Difference between revisions of "Module:Math"

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(clean whitespace; remove unintended global orig_precision which gives errors when used with a module that invokes Module:No globals such as 1994–95 Yemeni League)
Line 1: Line 1:
 
--[[
 
--[[
+
 
 
This module provides a number of basic mathematical operations.
 
This module provides a number of basic mathematical operations.
+
 
 
]]
 
]]
+
 
local yesno = require('Module:Yesno')
+
local yesno, getArgs -- lazily initialized
local getArgs = require('Module:Arguments').getArgs
+
 
 
 
local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
 
local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
 
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
 
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
+
 
 
--[[
 
--[[
 
Helper functions used to avoid redundant code.
 
Helper functions used to avoid redundant code.
 
]]
 
]]
+
 
 
local function err(msg)
 
local function err(msg)
 
-- Generates wikitext error messages.
 
-- Generates wikitext error messages.
 
return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg)
 
return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg)
 
end
 
end
+
 
 
local function unpackNumberArgs(args)
 
local function unpackNumberArgs(args)
 
-- Returns an unpacked list of arguments specified with numerical keys.
 
-- Returns an unpacked list of arguments specified with numerical keys.
Line 30: Line 29:
 
return unpack(ret)
 
return unpack(ret)
 
end
 
end
+
 
 
local function makeArgArray(...)
 
local function makeArgArray(...)
 
-- Makes an array of arguments from a list of arguments that might include nils.
 
-- Makes an array of arguments from a list of arguments that might include nils.
Line 49: Line 48:
 
return ret
 
return ret
 
end
 
end
+
 
local function applyFuncToArgs(func, ...)
+
local function fold(func, ...)
 
-- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters,
 
-- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters,
 
-- and must return a number as an output. This number is then supplied as input to the next function call.
 
-- and must return a number as an output. This number is then supplied as input to the next function call.
local vals = makeArgArray(...)
+
local vals = makeArgArray(...)
 
local count = #vals -- The number of valid arguments
 
local count = #vals -- The number of valid arguments
 
if count == 0 then return
 
if count == 0 then return
 
-- Exit if we have no valid args, otherwise removing the first arg would cause an error.
 
-- Exit if we have no valid args, otherwise removing the first arg would cause an error.
 
nil, 0
 
nil, 0
end  
+
end
 
local ret = table.remove(vals, 1)
 
local ret = table.remove(vals, 1)
 
for _, val in ipairs(vals) do
 
for _, val in ipairs(vals) do
Line 65: Line 64:
 
return ret, count
 
return ret, count
 
end
 
end
+
 
 +
--[[
 +
Fold arguments by selectively choosing values (func should return when to choose the current "dominant" value).
 +
]]
 +
local function binary_fold(func, ...)
 +
local value = fold((function(a, b) if func(a, b) then return a else return b end end), ...)
 +
return value
 +
end
 +
 
 
--[[
 
--[[
 
random
 
random
+
 
 
Generate a random number
 
Generate a random number
+
 
 
Usage:
 
Usage:
 
{{#invoke: Math | random }}
 
{{#invoke: Math | random }}
Line 76: Line 83:
 
{{#invoke: Math | random | minimum value | maximum value }}
 
{{#invoke: Math | random | minimum value | maximum value }}
 
]]
 
]]
+
 
 
function wrap.random(args)
 
function wrap.random(args)
 
local first = p._cleanNumber(args[1])
 
local first = p._cleanNumber(args[1])
Line 82: Line 89:
 
return p._random(first, second)
 
return p._random(first, second)
 
end
 
end
+
 
 
function p._random(first, second)
 
function p._random(first, second)
 
math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
 
math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
Line 96: Line 103:
 
end
 
end
 
end
 
end
+
 
 
--[[
 
--[[
 
order
 
order
+
 
 
Determine order of magnitude of a number
 
Determine order of magnitude of a number
+
 
 
Usage:
 
Usage:
 
{{#invoke: Math | order | value }}
 
{{#invoke: Math | order | value }}
 
]]
 
]]
+
 
 
function wrap.order(args)
 
function wrap.order(args)
 
local input_string = (args[1] or args.x or '0');
 
local input_string = (args[1] or args.x or '0');
Line 113: Line 120:
 
else
 
else
 
return p._order(input_number)
 
return p._order(input_number)
end  
+
end
 
end
 
end
+
 
 
function p._order(x)
 
function p._order(x)
 
if x == 0 then return 0 end
 
if x == 0 then return 0 end
 
return math.floor(math.log10(math.abs(x)))
 
return math.floor(math.log10(math.abs(x)))
 
end
 
end
+
 
 
--[[
 
--[[
 
precision
 
precision
+
 
 
Detemines the precision of a number using the string representation
 
Detemines the precision of a number using the string representation
+
 
 
Usage:
 
