Difference between revisions of "Module:ConvertNumeric/sandbox"

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blackwiki>Johnuniq
(Create sandbox version of Module:ConvertNumeric: it's transcluded on 785 pages so I'd better muck around here)
 
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-- Module for converting between different representations of numbers. See talk page for user documentation.
 
-- Module for converting between different representations of numbers. See talk page for user documentation.
 
-- For unit tests see: [[Module:ConvertNumeric/testcases]]
 
-- For unit tests see: [[Module:ConvertNumeric/testcases]]
-- When editing, preview with: Module_talk: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 = {
 
local ones_position = {
    [0] = 'zero',
+
[0] = 'zero',
    [1] = 'one',
+
[1] = 'one',
    [2] = 'two',
+
[2] = 'two',
    [3] = 'three',
+
[3] = 'three',
    [4] = 'four',
+
[4] = 'four',
    [5] = 'five',
+
[5] = 'five',
    [6] = 'six',
+
[6] = 'six',
    [7] = 'seven',
+
[7] = 'seven',
    [8] = 'eight',
+
[8] = 'eight',
    [9] = 'nine',
+
[9] = 'nine',
    [10] = 'ten',
+
[10] = 'ten',
    [11] = 'eleven',
+
[11] = 'eleven',
    [12] = 'twelve',
+
[12] = 'twelve',
    [13] = 'thirteen',
+
[13] = 'thirteen',
    [14] = 'fourteen',
+
[14] = 'fourteen',
    [15] = 'fifteen',
+
[15] = 'fifteen',
    [16] = 'sixteen',
+
[16] = 'sixteen',
    [17] = 'seventeen',
+
[17] = 'seventeen',
    [18] = 'eighteen',
+
[18] = 'eighteen',
    [19] = 'nineteen'
+
[19] = 'nineteen'
 
}
 
}
  
 
local ones_position_ord = {
 
local ones_position_ord = {
    [0] = 'zeroth',
+
[0] = 'zeroth',
    [1] = 'first',
+
[1] = 'first',
    [2] = 'second',
+
[2] = 'second',
    [3] = 'third',
+
[3] = 'third',
    [4] = 'fourth',
+
[4] = 'fourth',
    [5] = 'fifth',
+
[5] = 'fifth',
    [6] = 'sixth',
+
[6] = 'sixth',
    [7] = 'seventh',
+
[7] = 'seventh',
    [8] = 'eighth',
+
[8] = 'eighth',
    [9] = 'ninth',
+
[9] = 'ninth',
    [10] = 'tenth',
+
[10] = 'tenth',
    [11] = 'eleventh',
+
[11] = 'eleventh',
    [12] = 'twelfth',
+
[12] = 'twelfth',
    [13] = 'thirteenth',
+
[13] = 'thirteenth',
    [14] = 'fourteenth',
+
[14] = 'fourteenth',
    [15] = 'fifteenth',
+
[15] = 'fifteenth',
    [16] = 'sixteenth',
+
[16] = 'sixteenth',
    [17] = 'seventeenth',
+
[17] = 'seventeenth',
    [18] = 'eighteenth',
+
[18] = 'eighteenth',
    [19] = 'nineteenth'
+
[19] = 'nineteenth'
 
}
 
}
  
 
local ones_position_plural = {
 
local ones_position_plural = {
    [0] = 'zeros',
+
[0] = 'zeros',
    [1] = 'ones',
+
[1] = 'ones',
    [2] = 'twos',
+
[2] = 'twos',
    [3] = 'threes',
+
[3] = 'threes',
    [4] = 'fours',
+
[4] = 'fours',
    [5] = 'fives',
+
[5] = 'fives',
    [6] = 'sixes',
+
[6] = 'sixes',
    [7] = 'sevens',
+
[7] = 'sevens',
    [8] = 'eights',
+
[8] = 'eights',
    [9] = 'nines',
+
[9] = 'nines',
    [10] = 'tens',
+
[10] = 'tens',
    [11] = 'elevens',
+
[11] = 'elevens',
    [12] = 'twelves',
+
[12] = 'twelves',
    [13] = 'thirteens',
+
[13] = 'thirteens',
    [14] = 'fourteens',
+
[14] = 'fourteens',
    [15] = 'fifteens',
+
[15] = 'fifteens',
    [16] = 'sixteens',
+
[16] = 'sixteens',
    [17] = 'seventeens',
+
[17] = 'seventeens',
    [18] = 'eighteens',
+
[18] = 'eighteens',
    [19] = 'nineteens'
+
[19] = 'nineteens'
 
