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-- This module provides easy processing of arguments passed to Scribunto from #invoke.
--[[
-- It is intended for use by other Lua modules, and should not be called from #invoke directly.
local libraryUtil = require('libraryUtil')
This module provides a number of basic mathematical operations.
local checkType = libraryUtil.checkType
local arguments = {}
]]
local nilArg = {} -- Used for memoizing nil arguments in metaArgs.
local yesno = require('Module:Yesno')
local getArgs = require('Module:Arguments').getArgs
local-- pGenerate =four {}different -- HoldstidyVal functions, toso bethat returnedwe fromdon't #invoke,have andto functionscheck tothe makeoptions availableevery totime otherwe Luacall modulesit.
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
local function tidyValDefault(key, val)
--[[
if type(val) == 'string' then
Helper functions used to avoid redundant code.
val = val:match('^%s*(.-)%s*$')
]]
if val == '' then
return nil
local function err(msg)
else
-- Generates wikitext error messages.
return val
return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg)
end
local function unpackNumberArgs(args)
-- Returns an unpacked list of arguments specified with numerical keys.
local ret = {}
for k, v in pairs(args) do
if type(k) == 'number' then
table.insert(ret, v)
end
else
return val
end
return unpack(ret)
end
local function makeArgArraytidyValTrimOnly(...key, val)
if type(val) == 'string' then
-- Makes an array of arguments from a list of arguments that might include nils.
return val:match('^%s*(.-)%s*$')
local args = {...} -- Table of arguments. It might contain nils or non-number values, so we can't use ipairs.
else
local nums = {} -- Stores the numbers of valid numerical arguments.
return val
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 applyFuncToArgstidyValRemoveBlanksOnly(funckey, ...val)
if type(val) == 'string' then
-- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters,
if val:find('%S') then
-- and must return a number as an output. This number is then supplied as input to the next function call.
return val
local vals = makeArgArray(...)
else
local count = #vals -- The number of valid arguments
return nil
if count == 0 then return
-- Exit if we have no valid args, otherwise removing the first arg would cause an error.
nil, 0
end
local ret = table.remove(vals, 1)
for _, val in ipairs(vals) do
ret = func(ret, val)
end
return ret, count
end
--[[
random
Generate a random number
Usage:
{{#invoke: Math | random }}
{{#invoke: Math | random | maximum value }}
{{#invoke: Math | random | minimum value | maximum value }}
]]
function wrap.random(args)
local first = p._cleanNumber(args[1])
local second = p._cleanNumber(args[2])
return p._random(first, second)
end
function p._random(first, second)
math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
-- math.random will throw an error if given an explicit nil parameter, so we need to use if statements to check the params.
if first and second then
if first <= second then -- math.random doesn't allow the first number to be greater than the second.
return math.random(first, second)
end
elseif first then
return math.random(first)
else
return math.random()val
end
end
local function tidyValNoChange(key, val)
--[[
return val
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 parguments._ordergetArgs(xframe, options)
checkType('getArgs', 1, frame, 'table', true)
if x == 0 then return 0 end
checkType('getArgs', 2, options, 'table', true)
return math.floor(math.log10(math.abs(x)))
frame = frame or {}
end
options = options or {}
-- Get the arguments from the frame object if available. If the frame object is not available, we are being called
--[[
-- from another Lua module or from the debug console, so assign the args to a new variable so we can differentiate them.
precision
local fargs, pargs, luaArgs
if type(frame.args) == 'table' and type(frame.getParent) == 'function' then
Detemines the precision of a number using the string representation
if not options.parentOnly then
fargs = frame.args
Usage:
end
{{ #invoke: Math | precision | value }}
if not options.frameOnly then
]]
pargs = frame:getParent().args
end
function wrap.precision(args)
if options.parentFirst then
local input_string = (args[1] or args.x or '0');
fargs, pargs = pargs, fargs
local trap_fraction = args.check_fraction;
local input_number;
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
luaArgs = frame
return p._precision(input_string)
end
end
function p._precision(x)
if type(x) == 'number' then
x = tostring(x)
end
x = string.upper(x)
-- Set up the args and metaArgs tables. args will be the one accessed from functions, and metaArgs will hold the actual arguments.
local decimal = x:find('%.')
