Module:Convert

-- Convert a value from one unit of measurement to another. -- Example: 123 lb --> 123 pounds (56 kg) -- See en:Template:Convert/Transwiki guide if copying to another wiki.

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

-- Configuration options to keep magic values in one location. -- Conversion data and message text are defined in separate modules. local config, maxsigfig local numdot -- must be '.' or ',' or a character which works in a regex local numsep, numsep_remove, numsep_remove2 local data_code, all_units local text_code local varname       -- can be a code to use variable names that depend on value local from_en_table -- to translate an output string of en digits to local language local to_en_table   -- to translate an input string of digits in local language to en -- Use translation_table in convert/text to change the following. local en_default          -- true uses lang=en unless convert has lang=local or local digits local group_method = 3    -- code for how many digits are in a group local per_word = 'per'    -- for units like "liters per kilometer" local plural_suffix = 's' -- only other useful value is probably '' to disable plural unit names local omitsep             -- true to omit separator before local symbol/name

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

-- Some options in the invoking template can set variables used later in the module. local currency_text -- for a user-defined currency symbol: 12 $/ha (euro replaces dollar)

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

local function to_en(text) -- Input is a string representing a number in the local language with -- an optional numdot decimal mark and numsep digit grouping. -- Return the translation of the string with '.' mark and en digits, -- and no separators (they have to be removed here to handle cases like	-- numsep = '.' and numdot = ',' with input "1.234.567,8"). if to_en_table then text = ustring.gsub(text, '%d', to_en_table) end if numsep_remove then text = text:gsub(numsep_remove, '') end if numsep_remove2 then text = text:gsub(numsep_remove2, '') end if numdot ~= '.' then text = text:gsub(numdot, '.') end return text end

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

local add_warning, with_separator -- forward declarations local function to_en_with_check(text, parms) -- Version of to_en for a wiki using numdot = ',' and numsep = '.' to check -- text (an input number as a string) which might have been copied from enwiki. -- For example, in '1.234' the '.' could be a decimal mark or a group separator. -- From viwiki. if to_en_table then text = ustring.gsub(text, '%d', to_en_table) end if decimal_mark(text) == '.' then local original = text text = text:gsub(',', '') -- for example, interpret "1,234.5" as an enwiki value if parms then add_warning(parms, 0, 'cvt_enwiki_num', original, with_separator({}, text)) end else if numsep_remove then text = text:gsub(numsep_remove, '') end if numsep_remove2 then text = text:gsub(numsep_remove2, '') end if numdot ~= '.' then text = text:gsub(numdot, '.') end end return text end

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

local spell_module -- name of module that can spell numbers local speller      -- function from that module to handle spelling (set if needed) local wikidata_module, wikidata_data_module -- names of Wikidata modules local wikidata_code, wikidata_data -- exported tables from those modules (set if needed)

local function set_config(args) -- Set configuration options from template #invoke or defaults. config = args maxsigfig = config.maxsigfig or 14 -- maximum number of significant figures local data_module, text_module local sandbox = config.sandbox and ('/' .. config.sandbox) or '' data_module = "Module:Convert/data" .. sandbox text_module = "Module:Convert/text" .. sandbox extra_module = "Module:Convert/extra" .. sandbox wikidata_module = "Module:Convert/wikidata" .. sandbox wikidata_data_module = "Module:Convert/wikidata/data" .. sandbox spell_module = "Module:ConvertNumeric" data_code = mw.loadData(data_module) text_code = mw.loadData(text_module) all_units = data_code.all_units local translation = text_code.translation_table if translation then numdot = translation.numdot numsep = translation.numsep if numdot == ',' and numsep == '.' then if text_code.all_messages.cvt_enwiki_num then to_en = to_en_with_check end end if translation.group then group_method = translation.group end if translation.per_word then per_word = translation.per_word end if translation.plural_suffix then plural_suffix = translation.plural_suffix end varname = translation.varname from_en_table = translation.from_en local use_workaround = true if use_workaround then -- 2013-07-05 workaround bug by making a copy of the required table. -- mw.ustring.gsub fails with a table (to_en_table) as the replacement, -- if the table is accessed via mw.loadData. local source = translation.to_en if source then to_en_table = {} for k, v in pairs(source) do					to_en_table[k] = v				end end else to_en_table = translation.to_en end if translation.lang == 'en default' then en_default = true -- for hiwiki end omitsep = translation.omitsep -- for zhwiki end numdot = config.numdot or numdot or '.' -- decimal mark before fractional digits numsep = config.numsep or numsep or ',' -- group separator for numbers -- numsep should be ',' or '.' or '' or ' ' or a Unicode character. -- numsep_remove must work in a regex to identify separators to be removed. if numsep ~= '' then numsep_remove = (numsep == '.') and '%.' or numsep end if numsep ~= ',' and numdot ~= ',' then numsep_remove2 = ',' -- so numbers copied from enwiki will work end end

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

local function divide(numerator, denominator) -- Return integers quotient, remainder resulting from dividing the two -- given numbers, which should be unsigned integers. local quotient, remainder = floor(numerator / denominator), numerator % denominator if not (0 <= remainder and remainder < denominator) then -- Floating point limits may need this, as in 160.02 Ym. remainder = 0 end return quotient, remainder end