}
 
}
  
 
local tens_position = {
 
local tens_position = {
    [2] = 'twenty',
+
[2] = 'twenty',
    [3] = 'thirty',
+
[3] = 'thirty',
    [4] = 'forty',
+
[4] = 'forty',
    [5] = 'fifty',
+
[5] = 'fifty',
    [6] = 'sixty',
+
[6] = 'sixty',
    [7] = 'seventy',
+
[7] = 'seventy',
    [8] = 'eighty',
+
[8] = 'eighty',
    [9] = 'ninety'
+
[9] = 'ninety'
 
}
 
}
  
 
local tens_position_ord = {
 
local tens_position_ord = {
    [2] = 'twentieth',
+
[2] = 'twentieth',
    [3] = 'thirtieth',
+
[3] = 'thirtieth',
    [4] = 'fortieth',
+
[4] = 'fortieth',
    [5] = 'fiftieth',
+
[5] = 'fiftieth',
    [6] = 'sixtieth',
+
[6] = 'sixtieth',
    [7] = 'seventieth',
+
[7] = 'seventieth',
    [8] = 'eightieth',
+
[8] = 'eightieth',
    [9] = 'ninetieth'
+
[9] = 'ninetieth'
 
}
 
}
  
 
local tens_position_plural = {
 
local tens_position_plural = {
    [2] = 'twenties',
+
[2] = 'twenties',
    [3] = 'thirties',
+
[3] = 'thirties',
    [4] = 'forties',
+
[4] = 'forties',
    [5] = 'fifties',
+
[5] = 'fifties',
    [6] = 'sixties',
+
[6] = 'sixties',
    [7] = 'seventies',
+
[7] = 'seventies',
    [8] = 'eighties',
+
[8] = 'eighties',
    [9] = 'nineties'
+
[9] = 'nineties'
 
}
 
}
  
 
local groups = {
 
local groups = {
    [1] = 'thousand',
+
[1] = 'thousand',
    [2] = 'million',
+
[2] = 'million',
    [3] = 'billion',
+
[3] = 'billion',
    [4] = 'trillion',
+
[4] = 'trillion',
    [5] = 'quadrillion',
+
[5] = 'quadrillion',
    [6] = 'quintillion',
+
[6] = 'quintillion',
    [7] = 'sextillion',
+
[7] = 'sextillion',
    [8] = 'septillion',
+
[8] = 'septillion',
    [9] = 'octillion',
+
[9] = 'octillion',
    [10] = 'nonillion',
+
[10] = 'nonillion',
    [11] = 'decillion',
+
[11] = 'decillion',
    [12] = 'undecillion',
+
[12] = 'undecillion',
    [13] = 'duodecillion',
+
[13] = 'duodecillion',
    [14] = 'tredecillion',
+
[14] = 'tredecillion',
    [15] = 'quattuordecillion',
+
[15] = 'quattuordecillion',
    [16] = 'quindecillion',
+
[16] = 'quindecillion',
    [17] = 'sexdecillion',
+
[17] = 'sexdecillion',
    [18] = 'septendecillion',
+
[18] = 'septendecillion',
    [19] = 'octodecillion',
+
[19] = 'octodecillion',
    [20] = 'novemdecillion',
+
[20] = 'novemdecillion',
    [21] = 'vigintillion',
+
[21] = 'vigintillion',
    [22] = 'unvigintillion',
+
[22] = 'unvigintillion',
    [23] = 'duovigintillion',
+
[23] = 'duovigintillion',
    [24] = 'tresvigintillion',
+
[24] = 'tresvigintillion',
    [25] = 'quattuorvigintillion',
+
[25] = 'quattuorvigintillion',
    [26] = 'quinquavigintillion',
+
[26] = 'quinquavigintillion',
    [27] = 'sesvigintillion',
+
[27] = 'sesvigintillion',
    [28] = 'septemvigintillion',
+
[28] = 'septemvigintillion',
    [29] = 'octovigintillion',
+
[29] = 'octovigintillion',
    [30] = 'novemvigintillion',
+
[30] = 'novemvigintillion',
    [31] = 'trigintillion',
+
[31] = 'trigintillion',
    [32] = 'untrigintillion',
+
[32] = 'untrigintillion',
    [33] = 'duotrigintillion',
+
[33] = 'duotrigintillion',
    [34] = 'trestrigintillion',
+
[34] = 'trestrigintillion',
    [35] = 'quattuortrigintillion',
+
[35] = 'quattuortrigintillion',
    [36] = 'quinquatrigintillion',
+
[36] = 'quinquatrigintillion',
    [37] = 'sestrigintillion',
+
[37] = 'sestrigintillion',
    [38] = 'septentrigintillion',
+
[38] = 'septentrigintillion',
    [39] = 'octotrigintillion',
+
[39] = 'octotrigintillion',
    [40] = 'noventrigintillion',
+
[40] = 'noventrigintillion',
    [41] = 'quadragintillion',
+
[41] = 'quadragintillion',
    [51] = 'quinquagintillion',
+
[51] = 'quinquagintillion',
    [61] = 'sexagintillion',
+
[61] = 'sexagintillion',
    [71] = 'septuagintillion',
+
[71] = 'septuagintillion',
    [81] = 'octogintillion',
+
[81] = 'octogintillion',
    [91] = 'nonagintillion',
+
[91] = 'nonagintillion',
    [101] = 'centillion',
+
[101] = 'centillion',
    [102] = 'uncentillion',
+
[102] = 'uncentillion',
    [103] = 'duocentillion',
+
[103] = 'duocentillion',
    [104] = 'trescentillion',
+
[104] = 'trescentillion',
    [111] = 'decicentillion',
+
[111] = 'decicentillion',
    [112] = 'undecicentillion',
+
[112] = 'undecicentillion',
    [121] = 'viginticentillion',
+
[121] = 'viginticentillion',
    [122] = 'unviginticentillion',
+
[122] = 'unviginticentillion',
    [131] = 'trigintacentillion',
+
[131] = 'trigintacentillion',
    [141] = 'quadragintacentillion',
+
[141] = 'quadragintacentillion',
    [151] = 'quinquagintacentillion',
+
[151] = 'quinquagintacentillion',
    [161] = 'sexagintacentillion',
+
[161] = 'sexagintacentillion',
    [171] = 'septuagintacentillion',
+
[171] = 'septuagintacentillion',
    [181] = 'octogintacentillion',
+
[181] = 'octogintacentillion',
    [191] = 'nonagintacentillion',
+
[191] = 'nonagintacentillion',
    [201] = 'ducentillion',
+
[201] = 'ducentillion',
    [301] = 'trecentillion',
+
[301] = 'trecentillion',
    [401] = 'quadringentillion',
+
[401] = 'quadringentillion',
    [501] = 'quingentillion',
+
[501] = 'quingentillion',
    [601] = 'sescentillion',
+
[601] = 'sescentillion',
    [701] = 'septingentillion',
+
[701] = 'septingentillion',
    [801] = 'octingentillion',
+
[801] = 'octingentillion',
    [901] = 'nongentillion',
+
[901] = 'nongentillion',
    [1001] = 'millinillion',
+
[1001] = 'millinillion',
 