-- The metatable connects the two together.
local exponent_pos = x:find('E')
local resultargs, metaArgs, metatable = 0;{}, {}, {}
setmetatable(args, metatable)
-- Generate the tidyVal function. If it has been specified by the user, we use that; if not, we choose one of four functions
if exponent_pos ~= nil then
-- depending on the options chosen. This is so that we don't have to call the options table every time the function is called.
local exponent = string.sub(x, exponent_pos + 1)
local tidyVal = options.valueFunc
x = string.sub(x, 1, exponent_pos - 1)
if tidyVal then
result = result - tonumber(exponent)
if type(tidyVal) ~= 'function' then
end
error("bad value assigned to option 'valueFunc' (function expected, got " .. type(tidyVal) .. ')', 2)
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
elseif options.trim ~= false then
end
if options.removeBlanks ~= false then
tidyVal = tidyValDefault
return result
end
--[[
max
Finds the maximum argument
Usage:
{{#invoke:Math| max | value1 | value2 | ... }}
Note, any values that do not evaluate to numbers are ignored.
]]
function wrap.max(args)
return p._max(unpackNumberArgs(args))
end
function p._max(...)
local function maxOfTwo(a, b)
if a > b then
return a
else
tidyVal = tidyValTrimOnly
return b
end
else
end
if options.removeBlanks ~= false then
local max_value = applyFuncToArgs(maxOfTwo, ...)
tidyVal = tidyValRemoveBlanksOnly
if max_value then
return max_value
end
end
--[[
min
Finds the minimum argument
Usage:
{{#invoke:Math| min | value1 | value2 | ... }}
OR
{{#invoke:Math| min }}
When used with no arguments, it takes its input from the parent
frame. Note, any values that do not evaluate to numbers are ignored.
]]
function wrap.min(args)
return p._min(unpackNumberArgs(args))
end
function p._min(...)
local function minOfTwo(a, b)
if a < b then
return a
else
tidyVal = tidyValNoChange
return b
end
end
local min_value = applyFuncToArgs(minOfTwo, ...)
if min_value then
return min_value
end
end
local function mergeArgs(iterator, tables)
--[[
-- Accepts multiple tables as input and merges their keys and values into one table using the specified iterator.
average
-- If a value is already present it is not overwritten; tables listed earlier have precedence.
-- We are also memoizing nil values, but those values can be overwritten.
Finds the average
for _, t in ipairs(tables) do
for key, val in iterator(t) do
Usage:
local metaArgsVal = metaArgs[key]
{{#invoke:Math| average | value1 | value2 | ... }}
if metaArgsVal == nil or metaArgsVal == nilArg then
OR
local tidiedVal = tidyVal(key, val)
{{#invoke:Math| average }}
if tidiedVal == nil then
metaArgs[key] = nilArg
Note, any values that do not evaluate to numbers are ignored.
else
]]
metaArgs[key] = tidiedVal
end
function wrap.average(args)
end
return p._average(unpackNumberArgs(args))
end
function p._average(...)
local function getSum(a, b)
return a + b
end
local sum, count = applyFuncToArgs(getSum, ...)
if not sum then
return 0
else
return sum / count
end
end
--[[
round
Rounds a number to specified precision
Usage:
{{#invoke:Math | round | value | precision }}
--]]
function wrap.round(args)
local value = p._cleanNumber(args[1] or args.value or 0)
local precision = p._cleanNumber(args[2] or args.precision or 0)
if value == nil or precision == nil then
return err('round input appears non-numeric')
else
return p._round(value, precision)
end
end
function p._round(value, precision)
local rescale = math.pow(10, precision or 0);
return math.floor(value * rescale + 0.5) / rescale;
end
--[[
mod
Implements the modulo operator
Usage:
{{#invoke:Math | mod | x | y }}
--]]
function wrap.mod(args)
local x = p._cleanNumber(args[1])
local y = p._cleanNumber(args[2])
if not x then
return err('first argument to mod appears non-numeric')
elseif not y then
return err('second argument to mod appears non-numeric')
else
return p._mod(x, y)
end
end
function p._mod(x, y)
local ret = x % y
if not (0 <= ret and ret < y) then
ret = 0
end
return ret
end
--[[
gcd
Calculates the greatest common divisor of multiple numbers
Usage:
{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}
--]]
function wrap.gcd(args)
return p._gcd(unpackNumberArgs(args))
end
function p._gcd(...)
