Convert

މޮޑިއުލް ޑޮކިއުމަންޓޭޝަން

See how to copy the convert template for information on copying this module and modifying it for use on another wiki.

For example:

• {{convert|123|lb|kg}} → 123 pounds (56 kg)

The module is called using a template—parameters passed to the template are used by this module to control how a conversion is performed. For example, units can be abbreviated (like kg), or displayed as names (like kilogram), and the output value can be rounded to a specified precision. For usage information, see Help:Convert.

The template that invokes this module is:

• Template:Convert

The following modules are required:

• Module:Convert – (this module) code to convert units
• Module:Convert/data – unit definitions
• Module:Convert/text – text messages, and parameter names and values

The following modules are optional and are used only if required and if the module exists:

• Module:Convert/extra – extra (temporary) unit definitions; used if a unit is not found in Module:Convert/data
• Module:ConvertNumeric – code to spell an input value in words (only English is supported)

The following help pages are available:

• Help:Convert – overview
• Help:Convert messages – describes error and warning messages; messages link to this page so it is required when the module is copied to another wiki
• Help:Convert units – overview of units

A page containing a convert error is added to one of the following categories, providing the page is in a specified namespace (articles, by default):

• Category:Convert invalid units
• Category:Convert invalid options

Units are defined in the wikitext of the master list of units.

• Module:Convert/documentation/conversion data/doc – master list of unit definitions
• Module:Convert/makeunits – translates wikitext from the master list to Lua
• Module talk:Convert/makeunits – makeunits results; copy the text to Module:Convert/data

Module:Convert/data is transcluded into every page using the convert module, so experimenting with a new unit in that module would involve a significant overhead. The Module:Convert/extra module is an alternative which is only transcluded on pages with a unit that is not defined in the main data module.

Sandbox

When making a change, copy the current modules to the sandbox pages, then edit the sandbox copies:

• Module:Convert/sandbox
• Module:Convert/data/sandbox
• Module:Convert/text/sandbox
• Module:Convert/extra/sandbox

Use the following template to test the results (example {{convert/sandbox|123|lb|kg}}):

• Template:Convert/sandbox

Template:Convert/sandbox invokes Module:Convert/sandbox with parameter |sandbox=on which causes convert to use the sandbox modules rather than the normal modules.

The following should be used to test the results of editing the convert modules.

• Module:Convert/tester – module to run tests by comparing template output with fixed text
• Module:Convert/sandbox/testcases – templates to be tested, with expected outputs (uses the tester module)
• Module talk:Convert/sandbox/testcases – view test results

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

Configuration

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

• {{#invoke:convert|convert|numdot=,|numsep=.}}

Sets the decimal mark to be a comma, and the thousands separator to be a dot.

Other options, with default values, are:

• |maxsigfig=14 – maximum number of significant figures
• |nscat=0 – namespaces (comma separated) in which an error or warning adds a category to the page
• |warnings=0 – 0 (zero) disables warnings; 1 shows important warnings; 2 shows all warnings

An option in the template can specify that the sandbox versions of the modules be used. If specified, the text on the right-hand side of the equals sign must be the name of the subpage for each sandbox module.

• |sandbox=sandbox – omit for normal operation

All text used for input parameters and for output messages and categories can be customized. For example, at enwiki the option |lk=on can be used to link each displayed unit to its article. The "lk" and "on" can be replaced with any desired text. In addition, input and output numbers can be formatted and can use digits in the local language. See the translation guide for more information.

The above documentation is transcluded from މޮޑިއުލް:Convert/doc. (edit | history) Editors can experiment in this module's sandbox (create | mirror) and testcases (create) pages. Subpages of this module.