Usage:
 
{{ #invoke: Math | precision | value }}
 
{{ #invoke: Math | precision | value }}
 
]]
 
]]
+
 
 
function wrap.precision(args)
 
function wrap.precision(args)
 
local input_string = (args[1] or args.x or '0');
 
local input_string = (args[1] or args.x or '0');
 
local trap_fraction = args.check_fraction;
 
local trap_fraction = args.check_fraction;
 
local input_number;
 
local input_number;
+
 
 +
if not yesno then
 +
yesno = require('Module:Yesno')
 +
end
 
if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
 
if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
 
local pos = string.find(input_string, '/', 1, true);
 
local pos = string.find(input_string, '/', 1, true);
Line 144: Line 154:
 
return math.log10(denom_value);
 
return math.log10(denom_value);
 
end
 
end
end                      
+
end
 
end
 
end
end  
+
end
+
 
 
input_number, input_string = p._cleanNumber(input_string);
 
input_number, input_string = p._cleanNumber(input_string);
 
if input_string == nil then
 
if input_string == nil then
Line 153: Line 163:
 
else
 
else
 
return p._precision(input_string)
 
return p._precision(input_string)
end  
+
end
 
end
 
end
+
 
 
function p._precision(x)
 
function p._precision(x)
 
if type(x) == 'number' then
 
if type(x) == 'number' then
Line 161: Line 171:
 
end
 
end
 
x = string.upper(x)
 
x = string.upper(x)
+
 
 
local decimal = x:find('%.')
 
local decimal = x:find('%.')
 
local exponent_pos = x:find('E')
 
local exponent_pos = x:find('E')
 
local result = 0;
 
local result = 0;
+
 
 
if exponent_pos ~= nil then
 
if exponent_pos ~= nil then
 
local exponent = string.sub(x, exponent_pos + 1)
 
local exponent = string.sub(x, exponent_pos + 1)
 
x = string.sub(x, 1, exponent_pos - 1)
 
x = string.sub(x, 1, exponent_pos - 1)
 
result = result - tonumber(exponent)
 
result = result - tonumber(exponent)
end  
+
end
+
 
 
if decimal ~= nil then
 
if decimal ~= nil then
 
result = result + string.len(x) - decimal
 
result = result + string.len(x) - decimal
 
return result
 
return result
 
end
 
end
+
 
 
local pos = string.len(x);
 
local pos = string.len(x);
 
while x:byte(pos) == string.byte('0') do
 
while x:byte(pos) == string.byte('0') do
Line 185: Line 195:
 
end
 
end
 
end
 
end
+
 
 
return result
 
return result
 
end
 
end
+
 
 +
 
 
--[[
 
--[[
 
max
 
max
+
 
 
Finds the maximum argument
 
Finds the maximum argument
+
 
 
Usage:
 
Usage:
 
{{#invoke:Math| max | value1 | value2 | ... }}
 
{{#invoke:Math| max | value1 | value2 | ... }}
+
 
 
Note, any values that do not evaluate to numbers are ignored.
 
Note, any values that do not evaluate to numbers are ignored.
 
]]
 
]]
+
 
 
function wrap.max(args)
 
function wrap.max(args)
 
return p._max(unpackNumberArgs(args))
 
return p._max(unpackNumberArgs(args))
 
end
 
end
+
 
 
function p._max(...)
 
function p._max(...)
local function maxOfTwo(a, b)
+
local max_value = binary_fold((function(a, b) return a > b end), ...)
if a > b then
 
return a
 
else
 
return b
 
end
 
end
 
local max_value = applyFuncToArgs(maxOfTwo, ...)
 
 
if max_value then
 
if max_value then
 
return max_value
 
return max_value
 
end
 
end
 
end
 
end
+
 
 
--[[
 
--[[
min  
+
median
+
 
 +
Find the median of set of numbers
 +
 
 +
Usage:
 +
{{#invoke:Math | median | number1 | number2 | ...}}
 +
OR
 +
{{#invoke:Math | median }}
 +
]]
 +
 
