Module:Val

-- For Template:Val, output a number and optional unit. -- Format options include scientific and uncertainty notations.

local numdot = '.' -- decimal mark (use ',' for Italian) local numsep = ',' -- group separator (use ' ' for Italian) local mtext = { -- Message and other text that should be localized. ['mt-bad-exponent'] =      'exponent parameter (e)', ['mt-parameter'] =         'parameter ', ['mt-not-number'] =        'is not a valid number', ['mt-cannot-range'] =      'cannot use a range if the first parameter includes "e"', ['mt-need-range'] =        'needs a range in parameter 2', ['mt-should-range'] =      'should be a range', ['mt-cannot-with-e'] =     'cannot be used if the first parameter includes "e"', ['mt-not-range'] =         'does not accept a range', ['mt-cannot-e'] =          'cannot use e notation', ['mt-too-many-parameter'] = 'too many parameters', ['mt-need-number'] =       'need a number after the last parameter because it is a range.', ['mt-ignore-parameter4'] = 'Val parameter 4 ignored', ['mt-val-not-supported'] = 'Val parameter "%s=%s" is not supported', ['mt-invalid-scale'] =     'Unit "%s" has invalid scale "%s"', ['mt-both-u-ul'] =         'unit (u) and unit with link (ul) are both specified, only one is allowed.', ['mt-both-up-upl'] =       'unit per (up) and unit per with link (upl) are both specified, only one is allowed.', }

local data_module = 'Module:Val/units' local convert_module = 'Module:Convert'

local function valerror(msg, nocat, iswarning) -- Return formatted message text for an error or warning. -- Can append "#FormattingError" to URL of a page with a problem to find it. local anchor = ' ' local body, category if nocat or mw.title.getCurrentTitle:inNamespaces(1, 2, 3, 5) then -- No category in Talk, User, User_talk, or Wikipedia_talk. category = '' else category = '' end iswarning = false -- problems are infrequent so try showing large error so editor will notice if iswarning then body = '' .. 'warning '	else		body = ' ' ..			'Error in &#123;&#123;val&#125;&#125;: ' ..			msg ..			' '	end	return anchor .. body .. category end

local range_types = { -- No need for ' ' because nowrap applies to all output. [","]  = ", ",	["by"]  = " by ", ["-"]  = "–",	["–"]   = "–",	["and"] = " and ", ["or"] = " or " , ["to"] = " to " , ["x"]  = " × ", ["×"]  = " × ",	["/"]   = "/", } local range_repeat_unit = { -- WP:UNIT wants unit repeated when a "multiply" range is used. ["x"]  = true, ["×"]  = true, }

local function extract_item(index, numbers, arg) -- Extract an item from arg and store the result in numbers[index]. -- If no argument or if argument is valid, return nil (no error); -- otherwise, return an error message. -- The stored result is: -- * a table for a number (empty if there was no specified number); or	-- * a string for range text -- Input like 1e3 is regarded as invalid for all except argument 1 -- which accepts e notation as an alternative to the 'e' argument. -- Input group separators are removed. local which = index local function fail(msg) local description if which == 'e' then description = mtext['mt-bad-exponent'] else description = mtext['mt-parameter'] .. which end return description .. ' ' .. (msg or mtext['mt-not-number']) .. '.'	end local result = {} local range = range_types[arg] if range then if type(index) == 'number' and (index % 2 == 0) then if index == 2 then if numbers[1] and numbers[1].exp then return fail(mtext['mt-cannot-range']) end numbers.has_ranges = true else if not numbers.has_ranges then return fail(mtext['mt-need-range']) end end numbers[index] = range if range_repeat_unit[arg] then -- Any "repeat" range forces unit (if any) to be repeated for all items. numbers.isrepeat = true end return nil end return fail(mtext['mt-not-range']) end if numbers.has_ranges and type(index) == 'number' and (index % 2 == 0) then return fail(mtext['mt-should-range']) end if index == 'e' then local e = numbers[1] and numbers[1].exp if e then if arg then return fail(mtext['mt-cannot-with-e']) end arg = e			which = 1 end end if arg and arg ~= '' then arg = arg:gsub(numsep, '') if numdot ~= '.' then arg = arg:gsub(numdot, '.') end if arg:sub(1, 1) == '(' and arg:sub(-1) == ')' then result.parens = true arg = arg:sub(2, -2) end local a, b = arg:match('^(.+)[Ee](.+)$') if a then if index == 1 then arg = a				result.exp = b			else return fail(mtext['mt-cannot-e']) end end local isnegative, propersign, prefix local minus = '−' prefix, arg = arg:match('^(.-)([%d.]+)$') local value = tonumber(arg) if not value then return fail end if arg:sub(1, 1) == '.' then arg = '0' .. arg end if prefix == '' then -- Ignore. elseif prefix == '±' then -- Display for first number, ignore for others. if index == 1 then propersign = '±' end elseif prefix == '+' then propersign = '+' elseif prefix == '-' or prefix == minus then propersign = minus isnegative = true else return fail end result.clean = arg result.sign = propersign or '' result.value = isnegative and -value or value end numbers[index] = result return nil -- no error end