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

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

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

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

local function message(parms, mcode, is_warning) -- Return wikitext for an error message, including category if specified -- for the message type. -- mcode = numbered table specifying the message: --   mcode[1] = 'cvt_xxx' (string used as a key to get message info) --   mcode[2] = 'parm1' (string to replace '$1' if any in message) --   mcode[3] = 'parm2' (string to replace '$2' if any in message) --   mcode[4] = 'parm3' (string to replace '$3' if any in message) local msg if type(mcode) == 'table' then if mcode[1] == 'cvt_no_output' then -- Some errors should cause convert to output an empty string, -- for example, for an optional field in an infobox. return '' end msg = text_code.all_messages[mcode[1]] end parms.have_problem = true local function subparm(fmt, ...) local rep = {} for i, v in ipairs({...}) do rep['$' .. i] = v		end return (fmt:gsub('$%d+', rep)) end if msg then local parts = {} local regex, replace = msg.regex, msg.replace for i = 1, 3 do			local limit = 40 local s = mcode[i + 1] if s then if regex and replace then s = s:gsub(regex, replace) limit = nil -- allow long "should be" messages end -- Escape user input so it does not break the message. -- To avoid tags (like 1$23$ m) breaking -- the mouseover title, any strip marker starting with char(127) is -- replaced with '...' (text not needing i18n). local append local pos = s:find(string.char(127), 1, true) if pos then append = '...' s = s:sub(1, pos - 1) end if limit and ulen(s) > limit then s = usub(s, 1, limit) append = '...' end s = mw.text.nowiki(s) .. (append or '') else s = '?' end parts['$' .. i] = s		end local function ispreview -- Return true if a prominent message should be shown. if parms.test == 'preview' or parms.test == 'nopreview' then -- For testing, can preview a real message or simulate a preview -- when running automated tests. return parms.test == 'preview' end local success, revid = pcall(function 				return (parms.frame):preprocess('') end) return success and (revid == '') end local want_warning = is_warning and not config.warnings and -- show unobtrusive warnings if config.warnings not configured not msg.nowarn          -- but use msg settings, not standard warning, if specified local title = string.gsub(msg[1] or 'Missing message', '$%d+', parts) local text = want_warning and '*' or msg[2] or 'Missing message' local cat = wanted_category(msg[3], mcode[2], want_warning) local anchor = msg[4] or '' local fmtkey = ispreview and 'cvt_format_preview' or			(want_warning and 'cvt_format2' or msg.format or 'cvt_format') local fmt = text_code.all_messages[fmtkey] or 'convert: bug' return subparm(fmt, title:gsub('"', '&quot;'), text, cat, anchor)	end	return 'Convert internal error: unknown message' end

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

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

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

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

local function get_styles(parms) -- Return string of required template styles, empty if none. if parms.templatestyles then local t = {} for _, v in pairs(parms.templatestyles) do			table.insert(t, v)		end return table.concat(t) end return '' end

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

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

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

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

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

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

local unit_prefixed_mt = { -- Metatable to get missing values for a unit that accepts SI prefixes. -- Before use, fields si_name, si_prefix must be defined. -- The unit must define _symbol, _name1 and -- may define _sym_us, _name1_us, _name2_us -- (_sym_us, _name2_us may be defined for a language using sp=us	-- to refer to a variant unrelated to U.S. units). __index = function (self, key) local value if key == 'symbol' then value = self.si_prefix .. self._symbol elseif key == 'sym_us' then value = rawget(self, '_sym_us') if value then value = self.si_prefix .. value else value = self.symbol end elseif key == 'name1' then value = prefixed_name(self, self._name1, 1) elseif key == 'name2' then value = rawget(self, '_name2') if value then value = prefixed_name(self, value, 2) else value = self.name1 .. plural_suffix end elseif key == 'name1_us' then value = rawget(self, '_name1_us') if value then value = prefixed_name(self, value, 3) else value = self.name1 end elseif key == 'name2_us' then value = rawget(self, '_name2_us') if value then value = prefixed_name(self, value, 4) elseif rawget(self, '_name1_us') then value = self.name1_us .. plural_suffix else value = self.name2 end elseif key == 'link' then value = self.name1 else value = false end rawset(self, key, value) return value end }

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

local function make_per(unitcode, unit_table, ulookup) -- Return true, t where t is a per unit with unit codes expanded to unit tables, -- or return false, t where t is an error message table. local result = { unitcode = unitcode, utype = unit_table.utype, per = {} }	override_from(result, unit_table, { 'invert', 'iscomplex', 'default', 'link', 'symbol', 'symlink' }) result.symbol_raw = (result.symbol or false) -- to distinguish between a defined exception and a metatable calculation local prefix for i, v in ipairs(unit_table.per) do		if i == 1 and v == '' then -- First unit symbol can be empty; that gives a nil first unit table. elseif i == 1 and text_code.currency[v] then prefix = currency_text or v		else local success, t = ulookup(v) if not success then return false, t end result.per[i] = t		end end local multiplier = unit_table.multiplier if not result.utype then -- Creating an automatic per unit. local unit1 = result.per[1] local utype = (unit1 and unit1.utype or prefix or '') .. '/' .. result.per[2].utype local t = data_code.per_unit_fixups[utype] if t then if type(t) == 'table' then utype = t.utype or utype result.link = result.link or t.link multiplier = multiplier or t.multiplier else utype = t			end end result.utype = utype end result.scalemultiplier = multiplier or 1 result.vprefix = prefix or false -- set to non-nil to avoid calling __index return true, setmetatable(result, unit_per_mt) end