 +
function wrap.median(args)
 +
return p._median(unpackNumberArgs(args))
 +
end
 +
 
 +
function p._median(...)
 +
local vals = makeArgArray(...)
 +
local count = #vals
 +
table.sort(vals)
 +
 
 +
if count == 0 then
 +
return 0
 +
end
 +
 
 +
if p._mod(count, 2) == 0 then
 +
return (vals[count/2] + vals[count/2+1])/2
 +
else
 +
return vals[math.ceil(count/2)]
 +
end
 +
end
 +
 
 +
--[[
 +
min
 +
 
 
Finds the minimum argument
 
Finds the minimum argument
+
 
 
Usage:
 
Usage:
 
{{#invoke:Math| min | value1 | value2 | ... }}
 
{{#invoke:Math| min | value1 | value2 | ... }}
 
OR
 
OR
 
{{#invoke:Math| min }}
 
{{#invoke:Math| min }}
+
 
 
When used with no arguments, it takes its input from the parent
 
When used with no arguments, it takes its input from the parent
 
frame.  Note, any values that do not evaluate to numbers are ignored.
 
frame.  Note, any values that do not evaluate to numbers are ignored.
 
]]
 
]]
+
 
 
function wrap.min(args)
 
function wrap.min(args)
 
return p._min(unpackNumberArgs(args))
 
return p._min(unpackNumberArgs(args))
 
end
 
end
+
 
 
function p._min(...)
 
function p._min(...)
local function minOfTwo(a, b)
+
local min_value = binary_fold((function(a, b) return a < b end), ...)
if a < b then
 
return a
 
else
 
return b
 
end
 
end
 
local min_value = applyFuncToArgs(minOfTwo, ...)
 
 
if min_value then
 
if min_value then
 
return min_value
 
return min_value
 
end
 
end
 
end
 
end
+
 
 
--[[
 
--[[
average  
+
sum
+
 
 +
Finds the sum
 +
 
 +
Usage:
 +
{{#invoke:Math| sum | value1 | value2 | ... }}
 +
OR
 +
{{#invoke:Math| sum }}
 +
 
 +
Note, any values that do not evaluate to numbers are ignored.
 +
]]
 +
 
 +
function wrap.sum(args)
 +
return p._sum(unpackNumberArgs(args))
 +
end
 +
 
 +
function p._sum(...)
 +
local sums, count = fold((function(a, b) return a + b end), ...)
 +
if not sums then
 +
return 0
 +
else
 +
return sums
 +
end
 +
end
 +
 
 +
--[[
 +
average
 +
 
 
Finds the average
 
Finds the average
+
 
 
Usage:
 
Usage:
 
{{#invoke:Math| average | value1 | value2 | ... }}
 
{{#invoke:Math| average | value1 | value2 | ... }}
 
OR
 
OR
 
{{#invoke:Math| average }}
 
{{#invoke:Math| average }}
+
 
 
Note, any values that do not evaluate to numbers are ignored.
 
Note, any values that do not evaluate to numbers are ignored.
 
]]
 
]]
+
 
 
function wrap.average(args)
 
function wrap.average(args)
 
return p._average(unpackNumberArgs(args))
 
return p._average(unpackNumberArgs(args))
 
end
 
end
+
 
 
function p._average(...)
 
function p._average(...)
local function getSum(a, b)
+
local sum, count = fold((function(a, b) return a + b end), ...)
return a + b
 
end
 
local sum, count = applyFuncToArgs(getSum, ...)
 
 
if not sum then
 
if not sum then
 
return 0
 
return 0
Line 278: Line 329:
 
end
 
end
 
end
 
end
+
 
 
--[[
 
--[[
 
round
 
round
+
 
 
Rounds a number to specified precision
 
Rounds a number to specified precision
+
 
 
Usage:
 
Usage:
 
{{#invoke:Math | round | value | precision }}
 
{{#invoke:Math | round | value | precision }}
+
 
 
--]]
 
