Module:Math: Difference between revisions
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en>Dragons flight (add average) |
m (1 revision imported from wikipedia:Module:Math) |
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(17 intermediate revisions by 6 users not shown) | |||
Line 4: | Line 4: | ||
]] |
]] |
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local z = {} |
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local yesno, getArgs -- lazily initialized |
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-- Generate random number |
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function z.random( frame ) |
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first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil |
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second = tonumber(frame.args[2]) |
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local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules. |
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if first then -- if NaN or nil, will skip down to final return |
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local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua. |
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if first <= second then -- could match if both nil, but already checked that first is a number in last line |
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return math.random(first, second) |
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--[[ |
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end |
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Helper functions used to avoid redundant code. |
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return math.random(first) |
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]] |
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end |
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return math.random() |
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local function err(msg) |
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-- Generates wikitext error messages. |
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return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg) |
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end |
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local function unpackNumberArgs(args) |
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-- Returns an unpacked list of arguments specified with numerical keys. |
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local ret = {} |
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for k, v in pairs(args) do |
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if type(k) == 'number' then |
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table.insert(ret, v) |
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end |
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end |
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return unpack(ret) |
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end |
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local function makeArgArray(...) |
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-- Makes an array of arguments from a list of arguments that might include nils. |
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local args = {...} -- Table of arguments. It might contain nils or non-number values, so we can't use ipairs. |
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local nums = {} -- Stores the numbers of valid numerical arguments. |
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local ret = {} |
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for k, v in pairs(args) do |
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v = p._cleanNumber(v) |
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if v then |
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nums[#nums + 1] = k |
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args[k] = v |
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end |
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end |
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table.sort(nums) |
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for i, num in ipairs(nums) do |
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ret[#ret + 1] = args[num] |
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end |
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return ret |
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end |
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local function fold(func, ...) |
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-- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters, |
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-- and must return a number as an output. This number is then supplied as input to the next function call. |
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local vals = makeArgArray(...) |
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local count = #vals -- The number of valid arguments |
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if count == 0 then return |
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-- Exit if we have no valid args, otherwise removing the first arg would cause an error. |
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nil, 0 |
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end |
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local ret = table.remove(vals, 1) |
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for _, val in ipairs(vals) do |
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ret = func(ret, val) |
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end |
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return ret, count |
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end |
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--[[ |
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Fold arguments by selectively choosing values (func should return when to choose the current "dominant" value). |
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]] |
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local function binary_fold(func, ...) |
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local value = fold((function(a, b) if func(a, b) then return a else return b end end), ...) |
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return value |
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end |
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--[[ |
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random |
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Generate a random number |
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Usage: |
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{{#invoke: Math | random }} |
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{{#invoke: Math | random | maximum value }} |
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{{#invoke: Math | random | minimum value | maximum value }} |
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]] |
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function wrap.random(args) |
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local first = p._cleanNumber(args[1]) |
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local second = p._cleanNumber(args[2]) |
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return p._random(first, second) |
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end |
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function p._random(first, second) |
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math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000)) |
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-- math.random will throw an error if given an explicit nil parameter, so we need to use if statements to check the params. |
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if first and second then |
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if first <= second then -- math.random doesn't allow the first number to be greater than the second. |
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return math.random(first, second) |
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end |
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elseif first then |
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return math.random(first) |
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else |
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return math.random() |
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end |
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end |
end |
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Line 26: | Line 110: | ||
Usage: |
Usage: |
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{{#invoke: Math | order | value }} |
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]] |
]] |
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function z.order(frame) |
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function wrap.order(args) |
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local input_string = (frame.args[1] or frame.args.x or '0'); |
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local input_string = (args[1] or args.x or '0'); |
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local input_number; |
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local input_number = p._cleanNumber(input_string); |
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if input_number == nil then |
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return err('order of magnitude input appears non-numeric') |
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if input_number == nil then |
