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 format = string.format local floor = math.floor

-- Names when using engineering notation (a prefix of "eN" where N is a number). -- key = { "name", "linked name, if link wanted" } -- LATER: Perhaps this should be in convertdata to keep output text in one place. local eng_scales = { ["3"] = { "thousand" }, ["6"] = { "million" }, ["9"] = { "billion", "billion" }, ["12"] = { "trillion", "trillion" }, ["15"] = { "quadrillion", "quadrillion" }, }

-- Configuration options to keep magic values in one location. local numdot, numsep, maxsigfig, lang local limit_abuse = 30 -- avoid using very large precision/sigfig (need >20 to avoid values like 1e-22 rounding to 0) -- Following specify the conversion data which is defined in another module -- because it is too large to be conveniently included here. -- To allow easy comparison between "require" and "loadData", a config option -- can be set to control which is used. local SIprefixes, units, default_exceptions, link_exceptions

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 ','      -- thousands separator for numbers (',', '.', '') maxsigfig = args.maxsigfig or 14 -- maximum number of significant figures lang = args.lang or 'en'         -- language code for messages if maxsigfig > limit_abuse then maxsigfig = limit_abuse end -- Scribunto sets the global variable 'mw'. -- A testing program can set the global variable 'is_test_run'. local convertdata local data_module = is_test_run and "convertdata" or "Module:Convert/data" if args.use_require then convertdata = require(data_module) else convertdata = mw.loadData(data_module) end SIprefixes = convertdata.SIprefixes units = convertdata.units default_exceptions = convertdata.default_exceptions link_exceptions = convertdata.link_exceptions 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

-- BEGIN: Messages that may be displayed by Module:Convert. -- LATER: Perhaps move to Module:Convertmessages to simplify this module. local all_categories = { ['en'] = { general = '', unknown = '', mismatch = '', }, }

-- Following puts wanted style around each unit code marked like '...%{ft%}...'. local unitcode_regex = '%%([{}])' local unitcode_replace = { ['{'] = ' ' }

local all_messages = { -- All output messages. ['en'] = { -- The prefix is inserted before each message. -- LATER: Link should be to 'Template', not 'Module'. --       Put the correct name when have a template established. cvt_prefix = 'Conversion error:', -- Messages; each is a numbered table: { 'error text', 'category key', gsub_regex, gsub_table }. cvt_bad_default = { 'Unit "%s" has an invalid default', 'unknown' }, cvt_bad_num = { 'Value "%s" must be a number', 'general' }, cvt_bad_num2 = { 'Second value "%s" must be a number', 'general' }, cvt_bad_prec = { 'Parameter precision "%s" must be an integer', 'general' }, cvt_bad_sigfig = { 'Parameter sigfig "%s" must be an integer', 'general' }, cvt_bad_unit = { 'Unit "%s" is invalid here', 'unknown' }, cvt_mismatch = { 'Cannot convert "%s" to "%s"', 'mismatch' }, cvt_no_default = { 'Unit "%s" has no default output unit', 'unknown' }, cvt_no_num = { 'Need value', 'general' }, cvt_no_num2 = { 'Need second value', 'general' }, cvt_no_unit = { 'Need name of unit', 'unknown' }, cvt_should_be = { '%s', 'general', unitcode_regex, unitcode_replace }, cvt_sigfig_pos = { 'sigfig "%s" must be positive', 'general' }, cvt_unknown = { 'Unit "%s" is not known', 'unknown' }, }, }

local messages = {} -- simulating how it would be if in another module

function messages.message(msg, lang) -- Return wikitext for an error message, including category if specified -- for the message type. -- msg = numbered table: --   msg[1] = 'cvt_xxx' (string used as a key to get message info) --   msg[2] = 'parm1' (string to replace first %s if any in message) --   msg[3] = 'parm2' (string to replace second %s if any in message) --   msg[4] = 'parm3' (string to replace third %s if any in message) -- lang = 'en' (default), or other language code. lang = lang or 'en' local mlang = all_messages[lang] if mlang then local t = mlang[msg[1]] if t then -- t[1] = message text, t[2] = category, t[3] = gsub_regex, t[4] = gsub_replace local text = string.format(t[1] or 'Missing message',               msg[2] or '?',                msg[3] or '?',                msg[4] or '?') local cat = all_categories[lang][t[2]] or '' local prefix = mlang['cvt_prefix'] or '' local regex, replace = t[3], t[4] if regex and replace then text = text:gsub(regex, replace) end return ' ' .. prefix .. ' ' .. text .. cat .. ' '       end end return 'Convert internal error: unknown message' end -- END: Messages that may be displayed by Module:Convert.

