Module:Math: Difference between revisions

Jump to navigation Jump to search
imported>Dragons flight
(add average)
m (Protected "Module:Math": Important page ([Edit=Allow only administrators] (indefinite) [Move=Allow only administrators] (indefinite)))
 
(16 intermediate revisions by 3 users not shown)
Line 4: Line 4:


]]
]]
local z = {}


-- Generate random number
local yesno, getArgs -- lazily initialized
function z.random( frame )
    first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil
    second = tonumber(frame.args[2])


    if first then -- if NaN or nil, will skip down to final return
local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
        if first <= second then -- could match if both nil, but already checked that first is a number in last line
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
            return math.random(first, second)
 
        end
--[[
        return math.random(first)
Helper functions used to avoid redundant code.
    end 
]]
    return math.random()
 
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
end


Line 26: Line 110:


Usage:
Usage:
    {{#invoke: Math | order | value }}
{{#invoke: Math | order | value }}
]]
]]
function z.order(frame)
 
    local input_string = (frame.args[1] or frame.args.x or '0');
function wrap.order(args)
    local input_number;
local input_string = (args[1] or args.x or '0');
   
local input_number = p._cleanNumber(input_string);
    input_number = z._cleanNumber( frame, input_string );
if input_number == nil then
    if input_number == nil then
return err('order of magnitude input appears non-numeric')
        return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
else
    else
return p._order(input_number)
        return z._order( input_number )
end
    end  
end
end
function z._order(x)
 
    if x == 0 then return 0 end
function p._order(x)
    return math.floor(math.log10(math.abs(x)))
if x == 0 then return 0 end
return math.floor(math.log10(math.abs(x)))
end
end


Line 50: Line 134:


Usage:
Usage:
    {{ #invoke: Math | precision | value }}
{{ #invoke: Math | precision | value }}
]]
]]
function z.precision( frame )
 
    local input_string = (frame.args[1] or frame.args.x or '0');
function wrap.precision(args)
    local trap_fraction = frame.args.check_fraction or false;
local input_string = (args[1] or args.x or '0');
    local input_number;
local trap_fraction = args.check_fraction;
   
local input_number;
    if type( trap_fraction ) == 'string' then
 
        trap_fraction = trap_fraction:lower();
if not yesno then
        if trap_fraction == 'false' or trap_fraction == '0' or
yesno = require('Module:Yesno')
                trap_fraction == 'no' or trap_fraction == '' then
end
            trap_fraction = false;
if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
        else
local pos = string.find(input_string, '/', 1, true);
            trap_fraction = true;
if pos ~= nil then
        end
if string.find(input_string, '/', pos + 1, true) == nil then
    end
local denominator = string.sub(input_string, pos+1, -1);
   
local denom_value = tonumber(denominator);
    if trap_fraction then
if denom_value ~= nil then
        local pos = string.find( input_string, '/', 1, true );
return math.log10(denom_value);
        if pos ~= nil then
end
            if string.find( input_string, '/', pos + 1, true ) == nil then
end
                local denominator = string.sub( input_string, pos+1, -1 );
end
                local denom_value = tonumber( denominator );
end
                if denom_value ~= nil then
 
                    return math.log10(denom_value);
input_number, input_string = p._cleanNumber(input_string);
                end
if input_string == nil then
            end                      
return err('precision input appears non-numeric')
        end
else
    end  
return p._precision(input_string)
   
end
    input_number, input_string = z._cleanNumber( frame, input_string );
    if input_string == nil then
        return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>'
    else
        return z._precision( input_string )
    end  
end
end
function z._precision( x )   
    x = string.upper( x )


    local decimal = string.find( x, '.', 1, true )
function p._precision(x)
    local exponent_pos = string.find( x, 'E', 1, true )
if type(x) == 'number' then
    local result = 0;
x = tostring(x)
   
end
    if exponent_pos ~= nil then
x = string.upper(x)
        local exponent = string.sub( x, exponent_pos + 1 )
 
