thenin_unit_table = composite_uniti = inextendendif in_unit_table.builtin == 'mach' then-- As with old template, a number following Mach as the input unit is the altitude,-- and there is no way to specify an altitude for the output unit.-- Could put more code in this function to get any output unit and check for-- an altitude following that unit.local success, info = extract_number(parms, parms[i], false, true)if success theni = i + 1in_unit_table.altitude = info.valueendendlocal next = strip(parms[i])i = i + 1local precision, is_bad_precisionlocal function set_precision(text)local number, is_integer = get_number(text)if number thenif is_integer thenprecision = numberelseprecision = textis_bad_precision = trueendreturn true  -- text was used for precision, good or badendendif not set_precision(next) thenparms.out_unit = nextif set_precision(strip(parms[i])) theni = i + 1endendif parms.opt_adj_mid thennext = parms[i]i = i + 1if next then  -- mid-text wordsif next:sub(1, 1) == '-' thenparms.mid = nextelseparms.mid = ' ' .. nextendendendif parms.opt_one_preunit thenparms[parms.opt_flip and 'preunit2' or 'preunit1'] = preunits(1, parms[i])i = i + 1endif 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 + 2if strip(first) == '' then  -- user can enter '&#32;' rather than ' ' to avoid the defaultfirst = ' [&nbsp;' .. firstsecond = '&nbsp;]' .. secondendparms.joins = { first, second }elseif parms.opt_two_preunits thenlocal p1, p2 = preunits(2, parms[i], parms[i+1])i = i + 2if 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 .. p1parms.preunit2 = p2elseparms.preunit1, parms.preunit2 = p1, p2endendif precision == nil thenif set_precision(strip(parms[i])) theni = i + 1endendif is_bad_precision thenadd_warning(parms, 1, 'cvt_bad_prec', precision)elseparms.precision = precisionendreturn true, parms, in_unit_tableendlocal 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 thenlocal maxdef = out_current.max_default_precisionif maxdef thenif maxdef < precision thenparms.do_convert_again = trueout_current.max_default_precision = precisionelseprecision = out_current.max_default_precisionendelseout_current.max_default_precision = precisionendendreturn precisionendlocal function default_precision(parms, invalue, inclean, denominator, outvalue, in_current, out_current, extra)-- Return a default value for precision (an integer like 2, 0, -2).-- If denominator is not nil, it is the value of the denominator in inclean.-- Code follows procedures used in old template.local fudge = 1e-14  -- {{Order of magnitude}} adds this, so we do toolocal prec, minprec, adjustlocal utype = out_current.utypelocal subunit_ignore_trailing_zerolocal subunit_more_precision  -- kludge for "in" used in input like "|2|ft|6|in"local composite = in_current.compositeif composite thensubunit_ignore_trailing_zero = true  -- input "|2|st|10|lb" has precision 0, not -1if composite[#composite].exception == 'subunit_more_precision' thensubunit_more_precision = true  -- do not use standard precision with input like "|2|ft|6|in"endendif denominator and denominator > 0 thenprec = math.max(log10(denominator), 1)else-- Count digits after decimal mark, handling cases like '12.345e6'.local exponentlocal integer, dot, decimals, expstr = inclean:match('^(%d*)(%.?)(%d*)(.*)')local e = expstr:sub(1, 1)if e == 'e' or e == 'E' thenexponent = tonumber(expstr:sub(2))endif dot == '' thenprec = subunit_ignore_trailing_zero and 0 or -integer:match('0*$'):len()elseprec = #decimalsendif exponent then-- So '1230' and '1.23e3' both give prec = -1, and '0.00123' and '1.23e-3' give 5.prec = prec - exponentendendif 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 = 0local kelvin = abs((invalue - in_current.offset) * in_current.scale)if kelvin < 1e-8 then  -- assume nonzero due to input or calculation precision problemminprec = 2elseminprec = 2 - floor(log10(kelvin) + fudge)  -- 3 sigfigs in kelvinendelseif 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)endif out_current.exception == 'integer_more_precision' and floor(invalue) == invalue then-- With certain output units that sometimes give poor results-- with default rounding, use more precision when the input-- value is equal to an integer. An example of a poor result-- is when input 50 gives a smaller output than input 49.5.