 -- Convert a value from one unit of measurement to another. -- Example: {{convert|123|lb|kg}} --> 123 pounds (56 kg) -- See [[:en:Template:Convert/Transwiki guide]] if copying to another wiki.  local MINUS = '−'  -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92) local abs = math.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: {{convert|12|$/ha|$=€}} (euro replaces dollar)  local function from_en(text) -- Input is a string representing a number in en digits with '.' decimal mark, -- without digit grouping (which is done just after calling this). -- Return the translation of the string with numdot and digits in local language. if numdot ~= '.' 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 spelling is wanted)  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 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 {{convert|160.02|Ym|ydftin}}. 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(cat) -- Return cat if it is wanted in current namespace, otherwise return nil. -- This is so tracking categories only include pages that need correction. local title = mw.title.getCurrentTitle() if title 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 return cat end end end end  local function message(mcode) -- Return wikitext for an error message, including category if specified -- for the message type. -- mcode = numbered table specifying the message: --    mcode[1] = 'cvt_xxx' (string used as a key to get message info) --    mcode[2] = 'parm1' (string to replace first %s if any in message) --    mcode[3] = 'parm2' (string to replace second %s if any in message) --    mcode[4] = 'parm3' (string to replace third %s if any in message) local msg = text_code.all_messages[mcode[1]] local nowiki = mw.text.nowiki 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 {{convert|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 = nowiki(s) .. (append or '') else s = '?' end parts[i] = s end local title = format(msg[1] or 'Missing message', parts[1], parts[2], parts[3]) local text = msg[2] or 'Missing message' local cat = wanted_category(text_code.all_categories[msg[3]]) or '' local anchor = msg[4] or '' local fmt = text_code.all_messages[msg.format or 'cvt_format'] or 'convert: bug' title = title:gsub('"', '"') return format(fmt, anchor, title, text, cat) 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. -- To reduce output noise, only the first warning is displayed. if config.warnings or level < 0 then if level <= (tonumber(config.warnings) or 1) then if parms.warnings == nil then parms.warnings = message({ key, text1, text2 }) end 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') return nil end end local case if parms.spell_upper == inout then case = true parms.spell_upper = nil  -- only uppercase first word in a multiple unit end local sp = not parms.opt_sp_us local adj = parms.opt_adjectival return speller(number, numerator, denominator, case, sp, adj) end  ------------------------------------------------------------------------ -- BEGIN: Code required only for built-in units. -- LATER: If need much more code, move to another module to simplify this module. local function speed_of_sound(altitude) -- This is for the Mach built-in unit of speed. -- Return speed of sound in metres per second at given altitude in feet. -- If no altitude given, use default (zero altitude = sea level). -- Table gives speed of sound in miles per hour at various altitudes: --   altitude = -17,499 to 302,499 feet -- mach_table[a + 4] = s where --   a = (altitude / 5000) rounded to nearest integer (-3 to 60) --   s = speed of sound (mph) at that altitude -- LATER: Should calculate result from an interpolation between the next -- lower and higher altitudes in table, rather than rounding to nearest. -- From: http://www.aerospaceweb.org/question/atmosphere/q0112.shtml local mach_table = {                                                       -- a = 799.5, 787.0, 774.2, 761.207051,                                       -- -3 to  0 748.0, 734.6, 721.0, 707.0, 692.8, 678.3, 663.5, 660.1, 660.1, 660.1,  --  1 to 10 660.1, 660.1, 660.1, 662.0, 664.3, 666.5, 668.9, 671.1, 673.4, 675.6,  -- 11 to 20 677.9, 683.7, 689.9, 696.0, 702.1, 708.1, 714.0, 719.9, 725.8, 731.6,  -- 21 to 30 737.3, 737.7, 737.7, 736.2, 730.5, 724.6, 718.8, 712.9, 707.0, 701.1,  -- 31 to 40 695.0, 688.9, 682.8, 676.6, 670.4, 664.1, 657.8, 652.9, 648.3, 643.7,  -- 41 to 50 639.1, 634.4, 629.6, 624.8, 620.0, 615.2, 613.2, 613.2, 613.2, 613.5,  -- 51 to 60 } altitude = altitude or 0 local a = (altitude < 0) and -altitude or altitude a = floor(a / 5000 + 0.5) if altitude < 0 then a = -a end if a < -3 then a = -3 elseif a > 60 then a = 60 end return mach_table[a + 4] * 0.44704  -- mph converted to m/s end -- END: Code required only for built-in units. ------------------------------------------------------------------------  local function get_range(word) -- Return a range (string or table) corresponding to word (like "to"), -- or return nil if not a range word. local ranges = text_code.ranges return ranges.types[word] or ranges.types[ranges.aliases[word]] end  local function check_mismatch(unit1, unit2) -- If unit1 cannot be converted to unit2, return an error message table. -- This allows conversion between units of the same type, and between -- Nm (normally torque) and ftlb (energy), as in gun-related articles. -- This works because Nm is the base unit (scale = 1) for both the -- primary type (torque), and the alternate type (energy, where Nm = J). -- A match occurs if the primary types are the same, or if unit1 matches -- the alternate type of unit2, and vice versa. That provides a whitelist -- of which conversions are permitted between normally incompatible types. if unit1.utype == unit2.utype or (unit1.utype == unit2.alttype and unit1.alttype == unit2.utype) then return nil end return { 'cvt_mismatch', unit1.utype, unit2.utype } end  local function override_from(out_table, in_table, fields) -- Copy the specified fields from in_table to out_table, but do not -- copy nil fields (keep any corresponding field in out_table). for _, field in ipairs(fields) do if in_table[field] then out_table[field] = in_table[field] end end end  local function shallow_copy(t) -- Return a shallow copy of table t. -- Do not need the features and overhead of the Scribunto mw.clone(). local result = {} for k, v in pairs(t) do result[k] = v end return result end  local unit_mt = { -- Metatable to get missing values for a unit that does not accept SI prefixes. -- Warning: The boolean value 'false' is returned for any missing field -- so __index is not called twice for the same field in a given unit. __index = function (self, key) local value if key == 'name1' or key == 'sym_us' then value = self.symbol elseif key == 'name2' then value = self.name1 .. plural_suffix elseif key == 'name1_us' then value = self.name1 if not rawget(self, 'name2_us') then -- If name1_us is 'foot', do not make name2_us by appending plural_suffix. self.name2_us = self.name2 end elseif key == 'name2_us' then local raw1_us = rawget(self, 'name1_us') if raw1_us then value = raw1_us .. plural_suffix else value = self.name2 end elseif key == 'link' then value = self.name1 else value = false end rawset(self, key, value) return value end }  local function prefixed_name(unit, name, index) -- Return unit name with SI prefix inserted at correct position. -- index = 1 (name1), 2 (name2), 3 (name1_us), 4 (name2_us). -- The position is a byte (not character) index, so use Lua's sub(). local pos = rawget(unit, 'prefix_position') if type(pos) == 'string' then pos = tonumber(split(pos, ',')[index]) end if pos then return name:sub(1, pos - 1) .. unit.si_name .. name:sub(pos) end return unit.si_name .. name end  local unit_prefixed_mt = { -- Metatable to get missing values for a unit that accepts SI prefixes. -- Before use, fields