Module:Convert

-- Convert a value from one unit of measurement to another. -- Example: 123 lb --> 123 pounds (56 kg)

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

-- mw.ustring has two bugs: following works around one of them; see "2013-07-05" for second. -- Bug has been reported, and the fix will be deployed, possibly before August 2013. -- local usub = ustring.sub -- When fix is deployed, remove following usub function, and uncomment above usub variable. local function usub(s, i, j)   return (j and i > j) and '' or ustring.sub(s, i, j) end

-- Configuration options to keep magic values in one location. -- The conversion data and message text are defined in separate modules. -- To allow easy comparison between "require" and "loadData", a config option -- can be set to control which is used. local numdot, numsep -- each must be a single byte for simple regex search/replace local maxsigfig, warnings local default_exceptions, link_exceptions, units local SIprefixes, all_categories, all_messages, customary_units, disp_joins local en_option_value, eng_scales, local_option_name, range_aliases, range_types local group_method = 3    -- code for how many digits are in a group local plural_suffix = 's' -- only other useful value is probably '' to disable plural unit names 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

local function boolean(text) -- Return true if text represents a "true" option value. if text then text = text:lower if text == '1' or text == 'y' or text == 'yes' or text == 'on' or text == 'true' then return true end end end

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 numsep ~= '' then text = text:gsub('[' .. numsep .. ']', '') -- use '[x]' in case x is '.' end if numdot ~= '.' then text = text:gsub('[' .. numdot .. ']', '.') end if to_en_table then text = ustring.gsub(text, '%d', to_en_table) end return text 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(frame) -- Set configuration options from template #invoke or defaults. local args = frame.args numdot = args.numdot or '.'      -- decimal mark before fractional digits numsep = args.numsep or ','      -- group separator for numbers (',', '.', '') maxsigfig = args.maxsigfig or 14 -- maximum number of significant figures warnings = boolean(args.warnings) -- true if want warnings for invalid options -- Scribunto sets the global variable 'mw'. -- A testing program can set the global variable 'is_test_run'. local data_module, text_module, data_code, text_code if is_test_run then data_module = "convertdata" text_module = "converttext" spell_module = "ConvertNumeric" else data_module = "Module:Convert/data" text_module = "Module:Convert/text" spell_module = "Module:ConvertNumeric" end if args.use_require then data_code = require(data_module) text_code = require(text_module) else data_code = mw.loadData(data_module) text_code = mw.loadData(text_module) end default_exceptions = data_code.default_exceptions link_exceptions = data_code.link_exceptions units = data_code.units SIprefixes = text_code.SIprefixes all_categories = text_code.all_categories all_messages = text_code.all_messages customary_units = text_code.customary_units disp_joins = text_code.disp_joins en_option_value = text_code.en_option_value eng_scales = text_code.eng_scales local_option_name = text_code.local_option_name range_aliases = text_code.range_aliases range_types = text_code.range_types -- LATER: Simplify following by using a translation table if it is defined, -- without needing to check the current wiki's language. Am using this more -- generic treatment while testing. local lang = mw.language.getContentLanguage local translation = text_code.translation_table[lang.code] if translation then if translation.group then group_method = translation.group end if translation.plural_suffix then plural_suffix = translation.plural_suffix end 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 end 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 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 = all_messages[mcode[1]] if msg then local text = format(msg[1] or 'Missing message',           mcode[2] or '?',            mcode[3] or '?',            mcode[4] or '?') local cat = all_categories[msg[2]] or '' local prefix = all_messages[msg.warning and 'cvt_prefix_warning' or 'cvt_prefix_error'] or '' local suffix = (prefix == ) and  or ' ' local regex, replace = msg.regex, msg.replace if regex and replace then text = text:gsub(regex, replace) end return prefix .. ' ' .. text .. cat .. suffix end return 'Convert internal error: unknown message' end

local function add_warning(parms, mcode, text) -- If enabled, add a warning that will be displayed after the convert result. -- Currently, only the first warning is displayed. if warnings then if parms.warnings == nil then parms.warnings = message({ mcode, text }) end end end

local function spell_number(parms, number, numerator, denominator) -- Return result of spelling (number, numerator, denominator), or   -- return nil if spelling is not available or not supported for given text. -- Input should use one of these forms: --  number  numerator  denominator  example output --  --  -  ---  --    --   string    nil        nil        one point two three --  string  string     string       one and two thirds --   nil    string     string       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, 'cvt_spell_unavailable') return nil end end local case = parms.opt_spell_upper parms.opt_spell_upper = nil -- only uppercase first number in a multiple unit 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 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, -- or for a unit that accepts prefixes but where no prefix was used. -- In the latter case, and before use, fields symbol, name1, name1_us -- must be set from _symbol, _name1, _name1_us respectively. __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 elseif key == 'builtin' then value = false else return nil end rawset(self, key, value) return value end }