-- Experiment shows this helps, but it does not eliminate all-- surprises because it is not clear whether "50" should be-- interpreted as "from 45 to 55" or "from 49.5 to 50.5".adjust = -log10(in_current.scale)elseif subunit_more_precision then-- Conversion like "{{convert|6|ft|1|in|cm}}" (where subunit is "in")-- has a non-standard adjust value, to give more output precision.adjust = log10(out_current.scale) + 2elseadjust = log10(abs(invalue / outvalue))endadjust = adjust + log10(2)-- Ensure that the output has at least two significant figures.minprec = 1 - floor(log10(outvalue) + fudge)endif extra thenadjust = extra.adjust or adjustminprec = extra.minprec or minprecendreturn record_default_precision(parms, out_current, math.max(floor(prec + adjust), minprec))endlocal 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.scalelocal outscale = out_current.scaleif not in_current.iscomplex and not out_current.iscomplex thenreturn invalue * (inscale / outscale)  -- minimize overhead for most common caseendif 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 thenreturn 1 / (invalue * inscale * outscale)endreturn invalue * (inscale / outscale)elseif in_current.offset then-- Temperature (there are no built-ins for this type of unit).if info.is_change thenreturn invalue * (inscale / outscale)endreturn (invalue - in_current.offset) * (inscale / outscale) + out_current.offsetelse-- Built-in unit.local in_builtin = in_current.builtinlocal out_builtin = out_current.builtinif in_builtin and out_builtin thenif in_builtin == out_builtin thenreturn invalueend-- 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' }endif in_builtin == 'mach' or out_builtin == 'mach' thenlocal adjustif in_builtin == 'mach' theninscale = speed_of_sound(in_current.altitude)adjust = outscale / 0.1elseoutscale = speed_of_sound(out_current.altitude)adjust = 0.1 / inscaleendreturn 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 incheslocal factor = inscale / outscaleif factor == 4 then-- Am converting to inches: show exact result, and use "inches" not "in" by default.if parms.abbr_org == nil thenout_current.usename = trueendlocal show = format('%g', abs(inch_value))  -- show and clean are unsignedif not show:find('e', 1, true) thenreturn true, {invalue = inch_value,outvalue = inch_value,clean = show,show = show,}endendlocal outvalue = (integer + 2.5 * fracpart) * factorlocal fracstr = info.clean:match('%.(.*)') or ''local fmtif fracstr == '' thenfmt = '%.0f'elsefmt = '%.' .. format('%d', #fracstr - 1) .. 'f'endreturn true, {invalue = inch_value,clean = format(fmt, inch_value),outvalue = outvalue,minprec = 0,}endendreturn false, { 'cvt_bug_convert' }  -- should never occurendlocal function user_style(parms, i)-- Return text for a user-specified style for a table cell, or '' if none,-- given i = 1 (input style) or 2 (output style).local style = parms[(i == 1) and 'stylein' or 'styleout']if style thenstyle = style:gsub('"', '')if style ~= '' thenif style:sub(-1) ~= ';' thenstyle = style .. ';'endreturn styleendendreturn ''endlocal 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_valueif parms.opt_sortable_on thenlocal base = {  -- a fake unit with enough fields for a valid convertscale = 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 thenoutvalue = extra.outvalueendif 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 thenoutvalue = 0endendif scaled_top and outvalue ~= 0 thenoutvalue = scaled_top / outvalueendscaled_value = outvalueif not valid_number(outvalue) thenif outvalue < 0 thensortkey = '1000000000000000000'elsesortkey = '9000000000000000000'endelseif outvalue == 0 thensortkey = '5000000000000000000'elselocal mag = floor(log10(abs(outvalue)) + 1e-14)local prefixif outvalue > 0 thenprefix = 7000 + magelseprefix = 2999 - magoutvalue = outvalue + 10^(mag+1)endsortkey = format('%d', prefix) .. format('%015.0f', floor(outvalue * 10^(14-mag)))endendlocal sortspanif sortkey and (parms.opt_sortable_debug or not parms.table_align) thensortspan = parms.opt_sortable_debug and'<span style="border:1px solid;display:inline;" class="sortkey">' .. sortkey .. '♠</span>' or'<span style="display:none" class="sortkey">' .. sortkey .. '♠</span>'parms.join_before = sortspanendif parms.table_align thenlocal style = 'style="text-align:' .. parms.table_align .. ';'local sort = sortkey and ' data-sort-value="' .. sortkey .. '"' or ''local joins = {}for i = 1, 2 dojoins[i] = (i == 1 and '' or '\n|') .. style .. user_style(parms, i) .. '"' .. sort .. '|'endparms.table_joins = joinsendreturn sortspan, scaled_valueendlocal cvt_to_handlocal 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 true, nil if no value specified;-- or return false, t where t is an error message table.-- Input info.clean uses en digits (it has been translated, if necessary).