-- 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]]
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 eng_lt20 = {
['zeroth'] = 0,
['first'] = 1,
['second'] = 2,
['third'] = 3,
['fourth'] = 4,
['fifth'] = 5,
['sixth'] = 6,
['seventh'] = 7,
['eighth'] = 8,
['ninth'] = 9,
['tenth'] = 10,
['eleventh'] = 11,
['twelfth'] = 12,
['thirteenth'] = 13,
['fourteenth'] = 14,
['fifteenth'] = 15,
['sixteenth'] = 16,
['seventeenth'] = 17,
['eighteenth'] = 18,
['nineteenth'] = 19,
}
local eng_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_numerals[c]
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_ones[num]
elseif num % 10 == 0 then
return terminal_tens[num / 10]
else
return tens_position[math.floor(num / 10)] .. '-' .. terminal_ones[num % 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_position[num/100] .. ' hundred' .. standard_suffix(ordinal, plural)
else
return ones_position[math.floor(num/100)] .. ' hundred ' .. (use_and and 'and ' or '') .. numeral_to_english_less_100(num % 100, ordinal, plural, zero)
end
end
-- Converts an English-text ordinal between 'zeroth' and 'ninety-ninth' to a number [0–99], else -1
local function english_to_ordinal(english)
local eng = string.lower(english or '')
local eng_lt20 = eng_lt20
local eng_tens_end = eng_tens_end
local eng_tens_cont = eng_tens_cont
if eng_lt20[eng] then
return eng_lt20[eng] --e.g. first -> 1
elseif eng_tens_end[eng] then
return eng_tens_end[eng] --e.g. ninetieth -> 90
else
local tens, ones = string.match(eng, '^([a-z]+)%-([a-z]+)$')
if tens and ones then
local tens_cont = eng_tens_cont[tens]
local ones_end = eng_lt20[ones]
if tens_cont and ones_end then
return tens_cont + ones_end --e.g. ninety-ninth -> 99
end
end
end
return -1 --failed
end
-- Converts a number expressed as a string in scientific notation to a string in standard decimal notation
-- e.g. 1.23E5 -> 123000, 1.23E-5 = .0000123. Conversion is exact, no rounding is performed.
local function scientific_notation_to_decimal(num)
local exponent, subs = num:gsub("^%-?%d*%.?%d*%-?[Ee]([+%-]?%d+)$", "%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+$", "%1%2")
if negative and decimal_pos then decimal_pos = decimal_pos - 1 end
if not decimal_pos then decimal_pos = #mantissa + 1 end
-- Remove leading zeros unless decimal point is in first position
while decimal_pos > 1 and mantissa:sub(1,1) == '0' do
mantissa = mantissa:sub(2)
decimal_pos = decimal_pos - 1
end
-- Shift decimal point right for exponent > 0
while exponent > 0 do
decimal_pos = decimal_pos + 1
exponent = exponent - 1
if decimal_pos > #mantissa + 1 then mantissa = mantissa .. '0' end
-- Remove leading zeros unless decimal point is in first position
while decimal_pos > 1 and mantissa:sub(1,1) == '0' do
mantissa = mantissa:sub(2)
decimal_pos = decimal_pos - 1
end
end
-- Shift decimal point left for exponent < 0
while exponent < 0 do
if decimal_pos == 1 then
mantissa = '0' .. mantissa
else
decimal_pos = decimal_pos - 1
end
exponent = exponent + 1
end
-- Insert decimal point in correct position and return
return (negative and '-' or '') .. mantissa:sub(1, decimal_pos - 1) .. '.' .. mantissa:sub(decimal_pos)
end
-- Rounds a number to the nearest integer (NOT USED)
local function round_num(x)
if x%1 >= 0.5 then
return math.ceil(x)
else
return math.floor(x)
end
end
-- Rounds a number to the nearest two-word number (round = up, down, or "on" for round to nearest)
-- Numbers with two digits before the decimal will be rounded to an integer as specified by round.
-- Larger numbers will be rounded to a number with only one nonzero digit in front and all other digits zero.
-- Negative sign is preserved and does not count towards word limit.
local function round_for_english(num, round)
-- If an integer with at most two digits, just return
if num:find("^%-?%d?%d%.?$") 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 = denominators[denominator]
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 dendata[1]
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
if not denstr then
denstr = (sp_us and dendata.us or dendata[1]) .. 's'
end
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 for use 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*$", "%1")
if num == '' and decimal_places then num = '0' end
if subs == 0 or num == '' then error("Invalid decimal numeral") end
-- For each group of 3 digits except the last one, print with appropriate group name (e.g. million)
local s = ''
while #num > 3 do
if s ~= '' then s = s .. ' ' end
local group_num = math.floor((#num - 1) / 3)
local group = groups[group_num]
local group_digits = #num - group_num*3
s = s .. numeral_to_english_less_1000(num:sub(1, group_digits), false, false, false, zero) .. ' '
if links and (((links == 'on' and group_num >= 3) or links:find(group)) and group_num <= 13) then
s = s .. '[[Orders_of_magnitude_(numbers)#10' .. group_num*3 .. '|' .. group .. ']]'
else
s = s .. group
end
num = num:sub(1 + group_digits)
num = num:gsub("^0*", "") -- Trim leading zeros
end
-- Handle final three digits of integer part
if s ~= '' and num ~= '' then
if #num <= 2 and use_and then
s = s .. ' and '
else
s = s .. ' '
end
end
if s == '' or num ~= '' then
s = s .. numeral_to_english_less_1000(num, use_and, ordinal, plural, zero)
elseif ordinal or plural then
-- Round numbers like "one million" take standard suffixes for ordinal/plural
s = s .. standard_suffix(ordinal, plural)
end
-- For decimal places (if any) output "point" followed by spelling out digit by digit
if decimal_places then
s = s .. ' point'
for i = 1, #decimal_places do
s = s .. ' ' .. ones_position[tonumber(decimal_places:sub(i,i))]
end
end
s = s:gsub("^%s*(.-)%s*$", "%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 = args.num
if (not tonumber(num)) then
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 pass it through #expr to see
-- if that produces a number (e.g. "3 + 5" will become "8").
num = mw.getCurrentFrame():preprocess('{{#expr: ' .. num .. '}}')
end
end
end
-- Pass args from frame to helper function
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,
}
function p._roman_to_numeral(frame) -- Callable via {{#invoke:ConvertNumeric|_roman_to_numeral|VI}}
return roman_to_numeral(frame.args[1])
end
function p._english_to_ordinal(frame) -- callable via {{#invoke:ConvertNumeric|_english_to_ordinal|First}}
return english_to_ordinal(frame.args[1])
end
function p.numeral_to_english(frame)
local args = frame.args
local num = args[1]
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 pass it through #expr to see
-- if that produces a number (e.g. "3 + 5" will become "8").
num = frame:preprocess('{{#expr: ' .. num .. '}}')
end
end
-- Pass args from frame to helper function
return _numeral_to_english(
num,
args['numerator'],
args['denominator'],
args['case'] == 'U' or args['case'] == 'u',
args['sp'] ~= 'us',
args['adj'] == 'on',
args['ord'] == 'on',
args['pl'] == 'on',
args['lk'],
args['negative'],
args['round'],
args['zero'],
args['one'] == 'one' -- experiment: using '|one=one' makes fraction 2+1/2 give "two and one-half" instead of "two and a half"
) or ''
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)..dig[mod+1] else return dig[mod+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=args[1] or pargs[1] 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