local unit_prefixed_mt = { -- Metatable to get missing values for a unit that accepts SI prefixes, -- and where a prefix has been used. -- Before use, fields si_name, si_prefix must be defined. __index = function (self, key) local value if key == 'symbol' then value = self.si_prefix .. self._symbol elseif key == 'sym_us' then value = self.symbol -- always the same as sym_us for prefixed units elseif key == 'name1' then local pos = rawget(self, 'prefix_position') or 1 value = self._name1 value = usub(value, 1, pos - 1) .. self.si_name .. usub(value, pos) elseif key == 'name2' then value = self.name1 .. plural_suffix elseif key == 'name1_us' then value = rawget(self, '_name1_us') if value then local pos = rawget(self, 'prefix_position') or 1 value = usub(value, 1, pos - 1) .. self.si_name .. usub(value, pos) else value = self.name1 end elseif key == 'name2_us' then if rawget(self, '_name1_us') then value = self.name1_us .. plural_suffix else value = self.name2 end elseif key == 'link' then value = self.name1 elseif key == 'builtin' then value = false else return nil 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. __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) / unit2.scale elseif key == 'builtin' then value = false else return nil end rawset(self, key, value) return value end }

local function lookup(unitcode, opt_sp_us, what) -- 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 opt_sp_us is true for US spelling of SI prefixes and -- the symbol and name of the unit. If true, the result includes field -- sp_us = true (that field may also have been in the unit definition). -- 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, underscores in unitcode are replaced -- with spaces so 350 board_feet --> 350 board feet (0.83 m³). if unitcode == nil or unitcode == '' then return false, { 'cvt_no_unit' } end unitcode = unitcode:gsub('_', ' ') local t = units[unitcode] if t then if t.shouldbe then return false, { 'cvt_should_be', t.shouldbe } end local force_sp_us = opt_sp_us if t.sp_us then force_sp_us = true 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(target, opt_sp_us, what) 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 local per = t.per -- nil/false, or a numbered table for "x/y" units if per then local result = { utype = t.utype, per = {} } override_from(result, t, { 'default', 'invert', 'iscomplex', 'symbol', 'symlink' }) result.symbol_raw = (result.symbol or false) -- to distinguish between a defined exception and a metatable calculation local cvt = result.per local prefix for i, v in ipairs(per) do               if i == 1 and (v == '$' or v == '£') then prefix = v               else local success, t = lookup(v, opt_sp_us, 'no_combination') if not success then return false, t end cvt[i] = t                   if t.sp_us then  -- if the top or bottom unit forces sp=us, set the per unit to use the correct name/symbol force_sp_us = true end end end if prefix then result.vprefix = prefix else result.vprefix = false -- to avoid calling __index end result.sp_us = force_sp_us return true, setmetatable(result, unit_per_mt) 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 multiple == nil) 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(v, opt_sp_us, multiple and 'no_combination' or 'only_multiple') if not success then return false, t end cvt[i] = t           end return true, result end local result = shallow_copy(t) result.sp_us = force_sp_us if result.prefixes then result.symbol = result._symbol result.name1 = result._name1 result.name1_us = result._name1_us end return true, setmetatable(result, unit_mt) end for plen = 2, 1, -1 do       -- Look for an SI prefix; should never occur with an alias. -- Check for longer prefix first ('dam' is decametre). local prefix = usub(unitcode, 1, plen) local si = SIprefixes[prefix] if si then local t = units[usub(unitcode, plen+1)] if t and t.prefixes then local result = shallow_copy(t) if opt_sp_us then result.sp_us = true end if result.sp_us and si.name_us then result.si_name = si.name_us else result.si_name = si.name end 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 exponent, baseunit = unitcode:match('^e(%d+)(.*)') if exponent then local engscale = eng_scales[exponent] if engscale then local success, result = lookup(baseunit, opt_sp_us, 'no_combination') if not success then return false, result end if 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 return false, { 'cvt_unknown', unitcode } end

local function valid_number(num) -- Return true if num is a valid number. -- Expressed as a string, overflow or other problems are indicated with -- text like "1.#INF" or ".#IND" which are regarded as invalid here. if type(num) == 'number' and tostring(num):find('#', 1, true) == nil then return true end end

local function ntsh(num, debug) -- Return html text to be used for a hidden sort key so that -- the given number will be sorted in numeric order. -- If debug == 'yes', output is in a box (not hidden). -- This implements Template:Ntsh (number table sorting, hidden). local result, style if not valid_number(num) then if num < 0 then result = '1000000000000000000' else result = '9000000000000000000' end elseif num == 0 then result = '5000000000000000000' else local mag = floor(log10(abs(num)) + 1e-14) local prefix if num > 0 then prefix = 7000 + mag else prefix = 2999 - mag num = num + 10^(mag+1) end result = format('%d', prefix) .. format('%015.0f', floor(num * 10^(14-mag))) end if debug == 'yes' then style = 'border:1px solid' else style = 'display:none' end return ' ' .. result .. ' ' end

local function hyphenated(name) -- Return a hyphenated form of given name (for adjectival usage). -- 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)"]. 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, -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