local function shallow_copy(t) -- Return a shallow copy of t.   -- Do not need the features and overhead of mw.clone provided by Scribunto. 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 a 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 .. 's'       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 's'. 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 .. 's'           else value = self.name2 end elseif key == 'link' then value = self.name1 elseif key == 'engscale' then value = false else return nil -- some fields like invert and multiple may be 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 = value:sub(1, pos - 1) .. self.si_name .. value:sub(pos) elseif key == 'name2' then value = self.name1 .. 's'       elseif key == 'name1_us' then value = rawget(self, '_name1_us') if value then local pos = rawget(self, 'prefix_position') or 1 value = value:sub(1, pos - 1) .. self.si_name .. value:sub(pos) else value = self.name1 end elseif key == 'name2_us' then if rawget(self, '_name1_us') then value = self.name1_us .. 's'           else value = self.name2 end elseif key == 'link' then value = self.name1 elseif key == 'engscale' then value = false else return nil -- some fields like invert and multiple may be nil end rawset(self, key, value) return value end }

local function lookup(unitcode, sp, 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 'sp' is nil, or is 'us' for US spelling of SI prefixes and -- the symbol and names of the unit. If 'us', 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 multiple --  'only_multiple'   : single unit or 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 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 = (sp == 'us') if t.sp_us then force_sp_us = true sp = 'us' end local target = t.target -- nil, or unitcode is an alias for this target if target then local success, result = lookup(target, sp, what) if not success then return false, result end for _, item in ipairs({ 'customary', 'default', 'link', 'symbol' }) do               if t[item] then result[item] = t[item] end end return true, result 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 comboresult = { utype = t.utype, multiple = multiple, combination = {} } local cvt = comboresult.combination for i, v in ipairs(combo) do               local success, t = lookup(v, sp, multiple and 'no_combination' or 'only_multiple') if not success then return false, t end cvt[i] = t           end return true, comboresult 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). -- Micro (µ) is two bytes in utf-8, so is found with plen = 2. local prefix = string.sub(unitcode, 1, plen) local si = SIprefixes[prefix] if si then local t = units[unitcode:sub(plen+1)] if t and t.prefixes then local result = shallow_copy(t) if 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 "e6e6cuft", and -- not if the unit is a combination or multiple, and not if   -- the unit has an offset (temperature; would need extra work to handle). local exponent, baseunit = unitcode:match('^e(%d+)(.*)') if exponent then local engscale = eng_scales[exponent] if engscale then local success, result = lookup(baseunit, sp, 'no_combination') if not success then return false, result end if not (result.offset or result.engscale) then result.defkey = unitcode -- key to lookup default exception engscale.exponent = exponent result.engscale = engscale result.scale = result.scale * 10 ^ tonumber(exponent) return true, result end end end return false, { 'cvt_unknown', unitcode } end

local function ntsh_complement(text) -- Return text (string of digits) after subtracting each digit from 9. local result = '' local first, last = 1, #text while first <= last do       local lenblock = last + 1 - first if lenblock > 12 then lenblock = 12 end local block = tonumber(text:sub(first, first + lenblock - 1)) local nines = tonumber(string.rep('9', lenblock)) local fmt = '%0' .. tostring(lenblock) .. '.0f' result = result .. format(fmt, nines - block) first = first + lenblock end return result end

local function ntsh(n, 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, i, f, style if n >= 0 then if n > 1e16 then result = '~' else i, f = math.modf(n) f = floor(1e6 * f)           result = format('&1%016.0f%06d', i, f)        end else n = -n if n > 1e16 then result = '!' else i, f = math.modf(n) f = floor(1e6 * f)           result = format('%016.0f%06d', i, f)            result = '&0' .. ntsh_complement(result) end 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 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 with_separator(text) -- Return text with thousand separators inserted. -- 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 numdot, and not after 'e' or 'E'). -- Four-digit integer parts have a separator (like '1,234'). if numsep == '' then return text end local last = text:match('[' .. numdot .. '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 then local groups = {} local first = last % 3 if first > 0 then table.insert(groups, text:sub(1, first)) end first = first + 1 while first < last do           table.insert(groups, text:sub(first, first+2)) first = first + 3 end return table.concat(groups, numsep) .. text:sub(last+1) end return text end