si_name, si_prefix must be defined. -- The unit must define _symbol, _name1 and -- may define _sym_us, _name1_us, _name2_us -- (_sym_us, _name2_us may be defined for a language using sp=us -- to refer to a variant unrelated to U.S. units). __index = function (self, key) local value if key == 'symbol' then value = self.si_prefix .. self._symbol elseif key == 'sym_us' then value = rawget(self, '_sym_us') if value then value = self.si_prefix .. value else value = self.symbol end elseif key == 'name1' then value = prefixed_name(self, self._name1, 1) elseif key == 'name2' then value = rawget(self, '_name2') if value then value = prefixed_name(self, value, 2) else value = self.name1 .. plural_suffix end elseif key == 'name1_us' then value = rawget(self, '_name1_us') if value then value = prefixed_name(self, value, 3) else value = self.name1 end elseif key == 'name2_us' then value = rawget(self, '_name2_us') if value then value = prefixed_name(self, value, 4) elseif rawget(self, '_name1_us') then value = self.name1_us .. plural_suffix else value = self.name2 end elseif key == 'link' then value = self.name1 else value = false end rawset(self, key, value) return value end }  local unit_per_mt = { -- Metatable to get values for a per unit of form "x/y". -- This is never called to determine a unit name or link because per units -- are handled as a special case. -- Similarly, the default output is handled elsewhere. __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(unit_table, ulookup) -- Return true, t where t is a per unit with unit codes expanded to unit tables, -- or return false, t where t is an error message table. local result = { utype = unit_table.utype, per = {} } override_from(result, unit_table, { 'invert', 'iscomplex', 'default', 'link', 'symbol', 'symlink' }) result.symbol_raw = (result.symbol or false)  -- to distinguish between a defined exception and a metatable 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 {{convert|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 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 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 make_per(t, function (ucode) return lookup(parms, ucode, 'no_combination', utable, fails, depth) end) 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) 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.si_name = parms.opt_sp_us and si.name_us or si.name result.si_prefix = si.prefix or prefix result.scale = t.scale * 10 ^ (si.exponent * t.prefixes) return true, setmetatable(result, unit_prefixed_mt) end end end -- Accept any unit with an engineering notation prefix like "e6cuft" -- (million cubic feet), but not chained prefixes like "e3e6cuft", -- and not if the unit is a combination or multiple, -- and not if the unit has an offset or is a built-in. -- Only en digits are accepted. local has_plus = unitcode:find('+', 1, true) if not has_plus then local exponent, baseunit = unitcode:match('^e(%d+)(.*)') if exponent then local engscale = text_code.eng_scales[exponent] if engscale then local success, result = lookup(parms, baseunit, 'no_combination', utable, fails, depth) if success and not (result.offset or result.builtin or result.engscale) then result.defkey = unitcode  -- key to lookup default exception result.engscale = engscale result.scale = result.scale * 10 ^ tonumber(exponent) return true, result end end end end -- Accept user-defined combinations like "acre+m2+ha" or "acre m2 ha" for output. -- If '+' is used, each unit code can include a space, and any error is fatal. -- If ' ' is used and if each space-separated word is a unit code, it is a combo, -- but errors are not fatal so the unit code can be looked up as an extra unit. local err_is_fatal local combo = collection() if has_plus then err_is_fatal = true for item in (unitcode .. '+'):gmatch('%s*(.-)%s*%+') do if item ~= '' then combo:add(item) end end elseif unitcode:find('%s') then for item in unitcode:gmatch('%S+') do combo:add(item) end end if combo.n > 1 then local function lookup_combo() if what == 'no_combination' or what == 'only_multiple' then return false, { 'cvt_bad_unit', unitcode } end local result = { combination = {} } local cvt = result.combination for i, v in ipairs(combo) do local success, t = lookup(parms, v, 'only_multiple', utable, fails, depth) if not success then return false, t end if i == 1 then result.utype = t.utype else local mismatch = check_mismatch(result, t) if mismatch then return false, mismatch end end cvt[i] = t end return true, result end local success, result = lookup_combo() if success or err_is_fatal then return success, result end end -- Look for x/y; split on right-most slash to get scale correct (x/y/z is x/y per z). local top, bottom = unitcode:match('^(.-)/([^/]+)$') if top and not unitcode:find('e%d') then -- If valid, create an automatic per unit for an "x/y" unit code. -- The unitcode must not include extraneous spaces. -- Engineering notation (apart from at start and which has been stripped before here), -- is not supported so do not make a per unit if find text like 'e3' in unitcode. local success, result = make_per({ per = {top, bottom} }, function (ucode) return lookup(parms, ucode, 'no_combination', utable, fails, depth) end) 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 {{val}} -- or if looking up a range word which cannot be a unit. if not extra_units then local success, extra = pcall(function () return require(extra_module).extra_units end) if success and type(extra) == 'table' then extra_units = extra end end if extra_units then -- A unit in one data table might refer to a unit in the other table, so -- switch between them, relying on fails or depth to terminate loops. if not fails[unitcode] then fails[unitcode] = true local other = (utable == all_units) and extra_units or all_units local success, result = lookup(parms, unitcode, what, other, fails, depth) if success then return true, result end end end end if to_en_table then -- At fawiki it is common to translate all digits so a unit like "km2" becomes "km۲". local en_code = ustring.gsub(unitcode, '%d', to_en_table) if en_code ~= unitcode then return lookup(parms, en_code, what, utable, fails, depth) end end return false, { 'cvt_unknown', unitcode } end  local function valid_number(num) -- Return true if num is a valid number. -- In Scribunto (different from some standard Lua), when expressed as a string, -- overflow or other problems are indicated with text like "inf" or "nan" -- which are regarded as invalid here (each contains "n"). if type(num) == 'number' and tostring(num):find('n', 1, true) == nil then return true end end  local function hyphenated(name, parts) -- Return a hyphenated form of given name (for adjectival usage). -- The name may be linked and the target of the link must not be changed. -- Hypothetical examples: --   [[long ton|ton]]         →  [[long ton|ton]]          (no change) --   [[tonne|long ton]]       →  [[tonne|long-ton]] --   [[metric ton|long ton]]  →  [[metric ton|long-ton]] --   [[long ton]]             →  [[long ton|long-ton]] -- Input can also have multiple links in a single name like: --   [[United States customary units|U.S.]] [[US gallon|gallon]] --   [[mile]]s per [[United States customary units|U.S.]] [[quart]] --   [[long ton]]s per [[short ton]] -- Assume that links cannot be nested (never like "[[abc[[def]]ghi]]"). -- This uses a simple and efficient procedure that works for most cases. -- Some units (if used) would require more, and can later think about -- adding a method to handle exceptions. -- The procedure is to replace each space with a hyphen, but -- not a space after ')' [for "(pre-1954 US) nautical mile"], and -- not spaces immediately before '(' or in '(...)' [for cases like -- "British thermal unit (ISO)" and "Calorie (International Steam Table)"]. if name:find(' ', 1, true) then if parts then local