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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 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,
	}
	
	local denominators = {
		[2] = { 'half', plural = 'halves' },
		[3] = { 'third' },
		[4] = { 'quarter', us = 'fourth' },
		[5] = { 'fifth' },
		[6] = { 'sixth' },
		[8] = { 'eighth' },
		[9] = { 'ninth' },
		[10] = { 'tenth' },
		[16] = { 'sixteenth' },
	}
	
	local thai_ones_position = {
		[0] = "ศูนย์",
		[1] = "หนึ่ง",
		[2] = "สอง",
		[3] = "สาม",
		[4] = "สี่",
		[5] = "ห้า",
		[6] = "หก",
		[7] = "เจ็ด",
		[8] = "แปด",
		[9] = "เก้า"
	}
	
	local data = {
		['normal'] = {
			[0] = '',
			[1] = 'หนึ่ง',
			[2] = 'สอง',
			[3] = 'สาม',
			[4] = 'สี่',
			[5] = 'ห้า',
			[6] = 'หก',
			[7] = 'เจ็ด',
			[8] = 'แปด',
			[9] = 'เก้า',
		},
		[0] = {
			[0] = '',
			[1] = 'เอ็ด',
			[2] = 'สอง',
			[3] = 'สาม',
			[4] = 'สี่',
			[5] = 'ห้า',
			[6] = 'หก',
			[7] = 'เจ็ด',
			[8] = 'แปด',
			[9] = 'เก้า',
			['value'] = '',
			['mode'] = 1,
		},
		[1] = {
			[0] = '',
			[1] = ' ',
			[2] = 'ยี่',
			[3] = 'สาม',
			[4] = 'สี่',
			[5] = 'ห้า',
			[6] = 'หก',
			[7] = 'เจ็ด',
			[8] = 'แปด',
			[9] = 'เก้า',
			['value'] = 'สิบ',
			['mode'] = 1,
		},
		[2] = {
			['value'] = 'ร้อย',
			['mode'] = 0,
		},
		[3] = {
			['value'] = 'พัน',
			['mode'] = 0,
		},
		[4] = {
			['value'] = 'หมื่น',
			['mode'] = 0,
		},
		[5] = {
			['value'] = 'แสน',
			['mode'] = 0,
		},
		[6] = {
			[0] = '',
			[1] = 'เอ็ด',
			[2] = 'สอง',
			[3] = 'สาม',
			[4] = 'สี่',
			[5] = 'ห้า',
			[6] = 'หก',
			[7] = 'เจ็ด',
			[8] = 'แปด',
			[9] = 'เก้า',
			['value'] = 'ล้าน',
			['mode'] = 1,
		},
	}
	
	-- 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
	
	local function standard_suffix(ordinal, plural)
		if ordinal then return 'th' end
		if plural then return 's' end
		return ''
	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
	
	-- 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
	
	-- Cloned and localized to Thai of two above
	local function numeral_to_thai(num, _, _, _)
		num = tostring(num)
		number_num = tonumber(num)
		if not num or number_num < 0 or number_num == math.huge then
			return "เกิดข้อผิดพลาดกับตัวเลข: ว่าง น้อยกว่าศูนย์ หรือตรงกับ <code>math.huge</code>"
		end
		if num == '0' then
			return 'ศูนย์'
		end
		local level = 0
		result = {}
		for i = #num, 1, -1 do
			table.insert(result, data[level]['value'])
			if data[level]['mode'] == 0 then
				table.insert(result, data['normal'][tonumber(num:sub(i, i))])
			else
				table.insert(result, data[level][tonumber(num:sub(i, i))])
			end
			level = level + 1
			if level > 6 then
				level = 1
			end
		end
		for i = 1, #result do
			if result[i] == 'เอ็ด' and result[i + 2] == nil then
				result[i] = 'หนึ่ง'
			end
			if i % 2 == 0 and result[i] == '' and (i > 2 and (i - 2) % 12 ~= 0) then
				result[i - 1] = ''
			end
			if result[i] == ' ' then
				result[i] = ''
			end
		end
		newresult = {}
		for i = #result, 1, -1 do
			table.insert(newresult, result[i])
		end
		return table.concat(newresult)
	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 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
	
	-- ฟังก์ชันสำหรับแปลงเศษส่วนเป็นคำพูด เช่น ห้าเศษสามส่วนสี่ หรือ เศษแปดส่วนห้า
	-- โคลนจากฟังก์ชันด้านบน
	-- 		numerator - เศษ
	--		denominator - ส่วน
	local function fraction_to_thai(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 = thai_ones_position[denominator]
			if not (dendata and 1 <= numerator and numerator <= 99) then
				return 'unsupported', ''
			end
			local numstr, denstr
			numstr = numeral_to_thai(numerator)
			denstr = dendata
			if finished then
				return 'finished', sign .. "เศษ" .. numstr .. "ส่วน" .. denstr
			end
			return 'ok', 'เศษ' .. numstr .. 'ส่วน' .. 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
	
	-- Clone of above for Thai
	local function _numeral_to_thai(num, numerator, denominator, capitalize, use_and, hyphenate, ordinal, _, links, negative_word, round, zero, _)
		if not negative_word then
			negative_word = 'ลบ'
		end
		if negative_word == 'minus' then
			negative_word = 'ลบ'
		end
		local status, fraction_text = fraction_to_thai(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('โหมดการปัดไม่ถูกต้อง: ไม่รู้จัก "' .. round .. '"')
			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("เลขไม่ถูกต้อง") end
		local s = numeral_to_thai(num)
	
		-- For decimal places (if any) output "point" followed by spelling out digit by digit
		if decimal_places then
			s = s .. 'จุด'
			for i = 1, #decimal_places do
				s = s .. thai_ones_position[tonumber(decimal_places:sub(i,i))]
			end
		end
	
		s = s:gsub("^%s*(.-)%s*$", "%1")   -- Trim whitespace
		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
		if s == 'ลบศูนย์' then s = 'ศูนย์' end
		if s == 'ศูนย์' and zero then s = zero end
		return s
	end
	
	local p = {  -- Functions that can be called from another module
		roman_to_numeral = roman_to_numeral,
		spell_number_eng = _numeral_to_english,
		spell_number2_eng = _numeral_to_english2,	
		english_to_ordinal = english_to_ordinal,
		-- For Thai
		spell_number = _numeral_to_thai
	}
	
	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
	
	-- For Thai
	function p.numeral_to_thai(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_thai(
			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