Module:Val

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

local data_module -- name of module defining units local delimit_groups = require('Module:Gapnum').groups

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 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 commas are removed so 1,234 is the same as 1234. local which = index local function fail(msg) local description if which == 'e' then description = 'exponent parameter (e)' else description = 'parameter ' .. which end return description .. ' ' .. (msg or 'is not a valid 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('cannot use a range if the first parameter includes "e"') end numbers.has_ranges = true else if not numbers.has_ranges then return fail('needs a range in parameter 2') 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('does not accept a range') end if numbers.has_ranges and type(index) == 'number' and (index % 2 == 0) then return fail('should be a range') end if index == 'e' then local e = numbers[1] and numbers[1].exp if e then if arg then return fail('cannot be used if the first parameter includes "e"') end arg = e			which = 1 end end if arg and arg ~= '' then arg = arg:gsub(',', '') 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](.+)$') if a then if index == 1 then arg = a				result.exp = b			else return fail('cannot use e notation') end end local isnegative, propersign, prefix local minus = '−' prefix, arg = arg:match('^(.-)([%d.]+)$') 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 'too many parameters' end end if numbers.has_ranges and (#numbers % 2 == 0) then return 'need a number after the last parameter because it is a range.' 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('Unit "' .. ucode .. '" has invalid scale "' .. 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('\n', pos, true) if endline then local result = {} local n = 0 local text = definitions:sub(pos, 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('Module:Convert/sandbox')._unit -- TODO remove "/sandbox" when convert updated 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_result if result then use_result = true if result.alias then ucode = result.symbol use_result = false 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_result = false end end local convert_unit = convert_lookup(ucode, value, scaled_top, want_link, si, options) if use_result then if want_link then result.text =  .. result.symbol ..  else result.text = result.symbol end result.sortkey = convert_unit.sortspan result.scaled_top = value else result = { text = convert_unit.text, sortkey = convert_unit.sortspan, scaled_top = convert_unit.scaled_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 then text = ' ' .. text end return { text = text, isangle = unit.isangle, sortkey = sortkey } end

local function list_units -- 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) -- LATER Check for valid combinations of links/flags. if unit and not unit.more_ignored then if unit.si then 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 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 local flags, text if unit.alias then text = unit.symbol else text =  .. unit.display ..  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 },					}) 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 function delimit(sign, numstr, fmt) -- Return sign and numstr (unsigned digits or '.' 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, ',') if dpart then result = result .. '.' .. 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, '.' .. (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) data_module = 'Module:Val/units' .. (options.sandbox and '/sandbox' or '') local action = options.action if action then if action == 'list' then return list_units 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 fmt = options.fmt local want_sort = true local sortable = options.sortable if sortable == 'off' 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,						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 = '' if not e_10.clean then e_10.clean = '0' e_10.sign = '' end 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 return ' ' ..		(sortkey or '') .. (options.prefix or '') .. n_text .. e_text .. final_unit .. (options.suffix or '') .. ' ' ..		(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 = 'Val parameter "' .. k .. '=' .. v .. '" is not supported' return valerror(warning, nocat, true) end end if not has_ranges and args[4] then return valerror('Val parameter 4 ignored', nocat, true) end end

local function main(frame) local getArgs = require('Module:Arguments').getArgs local args = getArgs(frame, {wrappers = { 'Template:Val', 'Template:Val/sandboxlua' }}) 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('unit (u) and unit with link (ul) are both specified, only one is allowed.', nocat) end if args.up and args.upl then return valerror('unit per (up) and unit per with link (upl) are both specified, only one is allowed.', 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 'on'), suffix = args.s,			warning = check_parameters(args, numbers.has_ranges, nocat), }	return _main(values, unit_spec, options) end

return { main = main, _main = _main }