}
 
}
  
 
local roman_numerals = {
 
local roman_numerals = {
    I = 1,
+
I = 1,
    V = 5,
+
V = 5,
    X = 10,
+
X = 10,
    L = 50,
+
L = 50,
    C = 100,
+
C = 100,
    D = 500,
+
D = 500,
    M = 1000
+
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,
 
}
 
}
  
 
-- Converts a given valid roman numeral (and some invalid roman numerals) to a number. Returns -1, errorstring on error
 
-- 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)
 
local function roman_to_numeral(roman)
    if type(roman) ~= "string" then return -1, "roman numeral not a string" end
+
if type(roman) ~= "string" then return -1, "roman numeral not a string" end
    local rev = roman:reverse()
+
local rev = roman:reverse()
    local raising = true
+
local raising = true
    local last = 0
+
local last = 0
    local result = 0
+
local result = 0
    for i = 1, #rev do
+
for i = 1, #rev do
        local c = rev:sub(i, i)
+
local c = rev:sub(i, i)
        local next = roman_numerals[c]
+
local next = roman_numerals[c]
        if next == nil then return -1, "roman numeral contains illegal character " .. c end
+
if next == nil then return -1, "roman numeral contains illegal character " .. c end
        if next > last then
+
if next > last then
            result = result + next
+
result = result + next
            raising = true
+
raising = true
        elseif next < last then
+
elseif next < last then
            result = result - next
+
result = result - next
            raising = false
+
raising = false
        elseif raising then
+
elseif raising then
            result = result + next
+
result = result + next
        else
+
else
            result = result - next
+
result = result - next
        end
+
end
        last = next
+
last = next
    end
+
end
    return result
+
return result
 
end
 
end
  
 
-- Converts a given integer between 0 and 100 to English text (e.g. 47 -> forty-seven)
 