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

local function with_exponent(show, exponent) -- Return wikitext to display the implied value in exponent notation. if #show > 1 then show = show:sub(1, 1) .. numdot .. show:sub(2) end return format(fmtpower, show, use_minus(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(math.log10(value)) if frac >= 0 then frac = frac - 1 exp = exp + 1 end local digits = format('%.0f', floor((10^(frac + sigfig)) + 0.5)) 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(show, exponent, isnegative) -- Return t where t is a table with the results; fields: --  show = wikitext formatted to display implied value --  is_scientific = true if show uses scientific notation --  clean = unformatted show (possibly adjusted and with inserted numdot) --  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: -- * Includes a Unicode minus if isnegative. -- * Has numsep inserted where necessary. -- * Uses scientific notation for very small or large values. -- * 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*)([' .. numdot .. ']?)(.*)')       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' .. numdot .. zeros:sub(1, maxlen) end elseif #zeros >= 4 then show = figs exponent = -#zeros elseif #figs > maxlen then show = '0' .. numdot .. 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' .. numdot .. string.rep('0', -exponent) .. show else show = show:sub(1, exponent) .. numdot .. 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 return { clean = show, sign = sign, show = sign .. with_separator(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(text, negative) -- If text represents a fraction, return value, show where -- value is a number and show is a string. -- Otherwise, return nil. --   -- 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 if negative == negfrac or wholestr == nil then value = whole + numerator / denominator else value = whole - numerator / denominator numstr = change_sign(numstr) end if tostring(value):find('#', 1, true) 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(wholestr), sign, numstr, denstr) else local sign = negative and MINUS or '' wikitext = format(frac1, sign, numstr, denstr) end return value, wikitext end

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

local function extract_number(args, index, which) -- Return true, info if can extract a number from the text in args[index], -- where info is a table with the result, -- or return false, t where t is an error message table. -- 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 --  show     = text formatted for output -- For show: -- * Thousand separators are inserted. -- * If negative, a Unicode minus is used; otherwise the sign --  is '+' (if the input text used '+'), or is ''. -- TODO Think about fact that the input value might be like 1.23e+123. -- Will the exponent break anything? local text = strip(args[index]) if text == nil or text == '' then return false, { missing[which] } end local clean, sign if numsep == '' then clean = text else clean = text:gsub('[' .. numsep .. ']', '') -- use '[.]' if numsep is '.' end -- Remove any sign character (assuming a number starts with '.' or a digit). sign, clean = clean:match('^%s*([^ .%d]*)%s*(.*)') if sign == nil or clean == nil then return false, { missing[which] } -- should never occur end local propersign, negative if sign == MINUS or sign == '-' then propersign = MINUS negative = true elseif sign == '+' then propersign = '+' negative = false elseif sign == '' then propersign = '' negative = false else return false, { invalid[which], text } end local show, singular local value = tonumber(clean) if value == nil then value, show = extract_fraction(clean, negative) if value == nil then return false, { invalid[which], text } end singular = false -- any fraction (even with value 1) is regarded as plural end if show == nil then singular = (value == 1 and not negative) show = propersign .. with_separator(clean) end if negative and (value ~= 0) then value = -value end return true, { value = value, singular = singular, clean = clean, show = show } end

local function require_integer(text, invalid) -- Return true, n where n = integer equivalent to given text, -- or return false, t where t is an error message table. -- Input should be the text for a simple integer (no separators, no Unicode minus). -- Using regex avoids irritations with input like '-0.000001'. if text == nil then return false, { 'cvt_no_num' } end if string.match(text, '^-?%d+$') == nil then return false, { invalid, text } end return true, tonumber(text) end