--]]
+
 
 
function wrap.round(args)
 
function wrap.round(args)
 
local value = p._cleanNumber(args[1] or args.value or 0)
 
local value = p._cleanNumber(args[1] or args.value or 0)
Line 296: Line 347:
 
else
 
else
 
return p._round(value, precision)
 
return p._round(value, precision)
end  
+
end
 
end
 
end
+
 
 
function p._round(value, precision)
 
function p._round(value, precision)
 
local rescale = math.pow(10, precision or 0);
 
local rescale = math.pow(10, precision or 0);
 
return math.floor(value * rescale + 0.5) / rescale;
 
return math.floor(value * rescale + 0.5) / rescale;
 
end
 
end
+
 
 +
--[[
 +
log10
 +
 
 +
returns the log (base 10) of a number
 +
 
 +
Usage:
 +
{{#invoke:Math | log10 | x }}
 +
]]
 +
 
 +
function wrap.log10(args)
 +
return math.log10(args[1])
 +
end
 +
 
 
--[[
 
--[[
 
mod
 
mod
+
 
 
Implements the modulo operator
 
Implements the modulo operator
+
 
 
Usage:
 
Usage:
 
{{#invoke:Math | mod | x | y }}
 
{{#invoke:Math | mod | x | y }}
+
 
 
--]]
 
--]]
+
 
 
function wrap.mod(args)
 
function wrap.mod(args)
 
local x = p._cleanNumber(args[1])
 
local x = p._cleanNumber(args[1])
Line 323: Line 387:
 
else
 
else
 
return p._mod(x, y)
 
return p._mod(x, y)
end  
+
end
 
end
 
end
+
 
 
function p._mod(x, y)
 
function p._mod(x, y)
 
local ret = x % y
 
local ret = x % y
Line 333: Line 397:
 
return ret
 
return ret
 
end
 
end
+
 
 
--[[
 
--[[
 
gcd
 
gcd
+
 
 
Calculates the greatest common divisor of multiple numbers
 
Calculates the greatest common divisor of multiple numbers
+
 
 
Usage:
 
Usage:
 
{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}
 
{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}
 
--]]
 
--]]
+
 
 
function wrap.gcd(args)
 
function wrap.gcd(args)
 
return p._gcd(unpackNumberArgs(args))
 
return p._gcd(unpackNumberArgs(args))
 
end
 
end
+
 
 
function p._gcd(...)
 
function p._gcd(...)
 
local function findGcd(a, b)
 
local function findGcd(a, b)
Line 360: Line 424:
 
return oldr
 
return oldr
 
end
 
end
local result, count = applyFuncToArgs(findGcd, ...)
+
local result, count = fold(findGcd, ...)
 
return result
 
return result
 
end
 
end
+
 
 
--[[
 
--[[
 
precision_format
 
precision_format
+
 
Rounds a number to the specified precision and formats according to rules  
+
Rounds a number to the specified precision and formats according to rules
 
originally used for {{template:Rnd}}.  Output is a string.
 
originally used for {{template:Rnd}}.  Output is a string.
+
 
 
Usage:
 
Usage:
 
{{#invoke: Math | precision_format | number | precision }}
 
{{#invoke: Math | precision_format | number | precision }}
 
]]
 
]]
+
 
 
function wrap.precision_format(args)
 
function wrap.precision_format(args)
 
local value_string = args[1] or 0
 
local value_string = args[1] or 0
Line 379: Line 443:
 
return p._precision_format(value_string, precision)
 
return p._precision_format(value_string, precision)
 
end
 
end
+
 
 
function p._precision_format(value_string, precision)
 
function p._precision_format(value_string, precision)
 
-- For access to Mediawiki built-in formatter.
 
-- For access to Mediawiki built-in formatter.
 
local lang = mw.getContentLanguage();
 
local lang = mw.getContentLanguage();
+
 
 
local value
 
local value
 
value, value_string = p._cleanNumber(value_string)
 
value, value_string = p._cleanNumber(value_string)
 
precision = p._cleanNumber(precision)
 
precision = p._cleanNumber(precision)
+
 
 
-- Check for non-numeric input
 
-- Check for non-numeric input
 
if value == nil or precision == nil then
 
if value == nil or precision == nil then
 
return err('invalid input when rounding')
 
return err('invalid input when rounding')
 
end
 
end
+
 
 
local current_precision = p._precision(value)
 
local current_precision = p._precision(value)
 
local order = p._order(value)
 
local order = p._order(value)
+
 
 
-- Due to round-off effects it is neccesary to limit the returned precision under
 
-- Due to round-off effects it is neccesary to limit the returned precision under
 
-- some circumstances because the terminal digits will be inaccurately reported.
 