pos if name:sub(1, 1) == '(' then pos = name:find(')', 1, true) if pos then return name:sub(1, pos+1) .. name:sub(pos+2):gsub(' ', '-') end elseif name:sub(-1) == ')' then pos = name:find('(', 1, true) if pos then return name:sub(1, pos-2):gsub(' ', '-') .. name:sub(pos-1) end end return name:gsub(' ', '-') end parts = collection() for before, item, after in name:gmatch('([^[]*)(%[%[[^[]*%]%])([^[]*)') do if item:find(' ', 1, true) then local prefix local plen = item:find('|', 1, true) if plen then prefix = item:sub(1, plen) item = item:sub(plen + 1, -3) else prefix = item:sub(1, -3) .. '|' item = item:sub(3, -3) end item = prefix .. hyphenated(item, parts) .. ']]' end parts:add(before:gsub(' ', '-') .. item .. after:gsub(' ', '-')) end if parts.n == 0 then -- No link like "[[...]]" was found in the original name. parts:add(hyphenated(name, parts)) end return table.concat(parts) end return name end  local function hyphenated_maybe(parms, want_name, sep, id, inout) -- Return s, f where --   s = id, possibly modified --   f = true if hyphenated -- Possible modifications: hyphenate; prepend '-'; append mid text. if id == nil or id == '' then return '' end local mid = (inout == (parms.opt_flip and 'out' or 'in')) and parms.mid or '' if want_name then if parms.opt_adjectival then return '-' .. hyphenated(id) .. mid, true end if parms.opt_add_s and id:sub(-1) ~= 's' then id = id .. 's'  -- for nowiki end end return sep .. id .. mid end  local function change_sign(text) -- Change sign of text for correct appearance because it is negated. if text:sub(1, 1) == '-' then return text:sub(2) end return '-' .. text end  local function use_minus(text) -- Return text with Unicode minus instead of '-', if present. if text:sub(1, 1) == '-' then return MINUS .. text:sub(2) end return text end  local function digit_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. 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 {{frac}} (fraction slash). -- 1/2    : sign, numerator, denominator -- 1+2/3  : signed_wholenumber, numerator, denominator '%s%s⁄%s', '%s %s⁄%s', }, { -- Like {{sfrac}} (fraction horizontal bar). -- 1//2   : sign, numerator, denominator (sign should probably be before the fraction, but then it can wrap, and html is already too long) -- 1+2//3 : signed_wholenumber, numerator, denominator '%s%s/%s', '%s %s/%s', }, }  local function format_fraction(parms, inout, negative, wholestr, numstr, denstr, do_spell, style) -- Return wikitext for a fraction, possibly spelled. -- Inputs use en digits and have no sign; output uses digits in local language. local wikitext if not style then style = parms.opt_fraction_horizontal and 2 or 1 end if wholestr == '' then wholestr = nil end if wholestr then local decorated = with_separator(parms, wholestr) if negative then decorated = MINUS .. decorated end local fmt = fracfmt[style][2] wikitext = format(fmt, decorated, from_en(numstr), from_en(denstr)) else local sign = negative and MINUS or '' wikitext = format(fracfmt[style][1], sign, from_en(numstr), from_en(denstr)) end if do_spell then if negative then if wholestr then wholestr = '-' .. wholestr else numstr = '-' .. numstr end end wikitext = spell_number(parms, inout, wholestr, numstr, denstr) or wikitext end return wikitext end  local function format_number(parms, show, exponent, isnegative) -- Parameter show is a string or a table containing strings. -- Each string is a formatted number in en digits and optional '.' decimal mark. -- A table represents a fraction: integer, numerator, denominator; -- if a table is given, exponent must be nil. -- Return t where t is a table with fields: --   show = wikitext formatted to display implied value --          (digits in local language) --   is_scientific = true if show uses scientific notation --   clean = unformatted show (possibly adjusted and with inserted '.') --          (en digits) --   sign = '' or MINUS --   exponent = exponent (possibly adjusted) -- The clean and exponent fields can be used to calculate the -- rounded absolute value, if needed. -- -- The value implied by the arguments is found from: --   exponent is nil; and --   show is a string of digits (no sign), with an optional dot; --   show = '123.4' is value 123.4, '1234' is value 1234.0; -- or: --   exponent is an integer indicating where dot should be; --   show is a string of digits (no sign and no dot); --   there is an implied dot before show; --   show does not start with '0'; --   show = '1234', exponent = 3 is value 0.1234*10^3 = 123.4. -- -- The formatted result: -- * Is for an output value and is spelled if wanted and possible. -- * Includes a Unicode minus if isnegative and not spelled. -- * Uses a custom decimal mark, if wanted. -- * Has digits grouped where necessary, if wanted. -- * Uses scientific notation if requested, or for very small or large values --   (which forces result to not be spelled). -- * Has no more than maxsigfig significant digits --   (same as old template and {{#expr}}). local xhi, xlo  -- these control when scientific notation (exponent) is used if parms.opt_scientific then xhi, xlo = 4, 2  -- default for output if input uses e-notation elseif parms.opt_scientific_always then xhi, xlo = 0, 0  -- always use scientific notation (experimental) else xhi, xlo = 10, 4  -- default end local sign = isnegative and MINUS or '' local maxlen = maxsigfig local tfrac if type(show) == 'table' then tfrac = show show = tfrac.wholestr assert(exponent == nil, 'Bug: exponent given with fraction') end if not tfrac and not exponent then local integer, dot, decimals = show:match('^(%d*)(%.?)(.*)') if integer == '0' or integer == '' then local zeros, figs = decimals:match('^(0*)([^0]?.*)') if #figs == 0 then if #zeros > maxlen then show = '0.' .. zeros:sub(1, maxlen) end elseif #zeros >= xlo then show = figs exponent = -#zeros elseif #figs > maxlen then show = '0.' .. zeros .. figs:sub(1, maxlen) end elseif #integer >= xhi then show = integer .. decimals exponent = #integer else maxlen = maxlen + #dot if #show > maxlen then show = show:sub(1, maxlen) end end end if exponent then local function zeros(n) return string.rep('0', n) end if #show > maxlen then show = show:sub(1, maxlen) end if exponent > xhi or exponent <= -xlo or (exponent == xhi and show ~= '1' .. zeros(xhi - 1)) then -- When xhi, xlo = 10, 4 (the default), scientific notation is used if the -- rounded value satisfies: value >= 1e9 or value < 1e-4 (1e9 = 0.1e10), -- except if show is '1000000000' (1e9), for example: -- {{convert|1000000000|m|m|sigfig=10}} → 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 numstr, whole 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 wholestr if prefix == '' then wholestr = '' whole = 0 else -- Any prefix must be like '12+' or '12-' (whole number and fraction sign); -- '12.3+' and '12.3-' are also accepted (single digit after decimal point) -- because '12.3+1/2 hands' is valid (12 hands 3½ inches). local num1, num2, frac_sign = prefix:match('^(%d+)(%.?%d?)