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else |
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return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>' |
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return p._order(input_number) |
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else |
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end |
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return z._order( input_number ) |
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end |
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end |
end |
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function z._order(x) |
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function p._order(x) |
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if x == 0 then return 0 end |
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if x == 0 then return 0 end |
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return math.floor(math.log10(math.abs(x))) |
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return math.floor(math.log10(math.abs(x))) |
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end |
end |
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Line 50: | Line 134: | ||
Usage: |
Usage: |
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{{ #invoke: Math | precision | value }} |
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]] |
]] |
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function z.precision( frame ) |
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function wrap.precision(args) |
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local input_string = (frame.args[1] or frame.args.x or '0'); |
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local input_string = (args[1] or args.x or '0'); |
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local trap_fraction = frame.args.check_fraction or false; |
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local trap_fraction = args.check_fraction; |
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local input_number; |
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local input_number; |
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if type( trap_fraction ) == 'string' then |
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if not yesno then |
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trap_fraction = trap_fraction:lower(); |
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yesno = require('Module:Yesno') |
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if trap_fraction == 'false' or trap_fraction == '0' or |
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end |
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trap_fraction == 'no' or trap_fraction == '' then |
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if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]]. |
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trap_fraction = false; |
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local pos = string.find(input_string, '/', 1, true); |
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else |
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if pos ~= nil then |
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trap_fraction = true; |
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if string.find(input_string, '/', pos + 1, true) == nil then |
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end |
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local denominator = string.sub(input_string, pos+1, -1); |
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end |
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local denom_value = tonumber(denominator); |
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if denom_value ~= nil then |
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if trap_fraction then |
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return math.log10(denom_value); |
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local pos = string.find( input_string, '/', 1, true ); |
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end |
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if pos ~= nil then |
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end |
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if string.find( input_string, '/', pos + 1, true ) == nil then |
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end |
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local denominator = string.sub( input_string, pos+1, -1 ); |
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end |
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local denom_value = tonumber( denominator ); |
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if denom_value ~= nil then |
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input_number, input_string = p._cleanNumber(input_string); |
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return math.log10(denom_value); |
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if input_string == nil then |
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end |
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return err('precision input appears non-numeric') |
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end |
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else |
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end |
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return p._precision(input_string) |
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end |
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end |
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input_number, input_string = z._cleanNumber( frame, input_string ); |
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if input_string == nil then |
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return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>' |
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else |
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return z._precision( input_string ) |
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end |
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end |
end |
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function z._precision( x ) |
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x = string.upper( x ) |
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function p._precision(x) |
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local decimal = string.find( x, '.', 1, true ) |
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if type(x) == 'number' then |
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local exponent_pos = string.find( x, 'E', 1, true ) |
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x = tostring(x) |
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local result = 0; |
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end |
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x = string.upper(x) |
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if exponent_pos ~= nil then |
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local exponent = string.sub( x, exponent_pos + 1 ) |
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local decimal = x:find('%.') |
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x = string.sub( x, 1, exponent_pos - 1 ) |
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local exponent_pos = x:find('E') |
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result = result - tonumber( exponent ) |
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local result = 0; |
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end |
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if exponent_pos ~= nil then |
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local exponent = string.sub(x, exponent_pos + 1) |
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x = string.sub(x, 1, exponent_pos - 1) |
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return result |
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result = result - tonumber(exponent) |
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end |
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end |
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local pos = string.len( x ); |
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if decimal ~= nil then |
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while x:byte(pos) == string.byte('0') do |
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result = result + string.len(x) - decimal |
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pos = pos - 1 |
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return result |
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end |
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if pos <= 0 then |
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return 0 |
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local pos = string.len(x); |
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end |
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while x:byte(pos) == string.byte('0') do |
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end |
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pos = pos - 1 |
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result = result - 1 |
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return result |
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if pos <= 0 then |
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return 0 |
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end |
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end |
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return result |