local function get_args(numbers, args) -- Extract arguments and store the results in numbers. -- Return nothing (no error) if ok; otherwise, return an error message. for index = 1, 99 do		local which = index local arg = args[which] -- has been trimmed if not arg then which = 'e'			arg = args[which] end local msg = extract_item(which, numbers, arg) if msg then return msg end if which == 'e' then break end if index > 19 then return mtext['mt-too-many-parameter'] end end if numbers.has_ranges and (#numbers % 2 == 0) then return mtext['mt-need-number'] end end

local function get_scale(text, ucode) -- Return the value of text as a number, or throw an error. -- This supports extremely basic expressions of the form: --  a / b	--   a ^ b	-- where a and b are numbers or 'pi'. local n = tonumber(text) if n then return n	end n = text:gsub('pi', math.pi) for _, op in ipairs({ '/', '^' }) do local a, b = n:match('^(.-)' .. op .. '(.*)$') if a then a = tonumber(a) b = tonumber(b) if a and b then if op == '/' then return a / b				elseif op == '^' then return a ^ b				end end break end end error(string.format(mtext['mt-invalid-scale'], ucode, text)) end

local function get_builtin_unit(ucode, definitions) -- Return table of information for the specified built-in unit, or nil if not known. -- Each defined unit code must be followed by two spaces (not tab characters). local _, pos = definitions:find('\n' .. ucode .. ' ', 1, true) if pos then local endline = definitions:find('%s*\n', pos) if endline then local result = {} local n = 0 local text = definitions:sub(pos + 1, endline - 1):gsub('%s%s+', '\t') for item in (text .. '\t'):gmatch('(%S.-)\t') do				if item == 'ALIAS' then result.alias = true elseif item == 'ANGLE' then result.isangle = true result.nospace = true elseif item == 'NOSPACE' then result.nospace = true elseif item == 'SI' then result.si = true else n = n + 1 if n == 1 then local link, symbol = item:match('^%[%[([^|]+)|(.+)%]%]$') if link then result.symbol = symbol result.link = link n = 2 else result.symbol = item end elseif n == 2 then result.link = item elseif n == 3 then result.scale_text = item result.scale = get_scale(item, ucode) else result.more_ignored = item break end end end if result.si then local s = result.symbol if ucode == 'mc' .. s or ucode == 'mu' .. s then result.ucode = 'µ' .. s -- unit code for convert should be this end end if n >= 2 or (n >= 1 and result.alias) then return result end -- Ignore invalid definition, treating it as a comment. end end end

local function convert_lookup(ucode, value, scaled_top, want_link, si, options) local lookup = require(convert_module)._unit return lookup(ucode, {			value = value,			scaled_top = scaled_top,			link = want_link,			si = si,			sort = options.sortable,		}) end

local function get_unit(ucode, value, scaled_top, options) local want_link = options.want_link if scaled_top then want_link = options.want_per_link end local data = mw.loadData(data_module) local result = options.want_longscale and get_builtin_unit(ucode, data.builtin_units_long_scale) or		get_builtin_unit(ucode, data.builtin_units) local si, use_convert if result then if result.alias then ucode = result.symbol use_convert = true end if result.scale then -- Setting si means convert will use the unit as given, and the sort key -- will be calculated from the value without any extra scaling that may -- occur if convert found the unit code. For example, if val defines the -- unit 'year' with a scale and if si were not set, convert would also apply -- its own scale because convert knows that a year is 31,557,600 seconds. si = { result.symbol, result.link } value = value * result.scale end if result.si then ucode = result.ucode or ucode si = { result.symbol, result.link } use_convert = true end else result = {} use_convert = true end local convert_unit = convert_lookup(ucode, value, scaled_top, want_link, si, options) result.sortkey = convert_unit.sortspan if use_convert then result.text = convert_unit.text result.scaled_top = convert_unit.scaled_value else if want_link then result.text = '' else result.text = result.symbol end result.scaled_top = value end return result end

