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Module:ConvertNumeric (
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Usage
{{#invoke:ConvertNumeric|function_name}}
See also
- {{ Spellnum per MOS}}
- {{ Number to word}}
- Module:Strip to numbers – extract a number from a string (supports negatives and decimals) and return it, or optionally return a halved value
-- Module for converting between different representations of numbers. See talk page for user documentation.
-- For unit tests see: [[Module:ConvertNumeric/testcases]]
-- When editing, preview with: [[Module_talk:ConvertNumeric/testcases]]
-- First, edit [[Module:ConvertNumeric/sandbox]], then preview with [[Module_talk:ConvertNumeric/sandbox/testcases]]
require[[strict]]
local ones_position = {
0 = 'zero',
1 = 'one',
2 = 'two',
3 = 'three',
4 = 'four',
5 = 'five',
6 = 'six',
7 = 'seven',
8 = 'eight',
9 = 'nine',
10 = 'ten',
11 = 'eleven',
12 = 'twelve',
13 = 'thirteen',
14 = 'fourteen',
15 = 'fifteen',
16 = 'sixteen',
17 = 'seventeen',
18 = 'eighteen',
19 = 'nineteen'
}
local ones_position_ord = {
0 = 'zeroth',
1 = 'first',
2 = 'second',
3 = 'third',
4 = 'fourth',
5 = 'fifth',
6 = 'sixth',
7 = 'seventh',
8 = 'eighth',
9 = 'ninth',
10 = 'tenth',
11 = 'eleventh',
12 = 'twelfth',
13 = 'thirteenth',
14 = 'fourteenth',
15 = 'fifteenth',
16 = 'sixteenth',
17 = 'seventeenth',
18 = 'eighteenth',
19 = 'nineteenth'
}
local ones_position_plural = {
0 = 'zeros',
1 = 'ones',
2 = 'twos',
3 = 'threes',
4 = 'fours',
5 = 'fives',
6 = 'sixes',
7 = 'sevens',
8 = 'eights',
9 = 'nines',
10 = 'tens',
11 = 'elevens',
12 = 'twelves',
13 = 'thirteens',
14 = 'fourteens',
15 = 'fifteens',
16 = 'sixteens',
17 = 'seventeens',
18 = 'eighteens',
19 = 'nineteens'
}
local tens_position = {
2 = 'twenty',
3 = 'thirty',
4 = 'forty',
5 = 'fifty',
6 = 'sixty',
7 = 'seventy',
8 = 'eighty',
9 = 'ninety'
}
local tens_position_ord = {
2 = 'twentieth',
3 = 'thirtieth',
4 = 'fortieth',
5 = 'fiftieth',
6 = 'sixtieth',
7 = 'seventieth',
8 = 'eightieth',
9 = 'ninetieth'
}
local tens_position_plural = {
2 = 'twenties',
3 = 'thirties',
4 = 'forties',
5 = 'fifties',
6 = 'sixties',
7 = 'seventies',
8 = 'eighties',
9 = 'nineties'
}
local groups = {
1 = 'thousand',
2 = 'million',
3 = 'billion',
4 = 'trillion',
5 = 'quadrillion',
6 = 'quintillion',
7 = 'sextillion',
8 = 'septillion',
9 = 'octillion',
10 = 'nonillion',
11 = 'decillion',
12 = 'undecillion',
13 = 'duodecillion',
14 = 'tredecillion',
15 = 'quattuordecillion',
16 = 'quindecillion',
17 = 'sexdecillion',
18 = 'septendecillion',
19 = 'octodecillion',
20 = 'novemdecillion',
21 = 'vigintillion',
22 = 'unvigintillion',
23 = 'duovigintillion',
24 = 'tresvigintillion',
25 = 'quattuorvigintillion',
26 = 'quinquavigintillion',
27 = 'sesvigintillion',
28 = 'septemvigintillion',
29 = 'octovigintillion',
30 = 'novemvigintillion',
31 = 'trigintillion',
32 = 'untrigintillion',
33 = 'duotrigintillion',
34 = 'trestrigintillion',
35 = 'quattuortrigintillion',
36 = 'quinquatrigintillion',
37 = 'sestrigintillion',
38 = 'septentrigintillion',
39 = 'octotrigintillion',
40 = 'noventrigintillion',
41 = 'quadragintillion',
51 = 'quinquagintillion',
61 = 'sexagintillion',
71 = 'septuagintillion',
81 = 'octogintillion',
91 = 'nonagintillion',
101 = 'centillion',
102 = 'uncentillion',
103 = 'duocentillion',
104 = 'trescentillion',
111 = 'decicentillion',
112 = 'undecicentillion',
121 = 'viginticentillion',
122 = 'unviginticentillion',
131 = 'trigintacentillion',
141 = 'quadragintacentillion',
151 = 'quinquagintacentillion',
161 = 'sexagintacentillion',
171 = 'septuagintacentillion',
181 = 'octogintacentillion',
191 = 'nonagintacentillion',
201 = 'ducentillion',
301 = 'trecentillion',
401 = 'quadringentillion',
501 = 'quingentillion',
601 = 'sescentillion',
701 = 'septingentillion',
801 = 'octingentillion',
901 = 'nongentillion',
1001 = 'millinillion',
}
local roman_numerals = {
I = 1,
V = 5,
X = 10,
L = 50,
C = 100,
D = 500,
M = 1000
}
local engord_tens_end = {
'twentieth' = 20,
'thirtieth' = 30,
'fortieth' = 40,
'fiftieth' = 50,
'sixtieth' = 60,
'seventieth' = 70,
'eightieth' = 80,
'ninetieth' = 90,
}
local eng_tens_cont = {
'twenty' = 20,
'thirty' = 30,
'forty' = 40,
'fifty' = 50,
'sixty' = 60,
'seventy' = 70,
'eighty' = 80,
'ninety' = 90,
}
-- Converts a given valid roman numeral (and some invalid roman numerals) to a number. Returns { -1, errorstring } on error.
local function roman_to_numeral(roman)
if type(roman) ~= "string" then return -1, "roman numeral not a string" end
local rev = roman:reverse()
local raising = true
local last = 0
local result = 0
for i = 1, #rev do
local c = rev:sub(i, i)
local next = roman_numeralsc
if next == nil then return -1, "roman numeral contains illegal character " .. c end
if next > last then
result = result + next
raising = true
elseif next < last then
result = result - next
raising = false
elseif raising then
result = result + next
else
result = result - next
end
last = next
end
return result
end
-- Converts a given integer between 0 and 100 to English text (e.g. 47 -> forty-seven).