        x = string.sub( x, 1, exponent_pos - 1 )
local decimal = x:find('%.')
        result = result - tonumber( exponent )
local exponent_pos = x:find('E')
    end  
local result = 0;
   
 
    if decimal ~= nil then
if exponent_pos ~= nil then
        result = result + string.len( x ) - decimal
local exponent = string.sub(x, exponent_pos + 1)
        return result
x = string.sub(x, 1, exponent_pos - 1)
    end
result = result - tonumber(exponent)
       
end
    local pos = string.len( x );
 
    while x:byte(pos) == string.byte('0') do
if decimal ~= nil then
        pos = pos - 1
result = result + string.len(x) - decimal
        result = result - 1
return result
        if pos <= 0 then
end
            return 0
 
        end
local pos = string.len(x);
    end
while x:byte(pos) == string.byte('0') do
   
pos = pos - 1
    return result
result = result - 1
if pos <= 0 then
return 0
end
end
 
return result
end
end


--[[
--[[
Line 123: Line 206:


Usage:
Usage:
    {{#invoke:Math| max | value1 | value2 | ... }}
{{#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
OR
    {{#invoke:Math| max }}
{{#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
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 z.max( frame )
 
    local args = frame.args;
function wrap.min(args)
   
return p._min(unpackNumberArgs(args))
    if args[1] == nil then
end
        local parent = frame:getParent();
 
        args = parent.args;
function p._min(...)
    end
local min_value = binary_fold((function(a, b) return a < b end), ...)
    local max_value = nil;
if min_value then
   
return min_value
    local i = 1;
end
    while args[i] ~= nil do
        local val = z._cleanNumber( frame, args[i] );
        if val ~= nil then
            if max_value == nil or val > max_value then
                max_value = val;
            end
        end       
        i = i + 1;
    end
 
    return max_value
end
end


--[[
--[[
min
sum


Finds the minimum argument
Finds the sum


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


When used with no arguments, it takes its input from the parent
Note, any values that do not evaluate to numbers are ignored.
frame.  Note, any values that do not evaluate to numbers are ignored.
]]
]]
function z.min( frame )
 
    local args = frame.args;
function wrap.sum(args)
   
return p._sum(unpackNumberArgs(args))
    if args[1] == nil then
end
        local parent = frame:getParent();
 
        args = parent.args;
function p._sum(...)
    end
local sums, count = fold((function(a, b) return a + b end), ...)
    local min_value = nil;
if not sums then
   
return 0
    local i = 1;
else
    while args[i] ~= nil do
return sums
        local val = z._cleanNumber( frame, args[i] );
end
        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


--[[
--[[
average  
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 }}
 
When used with no arguments, it takes its input from the parent
Note, any values that do not evaluate to numbers are ignored.
frame.  Note, any values that do not evaluate to numbers are ignored.
]]
]]
function z.average( frame )
 
    local args = frame.args;
function wrap.average(args)
    if args[1] == nil then
return p._average(unpackNumberArgs(args))
        local parent = frame:getParent();
end
        args = parent.args;
 
    end
function p._average(...)
    local sum = 0;
local sum, count = fold((function(a, b) return a + b end), ...)
    local count = 0;
if not sum then
return 0
    local i = 1;
else
    while args[i] ~= nil do
return sum / count
        local val = z._cleanNumber( frame, args[i] );
end
        if val ~= nil then
            sum = sum + val
            count = count + 1
        end       
        i = i + 1;
    end
    return (count == 0 and 0 or sum/count)
end
end


Line 230: Line 336:


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


Line 253: Line 431:
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 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 );
function wrap.precision_format(args)
   
local value_string = args[1] or 0
    -- Due to round-off effects it is neccesary to limit the returned precision under
local precision = args[2] or 0
    -- some circumstances because the terminal digits will be inaccurately reported.
return p._precision_format(value_string, precision)
    if order + precision >= 14 then
end
        orig_precision = z._precision( value_string );
 
        if order + orig_precision >= 14 then
function p._precision_format(value_string, precision)
            precision = 13 - order;      
-- For access to Mediawiki built-in formatter.
        end      
local lang = mw.getContentLanguage();
    end
 