-- 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 function numeral_to_english_less_100(num, ordinal, plural, zero)
    local terminal_ones, terminal_tens
+
local terminal_ones, terminal_tens
    if ordinal then
+
if ordinal then
        terminal_ones = ones_position_ord
+
terminal_ones = ones_position_ord
        terminal_tens = tens_position_ord
+
terminal_tens = tens_position_ord
    elseif plural then
+
elseif plural then
        terminal_ones = ones_position_plural
+
terminal_ones = ones_position_plural
        terminal_tens = tens_position_plural
+
terminal_tens = tens_position_plural
    else
+
else
        terminal_ones = ones_position
+
terminal_ones = ones_position
        terminal_tens = tens_position
+
terminal_tens = tens_position
    end
+
end
  
    if num == 0 and zero ~= nil then
+
if num == 0 and zero ~= nil then
        return zero
+
return zero
    elseif num < 20 then
+
elseif num < 20 then
        return terminal_ones[num]
+
return terminal_ones[num]
    elseif num % 10 == 0 then
+
elseif num % 10 == 0 then
        return terminal_tens[num / 10]
+
return terminal_tens[num / 10]
    else
+
else
        return tens_position[math.floor(num / 10)] .. '-' .. terminal_ones[num % 10]
+
return tens_position[math.floor(num / 10)] .. '-' .. terminal_ones[num % 10]
    end
+
end
 
end
 
end
  
 
local function standard_suffix(ordinal, plural)
 
local function standard_suffix(ordinal, plural)
    if ordinal then return 'th' end
+
if ordinal then return 'th' end
    if plural then return 's' end
+
if plural then return 's' end
    return ''
+
return ''
 
end
 
end
  
 
-- Converts a given integer (in string form) between 0 and 1000 to English text (e.g. 47 -> forty-seven)
 
-- 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)
 
local function numeral_to_english_less_1000(num, use_and, ordinal, plural, zero)
    num = tonumber(num)
+
num = tonumber(num)
    if num < 100 then
+
if num < 100 then
        return numeral_to_english_less_100(num, ordinal, plural, zero)
+
return numeral_to_english_less_100(num, ordinal, plural, zero)
    elseif num % 100 == 0 then
+
elseif num % 100 == 0 then
        return ones_position[num/100] .. ' hundred' .. standard_suffix(ordinal, plural)
+
return ones_position[num/100] .. ' hundred' .. standard_suffix(ordinal, plural)
    else
+
else
        return ones_position[math.floor(num/100)] .. ' hundred ' .. (use_and and 'and ' or '') .. numeral_to_english_less_100(num % 100, ordinal, plural, zero)
+
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
 +
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
 
end
  
Line 261: Line 330:
 
-- e.g. 1.23E5 -> 123000, 1.23E-5 = .0000123. Conversion is exact, no rounding is performed.
 
-- e.g. 1.23E5 -> 123000, 1.23E-5 = .0000123. Conversion is exact, no rounding is performed.
 
local function scientific_notation_to_decimal(num)
 
local function scientific_notation_to_decimal(num)
    local exponent, subs = num:gsub("^%-?%d*%.?%d*%-?[Ee]([+%-]?%d+)$", "%1")
+
local exponent, subs = num:gsub("^%-?%d*%.?%d*%-?[Ee]([+%-]?%d+)$", "%1")
    if subs == 0 then return num end  -- Input not in scientific notation, just return unmodified
+
if subs == 0 then return num end  -- Input not in scientific notation, just return unmodified
    exponent = tonumber(exponent)
+
exponent = tonumber(exponent)
  