local function makeunit(value, options) -- Return table of information for the requested unit and options, or -- return nil if no unit. options = options or {} local unit local ucode = options.u	local percode = options.per if ucode then unit = get_unit(ucode, value, nil, options) elseif percode then unit = { nospace = true, scaled_top = value } else return nil end local text = unit.text or '' local sortkey = unit.sortkey if percode then local function bracketed(code, text) return code:find('[*./]') and '(' .. text .. ')' or text end local perunit = get_unit(percode, 1, unit.scaled_top, options) text = (ucode and bracketed(ucode, text) or '') .. '/' .. bracketed(percode, perunit.text) sortkey = perunit.sortkey end if not (unit.nospace or options.nospace) then text = ' ' .. text end return { text = text, isangle = unit.isangle, sortkey = sortkey } end

local function list_units(mode) -- Return wikitext to list the built-in units. -- A unit code should not contain wikimarkup so don't bother escaping. local data = mw.loadData(data_module) local definitions = data.builtin_units .. data.builtin_units_long_scale local last_was_blank = true local n = 0 local result = {} local function add(line) if line == '' then last_was_blank = true else if last_was_blank and n > 0 then n = n + 1 result[n] = '' end last_was_blank = false n = n + 1 result[n] = line end end local si_prefixes = { -- These are the prefixes recognized by convert; u is accepted for micro. y = 'y', z = 'z', a = 'a', f = 'f', p = 'p', n = 'n', u = 'µ', ['µ'] = 'µ', m = 'm', c = 'c', d = 'd', da = 'da', h = 'h', k = 'k', M = 'M', G = 'G', T = 'T', P = 'P', E = 'E', Z = 'Z', Y = 'Y', }	local function is_valid(ucode, unit) if unit and not unit.more_ignored then assert(type(unit.symbol) == 'string' and unit.symbol ~= '') if unit.alias then if unit.link or unit.scale_text or unit.si then return false end end if unit.si then if unit.scale_text then return false end ucode = unit.ucode or ucode local base = unit.symbol if ucode == base then unit.display = base return true end local plen = #ucode - #base if plen > 0 then local prefix = si_prefixes[ucode:sub(1, plen)] if prefix and ucode:sub(plen + 1) == base then unit.display = prefix .. base return true end end else unit.display = unit.symbol return true end end return false end local lookup = require(convert_module)._unit local function show_convert(ucode, unit) -- If a built-in unit defines a scale or sets the SI flag, any unit defined in -- convert is not used (the scale or SI prefix's scale is used for a sort key). -- If there is no scale or SI flag, and the unit is not defined in convert, -- the sort key may not be correct; this allows such units to be identified. if not (unit.si or unit.scale_text) then if mode == 'convert' then unit.show = not lookup(unit.alias and unit.symbol or ucode).unknown unit.show_text = 'CONVERT' elseif mode == 'unknown' then unit.show = lookup(unit.alias and unit.symbol or ucode).unknown unit.show_text = 'UNKNOWN' elseif not unit.alias then -- Show convert's scale in square brackets ('[1]' for an unknown unit). -- Don't show scale for an alias because it's misleading for temperature -- and an alias is probably not useful for anything else. local scale = lookup(ucode, {value=1, sort='on'}).scaled_value if type(scale) == 'number' then scale = string.format('%.5g', scale):gsub('e%+?(%-?)0*(%d+)', 'e%1%2') else scale = '?' end unit.show = true unit.show_text = '[' .. scale .. ']'			end end end for line in definitions:gmatch('([^\n]*)\n') do		local pos, _ = line:find(' ', 1, true) if pos then local ucode = line:sub(1, pos - 1) local unit = get_builtin_unit(ucode, '\n' .. line .. '\n') if is_valid(ucode, unit) then show_convert(ucode, unit) local flags, text if unit.alias then text = unit.symbol else text = '' end if unit.isangle then unit.nospace = nil -- don't show redundant flag end for _, f in ipairs({						{ 'alias', 'ALIAS' },						{ 'isangle', 'ANGLE' },						{ 'nospace', 'NOSPACE' },						{ 'si', 'SI' },						{ 'scale_text', unit.scale_text },						{ 'show', unit.show_text },					}) do					if unit[f[1]] then local t = f[2] if t:match('^%u+$') then t = ' ' .. t .. ' '						end if flags then flags = flags .. ' ' .. t						else flags = t						end end end if flags then text = text .. ' • ' .. flags end add(ucode .. ' = ' .. text .. ' ') else add(line .. ' ◆ invalid definition ') end else add(line) end end return table.concat(result, '\n') end