local function lookup(parms, unitcode, what, utable, fails, depth) -- Return true, t where t is a copy of the unit's converter table, -- or return false, t where t is an error message table. -- Parameter 'what' determines whether combination units are accepted: --  'no_combination'  : single unit only --  'any_combination' : single unit or combination or output multiple --  'only_multiple'   : single unit or output multiple only -- Parameter unitcode is a symbol (like 'g'), with an optional SI prefix (like 'kg'). -- If, for example, 'kg' is in this table, that entry is used; -- otherwise the prefix ('k') is applied to the base unit ('g'). -- If unitcode is a known combination code (and if allowed by what), -- a table of output multiple unit tables is included in the result. -- For compatibility with the old template, an underscore in a unitcode is -- replaced with a space so usage like 350 board_feet works. -- Wikignomes may also put two spaces or " " in combinations, so -- replace underscore, " ", and multiple spaces with a single space. utable = utable or parms.unittable or all_units fails = fails or {} depth = depth and depth + 1 or 1 if depth > 9 then -- There are ways to mistakenly define units which result in infinite -- recursion when lookup is called. That gives a long delay and very -- confusing error messages, so the depth parameter is used as a guard. return false, { 'cvt_lookup', unitcode } end if unitcode == nil or unitcode == '' then return false, { 'cvt_no_unit' } end unitcode = unitcode:gsub('_', ' '):gsub(' ', ' '):gsub(' +', ' ') local function call_make_per(t) return make_per(unitcode, t,			function (ucode) return lookup(parms, ucode, 'no_combination', utable, fails, depth) end		) end local t = utable[unitcode] if t then if t.shouldbe then return false, { 'cvt_should_be', t.shouldbe } end if t.sp_us then parms.opt_sp_us = true end local target = t.target -- nil, or unitcode is an alias for this target if target then local success, result = lookup(parms, target, what, utable, fails, depth) if not success then return false, result end override_from(result, t, { 'customary', 'default', 'link', 'symbol', 'symlink' }) local multiplier = t.multiplier if multiplier then result.multiplier = tostring(multiplier) result.scale = result.scale * multiplier end return true, result end if t.per then return call_make_per(t) end local combo = t.combination -- nil or a table of unitcodes if combo then local multiple = t.multiple if what == 'no_combination' or (what == 'only_multiple' and not multiple) then return false, { 'cvt_bad_unit', unitcode } end -- Recursively create a combination table containing the -- converter table of each unitcode. local result = { utype = t.utype, multiple = multiple, combination = {} } local cvt = result.combination for i, v in ipairs(combo) do				local success, t = lookup(parms, v, multiple and 'no_combination' or 'only_multiple', utable, fails, depth) if not success then return false, t end cvt[i] = t			end return true, result end local result = shallow_copy(t) result.unitcode = unitcode if result.prefixes then result.si_name = '' result.si_prefix = '' return true, setmetatable(result, unit_prefixed_mt) end return true, setmetatable(result, unit_mt) end local SIprefixes = text_code.SIprefixes for plen = SIprefixes[1] or 2, 1, -1 do -- Look for an SI prefix; should never occur with an alias. -- Check for longer prefix first ('dam' is decametre). -- SIprefixes[1] = prefix maximum #characters (as seen by mw.ustring.sub). local prefix = usub(unitcode, 1, plen) local si = SIprefixes[prefix] if si then local t = utable[usub(unitcode, plen+1)] if t and t.prefixes then local result = shallow_copy(t) result.unitcode = unitcode result.si_name = parms.opt_sp_us and si.name_us or si.name result.si_prefix = si.prefix or prefix result.scale = t.scale * 10 ^ (si.exponent * t.prefixes) return true, setmetatable(result, unit_prefixed_mt) end end end -- Accept user-defined combinations like "acre+m2+ha" or "acre m2 ha" for output. -- If '+' is used, each unit code can include a space, and any error is fatal. -- If ' ' is used and if each space-separated word is a unit code, it is a combo, -- but errors are not fatal so the unit code can be looked up as an extra unit. local err_is_fatal local combo = collection if unitcode:find('+', 1, true) then err_is_fatal = true for item in (unitcode .. '+'):gmatch('%s*(.-)%s*%+') do			if item ~= '' then combo:add(item) end end elseif unitcode:find('%s') then for item in unitcode:gmatch('%S+') do			combo:add(item) end end if combo.n > 1 then local function lookup_combo if what == 'no_combination' or what == 'only_multiple' then return false, { 'cvt_bad_unit', unitcode } end local result = { combination = {} } local cvt = result.combination for i, v in ipairs(combo) do				local success, t = lookup(parms, v, 'only_multiple', utable, fails, depth) if not success then return false, t end if i == 1 then result.utype = t.utype else local mismatch = check_mismatch(result, t)					if mismatch then return false, mismatch end end cvt[i] = t			end return true, result end local success, result = lookup_combo if success or err_is_fatal then return success, result end end -- Accept any unit with an engineering notation prefix like "e6cuft" -- (million cubic feet), but not chained prefixes like "e3e6cuft", -- and not if the unit is a combination or multiple, -- and not if the unit has an offset or is a built-in. -- Only en digits are accepted. local exponent, baseunit = unitcode:match('^e(%d+)(.*)') if exponent then local engscale = text_code.eng_scales[exponent] if engscale then local success, result = lookup(parms, baseunit, 'no_combination', utable, fails, depth) if success and not (result.offset or result.builtin or result.engscale) then result.unitcode = unitcode -- 'e6cuft' not 'cuft' result.defkey = unitcode -- key to lookup default exception result.engscale = engscale result.scale = result.scale * 10 ^ tonumber(exponent) return true, result end end end -- Look for x/y; split on right-most slash to get scale correct (x/y/z is x/y per z). local top, bottom = unitcode:match('^(.-)/([^/]+)$') if top and not unitcode:find('e%d') then -- If valid, create an automatic per unit for an "x/y" unit code. -- The unitcode must not include extraneous spaces. -- Engineering notation (apart from at start and which has been stripped before here), -- is not supported so do not make a per unit if find text like 'e3' in unitcode. local success, result = call_make_per({ per = {top, bottom} }) if success then return true, result end end if not parms.opt_ignore_error and not get_range(unitcode) then -- Want the "what links here" list for the extra_module to show only cases -- where an extra unit is used, so do not require it if invoked from -- or if looking up a range word which cannot be a unit. if not extra_units then local success, extra = pcall(function return require(extra_module).extra_units end) if success and type(extra) == 'table' then extra_units = extra end end if extra_units then -- A unit in one data table might refer to a unit in the other table, so -- switch between them, relying on fails or depth to terminate loops. if not fails[unitcode] then fails[unitcode] = true local other = (utable == all_units) and extra_units or all_units local success, result = lookup(parms, unitcode, what, other, fails, depth) if success then return true, result end end end end if to_en_table then -- At fawiki it is common to translate all digits so a unit like "km2" becomes "km۲". local en_code = ustring.gsub(unitcode, '%d', to_en_table) if en_code ~= unitcode then return lookup(parms, en_code, what, utable, fails, depth) end end return false, { 'cvt_unknown', unitcode } end