local function numeral_to_english_less_100(num, ordinal, plural, zero)
local terminal_ones, terminal_tens
if ordinal then
terminal_ones = ones_position_ord
terminal_tens = tens_position_ord
elseif plural then
terminal_ones = ones_position_plural
terminal_tens = tens_position_plural
else
terminal_ones = ones_position
terminal_tens = tens_position
end
if num == 0 and zero ~= nil then
return zero
elseif num < 20 then
return terminal_onesnum
elseif num % 10 == 0 then
return terminal_tensnum / 10
else
return tens_positionmath.floor(num / 10)] .. '-' .. terminal_onesnum % 10
end
end
local function standard_suffix(ordinal, plural)
if ordinal then return 'th' end
if plural then return 's' end
return ''
end
-- Converts a given integer (in string form) between 0 and 1000 to English text (e.g. 47 -> forty-seven).
local function numeral_to_english_less_1000(num, use_and, ordinal, plural, zero)
num = tonumber(num)
if num < 100 then
return numeral_to_english_less_100(num, ordinal, plural, zero)
elseif num % 100 == 0 then
return ones_positionnum/100 .. ' hundred' .. standard_suffix(ordinal, plural)
else
return ones_positionmath.floor(num/100)] .. ' hundred ' .. (use_and and 'and ' or '') .. numeral_to_english_less_100(num % 100, ordinal, plural, zero)
end
end
-- Converts an ordinal in English text from 'zeroth' to 'ninety-ninth' inclusive to a number [0–99], else -1.
local function english_to_ordinal(english)
local eng = string.lower(english or '')
local engord_lt20 = {} -- ones_position_ord{} keys & values swapped
for k, v in pairs( ones_position_ord ) do
engord_lt20v = k
end
if engord_lt20eng then
return engord_lt20eng -- e.g. first -> 1
elseif engord_tens_endeng then
return engord_tens_endeng -- e.g. ninetieth -> 90
else
local tens, ones = string.match(eng, '^([a-z]+)[%s%-]+([a-z]+)$')
if tens and ones then
local tens_cont = eng_tens_conttens
local ones_end = engord_lt20ones
if tens_cont and ones_end then
return tens_cont + ones_end -- e.g. ninety-ninth -> 99
end
end
end
return -1 -- Failed
end
-- Converts a number in English text from 'zero' to 'ninety-nine' inclusive to a number [0–99], else -1.
local function english_to_numeral(english)
local eng = string.lower(english or '')
local eng_lt20 = { 'single' = 1 } -- ones_position{} keys & values swapped
for k, v in pairs( ones_position ) do
eng_lt20v = k
end
if eng_lt20eng then
return eng_lt20eng -- e.g. one -> 1
elseif eng_tens_conteng then
return eng_tens_conteng -- e.g. ninety -> 90
else
local tens, ones = string.match(eng, '^([a-z]+)[%s%-]+([a-z]+)$')
if tens and ones then
local tens_cont = eng_tens_conttens
local ones_end = eng_lt20ones
if tens_cont and ones_end then
return tens_cont + ones_end -- e.g. ninety-nine -> 99
end
end
end
return -1 -- Failed
end
-- Converts a number expressed as a string in scientific notation to a string in standard decimal notation
-- e.g. 1.23E5 -> 123000, 1.23E-5 = .0000123. Conversion is exact, no rounding is performed.
local function scientific_notation_to_decimal(num)
local exponent, subs = num:gsub("^%-?%d*%.?%d*%-?[Ee]([+%-]?%d+)$", "%1")
if subs == 0 then return num end -- Input not in scientific notation, just return unmodified
exponent = tonumber(exponent)
local negative = num:find("^%-")
local _, decimal_pos = num:find("%.")
-- Mantissa will consist of all decimal digits with no decimal point
local mantissa = num:gsub("^%-?(%d*)%.?(%d*)%-?[Ee][+%-]?%d+$", "%1%2")
if negative and decimal_pos then decimal_pos = decimal_pos - 1 end
decimal_pos = decimal_pos or #mantissa + 1
-- Remove leading zeros unless decimal point is in first position
while decimal_pos > 1 and mantissa:sub(1,1) == '0' do
mantissa = mantissa:sub(2)
decimal_pos = decimal_pos - 1
end
-- Shift decimal point right for exponent > 0
while exponent > 0 do
decimal_pos = decimal_pos + 1
exponent = exponent - 1
if decimal_pos > #mantissa + 1 then mantissa = mantissa .. '0' end
-- Remove leading zeros unless decimal point is in first position
while decimal_pos > 1 and mantissa:sub(1,1) == '0' do
mantissa = mantissa:sub(2)
decimal_pos = decimal_pos - 1
end
end
-- Shift decimal point left for exponent < 0
while exponent < 0 do
if decimal_pos == 1 then
mantissa = '0' .. mantissa
else
decimal_pos = decimal_pos - 1
end
exponent = exponent + 1
end
-- Insert decimal point in correct position and return
return (negative and '-' or '') .. mantissa:sub(1, decimal_pos - 1) .. '.' .. mantissa:sub(decimal_pos)
end
-- Rounds a number to the nearest integer (NOT USED)
local function round_num(x)
if x%1 >= 0.5 then
return math.ceil(x)
else
return math.floor(x)
end
end
-- Rounds a number to the nearest two-word number (round = up, down, or "on" for round to nearest).
-- Numbers with two digits before the decimal will be rounded to an integer as specified by round.
-- Larger numbers will be rounded to a number with only one nonzero digit in front and all other digits zero.