local delimit_groups = require('Module:Gapnum').groups local function delimit(sign, numstr, fmt) -- Return sign and numstr (unsigned digits or numdot only) after formatting. -- Four-digit integers are not formatted with gaps. fmt = (fmt or ''):lower if fmt == 'none' or (fmt == '' and #numstr == 4 and numstr:match('^%d+$')) then return sign .. numstr end -- Group number by integer and decimal parts. -- If there is no decimal part, delimit_groups returns only one table. local ipart, dpart = delimit_groups(numstr) local result if fmt == 'commas' then result = sign .. table.concat(ipart, numsep) if dpart then result = result .. numdot .. table.concat(dpart) end else -- Delimit with a small gap by default. local groups = {} groups[1] = table.remove(ipart, 1) for _, v in ipairs(ipart) do table.insert(groups, ' ' .. v .. ' ') end if dpart then table.insert(groups, numdot .. (table.remove(dpart, 1) or '')) for _, v in ipairs(dpart) do table.insert(groups, ' ' .. v .. ' ') end end result = sign .. table.concat(groups) end return result end

local function sup_sub(sup, sub, align) -- Return the same result as Module:Su except val defaults to align=right. if align == 'l' or align == 'left' then align = 'left' elseif align == 'c' or align == 'center' then align = 'center' else align = 'right' end return '' .. sup .. ' ' .. sub .. ' ' end

local function range_text(items, unit_table, options) local fmt = options.fmt local nend = items.nend or '' if items.isrepeat or unit_table.isangle then nend = nend .. unit_table.text end local text = '' for i = 1, #items do		if i % 2 == 0 then text = text .. items[i] else text = text .. delimit(items[i].sign, items[i].clean, fmt) .. nend end end return text end

local function uncertainty_text(uncertainty, unit_table, options) local angle, text, need_parens if unit_table.isangle then angle = unit_table.text end local upper = uncertainty.upper or {} local lower = uncertainty.lower or {} local uncU = upper.clean if uncU then local fmt = options.fmt local uncL = lower.clean if uncL then uncU = delimit('+', uncU, fmt) .. (upper.errend or '') uncL = delimit('−', uncL, fmt) .. (lower.errend or '') if angle then uncU = uncU .. angle uncL = uncL .. angle end text = (angle or '') .. ' ' ..				sup_sub(uncU, uncL, options.align) .. ' '		else if upper.parens then text = '(' .. uncU .. ')' -- old template did not delimit else text = (angle or '') .. ' ± ' ..					delimit('', uncU, fmt) need_parens = true end if uncertainty.errend then text = text .. uncertainty.errend end if angle then text = text .. angle end end else if angle then text = angle end end return text, need_parens end