-- Output show uses en or non-en digits as appropriate, or can be spelled.local invalueif info theninvalue = info.valueif in_current.builtin == 'hand' theninvalue = info.altvalueendendif invalue == nil or invalue == '' thenreturn true, nilendif out_current.builtin == 'hand' thenreturn cvt_to_hand(parms, info, in_current, out_current)endlocal outvalue, extra = convert(parms, invalue, info, in_current, out_current)if parms.need_table_or_sort thenparms.need_table_or_sort = nil  -- process using first input value onlymake_table_or_sort(parms, invalue, info, in_current)endif extra thenif not outvalue then return false, extra endinvalue = extra.invalue or invalueoutvalue = extra.outvalueendif not valid_number(outvalue) thenreturn false, { 'cvt_invalid_num' }endlocal isnegativeif outvalue < 0 thenisnegative = trueoutvalue = -outvalueendlocal numerator, precision, success, show, exponentlocal denominator = out_current.fracif denominator thenshow = fraction_table(outvalue, denominator)elseprecision = parms.precisionif not precision thenif parms.sigfig thenshow, exponent = make_sigfig(outvalue, parms.sigfig)elseif parms.opt_round thenlocal n = parms.opt_roundif n == 0.5 thenlocal integer, fracpart = math.modf(floor(2 * outvalue + 0.5) / 2)if fracpart == 0 thenshow = format('%.0f', integer)elseshow = format('%.1f', integer + fracpart)endelseshow = format('%.0f', floor((outvalue / n) + 0.5) * n)endelselocal inclean = info.cleanif extra theninclean = extra.clean or incleanshow = extra.showendif not show thenprecision = default_precision(parms, invalue, inclean, info.denominator, outvalue, in_current, out_current, extra)endendendendif precision thenif precision >= 0 thenlocal fudgeif precision <= 8 then-- Add a fudge to handle common cases of bad rounding due to inability-- to precisely represent some values. This makes the following work:-- {{convert|-100.1|C|K}} and {{convert|5555000|um|m|2}}.-- Old template uses #expr round, which invokes PHP round().-- LATER: Investigate how PHP round() works.fudge = 2e-14elsefudge = 0endlocal fmt = '%.' .. format('%d', precision) .. 'f'local successsuccess, show = pcall(format, fmt, outvalue + fudge)if not success thenreturn false, { 'cvt_big_prec', tostring(precision) }endelseprecision = -precision  -- #digits to zero (in addition to any digits after dot)local shift = 10 ^ precisionshow = format('%.0f', outvalue/shift)if show ~= '0' thenexponent = #show + precisionendendendlocal 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 thent.singular = (exponent == 1 and show:match('^10*$'))elset.singular = (show == '1' or show:match('^1%.0*$'))endelset.fraction_table = showt.singular = (outvalue <= 1)  -- cannot have 'fraction == 1', but if it were possible it would be singularendt.raw_absvalue = outvalue  -- absolute value before roundingreturn 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 thenvalue = value * 10^exponentendrawset(self, key, value)return valueendend })endfunction 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 thenout_current.usename = true  -- default is to show name not symbolendlocal precision = parms.precisionlocal frac = out_current.fracif not frac and precision and precision > 1 thenfrac = (precision == 2) and 2 or 4endlocal out_next = out_current.out_nextif 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' thenout_next.frac = fracendend-- 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 endlocal tfrac = outinfo.fraction_tablelocal inches = outinfo.raw_absvalueif tfrac theninches = floor(inches)  -- integer part only; fraction added laterelseinches = floor(inches + 0.5)  -- a hands measurement never shows decimals of an inchendlocal hands, inches = divide(inches, 4)outinfo.absvalue = hands + inches/4  -- supposed to be the absolute rounded value, but this is close enoughlocal inchstr = tostring(inches)  -- '0', '1', '2' or '3'if precision and precision <= 0 then  -- using negative or 0 for precision rounds to nearest handhands = 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)elseinchstr = numdot .. from_en(inchstr)endoutinfo.show = outinfo.sign .. with_separator(parms, format('%.0f', hands)) .. inchstrreturn true, outinfoendlocal 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 thenerror('Invalid default expression', 0)elseif arithop == '*' thenfactor = tonumber(factor)if factor == nil thenerror('Invalid default expression', 0)endvalue = value * factorendlimit = tonumber(limit)if limit == nil thenerror('Invalid default expression', 0)endif compop == '<' thenreturn value < limitelseif compop == '<=' thenreturn value <= limitelseif compop == '>' thenreturn value > limitelseif compop == '>=' thenreturn value >= limitenderror('Invalid default expression', 0)  -- should not occurendlocal lhs, rhs = condition:match('^(.-%W)and(%W.*)')if lhs == nil thenreturn compare(value, condition)endreturn compare(value, lhs) and compare(value, rhs)endlocal 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.defaultif not default thenlocal per = unit_table.perif per thenlocal function a_default(v, u)local success, ucode = get_default(v, u)if not success thenreturn '?'  -- an unlikely error has occurred; will cause lookup of default to failend-- 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 thenlocal combo = t.combinationif 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 1ucode = combo[i]endelse-- Try for an automatically generated combination.local item = ucode:match('^(.