--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('Formatting error: %s', 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)
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 retend
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
--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 valueend
--random }}
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 endend
--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
function p._order(x) if x
--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 . local pos = string.find(input_string, '/', 1, true); if pos ~= nil then if string.find(input_string, '/', pos + 1, true)
input_number, input_string = p._cleanNumber(input_string); if input_string
function p._precision(x) if type(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)
return resultend
--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 endend
--median | number1 | number2 | ...}}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
if p._mod(count, 2)
--min | value1 | value2 | ... }}OR
When used with no arguments, it takes its input from the parentframe. 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 endend
--sum | value1 | value2 | ... }}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 endend
--average | value1 | value2 | ... }}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 endend
--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 then return err('round input appears non-numeric') else return p._round(value, precision) endend
function p._round(value, precision) local rescale = math.pow(10, precision or 0); return math.floor(value * rescale + 0.5) / rescale;end
--log10 | x }}
function wrap.log10(args) return math.log10(args[1])end
--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) endend
function p._mod(x, y) local ret = x % y if not (0 <= ret and ret < y) then ret = 0 end return retend
--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 resultend
--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 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 local sign
if order < -4 then formatted_num = lang:formatNum(math.abs(value),) else formatted_num = lang:formatNum(math.abs(value)) 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 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 .. '' endreturn formatted_numend
--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)endfunction p._divide(x, y, round, precision) if y
"" then return err("Empty divisor") elseif not tonumber(y) then if type(y)
'<' then return y else return err("Not a number: " .. y) end elseif x
"" then return err("Empty dividend") elseif not tonumber(x) then if type(x)
'<' 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 endend
--Helper function that interprets the input numerically. If theinput does not appear to be a number, attempts evaluating it asa parser functions expression.
function p._cleanNumber(number_string) if type(number_string)
-- Attempt basic conversion local number = tonumber(number_string)
-- If failed, attempt to evaluate input as an expression if number
return number, number_stringend
--Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the currentframe or the parent frame, and it also trims whitespace for all arguments and removes blank arguments.
local mt =
return setmetatable(p, mt)