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 if parms.opt_adjectival then if inout == (parms.opt_flip and 'out' or 'in') then mid = parms.mid end if want_name then return '-' .. hyphenated(id) .. (mid or ''), true end end return sep .. id .. (mid or '') 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_grouper(method, gaps) -- Return a table to hold groups of digits which can be joined with -- suitable separators (such as commas). -- Each group is separately translated to the local language because the -- separators may include '.' characters which should not be translated. -- Parameter method is a number or nil: --  3 for 3-digit grouping, or    --   2 for 3-then-2 grouping. -- Parameter gaps is true to use gaps (numsep ignored). return { n = 0, add = function (self, digits) self.n = self.n + 1 self[self.n] = from_en(digits) end, join = function (self, rhs) -- Concatenate in reverse order. if gaps then local result = '' for i = 1, self.n - 1 do                   result = ' ' .. self[i] .. ' ' .. result end return ' ' .. self[self.n] .. result .. from_en(rhs) .. ' '           else local result = self[1] for i = 2, self.n do                   result = self[i] .. numsep .. result end return result .. from_en(rhs) end end, step = 3, next_position = function (self, previous) -- Return position of digit just before next group. -- Digits are grouped from right-to-left (least significant first). local result = previous - self.step if method == 2 then self.step = 2 -- may need more (3, 2, 2, 3, 2, 2, ...) in some languages end return (result < 0) and 0 or result end, } end

local function with_separator(parms, text) -- Input text is a number in en digits and with '.' decimal mark. -- Return an equivalent of text, 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 '12345.6789' or '1.23e45' -- (e notation can only occur when processing an input value). -- The text has no sign (caller inserts that later, if necessary). -- Separator is inserted only in the integer part of the significand -- (not after the decimal mark, and not after 'e' or 'E'). if parms.opt_nocomma or numsep == '' then return from_en(text) end local last = text:match('[.eE]') --  returns position if last == nil then last = #text else last = last - 1 -- index of last character before dot/e/E end if last < 4 or (last == 4 and parms.opt_comma5) then return from_en(text) end local groups = digit_grouper(group_method, parms.opt_gaps) local i = last while i > 0 do       local position = groups:next_position(i) groups:add(text:sub(position+1, i)) i = position end return groups:join(text:sub(last+1)) end

-- Input values can use values like 1.23e12, but are never displayed -- using scientific notation like 1.23×10¹². -- Very small or very large output values use scientific notation. -- Use format(fmtpower, significand, '10', exponent) where each arg is a string. local fmtpower = '%s × %s%s'

local function with_exponent(show, exponent) -- Return wikitext to display the implied value in scientific notation. -- Input uses en digits; output uses digits in local language. if #show > 1 then show = show:sub(1, 1) .. '.' .. show:sub(2) end return format(fmtpower, from_en(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, frac = math.modf(log10(value)) if frac >= 0 then frac = frac - 1 exp = exp + 1 end local digits = format('%.0f', 10^(frac + 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

local function format_number(parms, show, exponent, isnegative) -- Parameter show is a number in en digits and with '.' decimal mark. -- 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. -- * Uses a custom decimal mark, if wanted. -- * Has digits grouped where necessary, if wanted. -- * Uses scientific notation for very small or large values --  (which forces output to not be spelled). -- * Has no more than maxsigfig significant digits --  (same as old template and ). local sign = isnegative and MINUS or '' local maxlen = maxsigfig if exponent == nil then local integer, dot, fraction = show:match('^(%d*)(%.?)(.*)') if #integer >= 10 then show = integer .. fraction exponent = #integer elseif integer == '0' or integer == '' then local zeros, figs = fraction:match('^(0*)([^0]?.*)') if #figs == 0 then if #zeros > maxlen then show = '0.' .. zeros:sub(1, maxlen) end elseif #zeros >= 4 then show = figs exponent = -#zeros elseif #figs > maxlen then show = '0.' .. zeros .. figs:sub(1, maxlen) end else maxlen = maxlen + #dot if #show > maxlen then show = show:sub(1, maxlen) end end end if exponent then if #show > maxlen then show = show:sub(1, maxlen) end if exponent > 10 or exponent <= -4 or (exponent == 10 and show ~= '1000000000') then -- Rounded value satisfies: value >= 1e9 or value < 1e-4 (1e9 = 0.1e10). return { clean = '.' .. show, exponent = exponent, sign = sign, show = sign .. with_exponent(show, exponent-1), is_scientific = true, }       end if exponent >= #show then show = show .. string.rep('0', exponent - #show) -- result has no dot elseif exponent <= 0 then show = '0.' .. string.rep('0', -exponent) .. show else show = show:sub(1, exponent) .. '.' .. show:sub(exponent+1) end end if isnegative and show:match('^0.?0*$') then sign = '' -- don't show minus if result is negative but rounds to zero end local formatted_show = sign .. with_separator(parms, show) if parms.opt_spell_out then formatted_show = spell_number(parms, sign .. show) or formatted_show end return { clean = show, sign = sign, show = formatted_show, } end

