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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 p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
-- Generate four different tidyVal functions, so that we don't have to check the options every time we call it.
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
end
else
return val
end
end
return unpack(ret)
end
end


local function makeArgArray(...)
local function tidyValTrimOnly(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
end
table.sort(nums)
for i, num in ipairs(nums) do
ret[#ret + 1] = args[num]
end
return ret
end
end


local function applyFuncToArgs(func, ...)
local function tidyValRemoveBlanksOnly(key, 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
end
elseif first then
return math.random(first)
else
else
return math.random()
return val
end
end
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
end


function p._order(x)
function arguments.getArgs(frame, 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
end

input_number, input_string = p._cleanNumber(input_string);
if input_string == nil then
return err('precision input appears non-numeric')
else
else
luaArgs = frame
return p._precision(input_string)
end
end

function p._precision(x)
if type(x) == 'number' then
x = tostring(x)
end
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 result = 0;
local args, metaArgs, metatable = {}, {}, {}
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
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
else
tidyVal = tidyValTrimOnly
return b
end
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
else
tidyVal = tidyValNoChange
return b
end
end
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
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
end
if oldr < 0 then
oldr = oldr * -1
end
return oldr
end
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
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
end
formatted_num = formatted_num .. string.rep('0', padding)
end
end
return nil
end
end


metatable.__newindex = function (t, key, val)
-- Add exponential notation, if necessary.
if order ~= 0 then
if options.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
else
metaArgs[key] = val
order = lang:formatNum(order)
end
end

formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
end
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
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
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
end


return args
for funcName in pairs(wrap) do
p[funcName] = makeWrapper(funcName)
end
end


return p
return arguments

Revisi per 3 Februari 2014 21.58

-- 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')
local checkType = libraryUtil.checkType

local arguments = {}

local nilArg = {} -- Used for memoizing nil arguments in metaArgs.

-- Generate four different tidyVal functions, so that we don't have to check the options every time we call it.

local function tidyValDefault(key, val)
	if type(val) == 'string' then
		val = val:match('^%s*(.-)%s*$')
		if val == '' then
			return nil
		else
			return val
		end
	else
		return val
	end
end

local function tidyValTrimOnly(key, val)
	if type(val) == 'string' then
		return val:match('^%s*(.-)%s*$')
	else
		return val
	end
end

local function tidyValRemoveBlanksOnly(key, val)
	if type(val) == 'string' then
		if val:find('%S') then
			return val
		else
			return nil
		end
	else
		return val
	end
end

local function tidyValNoChange(key, val)
	return val
end

function arguments.getArgs(frame, options)
	checkType('getArgs', 1, frame, 'table', true)
	checkType('getArgs', 2, options, 'table', true)
	frame = frame or {}
	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.
	local fargs, pargs, luaArgs
	if type(frame.args) == 'table' and type(frame.getParent) == 'function' then
		if not options.parentOnly then
			fargs = frame.args
		end
		if not options.frameOnly then
			pargs = frame:getParent().args
		end
		if options.parentFirst then
			fargs, pargs = pargs, fargs
		end
	else
		luaArgs = frame
	end

	-- Set up the args and metaArgs tables. args will be the one accessed from functions, and metaArgs will hold the actual arguments.
	-- The metatable connects the two together.
	local args, metaArgs, metatable = {}, {}, {}
	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
	-- 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 tidyVal = options.valueFunc
	if tidyVal then
		if type(tidyVal) ~= 'function' then
			error("bad value assigned to option 'valueFunc' (function expected, got " .. type(tidyVal) .. ')', 2)
		end
	elseif options.trim ~= false then
		if options.removeBlanks ~= false then
			tidyVal = tidyValDefault
		else
			tidyVal = tidyValTrimOnly
		end
	else
		if options.removeBlanks ~= false then
			tidyVal = tidyValRemoveBlanksOnly
		else
			tidyVal = tidyValNoChange
		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.
		-- 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.
		for _, t in ipairs(tables) do
			for key, val in iterator(t) do
				local metaArgsVal = metaArgs[key]
				if metaArgsVal == nil or metaArgsVal == nilArg then
					local tidiedVal = tidyVal(key, val)
					if tidiedVal == nil then
						metaArgs[key] = nilArg
					else
						metaArgs[key] = tidiedVal
					end
				end
			end
		end
	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.	
	local argTables = {fargs}
	argTables[#argTables + 1] = pargs
	argTables[#argTables + 1] = luaArgs

	--[[
	-- Define metatable behaviour. Arguments are memoized in the metaArgs table, and are only fetched from the
	-- 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)
		local val = metaArgs[key]
		if val ~= nil then
			if val == nilArg then
				return nil
			else
				return val
			end
		end
		for _, argTable in ipairs(argTables) do
			local argTableVal = tidyVal(key, argTable[key])
			if argTableVal == nil then
				metaArgs[key] = nilArg
			else
				metaArgs[key] = argTableVal
				return argTableVal
			end
		end
		return nil
	end

	metatable.__newindex = function (t, key, val)
		if options.readOnly then
			error('could not write to argument table key "' .. tostring(key) .. '"; the table is read-only', 2)
		elseif options.noOverwrite and args[key] ~= nil then
			error('could not write to argument table key "' .. tostring(key) .. '"; overwriting existing arguments is not permitted', 2)
		elseif val == nil then
			metaArgs[key] = nilArg -- Memoize nils.
		else
			metaArgs[key] = val
		end
	end

	metatable.__pairs = function ()
		if not metatable.donePairs then
			mergeArgs(pairs, argTables)
			metatable.donePairs = true
			metatable.doneIpairs = true
		end
		return function (t, k)
			local nk, val = next(metaArgs, k)
			if val == nilArg then
				val = nil
			end
			return nk, val
		end
	end

	metatable.__ipairs = function ()
		if not metatable.doneIpairs then
			mergeArgs(ipairs, argTables)
			metatable.doneIpairs = true
		end
		return function (t, i)
			local val = metaArgs[i + 1]
			if val == nil then
				return nil
			elseif val == nilArg then
				val = nil
			end
			return i + 1, val
		end, nil, 0
	end

	return args
end

return arguments