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-- SUPPORT Modul:Sports table/WL - SIEHE: Modul:Expr
--[[

This module provides a number of basic mathematical operations.

]]

local yesno, getArgs -- lazily initialized
local yesno, getArgs -- lazily initialized

local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
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.
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 applyFuncToArgs(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

--[[
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
order

Determine order of magnitude of a number
Determine order of magnitude of a number


Zeile 189: Zeile 96:


return result
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
return b
end
end
local max_value = applyFuncToArgs(maxOfTwo, ...)
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
return b
end
end
local min_value = applyFuncToArgs(minOfTwo, ...)
if min_value then
return min_value
end
end

--[[
add

Finds the result of additions

Usage:
{{#invoke:Math| add | value1 | value2 | ... }}
OR
{{#invoke:Math| add }}

Note, any values that do not evaluate to numbers are ignored.
]]

function wrap.add(args)
return p._add(unpackNumberArgs(args))
end

function p._add(...)
local function getSum(a, b)
return a + b
end
local sum, count = applyFuncToArgs(getSum, ...)
if not sum then
return 0
else
return sum
end
end

--[[
sub

Finds the result of subtractions

Usage:
{{#invoke:Math| sub | value1 | value2 | ... }}
OR
{{#invoke:Math| sub }}

Note, any values that do not evaluate to numbers are ignored.
]]

function wrap.sub(args)
return p._sub(unpackNumberArgs(args))
end

function p._sub(...)
local function getDiff(a, b)
return a - b
end
local diff, count = applyFuncToArgs(getDiff, ...)
if not diff then
return 0
else
return diff
end
end

--[[
mul

Finds the result of multiplications

Usage:
{{#invoke:Math| mul | value1 | value2 | ... }}
OR
{{#invoke:Math| mul }}

Note, any values that do not evaluate to numbers are ignored.
]]

function wrap.mul(args)
return p._mul(unpackNumberArgs(args))
end

function p._mul(...)
local function getFac(a, b)
return a * b
end
local fac, count = applyFuncToArgs(getFac, ...)
if not fac then
return 0
else
return fac
end
end

--[[
div

Finds the result of divisions

Usage:
{{#invoke:Math| div | value1 | value2 | ... }}
OR
{{#invoke:Math| div }}

Note, any values that do not evaluate to numbers are ignored.
Note, any values that do evaluate to zero are ignored.
]]

function wrap.div(args)
return p._div(unpackNumberArgs(args))
end

function p._div(...)
local function getQuote(a, b)
if b == 0 then b = 1 end
return a / b
end
local quote, count = applyFuncToArgs(getQuote, ...)
if not quote then
return 0
else
return quote
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 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
end


Zeile 422: Zeile 121:
local rescale = math.pow(10, precision or 0);
local rescale = math.pow(10, precision or 0);
return math.floor(value * rescale + 0.5) / rescale;
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

--[[
lcm

Calculates the least common multiple of multiple numbers

Usage:
{{#invoke:Math | lcm | value 1 | value 2 | value 3 | ... }}
--]]

function wrap.lcm(args)
return p._lcm(unpackNumberArgs(args))
end

function p._lcm(...)
local function findLcm(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 a * b / oldr
end
local result, count = applyFuncToArgs(findLcm, ...)
return result
end
end


Zeile 621: Zeile 230:
end
end


-- ftn
function wrap.ftn(args)
local x = p._cleanNumber(args[1])
if x then
return p._ftn(x)
else
return '&ndash;'
end
end

function p._ftn(x)
local a = mw.getLanguage('de'):formatNum(tonumber(x))
return a
end

-- prozent
function wrap.prozent(args)
local x = p._cleanNumber(args[1])
local y = p._cleanNumber(args[2])
if x and y then
return p._prozent(x, y)
else
return '&ndash;'
end
end

function p._prozent(x, y)
local a = string.format('%.1f', x / y * 100)
local b = string.gsub(a, "%.", "%,")
return b
end

