---  
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>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:  
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:  
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:  
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:  
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:  
OR  
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:  
OR  
When used with no arguments, it takes its input from the parent
. 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:  
OR  
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:  
OR  
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:  
---  
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:  
function wrap.log10(args)
return math.log10(args[1])
end  
---
mod  
Implements the modulo operator  
Usage:  
---  
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:  
---  
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, ...)