-- some circumstances because the terminal digits will be inaccurately reported.
 
if order + precision >= 14 then
 
if order + precision >= 14 then
orig_precision = p._precision(value_string)
+
if order + p._precision(value_string) >= 14 then
if order + orig_precision >= 14 then
+
precision = 13 - order;
precision = 13 - order;      
+
end
end      
 
 
end
 
end
+
 
 
-- If rounding off, truncate extra digits
 
-- If rounding off, truncate extra digits
 
if precision < current_precision then
 
if precision < current_precision then
 
value = p._round(value, precision)
 
value = p._round(value, precision)
 
current_precision = p._precision(value)
 
current_precision = p._precision(value)
end  
+
end
+
 
 
local formatted_num = lang:formatNum(math.abs(value))
 
local formatted_num = lang:formatNum(math.abs(value))
 
local sign
 
local sign
+
 
 
-- Use proper unary minus sign rather than ASCII default
 
-- Use proper unary minus sign rather than ASCII default
 
if value < 0 then
 
if value < 0 then
Line 419: Line 482:
 
else
 
else
 
sign = ''
 
sign = ''
end  
+
end
+
 
 
-- Handle cases requiring scientific notation
 
-- Handle cases requiring scientific notation
 
if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then
 
if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then
Line 428: Line 491:
 
formatted_num = lang:formatNum(math.abs(value))
 
formatted_num = lang:formatNum(math.abs(value))
 
else
 
else
order = 0;      
+
order = 0;
 
end
 
end
 
formatted_num = sign .. formatted_num
 
formatted_num = sign .. formatted_num
+
 
-- Pad with zeros, if needed  
+
-- Pad with zeros, if needed
 
if current_precision < precision then
 
if current_precision < precision then
 
local padding
 
local padding
Line 439: Line 502:
 
local zero_sep = lang:formatNum(1.1)
 
local zero_sep = lang:formatNum(1.1)
 
formatted_num = formatted_num .. zero_sep:sub(2,2)
 
formatted_num = formatted_num .. zero_sep:sub(2,2)
+
 
 
padding = precision
 
padding = precision
 
if padding > 20 then
 
if padding > 20 then
 
padding = 20
 
padding = 20
 
end
 
end
+
 
 
formatted_num = formatted_num .. string.rep('0', padding)
 
formatted_num = formatted_num .. string.rep('0', padding)
end          
+
end
else                  
+
else
 
padding = precision - current_precision
 
padding = precision - current_precision
 
if padding > 20 then
 
if padding > 20 then
Line 455: Line 518:
 
end
 
end
 
end
 
end
+
 
 
-- Add exponential notation, if necessary.
 
-- Add exponential notation, if necessary.
 
if order ~= 0 then
 
if order ~= 0 then
Line 463: Line 526:
 
else
 
else
 
order = lang:formatNum(order)
 
order = lang:formatNum(order)
end  
+
end
+
 
 
formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
 
formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
 
end
 
end
+
 
 
return formatted_num
 
return formatted_num
 
end
 
end
+
 
 
--[[
 
--[[
Helper function that interprets the input numerically.  If the  
+
Helper function that interprets the input numerically.  If the
 
input does not appear to be a number, attempts evaluating it as
 
input does not appear to be a number, attempts evaluating it as
 
a parser functions expression.
 
a parser functions expression.
 
]]
 
]]
+
 
 
function p._cleanNumber(number_string)
 
function p._cleanNumber(number_string)
 
if type(number_string) == 'number' then
 
if type(number_string) == 'number' then
Line 485: Line 548:
 
return nil, nil;
 
return nil, nil;
 
end
 
end
+
 
 
-- Attempt basic conversion
 
-- Attempt basic conversion
 
local number = tonumber(number_string)
 
local number = tonumber(number_string)
+
 
 
-- If failed, attempt to evaluate input as an expression
 
-- If failed, attempt to evaluate input as an expression
 
if number == nil then
 
if number == nil then
local frame = mw.getCurrentFrame()
+
local success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
local attempt = frame:callParserFunction('#expr', number_string)
+
if success then
attempt = tonumber(attempt)
+
number = tonumber(result)
if attempt ~= nil then
 
number = attempt
 
 
number_string = tostring(number)
 
number_string = tostring(number)
 
else
 
else
Line 509: Line 570:
 
end
 
end
 
end
 
end
+
 
 
return number, number_string
 
return number, number_string
 
end
 
end
+
 
 
--[[
 
--[[
 
Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the current
 
Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the current
 
frame or the parent frame, and it also trims whitespace for all arguments and removes blank arguments.
 
frame or the parent frame, and it also trims whitespace for all arguments and removes blank arguments.
 