local function get_parms(pframe) -- If successful, return true, args, unit where --  args 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. -- Some of the named args that are added here could be provided by the -- user of the template. -- 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 range_types = { -- text to separate input, output ranges; for 'x', depends on abbr ['and']  = {' and ', ' and '}, ['by']   = {' by ', ' by '}, ['to']   = {' to ', ' to '}, ['-']    = {'–', '–'},        ['to(-)'] = {' to ', '–'}, ['to-']  = {' to ', '–'}, ['x']    = {{ ['out'] = ' by '   , ['in'] = ' × ', ['off'] = ' by ', ['on'] = ' × ' }, { ['out'] = ' × ', ['in'] = ' by '  , ['off'] = ' by ', ['on'] = ' × ' }}, ['+/-']  = {' ± ', ' ± '},        ['±']     = {'±', '±'},    }    local success, info1, info2 local args = {} -- arguments passed to template for k, v in pairs(pframe.args) do       args[k] = v    end success, info1 = extract_number(args, 1, 1) if not success then return false, info1 end local in_unit, precision local next = strip(args[2]) local i = 3 local range = range_types[next] if range == nil then in_unit = next else args.range = range args.is_range_x = (next == 'x') success, info2 = extract_number(args, 3, 2) if not success then return false, info2 end in_unit = strip(args[4]) i = 5 end local success, in_unit_table = lookup(in_unit, args.sp, 'no_combination') if not success then return false, in_unit_table end if args.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 next = strip(args[i]) i = i + 1 if tonumber(next) == nil then args.out_unit = next next = strip(args[i]) if tonumber(next) then i = i + 1 precision = next end else precision = next end if args.adj == nil and args.sing ~= nil then args.adj = args.sing -- sing (singular) is apparently an old equivalent of adj end if args.adj == 'mid' then args.adj = 'on' next = args[i] i = i + 1 if next == nil then args.mid = '' else -- mid-text words if next:sub(1, 1) == '-' then args.mid = next else args.mid = ' ' .. next end end elseif args.adj == 'on' then args.mid = '' end if precision == nil then if tonumber(args[i]) then precision = strip(args[i]) i = i + 1 end end local disp = args.disp if disp == 'x' then args.joins = { args[i] or , args[i+1] or  } elseif disp == 's' or disp == '/' then args.disp = 'slash' end args.precision = args.precision or precision -- allow named parameter local abbr = args.abbr if abbr == nil then -- Default is to abbreviate output (use symbol), or input if flipped. args.abbr = (disp == 'flip') and 'in' or 'out' else args.abbr_org = abbr -- original abbr (as entered by user) if disp == 'flip' then -- 'in' = LHS, 'out' = RHS if abbr == 'in' then abbr = 'out' elseif abbr == 'out' then abbr = 'in' end end args.abbr = abbr end return true, args, in_unit_table end

local function default_precision(inclean, invalue, outvalue, in_current, out_current) -- Return a default value for precision (an integer like 2, 0, -2). -- Code follows procedures used in old template. -- Am putting exceptions to standard calculations here, as they are -- discovered. Can later decide if something cleaner should be done. -- LATER: Things like the hand unit of length will need special processing. local log10 = math.log10 local prec, minprec, adjust local utype = out_current.utype local fudge = 1e-14 -- 0 adds this, so we do too -- Find fractional digits, handling cases like inclean = '12.345e6'. local integer, dot, fraction = inclean:match('^(%d*)([' .. numdot .. ']?)(%d*)') local exception = (utype == 'temperature' and not           (in_current.exception == 'temperature' or out_current.exception == 'temperature')) if exception then -- LATER: Give an error message if (invalue < in_current.offset): below absolute zero? adjust = 0 local kelvin = (invalue - in_current.offset) * in_current.scale if kelvin <= 0 then -- can get zero, or small but negative value due to precision problems 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.symbol == 'ft' and dot == '' then -- More precision when output ft with integer input value. adjust = -log10(in_current.scale) else adjust = log10(math.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 dot == '' then prec = -integer:match('0*$'):len -- '12300' gives -2, but so does '12300e-5' else if fraction == '' and not exception then prec = 1 -- "123." has same precision as "123.0", like old template else prec = #fraction end end return math.max(floor(prec + adjust), minprec) end

