:ConvertNumeric

-- 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 and 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 }

-- 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 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 local prev_len = #num

-- 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 local small_int_len = #small_int 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 return '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 return '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 .. '' .. 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 p = { -- functions that can be called from another module roman_to_numeral = roman_to_numeral, spell_number = _numeral_to_english, }

function p.numeral_to_english(frame) local args = frame.args local num = args[1] num = num:gsub("^%s*(.-)%s*$", "%1") -- Trim whitespace num = num:gsub(",", "") -- Remove commas if num ~= then -- a fraction may have an empty whole number if not num:find("^%-?%d*%.?%d*%-?[Ee]?[+%-]?%d*$") 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