Module:Math

--[[

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('', 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: 0.12609103653864 0.12609103653864 0.85437912859692 ]]

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: 0

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

--[[ min

Finds the minimum argument

Usage: 0 OR

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

--[[ average

Finds the average

Usage: 0 OR 0

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

--[[ 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: 0 --]]

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 . Output is a string.

Usage: ]]

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 .. '×10^{' .. order .. '}' 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)