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

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

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

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

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

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

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

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

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

-- Fraction output format. local fracfmt = { { -- Like 1/undefined (fraction slash). ' {SIGN} {NUM} &frasl; {DEN} ',  -- 1/2 ' {SIGN}{WHOLE} + {NUM} &frasl; {DEN} ',  -- 1+2/3 style = 'frac', },	{ -- Like 1⁄undefined (stacked fraction, that is, horizontal bar). ' {SIGN} {NUM} / {DEN} ',  -- 1//2 ' {SIGN}{WHOLE} + {NUM} / {DEN}   ',  -- 1+2//3 style = 'sfrac', }, }

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

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

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

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

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

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

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

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

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

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

local function translate_parms(parms, kv_pairs) -- Update fields in parms by translating each key:value in kv_pairs to terms -- used by this module (may involve translating from local language to English). -- Also, checks are performed which may display warnings, if enabled. -- Return true if successful or return false, t where t is an error message table. currency_text = nil -- local testing can hold module in memory; must clear globals local accept_any_text = { input = true, qid = true, qual = true, stylein = true, styleout = true, tracking = true, }	if kv_pairs.adj and kv_pairs.sing then -- For enwiki (before translation), warn if attempt to use adj and sing -- as the latter is a deprecated alias for the former. if kv_pairs.adj ~= kv_pairs.sing and kv_pairs.sing ~= '' then add_warning(parms, 1, 'cvt_unknown_option', 'sing=' .. kv_pairs.sing) end kv_pairs.sing = nil end kv_pairs.comma = kv_pairs.comma or config.comma -- for plwiki who want default comma=5 for loc_name, loc_value in pairs(kv_pairs) do		local en_name = text_code.en_option_name[loc_name] if en_name then local en_value if en_name == '$' or en_name == 'frac' or en_name == 'sigfig' then if loc_value == '' then add_warning(parms, 2, 'cvt_empty_option', loc_name) elseif en_name == '$' then -- Value should be a single character like "€" for the euro currency symbol, but anything is accepted. currency_text = (loc_value == 'euro') and '€' or loc_value else local minimum local number, is_integer = get_number(loc_value) if en_name == 'frac' then minimum = 2 if number and number < 0 then parms.opt_fraction_horizontal = true number = -number end else minimum = 1 end if number and is_integer and number >= minimum then en_value = number else add_warning(parms, 1, (en_name == 'frac' and 'cvt_bad_frac' or 'cvt_bad_sigfig'), loc_name .. '=' .. loc_value) end end elseif accept_any_text[en_name] then en_value = loc_value ~= '' and loc_value or nil -- accept non-empty user text with no validation if en_name == 'input' then -- May have something like undefined undefined (empty input) if source is an infobox -- with optional fields. In that case, want to output nothing rather than an error. parms.input_text = loc_value -- keep input because parms.input is nil if loc_value == '' end else en_value = text_code.en_option_value[en_name][loc_value] if en_value and en_value:sub(-1) == '?' then en_value = en_value:sub(1, -2) add_warning(parms, -1, 'cvt_deprecated', loc_name .. '=' .. loc_value) end if en_value == nil then if loc_value == '' then add_warning(parms, 2, 'cvt_empty_option', loc_name) else add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value) end elseif en_value == '' then en_value = nil -- an ignored option like adj=off elseif type(en_value) == 'string' and en_value:sub(1, 4) == 'opt_' then for _, v in ipairs(split(en_value, ',')) do						local lhs, rhs = v:match('^(.-)=(.+)$') if rhs then parms[lhs] = tonumber(rhs) or rhs else parms[v] = true end end en_value = nil end end parms[en_name] = en_value else add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value) end end local abbr_entered = parms.abbr local cfg_abbr = config.abbr if cfg_abbr then -- Don't warn if invalid because every convert would show that warning. if cfg_abbr == 'on always' then parms.abbr = 'on' elseif cfg_abbr == 'off always' then parms.abbr = 'off' elseif parms.abbr == nil then if cfg_abbr == 'on default' then parms.abbr = 'on' elseif cfg_abbr == 'off default' then parms.abbr = 'off' end end end if parms.abbr then if parms.abbr == 'unit' then parms.abbr = 'on' parms.number_word = true end parms.abbr_org = parms.abbr -- original abbr, before any flip elseif parms.opt_hand_hh then parms.abbr_org = 'on' parms.abbr = 'on' else parms.abbr = 'out' -- default is to abbreviate output only (use symbol, not name) end if parms.opt_order_out then -- Disable options that do not work in a useful way with order=out. parms.opt_flip = nil -- override adj=flip parms.opt_spell_in = nil parms.opt_spell_out = nil parms.opt_spell_upper = nil end if parms.opt_spell_out and not abbr_entered then parms.abbr = 'off' -- should show unit name when spelling the output value end if parms.opt_flip then local function swap_in_out(option) local value = parms[option] if value == 'in' then parms[option] = 'out' elseif value == 'out' then parms[option] = 'in' end end swap_in_out('abbr') swap_in_out('lk') if parms.opt_spell_in and not parms.opt_spell_out then -- For simplicity, and because it does not appear to be needed, -- user cannot set an option to spell the output only. parms.opt_spell_in = nil parms.opt_spell_out = true end end if parms.opt_spell_upper then parms.spell_upper = parms.opt_flip and 'out' or 'in' end if parms.opt_table or parms.opt_tablecen then if abbr_entered == nil and parms.lk == nil then parms.opt_values = true end parms.table_align = parms.opt_table and 'right' or 'center' end if parms.table_align or parms.opt_sortable_on then parms.need_table_or_sort = true end local disp_joins = text_code.disp_joins local default_joins = disp_joins['b'] parms.join_between = default_joins[3] or '; ' local disp = parms.disp if disp == nil then -- special case for the most common setting parms.joins = default_joins elseif disp == 'x' then -- Later, parms.joins is set from the input parameters. else -- Old template does this. local abbr = parms.abbr if disp == 'slash' then if abbr_entered == nil then disp = 'slash-nbsp' elseif abbr == 'in' or abbr == 'out' then disp = 'slash-sp' else disp = 'slash-nosp' end elseif disp == 'sqbr' then if abbr == 'on' then disp = 'sqbr-nbsp' else disp = 'sqbr-sp' end end parms.joins = disp_joins[disp] or default_joins parms.join_between = parms.joins[3] or parms.join_between parms.wantname = parms.joins.wantname end if (en_default and not parms.opt_lang_local and (parms[1] or ''):find('%d')) or parms.opt_lang_en then from_en_table = nil end if en_default and from_en_table then -- For hiwiki: localized symbol/name is defined with the US symbol/name field, -- and is used if output uses localized numbers. parms.opt_sp_us = true end return true end