]]
 
]]
+
 
local function makeWrapper(funcName)
+
local mt = { __index = function(t, k)
return function (frame)
+
return function(frame)
local args = getArgs(frame) -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.
+
if not getArgs then
return wrap[funcName](args)
+
getArgs = require('Module:Arguments').getArgs
 +
end
 +
return wrap[k](getArgs(frame)-- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.
 
end
 
end
end
+
end }
+
 
for funcName in pairs(wrap) do
+
return setmetatable(p, mt)
p[funcName] = makeWrapper(funcName)
 
end
 
 
return p
 

Revision as of 01:55, 14 September 2019

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

--[[

This module provides a number of basic mathematical operations.

]]

local yesno, getArgs -- lazily initialized

local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.

--[[
Helper functions used to avoid redundant code.
]]

local function err(msg)
	-- Generates wikitext error messages.
	return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg)
end

local function unpackNumberArgs(args)
	-- Returns an unpacked list of arguments specified with numerical keys.
	local ret = {}
	for k, v in pairs(args) do
		if type(k) == 'number' then
			table.insert(ret, v)
		end
	end
	return unpack(ret)
end

local function makeArgArray(...)
	-- Makes an array of arguments from a list of arguments that might include nils.
	local args = {...} -- Table of arguments. It might contain nils or non-number values, so we can't use ipairs.
	local nums = {} -- Stores the numbers of valid numerical arguments.
	local ret = {}
	for k, v in pairs(args) do
		v = p._cleanNumber(v)
		if v then
			nums[#nums + 1] = k
			args[k] = v
		end
	end
	table.sort(nums)
	for i, num in ipairs(nums) do
		ret[#ret + 1] = args[num]
	end
	return ret
end

local function fold(func, ...)
	-- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters,
	-- and must return a number as an output. This number is then supplied as input to the next function call.
	local vals = makeArgArray(...)
	local count = #vals -- The number of valid arguments
	if count == 0 then return
		-- Exit if we have no valid args, otherwise removing the first arg would cause an error.
		nil, 0
	end
	local ret = table.remove(vals, 1)
	for _, val in ipairs(vals) do
		ret = func(ret, val)
	end
	return ret, count
end

--[[
Fold arguments by selectively choosing values (func should return when to choose the current "dominant" value).
]]
local function binary_fold(func, ...)
	local value = fold((function(a, b) if func(a, b) then return a else return b end end), ...)
	return value
end

--[[
random

Generate a random number

Usage:
{{#invoke: Math | random }}
{{#invoke: Math | random | maximum value }}
{{#invoke: Math | random | minimum value | maximum value }}
]]

function wrap.random(args)
	local first = p._cleanNumber(args[1])
	local second = p._cleanNumber(args[2])
	return p._random(first, second)
end

function p._random(first, second)
	math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
	-- math.random will throw an error if given an explicit nil parameter, so we need to use if statements to check the params.
	if first and second then
		if first <= second then -- math.random doesn't allow the first number to be greater than the second.
			return math.random(first, second)
		end
	elseif first then
		return math.random(first)
	else
		return math.random()
	end
end

--[[
order

Determine order of magnitude of a number

Usage:
{{#invoke: Math | order | value }}
]]

function wrap.order(args)
	local input_string = (args[1] or args.x or '0');
	local input_number = p._cleanNumber(input_string);
	if input_number == nil then
		return err('order of magnitude input appears non-numeric')
	else
		return p._order(input_number)
	end
end

function p._order(x)
	if x == 0 then return 0 end
	return math.floor(math.log10(math.abs(x)))
end

--[[
precision

Detemines the precision of a number using the string representation

Usage:
{{ #invoke: Math | precision | value }}
]]

function wrap.precision(args)
	local input_string = (args[1] or args.x or '0');
	local trap_fraction = args.check_fraction;
	local input_number;

	if not yesno then
		yesno = require('Module:Yesno')
	end
	if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
		local pos = string.find(input_string, '/', 1, true);
		if pos ~= nil then
			if string.find(input_string, '/', pos + 1, true) == nil then
				local denominator = string.sub(input_string, pos+1, -1);
				local denom_value = tonumber(denominator);
				if denom_value ~= nil then
					return math.log10(denom_value);
				end
			end
		end
	end

	input_number, input_string = p._cleanNumber(input_string);
	if input_string == nil then
		return err('precision input appears non-numeric')
	else
		return p._precision(input_string)
	end
end