local function convert(value, in_current, out_current) local inscale = in_current.scale local outscale = out_current.scale if in_current.invert then if in_current.invert * out_current.invert < 0 then return 1 / (value * inscale * outscale) end return value * (inscale / outscale) elseif in_current.offset then return (value - in_current.offset) * (inscale / outscale) + out_current.offset else return value * (inscale / outscale) end 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 from 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. -- This code combines convert/round because some rounding requires -- knowledge of what we are converting. 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 local outvalue = convert(invalue, in_current, out_current) local isnegative if outvalue < 0 then isnegative = true outvalue = -outvalue end local success local precision = parms.precision local sigfig = parms.sigfig local disp = parms.disp if precision then -- Ignore sigfig, disp. success, precision = require_integer(precision, 'cvt_bad_prec') if not success then return false, precision end elseif sigfig then -- Ignore disp. success, sigfig = require_integer(sigfig, 'cvt_bad_sigfig') if not success then return false, sigfig end if sigfig <= 0 then return false, { 'cvt_sigfig_pos', parms.sigfig } end show, exponent = make_sigfig(outvalue, sigfig) elseif disp == '5' then show = format('%.0f', floor((outvalue / 5) + 0.5) * 5) else precision = default_precision(inclean, invalue, outvalue, in_current, out_current) end if precision then if precision >= 0 then if precision > limit_abuse then precision = limit_abuse elseif 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'           show = format(fmt, outvalue) else precision = -precision -- #digits to zero (in addition to digits after dot) if precision > limit_abuse then precision = limit_abuse end local shift = 10 ^ precision if shift > outvalue then show = '0' -- like old template, user can zero all digits else show = format('%.0f', floor(outvalue/shift + 0.5)) exponent = #show + precision end end end -- TODO Does following work when exponent ~= nil? --     What if show = '1000' and exponent = 1 (value = .1000*10^1 = 1)? --     What if show = '1000' and exponent = 2 (value = .1000*10^2 = 10)? 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(show, exponent, isnegative) t.singular = singular 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

-- TODO Think about when to use ' ' and when to use ' '. -- For outputs, could use raw_absvalue (not bothering with calculated absvalue). -- Old template always uses nbsp before a unit symbol, but seems inconsistent -- before a unit name. Template:Convert/LoffAonSoff says --  "Numbers less than 1,000 is not wrapped nor are unit symbols" -- so 1000 is a threshold (use nbsp for smaller values), but no conclusive results. -- Possibly a concern is wrapping when using undefined undefined in a table -- (don't want to force a column to be unnecessarily wide by using nbsp). local disp_joins = { ['or']        = { ' or '   , ''  }, ['sqbr-sp']   = { ' ['     , ']' }, ['sqbr-nbsp'] = { ' [', ']' }, ['comma']     = { ', '     , ''  }, ['slash-sp']  = { ' / '    , ''  }, ['slash-nbsp'] = { ' / ', '' }, ['slash-nosp'] = { '/'     , ''  }, ['b']         = { ' ('     , ')' }, }

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) --   '<' 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 pipe-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. 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 = {} default = default .. '|' -- to get last item for item in default:gmatch('%s*(.-)%s*|') do       table.insert(t, item)  -- split on '|', removing leading/trailing whitespace end 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 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. local abbr = parms.abbr if abbr == 'values' then return '' end local inout = unit_table.inout local valinfo = unit_table.valinfo local abbr_org = parms.abbr_org local adj = parms.adj local disp = parms.disp local lk = parms.lk   local usename = unit_table.usename local singular = valinfo[which].singular or (inout == 'in' and adj == 'on') 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. if inout == 'in' then if adj ~= 'on' and (abbr_org == 'out' or disp == 'flip') then local value = valinfo[which].value singular = (0 < value and value < 1.0001) end else if (abbr_org == 'on') or               (disp == nil and (abbr_org == nil or abbr_org == 'out')) or                (disp == 'flip' and abbr_org == 'in') then singular = (valinfo[which].absvalue < 1.0001 and                               not valinfo[which].is_scientific) end end end end if unit_table.engscale then singular = false -- so 1 e3kg gives 1 thousand kilograms (plural) end local key_name = (singular and not parms.is_range_x) and 'name1' or 'name2' local key_symbol = 'symbol' if unit_table.sp_us then key_name = key_name .. '_us' key_symbol = 'sym_us' end local want_name if usename then want_name = true else if abbr_org == nil then if 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 if abbr == 'on' or abbr == inout or (abbr == 'mos' and inout == 'out') then want_name = false else want_name = true end end end local id = unit_table[want_name and key_name or key_symbol] if lk == 'on' or lk == inout then local link = link_exceptions[unit_table.symbol] or unit_table.link if link then local customary_units = { 'US ', 'U.S. ' }           local customary = customary_units[unit_table.customary] if customary then -- Omit any "US"/"U.S." from start of id since that will be inserted. for _, prefix in ipairs({ 'US ', 'US ', 'U.S. ', 'U.S. ', }) do                   local plen = #prefix if id:sub(1, plen) == prefix then id = id:sub(plen + 1) break end end else customary = '' end id = customary ..  .. id ..  end end return id, want_name end