%s*([+%-])$') if num1 == nil then return nil end if num2 == '' then  -- num2 must be '' or like '.1' but not '.' or '.12' wholestr = num1 else if #num2 ~= 2 then return nil end wholestr = num1 .. num2 end if frac_sign ~= (negative and '-' or '+') then return nil end whole = tonumber(wholestr) if whole == nil then return nil end end local value = whole + numerator / denominator if not valid_number(value) then return nil end local altvalue = whole + numerator / (denominator * 10) local style = #slashes  -- kludge: 1 or 2 slashes can be used to select style if style > 2 then style = 2 end local wikitext = format_fraction(parms, 'in', negative, leading_plus .. wholestr, numstr, denstr, parms.opt_spell_in, style) return value, altvalue, wikitext, denominator end  local function extract_number(parms, text, another, no_fraction) -- Return true, info if can extract a number from text, -- where info is a table with the result, -- or return false, t where t is an error message table. -- Input can use en digits or digits in local language and can -- have references at the end. Accepting references is intended -- for use in infoboxes with a field for a value passed to convert. -- Parameter another = true if the expected value is not the first. -- Before processing, the input text is cleaned: -- * Any thousand separators (valid or not) are removed. -- * Any sign (and optional following whitespace) is replaced with --   '-' (if negative) or '' (otherwise). --   That replaces Unicode minus with '-'. -- If successful, the returned info table contains named fields: --   value    = a valid number --   altvalue = a valid number, usually same as value but different --              if fraction used (for hands unit) --   singular = true if value is 1 or -1 (to use singular form of units) --   clean    = cleaned text with any separators and sign removed --              (en digits and '.' decimal mark) --   show     = text formatted for output, possibly with ref strip markers --              (digits in local language and custom decimal mark) -- The resulting show: -- * Is for an input value and is spelled if wanted and possible. -- * Has a rounded value, if wanted. -- * Has digits grouped where necessary, if wanted. -- * If negative, a Unicode minus is used; otherwise the sign is --   '+' (if the input text used '+'), or is '' (if no sign in input). text = strip(text or '') local reference local pos = text:find('\127', 1, true) if pos then local before = text:sub(1, pos - 1) local remainder = text:sub(pos) local refs = {} while #remainder > 0 do local ref, spaces ref, spaces, remainder = remainder:match('^(\127UNIQ[^\127]*%-ref%-%x+%-QINU\127)(%s*)(.*)') if ref then table.insert(refs, ref) else refs = {} break end end if #refs > 0 then text = strip(before) reference = table.concat(refs) end end local clean = to_en(text, parms) if clean == '' then return false, { another and 'cvt_no_num2' or 'cvt_no_num' } end local isnegative, propersign = false, ''  -- most common case local singular, show, denominator local value = tonumber(clean) local altvalue if value then local sign = clean:sub(1, 1) if sign == '+' or sign == '-' then propersign = (sign == '+') and '+' or MINUS clean = clean:sub(2) end if value < 0 then isnegative = true value = -value end else local valstr for _, prefix in ipairs({ '-', MINUS, '−' }) do -- Including '-' means inputs like '- 2' (with space) are accepted as -2. -- It also sets isnegative in case input is a fraction like '-2-3/4'. local plen = #prefix if clean:sub(1, plen) == prefix then valstr = clean:sub(plen + 1) break end end if valstr then isnegative = true propersign = MINUS clean = valstr value = tonumber(clean) end if value == nil then if not no_fraction then value, altvalue, show, denominator = extract_fraction(parms, clean, isnegative) end if value == nil then return false, { 'cvt_bad_num', text } end if value <= 1 then singular = true  -- for example, "½ mile" or "one half mile" (singular unit) end end end if not valid_number(value) then  -- for example, "1e310" may overflow return false, { 'cvt_invalid_num' } end if show == nil then -- clean is a non-empty string with no spaces, and does not represent a fraction, -- and value = tonumber(clean) is a number >= 0. -- If the input uses e-notation, show will be displayed using a power of ten, but -- we use the number as given so it might not be normalized scientific notation. -- The input value is spelled if specified so any e-notation is ignored; -- that allows input like 2e6 to be spelled as "two million" which works -- because the spell module converts '2e6' to '2000000' before spelling. local function rounded(value, default, exponent) local precision = parms.opt_ri if precision then local fmt = '%.' .. format('%d', precision) .. 'f' local result = fmt:format(tonumber(value) + 2e-14)  -- fudge for some common cases of bad rounding if not exponent then singular = (tonumber(result) == 1) end return result end return default end singular = (value == 1) local scientific local significand, exponent = clean:match('^([%d.]+)[Ee]([+%-]?%d+)') if significand then show = with_exponent(parms, rounded(significand, significand, exponent), exponent) scientific = true else show = with_separator(parms, rounded(value, clean)) end show = propersign .. show if parms.opt_spell_in then show = spell_number(parms, 'in', propersign .. rounded(value, clean)) or show scientific = false end if scientific then parms.opt_scientific = true end end local altvalue = altvalue or value if isnegative and (value ~= 0) then value = -value altvalue = -altvalue end return true, { value = value, altvalue = altvalue, 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 integer, 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 preceding space). local function withspace(text, i) -- Insert space at beginning if i == 1, or at end if i == -1. -- However, no space is inserted if there is a space or ' ' -- or '-' at that position ('-' is for adjectival text). local current = text:sub(i, i) if current == ' ' or current == '-' then return text end if i == 1 then current = text:sub(1, 6) else current = text:sub(-6, -1) end if current == ' ' then return text end if i == 1 then return ' ' .. text end return text .. ' ' end preunit1 = preunit1 or '' local trim1 = strip(preunit1) if count == 1 then if trim1 == '' then return nil end return withspace(withspace(preunit1, 1), -1) end preunit2 = preunit2 or '' local trim2 = strip(preunit2) if trim1 == '' and trim2 == '' then return nil, nil end if trim1 ~= '+' then preunit1 = withspace(preunit1, 1) end if trim2 == ' ' then  -- trick to make preunit2 empty preunit2 = nil elseif trim2 == '' then preunit2 = preunit1 elseif trim2 ~= '+' then preunit2 = withspace(preunit2, 1) end return preunit1, preunit2 end  local function range_text(range, want_name, parms, before, after, 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, "{{convert|1|yd|2|ft|3|in}}" -- would result in a call to this function with --   iparm = 3 (parms[iparm] = "2", just after the first unit) --   in_unit_table = (unit table for "yd"; contains value 1 for number of yards) -- Return true, iparm, unit where --   iparm = index just after the composite units (7 in above example) --   unit = composite unit table holding all input units, -- or return true if no composite unit is present in parms, -- or return false, t where t is an error message table. local default, subinfo local composite_units, count = { in_unit_table }, 1 local fixups = {} local total = in_unit_table.valinfo[1].value local subunit = in_unit_table while subunit.subdivs do  -- subdivs is nil or a table of allowed subdivisions local subcode = strip(parms[iparm+1]) local subdiv = subunit.subdivs[subcode] or subunit.subdivs[(all_units[subcode] or {}).target] if not subdiv then break end local success success, subunit = lookup(parms, subcode, 'no_combination') if not success then return false, subunit end  -- should never occur success, subinfo = extract_number(parms, parms[iparm]) if not success then return false, subinfo end iparm = iparm + 2 subunit.inout = 'in' subunit.valinfo = { subinfo } -- Recalculate total as a number of subdivisions. -- subdiv[1] = number of subdivisions per previous unit (integer > 1). total = total * subdiv[1] + subinfo.value if not default then  -- set by the first subdiv with a default defined default = subdiv.default end count = count + 1 composite_units[count] = subunit if subdiv.unit or subdiv.name then fixups[count] = { unit = subdiv.unit, name = subdiv.name, valinfo = subunit.valinfo } end end if count == 1 then return true  -- no error and no composite unit end for i, fixup in pairs(fixups) do local unit = fixup.unit local name = fixup.name if not unit or (count > 2 and name) then