    local negative = num:find("^%-")
+
local negative = num:find("^%-")
    local _, decimal_pos = num:find("%.")
+
local _, decimal_pos = num:find("%.")
    -- Mantissa will consist of all decimal digits with no decimal point
+
-- Mantissa will consist of all decimal digits with no decimal point
    local mantissa = num:gsub("^%-?(%d*)%.?(%d*)%-?[Ee][+%-]?%d+$", "%1%2")
+
local mantissa = num:gsub("^%-?(%d*)%.?(%d*)%-?[Ee][+%-]?%d+$", "%1%2")
    if negative and decimal_pos then decimal_pos = decimal_pos - 1 end
+
if negative and decimal_pos then decimal_pos = decimal_pos - 1 end
    if not decimal_pos then decimal_pos = #mantissa + 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
+
-- Remove leading zeros unless decimal point is in first position
    while decimal_pos > 1 and mantissa:sub(1,1) == '0' do
+
while decimal_pos > 1 and mantissa:sub(1,1) == '0' do
        mantissa = mantissa:sub(2)
+
mantissa = mantissa:sub(2)
        decimal_pos = decimal_pos - 1
+
decimal_pos = decimal_pos - 1
    end
+
end
    -- Shift decimal point right for exponent > 0
+
-- Shift decimal point right for exponent > 0
    while exponent > 0 do
+
while exponent > 0 do
        decimal_pos = decimal_pos + 1
+
decimal_pos = decimal_pos + 1
        exponent = exponent - 1
+
exponent = exponent - 1
        if decimal_pos > #mantissa + 1 then mantissa = mantissa .. '0' end
+
if decimal_pos > #mantissa + 1 then mantissa = mantissa .. '0' end
        -- Remove leading zeros unless decimal point is in first position
+
-- Remove leading zeros unless decimal point is in first position
        while decimal_pos > 1 and mantissa:sub(1,1) == '0' do
+
while decimal_pos > 1 and mantissa:sub(1,1) == '0' do
            mantissa = mantissa:sub(2)
+
mantissa = mantissa:sub(2)
            decimal_pos = decimal_pos - 1
+
decimal_pos = decimal_pos - 1
        end
+
end
    end
+
end
    -- Shift decimal point left for exponent < 0
+
-- Shift decimal point left for exponent < 0
    while exponent < 0 do
+
while exponent < 0 do
        if decimal_pos == 1 then
+
if decimal_pos == 1 then
            mantissa = '0' .. mantissa
+
mantissa = '0' .. mantissa
        else
+
else
            decimal_pos = decimal_pos - 1
+
decimal_pos = decimal_pos - 1
        end
+
end
        exponent = exponent + 1
+
exponent = exponent + 1
    end
+
end
  
    -- Insert decimal point in correct position and return
+
-- Insert decimal point in correct position and return
    return (negative and '-' or '') .. mantissa:sub(1, decimal_pos - 1) .. '.' .. mantissa:sub(decimal_pos)
+
return (negative and '-' or '') .. mantissa:sub(1, decimal_pos - 1) .. '.' .. mantissa:sub(decimal_pos)
 
end
 
end
  
 
-- Rounds a number to the nearest integer (NOT USED)
 
-- Rounds a number to the nearest integer (NOT USED)
 
local function round_num(x)
 
local function round_num(x)
    if x%1 >= 0.5 then
+
if x%1 >= 0.5 then
        return math.ceil(x)
+
return math.ceil(x)
    else
+
else
        return math.floor(x)
+
return math.floor(x)
    end
+
end
 
end
 
end
  
Line 317: Line 385:
 
-- Negative sign is preserved and does not count towards word limit.
 
-- Negative sign is preserved and does not count towards word limit.
 
local function round_for_english(num, round)
 
local function round_for_english(num, round)
    -- If an integer with at most two digits, just return
+
-- If an integer with at most two digits, just return
    if num:find("^%-?%d?%d%.?$") then return num end
+
if num:find("^%-?%d?%d%.?$") then return num end
  
    local negative = num:find("^%-")
+
local negative = num:find("^%-")
    if negative then
+
if negative then
        -- We're rounding magnitude so flip it
+
-- We're rounding magnitude so flip it
        if round == 'up' then round = 'down' elseif round == 'down' then round = 'up' end
+
if round == 'up' then round = 'down' elseif round == 'down' then round = 'up' end
    end
+
end
  
    -- If at most two digits before decimal, round to integer and return
+
-- 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*)$")
+
local _, _, small_int, trailing_digits, round_digit = num:find("^%-?(%d?%d?)%.((%d)%d*)$")
    if small_int then
+
if small_int then
        local small_int_len = #small_int
+
if small_int == '' then small_int = '0' end
        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
        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)
            small_int = tostring(tonumber(small_int) + 1)
+
end
        end
+
return (negative and '-' or '') .. small_int
        return (negative and '-' or '') .. small_int
+
end
    end
 
  
    -- When rounding up, any number with > 1 nonzero digit will round up (e.g. 1000000.001 rounds up to 2000000)
+
-- When rounding up, any number with > 1 nonzero digit will round up (e.g. 1000000.001 rounds up to 2000000)
    local nonzero_digits = 0
+
local nonzero_digits = 0
    for digit in num:gfind("[1-9]") do
+
for digit in num:gfind("[1-9]") do
        nonzero_digits = nonzero_digits + 1
+
nonzero_digits = nonzero_digits + 1
    end
+
end
  