-- Negative sign is preserved and does not count towards word limit.
local function round_for_english(num, round)
-- If an integer with at most two digits, just return
if num:find("^%-?%d?%d%.?$") then return num end
local negative = num:find("^%-")
if negative then
-- We're rounding magnitude so flip it
if round == 'up' then round = 'down' elseif round == 'down' then round = 'up' end
end
-- If at most two digits before decimal, round to integer and return
local _, _, small_int, trailing_digits, round_digit = num:find("^%-?(%d?%d?)%.((%d)%d*)$")
if small_int then
if small_int == '' then small_int = '0' end
if (round == 'up' and trailing_digits:find('[1-9]')) or (round == 'on' and tonumber(round_digit) >= 5) then
small_int = tostring(tonumber(small_int) + 1)
end
return (negative and '-' or '') .. small_int
end
-- When rounding up, any number with > 1 nonzero digit will round up (e.g. 1000000.001 rounds up to 2000000)
local nonzero_digits = 0
for digit in num:gfind("[1-9]") do
nonzero_digits = nonzero_digits + 1
end
num = num:gsub("%.%d*$", "") -- Remove decimal part
-- Second digit used to determine which way to round lead digit
local _, _, lead_digit, round_digit, round_digit_2, rest = num:find("^%-?(%d)(%d)(%d)(%d*)$")
if tonumber(lead_digit .. round_digit) < 20 and (1 + #rest) % 3 == 0 then
-- In English numbers < 20 are one word so put 2 digits in lead and round based on 3rd
lead_digit = lead_digit .. round_digit
round_digit = round_digit_2
else
rest = round_digit_2 .. rest
end
if (round == 'up' and nonzero_digits > 1) or (round == 'on' and tonumber(round_digit) >= 5) then
lead_digit = tostring(tonumber(lead_digit) + 1)
end
-- All digits but lead digit will turn to zero
rest = rest:gsub("%d", "0")
return (negative and '-' or '') .. lead_digit .. '0' .. rest
end
local denominators = {
2 = { 'half', plural = 'halves' },
3 = { 'third' },
4 = { 'quarter', us = 'fourth' },
5 = { 'fifth' },
6 = { 'sixth' },
8 = { 'eighth' },
9 = { 'ninth' },
10 = { 'tenth' },
16 = { 'sixteenth' },
}
-- Return status, fraction where:
-- status is a string:
-- "finished" if there is a fraction with no whole number;
-- "ok" if fraction is empty or valid;
-- "unsupported" if bad fraction;
-- fraction is a string giving (numerator / denominator) as English text, or is "".
-- Only unsigned fractions with a very limited range of values are supported,
-- except that if whole is empty, the numerator can use "-" to indicate negative.
-- whole (string or nil): nil or "" if no number before the fraction
-- numerator (string or nil): numerator, if any (default = 1 if a denominator is given)
-- denominator (string or nil): denominator, if any
-- sp_us (boolean): true if sp=us
-- negative_word (string): word to use for negative sign, if whole is empty
-- use_one (boolean): false: 2+1/2 → "two and a half"; true: "two and one-half"
local function fraction_to_english(whole, numerator, denominator, sp_us, negative_word, use_one)
if numerator or denominator then
local finished = (whole == nil or whole == '')
local sign = ''
if numerator then
if finished and numerator:sub(1, 1) == '-' then
numerator = numerator:sub(2)
sign = negative_word .. ' '
end
else
numerator = '1'
end
if not numerator:match('^%d+$') or not denominator or not denominator:match('^%d+$') then
return 'unsupported', ''
end
numerator = tonumber(numerator)
denominator = tonumber(denominator)
local dendata = denominatorsdenominator
if not (dendata and 1 <= numerator and numerator <= 99) then
return 'unsupported', ''
end
local numstr, denstr
local sep = '-'
if numerator == 1 then
denstr = sp_us and dendata.us or dendata1
if finished or use_one then
numstr = 'one'
elseif denstr:match('^[aeiou]') then
numstr = 'an'
sep = ' '
else
numstr = 'a'
sep = ' '
end
else
numstr = numeral_to_english_less_100(numerator)
denstr = dendata.plural or (sp_us and dendata.us or dendata1]) .. 's'
end
if finished then
return 'finished', sign .. numstr .. sep .. denstr
end
return 'ok', ' and ' .. numstr .. sep .. denstr
end
return 'ok', ''
end
-- Takes a decimal number and converts it to English text.
-- Return nil if a fraction cannot be converted (only some numbers are supported for fractions).
-- num (string or nil): the number to convert.
-- Can be an arbitrarily large decimal, such as "-123456789123456789.345", and
-- can use scientific notation (e.g. "1.23E5").
-- May fail for very large numbers not listed in "groups" such as "1E4000".
-- num is nil if there is no whole number before a fraction.
-- numerator (string or nil): numerator of fraction (nil if no fraction)
-- denominator (string or nil): denominator of fraction (nil if no fraction)
-- capitalize (boolean): whether to capitalize the result (e.g. 'One' instead of 'one')
-- use_and (boolean): whether to use the word 'and' between tens/ones place and higher places
-- hyphenate (boolean): whether to hyphenate all words in the result, useful as an adjective
-- ordinal (boolean): whether to produce an ordinal (e.g. 'first' instead of 'one')
-- plural (boolean): whether to pluralize the resulting number
-- links: nil: do not add any links; 'on': link "billion" and larger to Orders of magnitude article;
-- any other text: list of numbers to link (e.g. "billion,quadrillion")
-- negative_word: word to use for negative sign (typically 'negative' or 'minus'; nil to use default)
-- round: nil or '': no rounding; 'on': round to nearest two-word number; 'up'/'down': round up/down to two-word number
-- zero: word to use for value '0' (nil to use default)
-- use_one (boolean): false: 2+1/2 → "two and a half"; true: "two and one-half"
local function _numeral_to_english(num, numerator, denominator, capitalize, use_and, hyphenate, ordinal, plural, links, negative_word, round, zero, use_one)
if not negative_word then
if use_and then
-- TODO Should 'minus' be used when do not have sp=us?
-- If so, need to update testcases, and need to fix "minus zero".
-- negative_word = 'minus'
negative_word = 'negative'
else
negative_word = 'negative'
end
end
local status, fraction_text = fraction_to_english(num, numerator, denominator, not use_and, negative_word, use_one)
if status == 'unsupported' then
return nil
end
if status == 'finished' then
-- Input is a fraction with no whole number.
