Module:ConvertNumeric

Hægt er að búa til leiðbeiningar fyrir þessa skriftu á Module:ConvertNumeric/doc

-- Í vinnslu

-- 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 = {
	-- Karlkyn & rest
	[0] = 'núll',
	[1] = 'einn',
	[2] = 'tveir',
	[3] = 'þrír',
	[4] = 'fjórir',
	[5] = 'fimm',
	[6] = 'sex',
	[7] = 'sjö',
	[8] = 'átta',
	[9] = 'níu',
	[10] = 'tíu',
	[11] = 'ellefu',
	[12] = 'tólf',
	[13] = 'þrettán',
	[14] = 'fjórtán',
	[15] = 'fimmtán',
	[16] = 'sextán',
	[17] = 'sautján',
	[18] = 'átján',
	[19] = 'nítján'
}

local ones_position_kvk = {
	-- Kvenkyn
	[1] = 'ein',
	[2] = 'tvær',
	[3] = 'þrjár',
	[4] = 'fjórar'
}

local ones_position_hk = {
	-- Hvorugkyn
	[1] = 'eitt',
	[2] = 'tvö',
	[3] = 'þrjú',
	[4] = 'fjögur'
}

--------------------------------------------------

local ones_position_ord_2 = {
	['kk']  = 'annar',
	['kvk'] = 'önnur',
	['kvk'] = 'annað'
}

local ones_position_ord = {
	-- BASE (bætist við 'i' eða 'a')
	[0] = 'núllt',
	[1] = 'fyrst',
	[2] = 'annar',
	[3] = 'þriðj',
	[4] = 'fjórð',
	[5] = 'fimmt',
	[6] = 'sjött',
	[7] = 'sjöund',
	[8] = 'áttund',
	[9] = 'níund',
	[10] = 'tíund',
	[11] = 'elleft',
	[12] = 'tólft',
	[13] = 'þrettánd',
	[14] = 'fjórtánd',
	[15] = 'fimmtánd',
	[16] = 'sextánd',
	[17] = 'sautjánd',
	[18] = 'átjánd',
	[19] = 'nítjánd'
}

--------------------------------------------------
-- Skipting: 0 | 1 - 4 | 5 - 12 | 13 - 19

local ones_position_plural = {
	[0] = 'núll',
	[1] = 'ásar',
	[2] = 'tvistar',
	[3] = 'þristar',
	[4] = 'fjarkar',
	[5] = 'fimmur',
	[6] = 'sexur',
	[7] = 'sjöur',
	[8] = 'áttur',
	[9] = 'níur',
	[10] = 'tíur',
	[11] = 'ellefur',
	[12] = 'tólfur',
	[13] = 'þrettán',
	[14] = 'fjórtán',
	[15] = 'fimmtán',
	[16] = 'sextán',
	[17] = 'sautján',
	[18] = 'átján',
	[19] = 'nítján'
}

--------------------------------------------------

local tens_position = {
	[2] = 'tuttugu',
	[3] = 'þrjátíu',
	[4] = 'fjörutíu',
	[5] = 'fimmtíu',
	[6] = 'sextíu',
	[7] = 'sjötíu',
	[8] = 'áttatíu',
	[9] = 'níutíu'
}

--------------------------------------------------

local tens_position_ord = {
	[2] = 'tuttugast',
	[3] = 'þrítugast',
	[4] = 'fertugast',
	[5] = 'fimmtugast',
	[6] = 'sextugast',
	[7] = 'sjötugast',
	[8] = 'áttugast',
	[9] = 'nítugast'
}

--------------------------------------------------

local tens_position_plural = {
	[2] = 'tuttugu',
	[3] = 'þrjátíu',
	[4] = 'fjörutíu',
	[5] = 'fimmtíu',
	[6] = 'sextíu',
	[7] = 'sjötíu',
	[8] = 'áttatíu',
	[9] = 'níutíu'
}

--------------------------------------------------
-- TODO: Klára
local groups = {
	[1] = 'þúsund',			-- 1.000
	[2] = 'milljón',		-- 1.000.000
	[3] = 'milljarður',		-- 1.000.000.000
	[4] = 'billjón',		-- 1.000.000.000.000
	[5] = 'billjarður',		-- 1.000.000.000.000.000
	[6] = 'trilljón',		-- ...
	[7] = 'trilljarður',
	[8] = 'kvaðrilljón',
	[9] = 'kvaðrilljarður',
	[10] = 'kvintilljón',
	[11] = 'decillion', 			-- X
	[12] = 'sextilljón',
	[13] = 'duodecillion',			-- X
	[14] = 'septilljón',
	[15] = 'quattuordecillion', 	-- X
	[16] = 'oktilljón',
	[17] = 'sexdecillion',			-- XX
	[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
}