-- Fraction output format (like old template). -- frac1: sign, numerator, denominator -- frac2: wholenumber, sign, numerator, denominator local frac1 = ' %s%s&frasl;%s ' local frac2 = ' %s%s %s&frasl;%s '

local function extract_fraction(parms, text, negative) -- If text represents a fraction, return value, show, spelled where --  value is a number (value of the fraction in argument text) --  show is a string (formatted text for display of an input value,    --        and is spelled if wanted and possible) --  spelled is true if show was spelled -- Otherwise, return nil. -- Input uses en digits and '.' decimal mark (input has been translated). -- Output uses digits in local language and custom decimal mark, if any. --   -- In the following, '(3/8)' represents the wikitext required to    -- display a fraction with numerator 3 and denominator 8. -- In the wikitext, Unicode minus is used for a negative value. --  text          value, show            value, show --                if not negative       if negative --  3 / 8         0.375, '(3/8)'        -0.375, '−(3/8)'    --   2 + 3 / 8     2.375, '2(3/8)'       -1.625, '−2(−3/8)'    --   2 - 3 / 8     1.625, '2(−3/8)'      -2.375, '−2(3/8)'    --   1 + 20/8      3.5 , '1/(20/8)'     1.5   , '−1/(−20/8)'    --   1 - 20/8      -1.5., '1(−20/8)'     -3.5  , '−1(20/8)'    -- Wherever an integer appears above, numbers like 1.25 or 12.5e-3 -- (which may be negative) are also accepted (like old template). -- Template interprets '1.23e+2+12/24' as '123(12/24)' = 123.5! local lhs, negfrac, rhs, numstr, numerator, denstr, denominator, wholestr, whole, value lhs, denstr = text:match('^%s*([^/]-)%s*/%s*(.-)%s*$') denominator = tonumber(denstr) if denominator == nil then return nil end wholestr, negfrac, rhs = lhs:match('^%s*(.-[^eE])%s*([+-])%s*(.-)%s*$') if wholestr == nil or wholestr == '' then wholestr = nil whole = 0 numstr = lhs else whole = tonumber(wholestr) if whole == nil then return nil end numstr = rhs end negfrac = (negfrac == '-') numerator = tonumber(numstr) if numerator == nil then return nil end -- Spelling of silly inputs like "-2+3/8" or "2+3/+8" (mixed or excess signs) is not supported. local do_spell if negative == negfrac or wholestr == nil then value = whole + numerator / denominator do_spell = parms.opt_spell_in if do_spell then if not (numstr:match('^%d') and denstr:match('^%d')) then -- if either has a sign do_spell = false end end else value = whole - numerator / denominator numstr = change_sign(numstr) do_spell = false end if not valid_number(value) then return nil -- overflow or similar end numstr = use_minus(numstr) denstr = use_minus(denstr) local wikitext if wholestr then local sign = negative and MINUS or '+' if negative then wholestr = change_sign(wholestr) end wikitext = format(frac2, use_minus(from_en(wholestr)), sign, from_en(numstr), from_en(denstr)) else local sign = negative and MINUS or '' wikitext = format(frac1, sign, from_en(numstr), from_en(denstr)) end if do_spell then local numsign = (wholestr or not negative) and '' or '-' wikitext = spell_number(parms, wholestr, numsign .. numstr, denstr) or wikitext end return value, wikitext, do_spell end

local missing = { 'cvt_no_num', 'cvt_no_num2' } local invalid = { 'cvt_bad_num', 'cvt_bad_num2' }

local function extract_number(parms, text, which, 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. -- Parameter 'which' (1 or 2) selects which input value is being -- processed (to select the appropriate error message, if needed). -- 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 --  singular = true if value is 1 (to use singular form of units) --           = false if value is -1 (like old template) --  clean    = cleaned text with any separators and sign removed --             (en digits and '.' decimal mark) --  show     = text formatted for output --             (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 clean = to_en(text) if clean == '' then return false, { missing[which] } end local isnegative, propersign = false, '' -- most common case local singular, show local value = tonumber(clean) if value then local sign = clean:sub(1, 1) if sign == '+' or sign == '-' then propersign = (sign == '+') and '+' or MINUS clean = clean:sub(2) end if value < 0 then isnegative = true value = -value end else local valstr for _, prefix in ipairs({ '-', MINUS, '&minus;' }) do           -- Including '-' 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 local spelled if not no_fraction then value, show, spelled = extract_fraction(parms, clean, isnegative) end if value == nil then return false, { invalid[which], text } end if spelled and value <= 1 then singular = true -- for example, "one half mile" (singular unit) else singular = false -- any numeric fraction (even with value 1) is regarded as plural end end end if not valid_number(value) then -- for example, "1e310" overflows return false, { 'cvt_invalid_num' } end if show == nil then singular = (value == 1 and not isnegative) local precision = parms.input_precision if precision and 0 <= precision and precision <= 8 then value = value + 2e-14 -- fudge for some common cases of bad rounding local fmt = '%.' .. format('%d', precision) .. 'f'           show = fmt:format(value) else show = clean end show = propersign .. with_separator(parms, show) if parms.opt_spell_in then show = spell_number(parms, propersign .. clean) or show end end if isnegative and (value ~= 0) then value = -value end return true, { value = value, singular = singular, clean = clean, show = show, } 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, fraction = math.modf(number) return number, (fraction == 0) end end 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 == '&#32;' 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) -- 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 abbr=off and for abbr=on, -- and may specify range text for 'adj=on', -- and may specify exception = true. rtext = range[want_name and 'off' or 'on'] 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, total, in_unit_table) -- Look for a composite input unit. For example, "1 yd" -- would result in a call to this function with --  iparm = 3 (parms[iparm] = "2", just after the first unit) --  total = 1 (number of yards) --  in_unit_table = (unit table for "yd") -- 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 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] if not subdiv then break end local success success, subunit = lookup(subcode, parms.opt_sp_us, 'no_combination') if not success then return false, subunit end -- should never occur success, subinfo = extract_number(parms, parms[iparm], 1) 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(unit, parms.opt_sp_us, '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 } }, composite = composite_units, default = default or in_unit_table.default } end