-- Hack to avoid executing stuff that depends on num being a number.
local s = fraction_text
if hyphenate then s = s:gsub("%s", "-") end
if capitalize then s = s:gsub("^%l", string.upper) end
return s
end
num = scientific_notation_to_decimal(num)
if round and round ~= '' then
if round ~= 'on' and round ~= 'up' and round ~= 'down' then
error("Invalid rounding mode")
end
num = round_for_english(num, round)
end
-- Separate into negative sign, num (digits before decimal), decimal_places (digits after decimal)
local MINUS = '−' -- Unicode U+2212 MINUS SIGN (may be in values from [[Module:Convert]])
if num:sub(1, #MINUS) == MINUS then
num = '-' .. num:sub(#MINUS + 1) -- replace MINUS with '-'
elseif num:sub(1, 1) == '+' then
num = num:sub(2) -- ignore any '+'
end
local negative = num:find("^%-")
local decimal_places, subs = num:gsub("^%-?%d*%.(%d+)$", "%1")
if subs == 0 then decimal_places = nil end
num, subs = num:gsub("^%-?(%d*)%.?%d*$", "%1")
if num == '' and decimal_places then num = '0' end
if subs == 0 or num == '' then error("Invalid decimal numeral") end
-- For each group of 3 digits except the last one, print with appropriate group name (e.g. million)
local s = ''
while #num > 3 do
if s ~= '' then s = s .. ' ' end
local group_num = math.floor((#num - 1) / 3)
local group = groupsgroup_num
local group_digits = #num - group_num*3
s = s .. numeral_to_english_less_1000(num:sub(1, group_digits), false, false, false, zero) .. ' '
if links and (((links == 'on' and group_num >= 3) or links:find(group)) and group_num <= 13) then
s = s .. '[[Orders_of_magnitude_(numbers)#10' .. group_num*3 .. '|' .. group .. ']]'
else
s = s .. group
end
num = num:sub(1 + group_digits)
num = num:gsub("^0*", "") -- Trim leading zeros
end
-- Handle final three digits of integer part
if s ~= '' and num ~= '' then
if #num <= 2 and use_and then
s = s .. ' and '
else
s = s .. ' '
end
end
if s == '' or num ~= '' then
s = s .. numeral_to_english_less_1000(num, use_and, ordinal, plural, zero)
elseif ordinal or plural then
-- Round numbers like "one million" take standard suffixes for ordinal/plural
s = s .. standard_suffix(ordinal, plural)
end
-- For decimal places (if any) output "point" followed by spelling out digit by digit
if decimal_places then
s = s .. ' point'
for i = 1, #decimal_places do
s = s .. ' ' .. ones_positiontonumber(decimal_places:sub(i,i))]
end
end
s = s:gsub("^%s*(.-)%s*$", "%1") -- Trim whitespace
if ordinal and plural then s = s .. 's' end -- s suffix works for all ordinals
if negative and s ~= zero then s = negative_word .. ' ' .. s end
s = s:gsub("negative zero", "zero")
s = s .. fraction_text
if hyphenate then s = s:gsub("%s", "-") end
if capitalize then s = s:gsub("^%l", string.upper) end
return s
end
local function _numeral_to_english2(args)
local num = tostring(args.num)
num = num:gsub("^%s*(.-)%s*$", "%1") -- Trim whitespace
num = num:gsub(",", "") -- Remove commas
num = num:gsub("^<span[^<>]*></span>", "") -- Generated by Template:age
if num ~= '' then -- a fraction may have an empty whole number
if not num:find("^%-?%d*%.?%d*%-?[Ee]?[+%-]?%d*$") then
-- Input not in a valid format, try to eval it as an expr to see
-- if that produces a number (e.g. "3 + 5" will become "8").
local noerr, result = pcall(mw.ext.ParserFunctions.expr, num)
if noerr then
num = result
end
end
end
-- Call helper function passing args
return _numeral_to_english(
num,
args'numerator'],
args'denominator'],
args'capitalize'],
args'use_and'],
args'hyphenate'],
args'ordinal'],
args'plural'],
args'links'],
args'negative_word'],
args'round'],
args'zero'],
args'use_one'
) or ''
end
local p = { -- Functions that can be called from another module
roman_to_numeral = roman_to_numeral,
spell_number = _numeral_to_english,
spell_number2 = _numeral_to_english2,
english_to_ordinal = english_to_ordinal,
english_to_numeral = english_to_numeral,
}
function p._roman_to_numeral(frame) -- Callable via {{#invoke:ConvertNumeric|_roman_to_numeral|VI}}
return roman_to_numeral(frame.args1])
end
function p._english_to_ordinal(frame) -- callable via {{#invoke:ConvertNumeric|_english_to_ordinal|First}}
return english_to_ordinal(frame.args1])
end
function p._english_to_numeral(frame) -- callable via {{#invoke:ConvertNumeric|_english_to_numeral|One}}
return english_to_numeral(frame.args1])
end
function p.numeral_to_english(frame)
local args = frame.args
-- Tail call to helper function passing args from frame
return _numeral_to_english2{
'num' = args1],
'numerator' = args'numerator'],
'denominator' = args'denominator'],
'capitalize' = args'case' == 'U' or args'case' == 'u',
'use_and' = args'sp' ~= 'us',
'hyphenate' = args'adj' == 'on',
'ordinal' = args'ord' == 'on',
'plural' = args'pl' == 'on',
'links' = args'lk'],
'negative_word' = args'negative'],
'round' = args'round'],
'zero' = args'zero'],
'use_one' = args'one' == 'one' -- experiment: using '|one=one' makes fraction 2+1/2 give "two and one-half" instead of "two and a half"
}
end
---- recursive function for p.decToHex
local function decToHexDigit(dec)
local dig = {"0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"}
local div = math.floor(dec/16)
local mod = dec-(16*div)
if div >= 1 then return decToHexDigit(div)..digmod+1 else return digmod+1 end
end -- I think this is supposed to be done with a tail call but first I want something that works at all
---- finds all the decimal numbers in the input text and hexes each of them
function p.decToHex(frame)
local args=frame.args
local parent=frame.getParent(frame)
local pargs={}
if parent then pargs=parent.args end
local text=args1 or pargs1 or ""
local minlength=args.minlength or pargs.minlength or 1
minlength=tonumber(minlength)
local prowl=mw.ustring.gmatch(text,"(.-)(%d+)")
local output=""
repeat
local chaff,dec=prowl()
if not(dec) then break end
local hex=decToHexDigit(dec)
while (mw.ustring.len(hex)<minlength) do hex="0"..hex end
output=output..chaff..hex
until false
local chaff=mw.ustring.match(text,"(%D+)$") or ""
return output..chaff
end
return p
| This is the
module sandbox page for
Module:ConvertNumeric (
diff). See also the companion subpage for test cases ( run). |
| This Lua module is used on approximately 22,000 pages and changes may be widely noticed. Test changes in the module's /sandbox or /testcases subpages, or in your own module sandbox. Consider discussing changes on the talk page before implementing them. |
| This Lua module is used in
MediaWiki:Watchlist-messages, and on
approximately 22,000 pages. Changes to it can cause immediate changes to the Wikipedia user interface. To avoid major disruption, any changes should be tested in the module's /sandbox or /testcases subpages, or in your own module sandbox. The tested changes can be added to this page in a single edit. Please discuss changes on the talk page before implementing them. |
Usage
{{#invoke:ConvertNumeric|function_name}}
See also
- {{ Spellnum per MOS}}
- {{ Number to word}}
- Module:Strip to numbers – extract a number from a string (supports negatives and decimals) and return it, or optionally return a halved value
-- Module for converting between different representations of numbers. See talk page for user documentation.