composite_units[i].fixed_name = name else local success, alternate = lookup(parms, unit, 'no_combination') if not success then return false, alternate end  -- should never occur alternate.inout = 'in' alternate.valinfo = fixup.valinfo composite_units[i] = alternate end end return true, iparm, { utype = in_unit_table.utype, scale = subunit.scale,  -- scale of last (least significant) unit valinfo = { { value = total, clean = subinfo.clean, denominator = subinfo.denominator } }, composite = composite_units, default = default or in_unit_table.default } end  local function translate_parms(parms, kv_pairs) -- Update fields in parms by translating each key:value in kv_pairs to terms -- used by this module (may involve translating from local language to English). -- Also, checks are performed which may display warnings, if enabled. -- Return true if successful or return false, t where t is an error message table. currency_text = nil  -- local testing can hold module in memory; must clear globals if kv_pairs.adj and kv_pairs.sing then -- For enwiki (before translation), warn if attempt to use adj and sing -- as the latter is a deprecated alias for the former. if kv_pairs.adj ~= kv_pairs.sing and kv_pairs.sing ~= '' then add_warning(parms, 1, 'cvt_unknown_option', 'sing=' .. kv_pairs.sing) end kv_pairs.sing = nil end 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 == '$' then -- Value should be a single character like "€" for the euro currency symbol, but anything is accepted. currency_text = (loc_value == 'euro') and '€' or loc_value else local minimum local number, is_integer = get_number(loc_value) if en_name == 'frac' then minimum = 2 if number and number < 0 then parms.opt_fraction_horizontal = true number = -number end else minimum = 1 end if number and is_integer and number >= minimum then en_value = number else add_warning(parms, 1, (en_name == 'frac' and 'cvt_bad_frac' or 'cvt_bad_sigfig'), loc_value) end end elseif en_name == 'stylein' or en_name == 'styleout' then en_value = loc_value  -- accept user text with no validation else en_value = text_code.en_option_value[en_name][loc_value] if en_value and en_value:sub(-1) == '?' then en_value = en_value:sub(1, -2) add_warning(parms, -1, 'cvt_deprecated', loc_name .. '=' .. loc_value) end if en_value == nil then if loc_value == '' then add_warning(parms, 2, 'cvt_empty_option', loc_name) else add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value) end elseif en_value == '' then en_value = nil  -- an ignored option like adj=off elseif type(en_value) == 'string' and en_value:sub(1, 4) == 'opt_' then for _, v in ipairs(split(en_value, ',')) do local lhs, rhs = v:match('^(.-)=(.+)$') 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 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_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 {{convert|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 {{convert|5|±|5|°C}}) 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 "{{convert|valid_value|valid_unit|...}}", -- return true, 3, in_unit, in_unit_table -- 3 = index in parms of whatever follows valid_unit, if anything). -- The valid_value is not negative and does not use a fraction, and -- no options requiring further processing of the input are used. -- Otherwise, return nothing and caller will reparse the input. -- Testing shows this function is successful for 96% of converts in articles, -- and that on average it speeds up converts by 8%. if parms.opt_ri or parms.opt_spell_in then return end local clean = to_en(strip(parms[1] or ''), parms) if #clean > 10 or not clean:match('^[0-9.]+$') then return 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 get_parms(args) -- If successful, return true, parms, unit where --   parms is a table of all arguments passed to the template --        converted to named arguments, and --   unit is the input unit table; -- or return false, t where t is an error message table. -- The returned input unit table may be for a fake unit using the specified -- unit code as the symbol and name, and with bad_mcode = message code table. -- MediaWiki removes leading and trailing whitespace from the values of -- named arguments. However, the values of numbered arguments include any -- whitespace entered in the template, and whitespace is used by some -- parameters (example: the numbered parameters associated with "disp=x"). local parms = {}  -- arguments passed to template, after translation local kv_pairs = {}  -- table of input key:value pairs where key is a name; needed because cannot iterate parms and add new fields to it for k, v in pairs(args) do if type(k) == 'number' or k == 'test' then  -- parameter "test" is reserved for testing and is not translated parms[k] = v else kv_pairs[k] = v end end local success, msg = translate_parms(parms, kv_pairs) if not success then return false, msg end local success, i, in_unit, in_unit_table = simple_get_values(parms) if not success then 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 if in_unit == nil then in_unit = '' end if parms.opt_ignore_error then  -- display given unit code with no error (for use with {{val}}) in_unit_table = ''  -- suppress error message and prevent processing of output unit end in_unit_table = setmetatable({ symbol = in_unit, name2 = in_unit, default = "m", defkey = "m", linkey = "m", utype = "length", scale = 1, bad_mcode = in_unit_table }, unit_mt) 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 next = strip(parms[i]) i = i + 1 local precision, is_bad_precision local function set_precision(text) local number, is_integer = get_number(text) if number then if is_integer then precision = number else precision = text is_bad_precision = true end return true  -- text was used for precision, good or bad end end if not set_precision(next) then parms.out_unit = next if set_precision(strip(parms[i])) then i = i + 1 end end if parms.opt_adj_mid then next = parms[i] i = i + 1 if next then  -- mid-text words if next:sub(1, 1) == '-' then parms.mid = next else parms.mid = ' ' .. next end end end if parms.opt_one_preunit then parms[parms.opt_flip and 'preunit2' or 'preunit1'] = preunits(1, parms[i]) i = i + 1 end if parms.disp == 'x' then -- Following is reasonably compatible with the old template. local first = parms[i] or '' local second = parms[i+1] or '' i = i + 2 if strip(first) == '' then  -- user can enter ' ' 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 return true, parms, 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  -- {{Order of magnitude}} adds this, so we do too local prec, minprec, adjust local utype = out_current.utype local subunit_ignore_trailing_zero local subunit_more_precision  -- kludge for "in" used in input like "|2|ft|6|in" local composite = in_current.composite if composite then subunit_ignore_trailing_zero = true  -- input "|2|st|10|lb" has precision 0, not -1 if composite[#composite].exception == 'subunit_more_precision' then subunit_more_precision = true  -- do not use standard precision with input like "|2|ft|6|in" end end if denominator and denominator > 0 then prec = math.max(log10(denominator), 1) else -- Count digits after decimal mark, handling cases like '12.345e6'. local exponent local integer, dot, 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 "{{convert|6|ft|1|in|cm}}" (where subunit is "in") -- has a non-standard adjust value, to give more output precision. adjust = log10(out_current.scale) + 2 else adjust = log10(abs(invalue / outvalue)) end adjust = adjust + log10(2) -- Ensure that the output has at least two significant figures. minprec = 1 - floor(log10(outvalue) + fudge) end if extra then adjust = extra.adjust or adjust minprec = extra.minprec or minprec end return record_default_precision(parms, out_current, math.max(floor(prec + adjust), minprec)) end  local function