Mô đun:ConvertNumeric

-- Mô đun để chuyển đổi qua lại những cách trình bày số. Xem tài liệu tại trang thảo luận.
-- Có sẵn trường hợp thử thách tại: [[Mô đun:ConvertNumeric/testcases]]
-- Sử dụng trang này để xem trước khi sửa đổi: [[Thảo luận Mô đun:ConvertNumeric/testcases]]
-- Trước tiên sửa đổi [[Mô đun:ConvertNumeric/sandbox]] rồi xem trước dùng [[Thảo luận Mô đun: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_vi = {
	[0] = 'không',
	[1] = 'một',
	[2] = 'hai',
	[3] = 'ba',
	[4] = 'bốn',
	[5] = 'năm',
	[6] = 'sáu',
	[7] = 'bảy',
	[8] = 'tám',
	[9] = 'chín',
	[10] = 'mười',
	[11] = 'mười một',
	[12] = 'mười hai',
	[13] = 'mười ba',
	[14] = 'mười bốn',
	[15] = 'mười lăm',
	[16] = 'mười sáu',
	[17] = 'mười bảy',
	[18] = 'mười tám',
	[19] = 'mười chín'
}

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_ord_vi = {
	[0] = 'không',
	[1] = 'nhất',
	[2] = 'hai',	-- nhì
	[3] = 'ba',
	[4] = 'tư',
	[5] = 'năm',
	[6] = 'sáu',
	[7] = 'bảy',
	[8] = 'tám',
	[9] = 'chín',
	[10] = 'mười',
	[11] = 'mười một',
	[12] = 'mười hai',
	[13] = 'mười ba',
	[14] = 'mười bốn',
	[15] = 'mười lăm',
	[16] = 'mười sáu',
	[17] = 'mười bảy',
	[18] = 'mười tám',
	[19] = 'mười chín'
}

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_vi = {
	[2] = 'hai mươi',
	[3] = 'ba mươi',
	[4] = 'bốn mươi',
	[5] = 'năm mươi',
	[6] = 'sáu mươi',
	[7] = 'bảy mươi',
	[8] = 'tám mươi',
	[9] = 'chín mươi'
}

local tens_position_ord = {
	[2] = 'twentieth',
	[3] = 'thirtieth',
	[4] = 'fortieth',
	[5] = 'fiftieth',
	[6] = 'sixtieth',
	[7] = 'seventieth',
	[8] = 'eightieth',
	[9] = 'ninetieth'
}

local tens_position_ord_vi = {
	[2] = 'hai mươi',
	[3] = 'ba mươi',
	[4] = 'bốn mươi',
	[5] = 'năm mươi',
	[6] = 'sáu mươi',
	[7] = 'bảy mươi',
	[8] = 'tám mươi',
	[9] = 'chín mươi'
}

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 groups_vi = {
	[1] = 'ngàn',	-- nghìn
	[2] = 'triệu',
	[3] = 'tỷ',	-- tỉ
	[4] = 'ngàn tỷ',
	[5] = 'triệu tỷ',
	[6] = 'tỷ tỷ',
	[7] = 'ngàn tỷ tỷ',
	[8] = 'triệu tỷ tỷ',
	[9] = 'tỷ tỷ tỷ',
	[10] = 'ngàn tỷ tỷ tỷ',
	[11] = 'triệu tỷ tỷ tỷ',
	[12] = 'tỷ tỷ tỷ tỷ',
	[13] = 'ngàn tỷ tỷ tỷ tỷ',
	[14] = 'triệu tỷ tỷ tỷ tỷ',
}

local vie_tens_cont = {
	['hai mươi']	= 20,
	['ba mươi']	    = 30,
	['bôn mươi']	= 40,
	['năm mươi']	= 50,
	['sáu mươi']	= 60,
	['bảy mươi']	= 70,
	['tám mươi']	= 80,
	['chín mươi']	= 90,
}

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, "số La Mã không phải là chuỗi" 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, "số La Mã có ký tự không hợp lệ " .. 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 numeral_to_vietnamese_less_100(num, ordinal, plural, zero)
	-- TODO: Chục
	local terminal_ones
	if ordinal then
		terminal_ones = ones_position_ord_vi
	else
		terminal_ones = ones_position_vi
	end

	if num == 0 and zero ~= nil then
		return zero
	elseif num <= 10 then
		return terminal_ones[num]
	elseif num % 10 == 0 then
		return terminal_ones[num / 10] .. ' mươi'
	else
		local ten = math.floor(num / 10)
		local terminal_one = terminal_ones[num % 10]
		local terminal_ten = ones_position_vi[ten] .. ' mươi'
		if ten == 1 then
			terminal_ten = terminal_ones[10]
		elseif num % 10 == 1 then
			terminal_one = "mốt"
		end
		if num % 10 == 5 then terminal_one = "lăm" end
		return terminal_ten .. ' ' .. terminal_one
	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

local function numeral_to_vietnamese_less_1000(num, use_and, ordinal, plural, zero, half)
	num = tonumber(num)
	if num < 100 then
		return numeral_to_vietnamese_less_100(num, ordinal, plural, zero)
	elseif num % 100 == 0 then
		return ones_position_vi[num/100] .. ' trăm'
	elseif half and num % 100 == 50 then
		return ones_position_vi[math.floor(num/100)] .. ' trăm rưỡi'
	elseif num % 100 <= 10 then
		local terminal_ones
		if ordinal then
			terminal_ones = ones_position_ord_vi
		else
			terminal_ones = ones_position_vi
		end
		return ones_position_vi[math.floor(num/100)] .. ' trăm lẻ ' .. terminal_ones[num % 100]	-- linh
	else
		return ones_position_vi[math.floor(num/100)] .. ' trăm ' .. numeral_to_vietnamese_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' },
	[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