-- For unit tests see: [[Module:ConvertNumeric/testcases]]
-- When editing, preview with: [[Module_talk:ConvertNumeric/testcases]]
-- First, edit [[Module:ConvertNumeric/sandbox]], then preview with [[Module_talk:ConvertNumeric/sandbox/testcases]]
require[[strict]]
local ones_position = {
0 = 'zero',
1 = 'one',
2 = 'two',
3 = 'three',
4 = 'four',
5 = 'five',
6 = 'six',
7 = 'seven',
8 = 'eight',
9 = 'nine',
10 = 'ten',
11 = 'eleven',
12 = 'twelve',
13 = 'thirteen',
14 = 'fourteen',
15 = 'fifteen',
16 = 'sixteen',
17 = 'seventeen',
18 = 'eighteen',
19 = 'nineteen'
}
local ones_position_ord = {
0 = 'zeroth',
1 = 'first',
2 = 'second',
3 = 'third',
4 = 'fourth',
5 = 'fifth',
6 = 'sixth',
7 = 'seventh',
8 = 'eighth',
9 = 'ninth',
10 = 'tenth',
11 = 'eleventh',
12 = 'twelfth',
13 = 'thirteenth',
14 = 'fourteenth',
15 = 'fifteenth',
16 = 'sixteenth',
17 = 'seventeenth',
18 = 'eighteenth',
19 = 'nineteenth'
}
local ones_position_plural = {
0 = 'zeros',
1 = 'ones',
2 = 'twos',
3 = 'threes',
4 = 'fours',
5 = 'fives',
6 = 'sixes',
7 = 'sevens',
8 = 'eights',
9 = 'nines',
10 = 'tens',
11 = 'elevens',
12 = 'twelves',
13 = 'thirteens',
14 = 'fourteens',
15 = 'fifteens',
16 = 'sixteens',
17 = 'seventeens',
18 = 'eighteens',
19 = 'nineteens'
}
local tens_position = {
2 = 'twenty',
3 = 'thirty',
4 = 'forty',
5 = 'fifty',
6 = 'sixty',
7 = 'seventy',
8 = 'eighty',
9 = 'ninety'
}
local tens_position_ord = {
2 = 'twentieth',
3 = 'thirtieth',
4 = 'fortieth',
5 = 'fiftieth',
6 = 'sixtieth',
7 = 'seventieth',
8 = 'eightieth',
9 = 'ninetieth'
}
local tens_position_plural = {
2 = 'twenties',
3 = 'thirties',
4 = 'forties',
5 = 'fifties',
6 = 'sixties',
7 = 'seventies',
8 = 'eighties',
9 = 'nineties'
}
local groups = {
1 = 'thousand',
2 = 'million',
3 = 'billion',
4 = 'trillion',
5 = 'quadrillion',
6 = 'quintillion',
7 = 'sextillion',
8 = 'septillion',
9 = 'octillion',
10 = 'nonillion',
11 = 'decillion',
12 = 'undecillion',
13 = 'duodecillion',
14 = 'tredecillion',
15 = 'quattuordecillion',
16 = 'quindecillion',
17 = 'sexdecillion',
18 = 'septendecillion',
19 = 'octodecillion',
20 = 'novemdecillion',
21 = 'vigintillion',
22 = 'unvigintillion',
23 = 'duovigintillion',
24 = 'tresvigintillion',
25 = 'quattuorvigintillion',
26 = 'quinquavigintillion',
27 = 'sesvigintillion',
28 = 'septemvigintillion',
29 = 'octovigintillion',
30 = 'novemvigintillion',
31 = 'trigintillion',
32 = 'untrigintillion',
33 = 'duotrigintillion',
34 = 'trestrigintillion',
35 = 'quattuortrigintillion',
36 = 'quinquatrigintillion',
37 = 'sestrigintillion',
38 = 'septentrigintillion',
39 = 'octotrigintillion',
40 = 'noventrigintillion',
41 = 'quadragintillion',
51 = 'quinquagintillion',
61 = 'sexagintillion',
71 = 'septuagintillion',
81 = 'octogintillion',
91 = 'nonagintillion',
101 = 'centillion',
102 = 'uncentillion',
103 = 'duocentillion',
104 = 'trescentillion',
111 = 'decicentillion',
112 = 'undecicentillion',
121 = 'viginticentillion',
122 = 'unviginticentillion',
131 = 'trigintacentillion',
141 = 'quadragintacentillion',
151 = 'quinquagintacentillion',
161 = 'sexagintacentillion',
171 = 'septuagintacentillion',
181 = 'octogintacentillion',
191 = 'nonagintacentillion',
201 = 'ducentillion',
301 = 'trecentillion',
401 = 'quadringentillion',
501 = 'quingentillion',
601 = 'sescentillion',
701 = 'septingentillion',
801 = 'octingentillion',
901 = 'nongentillion',
1001 = 'millinillion',
}
local roman_numerals = {
I = 1,
V = 5,
X = 10,
L = 50,
C = 100,
D = 500,
M = 1000
}
local engord_tens_end = {
'twentieth' = 20,
'thirtieth' = 30,
'fortieth' = 40,
'fiftieth' = 50,
'sixtieth' = 60,
'seventieth' = 70,
'eightieth' = 80,
'ninetieth' = 90,
}
local eng_tens_cont = {
'twenty' = 20,
'thirty' = 30,
'forty' = 40,
'fifty' = 50,
'sixty' = 60,
'seventy' = 70,
'eighty' = 80,
'ninety' = 90,
}
-- Converts a given valid roman numeral (and some invalid roman numerals) to a number. Returns { -1, errorstring } on error.