-)%+') or ucode:match('^(%S+)%s')if all_units[item] thenreturn itemendendreturn ucodeendlocal 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 denominatorreturn true, def1 .. '/' .. def2endreturn false, { 'cvt_no_default', unit_table.symbol }endif default:find('!', 1, true) == nil thenreturn true, defaultendlocal t = split(default, '!')if #t == 3 or #t == 4 thenlocal success, result = pcall(evaluate_condition, value, t[1])if success thendefault = result and t[2] or t[3]if #t == 4 thendefault = default .. t[4]endreturn true, defaultendendreturn false, { 'cvt_bad_default', unit_table.symbol }endlocal linked_pages  -- to record linked pages so will not link to the same page more than oncelocal function make_link(link, id, link_key)-- Return wikilink "[[link|id]]", possibly abbreviated as in examples:--   [[Mile|mile]]  --> [[mile]]--   [[Mile|miles]] --> [[mile]]s-- However, just id is returned if:-- * no link given (so caller does not need to check if a link was defined); or-- * link has previously been used during the current convert (to avoid overlinking).-- Linking with a unit uses the unit table as the link key, which fails to detect-- overlinking for conversions like the following (each links "mile" twice):--   {{convert|1|impgal/mi|USgal/mi|lk=on}}--   {{convert|1|l/km|impgal/mi USgal/mi|lk=on}}link_key = link_key or link  -- use key if given (the key, but not the link, may be known when need to cancel a link record)if not link or link == '' or linked_pages[link_key] thenreturn idendlinked_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 thenreturn '[[' .. id .. ']]'elseif link .. 's' == id or l .. 's' == id thenreturn '[[' .. id:sub(1, -2) .. ']]s'elsereturn '[[' .. link .. '|' .. id .. ']]'endendlocal 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 vnameif clean == '1' thenvname = unit_table.name1elseif unit_table.varname thenlocal iif clean == '2' theni = 1elseif clean == '3' or clean == '4' theni = 2elseif clean:find('.', 1, true) theni = 4elsei = 3endvname = split(unit_table.varname, '!')[i]endif vname thenlocal si_name = rawget(unit_table, 'si_name') or ''local pos = vname:find('#', 1, true)if pos thenvname = vname:sub(1, pos - 1) .. si_name .. vname:sub(pos + 1)elsevname = si_name .. vnameendreturn vnameendreturn unit_table.name2endlocal 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 thenlocal symlink = rawget(unit_table, 'symlink')if symlink thenreturn symlink  -- for exceptions that have the linked symbol built-inendendlocal multiplier = rawget(unit_table, 'multiplier')local per = unit_table.perif per thenlocal unit1 = per[1]  -- top unit_table, or nillocal unit2 = per[2]  -- bottom unit_tableif abbr_on thenif not unit1 thenunit_table.sep = ''  -- no separator in "$2/acre"endif not want_link thenlocal symbol = unit_table.symbol_rawif symbol thenreturn symbol  -- for exceptions that have the symbol built-inendendendlocal key_id2  -- unit2 is always singularif key_id == 'name2' thenkey_id2 = 'name1'elseif key_id == 'name2_us' thenkey_id2 = 'name1_us'elsekey_id2 = key_idendlocal resultif abbr_on thenresult = '/'elseif omitsep thenresult = per_wordelseif unit1 thenresult = ' ' .. per_word .. ' 'elseresult = per_word .. ' 'endif want_link and unit_table.link thenif abbr_on or not varname thenresult = (unit1 and linked_id(parms, unit1, key_id, false, clean) or '') .. result .. linked_id(parms, unit2, key_id2, false, '1')elseresult = (unit1 and variable_name(clean, unit1) or '') .. result .. variable_name('1', unit2)endif omit_separator(result) thenunit_table.sep = ''endreturn make_link(unit_table.link, result, unit_table)endif unit1 thenresult = linked_id(parms, unit1, key_id, want_link, clean) .. resultif unit1.sep thenunit_table.sep = unit1.sependelseif omitsep thenunit_table.sep = ''endreturn result .. linked_id(parms, unit2, key_id2, want_link, '1')endif multiplier then-- A multiplier (like "100" in "100km") forces the unit to be plural.multiplier = from_en(multiplier)if not omitsep thenmultiplier = multiplier .. (abbr_on and '&nbsp;' or ' ')endif not abbr_on thenif key_id == 'name1' thenkey_id = 'name2'elseif key_id == 'name1_us' thenkey_id = 'name2_us'endendelsemultiplier = ''endlocal 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) thenunit_table.sep = ''endif want_link thenlocal link = data_code.link_exceptions[unit_table.linkey or unit_table.symbol] or unit_table.linkif link thenlocal before = ''local i = unit_table.customaryif i == 1 and parms.opt_sp_us theni = 2  -- show "U.S." not "US"endif i == 3 and abbr_on theni = 4  -- abbreviate "imperial" to "imp"endlocal 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 pertextif 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)elsepertext = ''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) dolocal plen = #prefixif id:sub(1, plen) == prefix thenid = id:sub(plen + 1)breakendendbefore = pertext .. make_link(customary.link, customary[1]) .. ' 'endid = before .. make_link(link, id, unit_table)endendreturn multiplier .. idendlocal 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 thenunit_table.sep = ''return ''endlocal inout = unit_table.inoutlocal info = unit_table.valinfo[which]local abbr_org = parms.abbr_orglocal adjectival = parms.opt_adjectivallocal disp = parms.displocal lk = parms.lklocal want_link = (lk == 'on' or lk == inout)local usename = unit_table.usenamelocal singular = info.singularlocal want_nameif usename thenwant_name = trueelseif abbr_org == nil thenif parms.wantname thenwant_name = trueendif unit_table.usesymbol thenwant_name = falseendendif want_name == nil thenlocal abbr = parms.abbrif abbr == 'on' or abbr == inout or (abbr == 'mos' and inout == 'out') thenwant_name = falseelsewant_name = trueendendendlocal keyif want_name thenif lk == nil and unit_table.builtin == 'hand' thenwant_link = trueendif parms.opt_use_nbsp thenunit_table.sep = '&nbsp;'elseunit_table.sep = ' 'endif parms.opt_singular thenlocal valueif inout == 'in' thenvalue = info.valueelsevalue = info.absvalueendif value then  -- some unusual units do not always set value fieldvalue = abs(value)singular = (0 < value and value < 1.0001)endendif unit_table.engscale then-- engscale: so "|1|e3kg" gives "1 thousand kilograms" (plural)singular = falseendkey = (adjectival or singular) and 'name1' or 'name2'if parms.opt_sp_us thenkey = key .. '_us'endelseif unit_table.builtin == 'hand' thenif parms.opt_hand_hh thenunit_table.symbol = 'hh'  -- LATER: might want i18n applied to thisendendunit_table.sep = '&nbsp;'key = parms.opt_sp_us and 'sym_us' or 'symbol'endreturn linked_id(parms, unit_table, key, want_link, info.clean), want_nameendlocal function decorate_value(parms, unit_table, which, number_word)-- If needed, update unit_table so values will be shown with extra information.-- For consistency with the old template (but different from fmtpower),-- the style to display powers of 10 includes "display:none" to allow some-- browsers to copy, for example, "10³" as "10^3", rather than as "103".local infolocal engscale = unit_table.engscalelocal prefix = unit_table.vprefixif engscale or prefix theninfo = unit_table.valinfo[which]if info.decorated thenreturn  -- do not redecorate if repeating convertendinfo.decorated = trueif engscale thenlocal inout = unit_table.inoutlocal abbr = parms.abbrif abbr == 'on' or abbr == inout theninfo.show = info.show ..'<span style="margin-left:0.2em">×<span style="margin-left:0.1em">' ..from_en('10') ..'</span></span><s style="display:none">^</s><sup>' ..from_en(tostring(engscale.exponent)) .. '</sup>'elseif number_word thenlocal number_idlocal lk = parms.lkif lk == 'on' or lk == inout thennumber_id = make_link(engscale.link, engscale[1])elsenumber_id = engscale[1]end-- WP:NUMERAL recommends "&nbsp;" in values like "12 million".info.show = info.show .. (parms.opt_adjectival and '-' or '&nbsp;') .. number_idendendif prefix theninfo.show = prefix .. info.showendendendlocal 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 thenparms.joins = { '', '' }return ''endlocal first_unitlocal composite = in_current.composite  -- nil or table of unitsif composite thenfirst_unit = composite[1]elsefirst_unit = in_currentendlocal id1, want_name = make_id(parms, 1, first_unit)local sep = first_unit.sep  -- separator between value and unit, set by make_idlocal preunit = parms.preunit1if preunit thensep = ''  -- any separator is included in preunitelsepreunit = ''endif parms.opt_input_unit_only thenparms.joins = { '', '' }if composite thenlocal parts = { id1 }for i, unit in ipairs(composite) doif i > 1 thentable.insert(parts, (make_id(parms, 1, unit)))endendid1 = table.concat(parts, ' ')endif want_name and parms.opt_adjectival thenreturn preunit .. hyphenated(id1)endreturn  preunit .. id1endif parms.opt_also_symbol and not composite thenlocal join1 = parms.joins[1]if join1 == ' (' or join1 == ' [' thenparms.joins = { ' [' .. first_unit[parms.opt_sp_us and 'sym_us' or 'symbol'] .. ']' .. join1 , parms.joins[2] }endendif in_current.builtin == 'mach' and first_unit.sep ~= '' then  -- '' means omitsep with non-enwiki namelocal prefix = id1 .. '&nbsp;'local range = parms.rangelocal valinfo = first_unit.valinfolocal result = prefix .. valinfo[1].showif 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')endreturn preunit .. resultendif 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 thensep1 = '-'sep2 = '-'endif omitsep and sep == '' then-- Testing the id of the most significant unit should be sufficient.sep1 = ''sep2 = ''endlocal parts = { first_unit.valinfo[1].show .. sep1 .. id1 }for i, unit in ipairs(composite) doif i > 1 thentable.insert(parts, unit.valinfo[1].show .. sep1 .. (make_id(parms, 1, unit)))endendreturn table.concat(parts, sep2) .. midendlocal add_unit = (parms.abbr == 'mos') orparms[parms.opt_flip and 'out_range_x' or 'in_range_x'] or(not want_name and parms.abbr_range_x)local range = parms.rangeif range and not add_unit thenlinked_pages[first_unit] = nil  -- so the final and only id will be linked, if wantedendlocal id = range and make_id(parms, range.n + 1, first_unit) or id1local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, 'in')if was_hyphenated thenadd_unit = falseendlocal resultlocal valinfo = first_unit.valinfoif range thenfor i = 0, range.n dolocal number_wordif i == range.n thenadd_unit = falsenumber_word = trueenddecorate_value(parms, first_unit, i+1, number_word)local show = valinfo[i+1].showif add_unit thenshow = show .. first_unit.sep .. (i == 0 and id1 or make_id(parms, i+1, first_unit))endif i == 0 thenresult = showelseresult = range_text(range[i], want_name, parms, result, show, 'in')endendelsedecorate_value(parms, first_unit, 1, true)result = valinfo[1].showendreturn result .. preunit .. extraendlocal function process_one_output(parms, out_current)-- Processing required for each output unit.-- Return block of text to represent output (value/unit).local id1, want_name = make_id(parms, 1, out_current)local sep = out_current.sep  -- set by make_idlocal preunit = parms.preunit2if preunit thensep = ''  -- any separator is included in preunitelsepreunit = ''endif parms.opt_output_unit_only thenif want_name and parms.opt_adjectival thenreturn preunit .. hyphenated(id1)endreturn preunit .. id1endif out_current.builtin == 'mach' and out_current.sep ~= '' then  -- '' means omitsep with non-enwiki namelocal prefix = id1 .. '&nbsp;'local range = parms.rangelocal valinfo = out_current.valinfolocal result = prefix .. valinfo[1].showif 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, 'out')endreturn preunit .. resultendlocal add_unit = (parms[parms.opt_flip and 'in_range_x' or 'out_range_x'] or(not want_name and parms.abbr_range_x)) andnot parms.opt_output_number_onlylocal range = parms.rangeif range and not add_unit thenlinked_pages[out_current] = nil  -- so the final and only id will be linked, if wantedendlocal id = range and make_id(parms, range.n + 1, out_current) or id1local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, 'out')if was_hyphenated thenadd_unit = falseendlocal resultlocal valinfo = out_current.valinfoif range thenfor i = 0, range.n dolocal number_wordif i == range.n thenadd_unit = falsenumber_word = trueenddecorate_value(parms, out_current, i+1, number_word)local show = valinfo[i+1].showif add_unit thenshow = show .. out_current.sep .. (i == 0 and id1 or make_id(parms, i+1, out_current))endif i == 0 thenresult = showelseresult = range_text(range[i], want_name, parms, result, show, 'out')endendelsedecorate_value(parms, out_current, 1, true)result = valinfo[1].showendif parms.opt_output_number_only thenreturn resultendreturn result .. preunit .. extraendlocal function make_output_single(parms, in_unit_table, out_unit_table)-- Return true, item where item = wikitext of the conversion result-- for a single output (which is not a combination or a multiple);-- or return false, t where t is an error message table.out_unit_table.valinfo = collection()local range = parms.rangefor i = 1, (range and (range.n + 1) or 1) dolocal success, info = cvtround(parms, in_unit_table.valinfo[i], in_unit_table, out_unit_table)if not success then return false, info endout_unit_table.valinfo:add(info)endreturn true, process_one_output(parms, out_unit_table)endlocal function make_output_multiple(parms, in_unit_table, out_unit_table)-- Return true, item where item = wikitext of the conversion result-- for an output which is a multiple (like 'ftin');-- or return false, t where t is an error message table.local multiple = out_unit_table.multiple  -- table of scaling factors (will not be nil)local combos = out_unit_table.combination  -- table of unit tables (will not be nil)local abbr = parms.abbrlocal abbr_org = parms.abbr_orglocal disp = parms.displocal want_name = (abbr_org == nil and (disp == 'or' or disp == 'slash')) ornot (abbr == 'on' or abbr == 'out' or abbr == 'mos')local want_link = (parms.lk == 'on' or parms.lk == 'out')local mid = parms.opt_flip and parms.mid or ''local sep1 = '&nbsp;'local sep2 = ' 'if parms.opt_adjectival and want_name thensep1 = '-'sep2 = '-'endlocal do_spell = parms.opt_spell_outparms.opt_spell_out = nil  -- so the call to cvtround does not spell the valuelocal function make_result(info, isfirst)local fmt, outvalue, signlocal results = {}for i = 1, #combos dolocal tfrac, thisvalue, strforcelocal out_current = combos[i]out_current.inout = 'out'local scale = multiple[i]if i == 1 then  -- least significant unit ('in' from 'ftin')local decimalsout_current.frac = out_unit_table.fraclocal success, outinfo = cvtround(parms, info, in_unit_table, out_current)if not success then return false, outinfo endif isfirst thenout_unit_table.valinfo = { outinfo }  -- in case output value of first least significant unit is neededendsign = outinfo.signtfrac = outinfo.fraction_tableif outinfo.is_scientific thenstrforce = outinfo.showdecimals = ''elseif tfrac thendecimals = ''elselocal show = outinfo.show  -- number as a string in local languagelocal p1, p2 = show:find(numdot, 1, true)decimals = p1 and show:sub(p2 + 1) or ''  -- text after numdot, if anyendfmt = '%.' .. ulen(decimals) .. 'f'  -- to reproduce precisionif decimals == '' thenif tfrac thenoutvalue = floor(outinfo.raw_absvalue)  -- integer part only; fraction added laterelseoutvalue = floor(outinfo.raw_absvalue + 0.5)  -- keep all integer digits of least significant unitendelseoutvalue = outinfo.absvalueendendif scale thenoutvalue, thisvalue = divide(outvalue, scale)elsethisvalue = outvalueendlocal idif want_name thenif varname thenlocal cleanif strforce or tfrac thenclean = '.1'  -- dummy value to force name for floating pointelseclean = format(fmt, thisvalue)endid = variable_name(clean, out_current)elselocal key = 'name2'if parms.opt_adjectival thenkey = 'name1'elseif tfrac thenif thisvalue == 0 thenkey = 'name1'endelseif parms.opt_singular thenif 0 < thisvalue and thisvalue < 1.0001 thenkey = 'name1'endelseif thisvalue == 1 thenkey = 'name1'endendid = out_current[key]endelseid = out_current['symbol']endif i == 1 and omit_separator(id) then-- Testing the id of the least significant unit should be sufficient.sep1 = ''sep2 = ''endif want_link thenlocal link = out_current.linkif link thenid = make_link(link, id, out_current)endendlocal strvallocal inout = (i == #combos or outvalue == 0) and 'out' or ''  -- trick so the last value processed (first displayed) has uppercase, if requestedif strforce and outvalue == 0 thensign = ''  -- any sign is in strforcestrval = strforce  -- show small values in scientific notation; will only use least significant unitelseif tfrac thenlocal wholestr = (thisvalue > 0) and tostring(thisvalue) or nilstrval = format_fraction(parms, inout, false, wholestr, tfrac.numstr, tfrac.denstr, do_spell)elsestrval = (thisvalue == 0) and from_en('0') or with_separator(parms, format(fmt, thisvalue))if do_spell thenstrval = spell_number(parms, inout, strval) or strvalendendtable.insert(results, strval .. sep1 .. id)if outvalue == 0 thenbreakendfmt = '%.0f'  -- only least significant unit can have a non-integral valueendlocal reversed, count = {}, #resultsfor i = 1, count doreversed[i] = results[count + 1 - i]endreturn true, sign .. table.concat(reversed, sep2)endlocal valinfo = in_unit_table.valinfolocal success, result = make_result(valinfo[1], true)if not success then return false, result endlocal range = parms.rangeif range thenfor i = 1, range.n dolocal success, result2 = make_result(valinfo[i+1])if not success then return false, result2 endresult = range_text(range[i], want_name, parms, result, result2, 'out')endendreturn true, result .. midendlocal function process(parms, in_unit_table, out_unit_table)-- Return true, s where s = final wikitext result,-- or return false, t where t is an error message table.linked_pages = {}local success, bad_outputlocal bad_input_mcode = in_unit_table.bad_mcode  -- false if input unit is validlocal invalue1 = in_unit_table.valinfo[1].valuelocal out_unit = parms.out_unitif out_unit == nil or out_unit == '' thenif bad_input_mcode or parms.opt_input_unit_only thenbad_output = ''elsesuccess, out_unit = get_default(invalue1, in_unit_table)parms.out_unit = out_unitif not success thenbad_output = out_unitendendendif not bad_output and not out_unit_table thensuccess, out_unit_table = lookup(parms, out_unit, 'any_combination')if success thenlocal mismatch = check_mismatch(in_unit_table, out_unit_table)if mismatch thenbad_output = mismatchendelsebad_output = out_unit_tableendendlocal flipped = parms.opt_flip and not bad_input_mcodelocal parts = {}for part = 1, 2 do-- The LHS (parts[1]) is normally the input, but is the output if flipped.-- Process LHS first so it will be linked, if wanted.