    num = num:gsub("%.%d*$", "") -- Remove decimal part
+
num = num:gsub("%.%d*$", "") -- Remove decimal part
    -- Second digit used to determine which way to round lead digit
+
-- 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*)$")
+
local _, _, lead_digit, round_digit, round_digit_2, rest = num:find("^%-?(%d)(%d)(%d)(%d*)$")
    if tonumber(lead_digit .. round_digit) < 20 and (1 + #rest) % 3 == 0 then
+
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
+
-- In English numbers < 20 are one word so put 2 digits in lead and round based on 3rd
        lead_digit = lead_digit .. round_digit
+
lead_digit = lead_digit .. round_digit
        round_digit = round_digit_2
+
round_digit = round_digit_2
    else
+
else
        rest = round_digit_2 .. rest
+
rest = round_digit_2 .. rest
    end
+
end
  
    if (round == 'up' and nonzero_digits > 1) or (round == 'on' and tonumber(round_digit) >= 5) then
+
if (round == 'up' and nonzero_digits > 1) or (round == 'on' and tonumber(round_digit) >= 5) then
        lead_digit = tostring(tonumber(lead_digit) + 1)
+
lead_digit = tostring(tonumber(lead_digit) + 1)
    end
+
end
    -- All digits but lead digit will turn to zero
+
-- All digits but lead digit will turn to zero
    rest = rest:gsub("%d", "0")
+
rest = rest:gsub("%d", "0")
    return (negative and '-' or '') .. lead_digit .. '0' .. rest
+
return (negative and '-' or '') .. lead_digit .. '0' .. rest
 
end
 
end
  
-- Return fraction (numerator / denominator) as English text.
+
local denominators = {
-- Return '' if no fraction; return nil if fraction is not supported.
+
[2] = { 'half', plural = 'halves' },
-- Only unsigned fractions with a very limited range of values are supported.
+
[3] = { 'third' },
-- whole (string or nil): nil if no number before the fraction (ignored apart from that)
+
[4] = { 'quarter', us = 'fourth' },
-- numerator (string or nil): numerator, if any
+
[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
 
-- denominator (string or nil): denominator, if any
 
-- sp_us (boolean): true if sp=us
 
-- sp_us (boolean): true if sp=us
local function fraction_to_english(whole, numerator, denominator, sp_us)
+
-- negative_word (string): word to use for negative sign, if whole is empty
    if numerator and denominator then
+
-- use_one (boolean): false: 2+1/2 → "two and a half"; true: "two and one-half"
        -- TODO Write code! Following is for quick testing.
+
local function fraction_to_english(whole, numerator, denominator, sp_us, negative_word, use_one)
        if numerator == '1' then
+
if numerator or denominator then
            if denominator == '2' then
+
local finished = (whole == nil or whole == '')
                if whole then
+
local sign = ''
                    return 'and a half'
+
if numerator then
                else
+
if finished and numerator:sub(1, 1) == '-' then
                    return 'one half'
+
numerator = numerator:sub(2)
                end
+
sign = negative_word .. ' '
            end
+
end
            if denominator == '4' then
+
else
                if sp_us then
+
numerator = '1'
                    if whole then
+
end
                        return 'and a fourth'
+
if not numerator:match('^%d+$') or not denominator or not denominator:match('^%d+$') then
                    else
+
return 'unsupported', ''
                        return 'one fourth'
+
end
                    end
+
numerator = tonumber(numerator)
                else
+
denominator = tonumber(denominator)
                    if whole then
+
local dendata = denominators[denominator]
                        return 'and a quarter'
+
if not (dendata and 1 <= numerator and numerator <= 99) then
                    else
+
return 'unsupported', ''
                        return 'one quarter'
+
end
                    end
+
local numstr, denstr
                end
+
local sep = '-'
            end
+
if numerator == 1 then
        end
+
denstr = sp_us and dendata.us or dendata[1]
    else
+
if finished or use_one then
        return ''
+
numstr = 'one'
    end
+
elseif denstr:match('^[aeiou]') then
    return nil
+
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
 
end
  
Line 421: Line 523:
 
-- round: nil or '': no rounding; 'on': round to nearest two-word number; 'up'/'down': round up/down to two-word number
 
-- 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)
 