function p._precision(x)
	if type(x) == 'number' then
		x = tostring(x)
	end
	x = string.upper(x)

	local decimal = x:find('%.')
	local exponent_pos = x:find('E')
	local result = 0;

	if exponent_pos ~= nil then
		local exponent = string.sub(x, exponent_pos + 1)
		x = string.sub(x, 1, exponent_pos - 1)
		result = result - tonumber(exponent)
	end

	if decimal ~= nil then
		result = result + string.len(x) - decimal
		return result
	end

	local pos = string.len(x);
	while x:byte(pos) == string.byte('0') do
		pos = pos - 1
		result = result - 1
		if pos <= 0 then
			return 0
		end
	end

	return result
end


--[[
max

Finds the maximum argument

Usage:
{{#invoke:Math| max | value1 | value2 | ... }}

Note, any values that do not evaluate to numbers are ignored.
]]

function wrap.max(args)
	return p._max(unpackNumberArgs(args))
end

function p._max(...)
	local max_value = binary_fold((function(a, b) return a > b end), ...)
	if max_value then
		return max_value
	end
end

--[[
median

Find the median of set of numbers

Usage:
{{#invoke:Math | median | number1 | number2 | ...}}
OR
{{#invoke:Math | median }}
]]

function wrap.median(args)
	return p._median(unpackNumberArgs(args))
end

function p._median(...)
	local vals = makeArgArray(...)
	local count = #vals
	table.sort(vals)

	if count == 0 then
		return 0
	end

	if p._mod(count, 2) == 0 then
		return (vals[count/2] + vals[count/2+1])/2
	else
		return vals[math.ceil(count/2)]
	end
end

--[[
min

Finds the minimum argument

Usage:
{{#invoke:Math| min | value1 | value2 | ... }}
OR
{{#invoke:Math| min }}

When used with no arguments, it takes its input from the parent
frame.  Note, any values that do not evaluate to numbers are ignored.
]]

function wrap.min(args)
	return p._min(unpackNumberArgs(args))
end

function p._min(...)
	local min_value = binary_fold((function(a, b) return a < b end), ...)
	if min_value then
		return min_value
	end
end

--[[
sum

Finds the sum

Usage:
{{#invoke:Math| sum | value1 | value2 | ... }}
OR
{{#invoke:Math| sum }}

Note, any values that do not evaluate to numbers are ignored.
]]

function wrap.sum(args)
	return p._sum(unpackNumberArgs(args))
end

function p._sum(...)
	local sums, count = fold((function(a, b) return a + b end), ...)
	if not sums then
		return 0
	else
		return sums
	end
end

--[[
average

Finds the average

Usage:
{{#invoke:Math| average | value1 | value2 | ... }}
OR
{{#invoke:Math| average }}

Note, any values that do not evaluate to numbers are ignored.
]]

function wrap.average(args)
	return p._average(unpackNumberArgs(args))
end

function p._average(...)
	local sum, count = fold((function(a, b) return a + b end), ...)
	if not sum then
		return 0
	else
		return sum / count
	end
end

--[[
round

Rounds a number to specified precision

Usage:
{{#invoke:Math | round | value | precision }}

--]]

function wrap.round(args)
	local value = p._cleanNumber(args[1] or args.value or 0)
	local precision = p._cleanNumber(args[2] or args.precision or 0)
	if value == nil or precision == nil then
		return err('round input appears non-numeric')
	else
		return p._round(value, precision)
	end
end

function p._round(value, precision)
	local rescale = math.pow(10, precision or 0);
	return math.floor(value * rescale + 0.5) / rescale;
end

--[[
log10

returns the log (base 10) of a number

Usage:
{{#invoke:Math | log10 | x }}
]]

function wrap.log10(args)
	return math.log10(args[1])
end

--[[
mod

Implements the modulo operator

Usage:
{{#invoke:Math | mod | x | y }}

--]]

function wrap.mod(args)
	local x = p._cleanNumber(args[1])
	local y = p._cleanNumber(args[2])
	if not x then
		return err('first argument to mod appears non-numeric')
	elseif not y then
		return err('second argument to mod appears non-numeric')
	else
		return p._mod(x, y)
	end
end

function p._mod(x, y)
	local ret = x % y
	if not (0 <= ret and ret < y) then
		ret = 0
	end
	return ret
end

