پودمان:ConvertNumeric: تفاوت میان نسخه‌ها

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    -- 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 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_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 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 -- 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_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 -- 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 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,
    	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.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._english_to_numeral(frame) -- callable via {{#invoke:ConvertNumeric|_english_to_numeral|One}}
    	return english_to_numeral(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