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template>Los688 (en:Module:Math5 March 2013 at 03:27.より転記) |
Triple-Zeta (トーク | 投稿記録) 細 (5版 をインポートしました) |
||
(6人の利用者による、間の8版が非表示) | |||
4行目: | 4行目: | ||
]] | ]] | ||
-- | 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">書式エラー: %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 | end | ||
26行目: | 110行目: | ||
Usage: | Usage: | ||
{{#invoke: Math | order | value }} | |||
]] | ]] | ||
function | |||
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関数に渡された引数が数字ではありません') | |||
else | |||
return p._order(input_number) | |||
end | |||
end | end | ||
function | |||
function p._order(x) | |||
if x == 0 then return 0 end | |||
return math.floor(math.log10(math.abs(x))) | |||
end | end | ||
50行目: | 134行目: | ||
Usage: | Usage: | ||
{{ #invoke: Math | precision | value }} | |||
]] | ]] | ||
function | |||
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関数に渡された引数が数字ではありません') | |||
else | |||
return p._precision(input_string) | |||
end | |||
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 | end | ||
--[[ | --[[ | ||
123行目: | 206行目: | ||
Usage: | 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 | 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 | When used with no arguments, it takes its input from the parent | ||
frame. Note, any values that do not evaluate to numbers are ignored. | frame. Note, any values that do not evaluate to numbers are ignored. | ||
]] | ]] | ||
function | |||
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 | end | ||
--[[ | --[[ | ||
sum | |||
Finds the sum | |||
Usage: | |||
{{#invoke:Math| sum | value1 | value2 | ... }} | |||
OR | |||
{{#invoke:Math| sum }} | |||
Finds the | 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: | Usage: | ||
{{#invoke:Math| average | value1 | value2 | ... }} | |||
OR | OR | ||
{{#invoke:Math| average }} | |||
Note, any values that do not evaluate to numbers are ignored. | |||
]] | ]] | ||
function | |||
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 | end | ||
195行目: | 336行目: | ||
Usage: | 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関数に渡された引数が数字ではありません') | |||
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 | |||
function wrap.mod(args) | |||
local x = p._cleanNumber(args[1]) | |||
local y = p._cleanNumber(args[2]) | |||
if not x then | |||
return err('mod関数に渡された第1引数が数字ではありません') | |||
elseif not y then | |||
return err('mod関数に渡された第2引数が数字ではありません') | |||
else | |||
return p._mod(x, y) | |||
end | |||
end | end | ||
function | |||
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 | end | ||
218行目: | 431行目: | ||
precision_format | precision_format | ||
Rounds a number to the specified precision and formats according to rules | Rounds a number to the specified precision and formats according to rules | ||
originally used for {{template:Rnd}}. Output is a string. | originally used for {{template:Rnd}}. Output is a string. | ||
Usage: | 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('_precision_format関数に渡された引数が不正です') | |||
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 | end | ||
--[[ | --[[ | ||
Helper function that interprets the input numerically. If the | 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 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 | end | ||
return | --[[ | ||
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) |
2021年3月3日 (水) 23:57時点における最新版
このモジュールについての説明文ページを モジュール:Math/doc に作成できます
--[[
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">書式エラー: %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関数に渡された引数が数字ではありません')
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関数に渡された引数が数字ではありません')
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関数に渡された引数が数字ではありません')
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('mod関数に渡された第1引数が数字ではありません')
elseif not y then
return err('mod関数に渡された第2引数が数字ではありません')
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('_precision_format関数に渡された引数が不正です')
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
--[[
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)