local function translate_parms(parms) -- Update fields in parms by translating parameters to those used at enwiki. for en_name, loc_name in pairs(local_option_name) do       if en_name ~= 'sing' then  -- 'sing' is an old equivalent of 'adj'; cannot have both local loc_value = parms[loc_name] if loc_value == nil and en_name == 'adj' then loc_name = local_option_name['sing'] loc_value = parms[loc_name] end if loc_value then local en_value = en_option_value[en_name][loc_value] if en_value == nil then if loc_value == '' then add_warning(parms, 'cvt_empty_option', loc_name) else add_warning(parms, 'cvt_unknown_option', loc_name .. '=' .. loc_value) end elseif en_value == '' then en_value = nil elseif en_value:sub(1, 4) == 'opt_' then for _, v in ipairs(split(en_value, ',')) do                       parms[v] = true end en_value = nil end parms[en_name] = en_value end end end if parms.adj then if parms.adj:sub(1, 2) == 'ri' then -- It is known that adj is 'ri1' or 'ri2' or 'ri3', so precision is valid. -- Only en digits are accepted. parms.input_precision = tonumber(parms.adj:sub(-1)) parms.adj = nil end end if parms.abbr then parms.abbr_org = parms.abbr -- original abbr that was set, before any flip else parms.abbr = 'out' -- default is to abbreviate output only (use symbol, not name) end 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 if parms.opt_flip then swap_in_out('abbr') swap_in_out('lk') if parms.opt_spell_in then -- For simplicity, and because it does not appear to be needed, -- user cannot set the option to spell the output. parms.opt_spell_in = nil parms.opt_spell_out = true end end if parms.opt_table or parms.opt_tablecen then if parms.abbr_org == nil and parms.lk == nil then parms.opt_values = true end local align = format('align="%s"', parms.opt_table and 'right' or 'center') parms.table_joins = { align .. '|', '\n|' .. align .. '|' }   end if parms.opt_lang_en then from_en_table = nil end end

local function get_parms(pframe) -- 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. -- 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 success, info1, info2 local parms = {} -- arguments passed to template for k, v in pairs(pframe.args) do       parms[k] = v    end translate_parms(parms) local range local next = strip(parms[2]) local i = 3 if next then range = range_types[next] or range_types[range_aliases[next]] if range == nil and next:sub(-7, -1) == 'nocomma' then local base = strip(next:sub(1, -8)) range = range_types[base] or range_types[range_aliases[base]] if range then parms.opt_nocomma = true end end end success, info1 = extract_number(parms, parms[1], 1) -- need to set parms.opt_nocomma before calling this if not success then return false, info1 end local in_unit if range == nil then in_unit = next else parms.range = range parms.is_range_x = range.is_range_x success, info2 = extract_number(parms, parms[3], 2) if not success then return false, info2 end in_unit = strip(parms[4]) i = 5 end local success, in_unit_table = lookup(in_unit, parms.opt_sp_us, 'no_combination') if not success then return false, in_unit_table 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.valinfo = { info1, info2 } -- info2 is nil if no range in_unit_table.inout = 'in' -- this is an input unit if not range then local success, inext, composite_unit = get_composite(parms, i, info1.value, 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], 1, true) if success then i = i + 1 in_unit_table.altitude = info.value end end 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 parms.opt_adjectival = true 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 '&#32;' rather than ' ' to avoid the default first = ' [ ' .. first second = ' ]' .. second end parms.joins = { first, second } elseif parms.opt_two_preunits then local p1, p2 = preunits(2, parms[i], parms[i+1]) i = i + 2 if parms.preunit1 then -- To simplify documentation, allow unlikely use of adj=pre with disp=preunit -- (however, an output unit must be specified with adj=pre and with disp=preunit). parms.preunit1 = parms.preunit1 .. p1           parms.preunit2 = p2        else parms.preunit1, parms.preunit2 = p1, p2       end end if precision == nil then if set_precision(strip(parms[i])) then i = i + 1 end end if is_bad_precision then return false, { 'cvt_bad_prec', precision } end parms.precision = precision local sigfig = parms.sigfig if sigfig then local number, is_integer = get_number(sigfig) if not number or not is_integer or number <= 0 then return false, { 'cvt_bad_sigfig', sigfig } end parms.sigfig = number end return true, parms, in_unit_table end