local function get_values(parms) -- If successful, update parms and return true, v, i where --  v = table of input values --  i = index to next entry in parms after those processed here -- or return false, t where t is an error message table. local valinfo = collection -- numbered table of input values local range = collection -- numbered table of range items (having, for example, 2 range items requires 3 input values) local had_nocomma -- true if removed "nocomma" kludge from second parameter (like "tonocomma") local parm2 = strip(parms[2]) if parm2 and parm2:sub(-7, -1) == 'nocomma' then parms[2] = strip(parm2:sub(1, -8)) parms.opt_nocomma = true had_nocomma = true end local function extractor(i) -- If the parameter is not a value, try unpacking it as a range ("1-23" for "1 to 23"). -- However, "-1-2/3" is a negative fraction (-1⅔), so it must be extracted first. -- Do not unpack a parameter if it is like "3-1/2" which is sometimes incorrectly -- used instead of "3+1/2" (and which should not be interpreted as "3 to ½"). -- Unpacked items are inserted into the parms table. -- The tail recursion allows combinations like "1x2 to 3x4". local valstr = strip(parms[i]) -- trim so any '-' as a negative sign will be at start local success, result = extract_number(parms, valstr, i > 1) if not success and valstr and i < 20 then -- check i to limit abuse local lhs, sep, rhs = valstr:match('^(%S+)%s+(%S+)%s+(%S.*)') if lhs and not (sep == '-' and rhs:match('/')) then if sep:find('%d') then return success, result -- to reject 1 234 567 m with a decent message (en only) end parms[i] = rhs table.insert(parms, i, sep) table.insert(parms, i, lhs) return extractor(i) end if not valstr:match('%-.*/') then for _, sep in ipairs(text_code.ranges.words) do					local start, stop = valstr:find(sep, 2, true) -- start at 2 to skip any negative sign for range '-' if start then parms[i] = valstr:sub(stop + 1) table.insert(parms, i, sep) table.insert(parms, i, valstr:sub(1, start - 1)) return extractor(i) end end end end return success, result end local i = 1 local is_change while true do		local success, info = extractor(i) -- need to set parms.opt_nocomma before calling this if not success then return false, info end i = i + 1 if is_change then info.is_change = true -- value is after "±" and so is a change (significant for range like 5 ±) is_change = nil end valinfo:add(info) local range_item = get_range(strip(parms[i])) if not range_item then break end i = i + 1 range:add(range_item) if type(range_item) == 'table' then -- For range "x", if append unit to some values, append it to all. parms.in_range_x = parms.in_range_x or range_item.in_range_x parms.out_range_x = parms.out_range_x or range_item.out_range_x parms.abbr_range_x = parms.abbr_range_x or range_item.abbr_range_x is_change = range_item.is_range_change end end if range.n > 0 then if range.n > 30 then -- limit abuse, although 4 is a more likely upper limit return false, { 'cvt_invalid_num' } -- misleading message but it will do		end parms.range = range elseif had_nocomma then return false, { 'cvt_unknown', parm2 } end return true, valinfo, i end

local function simple_get_values(parms) -- If input is like "valid_value valid_unit", -- return true, i, in_unit, in_unit_table -- i = index in parms of what follows valid_unit, if anything. -- The valid_value is not negative and does not use a fraction, and -- no options requiring further processing of the input are used. -- Otherwise, return nothing or return false, parm1 for caller to interpret. -- Testing shows this function is successful for 96% of converts in articles, -- and that on average it speeds up converts by 8%. local clean = to_en(strip(parms[1] or ''), parms) if parms.opt_ri or parms.opt_spell_in or #clean > 10 or not clean:match('^[0-9.]+$') then return false, clean end local value = tonumber(clean) if not value then return end local info = { value = value, altvalue = value, singular = (value == 1), clean = clean, show = with_separator(parms, clean), }	local in_unit = strip(parms[2]) local success, in_unit_table = lookup(parms, in_unit, 'no_combination') if not success then return end in_unit_table.valinfo = { info } return true, 3, in_unit, in_unit_table end