convert(parms, invalue, info, in_current, out_current) -- Convert given input value from one unit to another. -- Return output_value (a number) if a simple convert, or -- return f, t where --   f = true, t = table of information with results, or --   f = false, t = error message table. local inscale = in_current.scale local outscale = out_current.scale if not in_current.iscomplex and not out_current.iscomplex then return invalue * (inscale / outscale)  -- minimize overhead for most common case end if in_current.invert or out_current.invert then -- Inverted units, such as inverse length, inverse time, or -- fuel efficiency. Built-in units do not have invert set. if (in_current.invert or 1) * (out_current.invert or 1) < 0 then return 1 / (invalue * inscale * outscale) end return invalue * (inscale / outscale) elseif in_current.offset then -- Temperature (there are no built-ins for this type of unit). if info.is_change then return invalue * (inscale / outscale) end return (invalue - in_current.offset) * (inscale / outscale) + out_current.offset else -- Built-in unit. local in_builtin = in_current.builtin local out_builtin = out_current.builtin if in_builtin and out_builtin then if in_builtin == out_builtin then return invalue end -- There are no cases (yet) where need to convert from one -- built-in unit to another, so this should never occur. return false, { 'cvt_bug_convert' } end if in_builtin == 'mach' or out_builtin == 'mach' then local adjust if in_builtin == 'mach' then inscale = speed_of_sound(in_current.altitude) adjust = outscale / 0.1 else outscale = speed_of_sound(out_current.altitude) adjust = 0.1 / inscale end return true, { outvalue = invalue * (inscale / outscale), adjust = log10(adjust) + log10(2), } elseif in_builtin == 'hand' then -- 1 hand = 4 inches; 1.2 hands = 6 inches. -- Decimals of a hand are only defined for the first digit, and -- the first fractional digit should be a number of inches (1, 2 or 3). -- However, this code interprets the entire fractional part as the number -- of inches / 10 (so 1.75 inches would be 0.175 hands). -- A value like 12.3 hands is exactly 12*4 + 3 inches; base default precision on that. local integer, fracpart = math.modf(invalue) local inch_value = 4 * integer + 10 * fracpart  -- equivalent number of inches local factor = inscale / outscale if factor == 4 then -- Am converting to inches: show exact result, and use "inches" not "in" by default. if parms.abbr_org == nil then out_current.usename = true end local show = format('%g', abs(inch_value))  -- show and clean are unsigned if not show:find('e', 1, true) then return true, { invalue = inch_value, outvalue = inch_value, clean = show, show = show, } end end local outvalue = (integer + 2.5 * fracpart) * factor local fracstr = info.clean:match('%.(.*)') or '' local fmt if fracstr == '' then fmt = '%.0f' else fmt = '%.' .. format('%d', #fracstr - 1) .. 'f' end return true, { invalue = inch_value, clean = format(fmt, inch_value), outvalue = outvalue, minprec = 0, } end end return false, { 'cvt_bug_convert' }  -- should never occur end  local function user_style(parms, i) -- Return text for a user-specified style for a table cell, or '' if none, -- given i = 1 (input style) or 2 (output style). local style = parms[(i == 1) and 'stylein' or 'styleout'] if style then style = style:gsub('"', '') if style ~= '' then if style:sub(-1) ~= ';' then style = style .. ';' end return style end end return '' end  local function make_table_or_sort(parms, invalue, info, in_current, scaled_top) -- Set options to handle output for a table or a sort key, or both. -- The text sort key is based on the value resulting from converting -- the input to a fake base unit with scale = 1, and other properties -- required for a conversion derived from the input unit. -- For other modules, return the sort key in a hidden span element, and -- the scaled value used to generate the sort key. -- If scaled_top is set, it is the scaled value of the numerator of a per unit -- to be combined with this unit (the denominator) to make the sort key. -- Scaling only works with units that convert with a factor (not temperature). local sortkey, scaled_value if parms.opt_sortable_on then local base = {  -- a fake unit with enough fields for a valid convert scale = 1, invert = in_current.invert and 1, iscomplex = in_current.iscomplex, offset = in_current.offset and 0, } local outvalue, extra = convert(parms, invalue, info, in_current, base) if extra then outvalue = extra.outvalue end if in_current.istemperature then -- Have converted to kelvin; assume numbers close to zero have a -- rounding error and should be zero. if abs(outvalue) < 1e-12 then outvalue = 0 end end if scaled_top and outvalue ~= 0 then outvalue = scaled_top / outvalue end scaled_value = outvalue if not valid_number(outvalue) then if outvalue < 0 then sortkey = '1000000000000000000' else sortkey = '9000000000000000000' end elseif outvalue == 0 then sortkey = '5000000000000000000' else local mag = floor(log10(abs(outvalue)) + 1e-14) local prefix if outvalue > 0 then prefix = 7000 + mag else prefix = 2999 - mag outvalue = outvalue + 10^(mag+1) end sortkey = format('%d', prefix) .. format('%015.0f', floor(outvalue * 10^(14-mag))) end end local sortspan if sortkey and (parms.opt_sortable_debug or not parms.table_align) then sortspan = parms.opt_sortable_debug and '' .. sortkey .. '♠' or '' .. sortkey .. '♠' parms.join_before = sortspan end if parms.table_align then local style = 'style="text-align:' .. parms.table_align .. ';' local sort = sortkey and ' data-sort-value="' .. sortkey .. '"' or '' local joins = {} for i = 1, 2 do joins[i] = (i == 1 and '' or '\n|') .. style .. user_style(parms, i) .. '"' .. sort .. '|' end parms.table_joins = joins end return sortspan, scaled_value end  local cvt_to_hand  local function cvtround(parms, info, in_current, out_current) -- Return true, t where t is a table with the conversion results; fields: --   show = rounded, formatted string with the result of converting value in info, --      using the rounding specified in parms. --   singular = true if result (after rounding and ignoring any negative sign) --      is "1", or like "1.00", or is a fraction with value < 1; --   (and more fields shown below, and a calculated 'absvalue' field). -- or return true, nil if no value specified; -- or return false, t where t is an error message table. -- Input info.clean uses en digits (it has been translated, if necessary). -- Output show uses en or non-en digits as appropriate, or can be spelled. local invalue if info then invalue = info.value if in_current.builtin == 'hand' then invalue = info.altvalue end end if invalue == nil or invalue == '' then return true, nil end if out_current.builtin == 'hand' then return cvt_to_hand(parms, info, in_current, out_current) end 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 numerator, precision, success, 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: -- {{convert|-100.1|C|K}} and {{convert|5555000|um|m|2}}. -- Old template uses #expr round, which invokes PHP round(). -- LATER: Investigate how PHP round() works. fudge = 2e-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 make_link(link, id, link_key) -- Return wikilink "[[link|id]]", possibly abbreviated as in examples: --   [[Mile|mile]]  --> [[mile]] --   [[Mile|miles]] --> [[mile]]s -- However, just id is returned if: -- * no link given (so caller does not need to check if a link was defined); or -- * link has previously been used during the current convert (to avoid overlinking). -- Linking with a unit uses the unit table as the link key, which fails to detect -- overlinking for conversions like the following (each links "mile" twice): --   {{convert|1|impgal/mi|USgal/mi|lk=on}} --   {{convert|1|l/km|impgal/mi USgal/mi|lk=on}} link_key = link_key or link  -- use key if given (the key, but not the link, may be known when need to cancel a link record) if not link or link == '' or linked_pages[link_key] then return id end linked_pages[link_key] = true -- Following only works for language en, but it should be safe on other wikis, -- and overhead of doing it generally does not seem worthwhile. local l = link:sub(1, 1):lower() .. link:sub(2) if link == id or l == id then return '[[' .. id .. ']]' elseif link .. 