Module:ConvertNumeric explained

-- Module for converting between different representations of numbers. See talk page for user documentation.-- For unit tests see: -- When editing, preview with: -- First, edit, then preview with require('strict')

local ones_position =

local ones_position_ord =

local ones_position_plural =

local tens_position =

local tens_position_ord =

local tens_position_plural =

local groups =

local roman_numerals =

local engord_tens_end =

local eng_tens_cont =

-- Converts a given valid roman numeral (and some invalid roman numerals) to a number. Returns 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 resultend

-- 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] endend

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) endend

-- 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_lt20[v] = k end

if engord_lt20[eng] then return engord_lt20[eng] -- e.g. first -> 1 elseif engord_tens_end[eng] then return engord_tens_end[eng] -- 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_cont[tens] local ones_end = engord_lt20[ones] if tens_cont and ones_end then return tens_cont + ones_end -- e.g. ninety-ninth -> 99 end end end return -1 -- Failedend

-- 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 = -- ones_position keys & values swapped for k, v in pairs(ones_position) do eng_lt20[v] = k end

if eng_lt20[eng] then return eng_lt20[eng] -- e.g. one -> 1 elseif eng_tens_cont[eng] then return eng_tens_cont[eng] -- 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_cont[tens] local ones_end = eng_lt20[ones] if tens_cont and ones_end then return tens_cont + ones_end -- e.g. ninety-nine -> 99 end end end return -1 -- Failedend

-- 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) endend

-- 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' .. restend

local denominators =

-- 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 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) 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 .. '' .. 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 send

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("^

]*>", "") -- 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 =

function p._roman_to_numeral(frame) -- Callable via return roman_to_numeral(frame.args[1])end

function p._english_to_ordinal(frame) -- callable via return english_to_ordinal(frame.args[1])end

function p._english_to_numeral(frame) -- callable via return english_to_numeral(frame.args[1])end

function p.numeral_to_english(frame) local args = frame.args -- Tail call to helper function passing args from frame return _numeral_to_english2end

---- recursive function for p.decToHexlocal function decToHexDigit(dec) local dig = 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] endend -- 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 themfunction 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)

return p