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

local function get_parms(parms, args) -- If successful, update parms and return true, unit where --  parms is a table of all arguments passed to the template --       converted to named arguments, and --  unit is the input unit table; -- or return false, t where t is an error message table. -- For special processing (not a convert), can also return -- true, wikitext where wikitext is the final result. -- The returned input unit table may be for a fake unit using the specified -- unit code as the symbol and name, and with bad_mcode = message code table. -- MediaWiki removes leading and trailing whitespace from the values of -- named arguments. However, the values of numbered arguments include any -- whitespace entered in the template, and whitespace is used by some -- parameters (example: the numbered parameters associated with "disp=x"). local kv_pairs = {} -- table of input key:value pairs where key is a name; needed because cannot iterate parms and add new fields to it	for k, v in pairs(args) do		if type(k) == 'number' or k == 'test' then  -- parameter "test" is reserved for testing and is not translated parms[k] = v		else kv_pairs[k] = v		end end if parms.test == 'wikidata' then local ulookup = function (ucode) -- Use empty table for parms so it does not accumulate results when used repeatedly. return lookup({}, ucode, 'no_combination') end return wikidata_call(parms, '_listunits', ulookup) end local success, msg = translate_parms(parms, kv_pairs) if not success then return false, msg end if parms.input then success, msg = wikidata_call(parms, '_adjustparameters', parms, 1) if not success then return false, msg end end local success, i, in_unit, in_unit_table = simple_get_values(parms) if not success then if type(i) == 'string' and i:match('^NNN+$') then -- Some infoboxes have examples like NNN m (3 or more "N"). -- Output an empty string for these. return false, { 'cvt_no_output' } end local valinfo success, valinfo, i = get_values(parms) if not success then return false, valinfo end in_unit = strip(parms[i]) i = i + 1 success, in_unit_table = lookup(parms, in_unit, 'no_combination') if not success then in_unit = in_unit or '' if parms.opt_ignore_error then -- display given unit code with no error (for use with ) in_unit_table = '' -- suppress error message and prevent processing of output unit end in_unit_table = setmetatable({				symbol = in_unit, name2 = in_unit, utype = in_unit,				scale = 1, default = , defkey = , linkey = '',				bad_mcode = in_unit_table }, unit_mt) end in_unit_table.valinfo = valinfo end if parms.test == 'msg' then -- Am testing the messages produced when no output unit is specified, and -- the input unit has a missing or invalid default. -- Set two units for testing that. -- LATER: Remove this code. if in_unit == 'chain' then in_unit_table.default = nil -- no default elseif in_unit == 'rd' then in_unit_table.default = "ft!X!m"  -- an invalid expression end end in_unit_table.inout = 'in' -- this is an input unit if not parms.range then local success, inext, composite_unit = get_composite(parms, i, in_unit_table) if not success then return false, inext end if composite_unit then in_unit_table = composite_unit i = inext end end if in_unit_table.builtin == 'mach' then -- As with old template, a number following Mach as the input unit is the altitude, -- and there is no way to specify an altitude for the output unit. -- Could put more code in this function to get any output unit and check for -- an altitude following that unit. local success, info = extract_number(parms, parms[i], false, true) if success then i = i + 1 in_unit_table.altitude = info.value end end local word = strip(parms[i]) i = i + 1 local precision, is_bad_precision local function set_precision(text) local number, is_integer = get_number(text) if number then if is_integer then precision = number else precision = text is_bad_precision = true end return true -- text was used for precision, good or bad end end if word and not set_precision(word) then parms.out_unit = parms.out_unit or word if set_precision(strip(parms[i])) then i = i + 1 end end if parms.opt_adj_mid then word = parms[i] i = i + 1 if word then -- mid-text words if word:sub(1, 1) == '-' then parms.mid = word else parms.mid = ' ' .. word end end end if parms.opt_one_preunit then parms[parms.opt_flip and 'preunit2' or 'preunit1'] = preunits(1, parms[i]) i = i + 1 end if parms.disp == 'x' then -- Following is reasonably compatible with the old template. local first = parms[i] or '' local second = parms[i+1] or '' i = i + 2 if strip(first) == '' then -- user can enter '&#32;' rather than ' ' to avoid the default first = ' [ ' .. first second = ' ]' .. second end parms.joins = { first, second } elseif parms.opt_two_preunits then local p1, p2 = preunits(2, parms[i], parms[i+1]) i = i + 2 if parms.preunit1 then -- To simplify documentation, allow unlikely use of adj=pre with disp=preunit -- (however, an output unit must be specified with adj=pre and with disp=preunit). parms.preunit1 = parms.preunit1 .. p1			parms.preunit2 = p2		else parms.preunit1, parms.preunit2 = p1, p2		end end if precision == nil then if set_precision(strip(parms[i])) then i = i + 1 end end if is_bad_precision then add_warning(parms, 1, 'cvt_bad_prec', precision) else parms.precision = precision end for j = i, i + 3 do		local parm = parms[j] -- warn if find a non-empty extraneous parameter if parm and parm:match('%S') then add_warning(parms, 1, 'cvt_unknown_option', parm) break end end return true, in_unit_table end

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

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

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

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

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

local cvt_to_hand

local function cvtround(parms, info, in_current, out_current) -- Return true, t where t is a table with the conversion results; fields: --  show = rounded, formatted string with the result of converting value in info, --     using the rounding specified in parms. --  singular = true if result (after rounding and ignoring any negative sign) --     is "1", or like "1.00", or is a fraction with value < 1; --  (and more fields shown below, and a calculated 'absvalue' field). -- or return false, t where t is an error message table. -- Input info.clean uses en digits (it has been translated, if necessary). -- Output show uses en or non-en digits as appropriate, or can be spelled. if out_current.builtin == 'hand' then return cvt_to_hand(parms, info, in_current, out_current) end local invalue = in_current.builtin == 'hand' and info.altvalue or info.value local outvalue, extra = convert(parms, invalue, info, in_current, out_current) if parms.need_table_or_sort then parms.need_table_or_sort = nil -- process using first input value only make_table_or_sort(parms, invalue, info, in_current) end if extra then if not outvalue then return false, extra end invalue = extra.invalue or invalue outvalue = extra.outvalue end if not valid_number(outvalue) then return false, { 'cvt_invalid_num' } end local isnegative if outvalue < 0 then isnegative = true outvalue = -outvalue end local precision, show, exponent local denominator = out_current.frac if denominator then show = fraction_table(outvalue, denominator) else precision = parms.precision if not precision then if parms.sigfig then show, exponent = make_sigfig(outvalue, parms.sigfig) elseif parms.opt_round then local n = parms.opt_round if n == 0.5 then local integer, fracpart = math.modf(floor(2 * outvalue + 0.5) / 2) if fracpart == 0 then show = format('%.0f', integer) else show = format('%.1f', integer + fracpart) end else show = format('%.0f', floor((outvalue / n) + 0.5) * n)				end else local inclean = info.clean if extra then inclean = extra.clean or inclean show = extra.show end if not show then precision = default_precision(parms, invalue, inclean, info.denominator, outvalue, in_current, out_current, extra) end end end end if precision then if precision >= 0 then local fudge if precision <= 8 then -- Add a fudge to handle common cases of bad rounding due to inability -- to precisely represent some values. This makes the following work: -- -100.1 C and 5555000 um. -- Old template uses #expr round, which invokes PHP round. -- LATER: Investigate how PHP round works. fudge = 2e-14 else fudge = 0 end local fmt = '%.' .. format('%d', precision) .. 'f'			local success success, show = pcall(format, fmt, outvalue + fudge) if not success then return false, { 'cvt_big_prec', tostring(precision) } end else precision = -precision -- #digits to zero (in addition to any digits after dot) local shift = 10 ^ precision show = format('%.0f', outvalue/shift) if show ~= '0' then exponent = #show + precision end end end local t = format_number(parms, show, exponent, isnegative) if type(show) == 'string' then -- Set singular using match because on some systems 0.99999999999999999 is 1.0. if exponent then t.singular = (exponent == 1 and show:match('^10*$')) else t.singular = (show == '1' or show:match('^1%.0*$')) end else t.fraction_table = show t.singular = (outvalue <= 1) -- cannot have 'fraction == 1', but if it were possible it would be singular end t.raw_absvalue = outvalue -- absolute value before rounding return true, setmetatable(t, {		__index = function (self, key)			if key == 'absvalue' then				-- Calculate absolute value after rounding, if needed.				local clean, exponent = rawget(self, 'clean'), rawget(self, 'exponent')				local value = tonumber(clean) -- absolute value (any negative sign has been ignored)				if exponent then					value = value * 10^exponent				end				rawset(self, key, value)				return value			end		end }) end