's' == id or l .. 's' == id then return '[[' .. id:sub(1, -2) .. ']]s' else return '[[' .. link .. '|' .. id .. ']]' end end  local function 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 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 unit1 = per[1]  -- top unit_table, or nil local unit2 = per[2]  -- bottom unit_table if abbr_on then if not unit1 then unit_table.sep = ''  -- no separator in "$2/acre" end if not want_link then local symbol = unit_table.symbol_raw if symbol then return symbol  -- for exceptions that have the symbol built-in end end end local key_id2  -- unit2 is always singular if key_id == 'name2' then key_id2 = 'name1' elseif key_id == 'name2_us' then key_id2 = 'name1_us' else key_id2 = key_id end local result if abbr_on then result = '/' elseif 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 .. linked_id(parms, unit2, key_id2, want_link, '1') 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 disp = parms.disp 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 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 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 linked_pages[first_unit] = nil  -- so the final and only id will be linked, if wanted 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 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, 'out') 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 linked_pages[out_current] = nil  -- so the final and only id will be linked, if wanted 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, 'out') 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, 'out') 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. out_unit_table.valinfo = collection() local range = parms.range for i = 1, (range and (range.n + 1) or 1) do local success, info = cvtround(parms, in_unit_table.valinfo[i], in_unit_table, out_unit_table) if not success then return false, info end out_unit_table.valinfo:add(info) end return true, process_one_output(parms, out_unit_table) end  local function make_output_multiple(parms, in_unit_table, out_unit_table) -- Return true, item where item = wikitext of the conversion result -- for an output which is a multiple (like 'ftin'); -- or return false, t where t is an error message table. local multiple = out_unit_table.multiple  -- table of scaling factors (will not be nil) local combos = out_unit_table.combination  -- table of unit tables (will not be nil) local abbr = parms.abbr local abbr_org = parms.abbr_org local disp = parms.disp local want_name = (abbr_org == nil and (disp == 'or' or disp == 'slash')) or not (abbr == 'on' or abbr == 'out' or abbr == 'mos') local want_link = (parms.lk == 'on' or parms.lk == 'out') local mid = 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 = 'out' 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 inout = (i == #combos or outvalue == 0) and 'out' 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, 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, 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, 'out') end end return true, result .. mid end  local function process(parms, in_unit_table, out_unit_table) -- Return true, s where s = final wikitext result, -- or return false, t where t is an error message table. linked_pages = {} local success, bad_output local bad_input_mcode = in_unit_table.bad_mcode  -- false if input unit is valid local invalue1 = in_unit_table.valinfo[1].value local out_unit = parms.out_unit if out_unit == nil or out_unit == '' then if bad_input_mcode or parms.opt_input_unit_only then bad_output = '' else success, out_unit = get_default(invalue1, 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 flipped = parms.opt_flip and not bad_input_mcode local parts = {} for part = 1, 2 do -- The LHS (parts[1]) is normally the input, but is the output if flipped. -- Process LHS first so it will be linked, if wanted. -- Linking to the same item is suppressed in the RHS to avoid overlinking. if (part == 1 and not flipped) or (part == 2 and flipped) then parts[part] = process_input(parms, in_unit_table) elseif bad_output then parts[part] = (bad_output == '') and '' or message(bad_output) else local outputs = {} local combos  -- nil (for 'ft' or 'ftin'), or table of unit tables (for 'm ft') if not out_unit_table.multiple then  -- nil/false ('ft' or 'm ft'), or table of factors ('ftin') combos = out_unit_table.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: -- {{convert|156|cm|in hand|1|frac=2}} → 156 centimetres (61.4 in; 15.1½ hands) -- However, the following is handled elsewhere as a special case: -- {{convert|156|cm|hand in|1|frac=2}} → 156 centimetres (15.1½ hands; 61½ in) if combos 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 out_first local imax = combos and #combos or 1  -- 1 (single unit) or number of unit tables for i = 1, imax do local success, item local out_current = combos and combos[i] or out_unit_table out_current.inout = 'out' if i == 1 then out_first = out_current 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 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 table.insert(outputs, item) end if parms.opt_input_unit_only then parts[part] = '' else local sep = parms.table_joins and parms.table_joins[2] or parms.join_between parts[part] = table.concat(outputs, sep) end end end if parms.join_before then parts[1] = parms.join_before .. parts[1] end local wikitext if bad_input_mcode then if bad_input_mcode == '' then wikitext = parts[1] else wikitext = parts[1] .. message(bad_input_mcode) end elseif parms.table_joins then wikitext = parms.table_joins[1] .. parts[1] .. parms.table_joins[2] .. parts[2] else wikitext = parts[1] .. parms.joins[1] .. parts[2] .. parms.joins[2] end if parms.warnings and not bad_input_mcode then wikitext = wikitext .. parms.warnings end return true, wikitext, out_unit_table end  local function main_convert(frame) -- Do convert, and if needed, do it again with higher default precision. set_config(frame.args) local result, out_unit_table local success, parms, in_unit_table = get_parms(frame:getParent().args) if success then for i = 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 else result = parms end if success then return result end return message(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 {{ntsh}}, --     calculated from the result of converting value --     to a base unit with scale 1. --   unknown = true if the unitcode was not known unitcode = strip(unitcode) if unitcode == nil or unitcode == '' then return nil end set_config({}) linked_pages = {} options = options or {} local parms = { abbr = options.name and 'off' or 'on', lk = options.link and 'on' or nil, opt_sp_us = options.us and true or nil, opt_ignore_error = true,  -- do not add pages using this function to 'what links here' for Module:Convert/extra opt_sortable_on = options.sort == 'on' or options.sort == 'debug', opt_sortable_debug = options.sort == 'debug', } local utable 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 '?' utable = { [symbol] = { _name1 = symbol, _name2 = symbol, _symbol = symbol, utype = symbol, scale = symbol == 'g' and 0.001 or 1, prefixes = 1, default = symbol, link = options.si[2], }} end local success, unit_table = lookup(parms, unitcode, 'no_combination', utable) if not success then unit_table = setmetatable({ symbol = unitcode, name2 = unitcode, default = "m", defkey = "m", linkey = "m", utype = "length", scale = 1 }, 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 }