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end |
end |
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--[[ |
--[[ |
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Line 123: | Line 206: | ||
Usage: |
Usage: |
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{{#invoke:Math| max | value1 | value2 | ... }} |
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OR |
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{{#invoke:Math| max }} |
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Note, any values that do not evaluate to numbers are ignored. |
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When used with no arguments, it takes its input from the parent |
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frame. Note, any values that do not evaluate to numbers are ignored. |
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]] |
]] |
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function z.max( frame ) |
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function wrap.max(args) |
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local args = frame.args; |
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return p._max(unpackNumberArgs(args)) |
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end |
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if args[1] == nil then |
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local parent = frame:getParent(); |
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function p._max(...) |
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args = parent.args; |
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local max_value = binary_fold((function(a, b) return a > b end), ...) |
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end |
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if max_value then |
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return max_value |
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end |
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local i = 1; |
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end |
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while args[i] ~= nil do |
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local val = z._cleanNumber( frame, args[i] ); |
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--[[ |
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if val ~= nil then |
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median |
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if max_value == nil or val > max_value then |
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max_value = val; |
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Find the median of set of numbers |
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end |
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end |
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Usage: |
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i = i + 1; |
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{{#invoke:Math | median | number1 | number2 | ...}} |
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end |
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OR |
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{{#invoke:Math | median }} |
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return max_value |
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]] |
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function wrap.median(args) |
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return p._median(unpackNumberArgs(args)) |
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end |
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function p._median(...) |
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local vals = makeArgArray(...) |
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local count = #vals |
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table.sort(vals) |
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if count == 0 then |
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return 0 |
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end |
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if p._mod(count, 2) == 0 then |
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return (vals[count/2] + vals[count/2+1])/2 |
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else |
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return vals[math.ceil(count/2)] |
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end |
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end |
end |
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--[[ |
--[[ |
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min |
min |
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Finds the minimum argument |
Finds the minimum argument |
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Usage: |
Usage: |
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{{#invoke:Math| min | value1 | value2 | ... }} |
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OR |
OR |
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{{#invoke:Math| min }} |
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When used with no arguments, it takes its input from the parent |
When used with no arguments, it takes its input from the parent |
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frame. Note, any values that do not evaluate to numbers are ignored. |
frame. Note, any values that do not evaluate to numbers are ignored. |
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]] |
]] |
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function z.min( frame ) |
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function wrap.min(args) |
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local args = frame.args; |
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return p._min(unpackNumberArgs(args)) |
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end |
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if args[1] == nil then |
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local parent = frame:getParent(); |
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function p._min(...) |
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args = parent.args; |
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local min_value = binary_fold((function(a, b) return a < b end), ...) |
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end |
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if min_value then |
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return min_value |
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end |
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local i = 1; |
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while args[i] ~= nil do |
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local val = z._cleanNumber( frame, args[i] ); |
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if val ~= nil then |
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if min_value == nil or val < min_value then |
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min_value = val; |
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end |
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end |
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i = i + 1; |
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end |
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return min_value |
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end |
end |
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--[[ |
--[[ |
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sum |
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average |
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Finds the sum |
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Usage: |
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{{#invoke:Math| sum | value1 | value2 | ... }} |
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OR |
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{{#invoke:Math| sum }} |
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Note, any values that do not evaluate to numbers are ignored. |
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]] |
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function wrap.sum(args) |
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return p._sum(unpackNumberArgs(args)) |
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end |
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function p._sum(...) |
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local sums, count = fold((function(a, b) return a + b end), ...) |
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if not sums then |
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return 0 |
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else |
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return sums |
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end |
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end |
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--[[ |
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average |
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Finds the average |
Finds the average |
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Usage: |
Usage: |
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{{#invoke:Math| average | value1 | value2 | ... }} |
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OR |
OR |
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{{#invoke:Math| average }} |
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Note, any values that do not evaluate to numbers are ignored. |