local function default_precision(invalue, inclean, outvalue, in_current, out_current, extra) -- Return a default value for precision (an integer like 2, 0, -2). -- Code follows procedures used in old template. local fudge = 1e-14 -- 0 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 -- Count digits after decimal mark, handling cases like '12.345e6'. local exponent local integer, dot, fraction, expstr = inclean:match('^(%d*)(%.?)(%d*)(.*)') local e = expstr:sub(1, 1) local boost = 0 -- can increase default precision if e == 'e' or e == 'E' then exponent = tonumber(expstr:sub(2)) elseif expstr:find('/', 1, true) then boost = 1 -- any input fraction is regarded as one extra digit of precision end if dot == '' then prec = subunit_ignore_trailing_zero and 0 or -integer:match('0*$'):len else prec = #fraction 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 local exception = (utype == 'temperature' and not           (in_current.exception == 'temperature' or out_current.exception == 'temperature')) if exception then -- 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 0 end if out_current.exception == 'integer_more_precision' and floor(invalue) == invalue then -- With certain output units that sometimes give poor results -- with default rounding, use more precision when the input -- value is equal to an integer. An example of a poor result -- is when input 50 gives a smaller output than input 49.5. -- Experiment shows this helps, but it does not eliminate all -- surprises because it is not clear whether "50" should be           -- interpreted as "from 45 to 55" or "from 49.5 to 50.5". adjust = -log10(in_current.scale) elseif subunit_more_precision then -- Conversion like "6 ft" (where subunit is "in") -- has a non-standard adjust value, to give more output precision. adjust = log10(out_current.scale) + 2 else adjust = log10(abs(invalue / outvalue)) end adjust = adjust + log10(2) -- Ensure that the output has at least two significant figures. minprec = 1 - floor(log10(outvalue) + fudge) end if extra then adjust = extra.adjust or adjust minprec = extra.minprec or minprec end return math.max(floor(prec + adjust + boost), minprec) end

local function convert(invalue, inclean, 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 then -- Fuel efficiency (there are no built-ins for this type of unit). if in_current.invert * out_current.invert < 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). 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. -- Fractions 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 fraction 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, fraction = math.modf(invalue) local outvalue = (integer + 2.5 * fraction) * (inscale / outscale) local inch_value = 4 * integer + 10 * fraction -- equivalent number of inches local fracstr = inclean:match('%.(.*)') or '' local fmt if fracstr == '' then fmt = '%.0f' else fmt = '%.' .. format('%d', #fracstr - 1) .. 'f'           end return true, { invalue = inch_value, inclean = format(fmt, inch_value), outvalue = outvalue, minprec = 0, }       end end return false, { 'cvt_bug_convert' } -- should never occur end

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 is positive, and (after rounding) --     is "1", or like "1.00"; --  (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, inclean, show, exponent, singular if info then invalue, inclean = info.value, info.clean end if invalue == nil or invalue == '' then return true, nil end if out_current.builtin == 'hand' then -- Convert to hands, then convert the fractional part to inches. -- LATER: Code is not correct when output is spelled (but that's very rare). local dummy_unit_table = { scale = out_current.scale } local success, outinfo = cvtround(parms, info, in_current, dummy_unit_table) if not success then return false, outinfo end local fmt local fraction = (outinfo.show):match('[' .. numdot .. '](.*)') or '' -- outinfo.show is in local language if fraction == '' then if not outinfo.use_default_precision then return true, outinfo end fmt = '%.0f' else fmt = '%.' .. format('%d', ulen(fraction) - 1) .. 'f'       end local hands, inches = math.modf(outinfo.raw_absvalue) inches = format(fmt, inches * 4) if inches:sub(1, 1) == '4' then hands = hands + 1 inches = '0' .. inches:sub(2) if tonumber(inches) == 0 then inches = '0' end end if inches:sub(2, 2) == '.' then inches = inches:sub(1, 1) .. inches:sub(3) end return true, { sign = outinfo.sign, singular = outinfo.singular, show = outinfo.sign .. with_separator(parms, format('%d', hands)) .. numdot .. from_en(inches) }   end local outvalue, extra = convert(invalue, inclean, in_current, out_current) if extra then if not outvalue then return false, extra end invalue = extra.invalue or invalue inclean = extra.inclean or inclean 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 success, use_default_precision local precision = parms.precision if not precision then local sigfig = parms.sigfig if sigfig then show, exponent = make_sigfig(outvalue, sigfig) elseif parms.opt_round5 then show = format('%.0f', floor((outvalue / 5) + 0.5) * 5) else use_default_precision = true precision = default_precision(invalue, inclean, outvalue, in_current, out_current, extra) end end if precision then if precision >= 0 then if precision <= 8 then -- Add a fudge to handle common cases of bad rounding due to inability -- to precisely represent some values. This makes the following work: -- -100.1 C and 5555000 um. -- Old template uses #expr round, which invokes PHP round. -- LATER: Investigate how PHP round works. outvalue = outvalue + 2e-14 end local fmt = '%.' .. format('%d', precision) .. 'f'           local success success, show = pcall(format, fmt, outvalue) 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 if (show == '1' or show:match('^1%.0*$') ~= nil) and not isnegative then -- Use match because on some systems 0.99999999999999999 is 1.0. singular = true end local t = format_number(parms, show, exponent, isnegative) t.singular = singular t.raw_absvalue = outvalue -- absolute value before rounding t.use_default_precision = use_default_precision 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