local function findGcd(a, b)
local r = b
local oldr = a
while r ~= 0 do
local quotient = math.floor(oldr / r)
oldr, r = r, oldr - quotient * r
end
if oldr < 0 then
oldr = oldr * -1
end
return oldr
end
local result, count = applyFuncToArgs(findGcd, ...)
return result
end
-- Set the order of precedence of the argument tables. If the variables are nil, nothing will be added to the table,
--[[
-- which is how we avoid clashes between the frame/parent args and the Lua args.
precision_format
local argTables = {fargs}
argTables[#argTables + 1] = pargs
argTables[#argTables + 1] = luaArgs
--[[
Rounds a number to the specified precision and formats according to rules
-- Define metatable behaviour. Arguments are memoized in the metaArgs table, and are only fetched from the
originally used for {{template:Rnd}}. Output is a string.
-- argument tables once. Nil arguments are also memoized using the nilArg variable in order to increase
-- performance. Also, we keep a record in the metatable of when pairs and ipairs have been called, so we
-- do not run pairs and ipairs on fargs and pargs more than once. We also do not run ipairs on fargs and
-- pargs if pairs has already been run, as all the arguments will already have been copied over.
--]]
metatable.__index = function (t, key)
Usage:
local val = metaArgs[key]
{{#invoke: Math | precision_format | number | precision }}
if val ~= nil then
]]
if val == nilArg then
return nil
function wrap.precision_format(args)
else
local value_string = args[1] or 0
return val
local precision = args[2] or 0
end
return p._precision_format(value_string, precision)
end
for _, argTable in ipairs(argTables) do
local argTableVal = tidyVal(key, argTable[key])
function p._precision_format(value_string, precision)
if argTableVal == nil then
-- For access to Mediawiki built-in formatter.
metaArgs[key] = nilArg
local lang = mw.getContentLanguage();
else
metaArgs[key] = argTableVal
local value
return argTableVal
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
return nil
end
metatable.__newindex = function (t, key, val)
-- Add exponential notation, if necessary.
if order ~= 0options.readOnly then
error('could not write to argument table key "' .. tostring(key) .. '"; the table is read-only', 2)
-- Use proper unary minus sign rather than ASCII default
elseif options.noOverwrite and args[key] ~= nil then
if order < 0 then
error('could not write to argument table key "' .. tostring(key) .. '"; overwriting existing arguments is not permitted', 2)
order = '−' .. lang:formatNum(math.abs(order))
elseif val == nil then
metaArgs[key] = nilArg -- Memoize nils.
else
metaArgs[key] = val
order = lang:formatNum(order)
end
formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
end
metatable.__pairs = function ()
return formatted_num
if not metatable.donePairs then
end
mergeArgs(pairs, argTables)
metatable.donePairs = true
--[[
metatable.doneIpairs = true
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 frame = mw.getCurrentFrame()
local attempt = frame:preprocess('{{#expr: ' .. number_string .. '}}')
attempt = tonumber(attempt)
if attempt ~= nil then
number = attempt
number_string = tostring(number)
else
number = nil
number_string = nil
end
return function (t, k)
else
local nk, val = next(metaArgs, k)
number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it.
if val == nilArg then
number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs.
val = nil
if number_string:find('^%-?0[xX]') then
end
-- Number is using 0xnnn notation to indicate base 16; use the number that Lua detected instead.
return nk, val
number_string = tostring(number)
end
end
metatable.__ipairs = function ()
return number, number_string
if not metatable.doneIpairs then
end
mergeArgs(ipairs, argTables)
metatable.doneIpairs = true
--[[
end
Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the current
return function (t, i)
frame or the parent frame, and it also trims whitespace for all arguments and removes blank arguments.
local val = metaArgs[i + 1]
]]
if val == nil then
return nil
local function makeWrapper(funcName)
elseif val == nilArg then
return function (frame)
val = nil
local args = getArgs(frame) -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.
end
return wrap[funcName](args)
return i + 1, val
end, nil, 0
end
end
return args
for funcName in pairs(wrap) do
p[funcName] = makeWrapper(funcName)
end
return parguments
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