local function roman_to_numeral(roman)
if type(roman) ~= "string" then return -1, "roman numeral not a string" end
local rev = roman:reverse()
local raising = true
local last = 0
local result = 0
for i = 1, #rev do
local c = rev:sub(i, i)
local next = roman_numeralsc
if next == nil then return -1, "roman numeral contains illegal character " .. c end
if next > last then
result = result + next
raising = true
elseif next < last then
result = result - next
raising = false
elseif raising then
result = result + next
else
result = result - next
end
last = next
end
return result
end
-- Converts a given integer between 0 and 100 to English text (e.g. 47 -> forty-seven).
local function numeral_to_english_less_100(num, ordinal, plural, zero)
local terminal_ones, terminal_tens
if ordinal then
terminal_ones = ones_position_ord
terminal_tens = tens_position_ord
elseif plural then
terminal_ones = ones_position_plural
terminal_tens = tens_position_plural
else
terminal_ones = ones_position
terminal_tens = tens_position
end
if num == 0 and zero ~= nil then
return zero
elseif num < 20 then
return terminal_onesnum
elseif num % 10 == 0 then
return terminal_tensnum / 10
else
return tens_positionmath.floor(num / 10)] .. '-' .. terminal_onesnum % 10
end
end
local function standard_suffix(ordinal, plural)
if ordinal then return 'th' end
if plural then return 's' end
return ''
end
-- Converts a given integer (in string form) between 0 and 1000 to English text (e.g. 47 -> forty-seven).
local function numeral_to_english_less_1000(num, use_and, ordinal, plural, zero)
num = tonumber(num)
if num < 100 then
return numeral_to_english_less_100(num, ordinal, plural, zero)
elseif num % 100 == 0 then
return ones_positionnum/100 .. ' hundred' .. standard_suffix(ordinal, plural)
else
return ones_positionmath.floor(num/100)] .. ' hundred ' .. (use_and and 'and ' or '') .. numeral_to_english_less_100(num % 100, ordinal, plural, zero)
end
end
-- Converts an ordinal in English text from 'zeroth' to 'ninety-ninth' inclusive to a number [0–99], else -1.
local function english_to_ordinal(english)
local eng = string.lower(english or '')
local engord_lt20 = {} -- ones_position_ord{} keys & values swapped
for k, v in pairs( ones_position_ord ) do
engord_lt20v = k
end
if engord_lt20eng then
return engord_lt20eng -- e.g. first -> 1
elseif engord_tens_endeng then
return engord_tens_endeng -- e.g. ninetieth -> 90
else
local tens, ones = string.match(eng, '^([a-z]+)[%s%-]+([a-z]+)$')
if tens and ones then
local tens_cont = eng_tens_conttens
local ones_end = engord_lt20ones
if tens_cont and ones_end then
return tens_cont + ones_end -- e.g. ninety-ninth -> 99
end
end
end
return -1 -- Failed
end
-- Converts a number in English text from 'zero' to 'ninety-nine' inclusive to a number [0–99], else -1.
local function english_to_numeral(english)
local eng = string.lower(english or '')
local eng_lt20 = { 'single' = 1 } -- ones_position{} keys & values swapped
for k, v in pairs( ones_position ) do
eng_lt20v = k
end
if eng_lt20eng then
return eng_lt20eng -- e.g. one -> 1
elseif eng_tens_conteng then
return eng_tens_conteng -- e.g. ninety -> 90
else
local tens, ones = string.match(eng, '^([a-z]+)[%s%-]+([a-z]+)$')
if tens and ones then
local tens_cont = eng_tens_conttens
local ones_end = eng_lt20ones
if tens_cont and ones_end then
return tens_cont + ones_end -- e.g. ninety-nine -> 99
end
end
end
return -1 -- Failed
end
-- Converts a number expressed as a string in scientific notation to a string in standard decimal notation
-- e.g. 1.23E5 -> 123000, 1.23E-5 = .0000123. Conversion is exact, no rounding is performed.
local function scientific_notation_to_decimal(num)
local exponent, subs = num:gsub("^%-?%d*%.?%d*%-?[Ee]([+%-]?%d+)$", "%1")
if subs == 0 then return num end -- Input not in scientific notation, just return unmodified
exponent = tonumber(exponent)
local negative = num:find("^%-")
local _, decimal_pos = num:find("%.")
-- Mantissa will consist of all decimal digits with no decimal point
local mantissa = num:gsub("^%-?(%d*)%.?(%d*)%-?[Ee][+%-]?%d+$", "%1%2")
if negative and decimal_pos then decimal_pos = decimal_pos - 1 end
decimal_pos = decimal_pos or #mantissa + 1
-- Remove leading zeros unless decimal point is in first position
while decimal_pos > 1 and mantissa:sub(1,1) == '0' do
mantissa = mantissa:sub(2)
decimal_pos = decimal_pos - 1
end
-- Shift decimal point right for exponent > 0
while exponent > 0 do
decimal_pos = decimal_pos + 1
exponent = exponent - 1
if decimal_pos > #mantissa + 1 then mantissa = mantissa .. '0' end
-- Remove leading zeros unless decimal point is in first position
while decimal_pos > 1 and mantissa:sub(1,1) == '0' do
mantissa = mantissa:sub(2)
decimal_pos = decimal_pos - 1
end
end
-- Shift decimal point left for exponent < 0
while exponent < 0 do
if decimal_pos == 1 then
mantissa = '0' .. mantissa
else
decimal_pos = decimal_pos - 1
end
exponent = exponent + 1
end
-- Insert decimal point in correct position and return
return (negative and '-' or '') .. mantissa:sub(1, decimal_pos - 1) .. '.' .. mantissa:sub(decimal_pos)
end
-- Rounds a number to the nearest integer (NOT USED)
local function round_num(x)
if x%1 >= 0.5 then
return math.ceil(x)
else
return math.floor(x)
end
end
-- Rounds a number to the nearest two-word number (round = up, down, or "on" for round to nearest).
-- Numbers with two digits before the decimal will be rounded to an integer as specified by round.
-- Larger numbers will be rounded to a number with only one nonzero digit in front and all other digits zero.