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 = default_exceptions[unit_table.defkey or unit_table.symbol] or unit_table.default if default == nil then 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 "id", possibly abbreviated as in examples: --  mile  --> mile --  miles --> miles -- However, just id is returned if: -- * no link given (so caller does not need to check if a link was defined); or   -- * link has previously been used during the current convert (to avoid overlinking). -- Linking with a unit uses the unit table as the link key, which fails to detect -- overlinking for conversions like (each links "mile" twice): --  1 impgal/mi --  1 l/km 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 link == nil or link == '' or linked_pages[link_key] then return id   end linked_pages[link_key] = true -- Following only works for language en, but it should be safe on other wikis, -- and overhead of doing it generally does not seem worthwhile. local l = link:sub(1, 1):lower .. link:sub(2) if link == id or l == id then return  .. id ..  elseif link .. 's' == id or l .. 's' == id then return '' .. id:sub(1, -2) .. 's' else return  .. id ..  end end

local function linked_id(unit_table, key_id, want_link) -- 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 unit1 then result = ' per ' else result = 'per ' end if unit1 then result = linked_id(unit1, key_id, want_link) .. result end return result .. linked_id(unit2, key_id2, want_link) end if multiplier then -- A multiplier (like "100" in "100km") forces the unit to be plural. if abbr_on then multiplier = multiplier .. ' '       else multiplier = multiplier .. ' '           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 unit_table[key_id] if want_link then local link = link_exceptions[unit_table.symbol] or unit_table.link if link then local before = '' local i = unit_table.customary if i == 1 and unit_table.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 = 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 1st or 2nd values (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 valinfo = unit_table.valinfo local abbr_org = parms.abbr_org local adjectival = parms.opt_adjectival local disp = parms.disp local lk = parms.lk   local usename = unit_table.usename local singular = valinfo[which].singular if usename then -- Old template does something like this. if lk == 'on' or lk == inout then -- A linked unit uses the standard singular. else -- Set non-standard singular. local flipped = parms.opt_flip if inout == 'in' then if not adjectival and (abbr_org == 'out' or flipped) then local value = valinfo[which].value singular = (0 < value and value < 1.0001) end else if (abbr_org == 'on') or               (not flipped and (abbr_org == nil or abbr_org == 'out')) or                (flipped and abbr_org == 'in') then singular = (valinfo[which].absvalue < 1.0001 and                               not valinfo[which].is_scientific) end end end end local want_name if usename then want_name = true else if abbr_org == nil then if disp == 'br' or disp == 'or' or disp == 'slash' then want_name = true end if unit_table.utype == 'temperature' or unit_table.utype == 'temperature change' then if not (unit_table.exception == 'temperature') then want_name = false end 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 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 = valinfo[which].value else value = valinfo[which].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 or parms.is_range_x then -- engscale: so "|1|e3kg" gives "1 thousand kilograms" (plural) -- is_range_x: so "|0.5|x|0.9|mi" gives "0.5 by 0.9 miles" (plural) singular = false end key = (adjectival or singular) and 'name1' or 'name2' if unit_table.sp_us then key = key .. '_us' end else unit_table.sep = ' ' key = unit_table.sp_us and 'sym_us' or 'symbol' end return linked_id(unit_table, key, lk == 'on' or lk == inout), want_name end

