Module:Math: Difference between revisions

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(adds expression checking, more error messages, and better handling of some precision format cases, and precision flooding check)
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local z = {}
--[[
require( "mw.language" );


-- Clean numeric value
This module provides a number of basic mathematical operations.
function z._cleanNumber( frame, number_string )
 
    -- Attempt basic conversion
]]
    local number = tonumber( number_string )
 
   
local yesno, getArgs -- lazily initialized
    -- If failed, attempt to evaluate input as an expression
 
    if number == nil then
local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
        local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
        attempt = tonumber( attempt );
 
        if attempt ~= nil then
--[[
            number = attempt;
Helper functions used to avoid redundant code.
            number_string = tostring( number );
]]
        else
 
            number = nil;
local function err(msg)
            number_string = nil;
-- Generates wikitext error messages.
        end
return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg)
    else
    -- String is valid but may contain padding, clean it.
        number_string = number_string:match( "^%s*(.-)%s*$" );
    end
   
    return number, number_string;
end
end


-- Generate random number
local function unpackNumberArgs(args)
function z.random( frame )
-- Returns an unpacked list of arguments specified with numerical keys.
    first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil
local ret = {}
    second = tonumber(frame.args[2])
for k, v in pairs(args) do
if type(k) == 'number' then
table.insert(ret, v)
end
end
return unpack(ret)
end


    if first then -- if NaN or nil, will skip down to final return
local function makeArgArray(...)
        if first <= second then -- could match if both nil, but already checked that first is a number in last line
-- Makes an array of arguments from a list of arguments that might include nils.
            return math.random(first, second)
local args = {...} -- Table of arguments. It might contain nils or non-number values, so we can't use ipairs.
        end
local nums = {} -- Stores the numbers of valid numerical arguments.
        return math.random(first)
local ret = {}
    end  
for k, v in pairs(args) do
    return math.random()
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
end


-- Determine order of magnitude
local function fold(func, ...)
function z.order(frame)
-- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters,
    local input_string = (frame.args[1] or frame.args.x or '0');
-- and must return a number as an output. This number is then supplied as input to the next function call.
    local input_number;
local vals = makeArgArray(...)
   
local count = #vals -- The number of valid arguments
    input_number = z._cleanNumber( frame, input_string );
if count == 0 then return
    if input_number == nil then
-- Exit if we have no valid args, otherwise removing the first arg would cause an error.
        return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
nil, 0
    else
end
        return z._order( input_number )
local ret = table.remove(vals, 1)
    end  
for _, val in ipairs(vals) do
ret = func(ret, val)
end
return ret, count
end
end
function z._order(x)
 
    if x == 0 then return 0 end
--[[
    return math.floor(math.log10(math.abs(x)))
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
end


-- Determines precision of a number using the string representation
--[[
function z.precision( frame )
random
    local input_string = (frame.args[1] or frame.args.x or '0');
 
    local input_number;
Generate a random number
   
 
    input_number, input_string = z._cleanNumber( frame, input_string );
Usage:
    if input_string == nil then
{{#invoke: Math | random }}
        return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>'
{{#invoke: Math | random | maximum value }}
    else
{{#invoke: Math | random | minimum value | maximum value }}
        return z._precision( input_string )
]]
    end   
 
function wrap.random(args)
local first = p._cleanNumber(args[1])
local second = p._cleanNumber(args[2])
return p._random(first, second)
end
end
function z._precision( x )   
    x = string.upper( x )


    local decimal = string.find( x, '.', 1, true )
function p._random(first, second)
    local exponent_pos = string.find( x, 'E', 1, true )
math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
    local result = 0;
-- 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 exponent_pos ~= nil then
if first <= second then -- math.random doesn't allow the first number to be greater than the second.
        local exponent = string.sub( x, exponent_pos + 1 )
return math.random(first, second)
        x = string.sub( x, 1, exponent_pos - 1 )
end
        result = result - tonumber( exponent )
elseif first then
    end   
return math.random(first)
   
else
    if decimal ~= nil then
return math.random()
        result = result + string.len( x ) - decimal
end
        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
end