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When used with no arguments, it takes its input from the parent |
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frame. Note, any values that do not evaluate to numbers are ignored. |
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]] |
]] |
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function z.average( frame ) |
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function wrap.average(args) |
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local args = frame.args; |
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return p._average(unpackNumberArgs(args)) |
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if args[1] == nil then |
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end |
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local parent = frame:getParent(); |
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args = parent.args; |
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function p._average(...) |
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end |
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local sum, count = fold((function(a, b) return a + b end), ...) |
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local sum = 0; |
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if not sum then |
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local count = 0; |
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return 0 |
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else |
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local i = 1; |
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return sum / count |
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while args[i] ~= nil do |
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end |
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local val = z._cleanNumber( frame, args[i] ); |
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if val ~= nil then |
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sum = sum + val |
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count = count + 1 |
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end |
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i = i + 1; |
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end |
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return (count == 0 and 0 or sum/count) |
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end |
end |
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Line 230: | Line 336: | ||
Usage: |
Usage: |
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{{#invoke:Math | round | value | precision }} |
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--]] |
--]] |
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function z.round(frame) |
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function wrap.round(args) |
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local value, precision; |
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local value = p._cleanNumber(args[1] or args.value or 0) |
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local precision = p._cleanNumber(args[2] or args.precision or 0) |
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if value == nil or precision == nil then |
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return err('round input appears non-numeric') |
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else |
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if value == nil or precision == nil then |
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return p._round(value, precision) |
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return '<strong class="error">Formatting error: Round input appears non-numeric</strong>' |
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end |
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else |
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return z._round( value, precision ); |
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end |
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end |
end |
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function z._round( value, precision ) |
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function p._round(value, precision) |
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local rescale = math.pow(10, precision or 0); |
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return math.floor( value * rescale + 0.5 ) / rescale; |
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return math.floor(value * rescale + 0.5) / rescale; |
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end |
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--[[ |
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log10 |
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returns the log (base 10) of a number |
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Usage: |
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{{#invoke:Math | log10 | x }} |
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]] |
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function wrap.log10(args) |
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return math.log10(args[1]) |
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end |
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--[[ |
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mod |
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Implements the modulo operator |
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Usage: |
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{{#invoke:Math | mod | x | y }} |
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--]] |
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function wrap.mod(args) |
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local x = p._cleanNumber(args[1]) |
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local y = p._cleanNumber(args[2]) |
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if not x then |
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return err('first argument to mod appears non-numeric') |
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elseif not y then |
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return err('second argument to mod appears non-numeric') |
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else |
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return p._mod(x, y) |
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end |
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end |
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function p._mod(x, y) |
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local ret = x % y |
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if not (0 <= ret and ret < y) then |
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ret = 0 |
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end |
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return ret |
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end |
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--[[ |
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gcd |
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Calculates the greatest common divisor of multiple numbers |
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Usage: |
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{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }} |
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--]] |
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function wrap.gcd(args) |
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return p._gcd(unpackNumberArgs(args)) |
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end |
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function p._gcd(...) |
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local function findGcd(a, b) |
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local r = b |
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local oldr = a |
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while r ~= 0 do |
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local quotient = math.floor(oldr / r) |
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oldr, r = r, oldr - quotient * r |
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end |
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if oldr < 0 then |
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oldr = oldr * -1 |
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end |
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return oldr |
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end |
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local result, count = fold(findGcd, ...) |
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return result |
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end |
end |
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Line 253: | Line 431: | ||
precision_format |
precision_format |
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Rounds a number to the specified precision and formats according to rules |
Rounds a number to the specified precision and formats according to rules |
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originally used for {{template:Rnd}}. Output is a string. |
originally used for {{template:Rnd}}. Output is a string. |
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Usage: |
Usage: |
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{{#invoke: Math | precision_format | number | precision }} |
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]] |
]] |
||
function z.precision_format( frame ) |
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-- For access to Mediawiki built-in formatter. |