local function decorate_value(parms, unit_table, which) -- 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 engscale = unit_table.engscale if engscale then local inout = unit_table.inout local info = unit_table.valinfo[which] local abbr = parms.abbr if abbr == 'on' or abbr == inout then info.show = info.show .. ' × ' ..               from_en('10') .. ' ^ ' .. from_en(tostring(engscale.exponent)) .. ' '       else 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 local prefix = unit_table.vprefix if prefix then local info = unit_table.valinfo[which] info.show = prefix .. info.show 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 local abbr = parms.abbr local disp = parms.disp if disp == nil then -- special case for the most common setting parms.joins = disp_joins['b'] elseif disp ~= 'x' then -- Old template does this. if disp == 'slash' then if parms.abbr_org == 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 disp_joins['b'] end if parms.opt_also_symbol and not composite then local join1 = parms.joins[1] if join1 == ' (' or join1 == ' [' then           parms.joins = { join1 .. first_unit[first_unit.sp_us and 'sym_us' or 'symbol'] .. ', ', parms.joins[2] }        end    end    if in_current.builtin == 'mach' then        local prefix = id1 .. ' '        local range = parms.range        local valinfo = first_unit.valinfo        local result = prefix .. valinfo[1].show        if range then            local prefix2 = make_id(parms, 2, first_unit) .. ' '            result = range_text(range, want_name, parms, result, prefix2 .. valinfo[2].show)       end        return preunit .. result    end    if composite then        -- Simplify: assume there is no range, and no decoration.        local mid =         local sep1 = ' '        local sep2 = ' '        if parms.opt_adjectival then            if not parms.opt_flip then                mid = parms.mid or             end            if want_name then                sep1 = '-'                sep2 = '-'            end        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 result, mos    local range = parms.range    if range then        mos = (abbr == 'mos')        if not (mos or (parms.is_range_x and not want_name)) then            linked_pages[first_unit] = nil  -- so the second and only id will be linked, if wanted        end    end    local id = (range == nil) and id1 or make_id(parms, 2, first_unit)    local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, 'in')    if mos and was_hyphenated then        mos = false  -- suppress repeat of unit in a range        if linked_pages[first_unit] then            linked_pages[first_unit] = nil            id = make_id(parms, 2, first_unit)            extra = hyphenated_maybe(parms, want_name, sep, id, 'in')        end    end    local valinfo = first_unit.valinfo    if range then        local sep1 = first_unit.sep if mos then decorate_value(parms, in_current, 1) decorate_value(parms, in_current, 2) result = valinfo[1].show .. sep1 .. id1 elseif parms.is_range_x and not want_name then if abbr == 'in' or abbr == 'on' then decorate_value(parms, in_current, 1) end decorate_value(parms, in_current, 2) result = valinfo[1].show .. sep1 .. id1 else if abbr == 'in' or abbr == 'on' then decorate_value(parms, in_current, 1) end decorate_value(parms, in_current, 2) result = valinfo[1].show end result = range_text(range, want_name, parms, result, valinfo[2].show) else decorate_value(parms, first_unit, 1) 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' then local prefix = id1 .. ' '       local range = parms.range local valinfo = out_current.valinfo local result = prefix .. valinfo[1].show if range then result = range_text(range, want_name, parms, result, prefix .. valinfo[2].show) end return preunit .. result end local result local range = parms.range if range then if not (parms.is_range_x and not want_name) then linked_pages[out_current] = nil -- so the second and only id will be linked, if wanted end end local id = (range == nil) and id1 or make_id(parms, 2, out_current) local extra = hyphenated_maybe(parms, want_name, sep, id, 'out') local valinfo = out_current.valinfo if range then local sep1 = out_current.sep local abbr = parms.abbr if parms.is_range_x and not want_name then if abbr == 'out' or abbr == 'on' then decorate_value(parms, out_current, 1) end decorate_value(parms, out_current, 2) result = valinfo[1].show .. sep1 .. id1 else if abbr == 'out' or abbr == 'on' then decorate_value(parms, out_current, 1) end decorate_value(parms, out_current, 2) result = valinfo[1].show end result = range_text(range, want_name, parms, result, valinfo[2].show) else decorate_value(parms, out_current, 1) 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. local success, info1, info2 local valinfo = in_unit_table.valinfo success, info1 = cvtround(parms, valinfo[1], in_unit_table, out_unit_table) if not success then return false, info1 end success, info2 = cvtround(parms, valinfo[2], in_unit_table, out_unit_table) if not success then return false, info2 end out_unit_table.valinfo = { info1, info2 } 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 = '' local sep1 = ' ' local sep2 = ' ' if parms.opt_adjectival then if parms.opt_flip then mid = parms.mid or '' end if want_name then sep1 = '-' sep2 = '-' end end local function make_result(info) local outvalue, sign, fmt local results = {} for i = 1, #combos do           local thisvalue local out_current = combos[i] out_current.inout = 'out' local scale = multiple[i] if i == 1 then -- least significant unit ('in' from 'ftin') local success, outinfo = cvtround(parms, info, in_unit_table, out_current) if not success then return false, outinfo end sign = outinfo.sign local fraction = (outinfo.show):match('[' .. numdot .. '](.*)') or '' -- outinfo.show is in local language fmt = '%.' .. ulen(fraction) .. 'f' -- to reproduce precision if fraction == '' then outvalue = floor(outinfo.raw_absvalue + 0.5) -- keep all integer digits of least significant unit else outvalue = outinfo.absvalue end end if scale then outvalue, thisvalue = floor(outvalue / scale), outvalue % scale else thisvalue = outvalue end local id           if want_name then id = out_current[(thisvalue == 1) and 'name1' or 'name2'] else id = out_current['symbol'] end if want_link then local link = out_current.link if link then id = make_link(link, id, out_current) end end local strval = (thisvalue == 0) and from_en('0') or with_separator(parms, format(fmt, thisvalue)) table.insert(results, strval .. sep1 .. id) if outvalue == 0 then break end fmt = '%.0f' -- only least significant unit can have a fraction 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]) if not success then return false, result end local range = parms.range if range then local success, result2 = make_result(valinfo[2]) if not success then return false, result2 end result = range_text(range, want_name, parms, result, result2) end return true, result .. mid end

local function process(parms, in_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, out_unit_table local invalue1 = in_unit_table.valinfo[1].value local out_unit = parms.out_unit if out_unit == nil or out_unit == '' then success, out_unit = get_default(invalue1, in_unit_table) if not success then return false, out_unit end end success, out_unit_table = lookup(out_unit, parms.opt_sp_us, 'any_combination') if not success then return false, out_unit_table end if in_unit_table.utype ~= out_unit_table.utype then return false, { 'cvt_mismatch', in_unit_table.utype, out_unit_table.utype } end local flipped = parms.opt_flip 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) else local outputs = {} local combos -- nil (for 'ft' or 'ftin'), or table of unit tables (for 'm ft') if out_unit_table.multiple == nil then -- nil ('ft' or 'm ft'), or table of factors ('ftin') combos = out_unit_table.combination end 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 out_current.multiple == nil then success, item = make_output_single(parms, in_unit_table, out_current) else success, item = make_output_multiple(parms, in_unit_table, out_current) end if not success then return false, item end table.insert(outputs, item) end parts[part] = parms.opt_input_unit_only and '' or table.concat(outputs, '; ') end end if parms.opt_sortable then parts[1] = ntsh(invalue1, parms.debug) .. parts[1] end local wikitext if 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 then wikitext = wikitext .. parms.warnings end return true, wikitext end

local function main_convert(frame) set_config(frame) local result local success, parms, in_unit_table = get_parms(frame:getParent) if success then success, result = process(parms, in_unit_table) else result = parms end if success then return result end return message(result) end

return { convert = main_convert }