local function _main(values, unit_spec, options) if options.sandbox then data_module = data_module .. '/sandbox' convert_module = convert_module .. '/sandbox' end local action = options.action if action then if action == 'list' then -- Kludge: am using the align parameter (a=xxx) for type of list. return list_units(options.align) end return valerror('invalid action "' .. action .. '".', options.nocat) end local number = values.number or (values.numbers and values.numbers[1]) or {} local e_10 = options.e or {} local novalue = (number.value == nil and e_10.clean == nil) local fmt = options.fmt local want_sort = true local sortable = options.sortable if sortable == 'off' or (sortable == nil and novalue) then want_sort = false elseif sortable == 'debug' then -- Same as sortable = 'on' but the sort key is displayed. else sortable = 'on' end local sort_value = 1 if want_sort then sort_value = number.value or 1 if e_10.value and sort_value ~= 0 then -- The 'if' avoids $0$ giving an invalid sort_value due to overflow. sort_value = sort_value * 10^e_10.value end end local unit_table = makeunit(sort_value, {						u = unit_spec.u,						want_link = unit_spec.want_link,						per = unit_spec.per,						want_per_link = unit_spec.want_per_link,						nospace = novalue,						want_longscale = unit_spec.want_longscale,						sortable = sortable,					}) local sortkey if unit_table then if want_sort then sortkey = unit_table.sortkey end else unit_table = { text = '' } if want_sort then sortkey = convert_lookup('dummy', sort_value, nil, nil, nil, { sortable = sortable }).sortspan end end local final_unit = unit_table.isangle and '' or unit_table.text local e_text, n_text, need_parens local uncertainty = values.uncertainty if uncertainty then if number.clean then n_text = delimit(number.sign, number.clean, fmt) .. (number.nend or '') local text text, need_parens = uncertainty_text(uncertainty, unit_table, options) if text then n_text = n_text .. text end else n_text = '' end else if values.numbers.isrepeat then final_unit = '' end n_text = range_text(values.numbers, unit_table, options) need_parens = true end if e_10.clean then if need_parens then n_text = '(' .. n_text .. ')' end e_text = '10' .. delimit(e_10.sign, e_10.clean, fmt) .. ''		if number.clean then e_text = ' × ' .. e_text end else e_text = '' end local result = (sortkey or '') .. (options.prefix or '') .. n_text .. e_text .. final_unit .. (options.suffix or '') if result ~= '' then result = ' ' .. result .. ' '	end return result .. (options.warning or '') end

local function check_parameters(args, has_ranges, nocat) -- Return warning text for the first problem parameter found, or nothing if ok. local whitelist = { a = true, action = true, debug = true, e = true, ['end'] = true, errend = true, ['+errend'] = true, ['-errend'] = true, fmt = true, ['long scale'] = true, long_scale = true, longscale = true, nocategory = true, p = true, s = true, sortable = true, u = true, ul = true, up = true, upl = true, }	for k, v in pairs(args) do		if type(k) == 'string' and not whitelist[k] then local warning = string.format(mtext['mt-val-not-supported'], k, v)			return valerror(warning, nocat, true) end end if not has_ranges and args[4] then return valerror(mtext['mt-ignore-parameter4'], nocat, true) end end

local function main(frame) local getArgs = require('Module:Arguments').getArgs local args = getArgs(frame, {wrappers = { 'Template:Val' }}) local nocat = args.nocategory local numbers = {} -- table of number tables, perhaps with range text local msg = get_args(numbers, args) if msg then return valerror(msg, nocat) end if args.u and args.ul then return valerror(mtext['mt-both-u-ul'], nocat) end if args.up and args.upl then return valerror(mtext['mt-both-up-upl'], nocat) end local values if numbers.has_ranges then -- Multiple values with range separators but no uncertainty. numbers.nend = args['end'] values = { numbers = numbers, }	else -- A single value with optional uncertainty. local function setfield(i, dst, src) local v = args[src] if v then if numbers[i] then numbers[i][dst] = v				else numbers[i] = { [dst] = v } end end end setfield(1, 'nend', 'end') setfield(2, 'errend', '+errend') setfield(3, 'errend', '-errend') values = { number = numbers[1], uncertainty = { upper = numbers[2], lower = numbers[3], errend = args.errend, }		}	end local unit_spec = { u = args.ul or args.u,			want_link = args.ul ~= nil, per = args.upl or args.up, want_per_link = args.upl ~= nil, want_longscale = (args.longscale or args.long_scale or args['long scale']) == 'on', }	local options = { action = args.action, align = args.a,			e = numbers.e,			fmt = args.fmt, nocat = nocat, prefix = args.p,			sandbox = string.find(frame:getTitle, 'sandbox', 1, true) ~= nil, sortable = args.sortable or (args.debug == 'yes' and 'debug' or nil), suffix = args.s,			warning = check_parameters(args, numbers.has_ranges, nocat), }	return _main(values, unit_spec, options) end

return { main = main, _main = _main }