-- zero: word to use for value '0' (nil to use default)
local function _numeral_to_english(num, numerator, denominator, capitalize, use_and, hyphenate, ordinal, plural, links, negative_word, round, zero)
+
-- use_one (boolean): false: 2+1/2 → "two and a half"; true: "two and one-half"
    if not negative_word then
+
local function _numeral_to_english(num, numerator, denominator, capitalize, use_and, hyphenate, ordinal, plural, links, negative_word, round, zero, use_one)
        if use_and then
+
if not negative_word then
            -- TODO Should 'minus' be used when do not have sp=us?
+
if use_and then
            --      If so, need to update testcases, and need to fix "minus zero".
+
-- TODO Should 'minus' be used when do not have sp=us?
            -- negative_word = 'minus'
+
--      If so, need to update testcases, and need to fix "minus zero".
            negative_word = 'negative'
+
-- negative_word = 'minus'
        else
+
negative_word = 'negative'
            negative_word = 'negative'
+
else
        end
+
negative_word = 'negative'
    end
+
end
    local fraction_text = fraction_to_english(num, numerator, denominator, not use_and)
+
end
    if not fraction_text then
+
local status, fraction_text = fraction_to_english(num, numerator, denominator, not use_and, negative_word, use_one)
        return nil
+
if status == 'unsupported' then
    end
+
return nil
    if not num then
+
end
        return fraction_text
+
if status == 'finished' then
    end
+
-- Input is a fraction with no whole number.
    if fraction_text ~= '' then
+
-- Hack to avoid executing stuff that depends on num being a number.
        fraction_text = ' ' .. fraction_text
+
local s = fraction_text
    end
+
if hyphenate then s = s:gsub("%s", "-") end
    num = scientific_notation_to_decimal(num)
+
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
  
    if round and round ~= '' and round ~= 'on' and round ~= 'up' and round ~= 'down' then return 'Invalid rounding mode' end
+
s = s:gsub("^%s*(.-)%s*$", "%1")  -- Trim whitespace
    if round and round ~= '' then num = round_for_english(num, round) end
+
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
  
    -- Separate into negative sign, num (digits before decimal), decimal_places (digits after decimal)
+
local function _numeral_to_english2(args)
    local MINUS = '−'  -- Unicode U+2212 MINUS SIGN (may be in values from [[Module:Convert]])
+
local num = args.num
    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 'Invalid decimal numeral' end
 
  
    -- For each group of 3 digits except the last one, print with appropriate group name (e.g. million)
+
if (not tonumber(num)) then
    local s = ''
+
num = num:gsub("^%s*(.-)%s*$", "%1")   -- Trim whitespace
    while #num > 3 do
+
num = num:gsub(",", "")  -- Remove commas
        if s ~= '' then s = s .. ' ' end
+
num = num:gsub("^<span[^<>]*></span>", "") -- Generated by Template:age
        local group_num = math.floor((#num - 1) / 3)
+
if num ~= '' then  -- a fraction may have an empty whole number
        local group = groups[group_num]
+
if not num:find("^%-?%d*%.?%d*%-?[Ee]?[+%-]?%d*$") then
        local group_digits = #num - group_num*3
+
-- Input not in a valid format, try to pass it through #expr to see
        s = s .. numeral_to_english_less_1000(num:sub(1, group_digits), false, false, false, zero) .. ' '
+
-- if that produces a number (e.g. "3 + 5" will become "8").
        if links and (((links == 'on' and group_num >= 3) or links:find(group)) and group_num <= 13) then
+
num = mw.getCurrentFrame():preprocess('{{#expr: ' .. num .. '}}')
            s = s .. '[[Orders_of_magnitude_(numbers)#10' .. group_num*3 .. '|' .. group .. ']]'
+
end
        else
+
end
            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
+
-- Pass args from frame to helper function
    if s ~= '' and num ~= '' then
+
return _numeral_to_english(
        if #num <= 2 and use_and then
+
num,
            s = s .. ' and '
+
args['numerator'],
        else
+
args['denominator'],
            s = s .. ' '
+
args['capitalize'],
        end
+
args['use_and'],
    end
+
args['hyphenate'],
    if s == '' or num ~= '' then
+
args['ordinal'],
        s = s .. numeral_to_english_less_1000(num, use_and, ordinal, plural, zero)
+
args['plural'],
    elseif ordinal or plural then
+
args['links'],
        -- Round numbers like "one million" take standard suffixes for ordinal/plural
+
args['negative_word'],
        s = s .. standard_suffix(ordinal, plural)
+
args['round'],
    end
+
args['zero'],
 +
args['use_one']
 +
) or ''
 +
end
  
    -- For decimal places (if any) output "point" followed by spelling out digit by digit
+
local p = {  -- Functions that can be called from another module
    if decimal_places then
+
roman_to_numeral = roman_to_numeral,
        s = s .. ' point'
+
spell_number = _numeral_to_english,
        for i = 1, #decimal_places do
+
spell_number2 = _numeral_to_english2,
            s = s .. ' ' .. ones_position[tonumber(decimal_places:sub(i,i))]
+
english_to_ordinal = english_to_ordinal,
        end
+
}
    end
 
