Module:Math: Difference between revisions

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    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


    When used with no arguments, it takes its input from the parent
    function p._median(...)
    frame. Note, any values that do not evaluate to numbers are ignored.
    local vals = makeArgArray(...)
    ]]
    local count = #vals
    function z.max( frame )
    table.sort(vals)
        local args = frame.args;
       
    if count == 0 then
        if args[1] == nil then
    return 0
            local parent = frame:getParent();
    end
            args = parent.args;
        end
    if p._mod(count, 2) == 0 then
        local max_value = nil;
    return (vals[count/2] + vals[count/2+1])/2
       
    else
        local i = 1;
    return vals[math.ceil(count/2)]
        while args[i] ~= nil do
    end
            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


    Line 159: Line 259:


    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 z.min( 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 min_value = nil;
    if min_value then
       
    return min_value
        local i = 1;
    end
        while args[i] ~= nil do
    end
            local val = z._cleanNumber( frame, args[i] );
     
            if val ~= nil then
    --[[
                if min_value == nil or val < min_value then
    sum
                    min_value = val;
     
                end
    Finds the sum
            end      
     
            i = i + 1;
    Usage:
        end
    {{#invoke:Math| sum | value1 | value2 | ... }}
     
    OR
        return min_value
    {{#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
    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     
     
    function p._round(value, precision)
    local rescale = math.pow(10, precision or 0);
    return math.floor(value * rescale + 0.5) / rescale;
    end
    end
    function z._round( value, precision )
     
        local rescale = math.pow( 10, precision );
    --[[
        return math.floor( value * rescale + 0.5 ) / rescale;
    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 257: Line 435:


    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


        -- If rounding off, truncate extra digits
    local current_precision = p._precision(value)
        if precision < current_precision then
    local order = p._order(value)
            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;
    -- Due to round-off effects it is neccesary to limit the returned precision under
                    if padding > 20 then
    -- some circumstances because the terminal digits will be inaccurately reported.
                        padding = 20;
    if order + precision >= 14 then
                    end
    orig_precision = p._precision(value_string)
                   
    if order + orig_precision >= 14 then
                    formatted_num = formatted_num .. string.rep( '0', padding );
    precision = 13 - order;      
                end           
    end      
            else                 
    end
                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 rounding off, truncate extra digits
        if order ~= 0 then
    if precision < current_precision then
            -- Use proper unary minus sign rather than ASCII default
    value = p._round(value, precision)
            if order < 0 then
    current_precision = p._precision(value)
                order = '−' .. lang:formatNum( math.abs(order) );
    end   
            else
     
                order = lang:formatNum( order );
    local formatted_num = lang:formatNum(math.abs(value))
            end     
    local sign
           
     
            formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
    -- Use proper unary minus sign rather than ASCII default
        end
    if value < 0 then
       
    sign = '−'
        return formatted_num;
    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
    end


    Line 357: Line 541:
    ]]
    ]]


    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 09:59, 16 November 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
    		orig_precision = p._precision(value_string)
    		if order + orig_precision >= 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)