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local lang = mw.getContentLanguage(); |
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local value_string, value, precision; |
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value, value_string = z._cleanNumber( frame, frame.args[1] or 0 ); |
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precision = z._cleanNumber( frame, frame.args[2] or 0 ); |
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-- Check for non-numeric input |
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if value == nil or precision == nil then |
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return '<strong class="error">Formatting error: invalid input when rounding</strong>' |
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end |
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local current_precision = z._precision( value ); |
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function wrap.precision_format(args) |
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local order = z._order( value ); |
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local value_string = args[1] or 0 |
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local precision = args[2] or 0 |
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-- Due to round-off effects it is neccesary to limit the returned precision under |
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return p._precision_format(value_string, precision) |
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-- some circumstances because the terminal digits will be inaccurately reported. |
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end |
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if order + precision >= 14 then |
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orig_precision = z._precision( value_string ); |
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if order + orig_precision >= 14 then |
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precision = 13 - order; |
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end |
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end |
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function p._precision_format(value_string, precision) |
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-- If rounding off, truncate extra digits |
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-- For access to Mediawiki built-in formatter. |
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if precision < current_precision then |
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local lang = mw.getContentLanguage(); |
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value = z._round( value, precision ); |
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current_precision = z._precision( value ); |
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end |
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local formatted_num = lang:formatNum( math.abs(value) ); |
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local sign; |
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-- Use proper unary minus sign rather than ASCII default |
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if value < 0 then |
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sign = '−'; |
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else |
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sign = ''; |
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end |
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-- Handle cases requiring scientific notation |
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if string.find( formatted_num, 'E', 1, true ) ~= nil or math.abs(order) >= 9 then |
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value = value * math.pow( 10, -order ); |
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current_precision = current_precision + order; |
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precision = precision + order; |
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formatted_num = lang:formatNum( math.abs(value) ); |
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else |
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order = 0; |
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end |
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formatted_num = sign .. formatted_num; |
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-- Pad with zeros, if needed |
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if current_precision < precision then |
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local padding; |
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if current_precision <= 0 then |
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if precision > 0 then |
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local zero_sep = lang:formatNum( 1.1 ); |
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formatted_num = formatted_num .. zero_sep:sub(2,2); |
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local value |
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padding = precision; |
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value, value_string = p._cleanNumber(value_string) |
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if padding > 20 then |
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precision = p._cleanNumber(precision) |
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padding = 20; |
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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 |
|||
-- Check for non-numeric input |
|||
-- Add exponential notation, if necessary. |
|||
if value == nil or precision == nil then |
|||
return err('invalid input when rounding') |
|||
-- Use proper unary minus sign rather than ASCII default |
|||
end |
|||
if order < 0 then |
|||
order = '−' .. lang:formatNum( math.abs(order) ); |
|||
local current_precision = p._precision(value) |
|||
else |
|||
local order = p._order(value) |
|||
end |
|||
-- Due to round-off effects it is neccesary to limit the returned precision under |
|||
-- some circumstances because the terminal digits will be inaccurately reported. |
|||
formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>' |
|||
if order + precision >= 14 then |
|||
end |
|||
if order + p._precision(value_string) >= 14 then |
|||
precision = 13 - order; |
|||
return formatted_num; |
|||
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 |
end |
||
--[[ |
--[[ |
||
divide |
|||
Helper function that interprets the input numerically. If the |
|||
Implements the division operator |
|||
Usage: |
|||
{{#invoke:Math | 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) |
|||
end |
|||
function p._divide(x, y, round, precision) |
|||
if y == nil or y == "" then |
|||
return err("Empty divisor") |
|||
elseif not tonumber(y) then |
|||
if type(y) == 'string' and string.sub(y, 1, 1) == '<' then |
|||
return y |
|||
else |
|||
return err("Not a number: " .. y) |
|||
end |
|||
elseif x == nil or x == "" then |
|||
return err("Empty dividend") |
|||
elseif not tonumber(x) then |
|||
if type(x) == 'string' and string.sub(x, 1, 1) == '<' 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 |
|||
end |
|||
end |
|||
--[[ |
|||
Helper function that interprets the input numerically. If the |
|||
input does not appear to be a number, attempts evaluating it as |
input does not appear to be a number, attempts evaluating it as |
||
a parser functions expression. |
a parser functions expression. |
||
]] |
]] |
||
function |
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 nil, nil; |
|||
return number_string, tostring(number_string) |
|||
end |
|||
elseif type(number_string) ~= 'string' or not number_string:find('%S') then |
|||
-- We were passed a non-string or a blank string, so exit. |
|||
-- Attempt basic conversion |
|||
return nil, nil; |
|||
local number = tonumber( number_string ) |
|||
end |
|||
-- If failed, attempt to evaluate input as an expression |
|||
-- Attempt basic conversion |
|||
if number == nil then |
|||
local number = tonumber(number_string) |
|||
attempt = tonumber( attempt ); |
|||
-- If failed, attempt to evaluate input as an expression |
|||
if attempt ~= nil then |
|||
if number == nil then |
|||
local success, result = pcall(mw.ext.ParserFunctions.expr, number_string) |
|||
number_string = tostring( number ); |
|||
if success then |
|||
else |
|||
number = tonumber(result) |
|||
number_string = tostring(number) |
|||
else |
|||
end |
|||
number = nil |
|||
else |
|||
number_string = nil |
|||
-- String is valid but may contain padding, clean it. |
|||
end |
|||
number_string = number_string:match( "^%s*(.-)%s*$" ); |
|||
else |
|||
end |
|||
number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it. |
|||
number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs. |
|||
return number, number_string; |
|||
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 23:27, 31 October 2022
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
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 = 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
--[[
divide
Implements the division operator
Usage:
{{#invoke:Math | 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)
end
function p._divide(x, y, round, precision)
if y == nil or y == "" then
return err("Empty divisor")
elseif not tonumber(y) then
if type(y) == 'string' and string.sub(y, 1, 1) == '<' then
return y
else
return err("Not a number: " .. y)
end
elseif x == nil or x == "" then
return err("Empty dividend")
elseif not tonumber(x) then
if type(x) == 'string' and string.sub(x, 1, 1) == '<' 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
end
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)