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


    -- If rounding off, truncate extra digits
-- Add exponential notation, if necessary.
    if precision < current_precision then
if order ~= 0 then
        value = z._round( value, precision );
-- Use proper unary minus sign rather than ASCII default
        current_precision = z._precision( value );
if order < 0 then
    end   
order = '−' .. lang:formatNum(math.abs(order))
   
else
    local formatted_num = lang:formatNum( math.abs(value) );
order = lang:formatNum(order)
    local sign;
end
   
    -- 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;
formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
                if padding > 20 then
end
                    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.
return formatted_num
    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
end


--[[
--[[
Helper function that interprets the input numerically.  If the  
divide
 
Implements the division operator
 
Usage:
{{#invoke:Math | divide | x | y | round= | precision= }}
 
--]]
function wrap.divide(args)
local x = args[1]
local y = args[2]
local round = args.round
local precision =  args.precision
if not yesno then
yesno = require('Module:Yesno')
end
return p._divide(x, y, yesno(round), precision)
end
 
function p._divide(x, y, round, precision)
if y == nil or y == "" then
return err("Empty divisor")
elseif not tonumber(y) then
if type(y) == 'string' and string.sub(y, 1, 1) == '<' then
return y
else
return err("Not a number: " .. y)
end
elseif x == nil or x == "" then
return err("Empty dividend")
elseif not tonumber(x) then
if type(x) == 'string' and string.sub(x, 1, 1) == '<' then
return x
else
return err("Not a number: " .. x)
end
else
local z = x / y
if round then
return p._round(z, 0)
elseif precision then
return p._round(z, precision)
else
return z
end
end
end
 
--[[
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 z._cleanNumber( frame, number_string )
function p._cleanNumber(number_string)
    if number_string == nil or number_string:len() == 0 then
if type(number_string) == 'number' then
        return nil, nil;
-- We were passed a number, so we don't need to do any processing.
    end  
return number_string, tostring(number_string)
   
elseif type(number_string) ~= 'string' or not number_string:find('%S') then
    -- Attempt basic conversion
-- We were passed a non-string or a blank string, so exit.
    local number = tonumber( number_string )
return nil, nil;
   
end
    -- If failed, attempt to evaluate input as an expression
 
    if number == nil then      
-- Attempt basic conversion
        local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
local number = tonumber(number_string)
        attempt = tonumber( attempt );
 
        if attempt ~= nil then
-- If failed, attempt to evaluate input as an expression
            number = attempt;
if number == nil then
            number_string = tostring( number );
local success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
        else
if success then
            number = nil;
number = tonumber(result)
            number_string = nil;
number_string = tostring(number)
        end
else
    else
number = nil
    -- String is valid but may contain padding, clean it.
number_string = nil
        number_string = number_string:match( "^%s*(.-)%s*$" );
end
    end
else
   
number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it.
    return number, number_string;
number_string = number_string:match("^%+(.*)$") 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
end


return z
--[[
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 03:33, 15 September 2023

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

--[[
divide

Implements the division operator

Usage:
{{#invoke:Math | divide | x | y | round= | precision= }}

--]]
function wrap.divide(args)
	local x = args[1]
	local y = args[2]
	local round = args.round
	local precision =  args.precision
	if not yesno then
		yesno = require('Module:Yesno')
	end
	return p._divide(x, y, yesno(round), precision)
end

function p._divide(x, y, round, precision)
	if y == nil or y == "" then
		return err("Empty divisor")
	elseif not tonumber(y) then
		if type(y) == 'string' and string.sub(y, 1, 1) == '<' then
			return y
		else
			return err("Not a number: " .. y)
		end
	elseif x == nil or x == "" then
		return err("Empty dividend")
	elseif not tonumber(x) then
		if type(x) == 'string' and string.sub(x, 1, 1) == '<' then
			return x
		else
			return err("Not a number: " .. x)
		end
	else
		local z = x / y
		if round then
			return p._round(z, 0)
		elseif precision then
			return p._round(z, precision)
		else
			return z	
		end
	end
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)