local function decorate_value(parms, unit_table, which) -- If needed, update unit_table.valinfo so values will be shown with -- extra information. -- Currently, this is used only for engineering notation, but might include -- prefacing a value with a currency symbol like "$", or handling "per" units. -- 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 info = unit_table.valinfo[which] local abbr = parms.abbr if abbr == 'on' or abbr == unit_table.inout then info.show = info.show .. ' × 10 ^ ' .. engscale.exponent .. ' '       else local number_id local lk = parms.lk           if lk == 'on' or lk == 'in' then number_id = engscale[2] or engscale[1] else number_id = engscale[1] end info.show = info.show .. ' ' .. number_id end end end

local function process_input(parms, in_current) -- Processing required once per conversion. -- Return block of text to represent input (value/unit). local id1, want_name = make_id(parms, 1, in_current) local extra = '' local result local adj = parms.adj local disp = parms.disp if disp == 'output only' or      disp == 'output number only' or disp == 'number' or       disp == 'u2' or disp == 'unit2' then result = '' parms.joins = { ,  } elseif disp == 'unit' then if adj == 'on' then result = hyphenated(id1) else result = id1 end parms.joins = { ,  } else local abbr = parms.abbr local mos = (abbr == 'mos') local range = parms.range local id = (range == nil) and id1 or make_id(parms, 2, in_current) if id ~= '' then if adj == 'on' then mos = false -- if hyphenated, suppress repeat of unit in a range extra = '-' .. hyphenated(id) .. parms.mid else extra = ' ' .. id           end end local valinfo = in_current.valinfo if range == nil then decorate_value(parms, in_current, 1) result = valinfo[1].show else local rtext = range[1] if type(rtext) == 'table' then rtext = rtext[abbr] or rtext['off'] end if mos then decorate_value(parms, in_current, 1) decorate_value(parms, in_current, 2) result = valinfo[1].show .. ' ' .. id1 .. rtext .. valinfo[2].show 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 .. ' ' .. id .. rtext .. valinfo[2].show 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 .. rtext .. valinfo[2].show end end 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 end return result .. 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 extra = '' local result local disp = parms.disp if disp == 'u2' or disp == 'unit2' then -- 'unit2' is not in old template if parms.adj == 'on' then result = hyphenated(id1) else result = id1 end else local range = parms.range if not (disp == 'output number only' or disp == 'number') then local id = (range == nil) and id1 or make_id(parms, 2, out_current) if id ~= '' then extra = ' ' .. id           end end local valinfo = out_current.valinfo if range == nil then decorate_value(parms, out_current, 1) result = valinfo[1].show else local abbr = parms.abbr local rtext = range[2] if type(rtext) == 'table' then rtext = rtext[abbr] or rtext['on'] end 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 .. extra .. rtext .. valinfo[2].show 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 .. rtext .. valinfo[2].show end end end return result .. extra end

local function make_output_single(parms, info, 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 success, info1 = cvtround(parms, info[1], in_unit_table, out_unit_table) if not success then return false, info1 end success, info2 = cvtround(parms, info[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, info, 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 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 '' fmt = '%.' .. #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 =  .. id ..  end end local strval = (thisvalue == 0) and '0' or with_separator(format(fmt, thisvalue)) table.insert(results, strval .. ' ' .. 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 sign .. table.concat(reversed, ' ') end local result = make_result(info[1]) local range = parms.range if range then local rtext = range[2] if type(rtext) == 'table' then rtext = rtext[abbr] or rtext['on'] end result = result .. rtext .. make_result(info[2]) end return true, result 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. local success, out_unit_table local info = in_unit_table.valinfo local invalue1 = info[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.sp, '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 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, info, in_unit_table, out_current) else success, item = make_output_multiple(parms, info, in_unit_table, out_current) end if not success then return false, item end table.insert(outputs, item) end local disp = parms.disp local in_block = process_input(parms, in_unit_table) local out_block = (disp == 'unit') and '' or table.concat(outputs, '; ') if disp == 'flip' then in_block, out_block = out_block, in_block end local wikitext = in_block .. parms.joins[1] .. out_block .. parms.joins[2] if parms.sortable == 'on' then wikitext = ntsh(invalue1, parms.debug) .. wikitext end return true, wikitext end

local function 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 messages.message(result, lang) end

return { convert = convert }