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--[[
 
This module provides a number of basic mathematical operations.
 
Taken from https://en.wikipedia.org/wiki/Module:Math?oldid=613638641
 
]]
 
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 applyFuncToArgs(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
 
--[[
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 function maxOfTwo(a, b)
		if a > b then
			return a
		else
			return b
		end
	end
	local max_value = applyFuncToArgs(maxOfTwo, ...)
	if max_value then
		return max_value
	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 function minOfTwo(a, b)
		if a < b then
			return a
		else
			return b
		end
	end
	local min_value = applyFuncToArgs(minOfTwo, ...)
	if min_value then
		return min_value
	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 function getSum(a, b)
		return a + b
	end
	local sum, count = applyFuncToArgs(getSum, ...)
	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
 
--[[
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 = applyFuncToArgs(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)

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