-- Negative sign is preserved and does not count towards word limit.
local function round_for_english(num, round)
-- If an integer with at most two digits, just return
if num:find("^%-?%d?%d%.?$") then return num end
local negative = num:find("^%-")
if negative then
-- We're rounding magnitude so flip it
if round == 'up' then round = 'down' elseif round == 'down' then round = 'up' end
end
-- If at most two digits before decimal, round to integer and return
local _, _, small_int, trailing_digits, round_digit = num:find("^%-?(%d?%d?)%.((%d)%d*)$")
if small_int then
if small_int == '' then small_int = '0' end
if (round == 'up' and trailing_digits:find('[1-9]')) or (round == 'on' and tonumber(round_digit) >= 5) then
small_int = tostring(tonumber(small_int) + 1)
end
return (negative and '-' or '') .. small_int
end
-- When rounding up, any number with > 1 nonzero digit will round up (e.g. 1000000.001 rounds up to 2000000)
local nonzero_digits = 0
for digit in num:gfind("[1-9]") do
nonzero_digits = nonzero_digits + 1
end
num = num:gsub("%.%d*$", "") -- Remove decimal part
-- Second digit used to determine which way to round lead digit
local _, _, lead_digit, round_digit, round_digit_2, rest = num:find("^%-?(%d)(%d)(%d)(%d*)$")
if tonumber(lead_digit .. round_digit) < 20 and (1 + #rest) % 3 == 0 then
-- In English numbers < 20 are one word so put 2 digits in lead and round based on 3rd
lead_digit = lead_digit .. round_digit
round_digit = round_digit_2
else
rest = round_digit_2 .. rest
end
if (round == 'up' and nonzero_digits > 1) or (round == 'on' and tonumber(round_digit) >= 5) then
lead_digit = tostring(tonumber(lead_digit) + 1)
end
-- All digits but lead digit will turn to zero
rest = rest:gsub("%d", "0")
return (negative and '-' or '') .. lead_digit .. '0' .. rest
end
local denominators = {
2 = { 'half', plural = 'halves' },
3 = { 'third' },
4 = { 'quarter', us = 'fourth' },
5 = { 'fifth' },
6 = { 'sixth' },
8 = { 'eighth' },
9 = { 'ninth' },
10 = { 'tenth' },
16 = { 'sixteenth' },
}
-- Return status, fraction where:
-- status is a string:
-- "finished" if there is a fraction with no whole number;
-- "ok" if fraction is empty or valid;
-- "unsupported" if bad fraction;
-- fraction is a string giving (numerator / denominator) as English text, or is "".
-- Only unsigned fractions with a very limited range of values are supported,
-- except that if whole is empty, the numerator can use "-" to indicate negative.
-- whole (string or nil): nil or "" if no number before the fraction
-- numerator (string or nil): numerator, if any (default = 1 if a denominator is given)
-- denominator (string or nil): denominator, if any
-- sp_us (boolean): true if sp=us
-- negative_word (string): word to use for negative sign, if whole is empty
-- use_one (boolean): false: 2+1/2 → "two and a half"; true: "two and one-half"
local function fraction_to_english(whole, numerator, denominator, sp_us, negative_word, use_one)
if numerator or denominator then
local finished = (whole == nil or whole == '')
local sign = ''
if numerator then
if finished and numerator:sub(1, 1) == '-' then
numerator = numerator:sub(2)
sign = negative_word .. ' '
end
else
numerator = '1'
end
if not numerator:match('^%d+$') or not denominator or not denominator:match('^%d+$') then
return 'unsupported', ''
end
numerator = tonumber(numerator)
denominator = tonumber(denominator)
local dendata = denominatorsdenominator
if not (dendata and 1 <= numerator and numerator <= 99) then
return 'unsupported', ''
end
local numstr, denstr
local sep = '-'
if numerator == 1 then
denstr = sp_us and dendata.us or dendata1
if finished or use_one then
numstr = 'one'
elseif denstr:match('^[aeiou]') then
numstr = 'an'
sep = ' '
else
numstr = 'a'
sep = ' '
end
else
numstr = numeral_to_english_less_100(numerator)
denstr = dendata.plural or (sp_us and dendata.us or dendata1]) .. 's'
end
if finished then
return 'finished', sign .. numstr .. sep .. denstr
end
return 'ok', ' and ' .. numstr .. sep .. denstr
end
return 'ok', ''
end
-- Takes a decimal number and converts it to English text.
-- Return nil if a fraction cannot be converted (only some numbers are supported for fractions).
-- num (string or nil): the number to convert.
-- Can be an arbitrarily large decimal, such as "-123456789123456789.345", and
-- can use scientific notation (e.g. "1.23E5").
-- May fail for very large numbers not listed in "groups" such as "1E4000".
-- num is nil if there is no whole number before a fraction.
-- numerator (string or nil): numerator of fraction (nil if no fraction)
-- denominator (string or nil): denominator of fraction (nil if no fraction)
-- capitalize (boolean): whether to capitalize the result (e.g. 'One' instead of 'one')
-- use_and (boolean): whether to use the word 'and' between tens/ones place and higher places
-- hyphenate (boolean): whether to hyphenate all words in the result, useful as an adjective
-- ordinal (boolean): whether to produce an ordinal (e.g. 'first' instead of 'one')
-- plural (boolean): whether to pluralize the resulting number
-- links: nil: do not add any links; 'on': link "billion" and larger to Orders of magnitude article;
-- any other text: list of numbers to link (e.g. "billion,quadrillion")
-- negative_word: word to use for negative sign (typically 'negative' or 'minus'; nil to use default)
-- round: nil or '': no rounding; 'on': round to nearest two-word number; 'up'/'down': round up/down to two-word number
-- zero: word to use for value '0' (nil to use default)
-- use_one (boolean): false: 2+1/2 → "two and a half"; true: "two and one-half"
local function _numeral_to_english(num, numerator, denominator, capitalize, use_and, hyphenate, ordinal, plural, links, negative_word, round, zero, use_one)
if not negative_word then
if use_and then
-- TODO Should 'minus' be used when do not have sp=us?
-- If so, need to update testcases, and need to fix "minus zero".
-- negative_word = 'minus'
negative_word = 'negative'
else
negative_word = 'negative'
end
end
local status, fraction_text = fraction_to_english(num, numerator, denominator, not use_and, negative_word, use_one)
if status == 'unsupported' then
return nil
end
if status == 'finished' then
-- Input is a fraction with no whole number.