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

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

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

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

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

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

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

local function linked_id(parms, unit_table, key_id, want_link, clean) -- Return final unit id (symbol or name), optionally with a wikilink, -- and update unit_table.sep if required. -- key_id is one of: 'symbol', 'sym_us', 'name1', 'name1_us', 'name2', 'name2_us'. local abbr_on = (key_id == 'symbol' or key_id == 'sym_us') if abbr_on and want_link then local symlink = rawget(unit_table, 'symlink') if symlink then return symlink -- for exceptions that have the linked symbol built-in end end local multiplier = rawget(unit_table, 'multiplier') local per = unit_table.per if per then local paren1, paren2 = ,  -- possible parentheses around bottom unit local unit1 = per[1] -- top unit_table, or nil local unit2 = per[2] -- bottom unit_table if abbr_on then if not unit1 then unit_table.sep = '' -- no separator in "$2/acre" end if not want_link then local symbol = unit_table.symbol_raw if symbol then return symbol -- for exceptions that have the symbol built-in end end if (unit2.symbol):find('⋅', 1, true) then paren1, paren2 = '(', ')' end end local key_id2 -- unit2 is always singular if key_id == 'name2' then key_id2 = 'name1' elseif key_id == 'name2_us' then key_id2 = 'name1_us' else key_id2 = key_id end local result if abbr_on then result = '/' elseif omitsep then result = per_word elseif unit1 then result = ' ' .. per_word .. ' '		else result = per_word .. ' '		end if want_link and unit_table.link then if abbr_on or not varname then result = (unit1 and linked_id(parms, unit1, key_id, false, clean) or '') .. result .. linked_id(parms, unit2, key_id2, false, '1') else result = (unit1 and variable_name(clean, unit1) or '') .. result .. variable_name('1', unit2) end if omit_separator(result) then unit_table.sep = '' end return make_link(unit_table.link, result, unit_table) end if unit1 then result = linked_id(parms, unit1, key_id, want_link, clean) .. result if unit1.sep then unit_table.sep = unit1.sep end elseif omitsep then unit_table.sep = '' end return result .. paren1 .. linked_id(parms, unit2, key_id2, want_link, '1') .. paren2 end if multiplier then -- A multiplier (like "100" in "100km") forces the unit to be plural. multiplier = from_en(multiplier) if not omitsep then multiplier = multiplier .. (abbr_on and ' ' or ' ') end if not abbr_on then if key_id == 'name1' then key_id = 'name2' elseif key_id == 'name1_us' then key_id = 'name2_us' end end else multiplier = '' end local id = unit_table.fixed_name or ((varname and not abbr_on) and variable_name(clean, unit_table) or unit_table[key_id]) if omit_separator(id) then unit_table.sep = '' end if want_link then local link = data_code.link_exceptions[unit_table.linkey or unit_table.symbol] or unit_table.link if link then local before = '' local i = unit_table.customary if i == 1 and parms.opt_sp_us then i = 2 -- show "U.S." not "US" end if i == 3 and abbr_on then i = 4 -- abbreviate "imperial" to "imp" end local customary = text_code.customary_units[i] if customary then -- LATER: This works for language en only, but it's esoteric so ignore for now. local pertext if id:sub(1, 1) == '/' then -- Want unit "/USgal" to display as "/U.S. gal", not "U.S. /gal". pertext = '/' id = id:sub(2) elseif id:sub(1, 4) == 'per ' then -- Similarly want "per U.S. gallon", not "U.S. per gallon" (but in practice this is unlikely to be used). pertext = 'per ' id = id:sub(5) else pertext = '' end -- Omit any "US"/"U.S."/"imp"/"imperial" from start of id since that will be inserted. local removes = (i < 3) and { 'US ', 'US ', 'U.S. ', 'U.S. ' } or { 'imp ', 'imp ', 'imperial ' } for _, prefix in ipairs(removes) do					local plen = #prefix if id:sub(1, plen) == prefix then id = id:sub(plen + 1) break end end before = pertext .. make_link(customary.link, customary[1]) .. ' '			end id = before .. make_link(link, id, unit_table) end end return multiplier .. id end