-- Linking to the same item is suppressed in the RHS to avoid overlinking.if (part == 1 and not flipped) or (part == 2 and flipped) thenparts[part] = process_input(parms, in_unit_table)elseif bad_output thenparts[part] = (bad_output == '') and '' or message(bad_output)elselocal outputs = {}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.combinationendlocal frac = parms.frac  -- nil or denominator of fraction for output valuesif frac then-- Apply fraction to the unit (if only one), or to non-SI units (if a combination),-- except that if a precision is also specified, the fraction only applies to-- the hand unit; that allows the following result:-- {{convert|156|cm|in hand|1|frac=2}} → 156 centimetres (61.4 in; 15.1½ hands)-- However, the following is handled elsewhere as a special case:-- {{convert|156|cm|hand in|1|frac=2}} → 156 centimetres (15.1½ hands; 61½ in)if combos thenlocal precision = parms.precisionfor _, unit in ipairs(combos) doif unit.builtin == 'hand' or (not precision and not unit.prefixes) thenunit.frac = fracendendelseout_unit_table.frac = fracendendlocal out_firstlocal imax = combos and #combos or 1  -- 1 (single unit) or number of unit tablesfor i = 1, imax dolocal success, itemlocal out_current = combos and combos[i] or out_unit_tableout_current.inout = 'out'if i == 1 thenout_first = out_currentif imax > 1 and out_current.builtin == 'hand' thenout_current.out_next = combos[2]  -- built-in hand can influence next unit in a combinationendendif out_current.multiple thensuccess, item = make_output_multiple(parms, in_unit_table, out_current)elsesuccess, item = make_output_single(parms, in_unit_table, out_current)endif not success then return false, item endtable.insert(outputs, item)endif parms.opt_input_unit_only thenparts[part] = ''elselocal sep = parms.table_joins and parms.table_joins[2] or parms.join_betweenparts[part] = table.concat(outputs, sep)endendendif parms.join_before thenparts[1] = parms.join_before .. parts[1]endlocal wikitextif bad_input_mcode thenif bad_input_mcode == '' thenwikitext = parts[1]elsewikitext = parts[1] .. message(bad_input_mcode)endelseif parms.table_joins thenwikitext = parms.table_joins[1] .. parts[1] .. parms.table_joins[2] .. parts[2]elsewikitext = parts[1] .. parms.joins[1] .. parts[2] .. parms.joins[2]endif parms.warnings and not bad_input_mcode thenwikitext = wikitext .. parms.warningsendreturn true, wikitext, out_unit_tableendlocal function main_convert(frame)-- Do convert, and if needed, do it again with higher default precision.set_config(frame.args)local result, out_unit_tablelocal success, parms, in_unit_table = get_parms(frame:getParent().args)if success thenfor i = 1, 2 do  -- use counter so cannot get stuck repeating convertsuccess, result, out_unit_table = process(parms, in_unit_table, out_unit_table)if success and parms.do_convert_again thenparms.do_convert_again = falseelsebreakendendelseresult = parmsendif success thenreturn resultendreturn message(result)endlocal function _unit(unitcode, options)-- Helper function for Module:Val to look up a unit.-- Parameter unitcode must be a string to identify the wanted unit.-- Parameter options must be nil or a table with optional fields:--   value = number (for sort key; default value is 1)--   scaled_top = nil for a normal unit, or a number for a unit which is--                the denominator of a per unit (for sort key)--   si = { 'symbol', 'link' }--                (a table with two strings) to make an SI unit--                that will be used for the look up--   link = true if result should be [[linked]]--   sort = 'on' or 'debug' if result should include a sort key in a--                span element ('debug' makes the key visible)--   name = true for the name of the unit instead of the symbol--   us = true for the US spelling of the unit, if any-- Return nil if unitcode is not a non-empty string.-- Otherwise return a table with fields:--   text = requested symbol or name of unit, optionally linked--   scaled_value = input value adjusted by unit scale; used for sort key--   sortspan = span element with sort key like that provided by {{ntsh}},--     calculated from the result of converting value--     to a base unit with scale 1.--   unknown = true if the unitcode was not knownunitcode = strip(unitcode)if unitcode == nil or unitcode == '' thenreturn nilendset_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/extraopt_sortable_on = options.sort == 'on' or options.sort == 'debug',opt_sortable_debug = options.sort == 'debug',}local utableif 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 '?'utable = { [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],}}endlocal success, unit_table = lookup(parms, unitcode, 'no_combination', utable)if not success thenunit_table = setmetatable({symbol = unitcode, name2 = unitcode,default = "m", defkey = "m", linkey = "m",utype = "length", scale = 1 }, unit_mt)endlocal value = tonumber(options.value) or 1local 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_valueif options.sort thensortspan, scaled_value = make_table_or_sort(parms, value, info, unit_table, options.scaled_top)endreturn {text = make_id(parms, 1, unit_table),sortspan = sortspan,scaled_value = scaled_value,unknown = not success and true or nil,}endreturn { convert = main_convert, _unit = _unit }