Module:ConvertNumeric

Documentation for this module may be created at Module:ConvertNumeric/doc

-- 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