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

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

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

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

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

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

local function process(parms, in_unit_table, out_unit_table) -- Return true, s, outunit where s = final wikitext result, -- or return false, t where t is an error message table. linked_pages = {} local success, bad_output local bad_input_mcode = in_unit_table.bad_mcode -- nil if input unit is a valid convert unit local out_unit = parms.out_unit if out_unit == nil or out_unit == '' or type(out_unit) == 'function' then if bad_input_mcode or parms.opt_input_unit_only then bad_output = '' else local getdef = type(out_unit) == 'function' and out_unit or get_default success, out_unit = getdef(in_unit_table.valinfo[1].value, in_unit_table) parms.out_unit = out_unit if not success then bad_output = out_unit end end end if not bad_output and not out_unit_table then success, out_unit_table = lookup(parms, out_unit, 'any_combination') if success then local mismatch = check_mismatch(in_unit_table, out_unit_table) if mismatch then bad_output = mismatch end else bad_output = out_unit_table end end local lhs, rhs local flipped = parms.opt_flip and not bad_input_mcode if bad_output then rhs = (bad_output == ) and  or message(parms, bad_output) elseif parms.opt_input_unit_only then rhs = '' else local combos -- nil (for 'ft' or 'ftin'), or table of unit tables (for 'm ft') if not out_unit_table.multiple then -- nil/false ('ft' or 'm ft'), or table of factors ('ftin') combos = out_unit_table.combination end local frac = parms.frac -- nil or denominator of fraction for output values if frac then -- Apply fraction to the unit (if only one), or to non-SI units (if a combination), -- except that if a precision is also specified, the fraction only applies to			-- the hand unit; that allows the following result: -- 156 cm → 156 centimetres (61.4 in; 15.1½ hands) -- However, the following is handled elsewhere as a special case: -- 156 cm → 156 centimetres (15.1½ hands; 61½ in) if combos then local precision = parms.precision for _, unit in ipairs(combos) do					if unit.builtin == 'hand' or (not precision and not unit.prefixes) then unit.frac = frac end end else out_unit_table.frac = frac end end local outputs = {} local imax = combos and #combos or 1 -- 1 (single unit) or number of unit tables if imax == 1 then parms.opt_order_out = nil -- only useful with an output combination end if not flipped and not parms.opt_order_out then -- Process left side first so any duplicate links (from lk=on) are suppressed -- on right. Example: 28 e9pc lhs = process_input(parms, in_unit_table) end for i = 1, imax do			local success, item local out_current = combos and combos[i] or out_unit_table out_current.inout = 'out' if i == 1 then if imax > 1 and out_current.builtin == 'hand' then out_current.out_next = combos[2] -- built-in hand can influence next unit in a combination end if parms.opt_order_out then out_current.inout = 'in' end end if out_current.multiple then success, item = make_output_multiple(parms, in_unit_table, out_current) else success, item = make_output_single(parms, in_unit_table, out_current) end if not success then return false, item end outputs[i] = item end if parms.opt_order_out then lhs = outputs[1] table.remove(outputs, 1) end local sep = parms.table_joins and parms.table_joins[2] or parms.join_between rhs = table.concat(outputs, sep) end if flipped or not lhs then local input = process_input(parms, in_unit_table) if flipped then lhs = rhs rhs = input else lhs = input end end if parms.join_before then lhs = parms.join_before .. lhs end local wikitext if bad_input_mcode then if bad_input_mcode == '' then wikitext = lhs else wikitext = lhs .. message(parms, bad_input_mcode) end elseif parms.table_joins then wikitext = parms.table_joins[1] .. lhs .. parms.table_joins[2] .. rhs else wikitext = lhs .. parms.joins[1] .. rhs .. parms.joins[2] end if parms.warnings and not bad_input_mcode then wikitext = wikitext .. parms.warnings end return true, get_styles(parms) .. wikitext, out_unit_table end

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

local function _unit(unitcode, options) -- Helper function for Module:Val to look up a unit. -- Parameter unitcode must be a string to identify the wanted unit. -- Parameter options must be nil or a table with optional fields: --  value = number (for sort key; default value is 1) --  scaled_top = nil for a normal unit, or a number for a unit which is	--                the denominator of a per unit (for sort key) --  si = { 'symbol', 'link' } --               (a table with two strings) to make an SI unit --               that will be used for the look up	--   link = true if result should be linked --  sort = 'on' or 'debug' if result should include a sort key in a	--                span element ('debug' makes the key visible) --  name = true for the name of the unit instead of the symbol --  us = true for the US spelling of the unit, if any -- Return nil if unitcode is not a non-empty string. -- Otherwise return a table with fields: --  text = requested symbol or name of unit, optionally linked --  scaled_value = input value adjusted by unit scale; used for sort key --  sortspan = span element with sort key like that provided by , --    calculated from the result of converting value --    to a base unit with scale 1. --  unknown = true if the unitcode was not known unitcode = strip(unitcode) if unitcode == nil or unitcode == '' then return nil end set_config({}) linked_pages = {} options = options or {} local parms = { abbr = options.name and 'off' or 'on', lk = options.link and 'on' or nil, opt_sp_us = options.us and true or nil, opt_ignore_error = true, -- do not add pages using this function to 'what links here' for Module:Convert/extra opt_sortable_on = options.sort == 'on' or options.sort == 'debug', opt_sortable_debug = options.sort == 'debug', }	if options.si then -- Make a dummy table of units (just one unit) for lookup to use. -- This makes lookup recognize any SI prefix in the unitcode. local symbol = options.si[1] or '?' parms.unittable = { [symbol] = { _name1 = symbol, _name2 = symbol, _symbol = symbol, utype = symbol, scale = symbol == 'g' and 0.001 or 1, prefixes = 1, default = symbol, link = options.si[2], }}	end local success, unit_table = lookup(parms, unitcode, 'no_combination') if not success then unit_table = setmetatable({			symbol = unitcode, name2 = unitcode, utype = unitcode,			scale = 1, default = , defkey = , linkey = '' }, unit_mt) end local value = tonumber(options.value) or 1 local clean = tostring(abs(value)) local info = { value = value, altvalue = value, singular = (clean == '1'), clean = clean, show = clean, }	unit_table.inout = 'in' unit_table.valinfo = { info } local sortspan, scaled_value if options.sort then sortspan, scaled_value = make_table_or_sort(parms, value, info, unit_table, options.scaled_top) end return { text = make_id(parms, 1, unit_table), sortspan = sortspan, scaled_value = scaled_value, unknown = not success and true or nil, } end

return { convert = main_convert, _unit = _unit }