-- Taka út?
local engord_tens_end  = {
	['twentieth']	= 20,
	['thirtieth']	= 30,
	['fortieth']	= 40,
	['fiftieth']	= 50,
	['sixtieth']	= 60,
	['seventieth']	= 70,
	['eightieth']	= 80,
	['ninetieth']	= 90,
}

-- Taka út?
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, "rómverskur tölustafur ekki strengur" 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, "rómverskur tölustafur inniheldur ógilt tákn, " .. 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 numeral_to_english_less_100(num, ordinal, plural, zero)
-- 	return numeral_to_icelandic_less_100(num, ordinal, plural, zero)
-- end

	-- ordinal
	-- fyrsti, annar, þriðji, fjórði, fimmti
	-- fyrsta, önnur, þriðja, fjórða, fimmta
	-- fyrsta, annað, þriðja, fjórða, fimmta
	
	-- plural
	-- ásar, tvistar, þristar, fjarkar, fimmur

	-- else
	-- einn, tveir, þrír, fjórir, fimm
	-- ein, tvær, þrjár, fjórar, fimm
	-- eitt, tvö, þrjú, fjögur, fimm

-- Converts a given integer between 0 and 100 to Icelandic text (e.g. 47 -> fjörutíu og sjö).
-- Breytir tölu á milli 0 og 100 yfir í íslenskan texta (t.d. 47 -> fjörutíu og sjö)
local function numeral_to_english_less_100(num, ordinal, plural, zero, gender)
	--gender = 'kvk' -- REMOVE
	
	if num == 0 and zero ~= nil then
		return zero
		
	elseif ordinal then
		local ord_ones, ord_tens, ending
		local num_mod = num % 10
		if gender == 'kvk' or gender == 'hk' then ending = 'a' else ending = 'i' end
		
		if num_mod == 2 then
			if gender == 'kvk' or gender == 'hk' then 
				ord_ones = ones_position_ord_2[gender] else 
				ord_ones = ones_position_ord_2['kk'] 
			end			
		else
			ord_ones = ones_position_ord[num_mod] .. ending
		end
		
		if num < 10 then
			return ord_ones
		elseif num < 20 then
			return ones_position_ord[num] .. ending
		elseif num % 10 == 0 then
			return tens_position_ord[num / 10] .. ending
		else
			return tens_position_ord[math.floor(num / 10)] .. ending .. ' og ' .. ord_ones
		end

	elseif plural then
		if num < 20 then
			return ones_position_plural[num]
		elseif num % 10 == 0 then
			return tens_position_plural[num / 10]
		else
			return tens_position_plural[math.floor(num / 10)] .. ' og ' .. ones_position_plural[num % 10]
		end
		
	else
		if num == 0 then return ones_position[num] end
		local reg_ones, reg_tens
		local num_mod = num % 10
		
		if num_mod < 5 then
			if gender == 'kvk' then reg_ones = ones_position_kvk[num_mod] elseif 
				gender == 'hk' then reg_ones = ones_position_hk[num_mod] else
				reg_ones = ones_position[num_mod]
				end
		else
			reg_ones = ones_position[num_mod]
		end

		if num < 5 then
			return reg_ones
		elseif num < 20 then
			return ones_position[num]
		elseif num % 10 == 0 then
			return tens_position[num / 10]
		else
			return tens_position[math.floor(num / 10)] .. ' og ' .. reg_ones
		end
	end
end

local function standard_suffix(ordinal, plural)
	if ordinal then return 'asti' end	-- eng: th
	if plural then return 'ur' end		-- eng: s
	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] .. ' hundrað' .. standard_suffix(ordinal, plural)
	else
		return ones_position[math.floor(num/100)] .. ' hundrað ' .. (use_and and 'og ' 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

-- TODO: Laga
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 = 'mínus'
		else
			negative_word = 'mínus'
		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("Ógild námundunaraðferð")
		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("Ógild tugatala") 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 .. ' og '
		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 .. ' komma'
		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