--[[
gcd

Calculates the greatest common divisor of multiple numbers

Usage:
{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}
--]]

function wrap.gcd(args)
	return p._gcd(unpackNumberArgs(args))
end

function p._gcd(...)
	local function findGcd(a, b)
		local r = b
		local oldr = a
		while r ~= 0 do
			local quotient = math.floor(oldr / r)
			oldr, r = r, oldr - quotient * r
		end
		if oldr < 0 then
			oldr = oldr * -1
		end
		return oldr
	end
	local result, count = fold(findGcd, ...)
	return result
end

--[[
precision_format

Rounds a number to the specified precision and formats according to rules
originally used for {{template:Rnd}}.  Output is a string.

Usage:
{{#invoke: Math | precision_format | number | precision }}
]]

function wrap.precision_format(args)
	local value_string = args[1] or 0
	local precision = args[2] or 0
	return p._precision_format(value_string, precision)
end

function p._precision_format(value_string, precision)
	-- For access to Mediawiki built-in formatter.
	local lang = mw.getContentLanguage();

	local value
	value, value_string = p._cleanNumber(value_string)
	precision = p._cleanNumber(precision)

	-- Check for non-numeric input
	if value == nil or precision == nil then
		return err('invalid input when rounding')
	end

	local current_precision = p._precision(value)
	local order = p._order(value)

	-- Due to round-off effects it is neccesary to limit the returned precision under
	-- some circumstances because the terminal digits will be inaccurately reported.
	if order + precision >= 14 then
		if order + p._precision(value_string) >= 14 then
			precision = 13 - order;
		end
	end

	-- If rounding off, truncate extra digits
	if precision < current_precision then
		value = p._round(value, precision)
		current_precision = p._precision(value)
	end

	local formatted_num = lang:formatNum(math.abs(value))
	local sign

	-- Use proper unary minus sign rather than ASCII default
	if value < 0 then
		sign = '−'
	else
		sign = ''
	end

	-- Handle cases requiring scientific notation
	if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then
		value = value * math.pow(10, -order)
		current_precision = current_precision + order
		precision = precision + order
		formatted_num = lang:formatNum(math.abs(value))
	else
		order = 0;
	end
	formatted_num = sign .. formatted_num

	-- Pad with zeros, if needed
	if current_precision < precision then
		local padding
		if current_precision <= 0 then
			if precision > 0 then
				local zero_sep = lang:formatNum(1.1)
				formatted_num = formatted_num .. zero_sep:sub(2,2)

				padding = precision
				if padding > 20 then
					padding = 20
				end

				formatted_num = formatted_num .. string.rep('0', padding)
			end
		else
			padding = precision - current_precision
			if padding > 20 then
				padding = 20
			end
			formatted_num = formatted_num .. string.rep('0', padding)
		end
	end

	-- Add exponential notation, if necessary.
	if order ~= 0 then
		-- Use proper unary minus sign rather than ASCII default
		if order < 0 then
			order = '−' .. lang:formatNum(math.abs(order))
		else
			order = lang:formatNum(order)
		end

		formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
	end

	return formatted_num
end

--[[
Helper function that interprets the input numerically.  If the
input does not appear to be a number, attempts evaluating it as
a parser functions expression.
]]

function p._cleanNumber(number_string)
	if type(number_string) == 'number' then
		-- We were passed a number, so we don't need to do any processing.
		return number_string, tostring(number_string)
	elseif type(number_string) ~= 'string' or not number_string:find('%S') then
		-- We were passed a non-string or a blank string, so exit.
		return nil, nil;
	end

	-- Attempt basic conversion
	local number = tonumber(number_string)

	-- If failed, attempt to evaluate input as an expression
	if number == nil then
		local success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
		if success then
			number = tonumber(result)
			number_string = tostring(number)
		else
			number = nil
			number_string = nil
		end
	else
		number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it.
		number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs.
		if number_string:find('^%-?0[xX]') then
			-- Number is using 0xnnn notation to indicate base 16; use the number that Lua detected instead.
			number_string = tostring(number)
		end
	end

	return number, number_string
end

--[[
Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the current
frame or the parent frame, and it also trims whitespace for all arguments and removes blank arguments.
]]

local mt = { __index = function(t, k)
	return function(frame)
		if not getArgs then
			getArgs = require('Module:Arguments').getArgs
		end
		return wrap[k](getArgs(frame))  -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.
	end
end }

return setmetatable(p, mt)