-- Hack to avoid executing stuff that depends on num being a number.
local s = fraction_text
if hyphenate then s = s:gsub("%s", "-") end
if capitalize then s = s:gsub("^%l", string.upper) end
return s
end
num = scientific_notation_to_decimal(num)
if round and round ~= '' then
if round ~= 'on' and round ~= 'up' and round ~= 'down' then
error("Invalid rounding mode")
end
num = round_for_english(num, round)
end
-- Separate into negative sign, num (digits before decimal), decimal_places (digits after decimal)
local MINUS = '−' -- Unicode U+2212 MINUS SIGN (may be in values from [[Module:Convert]])
if num:sub(1, #MINUS) == MINUS then
num = '-' .. num:sub(#MINUS + 1) -- replace MINUS with '-'
elseif num:sub(1, 1) == '+' then
num = num:sub(2) -- ignore any '+'
end
local negative = num:find("^%-")
local decimal_places, subs = num:gsub("^%-?%d*%.(%d+)$", "%1")
if subs == 0 then decimal_places = nil end
num, subs = num:gsub("^%-?(%d*)%.?%d*$", "%1")
if num == '' and decimal_places then num = '0' end
if subs == 0 or num == '' then error("Invalid decimal numeral") end
-- For each group of 3 digits except the last one, print with appropriate group name (e.g. million)
local s = ''
while #num > 3 do
if s ~= '' then s = s .. ' ' end
local group_num = math.floor((#num - 1) / 3)
local group = groupsgroup_num
local group_digits = #num - group_num*3
s = s .. numeral_to_english_less_1000(num:sub(1, group_digits), false, false, false, zero) .. ' '
if links and (((links == 'on' and group_num >= 3) or links:find(group)) and group_num <= 13) then
s = s .. '[[Orders_of_magnitude_(numbers)#10' .. group_num*3 .. '|' .. group .. ']]'
else
s = s .. group
end
num = num:sub(1 + group_digits)
num = num:gsub("^0*", "") -- Trim leading zeros
end
-- Handle final three digits of integer part
if s ~= '' and num ~= '' then
if #num <= 2 and use_and then
s = s .. ' and '
else
s = s .. ' '
end
end
if s == '' or num ~= '' then
s = s .. numeral_to_english_less_1000(num, use_and, ordinal, plural, zero)
elseif ordinal or plural then
-- Round numbers like "one million" take standard suffixes for ordinal/plural
s = s .. standard_suffix(ordinal, plural)
end
-- For decimal places (if any) output "point" followed by spelling out digit by digit
if decimal_places then
s = s .. ' point'
for i = 1, #decimal_places do
s = s .. ' ' .. ones_positiontonumber(decimal_places:sub(i,i))]
end
end
s = s:gsub("^%s*(.-)%s*$", "%1") -- Trim whitespace
if ordinal and plural then s = s .. 's' end -- s suffix works for all ordinals
if negative and s ~= zero then s = negative_word .. ' ' .. s end
s = s:gsub("negative zero", "zero")
s = s .. fraction_text
if hyphenate then s = s:gsub("%s", "-") end
if capitalize then s = s:gsub("^%l", string.upper) end
return s
end
local function _numeral_to_english2(args)
local num = tostring(args.num)
num = num:gsub("^%s*(.-)%s*$", "%1") -- Trim whitespace
num = num:gsub(",", "") -- Remove commas
num = num:gsub("^<span[^<>]*></span>", "") -- Generated by Template:age
if num ~= '' then -- a fraction may have an empty whole number
if not num:find("^%-?%d*%.?%d*%-?[Ee]?[+%-]?%d*$") then
-- Input not in a valid format, try to eval it as an expr to see
-- if that produces a number (e.g. "3 + 5" will become "8").
local noerr, result = pcall(mw.ext.ParserFunctions.expr, num)
if noerr then
num = result
end
end
end
-- Call helper function passing args
return _numeral_to_english(
num,
args'numerator'],
args'denominator'],
args'capitalize'],
args'use_and'],
args'hyphenate'],
args'ordinal'],
args'plural'],
args'links'],
args'negative_word'],
args'round'],
args'zero'],
args'use_one'
) or ''
end
local p = { -- Functions that can be called from another module
roman_to_numeral = roman_to_numeral,
spell_number = _numeral_to_english,
spell_number2 = _numeral_to_english2,
english_to_ordinal = english_to_ordinal,
english_to_numeral = english_to_numeral,
}
function p._roman_to_numeral(frame) -- Callable via {{#invoke:ConvertNumeric|_roman_to_numeral|VI}}
return roman_to_numeral(frame.args1])
end
function p._english_to_ordinal(frame) -- callable via {{#invoke:ConvertNumeric|_english_to_ordinal|First}}
return english_to_ordinal(frame.args1])
end
function p._english_to_numeral(frame) -- callable via {{#invoke:ConvertNumeric|_english_to_numeral|One}}
return english_to_numeral(frame.args1])
end
function p.numeral_to_english(frame)
local args = frame.args
-- Tail call to helper function passing args from frame
return _numeral_to_english2{
'num' = args1],
'numerator' = args'numerator'],
'denominator' = args'denominator'],
'capitalize' = args'case' == 'U' or args'case' == 'u',
'use_and' = args'sp' ~= 'us',
'hyphenate' = args'adj' == 'on',
'ordinal' = args'ord' == 'on',
'plural' = args'pl' == 'on',
'links' = args'lk'],
'negative_word' = args'negative'],
'round' = args'round'],
'zero' = args'zero'],
'use_one' = args'one' == 'one' -- experiment: using '|one=one' makes fraction 2+1/2 give "two and one-half" instead of "two and a half"
}
end
---- recursive function for p.decToHex
local function decToHexDigit(dec)
local dig = {"0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"}
local div = math.floor(dec/16)
local mod = dec-(16*div)
if div >= 1 then return decToHexDigit(div)..digmod+1 else return digmod+1 end
end -- I think this is supposed to be done with a tail call but first I want something that works at all
---- finds all the decimal numbers in the input text and hexes each of them
function p.decToHex(frame)
local args=frame.args
local parent=frame.getParent(frame)
local pargs={}
if parent then pargs=parent.args end
local text=args1 or pargs1 or ""
local minlength=args.minlength or pargs.minlength or 1
minlength=tonumber(minlength)
local prowl=mw.ustring.gmatch(text,"(.-)(%d+)")
local output=""
repeat
local chaff,dec=prowl()
if not(dec) then break end
local hex=decToHexDigit(dec)
while (mw.ustring.len(hex)<minlength) do hex="0"..hex end
output=output..chaff..hex
until false
local chaff=mw.ustring.match(text,"(%D+)$") or ""
return output..chaff
end
return p