-- Finds maximum argument
--[[
function z.max( frame )
order
    if frame.args[1] == nil then
 
        return ''
Determine order of magnitude of a number
    end
 
    local max_value = nil;
Usage:
   
{{#invoke: Math | order | value }}
    local i = 1;
]]
    while frame.args[i] ~= nil do
 
        local val = z._cleanNumber( frame, frame.args[i] );
function wrap.order(args)
        if val ~= nil then
local input_string = (args[1] or args.x or '0');
            if max_value == nil or val > max_value then
local input_number = p._cleanNumber(input_string);
                max_value = val;
if input_number == nil then
            end
return err('order of magnitude input appears non-numeric')
        end       
else
        i = i + 1;
return p._order(input_number)
    end
end
 
    return max_value
end
end


-- Finds minimum argument
function p._order(x)
function z.min( frame )
if x == 0 then return 0 end
    if frame.args[1] == nil then
return math.floor(math.log10(math.abs(x)))
        return ''
    end
    local min_value = nil;
   
    local i = 1;
    while frame.args[i] ~= nil do
        local val = z._cleanNumber( frame, frame.args[i] );
        if val ~= nil then
            if min_value == nil or val < min_value then
                min_value = val;
            end
        end       
        i = i + 1;
    end
 
    return min_value
end
end


-- Rounds a number to specified precision
--[[
function z.round(frame)
precision
    local value, precision;
 
   
Detemines the precision of a number using the string representation
    value = z._cleanNumber( frame, frame.args[1] or frame.args.value or 0 );
 
    precision = z._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 );
Usage:
   
{{ #invoke: Math | precision | value }}
    if value == nil or precision == nil then
]]
        return '<strong class="error">Formatting error: Round input appears non-numeric</strong>'
 
    else
function wrap.precision(args)
        return z._round( value, precision );
local input_string = (args[1] or args.x or '0');
    end  
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
end
function z._round( value, precision )
 
    local rescale = math.pow( 10, precision );
function p._precision(x)
    return math.floor( value * rescale + 0.5 ) / rescale;
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
end


-- Rounds a number to the specified precision and formats according to rules
-- originally used for {{template:Rnd}}.  Output is a string.
function z.precision_format( frame )
    -- For access to Mediawiki built-in formatter.
    local lang = mw.getContentLanguage();
   
    local value_string, value, precision;
    value, value_string = z._cleanNumber( frame, frame.args[1] or 0 );
    precision = z._cleanNumber( frame, frame.args[2] or 0 );
   
    -- Check for non-numeric input
    if value == nil or precision == nil then
        return '<strong class="error">Formatting error: invalid input when rounding</strong>'
    end
   
    local current_precision = z._precision( value );


    local order = z._order( value );
--[[
   
max
    -- Due to round-off effects it is neccesary to limit the returned precision under
 
    -- some circumstances because the terminal digits will be inaccurately reported.
Finds the maximum argument
    if order + precision >= 14 then
 
        orig_precision = z._precision( value_string );
Usage:
        if order + orig_precision >= 14 then
{{#invoke:Math| max | value1 | value2 | ... }}
            precision = 13 - order;       
        end       
    end


    -- If rounding off, truncate extra digits
Note, any values that do not evaluate to numbers are ignored.
    if precision < current_precision then
]]
        value = z._round( value, precision );
        current_precision = z._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;
function wrap.max(args)
                if padding > 20 then
return p._max(unpackNumberArgs(args))
                    padding = 20;
end
                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.
function p._max(...)
    if order ~= 0 then
local max_value = binary_fold((function(a, b) return a > b end), ...)
        -- Use proper unary minus sign rather than ASCII default
if max_value then
        if order < 0 then
return max_value
            order = '−' .. lang:formatNum( math.abs(order) );
end
        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
end


return z
--[[
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)

Latest revision as of 00:52, 3 September 2020

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)