-- df
function wrap.df(args)
local x = p._cleanNumber(args[1])
local y = p._cleanNumber(args[2])
if x and y then
return p._df(x, y)
end
end

function p._df(x, y)
local a = mw.getLanguage('de'):formatNum(tonumber(x - y))
return a
end

-- variation %
function wrap.var(args)
local x = p._cleanNumber(args[1])
local y = p._cleanNumber(args[2])
if x and y then
return p._var(x, y)
end
end

function p._var(x, y)
local a = string.format('%.1f', (y-x)/y * 100)
local b = string.gsub(a, "%.", "%,")
return b
end


--[[
--[[
Zeile 687: Zeile 236:
a parser functions expression.
a parser functions expression.
]]
]]

function p._cleanNumber(number_string)
function p._cleanNumber(number_string)
if type(number_string) == 'number' then
if type(number_string) == 'number' then
Zeile 722: Zeile 270:
end
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)
return p

Version vom 29. Dezember 2023, 16:53 Uhr

Die Dokumentation für dieses Modul kann unter Modul:Sports table/Math/Doku erstellt werden 

-- SUPPORT Modul:Sports table/WL - SIEHE: Modul:Expr
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.

--[[
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

--[[
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

--[[
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
		orig_precision = p._precision(value_string)
		if order + orig_precision >= 14 then
			precision = 13 - order;        
		end        
	end

	-- If rounding off, truncate extra digits
	if precision < current_precision then
		value = p._round(value, precision)
		current_precision = p._precision(value)
	end    

	local formatted_num = lang:formatNum(math.abs(value))
	local sign

	-- Use proper unary minus sign rather than ASCII default
	if value < 0 then
		sign = '−'
	else
		sign = ''
	end    

	-- Handle cases requiring scientific notation
	if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then
		value = value * math.pow(10, -order)
		current_precision = current_precision + order
		precision = precision + order
		formatted_num = lang:formatNum(math.abs(value))
	else
		order = 0;        
	end
	formatted_num = sign .. formatted_num

	-- Pad with zeros, if needed    
	if current_precision < precision then
		local padding
		if current_precision <= 0 then
			if precision > 0 then
				local zero_sep = lang:formatNum(1.1)
				formatted_num = formatted_num .. zero_sep:sub(2,2)

				padding = precision
				if padding > 20 then
					padding = 20
				end

				formatted_num = formatted_num .. string.rep('0', padding)
			end            
		else                   
			padding = precision - current_precision
			if padding > 20 then
				padding = 20
			end
			formatted_num = formatted_num .. string.rep('0', padding)
		end
	end

	-- Add exponential notation, if necessary.
	if order ~= 0 then
		-- Use proper unary minus sign rather than ASCII default
		if order < 0 then
			order = '−' .. lang:formatNum(math.abs(order))
		else
			order = lang:formatNum(order)
		end    

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

	return formatted_num
end


--[[
Helper function that interprets the input numerically.  If the 
input does not appear to be a number, attempts evaluating it as
a parser functions expression.
]]
function p._cleanNumber(number_string)
	if type(number_string) == 'number' then
		-- We were passed a number, so we don't need to do any processing.
		return number_string, tostring(number_string)
	elseif type(number_string) ~= 'string' or not number_string:find('%S') then
		-- We were passed a non-string or a blank string, so exit.
		return nil, nil;
	end

	-- Attempt basic conversion
	local number = tonumber(number_string)

	-- If failed, attempt to evaluate input as an expression
	if number == nil then
		local success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
		if success then
			number = tonumber(result)
			number_string = tostring(number)
		else
			number = nil
			number_string = nil
		end
	else
		number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it.
		number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs.
		if number_string:find('^%-?0[xX]') then
			-- Number is using 0xnnn notation to indicate base 16; use the number that Lua detected instead.
			number_string = tostring(number)
		end
	end

	return number, number_string
end


return p
Abgerufen von „https://de.wikipedia.org/w/index.php?title=Modul:Sports_table/Math&oldid=240635335“