local function fraction_to_vietnamese(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)
		if numerator > 0 and numerator * 2 == denominator then
			return 'ok', ' rưỡi'
		end
		if not (1 <= numerator and numerator <= 999 and denominator <= 999) then
			return 'unsupported', ''
		end
		local numstr = numeral_to_vietnamese_less_1000(numerator)
		local denstr = numeral_to_vietnamese_less_1000(denominator, false, true)
		denstr = denstr:gsub("^một ", "")
		if finished then
			return 'finished', sign .. numstr .. ' phần ' .. denstr
		end
		return 'ok', ' ' .. numstr .. ' phần ' .. 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)
	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 'Chế độ làm tròn không hợp lệ'
		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 [[Mô đun: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 'Chữ số thập phân không hợp lệ' 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 .. '[[Bậc độ lớn (số)#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_vietnamese(num, numerator, denominator, capitalize, use_and, hyphenate, ordinal, plural, links, negative_word, round, zero, use_one)
	if not negative_word then
		negative_word = 'âm'
	end
	local status, fraction_text = fraction_to_vietnamese(num, numerator, denominator, not use_and, negative_word)
	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 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 'Chế độ làm tròn không hợp lệ'
		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 [[Mô đun: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 'Chữ số thập phân không hợp lệ' end
	
	local entire_num = num

	-- 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_vi[group_num]
		local group_digits = #num - group_num*3
		if tonumber(num:gsub("^500", ""), 10)  == 0 and tonumber(num:gsub("^1000", ""), 10) == 0 then
			s = s .. "rưỡi"
		else
			s = s .. numeral_to_vietnamese_less_1000(num:sub(1, group_digits), false, false, false, zero, false) .. ' '
			if links and (((links == 'on' and group_num >= 3) or links:find(group)) and group_num <= 13) then
				s = s .. '[[Bậc độ lớn (số)#10' .. group_num*3 .. '|' .. group .. ']]'
			else
				s = s .. group
			end
		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
		s = s .. ' '
	end
	if tonumber(entire_num) > 500 and tonumber(num) == 500 then
		s = s .. "rưỡi"
	elseif s == '' or num ~= '' then
		if tonumber(entire_num) > 1000 and tonumber(num) <= 10 then
			s = s .. "lẻ "
		end
		s = s .. numeral_to_vietnamese_less_1000(num, use_and, ordinal, plural, zero, #entire_num <= 3)
	end

	-- For decimal places (if any) output "point" followed by spelling out digit by digit
	if decimal_places then
		s = s .. ' phẩy'
		for i = 1, #decimal_places do
			s = s .. ' ' .. ones_position_vi[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("âm không", "không")
	s = s .. fraction_text
	if capitalize then s = s:gsub("^%l", string.upper) end
	return s
end

local function _numeral_to_vietnamese2(args)
	local num = tostring(args.num)

	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 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_vietnamese(
		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 function vietnamese_to_numeral(vietnamese)
	local vie = string.lower(vietnamese or '')

	local vie_lt20 = {} -- hoán đổi khoá và giá trị của ones_position_vi{}
	for k, v in pairs( ones_position_vi ) do
		vie_lt20[v] = k
	end
	local vie_lt20_special = vie_lt20
	vie_lt20_special['mốt'] = 1

	if vie_lt20[vie] then
		return vie_lt20[vie] -- e.g. một -> 1
	elseif vie_tens_cont[vie] then
		return vie_tens_cont[vie] -- e.g. chín mươi -> 90
	else
		local tens, ones = string.match(vie, '^(.+%s.+)%s+(.+)$')
		if tens and ones then
			local tens_cont = vie_tens_cont[tens]
			local ones_end  = vie_lt20_special[ones]
			if tens_cont and ones_end then
				return tens_cont + ones_end -- e.g. chín mươi chín -> 99
			end
		end
	end
	return -1 -- Failed
end

local p = {	-- functions that can be called from another module
	roman_to_numeral = roman_to_numeral,
	spell_number = _numeral_to_vietnamese,
	spell_number2 = _numeral_to_vietnamese2,
	vietnamese_to_numeral = vietnamese_to_numeral,
}

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

function p.numeral_to_vietnamese(frame)
	local args = frame.args
	local num = args[1]
	num = mw.text.trim(num)   -- Trim whitespace
	num = num:gsub("%.", ""):gsub(",", ".")   -- Convert to computer format
	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
	local numerator = mw.text.trim(args['numerator'] or args[2])
	if #numerator == 0 then numerator = nil end
	local denominator = mw.text.trim(args['denominator'] or args[3])
	if #denominator == 0 then denominator = nil end
	local case = args['case']
	local sp = args['sp']
	local adj = args['adj']
	local ord = args['ord']
	local pl = args['pl']
	local lk = args['lk']
	local negative = args['negative']
	local round = args['round']
	local zero = args['zero']
	return _numeral_to_vietnamese(num, numerator, denominator,
		case == 'U' or case == 'u', sp ~= 'us', adj == 'on',
		ord == 'on', pl == 'on', lk, negative, round, zero) 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

--p.numeral_to_vietnamese_less_100 = numeral_to_vietnamese_less_100				-- debug
--p.numeral_to_vietnamese_less_1000 = numeral_to_vietnamese_less_1000				-- debug
return p