  
    s = s:gsub("^%s*(.-)%s*$", "%1")  -- Trim whitespace
+
function p._roman_to_numeral(frame) -- Callable via {{#invoke:ConvertNumeric|_roman_to_numeral|VI}}
    if ordinal and plural then s = s .. 's' end  -- s suffix works for all ordinals
+
return roman_to_numeral(frame.args[1])
    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
 
end
  
local p = { spell_number = _numeral_to_english } -- can be called from another module
+
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)
 
function p.numeral_to_english(frame)
    local args = frame.args
+
local args = frame.args
    local num = args[1]
+
local num = args[1]
    num = num:gsub("^%s*(.-)%s*$", "%1")  -- Trim whitespace
+
num = num:gsub("^%s*(.-)%s*$", "%1")  -- Trim whitespace
    num = num:gsub(",", "")  -- Remove commas
+
num = num:gsub(",", "")  -- Remove commas
    if not num:find("^%-?%d*%.?%d*%-?[Ee]?[+%-]?%d*$") then
+
num = num:gsub("^<span[^<>]*></span>", "") -- Generated by Template:age
        -- Input not in a valid format, try to pass it through #expr to see if that produces a number
+
if num ~= '' then  -- a fraction may have an empty whole number
        -- (e.g. "3 + 5" will become 8)
+
if not num:find("^%-?%d*%.?%d*%-?[Ee]?[+%-]?%d*$") then
        num = frame:preprocess('{{#expr: ' .. num .. '}}')
+
-- Input not in a valid format, try to pass it through #expr to see
    end
+
-- 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
+
-- Pass args from frame to helper function
    local numerator = args['numerator']
+
return _numeral_to_english(
    local denominator = args['denominator']
+
num,
    local case = args['case']
+
args['numerator'],
    local sp = args['sp']
+
args['denominator'],
    local adj = args['adj']
+
args['case'] == 'U' or args['case'] == 'u',
    local ord = args['ord']
+
args['sp'] ~= 'us',
    local pl = args['pl']
+
args['adj'] == 'on',
    local lk = args['lk']
+
args['ord'] == 'on',
    local negative = args['negative']
+
args['pl'] == 'on',
    local round = args['round']
+
args['lk'],
    local zero = args['zero']
+
args['negative'],
    return _numeral_to_english(num, numerator, denominator,
+
args['round'],
        case == 'U' or case == 'u', sp ~= 'us', adj == 'on',
+
args['zero'],
        ord == 'on', pl == 'on', lk, negative, round, zero) or ''
+
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
 
end
  
 
---- recursive function for p.decToHex
 
---- recursive function for p.decToHex
 
local function decToHexDigit(dec)
 
local function decToHexDigit(dec)
  local dig = {"0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"}
+
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 div = math.floor(dec/16)
  local mod = dec-(16*div)
+
local mod = dec-(16*div)
  if div >= 1 then return decToHexDigit(div)..dig[mod+1] else return dig[mod+1] end
+
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
 
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
 
---- finds all the decimal numbers in the input text and hexes each of them
 
function p.decToHex(frame)
 
function p.decToHex(frame)
  local args=frame.args
+
local args=frame.args
  local parent=frame.getParent(frame)
+
local parent=frame.getParent(frame)
  local pargs={}
+
local pargs={}
  if parent then pargs=parent.args end
+
if parent then pargs=parent.args end
  local text=args[1] or pargs[1] or ""
+
local text=args[1] or pargs[1] or ""
  local minlength=args.minlength or pargs.minlength or 1
+
local minlength=args.minlength or pargs.minlength or 1
  minlength=tonumber(minlength)
+
minlength=tonumber(minlength)
  local prowl=mw.ustring.gmatch(text,"(.-)(%d+)")
+
local prowl=mw.ustring.gmatch(text,"(.-)(%d+)")
  local output=""
+
local output=""
  repeat
+
repeat
      local chaff,dec=prowl()
+
local chaff,dec=prowl()
      if not(dec) then break end
+
if not(dec) then break end
      local hex=decToHexDigit(dec)
+
local hex=decToHexDigit(dec)
      while (mw.ustring.len(hex)<minlength) do hex="0"..hex end
+
while (mw.ustring.len(hex)<minlength) do hex="0"..hex end
      output=output..chaff..hex
+
output=output..chaff..hex
  until false
+
until false
  local chaff=mw.ustring.match(text,"(%D+)$") or ""
+
local chaff=mw.ustring.match(text,"(%D+)$") or ""
  return output..chaff
+
return output..chaff
 
end
 
end
  
 
return p
 
return p

Latest revision as of 15:53, 26 September 2020

Documentation for this module may be created at Module:ConvertNumeric/sandbox/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 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,
}

-- 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 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 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 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

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,
}

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

---- 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